From 02511aebc203b7658f8353c812e0dc476851fdea Mon Sep 17 00:00:00 2001 From: Dan Howe Date: Fri, 19 Jul 2019 16:23:34 +1000 Subject: [PATCH] Remove modules --- wafo/__init__.py | 46 +- wafo/data/__init__.py | 3 - wafo/data/atlantic.dat | 582 - wafo/data/gfaks89.dat | 39000 ------- wafo/data/gfaksr89.dat | 39000 ------- wafo/data/info.py | 485 - wafo/data/japansea.dat | 692 - wafo/data/northsea.dat | 60646 ----------- wafo/data/sea.dat | 9524 -- wafo/data/sea.m | 16 - wafo/data/sfa89.dat | 144 - wafo/data/sn.dat | 40 - wafo/data/wafoLogoNewWithBorder.png | Bin 23976 -> 0 bytes wafo/data/wafoLogoNewWithBorder.svg | 211 - wafo/data/wafoLogoNewWithoutBorder.png | Bin 13118 -> 0 bytes wafo/data/wafoLogoNewWithoutBorder.svg | 243 - wafo/data/wafologoWithBorder.png | Bin 24186 -> 0 bytes wafo/data/yura87.dat | 85547 ---------------- wafo/doc/__init__.py | 0 .../doc/tutorial_scripts/WAFO Chapter 1.ipynb | 462 - .../doc/tutorial_scripts/WAFO Chapter 2.ipynb | 706 - .../doc/tutorial_scripts/WAFO 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wafo/source/mvnprd/mvnprd.pyf | 23 - wafo/source/mvnprd/mvnprd_interface.f | 88 - wafo/source/mvnprd/mvnprodcorrprb.f | 4334 - wafo/source/mvnprd/mvnprodcorrprb_interface.f | 33 - .../mvnprd/old/mvnprodcorrprb/build_all.py | 24 - .../old/mvnprodcorrprb/mvnprodcorrprb.f | 4335 - .../mvnprodcorrprb/mvnprodcorrprb_interface.f | 33 - .../old/AdaptiveGaussKronrod.f90 | 1802 - .../old/adaptivegausskronrod.pyf | 157 - .../mvnprd/old/mvnprodcorrprb/old/dea.f | 390 - .../mvnprd/old/mvnprodcorrprb/old/deamod.pyf | 6 - .../mvnprd/old/mvnprodcorrprb/old/erfcore.f90 | 344 - .../mvnprodcorrprb/old/integration1Dmodule.f | 1460 - .../old/integration1Dmodule.f90 | 1461 - .../old/mvnprodcorrprb/old/mvnprodcorrprb.f90 | 4329 - .../old/mvnprodcorrprb/old/mvnprodcorrprb.pyf | 24 - .../mvnprodcorrprb/old/mvnprodcorrprbmod.f90 | 666 - .../old/test_mvnprodcorrprb.dsp | 97 - .../old/test_mvnprodcorrprb.dsw | 29 - .../mvnprodcorrprb/old/test_mvnprodcorrprb.f | 39 - wafo/source/mvnprd/setup.py | 32 - wafo/source/old/dunnettprb.f | 1209 - wafo/source/old/erfcore.f | 524 - wafo/source/old/erfcore.pyf | 39 - wafo/source/old/erfcoremod.f | 346 - wafo/source/old/erfcoremod.f90 | 346 - wafo/source/old/erfcoremod.pyf | 29 - wafo/source/old/erfcoremod0.f90 | 346 - wafo/source/old/erfcoremod1.pyf | 27 - wafo/source/old/erfcoremod_interface.f90 | 11 - wafo/source/rind2007/.cproject | 608 - wafo/source/rind2007/.project | 81 - wafo/source/rind2007/Debug/makefile | 43 - wafo/source/rind2007/Debug/objects.mk | 7 - wafo/source/rind2007/Debug/sources.mk | 21 - wafo/source/rind2007/Debug/subdir.mk | 47 - wafo/source/rind2007/build_all.py | 31 - wafo/source/rind2007/erfcoremod.f | 339 - wafo/source/rind2007/fimod.f | 1595 - wafo/source/rind2007/intmodule.f | 3856 - wafo/source/rind2007/jacobmod.f | 20 - wafo/source/rind2007/rind71mod.f | 4157 - wafo/source/rind2007/rind_interface.f | 223 - wafo/source/rind2007/rindmod.f | 2435 - wafo/source/rind2007/swapmod.f | 27 - 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delete mode 100644 wafo/tests/test_integrate.py delete mode 100644 wafo/tests/test_integrate_oscillating.py delete mode 100644 wafo/tests/test_misc.py delete mode 100644 wafo/tests/test_objects.py delete mode 100644 wafo/tests/test_padua.py diff --git a/wafo/__init__.py b/wafo/__init__.py index 48d6db0..c3a88ee 100644 --- a/wafo/__init__.py +++ b/wafo/__init__.py @@ -2,28 +2,28 @@ from __future__ import division, print_function, absolute_import from .info import __doc__ -from . import misc -from . import data -from . import demos -from . import kdetools -from . import objects -from . import spectrum -from . import transform -from . import definitions -from . import polynomial -from . import stats -from . import interpolate -from . import dctpack -from . import wave_theory -try: - from . import fig -except ImportError: - print('fig import only supported on Windows') +# from . import misc +# from . import data +# from . import demos +# from . import kdetools +# from . import objects +# from . import spectrum +# from . import transform +# from . import definitions +# from . import polynomial +# from . import stats +# from . import interpolate +# from . import dctpack +# from . import wave_theory +# try: +# from . import fig +# except ImportError: +# print('fig import only supported on Windows') -try: - from wafo.version import version as __version__ -except ImportError: - __version__ = 'nobuilt' +# try: +# from wafo.version import version as __version__ +# except ImportError: +# __version__ = 'nobuilt' -from numpy.testing import Tester -test = Tester().test +# from numpy.testing import Tester +# test = Tester().test diff --git a/wafo/data/__init__.py b/wafo/data/__init__.py deleted file mode 100644 index d9eb13b..0000000 --- a/wafo/data/__init__.py +++ /dev/null @@ -1,3 +0,0 @@ -from __future__ import absolute_import -from .info import __doc__ -from .info import * diff --git a/wafo/data/atlantic.dat b/wafo/data/atlantic.dat deleted file mode 100644 index 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1.5594000e+04 2.0887668e+00 - 1.5594400e+04 8.3202808e-01 - 1.5594800e+04 -3.3789873e-01 - 1.5595200e+04 -1.1179195e+00 - 1.5595600e+04 -2.3579927e+00 - 1.5596000e+04 -2.8679834e+00 - 1.5596400e+04 -3.0479837e+00 - 1.5596800e+04 -2.7279855e+00 - 1.5597200e+04 -2.2280050e+00 - 1.5597600e+04 -1.4379712e+00 - 1.5598000e+04 -2.7785596e-01 - 1.5598400e+04 5.2204022e-01 - 1.5598800e+04 1.0220225e+00 - 1.5599200e+04 1.0943089e+00 - 1.5599600e+04 1.0254654e+00 diff --git a/wafo/data/info.py b/wafo/data/info.py deleted file mode 100644 index 6eb1206..0000000 --- a/wafo/data/info.py +++ /dev/null @@ -1,485 +0,0 @@ -""" -Data package in WAFO Toolbox. - -Contents --------- -atlantic - Significant wave-height data recorded in the Atlantic Ocean -gfaks89 - Surface elevation measured at Gullfaks C 24.12.1989 -gfaksr89 - Reconstructed surface elevation measured at Gullfaks C 24.12.1989. -japansea - coastline map of The Japan Sea -northsea - coastline map of The Nortsea -sea - Surface elevation dataset used in WAT version 1.1. -sfa89 - Wind measurements at Statfjord A 24.12.1989 -sn - Fatigue experiment, constant-amplitude loading. -yura87 - Surface elevation measured off the coast of Yura - - - -This module gives gives detailed information and easy access to all datasets -included in WAFO - -""" -import numpy as np - -import os -__path2data = os.path.dirname(os.path.realpath(__file__)) - -__all__ = ['atlantic', 'gfaks89', 'gfaksr89', 'japansea', 'northsea', 'sea', - 'sfa89', 'sn', 'yura87'] - -_NANS = set(['nan', 'NaN', '-1.#IND00+00', '1.#IND00+00', '-1.#INF00+00']) - - -def _tofloat(x): - return np.nan if x in _NANS else float(x or 0) - - -_MYCONVERTER = {} -for i in range(2): - _MYCONVERTER[i] = _tofloat - - -def _load(file): # @ReservedAssignment - """ local load function - """ - return np.loadtxt(os.path.join(__path2data, file)) - - -def _loadnan(file): # @ReservedAssignment - """ local load function accepting nan's - """ - return np.loadtxt(os.path.join(__path2data, file), converters=_MYCONVERTER) - - -def atlantic(): - """ - Return Significant wave-height data recorded in the Atlantic Ocean - - Data summary - ------------ - Size : 582 X 1 - Sampling Rate : ~ 14 times a month - Device : - Source : - Format : ascii - - Description - ------------ - atlantic.dat contains average significant wave-height data recorded - approximately 14 times a month in December-February during 7 years and - at 2 locations in the Atlantic Ocean - - Example - -------- - >>> import pylab - >>> import wafo - >>> Hs = wafo.data.atlantic() - >>> np.allclose(Hs[:3], [ 5.48296296, 4.3615 , 5.26023256]) - True - - h = pylab.plot(Hs) - - Acknowledgement: - --------------- - This dataset were made available by Dr. David Carter - and Dr. David Cotton, Satellite Observing Systems, UK. - """ - return _load('atlantic.dat') - - -def gfaks89(): - """ - Return Surface elevation measured at Gullfaks C 24.12.1989 - - Data summary - ------------ - Size : 39000 X 2 - Sampling Rate : 2.5 Hz - Device : EMI laser - Source : STATOIL - Format : ascii, c1: time c2: surface elevation - - Description - ------------ - The wave data was measured 24th December 1989 at the Gullfaks C platform - in the North Sea from 17.00 to 21.20. The period from 20.00 to 20.20 - is missing and contains NaNs. The water depth of 218 m is - regarded as deep water for the most important wave components. - There are two EMI laser sensors named 219 and 220. This data set is - obtained from sensor 219, which is located in the Northwest - corner approximately two platform leg diameters away from - the closest leg. - Thus the wave elevation is not expected to be significantly - affected by diffraction effects for incoming waves in the western sector. - The wind direction for this period is from the south. - Some difficulties in calibration of the instruments have been reported - resulting in several consecutive measured values being equal or almost - equal in the observed data set. - - This dataset is for non-commercial use only. - - Hm0 = 6.8m, Tm02 = 8s, Tp = 10.5 - - Example - ------- - >>> import pylab - >>> import wafo - >>> x = wafo.data.gfaks89() - >>> np.allclose(x[:3, 1], [-0.19667949, -0.46667949, -0.38667949]) - True - - h = pylab.plot(x[:,0],x[:,1]) - - Acknowledgement: - --------------- - This dataset were prepared and made available by Dr. S. Haver, - STATOIL, Norway - - See also - -------- - gfaksr89, northsea - - """ - return _loadnan('gfaks89.dat') - - -def gfaksr89(): - """ - Return a reconstruction of surface elevation measured at Gullfaks C - 24.12.1989. - - - Data summary - ------------ - Size : 39000 X 2 - Sampling Rate : 2.5 Hz - Device : EMI laser - Source : STATOIL - Format : ascii, c1: time c2: surface elevation - - Description - ----------- - This is a reconstructed version of the data in the GFAKS89.DAT file. - The following calls were made to reconstruct the data: - - inds = findoutliers(gfaks89,.02,2,1.23); - gfaksr89 = reconstruct(gfaks89,inds,6); - - The wave data was measured 24th December 1989 at the Gullfaks C platform - in the North Sea from 17.00 to 21.20. The period from 20.00 to 20.20 - is missing in the original data. The water depth of 218 m is - regarded as deep water for the most important wave components. - There are two EMI laser sensors named 219 and 220. This data set is - obtained from sensor 219, which is located in the Northwest - corner approximately two platform leg diameters away from - the closest leg. - Thus the wave elevation is not expected to be significantly - affected by diffraction effects for incoming waves in the western sector. - The wind direction for this period is from the south. - Some difficulties in calibration of the instruments have been reported - resulting in several consecutive measured values being equal or almost - equal in the observed data set. - - Hm0 = 6.8m, Tm02 = 8s, Tp = 10.5 - - - Example - ------- - >>> import pylab - >>> import wafo - >>> x = wafo.data.gfaksr89() - - h = pylab.plot(x[:,0],x[:,1]) - - See also - -------- - gfaks89 - """ - return _loadnan('gfaksr89.dat') - - -def japansea(): - """ - Return coastline map of The Japan Sea - - - Data summary - ------------ - Size : 692 X 2 - Sampling Rate : - Device : - Source : http://crusty.er.usgs.gov/coast/getcoast.html - Format : ascii, c1: longitude c2: latitude - - Description - ----------- - JAPANSEA.DAT contains data for plotting a map of The Japan Sea. - The data is obtained from USGS coastline extractor. - - Example: - ------- - #the map is seen by - - >>> import pylab - >>> import wafo - >>> map1 = wafo.data.japansea() - >>> np.allclose(map1[1:4, 0], [ 141.960057, 142.058624, 142.103214]) - True - - h = pylab.plot(map1[:,0],map1[:,1]) - lon_loc = [131,132,132,135,139.5,139] - lat_loc = [46, 43, 40, 35, 38.3, 35.7] - loc = ['China','Vladivostok','Japan Sea', 'Japan', 'Yura','Tokyo'] - algn = 'right' - for lon, lat, name in zip(lon_loc,lat_loc,loc): - pylab.text(lon,lat,name,horizontalalignment=algn) - - - # If you have the m_map toolbox (see http://www.ocgy.ubc.ca/~rich/): - m_proj('lambert','long',[130 148],'lat',[30 48]); - m_line(map(:,1),map(:,2)); - m_grid('box','fancy','tickdir','out'); - m_text(131,46,'China'); - m_text(132,43,'Vladivostok'); - m_text(132,40,'Japan Sea'); - m_text(135,35,'Japan'); - m_text(139.5,38.3,'Yura'); - m_text(139,35.7,'Tokyo'); - """ - return _loadnan('japansea.dat') - - -def northsea(): - """ - NORTHSEA coastline map of The Nortsea - - Data summary - ------------- - Size : 60646 X 2 - Sampling Rate : - Device : - Source : http://crusty.er.usgs.gov/coast/getcoast.html - Format : ascii, c1: longitude c2: latitude - - Description - ----------- - NORTHSEA.DAT contains data for plotting a map of The Northsea. - The data is obtained from USGS coastline extractor. - - Example - ------- - # the map is seen by - - >>> import pylab - >>> import wafo - >>> map1 = wafo.data.northsea() - >>> np.allclose(map1[1:4, 0], [ 1.261996, 1.264064, 1.268171]) - True - - h = pylab.plot(map1[:,0],map1[:,1]) - lon_pltfrm = [1.8, 2.3, 2., 1.9, 2.6] - lat_pltfrm = [61.2, 61.2, 59.9, 58.4, 57.7] - pltfrm = ['Statfjord A', 'Gullfaks C', 'Frigg', 'Sleipner', 'Draupner'] - h = pylab.scatter(lon_pltfrm,lat_pltfrm); - algn = 'right' - for lon, lat, name in zip(lon_pltfrm,lat_pltfrm,pltfrm): - pylab.text(lon,lat,name,horizontalalignment=algn); algn = 'left' - - - lon_city = [10.8, 10.8, 5.52, 5.2] - lat_city = [59.85, 63.4, 58.9, 60.3] - city = ['Oslo','Trondheim','Stavanger', 'Bergen'] - h = pylab.scatter(lon_city,lat_city); - algn = 'right' - for lon, lat, name in zip(lon_city,lat_city,city): - pylab.text(lon,lat,name,horizontalalignment=algn) - - # If you have the mpl_toolkits.basemap installed - from mpl_toolkits.basemap import Basemap - import matplotlib.pyplot as plt - - # setup Lambert Conformal basemap. - m = Basemap(width=1200000,height=900000,projection='lcc', - resolution='f',lat_1=56.,lat_2=64,lat_0=58,lon_0=5.) - m.drawcoastlines() - h = m.scatter(lon_pltfrm,lat_pltfrm); - algn = 'right' - for lon, lat, name in zip(lon_pltfrm,lat_pltfrm,pltfrm): - m.text(lon,lat,name,horizontalalignment=algn); algn = 'left' - m.scatter(lon_city,lat_city) - algn = 'right' - for lon, lat, name in zip(lon_city,lat_city,city): - m.text(lon,lat,name,horizontalalignment=algn) - """ - return _loadnan('northsea.dat') - - -def sea(): - """ - Return Surface elevation dataset used in WAT version 1.1. - - Data summary - ------------ - Size : 9524 X 2 - Sampling Rate : 4.0 Hz - Device : unknown - Source : unknown - Format : ascii, c1: time c2: surface elevation - - Description - ----------- - The wave data was used in one of WAFO predecessors, i.e. the Wave - Analysis Toolbox version 1.1 (WAT) - Hm0 = 1.9m, Tm02 = 4.0s, Tp2 = 11.5s Tp1=5.6s - - Example - ------- - >>> import pylab - >>> import wafo - >>> x = wafo.data.sea() - >>> np.allclose(x[:3,1],[-1.2004945 , -1.0904945 , -0.79049454]) - True - - h = pylab.plot(x[:,0],x[:,1]) - """ - return _load('sea.dat') - - -def sfa89(): - """ - Return Wind measurements at Statfjord A 24.12.1989 - - Data summary - ------------ - Size : 144 X 3 - Sampling Rate : 1/600 Hz - Device : - Source : DNMI (The Norwegian Meteorological Institute) - Format : ascii, c1: time (hours) - c2: velocity (m/s) - c3: direction (degrees) - Description - ----------- - The registration of wind speeds at the Gullfaks field - started up on Statfjord A in 1978 and continued until 1990. - The dataregistration was transferred to Gullfaks C in Nov 1989. - Due to some difficulties of the windregistration on Gullfaks C in - the beginning, they continued to use the registered data from - Statfjord A. - The windspeed is measured in (meter/second), 110 m above mean water - level (MWL) and the wind direction is given in degrees for the data. - The data are a mean value of every 10 minutes. - Wind directions are defined in the meteorological convention, i.e., - 0 degrees = wind approaching from North, 90 degrees = wind from East, etc. - This dataset is for non-commercial use only. - - Example - ------- - >>> import pylab - >>> import wafo - >>> x = wafo.data.sfa89() - - h = pylab.plot(x[:,0],x[:,1]) - - Acknowledgement - ---------------- - These data are made available by Knut A. Iden, DNMI. - - See also - -------- - northsea - """ - return _load('sfa89.dat') - - -def sn(): - """ - Return SN Fatigue experiment, constant-amplitude loading. - - - Data summary - ------------ - Size : 40 X 2 - Source : unknown - Format : ascii, c1: Amplitude MPa c2: Number of cycles - - Description - ----------- - A fatigue experiment with constant amplitudes at five levels: - 10,15,20,25 and 30 MPa. For each level is related 8 observations of - the number of cycles to failure. - - The origin of the data is unknown. - - Example - ------- - >>> import pylab - >>> import wafo - >>> x = wafo.data.sn() - - h = pylab.plot(x[:,0],x[:,1]) - - See also - -------- - The same data appear in the directory wdemos/itmkurs/ - as SN.mat. - - """ - return _load('sn.dat') - - -def yura87(): - """ - Return Surface elevation measured off the coast of Yura. - - - Data summary - ----------- - Size : 85547 X 4 - Sampling Rate : 1 Hz - Device : ultrasonic wave gauges - Source : SRI, Ministry of Transport, Japan - Format : ascii, c1: time (sec) c2-4: surface elevation (m) - - Description - ----------- - The wave data was measured at the Poseidon platform - in the Japan Sea from 24th November 1987 08.12 hours to 25th November - 1987 07.57 hours. Poseidon was located 3 km off the coast of Yura - in the Yamagata prefecture, in the Japan Sea during the measurements. - The most important wave components are to some extent influenced by the - water depth of 42 m. The data are measured with three ultrasonic wave - gauges located at the sea floor and the relative coordinates of the - gauges are as follows (x-axis points to the East, y-axis points to - the North): - X (m) Y (m) - c2: -4.93, 25.02 - c3: 5.80, 92.12 - c4: 0.00, 0.00 - - This dataset is for non-commercial use only. - - Hm0 = 5.1m, Tm02 = 7.7s, Tp = 12.8s - Example - ------- - >>> import pylab - >>> import wafo - >>> x = wafo.data.yura87() - - h = pylab.plot(x[:,0],x[:,1]) - - Acknowledgement: - ----------------- - This dataset were prepared and made available by Dr. Sc. H. Tomita, - Ship Research Institute, Ministry of Transport, Japan. - - See also - -------- - japansea - """ - return _load('yura87.dat') - - -if __name__ == '__main__': - import doctest - doctest.testmod() diff --git a/wafo/data/japansea.dat b/wafo/data/japansea.dat deleted file mode 100644 index a9fc01f..0000000 --- a/wafo/data/japansea.dat +++ /dev/null @@ -1,692 +0,0 @@ -nan nan -141.960057 40.022926 -142.058624 39.818752 -142.103214 39.640392 -142.157191 39.469073 -142.136070 39.332957 -142.070358 39.229696 -142.046890 39.074805 -141.927201 38.955116 -141.805166 38.948076 -141.727720 38.765023 -141.638541 38.542073 -141.638541 38.368408 -141.629153 38.316777 -141.396817 38.333205 -141.143358 38.194742 -141.054179 37.934243 -141.087034 37.671397 -141.143358 37.453142 -141.143358 37.143360 -141.164480 36.957960 -140.976733 36.826537 -140.854698 36.603588 -140.812455 36.533182 -140.756131 36.258603 -140.744396 35.944127 -140.887553 35.791583 -140.922756 35.683628 -140.767865 35.603836 -140.589505 35.359765 -140.479204 35.162631 -140.237480 35.007740 -nan nan -139.984022 35.233036 -140.016877 35.369152 -140.148300 35.495881 -140.192890 35.622610 -nan nan -139.972288 39.161638 -140.070855 39.323569 -140.138913 39.530091 -140.148300 39.750693 -140.016877 39.844567 -nan nan -140.237480 35.007740 -139.993409 34.862236 -139.951166 35.007740 -139.984022 35.233036 -nan nan -140.192890 35.622610 -139.951166 35.622610 -139.894842 35.451291 -139.805662 35.305788 -139.784541 35.153243 -139.653118 35.233036 -139.409047 35.261198 -139.298746 35.115694 -139.254156 34.918560 -139.209566 34.726119 -139.089878 34.618165 -138.956108 34.636940 -138.911518 34.871623 -138.946721 35.035902 -138.791830 35.052329 -138.625204 34.925600 -138.460926 34.763669 -138.348278 34.580616 -138.315422 34.554800 -138.195733 34.571228 -137.996252 34.608778 -137.731060 34.618165 -137.477602 34.618165 -137.256999 34.554800 -137.212409 34.554800 -137.278121 34.636940 -137.388422 34.709692 -137.266387 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37.950671 -138.449192 38.204129 -138.604083 38.272187 -nan nan -134.276519 33.268735 -134.065304 33.379036 -133.800111 33.454135 -133.570121 33.397811 -133.391762 33.296897 -133.293195 33.111497 -133.105448 32.879160 -133.084326 32.712535 -132.905967 32.693760 -132.751076 32.804061 -132.685365 32.879160 -132.553942 33.083335 -132.575063 33.167821 -132.509352 33.278122 -132.387316 33.360261 -132.223038 33.360261 -132.488230 33.536274 -132.697099 33.756876 -132.896580 33.977479 -133.105448 33.949317 -133.239218 33.895340 -133.436352 33.932889 -133.624099 34.005641 -133.689810 34.134717 -133.823580 34.226244 -133.933881 34.317770 -134.065304 34.334198 -134.264785 34.289608 -134.452531 34.198081 -134.619157 34.188694 -134.661400 33.996254 -134.717724 33.822588 -134.762314 33.803813 -134.771701 33.794426 -134.762314 33.766264 -134.652012 33.665350 -134.551098 33.618413 -134.452531 33.517499 -134.363352 33.369649 -134.276519 33.268735 -nan nan -135.060362 34.571228 -135.027506 34.526638 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30.325804 -130.545051 30.353966 -nan nan -130.897076 37.539975 -130.843099 37.495385 -130.843099 37.478957 -130.885342 37.453142 -130.974522 37.504772 -130.897076 37.539975 -nan nan -130.035788 33.416585 -130.000000 33.445983 -nan nan -142.678694 48.000000 -142.654720 47.880130 -142.666454 47.650140 -142.809611 47.448313 -142.952768 47.335665 -143.107659 47.194854 -143.140515 47.028229 -143.206226 46.915581 -143.307140 46.840482 -143.462031 46.772424 -143.516009 46.802933 -143.572333 46.755996 -143.626310 46.582330 -143.670900 46.415705 -143.649778 46.225612 -143.548864 46.070720 -143.494887 46.270201 -143.417442 46.537741 -143.173371 46.605799 -142.943381 46.687938 -142.699310 46.697325 -142.523297 46.558862 -142.434118 46.361728 -142.356672 46.148166 -142.258105 45.955725 -142.025768 46.049599 -141.969444 46.354687 -141.960057 46.657429 -142.025768 46.983639 -142.070358 47.194854 -142.091480 47.441272 -142.124335 47.671262 -142.157191 47.894211 -142.248875 48.000000 -nan nan 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58.082409 --3.710053 58.081236 --3.715333 58.079476 --3.720907 58.078009 --3.726481 58.076249 --3.730588 58.073902 --3.733521 58.070968 --3.736162 58.067155 --3.739095 58.064221 --3.743202 58.061581 --3.747896 58.059821 --3.753469 58.058061 --3.759043 58.056594 --3.764324 58.055127 --3.771364 58.054541 --3.779285 58.054541 --3.785445 58.053367 --3.791019 58.051900 --3.795419 58.049554 --3.799233 58.046913 --3.804513 58.045153 --3.810087 58.043980 --3.816247 58.042806 --3.822408 58.041633 --3.825635 58.038700 --3.827981 58.034886 --3.831502 58.031952 --3.835609 58.029312 --3.839422 58.026965 --3.842356 58.024032 --3.844996 58.020218 --3.846463 58.016405 --3.847636 58.012004 --3.847636 58.007897 --3.847636 58.003497 --3.847636 57.999977 --3.853503 57.998217 --3.858784 57.996750 --3.863184 57.994110 --3.867878 57.992350 --3.873745 57.991176 --3.880785 57.990589 --3.886359 57.989123 --3.891933 57.987362 --3.896626 57.985602 --3.902200 57.983842 --3.906894 57.982082 --3.911587 57.980029 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57.703102 --3.974659 57.700462 --3.978179 57.697528 --3.981993 57.694595 --3.984926 57.691661 --3.987273 57.688434 --3.990500 57.685207 --3.996074 57.683741 --4.000000 57.682024 -nan nan --4.000000 57.672011 --3.999887 57.672007 --3.999007 57.668193 --4.000000 57.667759 -nan nan --4.000000 57.591041 --3.992847 57.591041 --3.984046 57.590747 --3.976712 57.590747 --3.967911 57.590161 --3.959404 57.589867 --3.950897 57.589574 --3.942390 57.588987 --3.934176 57.588401 --3.926255 57.588401 --3.917748 57.588107 --3.909534 57.587520 --3.900733 57.587227 --3.893399 57.586054 --3.884599 57.585760 --3.877265 57.585760 --3.869931 57.586347 --3.863771 57.587520 --3.857904 57.588401 --3.854090 57.589867 --3.853210 57.589867 --3.849690 57.590161 --3.844116 57.591627 --3.837955 57.592801 --3.832675 57.594561 --3.826515 57.595441 --3.820354 57.596321 --3.815661 57.598668 --3.810087 57.600135 --3.805980 57.602482 --3.801286 57.604828 --3.797473 57.607175 --3.793072 57.609229 --3.788379 57.611282 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57.678167 --2.931197 57.678167 --2.927090 57.680514 --2.930904 57.683154 --2.932370 57.686381 --2.932077 57.689901 --2.927970 57.692541 --2.920343 57.692541 --2.913009 57.693128 --2.908315 57.694888 --2.902155 57.696062 --2.893941 57.695475 --2.886020 57.695475 --2.879860 57.696355 --2.873700 57.697528 --2.868126 57.698995 --2.861965 57.699875 --2.855512 57.700755 --2.849645 57.699875 --2.847884 57.696648 --2.847004 57.693128 --2.844951 57.689608 --2.840257 57.687554 --2.832923 57.687554 --2.826470 57.688728 --2.820896 57.689901 --2.814735 57.691075 --2.807402 57.691661 --2.801534 57.692541 --2.795961 57.694008 --2.790680 57.695475 --2.785107 57.694008 --2.781880 57.690781 --2.773372 57.690194 --2.765745 57.689314 --2.761052 57.689021 --2.754891 57.687261 --2.749317 57.685501 --2.745797 57.683154 --2.743157 57.679927 --2.738463 57.678167 --2.732303 57.678167 --2.727609 57.679927 --2.722329 57.681394 --2.714408 57.681394 --2.708541 57.679634 --2.704141 57.677874 --2.696807 57.676700 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--2.081643 57.079137 --2.083696 57.075030 --2.084576 57.070630 --2.086336 57.066523 --2.088390 57.062416 --2.089857 57.058309 --2.092790 57.055082 --2.096604 57.052442 --2.099831 57.049509 --2.102178 57.045695 --2.105111 57.042468 --2.107458 57.038948 --2.110685 57.035721 --2.114498 57.033374 --2.120072 57.031321 --2.125646 57.029854 --2.129753 57.027507 --2.131513 57.023693 --2.134447 57.020466 --2.139140 57.018706 --2.144714 57.016946 --2.148528 57.014599 --2.152048 57.011666 --2.154101 57.008146 --2.155568 57.003745 --2.155568 56.999345 --2.156448 56.994651 --2.157915 56.990251 --2.158502 56.985851 --2.161142 56.982330 --2.165249 56.979690 --2.170529 56.978223 --2.175223 56.976463 --2.179916 56.974410 --2.183143 56.971476 --2.182557 56.967369 --2.179623 56.964729 --2.178156 56.961502 --2.176396 56.957982 --2.174343 56.954755 --2.171996 56.951235 --2.169942 56.947715 --2.170236 56.943608 --2.170236 56.939501 --2.171409 56.935100 --2.173169 56.930993 --2.175516 56.927473 --2.177276 56.923366 --2.177570 56.919553 --2.176690 56.915446 --2.177863 56.911045 --2.180797 56.908112 --2.183437 56.904298 --2.186370 56.901365 --2.189304 56.898138 --2.192531 56.894911 --2.195464 56.891977 --2.198104 56.888457 --2.200451 56.884937 --2.204852 56.882590 --2.207785 56.879363 --2.210719 56.876429 --2.212772 56.872616 --2.213946 56.867922 --2.214826 56.863228 --2.216586 56.859415 --2.220693 56.857068 --2.224800 56.854428 --2.229200 56.852081 --2.233014 56.849734 --2.236827 56.847094 --2.240347 56.844454 --2.244161 56.841814 --2.248855 56.840053 --2.254428 56.838293 --2.258242 56.835947 --2.259122 56.831253 --2.261176 56.827146 --2.264109 56.824506 --2.267336 56.821279 --2.271443 56.818932 --2.274670 56.815705 --2.278484 56.813358 --2.282591 56.810718 --2.286404 56.808371 --2.290218 56.805731 --2.294031 56.803384 --2.298138 56.800744 --2.302245 56.798397 --2.306939 56.796344 --2.310753 56.793997 --2.315446 56.791943 --2.320140 56.789890 --2.323953 56.787543 --2.328647 56.785196 --2.333341 56.783436 --2.339501 56.782556 --2.344782 56.780796 --2.349475 56.779036 --2.352409 56.775809 --2.355929 56.773169 --2.360623 56.770822 --2.367957 56.771115 --2.375584 56.771995 --2.383798 56.772582 --2.389958 56.771702 --2.394359 56.769355 --2.399052 56.767595 --2.403159 56.764955 --2.406386 56.762021 --2.408733 56.758501 --2.410493 56.757034 --2.406386 56.758208 --2.408440 56.755861 --2.410786 56.752341 --2.413427 56.748527 --2.414307 56.747647 --2.416360 56.743833 --2.418120 56.739726 --2.419587 56.735913 --2.421347 56.731806 --2.423107 56.727699 --2.424867 56.723592 --2.426334 56.719778 --2.428388 56.715671 --2.430734 56.712151 --2.433375 56.708631 --2.437188 56.705991 --2.440415 56.703057 --2.441002 56.699537 --2.436308 56.697190 --2.430148 56.695723 --2.424867 56.694256 --2.422814 56.690736 --2.423107 56.686629 --2.424867 56.682816 --2.428094 56.679589 --2.431028 56.676655 --2.435135 56.674308 --2.438948 56.671668 --2.443642 56.669615 --2.448922 56.668148 --2.455083 56.667268 --2.461830 56.666681 --2.467990 56.665801 --2.473271 56.664041 --2.477965 56.662281 --2.482658 56.660227 --2.485885 56.657294 --2.488819 56.654067 --2.492339 56.651133 --2.493806 56.647320 --2.496446 56.643506 --2.497913 56.639692 --2.497913 56.635585 --2.496446 56.632359 --2.491752 56.630012 --2.487352 56.627665 --2.480898 56.626785 --2.476498 56.624438 --2.474738 56.621211 --2.474738 56.616811 --2.477671 56.613877 --2.480898 56.610944 --2.485005 56.608303 --2.488819 56.605957 --2.493219 56.603903 --2.496739 56.600970 --2.500553 56.598329 --2.503486 56.595396 --2.506127 56.591876 --2.507887 56.587769 --2.511114 56.584835 --2.515514 56.582782 --2.519328 56.580141 --2.522848 56.577208 --2.524315 56.573394 --2.526955 56.569581 --2.529888 56.566647 --2.533995 56.564300 --2.537809 56.561660 --2.540742 56.559900 --2.545143 56.558140 --2.550716 56.556673 --2.555703 56.554913 --2.561864 56.554033 --2.568024 56.553153 --2.575065 56.552566 --2.581812 56.552273 --2.587679 56.551099 --2.593840 56.550219 --2.598240 56.548459 --2.602934 56.546112 --2.607040 56.543472 --2.609387 56.540245 --2.612614 56.537312 --2.614961 56.533498 --2.618188 56.530565 --2.622002 56.527924 --2.626109 56.525578 --2.630509 56.523524 --2.635202 56.521764 --2.640190 56.520004 --2.644883 56.517950 --2.649577 56.516190 --2.652804 56.512963 --2.656031 56.510030 --2.661311 56.508563 --2.668352 56.507976 --2.674219 56.507096 --2.679499 56.505629 --2.683313 56.502989 --2.688006 56.501229 --2.693287 56.499762 --2.698567 56.498002 --2.704727 56.497122 --2.710008 56.495655 --2.714702 56.493602 --2.718515 56.491255 --2.720862 56.487441 --2.723209 56.484215 --2.724969 56.480108 --2.726142 56.475414 --2.727022 56.470720 --2.726142 56.467200 --2.727022 56.462800 --2.732596 56.461040 --2.740810 56.461626 --2.746971 56.463093 --2.752544 56.464853 --2.758118 56.466613 --2.763398 56.468373 --2.768972 56.470134 --2.775133 56.471307 --2.781000 56.472187 --2.787160 56.473654 --2.794787 56.474534 --2.801828 56.474534 --2.807988 56.473654 --2.814149 56.472480 --2.820309 56.471307 --2.825589 56.470134 --2.829990 56.468080 --2.835564 56.466320 --2.839964 56.464560 --2.845538 56.463093 --2.849938 56.461040 --2.855218 56.459573 --2.860499 56.458106 --2.868126 56.458106 --2.873700 56.459866 --2.879273 56.461333 --2.884554 56.463386 --2.890714 56.464560 --2.898341 56.464560 --2.903915 56.463093 --2.909782 56.461920 --2.917996 56.462506 --2.925330 56.463680 --2.932077 56.463093 --2.937358 56.461920 --2.937358 56.462800 --2.940878 56.461333 --2.945278 56.459279 --2.949972 56.457226 --2.954665 56.455173 --2.958772 56.453412 --2.962879 56.450772 --2.967573 56.448719 --2.972853 56.447252 --2.979601 56.446665 --2.986934 56.446665 --2.993682 56.448132 --3.000135 56.449305 --3.006296 56.450479 --3.014510 56.451066 --3.021550 56.452239 --3.030058 56.452532 --3.036805 56.452239 --3.043552 56.451652 --3.048832 56.449892 --3.054113 56.448719 --3.059393 56.447252 --3.064967 56.445492 --3.069367 56.443732 --3.073474 56.441091 --3.077874 56.439038 --3.081688 56.436691 --3.086088 56.434344 --3.092249 56.433758 --3.097822 56.431998 --3.102809 56.430531 --3.108970 56.429357 --3.114250 56.428184 --3.119824 56.426424 --3.124811 56.424957 --3.129505 56.423197 --3.133318 56.420263 --3.136839 56.417916 --3.140945 56.415276 --3.144172 56.412343 --3.148573 56.410289 --3.152973 56.408236 --3.157667 56.406476 --3.162947 56.404716 --3.166761 56.402369 --3.171454 56.400315 --3.175268 56.397675 --3.178201 56.394742 --3.182308 56.392101 --3.186709 56.390048 --3.191402 56.387994 --3.196683 56.386528 --3.201083 56.384474 --3.205777 56.382421 --3.210470 56.380660 --3.214284 56.378020 --3.218098 56.375673 --3.221031 56.372447 --3.224845 56.370100 --3.228952 56.367460 --3.234232 56.365699 --3.240099 56.365113 --3.246846 56.364526 --3.253007 56.363353 --3.258874 56.362179 --3.264154 56.360712 --3.269435 56.359246 --3.274715 56.357779 --3.280876 56.356605 --3.288796 56.357192 --3.296130 56.358072 --3.301704 56.360126 --3.307277 56.361592 --3.312851 56.363353 --3.319305 56.364819 --3.324292 56.363059 --3.324879 56.360419 --3.321358 56.357779 --3.316665 56.355725 --3.311971 56.353672 --3.306691 56.351912 --3.301410 56.350152 --3.294663 56.348978 --3.287329 56.348098 --3.280289 56.346925 --3.272075 56.346631 --3.264448 56.346631 --3.258581 56.347511 --3.252420 56.348685 --3.246846 56.349858 --3.240979 56.351032 --3.235699 56.352792 --3.229245 56.353085 --3.223965 56.354845 --3.216924 56.355139 --3.210764 56.356019 --3.204897 56.357192 --3.199030 56.358366 --3.193163 56.359246 --3.187882 56.360712 --3.183188 56.362766 --3.178495 56.364819 --3.174095 56.366579 --3.168521 56.368340 --3.162360 56.369513 --3.156787 56.370393 --3.151506 56.371860 --3.146226 56.373327 --3.141532 56.375380 --3.136839 56.377727 --3.133025 56.380367 --3.129211 56.382714 --3.124811 56.385061 --3.119531 56.386528 --3.113370 56.387408 --3.107210 56.388288 --3.101343 56.389461 --3.095182 56.390635 --3.089022 56.391515 --3.084035 56.392981 --3.079341 56.395035 --3.074647 56.397088 --3.070247 56.398848 --3.065553 56.401195 --3.060273 56.402369 --3.053233 56.402955 --3.047072 56.403542 --3.040912 56.404422 --3.036218 56.406476 --3.032404 56.409116 --3.027124 56.410583 --3.021257 56.411756 --3.015096 56.412636 --3.008349 56.412929 --3.002189 56.414103 --2.995148 56.414396 --2.990161 56.416156 --2.984881 56.417623 --2.980187 56.419383 --2.975494 56.421730 --2.971093 56.423490 --2.966693 56.425544 --2.961119 56.427304 --2.955839 56.428477 --2.951439 56.430531 --2.946745 56.432584 --2.942345 56.434638 --2.938824 56.437865 --2.935011 56.440211 --2.932077 56.443438 --2.928264 56.445785 --2.923570 56.447839 --2.918876 56.449599 --2.913889 56.451066 --2.906849 56.451652 --2.900688 56.452826 --2.892474 56.452239 --2.884554 56.451652 --2.877220 56.450772 --2.869886 56.449599 --2.864312 56.448132 --2.859912 56.445785 --2.855218 56.444025 --2.851698 56.441385 --2.847884 56.438745 --2.840551 56.437865 --2.834683 56.438745 --2.828523 56.439625 --2.821776 56.440211 --2.815322 56.440798 --2.808868 56.439331 --2.805935 56.436398 --2.804175 56.433171 --2.804175 56.428771 --2.803295 56.425250 --2.801534 56.422023 --2.798894 56.418797 --2.798014 56.415276 --2.799774 56.411169 --2.801828 56.407649 --2.804468 56.404129 --2.806815 56.400609 --2.809455 56.397088 --2.810335 56.392395 --2.809455 56.388874 --2.808575 56.385061 --2.809455 56.380660 --2.811508 56.376260 --2.815322 56.373913 --2.818842 56.371273 --2.823536 56.369513 --2.828816 56.368046 --2.833803 56.366286 --2.837910 56.363939 --2.836150 56.360419 --2.831750 56.358659 --2.828230 56.358366 --2.822949 56.359832 --2.819136 56.362179 --2.813269 56.363353 --2.809455 56.361592 --2.807402 56.358366 --2.806521 56.354552 --2.805935 56.350738 --2.803881 56.347511 --2.800361 56.344871 --2.795961 56.342818 --2.788627 56.341938 --2.782173 56.340471 --2.779533 56.337537 --2.775719 56.334897 --2.771026 56.332844 --2.764865 56.331670 --2.759291 56.332550 --2.751371 56.332550 --2.744037 56.331670 --2.738757 56.329910 --2.734943 56.327270 --2.730836 56.325217 --2.723209 56.324043 --2.718222 56.324630 --2.710595 56.324630 --2.704141 56.325217 --2.695927 56.324630 --2.687713 56.324043 --2.680379 56.324043 --2.675392 56.323750 --2.668938 56.322576 --2.664538 56.320229 --2.658964 56.318469 --2.651630 56.317883 --2.643710 56.317296 --2.638136 56.315242 --2.633736 56.313189 --2.631976 56.309962 --2.629922 56.306735 --2.628162 56.303215 --2.623762 56.301161 --2.619068 56.298521 --2.614668 56.296468 --2.609387 56.294708 --2.603814 56.292654 --2.599413 56.290894 --2.594720 56.288547 --2.590319 56.286494 --2.585626 56.284147 --2.582105 56.281800 --2.579759 56.278867 --2.577705 56.275640 --2.579465 56.271533 --2.582399 56.268306 --2.586506 56.265959 --2.591199 56.263905 --2.595893 56.261852 --2.600293 56.260092 --2.603814 56.257452 --2.607921 56.255105 --2.612614 56.252758 --2.616428 56.250411 --2.620828 56.248358 --2.624642 56.245717 --2.628749 56.243371 --2.633442 56.241317 --2.637256 56.238970 --2.640776 56.236330 --2.644590 56.233983 --2.649577 56.231930 --2.653390 56.229583 --2.657791 56.227236 --2.661604 56.224596 --2.665418 56.222249 --2.669525 56.219609 --2.673045 56.217262 --2.677739 56.215209 --2.683019 56.214035 --2.688886 56.212862 --2.696807 56.212862 --2.704141 56.212862 --2.710008 56.211982 --2.716168 56.210808 --2.722035 56.209928 --2.726729 56.207875 --2.731129 56.205821 --2.735530 56.203768 --2.741690 56.202888 --2.748437 56.202594 --2.754304 56.201421 --2.760465 56.200541 --2.765452 56.198781 --2.771026 56.197021 --2.775426 56.194967 --2.780413 56.192914 --2.784227 56.190567 --2.787747 56.187927 --2.793907 56.187047 --2.800654 56.186460 --2.807402 56.186167 --2.813562 56.184993 --2.820016 56.184406 --2.827056 56.184113 --2.834097 56.184113 --2.841724 56.184993 --2.847004 56.186753 --2.851698 56.188807 --2.856978 56.190567 --2.861379 56.192914 --2.865779 56.194967 --2.870179 56.197021 --2.874873 56.199074 --2.880153 56.200834 --2.886607 56.202301 --2.894234 56.203181 --2.901275 56.204061 --2.909489 56.204648 --2.916529 56.205528 --2.924157 56.205528 --2.931784 56.205528 --2.938238 56.204941 --2.944985 56.204355 --2.951145 56.203474 --2.957012 56.202594 --2.961706 56.200541 --2.966693 56.199074 --2.971387 56.197021 --2.976080 56.194967 --2.979601 56.192620 --2.983708 56.189980 --2.986934 56.187047 --2.990455 56.184406 --2.993682 56.181473 --2.997495 56.178833 --3.001309 56.176486 --3.005122 56.173846 --3.009229 56.171499 --3.013336 56.169445 --3.018030 56.167098 --3.022724 56.165338 --3.027711 56.163872 --3.033284 56.162111 --3.038271 56.160938 --3.044432 56.159765 --3.049126 56.157711 --3.052059 56.154778 --3.055873 56.152137 --3.059100 56.149204 --3.062913 56.146564 --3.066727 56.144217 --3.071420 56.142163 --3.074941 56.139817 --3.078754 56.137176 --3.083448 56.135123 --3.088728 56.133656 --3.093422 56.131603 --3.097822 56.129549 --3.102223 56.127496 --3.105743 56.124855 --3.110143 56.122509 --3.113077 56.119575 --3.115717 56.116348 --3.121291 56.114881 --3.128038 56.114588 --3.134785 56.114001 --3.138305 56.111361 --3.141532 56.108428 --3.143292 56.104321 --3.145639 56.100800 --3.147986 56.097280 --3.150333 56.093467 --3.152386 56.090240 --3.154146 56.086133 --3.151800 56.083199 --3.150039 56.079679 --3.150039 56.075865 --3.150626 56.071172 --3.152093 56.067358 --3.154733 56.063544 --3.157960 56.060611 --3.161774 56.057971 --3.165587 56.055624 --3.172334 56.055037 --3.179375 56.055037 --3.187882 56.055624 --3.194629 56.056504 --3.203137 56.057091 --3.211057 56.057384 --3.216631 56.055917 --3.220738 56.053864 --3.226898 56.052690 --3.229245 56.053570 --3.228365 56.054450 --3.234232 56.054157 --3.240686 56.055624 --3.246846 56.057091 --3.254180 56.057091 --3.260341 56.055917 --3.265328 56.054450 --3.270021 56.052104 --3.274422 56.050343 --3.278235 56.047703 --3.283222 56.046530 --3.290263 56.045943 --3.295250 56.044183 --3.299357 56.041543 --3.302290 56.038609 --3.306104 56.035969 --3.311971 56.035089 --3.319012 56.034796 --3.324585 56.033622 --3.329572 56.031569 --3.333679 56.029515 --3.337786 56.026875 --3.341307 56.024528 --3.346587 56.023061 --3.353921 56.023061 --3.360375 56.024235 --3.367415 56.025408 --3.374162 56.024822 --3.377976 56.022181 --3.381203 56.019248 --3.384136 56.016021 --3.387950 56.013674 --3.392350 56.011327 --3.399097 56.010741 --3.404378 56.012207 --3.404378 56.012794 --3.409365 56.013087 --3.414058 56.015141 --3.419339 56.016901 --3.425793 56.018074 --3.432833 56.018955 --3.441047 56.019541 --3.446621 56.021008 --3.451021 56.023355 --3.455421 56.025702 --3.460702 56.027168 --3.468329 56.028049 --3.474489 56.026875 --3.480356 56.025995 --3.487397 56.026875 --3.492091 56.028929 --3.494731 56.031862 --3.497078 56.034796 --3.503531 56.035969 --3.511159 56.035969 --3.517319 56.035089 --3.523186 56.034209 --3.530227 56.035089 --3.535800 56.036556 --3.540201 56.038903 --3.544894 56.040956 --3.548708 56.043303 --3.553108 56.045650 --3.556629 56.047997 --3.561322 56.050343 --3.565429 56.052104 --3.571296 56.053864 --3.578337 56.054744 --3.582444 56.055624 --3.588311 56.054450 --3.594471 56.053570 --3.600338 56.052397 --3.606499 56.051517 --3.612953 56.050930 --3.620287 56.050930 --3.628500 56.051517 --3.634368 56.050343 --3.641408 56.049757 --3.648742 56.049757 --3.656076 56.050637 --3.662236 56.051224 --3.668397 56.050050 --3.675144 56.049463 --3.682478 56.049463 --3.688638 56.047997 --3.692452 56.045650 --3.694505 56.041836 --3.695385 56.038316 --3.690105 56.036556 --3.684531 56.034796 --3.681598 56.031862 --3.681598 56.027755 --3.684531 56.024822 --3.685998 56.021595 --3.680424 56.020128 --3.675144 56.018368 --3.672504 56.015141 --3.670450 56.011914 --3.666930 56.009567 --3.662236 56.007220 --3.654902 56.006340 --3.648449 56.006927 --3.643462 56.008687 --3.637301 56.009567 --3.632021 56.011034 --3.626740 56.012501 --3.619993 56.013087 --3.613539 56.013674 --3.606792 56.014261 --3.600045 56.014848 --3.593591 56.015141 --3.585964 56.015141 --3.579510 56.015141 --3.573056 56.013674 --3.567483 56.011914 --3.560442 56.011034 --3.554869 56.009274 --3.549588 56.007514 --3.544894 56.005460 --3.540201 56.005167 --3.533454 56.005754 --3.527000 56.006047 --3.519079 56.006340 --3.511159 56.005754 --3.505878 56.004287 --3.501185 56.001940 --3.497078 55.999593 --3.492091 55.997833 --3.487397 55.995486 --3.482117 55.994019 --3.474196 55.993433 --3.468916 55.994313 --3.461582 55.994313 --3.454248 55.994313 --3.447501 55.994313 --3.440167 55.994606 --3.434300 55.994019 --3.429313 55.991966 --3.423739 55.990206 --3.417285 55.989032 --3.409951 55.989032 --3.403204 55.989619 --3.395284 55.989032 --3.388830 55.987859 --3.382376 55.986392 --3.376216 55.985219 --3.369762 55.984632 --3.365362 55.986979 --3.360668 55.989032 --3.356854 55.991379 --3.353041 55.994019 --3.347174 55.994899 --3.340426 55.994313 --3.335146 55.992846 --3.330452 55.990499 --3.326052 55.988739 --3.321652 55.986392 --3.317251 55.984339 --3.311678 55.982579 --3.307277 55.980525 --3.302877 55.978472 --3.297303 55.976711 --3.290850 55.975245 --3.283222 55.975245 --3.277355 55.976418 --3.270315 55.975538 --3.263861 55.974071 --3.257407 55.973778 --3.252127 55.975245 --3.246846 55.976711 --3.240979 55.977885 --3.233939 55.977005 --3.226312 55.977005 --3.220445 55.978178 --3.213697 55.978472 --3.206657 55.977592 --3.198736 55.977005 --3.191989 55.976711 --3.184362 55.976711 --3.177908 55.977298 --3.170281 55.977298 --3.162360 55.976711 --3.155026 55.975538 --3.148279 55.975245 --3.141532 55.974365 --3.135078 55.973191 --3.129798 55.971431 --3.125104 55.969084 --3.120411 55.967031 --3.116010 55.964977 --3.112490 55.962630 --3.107796 55.960284 --3.103689 55.957937 --3.098996 55.956177 --3.094302 55.953830 --3.089608 55.951776 --3.084328 55.950016 --3.079048 55.948256 --3.072887 55.947083 --3.066433 55.945616 --3.059393 55.944736 --3.051472 55.944149 --3.045312 55.945323 --3.039445 55.946496 --3.033284 55.947083 --3.025364 55.946789 --3.018030 55.945909 --3.012456 55.944149 --3.006002 55.942682 --3.001015 55.943269 --2.995735 55.945029 --2.991335 55.947083 --2.988401 55.950016 --2.984588 55.952363 --2.979894 55.954417 --2.975200 55.956470 --2.971680 55.958817 --2.966986 55.961164 --2.963466 55.963511 --2.959359 55.966151 --2.954959 55.967911 --2.948798 55.969084 --2.941758 55.968791 --2.933544 55.968498 --2.925330 55.967911 --2.917996 55.967911 --2.911249 55.968204 --2.905382 55.969378 --2.900395 55.970844 --2.895701 55.973191 --2.891888 55.975538 --2.888074 55.978178 --2.884260 55.980525 --2.881033 55.983752 --2.879567 55.987566 --2.878393 55.992259 --2.878393 55.996366 --2.879273 55.999886 --2.877807 56.004287 --2.874580 56.006927 --2.869299 56.008687 --2.861965 56.008687 --2.854338 56.008687 --2.851991 56.011914 --2.853752 56.015141 --2.856392 56.018368 --2.858152 56.021595 --2.859032 56.025408 --2.858152 56.030102 --2.853752 56.031862 --2.847884 56.033036 --2.841137 56.033329 --2.834097 56.033916 --2.831457 56.036849 --2.830283 56.041249 --2.829990 56.045650 --2.827350 56.047703 --2.821483 56.048583 --2.814735 56.049170 --2.810922 56.051810 --2.809162 56.055917 --2.806521 56.059144 --2.801534 56.060904 --2.793907 56.060904 --2.789214 56.061491 --2.782173 56.062078 --2.774252 56.061491 --2.768972 56.059437 --2.763105 56.057677 --2.754891 56.057091 --2.746971 56.056797 --2.740810 56.057677 --2.735823 56.059144 --2.730543 56.060904 --2.724382 56.061784 --2.717048 56.061784 --2.711768 56.060024 --2.705314 56.058557 --2.698274 56.057677 --2.690060 56.057091 --2.682433 56.057091 --2.676272 56.057971 --2.670698 56.059144 --2.664538 56.060024 --2.657204 56.060024 --2.649870 56.059144 --2.643710 56.057677 --2.637256 56.056504 --2.631096 56.055037 --2.625815 56.053277 --2.619948 56.051810 --2.615841 56.049463 --2.611147 56.047117 --2.605867 56.045650 --2.600293 56.043890 --2.597066 56.041249 --2.594133 56.038316 --2.591786 56.035382 --2.589733 56.031862 --2.587092 56.029222 --2.584452 56.025995 --2.579759 56.023942 --2.574478 56.022181 --2.571251 56.019835 --2.570078 56.015728 --2.571545 56.011914 --2.575065 56.008980 --2.577998 56.005754 --2.580345 56.002527 --2.580052 56.000473 --2.579465 55.999886 --2.577412 55.998126 --2.572718 55.995780 --2.568024 55.994606 --2.563331 55.994313 --2.560104 55.997246 --2.556877 56.000180 --2.552477 56.002233 --2.547196 56.000473 --2.542503 55.998420 --2.537222 55.996660 --2.529595 55.996660 --2.525781 55.999300 --2.521381 56.001060 --2.516101 56.002820 --2.509940 56.003700 --2.502020 56.003113 --2.497326 56.001940 --2.492926 55.999593 --2.489112 55.997246 --2.485885 55.994313 --2.479431 55.993433 --2.472684 55.992846 --2.466524 55.991379 --2.461243 55.989619 --2.457723 55.987272 --2.454203 55.984632 --2.448629 55.982872 --2.440415 55.982285 --2.433375 55.981405 --2.428974 55.979058 --2.423694 55.977592 --2.419294 55.975245 --2.415480 55.972898 --2.411080 55.970551 --2.406386 55.968204 --2.401106 55.966737 --2.394652 55.965271 --2.388491 55.963804 --2.384091 55.962044 --2.379691 55.959697 --2.375291 55.957643 --2.371770 55.955003 --2.367957 55.952363 --2.364436 55.949723 --2.360036 55.947669 --2.356516 55.945323 --2.351822 55.942976 --2.346542 55.941216 --2.340381 55.940042 --2.334221 55.938575 --2.328647 55.936522 --2.324247 55.934762 --2.320727 55.931828 --2.316033 55.930068 --2.309872 55.928601 --2.301659 55.928015 --2.294618 55.926841 --2.288458 55.925668 --2.283177 55.923908 --2.277017 55.922441 --2.270563 55.920974 --2.265576 55.920974 --2.260296 55.919214 --2.252082 55.918627 --2.245335 55.918921 --2.242401 55.921854 --2.238587 55.924494 --2.232427 55.925668 --2.225093 55.925374 --2.219519 55.924494 --2.212185 55.924494 --2.204265 55.923908 --2.198691 55.922148 --2.193411 55.920387 --2.186957 55.918921 --2.180503 55.917747 --2.174343 55.916280 --2.169062 55.914520 --2.163782 55.912760 --2.156448 55.911587 --2.149408 55.910707 --2.141194 55.910413 --2.133860 55.910413 --2.129460 55.908067 --2.126526 55.905133 --2.126819 55.900733 --2.128579 55.896919 --2.131220 55.893399 --2.132686 55.889585 --2.130046 55.886358 --2.125939 55.884305 --2.120366 55.882545 --2.115085 55.880785 --2.111565 55.878144 --2.107751 55.875504 --2.102471 55.873744 --2.095430 55.872864 --2.089270 55.871397 --2.083696 55.869637 --2.079589 55.867584 --2.075776 55.864943 --2.074309 55.861717 --2.072549 55.858196 --2.072549 55.854089 --2.069615 55.851156 --2.068148 55.847636 --2.064628 55.845289 --2.061988 55.842355 --2.060815 55.840302 --2.057588 55.837662 --2.053774 55.835315 --2.049374 55.832968 --2.047027 55.830328 --2.043213 55.827394 --2.039693 55.825047 --2.037346 55.821820 --2.033533 55.819474 --2.030012 55.816833 --2.027372 55.813900 --2.025025 55.810966 --2.022092 55.808033 --2.020625 55.804806 --2.017985 55.801579 --2.015345 55.798939 --2.013585 55.795418 --2.011238 55.792485 --2.008598 55.789551 --2.005957 55.786618 --2.003024 55.783684 --2.000970 55.780457 --1.996863 55.778111 --1.994810 55.775177 --1.990703 55.772537 --1.988356 55.769603 --1.985716 55.766670 --1.984249 55.763443 --1.981316 55.760216 --1.979849 55.756989 --1.976329 55.754349 --1.972808 55.752002 --1.968408 55.749655 --1.964008 55.747602 --1.958727 55.745842 --1.954034 55.743495 --1.949633 55.741441 --1.946406 55.738801 --1.942593 55.736454 --1.939073 55.733814 --1.936726 55.730881 --1.934086 55.727654 --1.931445 55.725013 --1.928805 55.722080 --1.925285 55.719440 --1.922645 55.716506 --1.918244 55.714159 --1.914724 55.711812 --1.910324 55.709466 --1.906217 55.707119 --1.900643 55.705652 --1.896243 55.703305 --1.891842 55.701252 --1.887442 55.699198 --1.884215 55.696265 --1.880402 55.693918 --1.876881 55.691278 --1.875415 55.688051 --1.872481 55.685117 --1.870134 55.682184 --1.867494 55.679250 --1.864854 55.676023 --1.862214 55.673383 --1.860454 55.669863 --1.857813 55.666929 --1.856347 55.663702 --1.854000 55.660475 --1.851066 55.657542 --1.847839 55.654902 --1.843439 55.652848 --1.839625 55.650208 --1.836398 55.647861 --1.831705 55.645514 --1.828478 55.643168 --1.824958 55.640527 --1.822317 55.637594 --1.819677 55.634367 --1.815570 55.632607 --1.808236 55.631433 --1.801489 55.632020 --1.797676 55.634367 --1.794742 55.637300 --1.792689 55.641407 --1.791809 55.645808 --1.790929 55.650208 --1.787115 55.651968 --1.782421 55.650795 --1.779194 55.648155 --1.775381 55.645514 --1.773034 55.642581 --1.770394 55.639647 --1.766873 55.637300 --1.764233 55.634074 --1.760713 55.631727 --1.756313 55.629380 --1.751032 55.627620 --1.746632 55.625273 --1.744872 55.622046 --1.748979 55.619406 --1.755139 55.618526 --1.760713 55.617646 --1.765993 55.616179 --1.768340 55.612659 --1.766873 55.609432 --1.763060 55.607085 --1.758073 55.605031 --1.750739 55.605031 --1.746925 55.607378 --1.743112 55.610019 --1.739885 55.612072 --1.734311 55.612952 --1.727564 55.613245 --1.719350 55.612659 --1.713190 55.611485 --1.707909 55.609725 --1.701455 55.609138 --1.695295 55.607672 --1.690015 55.605912 --1.685614 55.603858 --1.682094 55.601218 --1.678280 55.598578 --1.674467 55.596524 --1.670067 55.594177 --1.664493 55.592417 --1.659212 55.590657 --1.654225 55.588897 --1.648652 55.587137 --1.643371 55.585377 --1.638091 55.583617 --1.633984 55.581270 --1.631930 55.578043 --1.634571 55.574523 --1.637798 55.571296 --1.639558 55.567482 --1.637798 55.564255 --1.634277 55.561615 --1.629877 55.559562 --1.626357 55.556921 --1.623130 55.554281 --1.620196 55.551348 --1.620490 55.547241 --1.624010 55.544307 --1.626943 55.541080 --1.629877 55.538147 --1.633104 55.535213 --1.631637 55.531693 --1.624303 55.530813 --1.618143 55.529346 --1.614623 55.526999 --1.610222 55.524652 --1.607875 55.521719 --1.604062 55.519079 --1.605529 55.514678 --1.607289 55.510571 --1.608169 55.507051 --1.608169 55.502651 --1.606409 55.499424 --1.603768 55.496490 --1.600542 55.493850 --1.596141 55.491797 --1.591741 55.489450 --1.585580 55.487983 --1.581474 55.485930 --1.580593 55.482116 --1.580593 55.478009 --1.581767 55.473609 --1.582060 55.469502 --1.582940 55.464808 --1.583234 55.460701 --1.582647 55.456888 --1.581767 55.453367 --1.581767 55.449260 --1.582940 55.444567 --1.582940 55.440166 --1.581767 55.436939 --1.579713 55.433713 --1.577953 55.430192 --1.575606 55.427259 --1.573846 55.424032 --1.573260 55.420218 --1.574140 55.415818 --1.575606 55.411124 --1.577367 55.407311 --1.579713 55.403497 --1.582060 55.399977 --1.585287 55.397337 --1.589101 55.394696 --1.592914 55.392350 --1.596141 55.389123 --1.599075 55.386189 --1.598195 55.382375 --1.597315 55.380615 --1.594674 55.377388 --1.592328 55.374748 --1.590568 55.371228 --1.587634 55.368294 --1.586461 55.365068 --1.584700 55.361547 --1.582940 55.358027 --1.581767 55.354800 --1.580887 55.350987 --1.580887 55.346880 --1.579420 55.343653 --1.578247 55.339839 --1.574140 55.337786 --1.567099 55.336612 --1.561525 55.334852 --1.558299 55.332212 --1.555952 55.329572 --1.552138 55.326638 --1.549791 55.323998 --1.547444 55.320771 --1.547444 55.316664 --1.549498 55.312557 --1.551551 55.309037 --1.555072 55.306103 --1.557418 55.302876 --1.559765 55.299063 --1.562112 55.295543 --1.563872 55.291729 --1.565632 55.287622 --1.567393 55.283515 --1.568566 55.278821 --1.567686 55.275301 --1.566806 55.272368 --1.565339 55.269141 --1.563579 55.265914 --1.561232 55.262687 --1.559472 55.259460 --1.557712 55.256233 --1.555365 55.253006 --1.552725 55.250073 --1.549498 55.247432 --1.545978 55.245086 --1.542457 55.242445 --1.538057 55.240392 --1.534830 55.237458 --1.531310 55.235112 --1.528670 55.232178 --1.526030 55.229245 --1.523683 55.226018 --1.524856 55.221617 --1.526323 55.217510 --1.528963 55.214283 --1.530723 55.209883 --1.528083 55.207243 --1.524856 55.204309 --1.521043 55.201963 --1.516936 55.199616 --1.513415 55.197269 --1.509895 55.194629 --1.507548 55.191695 --1.505788 55.188468 --1.506081 55.184068 --1.508722 55.180548 --1.511655 55.177321 --1.514882 55.174094 --1.518109 55.171160 --1.521043 55.168227 --1.520456 55.164413 --1.518989 55.161186 --1.518109 55.157373 --1.516642 55.153559 --1.514882 55.150332 --1.512535 55.147105 --1.509308 55.144758 --1.505495 55.141825 --1.502268 55.139478 --1.498748 55.136838 --1.496987 55.133611 --1.496401 55.129797 --1.494641 55.126277 --1.493761 55.122757 --1.492587 55.119530 --1.491707 55.115423 --1.489947 55.112196 --1.489067 55.108676 --1.487600 55.104862 --1.487013 55.101342 --1.486427 55.097528 --1.485547 55.094008 --1.484960 55.089901 --1.482613 55.086674 --1.480853 55.083447 --1.477333 55.080807 --1.472639 55.078754 --1.466772 55.077287 --1.459731 55.076994 --1.453278 55.076700 --1.450637 55.073473 --1.451811 55.069073 --1.452691 55.064379 --1.453864 55.060859 --1.454158 55.056752 --1.453278 55.052939 --1.450637 55.050005 --1.448291 55.047071 --1.445357 55.045898 --1.446237 55.046191 --1.445357 55.045898 --1.442424 55.043845 --1.439197 55.041498 --1.435970 55.038564 --1.432449 55.036217 --1.429809 55.032990 --1.428343 55.029764 --1.426289 55.026243 --1.425702 55.022723 --1.425116 55.018909 --1.423649 55.015683 --1.422769 55.011869 --1.420422 55.008935 --1.418662 55.005415 --1.415142 55.002775 --1.412795 55.000135 --1.409568 54.997495 --1.405168 54.994854 --1.401941 54.992214 --1.398420 54.989574 --1.394900 54.986934 --1.391673 54.984587 --1.388153 54.981947 --1.384633 54.979307 --1.381406 54.976666 --1.377006 54.974320 --1.373485 54.971973 --1.369085 54.969626 --1.364978 54.967572 --1.360578 54.965226 --1.357937 54.962585 --1.356764 54.958478 --1.357057 54.954371 --1.357644 54.949971 --1.359111 54.945277 --1.360871 54.941464 --1.362044 54.936770 --1.362925 54.932077 --1.364685 54.928263 --1.364978 54.924156 --1.363218 54.920929 --1.362044 54.917409 --1.359111 54.914475 --1.355884 54.911835 --1.352364 54.909195 --1.352070 54.905675 --1.352657 54.900688 --1.353831 54.896287 --1.353831 54.892180 --1.352364 54.888953 --1.352070 54.885140 --1.350017 54.881620 --1.348550 54.878393 --1.347083 54.874872 --1.345617 54.871646 --1.342683 54.869005 --1.340336 54.865778 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54.718221 --1.229742 54.716461 --1.225341 54.714114 --1.220354 54.712354 --1.215074 54.710594 --1.208913 54.709127 --1.203926 54.707367 --1.197766 54.706194 --1.192486 54.704140 --1.186325 54.702673 --1.181338 54.701207 --1.175471 54.699446 --1.171071 54.697100 --1.168724 54.694459 --1.172538 54.691819 --1.177818 54.690646 --1.183392 54.689766 --1.189259 54.688592 --1.192486 54.685659 --1.190139 54.682725 --1.188379 54.679498 --1.186619 54.675978 --1.186032 54.672165 --1.185152 54.668644 --1.183978 54.665124 --1.183098 54.661310 --1.181338 54.658084 --1.178991 54.654857 --1.174004 54.653390 --1.166084 54.652510 --1.160803 54.650750 --1.162270 54.647816 --1.166964 54.645763 --1.169311 54.642242 --1.169604 54.638135 --1.172244 54.634322 --1.176351 54.632562 --1.181631 54.631095 --1.186032 54.629041 --1.190432 54.627281 --1.193659 54.624348 --1.195419 54.620241 --1.195419 54.616134 --1.195126 54.612614 --1.193366 54.609093 --1.191899 54.605573 --1.188672 54.602933 --1.185738 54.601173 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54.590612 --0.985377 54.588559 --0.980390 54.586798 --0.975110 54.585038 --0.968069 54.584158 --0.960736 54.583865 --0.954869 54.584158 --0.948121 54.584745 --0.941374 54.585038 --0.934920 54.585625 --0.927293 54.584745 --0.921133 54.583278 --0.916146 54.581811 --0.910865 54.579758 --0.906758 54.577411 --0.902358 54.575358 --0.897078 54.573597 --0.890331 54.572424 --0.883583 54.571251 --0.875956 54.570957 --0.869209 54.571251 --0.862755 54.571251 --0.856008 54.571837 --0.849261 54.571544 --0.842220 54.570957 --0.837233 54.568904 --0.831953 54.566850 --0.827553 54.565090 --0.822566 54.563037 --0.817579 54.560983 --0.811418 54.559810 --0.804378 54.558636 --0.797631 54.558636 --0.790297 54.558343 --0.782963 54.558343 --0.777096 54.556876 --0.772989 54.554823 --0.769469 54.551889 --0.766242 54.549542 --0.763601 54.546315 --0.760668 54.543969 --0.756854 54.541328 --0.753041 54.539275 --0.747760 54.537221 --0.741600 54.535755 --0.736613 54.533995 --0.734266 54.531061 --0.729866 54.529008 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54.432787 --0.517477 54.428094 --0.518944 54.423693 --0.519237 54.419586 --0.518357 54.415773 --0.515717 54.412839 --0.511610 54.410492 --0.505743 54.409026 --0.499583 54.407559 --0.493129 54.406385 --0.487848 54.404625 --0.480808 54.403745 --0.477581 54.401105 --0.474354 54.398465 --0.472007 54.395238 --0.468780 54.392891 --0.466433 54.389664 --0.463793 54.387024 --0.461446 54.383797 --0.459980 54.380570 --0.457633 54.377637 --0.454113 54.374997 --0.450886 54.372356 --0.449419 54.368836 --0.447952 54.365609 --0.446485 54.362089 --0.444725 54.358862 --0.441792 54.356222 --0.438271 54.353582 --0.435925 54.350648 --0.434458 54.347128 --0.432698 54.343901 --0.432404 54.340087 --0.428884 54.337447 --0.423897 54.335687 --0.421257 54.332753 --0.420083 54.329233 --0.419497 54.325420 --0.419790 54.321313 --0.418910 54.317499 --0.417443 54.314272 --0.415977 54.310752 --0.414510 54.307525 --0.414803 54.303418 --0.413336 54.299898 --0.411870 54.296671 --0.410403 54.293444 --0.408643 54.289924 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54.174929 --0.259032 54.172289 --0.255512 54.169648 --0.251405 54.167595 --0.247298 54.165248 --0.243191 54.163195 --0.237910 54.161141 --0.232337 54.159674 --0.226470 54.157914 --0.220603 54.156447 --0.213562 54.155274 --0.207402 54.153807 --0.201534 54.152341 --0.194787 54.151167 --0.188920 54.149700 --0.183053 54.148234 --0.176893 54.147060 --0.170146 54.145887 --0.164572 54.144127 --0.158411 54.142660 --0.151664 54.141780 --0.145504 54.140313 --0.140517 54.138260 --0.134356 54.137086 --0.128489 54.135619 --0.122915 54.133859 --0.116755 54.132392 --0.112061 54.130926 --0.106781 54.128872 --0.101794 54.126819 --0.096807 54.125059 --0.092407 54.122712 --0.087420 54.121245 --0.082433 54.119191 --0.078326 54.116845 --0.075979 54.113911 --0.075685 54.113031 -nan nan --0.074805 54.112444 --0.077739 54.109511 --0.080966 54.106577 --0.086246 54.105404 --0.091527 54.103937 --0.096514 54.102470 --0.102087 54.101590 --0.107368 54.100417 --0.112355 54.098950 --0.117928 54.098070 --0.124382 54.097483 --0.130249 54.096603 --0.136116 54.095723 --0.141103 54.094550 --0.146090 54.093083 --0.150491 54.091029 --0.155771 54.089856 --0.160758 54.088389 --0.165159 54.086336 --0.170146 54.084576 --0.173666 54.082229 --0.176893 54.078709 --0.179533 54.075188 --0.182466 54.072255 --0.185107 54.069028 --0.188627 54.066388 --0.191854 54.063454 --0.196254 54.060521 --0.198894 54.057587 --0.202708 54.055240 --0.205348 54.051720 --0.208575 54.048493 --0.209748 54.044093 --0.211802 54.040279 --0.213269 54.036172 --0.214735 54.031772 --0.215909 54.027078 --0.216202 54.022971 --0.215615 54.019158 --0.214735 54.015637 --0.213269 54.012117 --0.211802 54.008890 --0.209455 54.005957 --0.207988 54.002436 --0.206521 53.998916 --0.205055 53.995689 --0.203588 53.992169 --0.202121 53.988942 --0.199774 53.985715 --0.198308 53.982488 --0.196254 53.979555 --0.193614 53.976328 --0.192147 53.973101 --0.190094 53.970167 --0.188334 53.966647 --0.185987 53.964007 --0.184520 53.960193 --0.183053 53.956967 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50.835969 --0.965136 50.833036 --0.961909 50.830689 --0.957215 50.828635 --0.951642 50.827169 --0.947828 50.825115 --0.944308 50.822768 --0.943428 50.819248 --0.945481 50.815434 --0.949295 50.813088 --0.951935 50.810154 --0.954282 50.806634 --0.954575 50.802527 --0.952815 50.799300 --0.953108 50.794900 --0.954869 50.791086 --0.954869 50.786979 --0.952815 50.783752 --0.950468 50.781112 --0.949882 50.777298 --0.953402 50.774658 --0.959562 50.774365 --0.965723 50.774365 --0.973057 50.775245 --0.979510 50.776125 --0.985964 50.777298 --0.991244 50.778472 --0.997698 50.778765 --1.001805 50.777005 --1.004739 50.773778 --1.008846 50.772018 --1.014126 50.771138 --1.017940 50.773191 --1.020287 50.776125 --1.020873 50.779938 --1.018526 50.783752 --1.015593 50.786392 --1.012366 50.789032 --1.008259 50.790793 --1.004152 50.792846 --1.000045 50.794606 --0.995938 50.796660 --0.992418 50.799300 --0.990364 50.802527 --0.988604 50.806634 --0.988311 50.810741 --0.989778 50.814261 --0.988898 50.817781 --0.986844 50.821008 --0.984497 50.824822 --0.982737 50.828635 --0.982737 50.832742 --0.984204 50.835969 --0.986844 50.838903 --0.991538 50.840663 --0.997992 50.841543 --1.005325 50.842130 --1.012366 50.842716 --1.017646 50.841836 --1.022633 50.840663 --1.025860 50.838023 --1.028794 50.835382 --1.031141 50.831569 --1.032314 50.827169 --1.033488 50.823062 --1.033781 50.818955 --1.035541 50.815141 --1.037301 50.811034 --1.038475 50.806340 --1.037594 50.802820 --1.037008 50.799006 --1.037008 50.795780 --1.039355 50.792259 --1.042875 50.789619 --1.047569 50.788446 --1.051969 50.786979 --1.056956 50.785512 --1.061356 50.784045 --1.065463 50.782285 --1.069863 50.780232 --1.075144 50.779352 --1.079838 50.777885 --1.085998 50.778178 --1.092452 50.779058 --1.097145 50.780819 --1.100372 50.783459 --1.103599 50.786099 --1.105946 50.789032 --1.106239 50.792846 --1.106239 50.796953 --1.104479 50.800767 --1.101252 50.803407 --1.095972 50.804580 --1.092158 50.806634 --1.089518 50.809861 --1.087758 50.813674 --1.090105 50.816608 --1.092158 50.819835 --1.091865 50.823942 --1.090105 50.826288 --1.083651 50.825995 --1.078077 50.827169 --1.073970 50.829222 --1.070450 50.831275 --1.068397 50.835089 --1.069863 50.838316 --1.072797 50.840956 --1.076611 50.843010 --1.080424 50.845356 --1.085998 50.846530 --1.091572 50.847117 --1.097145 50.846530 --1.101839 50.845063 --1.106533 50.843596 --1.110640 50.841543 --1.115920 50.840663 --1.122081 50.840369 --1.129121 50.840956 --1.136162 50.841543 --1.142029 50.843010 --1.148189 50.843890 --1.154350 50.845063 --1.159923 50.844183 --1.163444 50.841543 --1.163444 50.838316 --1.160803 50.835676 --1.155523 50.834209 --1.148189 50.833329 --1.142909 50.831862 --1.141442 50.828635 --1.139095 50.825702 --1.136162 50.823062 --1.132055 50.820715 --1.127948 50.818661 --1.124134 50.816314 --1.120320 50.814554 --1.117974 50.811327 --1.117680 50.807514 --1.117680 50.803407 --1.120027 50.799887 --1.122667 50.796953 --1.124427 50.793139 --1.125601 50.788446 --1.126481 50.783752 --1.129414 50.781112 --1.134108 50.779352 --1.139388 50.778472 --1.145256 50.778472 --1.151123 50.778765 --1.157576 50.779645 --1.163737 50.780819 --1.168431 50.782579 --1.174004 50.783752 --1.178698 50.785806 --1.182512 50.788152 --1.186325 50.790206 --1.190139 50.792553 --1.194246 50.794606 --1.197179 50.797246 --1.199819 50.799300 --1.202753 50.801647 --1.205980 50.804580 --1.208913 50.806927 --1.211847 50.809567 --1.215954 50.811621 --1.219768 50.813968 --1.223581 50.816021 --1.228275 50.818075 --1.232969 50.819835 --1.237662 50.821301 --1.242356 50.823355 --1.247343 50.825115 --1.252917 50.826288 --1.258197 50.828049 --1.263771 50.829515 --1.269051 50.830689 --1.275505 50.831569 --1.281372 50.833036 --1.285772 50.835089 --1.290759 50.836556 --1.294866 50.838903 --1.298680 50.841250 --1.302493 50.843303 --1.306307 50.845650 --1.309534 50.847997 --1.313348 50.850344 --1.316281 50.852690 --1.320388 50.855037 --1.324202 50.857091 --1.328015 50.859437 --1.331242 50.862078 --1.335056 50.864131 --1.338869 50.866478 --1.342683 50.868531 --1.346790 50.870878 --1.350604 50.872638 --1.354417 50.874985 --1.357644 50.877919 --1.361751 50.879679 --1.366151 50.881732 --1.370258 50.883786 --1.373779 50.886133 --1.378766 50.887893 --1.385219 50.888773 --1.391967 50.888773 --1.396367 50.890826 --1.399594 50.893467 --1.403701 50.895520 --1.406341 50.898160 --1.410155 50.900214 --1.414555 50.902561 --1.418368 50.904614 --1.423062 50.906374 --1.428636 50.907841 --1.434210 50.909308 --1.439783 50.910481 --1.445357 50.911948 --1.450637 50.913415 --1.456505 50.914588 --1.463545 50.915468 --1.468825 50.914295 --1.472639 50.911655 --1.472639 50.908428 --1.469119 50.905787 --1.465012 50.904321 --1.459731 50.903147 --1.454744 50.901387 --1.449171 50.899920 --1.443890 50.898747 --1.438317 50.897280 --1.433623 50.895227 --1.428049 50.893760 --1.422475 50.892587 --1.416902 50.891120 --1.412208 50.889360 --1.407514 50.887600 --1.404287 50.884959 --1.401061 50.882612 --1.399887 50.879092 --1.396660 50.876452 --1.394313 50.873519 --1.392260 50.870585 --1.388153 50.868238 --1.383753 50.866771 --1.378472 50.864718 --1.374952 50.862371 --1.369378 50.861198 --1.364391 50.859437 --1.359991 50.857384 --1.355297 50.855917 --1.351484 50.853570 --1.347377 50.851517 --1.343563 50.849170 --1.340336 50.846530 --1.337403 50.844183 --1.334176 50.841250 --1.331242 50.838903 --1.328895 50.835969 --1.326549 50.833036 --1.324202 50.830102 --1.322735 50.826582 --1.320681 50.823648 --1.317455 50.821008 --1.310414 50.820421 --1.306307 50.818368 --1.307481 50.813968 --1.309534 50.810154 --1.311587 50.806927 --1.315694 50.804580 --1.318921 50.801940 --1.322148 50.799300 --1.325375 50.796366 --1.328602 50.794019 --1.331536 50.791086 --1.334176 50.788152 --1.338283 50.786099 --1.341803 50.783752 --1.345910 50.781699 --1.349724 50.779645 --1.355297 50.778765 --1.360578 50.777885 --1.365858 50.777005 --1.370552 50.775538 --1.375832 50.774365 --1.381112 50.773485 --1.386980 50.773191 --1.393140 50.772898 --1.399007 50.772605 --1.405461 50.772605 --1.411328 50.772311 --1.417195 50.771725 --1.422475 50.770844 --1.428343 50.770258 --1.433916 50.769378 --1.439197 50.768498 --1.444477 50.767618 --1.448877 50.766151 --1.454451 50.765271 --1.458851 50.763804 --1.463545 50.762631 --1.467652 50.760577 --1.472052 50.758230 --1.476746 50.757057 --1.480853 50.755003 --1.484667 50.752950 --1.488774 50.751190 --1.493467 50.749723 --1.497574 50.747669 --1.502268 50.746496 --1.506081 50.744443 --1.510188 50.742389 --1.514589 50.740629 --1.517816 50.737989 --1.521923 50.736229 --1.525149 50.733588 --1.528963 50.731242 --1.532190 50.728601 --1.536004 50.726548 --1.539817 50.724201 --1.541577 50.720974 --1.543924 50.717161 --1.546271 50.713640 --1.549791 50.711000 --1.555072 50.710413 --1.561525 50.711294 --1.566219 50.713054 --1.570033 50.715400 --1.573846 50.717454 --1.577660 50.719801 --1.581767 50.721561 --1.587341 50.723028 --1.592914 50.724788 --1.597608 50.726255 --1.600248 50.726548 --1.606702 50.727428 --1.612276 50.728895 --1.618730 50.730068 --1.624010 50.731535 --1.629584 50.732708 --1.636037 50.733882 --1.643078 50.734469 --1.649532 50.735349 --1.655692 50.736522 --1.662146 50.737402 --1.668306 50.738282 --1.675640 50.738869 --1.682387 50.739749 --1.689135 50.739749 --1.694415 50.738575 --1.700575 50.738282 --1.704976 50.736815 --1.709669 50.735642 --1.714656 50.733882 --1.719057 50.732415 --1.723750 50.731242 --1.728737 50.729775 --1.734018 50.728601 --1.738711 50.727135 --1.743699 50.726255 --1.749859 50.725961 --1.756313 50.725961 --1.756899 50.723321 --1.753086 50.720974 --1.746632 50.720094 --1.739298 50.719507 --1.732844 50.718627 --1.729911 50.715694 --1.731378 50.711880 --1.736071 50.710413 --1.740765 50.708947 --1.747219 50.709240 --1.754553 50.709827 --1.761006 50.710413 --1.767167 50.711587 --1.773327 50.712760 --1.779781 50.713640 --1.785061 50.714520 --1.790342 50.715694 --1.795916 50.717161 --1.802076 50.718334 --1.808823 50.718334 --1.815277 50.718334 --1.820557 50.717454 --1.825838 50.716574 --1.831705 50.715987 --1.837279 50.715400 --1.841679 50.713640 --1.846959 50.712760 --1.852240 50.711880 --1.857520 50.710707 --1.862800 50.710120 --1.868667 50.709533 --1.873948 50.708653 --1.878642 50.707187 --1.883335 50.705426 --1.888029 50.704253 --1.891256 50.701613 --1.895656 50.699853 --1.898883 50.697213 --1.902697 50.695159 --1.906510 50.692812 --1.909737 50.690172 --1.913844 50.688412 --1.916484 50.685185 --1.920004 50.682838 --1.923231 50.680198 --1.927632 50.678438 --1.932912 50.677558 --1.938192 50.679025 --1.940539 50.681958 --1.940539 50.685772 --1.939366 50.690465 --1.939366 50.694866 --1.939366 50.698679 --1.940833 50.702200 --1.943179 50.705133 --1.945233 50.708067 --1.948753 50.710413 --1.954034 50.711880 --1.960487 50.712760 --1.966354 50.712467 --1.972222 50.711880 --1.977502 50.711000 --1.982782 50.710120 --1.988063 50.709240 --1.992756 50.707773 --1.998037 50.706600 --2.003904 50.706307 --2.009771 50.705720 --2.015051 50.705133 --2.022092 50.705426 --2.027666 50.706893 --2.031186 50.709533 --2.033826 50.711880 --2.038813 50.713934 --2.045267 50.713934 --2.049960 50.712467 --2.054654 50.710707 --2.058468 50.708947 --2.061988 50.706307 --2.063748 50.702493 --2.064335 50.697799 --2.066682 50.694572 --2.069909 50.691932 --2.072842 50.688999 --2.076069 50.686358 --2.079589 50.684012 --2.079589 50.679611 --2.074896 50.678144 --2.071375 50.678438 --2.067562 50.680198 --2.063455 50.682251 --2.059641 50.684598 --2.055828 50.686652 --2.051721 50.688705 --2.048200 50.691052 --2.043507 50.693106 --2.039400 50.694866 --2.034999 50.696332 --2.029132 50.696919 --2.024439 50.694866 --2.023559 50.691345 --2.024732 50.686945 --2.027079 50.684012 --2.029132 50.679611 --2.028839 50.676678 --2.025612 50.674038 --2.020332 50.672864 --2.012998 50.672277 --2.008304 50.673744 --2.004491 50.675504 --2.000970 50.678144 --1.997450 50.680491 --1.993343 50.682545 --1.988063 50.681078 --1.984249 50.679025 --1.980142 50.676678 --1.974862 50.675211 --1.967528 50.674624 --1.961074 50.673744 --1.954620 50.672864 --1.948753 50.671984 --1.941419 50.671397 --1.934966 50.670224 --1.930272 50.668757 --1.927925 50.665530 --1.930565 50.662597 --1.934086 50.659957 --1.938192 50.658196 --1.941713 50.655556 --1.943766 50.652329 --1.942299 50.648809 --1.938192 50.646756 --1.932325 50.645582 --1.925872 50.644702 --1.920298 50.643235 --1.914431 50.642062 --1.910617 50.639715 --1.908270 50.637075 --1.908270 50.632675 --1.912084 50.630328 --1.916484 50.628568 --1.921178 50.627101 --1.926458 50.626514 --1.931152 50.625047 --1.935846 50.623287 --1.938486 50.620354 --1.941419 50.617420 --1.940539 50.613607 --1.938486 50.610966 --1.937019 50.607446 --1.937019 50.603339 --1.940539 50.600699 --1.943179 50.597765 --1.945526 50.593952 --1.948460 50.590725 --1.951687 50.588378 --1.956380 50.586911 --1.962248 50.586325 --1.969581 50.586911 --1.975448 50.588085 --1.982782 50.588671 --1.990116 50.589258 --1.996863 50.589845 --2.003610 50.589845 --2.009478 50.589551 --2.015345 50.588965 --2.020918 50.588085 --2.025905 50.586911 --2.030599 50.585444 --2.035293 50.584271 --2.038520 50.581631 --2.042920 50.579577 --2.047614 50.578111 --2.052601 50.577231 --2.057294 50.578991 --2.059348 50.581924 --2.061988 50.584858 --2.064922 50.587498 --2.068148 50.590138 --2.071962 50.592192 --2.077536 50.593658 --2.083696 50.594538 --2.091030 50.595125 --2.097484 50.595125 --2.103938 50.596005 --2.108631 50.597765 --2.111565 50.600699 --2.115965 50.602459 --2.120366 50.604513 --2.126526 50.605393 --2.133860 50.605979 --2.140900 50.606273 --2.147354 50.606566 --2.152928 50.607739 --2.157035 50.610086 --2.161729 50.611846 --2.167302 50.612140 --2.172583 50.611260 --2.179036 50.611260 --2.183143 50.613607 --2.186957 50.615660 --2.192531 50.616833 --2.198985 50.618007 --2.204852 50.617420 --2.208665 50.615660 --2.214239 50.614780 --2.220106 50.614193 --2.226266 50.614193 --2.233600 50.614780 --2.240054 50.615953 --2.246801 50.616247 --2.253255 50.617127 --2.259709 50.618300 --2.267043 50.618887 --2.273790 50.619474 --2.281417 50.620060 --2.288458 50.620647 --2.295205 50.621234 --2.301952 50.621234 --2.309286 50.621527 --2.316033 50.622114 --2.321607 50.623581 --2.328060 50.624461 --2.332754 50.626514 --2.338328 50.627688 --2.345662 50.628274 --2.351529 50.627688 --2.356809 50.626807 --2.363263 50.626807 --2.368543 50.628274 --2.374117 50.629448 --2.380571 50.630621 --2.387025 50.631501 --2.394065 50.632088 --2.398466 50.630621 --2.403453 50.629154 --2.409906 50.629154 --2.415773 50.628568 --2.421640 50.628274 --2.426921 50.626807 --2.431615 50.625341 --2.435135 50.622701 --2.438655 50.620354 --2.440415 50.616540 --2.441295 50.612140 --2.441589 50.608033 --2.440415 50.604513 --2.440709 50.600406 --2.444522 50.597765 --2.447456 50.595419 --2.450976 50.592778 --2.454496 50.590138 --2.457723 50.587791 --2.460070 50.584271 --2.460070 50.579871 --2.457723 50.577231 --2.455376 50.574297 --2.451269 50.571950 --2.447456 50.569897 --2.441882 50.568723 --2.435135 50.568723 --2.429268 50.567550 --2.426041 50.564910 --2.423694 50.562269 --2.421347 50.559043 --2.419000 50.556109 --2.417534 50.552882 --2.414893 50.549949 --2.414307 50.546135 --2.414307 50.542028 --2.416360 50.538508 --2.420467 50.536748 --2.424574 50.534401 --2.428094 50.532347 --2.431321 50.529707 --2.434255 50.526774 --2.436602 50.523547 --2.438948 50.520026 --2.441589 50.516800 --2.443935 50.513573 --2.445696 50.510052 --2.448629 50.506826 --2.452149 50.504479 --2.456256 50.502425 -nan nan --2.455376 50.503012 --2.458603 50.503599 --2.460950 50.506532 --2.462710 50.510052 --2.461537 50.514453 --2.460950 50.517973 --2.458897 50.521787 --2.456256 50.524720 --2.453323 50.527360 --2.450096 50.530001 --2.449216 50.534694 --2.450683 50.537921 --2.453029 50.540855 --2.453616 50.544668 --2.452736 50.549069 --2.450683 50.552882 --2.450096 50.557282 --2.452149 50.560216 --2.455376 50.562856 --2.459190 50.564910 --2.464177 50.566670 --2.468871 50.568430 --2.473271 50.569897 --2.476791 50.572830 --2.481191 50.574590 --2.485298 50.576644 --2.488525 50.579284 --2.492632 50.581044 --2.496446 50.583391 --2.499379 50.585738 --2.503193 50.588085 --2.507300 50.590138 --2.511114 50.592192 --2.514927 50.594538 --2.519034 50.596592 --2.524021 50.598352 --2.527835 50.600699 --2.532528 50.602166 --2.536342 50.604513 --2.540156 50.606566 --2.544556 50.608619 --2.548370 50.610966 --2.552183 50.613020 --2.555410 50.615660 --2.559517 50.617713 --2.563917 50.619767 --2.566558 50.621234 --2.570665 50.622994 --2.574478 50.625341 --2.578292 50.627394 --2.581812 50.630034 --2.585626 50.632088 --2.588853 50.634728 --2.592666 50.636782 --2.595893 50.639128 --2.599707 50.641475 --2.603814 50.643529 --2.608214 50.645289 --2.612321 50.647636 --2.617308 50.649102 --2.621121 50.651449 --2.626695 50.652916 --2.631976 50.653796 --2.636963 50.655850 --2.641656 50.657610 --2.647230 50.658783 --2.652217 50.660543 --2.657497 50.662010 --2.663071 50.663477 --2.668645 50.664650 --2.674512 50.665824 --2.678912 50.667877 --2.684486 50.668757 --2.689180 50.670811 --2.694753 50.672277 --2.699740 50.673744 --2.704434 50.675504 --2.709128 50.677264 --2.713821 50.679025 --2.718808 50.680785 --2.723209 50.682545 --2.728196 50.684305 --2.732303 50.686358 --2.736116 50.688705 --2.739930 50.690465 --2.744624 50.692519 --2.749024 50.694572 --2.752838 50.696626 --2.756651 50.698973 --2.760465 50.700733 --2.764865 50.703080 --2.769265 50.704840 --2.773079 50.706893 --2.778946 50.708360 --2.785400 50.709240 --2.792147 50.709827 --2.799481 50.710413 --2.806521 50.710707 --2.812975 50.711587 --2.819429 50.712760 --2.825589 50.713640 --2.832043 50.714520 --2.836150 50.715694 --2.842604 50.716574 --2.849058 50.717454 --2.855218 50.718627 --2.861965 50.719507 --2.867246 50.720974 --2.872820 50.722148 --2.879273 50.723028 --2.885434 50.723908 --2.891888 50.725081 --2.899221 50.725668 --2.905969 50.725668 --2.912129 50.725668 --2.917409 50.724494 --2.922396 50.723321 --2.927090 50.721854 --2.931490 50.720094 --2.935304 50.718041 --2.939118 50.715694 --2.944105 50.714520 --2.948505 50.713054 --2.953199 50.711294 --2.957892 50.710120 --2.962586 50.708360 --2.966986 50.706893 --2.971680 50.705426 --2.975787 50.703373 --2.980481 50.701906 --2.984881 50.700146 --2.989575 50.698973 --2.994268 50.697506 --2.998962 50.695746 --3.004242 50.694866 --3.008936 50.693399 --3.015390 50.693399 --3.021550 50.693399 --3.029177 50.693986 --3.036218 50.694572 --3.042378 50.695159 --3.048832 50.696332 --3.056166 50.696919 --3.062033 50.696332 --3.067900 50.695746 --3.072594 50.694279 --3.077288 50.692812 --3.081688 50.691345 --3.085501 50.689292 --3.089608 50.687238 --3.094009 50.685185 --3.097822 50.683425 --3.102223 50.681665 --3.107503 50.680785 --3.113664 50.680198 --3.120117 50.680198 --3.126864 50.680785 --3.134198 50.681371 --3.141532 50.681665 --3.147986 50.681665 --3.155026 50.682251 --3.162360 50.682838 --3.168521 50.682838 --3.175268 50.682838 --3.181135 50.682251 --3.187882 50.682251 --3.193749 50.681665 --3.199323 50.681371 --3.205190 50.680785 --3.210470 50.679611 --3.215751 50.679025 --3.221618 50.678438 --3.226898 50.677264 --3.232472 50.676091 --3.237459 50.675211 --3.243033 50.674038 --3.247140 50.672864 --3.251833 50.671104 --3.256527 50.669637 --3.260634 50.667877 --3.264741 50.665530 --3.267675 50.663183 --3.271195 50.660543 --3.274715 50.658196 --3.277649 50.655556 --3.280876 50.652623 --3.283222 50.649396 --3.287036 50.646462 --3.289383 50.643529 --3.292316 50.640595 --3.294076 50.637075 --3.297010 50.633848 --3.300237 50.631501 --3.304931 50.630034 --3.308744 50.627688 --3.314025 50.626807 --3.319305 50.625927 --3.323999 50.624167 --3.327812 50.622114 --3.331332 50.619767 --3.334559 50.617127 --3.337786 50.614780 --3.341307 50.612140 --3.344533 50.609793 --3.349227 50.608033 --3.354507 50.607153 --3.359788 50.605979 --3.365068 50.605099 --3.370935 50.604806 --3.377096 50.604513 --3.383843 50.604513 --3.390297 50.604513 --3.396750 50.605686 --3.402324 50.606566 --3.407898 50.608033 --3.412592 50.609793 --3.417285 50.611260 --3.419632 50.614487 --3.419045 50.618007 --3.416992 50.621527 --3.415819 50.625634 --3.415819 50.629741 --3.418459 50.632675 --3.420219 50.635608 --3.424326 50.637662 --3.427846 50.640302 --3.430780 50.642649 --3.433420 50.645582 --3.435473 50.648516 --3.437233 50.652036 --3.439580 50.654676 --3.441047 50.658196 --3.442807 50.661423 --3.445154 50.664357 --3.447794 50.667290 --3.450728 50.669637 --3.454248 50.672277 --3.460702 50.673451 --3.465689 50.672277 --3.468916 50.669637 --3.469796 50.666117 --3.467156 50.663183 --3.464222 50.660543 --3.460702 50.658196 --3.457768 50.655556 --3.455421 50.652623 --3.452194 50.649982 --3.449848 50.647342 --3.447207 50.644115 --3.445447 50.640888 --3.444861 50.637368 --3.444861 50.632968 --3.444861 50.628861 --3.445447 50.624461 --3.446914 50.620354 --3.448674 50.616247 --3.449261 50.611553 --3.449261 50.607739 --3.448381 50.603926 --3.441927 50.603046 --3.437233 50.601286 --3.435473 50.598059 --3.436353 50.594538 --3.438994 50.591312 --3.442220 50.588965 --3.445447 50.586325 --3.448381 50.583391 --3.449848 50.579284 --3.450434 50.574590 --3.451901 50.570483 --3.453955 50.567257 --3.456595 50.564030 --3.460115 50.561683 --3.463049 50.558749 --3.466569 50.556402 --3.469796 50.553762 --3.472436 50.550829 --3.475956 50.548188 --3.479183 50.545842 --3.482410 50.543201 --3.485930 50.540855 --3.488570 50.537921 --3.491797 50.535281 --3.494438 50.532347 --3.497078 50.529120 --3.499718 50.526187 --3.501771 50.522373 --3.503825 50.519146 --3.505878 50.515626 --3.507345 50.511519 --3.508812 50.507412 --3.509399 50.503012 --3.510279 50.498318 --3.509399 50.494798 --3.508519 50.490691 --3.507052 50.487464 --3.505292 50.484237 --3.502945 50.481304 --3.500598 50.478370 --3.498251 50.475437 --3.495904 50.472503 --3.492677 50.469863 --3.489450 50.467516 --3.486810 50.464582 --3.483877 50.462236 --3.482117 50.459009 --3.485637 50.456369 --3.490917 50.455195 --3.497078 50.455195 --3.504412 50.455782 --3.511159 50.455782 --3.517319 50.455782 --3.522893 50.454608 --3.527880 50.453728 --3.533160 50.452848 --3.537561 50.451088 --3.541374 50.449035 --3.544894 50.446688 --3.546948 50.443168 --3.549295 50.439354 --3.549001 50.435247 --3.548121 50.431727 --3.548121 50.427620 --3.547535 50.423806 --3.548121 50.419113 --3.548121 50.415006 --3.546948 50.412365 --3.544601 50.409432 --3.541374 50.407085 --3.535800 50.405618 --3.528760 50.405032 --3.522600 50.404151 --3.518493 50.402098 --3.514972 50.399458 --3.512039 50.396818 --3.507345 50.395351 --3.501185 50.394471 --3.495024 50.395057 --3.489157 50.395644 --3.483583 50.395057 --3.480650 50.392417 --3.480943 50.388897 --3.485050 50.386844 --3.489450 50.385670 --3.493264 50.383323 --3.497078 50.381270 --3.501478 50.379510 --3.504705 50.376870 --3.507345 50.373936 --3.508812 50.369829 --3.509399 50.365135 --3.511452 50.361615 --3.513506 50.358095 --3.514972 50.354281 --3.513212 50.350761 --3.512625 50.346947 --3.512625 50.342840 --3.517906 50.341960 --3.523186 50.340787 --3.526120 50.338440 --3.530227 50.336387 --3.536094 50.335800 --3.541374 50.336973 --3.546361 50.339027 --3.550175 50.340787 --3.554282 50.343134 --3.557509 50.345481 --3.559856 50.348414 --3.563082 50.350761 --3.568656 50.352228 --3.571296 50.349294 --3.572470 50.345187 --3.572470 50.341080 --3.570123 50.338147 --3.567776 50.335213 --3.565429 50.332280 --3.562202 50.329639 --3.559856 50.326999 --3.559269 50.323186 --3.563082 50.321132 --3.568950 50.320545 --3.573937 50.319372 --3.579804 50.318785 --3.585084 50.318199 --3.590364 50.317025 --3.595645 50.315852 --3.600045 50.314385 --3.604445 50.312918 --3.609726 50.312038 --3.613833 50.309691 --3.617646 50.307638 --3.620873 50.305291 --3.624100 50.302651 --3.627620 50.300304 --3.629967 50.297077 --3.632901 50.294144 --3.635541 50.291210 --3.637594 50.287396 --3.639941 50.284463 --3.642288 50.281236 --3.644635 50.278009 --3.646688 50.274489 --3.648742 50.270969 --3.650209 50.266862 --3.651675 50.262755 --3.653729 50.259234 --3.654022 50.254834 --3.654902 50.250140 --3.655782 50.245447 --3.654902 50.241927 --3.654022 50.238113 --3.652556 50.234886 --3.650795 50.231659 --3.648742 50.228726 --3.646102 50.225792 --3.646688 50.222272 --3.651382 50.220512 --3.658423 50.221098 --3.664583 50.221098 --3.671917 50.221392 --3.678371 50.221392 --3.683651 50.220512 --3.688345 50.218752 --3.693332 50.217871 --3.698025 50.216405 --3.702426 50.214645 --3.706533 50.212884 --3.710346 50.210831 --3.714747 50.209071 --3.719440 50.207897 --3.724721 50.206724 --3.730001 50.207897 --3.734108 50.209951 --3.737922 50.212298 --3.742909 50.214058 --3.748189 50.215525 --3.753469 50.216991 --3.758750 50.218752 --3.762563 50.220512 --3.767257 50.222272 --3.771071 50.224325 --3.776058 50.224032 --3.778405 50.220805 --3.779285 50.216111 --3.783098 50.214058 --3.787205 50.212591 --3.793072 50.213764 --3.799526 50.214645 --3.803926 50.216405 --3.809500 50.217871 --3.814194 50.219338 --3.819181 50.221098 --3.823581 50.222858 --3.829448 50.224032 --3.833262 50.226085 --3.836489 50.228726 --3.840596 50.230779 --3.843823 50.233419 --3.845876 50.236059 --3.848223 50.239286 --3.849983 50.242513 --3.850863 50.246033 --3.852623 50.249554 --3.853210 50.253367 --3.854970 50.256301 --3.856730 50.259821 --3.859077 50.262755 --3.863184 50.264808 --3.866998 50.266862 --3.871985 50.268622 --3.875798 50.270969 --3.878145 50.273609 --3.880492 50.276542 --3.884012 50.279183 --3.887826 50.281236 --3.891639 50.283289 --3.897213 50.284463 --3.902787 50.285930 --3.908361 50.286810 --3.913934 50.288276 --3.920388 50.289157 --3.926255 50.290037 --3.932122 50.291503 --3.936523 50.292970 --3.938576 50.296490 --3.938576 50.300597 --3.939163 50.304118 --3.942390 50.306758 --3.948257 50.307051 --3.951484 50.304411 --3.955297 50.302358 --3.959991 50.300891 --3.965858 50.300304 --3.972312 50.300304 --3.979352 50.300891 --3.985513 50.301771 --3.993140 50.302358 --3.999300 50.302064 --4.000000 50.301991 -nan nan --4.000000 51.211229 --3.999007 51.211463 --3.992847 51.212049 --3.986099 51.212049 --3.979352 51.212049 --3.972312 51.211463 --3.965858 51.210583 --3.958524 51.210289 --3.952364 51.210583 --3.947963 51.212343 --3.943270 51.213810 --3.938576 51.215276 --3.934176 51.217036 --3.930069 51.218797 --3.924788 51.219970 --3.918628 51.220557 --3.911587 51.219970 --3.905720 51.218797 --3.900147 51.217623 --3.893986 51.216743 --3.887239 51.216743 --3.881959 51.217917 --3.877265 51.219090 --3.873451 51.220263 --3.868758 51.222024 --3.862891 51.222610 --3.857610 51.223490 --3.852037 51.224370 --3.846169 51.224957 --3.839716 51.224957 --3.832088 51.224664 --3.827395 51.223197 --3.822408 51.221437 --3.817421 51.219383 --3.811260 51.218503 --3.805980 51.219677 --3.801286 51.221437 --3.797473 51.223197 --3.793366 51.225250 --3.789552 51.227597 --3.783978 51.228477 --3.777231 51.228477 --3.771071 51.227597 --3.764324 51.226717 --3.758163 51.225837 --3.751416 51.225837 --3.745256 51.226424 --3.738802 51.226424 --3.733815 51.225544 --3.728241 51.224370 --3.722374 51.223197 --3.715333 51.222610 --3.708000 51.222317 --3.703012 51.220557 --3.699199 51.218210 --3.694505 51.216743 --3.688345 51.217330 --3.681598 51.217330 --3.675731 51.217917 --3.669863 51.218210 --3.663996 51.218797 --3.656369 51.218210 --3.651969 51.216743 --3.646102 51.215276 --3.640235 51.213810 --3.633194 51.213516 --3.626740 51.212636 --3.619993 51.212636 --3.615300 51.211169 --3.610312 51.209116 --3.603272 51.208823 --3.597698 51.209703 --3.591538 51.210289 --3.585377 51.210289 --3.580097 51.211463 --3.576577 51.213810 --3.574523 51.217623 --3.571590 51.220557 --3.568363 51.223197 --3.562496 51.223490 --3.556042 51.222904 --3.550468 51.221437 --3.544014 51.220557 --3.537561 51.219677 --3.531107 51.218503 --3.525240 51.217623 --3.519079 51.216450 --3.511745 51.216156 --3.506172 51.214690 --3.501185 51.212930 --3.495611 51.211756 --3.488277 51.211463 --3.480943 51.210876 --3.475369 51.209409 --3.469796 51.207943 --3.467742 51.206182 --3.465689 51.203249 --3.461288 51.201195 --3.455715 51.200022 --3.450141 51.200315 --3.443100 51.200315 --3.436647 51.199142 --3.434300 51.197382 --3.431660 51.194448 --3.428433 51.191808 --3.424326 51.190048 --3.420219 51.187701 --3.416405 51.185941 --3.413178 51.183301 --3.409951 51.180954 --3.406725 51.178020 --3.402031 51.176260 --3.395577 51.175674 --3.388830 51.175674 --3.382083 51.175674 --3.375042 51.175087 --3.368295 51.175087 --3.361255 51.174793 --3.354507 51.174793 --3.347174 51.174500 --3.340133 51.174207 --3.333679 51.174207 --3.326052 51.173620 --3.319012 51.173033 --3.311678 51.172447 --3.304344 51.172153 --3.297303 51.171567 --3.289676 51.170980 --3.282636 51.170687 --3.276475 51.169806 --3.271195 51.170980 --3.265621 51.171567 --3.261221 51.173327 --3.255647 51.174207 --3.250367 51.175380 --3.245673 51.176554 --3.240979 51.178314 --3.236286 51.179780 --3.232472 51.181834 --3.228365 51.183887 --3.223671 51.185354 --3.218978 51.186821 --3.214577 51.188288 --3.209590 51.190048 --3.204603 51.191515 --3.199616 51.192395 --3.193163 51.192395 --3.186415 51.192395 --3.179962 51.191515 --3.172921 51.191221 --3.166761 51.191515 --3.162360 51.192981 --3.157960 51.195035 --3.154146 51.197088 --3.149453 51.198555 --3.143292 51.199142 --3.138012 51.200022 --3.131851 51.200609 --3.125691 51.200609 --3.119237 51.199729 --3.113664 51.198262 --3.106916 51.197382 --3.099582 51.197088 --3.094009 51.197382 --3.088142 51.196208 --3.082568 51.194742 --3.076114 51.193862 --3.069367 51.193862 --3.063500 51.194448 --3.057926 51.195328 --3.054113 51.197088 --3.050006 51.199435 --3.046192 51.201489 --3.041498 51.202662 --3.037098 51.205009 --3.032111 51.205889 --3.026244 51.206476 --3.018910 51.206476 --3.013043 51.206769 --3.008056 51.208236 --3.005122 51.209409 --3.001602 51.212049 --2.999549 51.215570 --2.998962 51.219970 --2.996908 51.224077 --2.996322 51.228477 --2.994855 51.232878 --2.995442 51.236398 --2.997202 51.239625 --2.999842 51.242852 --3.003069 51.245199 --3.006002 51.247839 --3.009229 51.250186 --3.011576 51.253119 --3.013336 51.256346 --3.014216 51.260160 --3.014216 51.264560 --3.013043 51.268960 --3.013043 51.273067 --3.012456 51.277468 --3.010989 51.281574 --3.010403 51.285975 --3.009229 51.290962 --3.008643 51.295362 --3.006883 51.299176 --3.006002 51.303869 --3.006883 51.307390 --3.008643 51.310910 --3.011576 51.313257 --3.015976 51.315604 --3.019790 51.317657 --3.022137 51.320591 --3.018323 51.321764 --3.012456 51.321471 --3.009229 51.318830 --3.004536 51.317070 --2.998962 51.315897 --2.992215 51.315897 --2.988401 51.317657 --2.985174 51.320884 --2.984588 51.325284 --2.983708 51.329685 --2.983708 51.333792 --2.985174 51.337312 --2.986934 51.340539 --2.989281 51.343472 --2.989575 51.346699 --2.986054 51.349339 --2.980774 51.350219 --2.975200 51.351393 --2.971387 51.353446 --2.967280 51.355206 --2.964639 51.358433 --2.963173 51.362540 --2.961706 51.366354 --2.960533 51.370754 --2.959946 51.375448 --2.963759 51.377795 --2.969333 51.378968 --2.971973 51.381902 --2.970507 51.385715 --2.965813 51.387475 --2.960533 51.388355 --2.956719 51.390702 --2.951732 51.391876 --2.945278 51.390996 --2.939704 51.389822 --2.932370 51.389236 --2.927090 51.390409 --2.922396 51.391582 --2.917409 51.393049 --2.913596 51.395396 --2.909489 51.397156 --2.905969 51.399796 --2.903328 51.402730 --2.900102 51.405370 --2.896288 51.406837 --2.893354 51.409477 --2.890421 51.412411 --2.887781 51.415344 --2.884260 51.417691 --2.880740 51.420331 --2.878100 51.423265 --2.874580 51.425905 --2.871059 51.428252 --2.868126 51.430892 --2.864899 51.433825 --2.861672 51.436466 --2.859032 51.439399 --2.855512 51.442039 --2.852578 51.444973 --2.849058 51.447613 --2.845831 51.449960 --2.842311 51.452600 --2.838790 51.454947 --2.836150 51.458174 --2.832043 51.459934 --2.828523 51.462867 --2.824416 51.464628 --2.820602 51.466681 --2.817082 51.469028 --2.812975 51.471081 --2.808282 51.472842 --2.804175 51.474602 --2.800068 51.476655 --2.796254 51.478709 --2.792734 51.481055 --2.788627 51.483402 --2.783346 51.484282 --2.779240 51.486042 --2.774546 51.487803 --2.770146 51.489856 --2.764865 51.490443 --2.759585 51.490736 --2.753131 51.490736 --2.745797 51.490149 --2.738757 51.489856 --2.732009 51.489856 --2.726729 51.490443 --2.721155 51.491616 --2.717048 51.493670 --2.713528 51.496017 --2.710888 51.499243 --2.708541 51.502764 --2.706781 51.505991 --2.702381 51.508044 --2.698567 51.510391 --2.695047 51.512738 --2.691527 51.515378 --2.688300 51.517725 --2.685366 51.520952 --2.681846 51.523298 --2.680966 51.524179 --2.680966 51.523592 --2.677739 51.526232 --2.674805 51.529166 --2.672165 51.532099 --2.670112 51.535619 --2.666885 51.538553 --2.665125 51.542367 --2.662778 51.545887 --2.660431 51.549114 --2.659258 51.553221 --2.657791 51.557328 --2.655444 51.560848 --2.653390 51.564368 --2.650164 51.567595 --2.647817 51.570235 --2.644883 51.573462 --2.642243 51.576396 --2.639309 51.579329 --2.635789 51.581969 --2.633149 51.584903 --2.629629 51.587543 --2.626109 51.589890 --2.622002 51.591943 --2.618481 51.594584 --2.615841 51.597517 --2.612321 51.599864 --2.608214 51.601917 --2.604987 51.604558 --2.600880 51.606318 --2.596773 51.608665 --2.592373 51.610425 --2.588266 51.612478 --2.585039 51.615118 --2.581812 51.617465 --2.579465 51.620985 --2.577118 51.624506 --2.575652 51.628613 --2.573598 51.632133 --2.571251 51.635653 --2.569491 51.639173 --2.566264 51.642107 --2.564211 51.645627 --2.561277 51.648561 --2.558637 51.651788 --2.555703 51.654721 --2.553063 51.657655 --2.549543 51.660295 --2.546023 51.662642 --2.542503 51.665869 --2.539276 51.668216 --2.535462 51.670856 --2.531355 51.672909 --2.527248 51.674669 --2.523434 51.676723 --2.518741 51.678190 --2.514340 51.680243 --2.510234 51.682297 --2.506420 51.684057 --2.502313 51.686110 --2.498793 51.688750 --2.495272 51.691097 --2.492632 51.694031 --2.489405 51.697258 --2.487059 51.700191 --2.485298 51.704298 --2.482952 51.707818 --2.481485 51.711632 --2.480018 51.715739 --2.477671 51.719259 --2.475031 51.722193 --2.471511 51.724833 --2.467110 51.726886 --2.463297 51.728940 --2.459190 51.730700 --2.454496 51.732167 --2.450683 51.733340 --2.445109 51.734514 --2.439828 51.735394 --2.434548 51.736274 --2.428974 51.737154 --2.422814 51.737741 --2.417534 51.738621 --2.412253 51.739794 --2.406093 51.740087 --2.401399 51.741554 --2.396412 51.743021 --2.392012 51.744488 --2.388198 51.746835 --2.384678 51.749475 --2.382038 51.752408 --2.379984 51.756222 --2.378811 51.760622 --2.379691 51.764436 --2.381158 51.767663 --2.383504 51.770596 --2.386731 51.773236 --2.390838 51.775290 --2.396412 51.776757 --2.399932 51.774116 --2.399052 51.771476 --2.397585 51.767956 --2.396705 51.764142 --2.396705 51.760329 --2.397879 51.755635 --2.402279 51.752995 --2.406679 51.751528 --2.412253 51.750941 --2.418414 51.750355 --2.424574 51.749768 --2.430148 51.749475 --2.436895 51.749475 --2.442762 51.748888 --2.449803 51.748888 --2.455083 51.748008 --2.460657 51.746835 --2.465057 51.745661 --2.470044 51.744194 --2.474151 51.741848 --2.478845 51.740674 --2.482365 51.738034 --2.485885 51.735687 --2.489112 51.733047 --2.492339 51.730113 --2.494979 51.726886 --2.497913 51.724246 --2.500553 51.721019 --2.503193 51.718086 --2.507007 51.715446 --2.509353 51.712512 --2.513167 51.709872 --2.517274 51.708112 --2.521088 51.706058 --2.524608 51.703711 --2.529008 51.701365 --2.533115 51.699311 --2.537222 51.697551 --2.540449 51.694911 --2.544849 51.693151 --2.548956 51.691097 --2.552183 51.688750 --2.556290 51.686404 --2.560397 51.684350 --2.565384 51.683177 --2.569784 51.681710 --2.573891 51.679363 --2.578878 51.678190 --2.582692 51.676136 --2.586799 51.674083 --2.591199 51.672029 --2.594426 51.669389 --2.598533 51.667629 --2.602053 51.664989 --2.606160 51.662935 --2.609681 51.660588 --2.613788 51.658535 --2.616428 51.655601 --2.619948 51.652961 --2.622882 51.650028 --2.625522 51.646801 --2.628749 51.644454 --2.631976 51.641520 --2.634029 51.638000 --2.636669 51.635067 --2.639896 51.632426 --2.643123 51.629493 --2.645763 51.626266 --2.649870 51.624506 --2.654271 51.622452 --2.657497 51.620105 --2.661604 51.618052 --2.665125 51.615412 --2.668352 51.612772 --2.671872 51.610425 --2.674805 51.607491 --2.678326 51.605144 --2.681552 51.602504 --2.685073 51.599864 --2.688593 51.597224 --2.691820 51.594584 --2.695340 51.592237 --2.698567 51.589597 --2.702674 51.587836 --2.706488 51.585196 --2.710595 51.583436 --2.714702 51.581383 --2.719102 51.579623 --2.724676 51.579036 --2.730836 51.578449 --2.736703 51.577862 --2.742864 51.577569 --2.749024 51.576982 --2.754304 51.575809 --2.759291 51.574929 --2.764865 51.573755 --2.769559 51.572582 --2.774252 51.570822 --2.779533 51.569942 --2.783640 51.568182 --2.788333 51.566422 --2.793321 51.564955 --2.797134 51.563195 --2.801828 51.561435 --2.805935 51.559381 --2.810922 51.557914 --2.814735 51.555861 --2.819429 51.554394 --2.823536 51.552634 --2.828230 51.551167 --2.832923 51.549407 --2.837910 51.547940 --2.843191 51.547060 --2.847884 51.545593 --2.853458 51.544420 --2.858739 51.543540 --2.864019 51.542367 --2.869886 51.542073 --2.875166 51.541193 --2.881327 51.540606 --2.886607 51.539433 --2.892768 51.539140 --2.899515 51.539140 --2.905382 51.538553 --2.911249 51.537966 --2.918583 51.537966 --2.926210 51.538553 --2.933251 51.539140 --2.940584 51.539726 --2.947332 51.539726 --2.954665 51.540313 --2.960533 51.540900 --2.966106 51.542073 --2.967866 51.545300 --2.965520 51.548820 --2.964639 51.552634 --2.966693 51.555861 --2.970507 51.557914 --2.976667 51.557621 --2.981067 51.557034 --2.985761 51.555274 --2.988108 51.552047 --2.989575 51.547647 --2.991628 51.544127 --2.994855 51.541780 --2.998962 51.539726 --3.004536 51.538846 --3.009816 51.537673 --3.013923 51.535913 --3.014803 51.531219 --3.017443 51.528286 --3.021257 51.525645 --3.025070 51.523592 --3.029764 51.522125 --3.035631 51.521538 --3.041205 51.520658 --3.045312 51.518605 --3.049712 51.517138 --3.053819 51.515085 --3.057633 51.513031 --3.062033 51.510978 --3.066140 51.509217 --3.069954 51.506871 --3.074061 51.505111 --3.078461 51.503057 --3.082275 51.501004 --3.086968 51.499537 --3.091075 51.497483 --3.095769 51.496017 --3.100463 51.494550 --3.105156 51.493083 --3.110437 51.491910 --3.115424 51.490443 --3.118651 51.488096 --3.121877 51.485456 --3.125104 51.482522 --3.127745 51.479589 --3.129798 51.475775 --3.131851 51.472255 --3.134492 51.469028 --3.133905 51.465508 --3.135372 51.461401 --3.138012 51.458467 --3.140945 51.455534 --3.145639 51.453773 --3.151800 51.453480 --3.157960 51.454360 --3.164414 51.455240 --3.167347 51.452307 --3.169988 51.449080 --3.168227 51.445853 --3.166174 51.442919 --3.163534 51.439986 --3.160307 51.437639 --3.158547 51.434119 --3.157960 51.430598 --3.157960 51.426492 --3.158547 51.421798 --3.160307 51.417691 --3.161774 51.413584 --3.163534 51.410357 --3.166467 51.407130 --3.169988 51.404783 --3.173214 51.402143 --3.176441 51.399503 --3.180548 51.397449 --3.185242 51.395983 --3.192576 51.396569 --3.198443 51.397743 --3.204603 51.398916 --3.210470 51.398330 --3.216631 51.397743 --3.222791 51.397156 --3.228072 51.395983 --3.233352 51.395396 --3.238926 51.394223 --3.243326 51.392756 --3.247433 51.390702 --3.251247 51.388649 --3.255647 51.386595 --3.259461 51.384835 --3.264448 51.383075 --3.268261 51.381022 --3.273542 51.380142 --3.280289 51.380142 --3.287623 51.380435 --3.293196 51.382195 --3.298183 51.384249 --3.303757 51.385422 --3.309331 51.386595 --3.315785 51.386595 --3.320478 51.385129 --3.324585 51.383075 --3.328986 51.381022 --3.334266 51.380142 --3.340133 51.379555 --3.346000 51.379261 --3.352747 51.379261 --3.359494 51.379261 --3.365948 51.380142 --3.372109 51.380728 --3.378563 51.381608 --3.385310 51.381608 --3.391470 51.381022 --3.397337 51.380728 --3.403204 51.380142 --3.410538 51.380435 --3.416405 51.381022 --3.421099 51.382782 --3.425206 51.385129 --3.431953 51.385715 --3.438994 51.386302 --3.444861 51.385715 --3.450728 51.385422 --3.457768 51.385422 --3.465102 51.385715 --3.470969 51.386889 --3.476836 51.387769 --3.482703 51.389236 --3.488570 51.390702 --3.494144 51.391876 --3.499718 51.393049 --3.504705 51.394809 --3.509399 51.396276 --3.517026 51.396863 --3.523186 51.397743 --3.529640 51.397743 --3.535800 51.397156 --3.542254 51.398330 --3.547241 51.400090 --3.551348 51.401850 --3.555455 51.404197 --3.560149 51.405957 --3.562789 51.408890 --3.565136 51.411530 --3.566896 51.415051 --3.569536 51.417984 --3.571590 51.420918 --3.575697 51.422971 --3.579804 51.425025 --3.584791 51.426785 --3.589778 51.428545 --3.593591 51.430598 --3.597698 51.432652 --3.599458 51.436172 --3.602392 51.438519 --3.606792 51.440573 --3.610606 51.442919 --3.615593 51.444386 --3.619700 51.446733 --3.624394 51.448200 --3.628500 51.450253 --3.632607 51.452600 --3.636128 51.454947 --3.638475 51.457880 --3.639941 51.461107 --3.643462 51.463748 --3.646395 51.466094 --3.650502 51.468441 --3.654609 51.470495 --3.659596 51.472255 --3.665170 51.473428 --3.671917 51.474308 --3.676904 51.473428 --3.680424 51.470788 --3.684531 51.468735 --3.689812 51.468735 --3.692452 51.469615 --3.697145 51.471375 --3.703306 51.470788 --3.710053 51.470788 --3.714747 51.472548 --3.718854 51.474602 --3.721494 51.477535 --3.722961 51.480762 --3.725601 51.483989 --3.727361 51.487216 --3.731175 51.489269 --3.736162 51.490736 --3.740268 51.493083 --3.744375 51.495136 --3.746136 51.498363 --3.744962 51.503057 --3.744375 51.507457 --3.745256 51.510978 --3.746136 51.515085 --3.747016 51.518605 --3.747896 51.522418 --3.749362 51.525939 --3.751123 51.529166 --3.753176 51.532392 --3.754643 51.535913 --3.756990 51.538553 --3.758750 51.542073 --3.761097 51.545007 --3.763737 51.547647 --3.766084 51.550874 --3.768724 51.553514 --3.771071 51.556741 --3.773418 51.559381 --3.776938 51.562021 --3.779285 51.564955 --3.781631 51.567888 --3.784858 51.570235 --3.790139 51.571995 --3.793952 51.574049 --3.797179 51.576982 --3.798939 51.580209 --3.801286 51.583436 --3.803633 51.586076 --3.807153 51.588717 --3.812727 51.589890 --3.816834 51.592237 --3.821234 51.594290 --3.825048 51.596344 --3.828275 51.598984 --3.831795 51.601331 --3.834142 51.604264 --3.835022 51.608078 --3.833555 51.611892 --3.833555 51.615998 --3.835609 51.619519 --3.840302 51.620985 --3.845583 51.620985 --3.851743 51.620692 --3.857024 51.619519 --3.863477 51.619519 --3.869344 51.618932 --3.875505 51.618345 --3.881665 51.617759 --3.886946 51.616585 --3.892813 51.615998 --3.897506 51.614825 --3.902200 51.613065 --3.906307 51.611011 --3.910707 51.609545 --3.917748 51.609545 --3.924202 51.610425 --3.930069 51.611598 --3.935643 51.612772 --3.942683 51.613358 --3.949430 51.613358 --3.954711 51.612185 --3.960284 51.611011 --3.965565 51.610425 --3.970258 51.608665 --3.974659 51.607198 --3.979646 51.605438 --3.984339 51.603971 --3.988446 51.601917 --3.991673 51.599571 --3.995780 51.597517 --3.998714 51.594584 --4.000000 51.592815 -nan nan --4.000000 51.584430 --3.999887 51.584316 --3.996954 51.581969 --3.993433 51.579329 --3.990206 51.576982 --3.986099 51.574636 --3.981993 51.572582 --3.977886 51.570529 --3.973779 51.568475 --3.972312 51.564955 --3.973485 51.561141 --3.977005 51.558501 --3.983753 51.558501 --3.989913 51.559381 --3.994900 51.561141 --3.999594 51.562901 --4.000000 51.563014 -nan nan --4.000000 52.525600 --3.999594 52.525690 --3.994313 52.526277 --3.989326 52.528037 --3.985219 52.530091 --3.980526 52.531558 --3.975832 52.533024 --3.971725 52.535371 --3.966738 52.536545 --3.962924 52.538891 --3.957937 52.540358 --3.953830 52.542412 --3.950604 52.545052 --3.947083 52.547399 --3.945617 52.551799 --3.949724 52.553559 --3.956764 52.553559 --3.962924 52.552972 --3.968792 52.552386 --3.974072 52.551506 --3.979646 52.550626 --3.984926 52.549452 --3.990793 52.548279 --3.996074 52.547105 --4.000000 52.546452 -nan nan --4.000000 52.720906 --3.996660 52.723411 --3.993140 52.725758 --3.989620 52.728692 --3.989033 52.732212 --3.994313 52.733972 --4.000000 52.733972 -nan nan --4.000000 53.243913 --3.999007 53.244409 --3.994607 53.246462 --3.990500 53.248516 --3.985513 53.249982 --3.981406 53.252329 --3.977299 53.254089 --3.972899 53.256436 --3.967911 53.257903 --3.962924 53.259370 --3.959111 53.260543 --3.954417 53.262010 --3.949430 53.263477 --3.944443 53.264944 --3.938869 53.266117 --3.934176 53.267877 --3.928602 53.268757 --3.923028 53.269637 --3.916574 53.270224 --3.911001 53.271397 --3.905720 53.272571 --3.900733 53.273744 --3.896626 53.276091 --3.893106 53.278731 --3.888999 53.280491 --3.882545 53.281078 --3.874918 53.280785 --3.868758 53.280198 --3.863771 53.281958 --3.859957 53.284012 --3.854090 53.284892 --3.847636 53.284305 --3.840889 53.283425 --3.833262 53.282838 --3.829155 53.284598 --3.828275 53.288412 --3.830035 53.291639 --3.833555 53.294279 --3.836195 53.297212 --3.838542 53.300146 --3.840302 53.303373 --3.841476 53.307187 --3.842943 53.310413 --3.846463 53.313054 --3.849690 53.315694 --3.854090 53.317454 --3.859370 53.319214 --3.863477 53.321268 --3.868758 53.323028 --3.872865 53.325375 --3.876092 53.327721 --3.877265 53.331535 --3.873745 53.333882 --3.867584 53.334468 --3.861717 53.333295 --3.858490 53.332122 --3.853503 53.330655 --3.847636 53.329188 --3.841769 53.327721 --3.834729 53.328015 --3.830328 53.326548 --3.825928 53.324788 --3.822408 53.322148 --3.818301 53.320094 --3.813900 53.318041 --3.807447 53.316867 --3.800993 53.317454 --3.795419 53.318627 --3.789845 53.319801 --3.783685 53.320387 --3.777524 53.318921 --3.774591 53.316281 --3.770777 53.313934 --3.767257 53.311293 --3.764030 53.308947 --3.759630 53.306600 --3.753763 53.305426 --3.747896 53.304253 --3.743495 53.302200 --3.740268 53.299559 --3.737628 53.296626 --3.735868 53.293399 --3.732641 53.290759 --3.727361 53.289292 --3.720907 53.288412 --3.713573 53.288412 --3.706239 53.287825 --3.698612 53.287238 --3.692452 53.286065 --3.685705 53.285185 --3.678957 53.284305 --3.671330 53.284012 --3.664583 53.284012 --3.657543 53.284012 --3.651969 53.284892 --3.644928 53.284892 --3.638181 53.284012 --3.632314 53.282838 --3.626447 53.281371 --3.619700 53.280491 --3.612659 53.279611 --3.606792 53.280198 --3.601219 53.281078 --3.594765 53.281665 --3.589191 53.282838 --3.584497 53.284305 --3.579510 53.285772 --3.574817 53.287238 --3.571883 53.289585 --3.566309 53.290465 --3.561322 53.291932 --3.557215 53.294279 --3.553108 53.296039 --3.549001 53.298093 --3.544014 53.299853 --3.539321 53.301613 --3.534040 53.302786 --3.529053 53.304253 --3.524360 53.305720 --3.518786 53.306893 --3.513799 53.308360 --3.508225 53.309533 --3.503238 53.310707 --3.498544 53.312467 --3.493557 53.313934 --3.488864 53.315694 --3.483877 53.316867 --3.478890 53.318627 --3.472729 53.319214 --3.466275 53.319507 --3.461288 53.320974 --3.456595 53.322441 --3.452488 53.324788 --3.448381 53.326548 --3.443981 53.328601 --3.437820 53.329188 --3.432246 53.330362 --3.426379 53.331535 --3.420806 53.332122 --3.416112 53.333882 --3.411125 53.335349 --3.406431 53.336815 --3.402324 53.338869 --3.397337 53.340629 --3.392644 53.342389 --3.387950 53.343856 --3.381789 53.344443 --3.376216 53.345616 --3.370055 53.346203 --3.362721 53.346496 --3.355388 53.346203 --3.348934 53.346496 --3.342773 53.347083 --3.336319 53.347376 --3.329866 53.347376 --3.322532 53.347376 --3.314905 53.347083 --3.311384 53.345323 --3.307277 53.343269 --3.303170 53.341216 --3.298477 53.339162 --3.295250 53.336522 --3.292023 53.333882 --3.287623 53.331828 --3.283222 53.329775 --3.279115 53.327721 --3.275008 53.325668 --3.270901 53.323321 --3.266794 53.321268 --3.262981 53.318921 --3.258874 53.316574 --3.253887 53.315107 --3.249487 53.312760 --3.245380 53.310413 --3.240979 53.308653 --3.235992 53.306893 --3.231885 53.304840 --3.226898 53.303080 --3.221618 53.301319 --3.216631 53.299559 --3.211351 53.297799 --3.207244 53.295746 --3.203137 53.293692 --3.198736 53.291345 --3.193749 53.289585 --3.189349 53.287825 --3.184362 53.285772 --3.180255 53.284012 --3.174975 53.282251 --3.170868 53.279905 --3.166761 53.277851 --3.163240 53.275211 --3.160014 53.272864 --3.156493 53.270224 --3.151800 53.268757 --3.146519 53.266997 --3.142119 53.264650 --3.138012 53.262597 --3.133905 53.260543 --3.130385 53.257903 --3.125691 53.256143 --3.120997 53.254089 --3.115424 53.252916 --3.110143 53.251156 --3.106623 53.248516 --3.103689 53.245875 --3.101929 53.242355 --3.099289 53.239715 --3.095769 53.237368 --3.094009 53.235315 --3.090489 53.232675 --3.085501 53.230914 --3.079634 53.229741 --3.073474 53.230034 --3.068194 53.231794 --3.067314 53.234728 --3.069367 53.237662 --3.071420 53.241182 --3.072007 53.244702 --3.070540 53.248809 --3.069367 53.253209 --3.071420 53.256730 --3.070540 53.261130 --3.067607 53.264063 --3.065553 53.267877 --3.064673 53.271397 --3.067607 53.274331 --3.069660 53.277264 --3.075527 53.278731 --3.080808 53.280198 --3.084915 53.282545 --3.088435 53.284892 --3.090782 53.288118 --3.094302 53.290465 --3.098409 53.292519 --3.099582 53.296332 --3.096356 53.299559 --3.092835 53.301906 --3.092249 53.305426 --3.095476 53.308067 --3.099582 53.310413 --3.104863 53.311880 --3.107503 53.314814 --3.110143 53.317747 --3.112490 53.320974 --3.115130 53.323614 --3.119237 53.325961 --3.123638 53.327721 --3.128331 53.329775 --3.132732 53.331535 --3.137719 53.333295 --3.142119 53.335642 --3.145346 53.337989 --3.147986 53.341216 --3.151506 53.343562 --3.154733 53.346203 --3.158253 53.348550 --3.161480 53.351190 --3.164707 53.353537 --3.168227 53.356177 --3.171748 53.358524 --3.174095 53.361750 --3.177615 53.364097 --3.180842 53.366737 --3.184362 53.369084 --3.186709 53.372311 --3.189349 53.374951 --3.191109 53.378472 --3.192869 53.381699 --3.192869 53.385806 --3.191109 53.389912 --3.188469 53.393139 --3.184655 53.395486 --3.181135 53.398126 --3.177028 53.399887 --3.172921 53.402233 --3.168227 53.404287 --3.163534 53.405460 --3.157960 53.406634 --3.152093 53.407807 --3.146813 53.408687 --3.141826 53.410154 --3.138012 53.410154 --3.131851 53.410741 --3.125984 53.411914 --3.120411 53.412794 --3.115130 53.413968 --3.110437 53.415728 --3.105743 53.417488 --3.101636 53.419541 --3.096649 53.420715 --3.092249 53.423062 --3.087555 53.424528 --3.082568 53.425995 --3.077581 53.427462 --3.072007 53.428635 --3.067314 53.430102 --3.060860 53.430689 --3.054406 53.430982 --3.048245 53.431275 --3.040618 53.430982 --3.033578 53.430102 --3.027711 53.428635 --3.023604 53.426582 --3.020377 53.424235 --3.018617 53.420715 --3.017737 53.416901 --3.016857 53.413381 --3.015096 53.409861 --3.013630 53.406634 --3.010403 53.404287 --3.007469 53.401060 --3.005122 53.398126 --3.002776 53.395193 --3.000135 53.392259 --2.998375 53.389032 --2.994855 53.386392 --2.993388 53.383165 --2.993388 53.378765 --2.994268 53.374365 --2.992508 53.371138 --2.989868 53.367911 --2.987521 53.365271 --2.984294 53.362924 --2.980774 53.359990 --2.977254 53.357643 --2.974614 53.354710 --2.972560 53.351776 --2.969627 53.348843 --2.967280 53.345909 --2.964639 53.342682 --2.962293 53.340042 --2.959652 53.336815 --2.957306 53.334175 --2.954665 53.331242 --2.952319 53.328308 --2.949678 53.325375 --2.947918 53.321854 --2.944398 53.319507 --2.942345 53.316281 --2.938531 53.313934 --2.935304 53.311293 --2.931197 53.309240 --2.927677 53.306600 --2.922396 53.305133 --2.920050 53.303080 --2.915943 53.300733 --2.911542 53.298679 --2.907435 53.296626 --2.902155 53.294866 --2.897168 53.293106 --2.892181 53.291345 --2.885434 53.290465 --2.880153 53.288705 --2.873700 53.287825 --2.868713 53.286065 --2.862552 53.284598 --2.856685 53.283425 --2.850818 53.281958 --2.844071 53.281078 --2.837910 53.279611 --2.831457 53.279611 --2.824416 53.279611 --2.817962 53.280198 --2.812389 53.281371 --2.806815 53.282251 --2.801828 53.283718 --2.797721 53.285772 --2.793321 53.287825 --2.789507 53.289585 --2.785693 53.292225 --2.782173 53.294866 --2.778653 53.297212 --2.774546 53.299266 --2.769265 53.300733 --2.764572 53.302200 --2.759585 53.303960 --2.754598 53.305133 --2.751664 53.308360 --2.750784 53.312760 --2.752544 53.315987 --2.754891 53.319214 --2.754891 53.323321 --2.751958 53.326255 --2.749024 53.329481 --2.744917 53.331535 --2.741103 53.333882 --2.738463 53.336815 --2.735236 53.340042 --2.736410 53.343562 --2.740517 53.345909 --2.746090 53.344736 --2.751077 53.343269 --2.755771 53.341802 --2.760171 53.339749 --2.763692 53.337109 --2.768092 53.335349 --2.771319 53.332708 --2.775719 53.330948 --2.780120 53.328601 --2.785693 53.327721 --2.791267 53.326548 --2.798894 53.327135 --2.806521 53.327721 --2.812389 53.329188 --2.820016 53.329775 --2.827056 53.329775 --2.833803 53.329188 --2.841724 53.329775 --2.848471 53.329775 --2.855218 53.330948 --2.861085 53.332122 --2.866072 53.333882 --2.870179 53.335935 --2.874580 53.337989 --2.878100 53.340629 --2.881327 53.342976 --2.885434 53.345323 --2.890421 53.347083 --2.896288 53.348256 --2.901568 53.350016 --2.906555 53.352070 --2.911836 53.353537 --2.916529 53.355297 --2.921223 53.357643 --2.925330 53.359404 --2.929437 53.361750 --2.933837 53.363804 --2.937358 53.366444 --2.942345 53.367911 --2.947332 53.369671 --2.953199 53.371138 --2.958479 53.372898 --2.961706 53.374365 --2.966693 53.376125 --2.970213 53.378765 --2.973733 53.381405 --2.976960 53.383752 --2.980481 53.386392 --2.982827 53.389032 --2.986348 53.391966 --2.988988 53.394606 --2.991041 53.397833 --2.993095 53.401060 --2.996322 53.403700 --2.998962 53.406340 --3.000429 53.409861 --3.002189 53.413087 --3.003949 53.416314 --3.005122 53.420421 --3.005416 53.423942 --3.006296 53.427755 --3.007176 53.431275 --3.009229 53.434796 --3.011283 53.437729 --3.013923 53.440663 --3.016563 53.443596 --3.019203 53.446530 --3.019203 53.450930 --3.019790 53.454450 --3.021257 53.457677 --3.025070 53.460318 --3.028297 53.462664 --3.032404 53.465011 --3.036805 53.467358 --3.040032 53.469705 --3.043258 53.472345 --3.045312 53.475572 --3.047659 53.478212 --3.048832 53.481439 --3.050592 53.484666 --3.051472 53.488480 --3.052939 53.491706 --3.053526 53.495520 --3.055579 53.498747 --3.057339 53.502267 --3.059686 53.504907 --3.063207 53.507548 --3.066727 53.509894 --3.069660 53.512535 --3.073474 53.515175 --3.076701 53.517815 --3.079928 53.520162 --3.083741 53.522802 --3.086968 53.525149 --3.089315 53.528376 --3.092835 53.531016 --3.095182 53.534243 --3.097822 53.536883 --3.100169 53.540110 --3.102809 53.543043 --3.105450 53.545977 --3.107210 53.549204 --3.107796 53.553018 --3.107796 53.557124 --3.106330 53.561231 --3.104276 53.564752 --3.101929 53.568272 --3.099289 53.571205 --3.096942 53.574726 --3.094009 53.577659 --3.091075 53.580886 --3.088142 53.583820 --3.085208 53.587047 --3.082275 53.589980 --3.079341 53.592914 --3.075527 53.595847 --3.072887 53.598781 --3.069367 53.601421 --3.066433 53.604355 --3.064087 53.608168 --3.061446 53.611102 --3.058220 53.614035 --3.055579 53.617262 --3.052646 53.620196 --3.048832 53.622836 --3.045899 53.625769 --3.042085 53.628703 --3.039445 53.631636 --3.036511 53.634863 --3.033578 53.637797 --3.030938 53.640730 --3.027124 53.643371 --3.024190 53.646304 --3.021257 53.649531 --3.017443 53.651878 --3.014803 53.655105 --3.011576 53.658038 --3.008349 53.660679 --3.005416 53.663612 --3.001602 53.666252 --2.998082 53.668599 --2.994855 53.671239 --2.990748 53.673586 --2.987228 53.676226 --2.983708 53.678573 --2.980187 53.681213 --2.976667 53.683560 --2.971680 53.685320 --2.965226 53.685614 --2.958479 53.684734 --2.951732 53.683854 --2.946745 53.685320 --2.942638 53.687080 --2.938531 53.689721 --2.934424 53.692067 --2.930904 53.694414 --2.927090 53.697055 --2.924450 53.699988 --2.920636 53.702628 --2.917996 53.705562 --2.914476 53.708202 --2.910076 53.709962 --2.906262 53.712602 --2.902155 53.714362 --2.896875 53.716123 --2.892181 53.717589 --2.887194 53.718763 --2.881620 53.719936 --2.876340 53.721403 --2.871646 53.723163 --2.865779 53.723750 --2.860205 53.724923 --2.854632 53.726097 --2.849645 53.727563 --2.847591 53.731084 --2.843191 53.733137 --2.839671 53.735484 --2.839084 53.738417 --2.845244 53.738711 --2.850818 53.737831 --2.855805 53.736071 --2.861379 53.735191 --2.866366 53.733724 --2.871059 53.733137 --2.877513 53.732550 --2.884554 53.732844 --2.890127 53.731670 --2.896288 53.731084 --2.902742 53.730497 --2.909782 53.731670 --2.914769 53.733430 --2.920050 53.734897 --2.926797 53.736071 --2.933544 53.736071 --2.939998 53.735484 --2.944398 53.733724 --2.948505 53.731377 --2.952905 53.729324 --2.958772 53.729910 --2.964933 53.730204 --2.970800 53.729324 --2.975787 53.727857 --2.982241 53.727270 --2.988108 53.728737 --2.992508 53.730790 --2.998962 53.730204 --3.004536 53.729030 --3.010696 53.729030 --3.015683 53.730497 --3.021550 53.731964 --3.025951 53.734017 --3.030351 53.736071 --3.033578 53.738711 --3.037685 53.740764 --3.041498 53.743405 --3.044725 53.745751 --3.046779 53.747218 --3.046779 53.748392 --3.049419 53.749565 --3.052059 53.752205 --3.054406 53.755139 --3.057339 53.758072 --3.058806 53.761299 --3.059686 53.765406 --3.060566 53.768926 --3.062326 53.772153 --3.062326 53.776260 --3.062913 53.780367 --3.063500 53.784474 --3.063500 53.788581 --3.063500 53.792688 --3.062913 53.797088 --3.061446 53.801489 --3.059686 53.805302 --3.057926 53.809409 --3.057633 53.813810 --3.055873 53.817917 --3.054993 53.822610 --3.054993 53.826717 --3.054993 53.830824 --3.054993 53.834931 --3.054993 53.839038 --3.053819 53.843732 --3.052646 53.847839 --3.050886 53.851652 --3.050006 53.856346 --3.049126 53.860746 --3.047365 53.865147 --3.046779 53.869547 --3.045312 53.873361 --3.044139 53.878054 --3.044139 53.882161 --3.045312 53.885975 --3.045899 53.889788 --3.046779 53.893309 --3.047365 53.897122 --3.048245 53.900936 --3.049419 53.904749 --3.049419 53.908563 --3.048245 53.913257 --3.047365 53.917070 --3.045312 53.920591 --3.042378 53.923524 --3.038271 53.925578 --3.034751 53.927924 --3.029177 53.928804 --3.021844 53.928804 --3.015096 53.928804 --3.009229 53.929978 --3.003069 53.930565 --2.996908 53.929098 --2.989868 53.928218 --2.984588 53.929098 --2.979307 53.930858 --2.974320 53.932325 --2.969040 53.933792 --2.964346 53.935258 --2.958479 53.936432 --2.952905 53.937312 --2.947332 53.938192 --2.940878 53.938779 --2.936184 53.940245 --2.930904 53.941712 --2.926210 53.943472 --2.920343 53.944059 --2.916529 53.944352 --2.910369 53.944939 --2.903035 53.943766 --2.898928 53.942005 --2.895701 53.939365 --2.893941 53.936138 --2.888661 53.934085 --2.884260 53.936432 --2.881914 53.939659 --2.877807 53.942005 --2.873700 53.943766 --2.869886 53.946406 --2.867539 53.949926 --2.864312 53.952860 --2.861085 53.955500 --2.855805 53.956967 --2.849645 53.957553 --2.845244 53.959313 --2.841724 53.961954 --2.839964 53.966060 --2.841724 53.969581 --2.848471 53.970167 --2.854045 53.969287 --2.859912 53.968407 --2.866072 53.968701 --2.868126 53.971928 --2.866072 53.976035 --2.863432 53.979261 --2.862552 53.983662 --2.859912 53.987182 --2.855805 53.989235 --2.852285 53.991582 --2.848471 53.994223 --2.847884 53.997743 --2.849645 54.000970 --2.854632 54.002730 --2.861085 54.002436 --2.866072 54.000970 --2.869593 53.998329 --2.873406 53.995689 --2.877807 53.993929 --2.883380 53.992756 --2.887781 53.995103 --2.891008 53.997449 --2.892768 54.000970 --2.892768 54.005077 --2.891008 54.009184 --2.890127 54.013584 --2.892768 54.016811 --2.896875 54.018571 --2.901275 54.020918 --2.904795 54.023265 --2.907435 54.026492 --2.910076 54.029132 --2.911542 54.032359 --2.911542 54.036759 --2.908022 54.039106 --2.905089 54.042333 --2.902155 54.045266 --2.899221 54.048200 --2.895995 54.051427 --2.893061 54.054360 --2.889834 54.057000 --2.886607 54.059934 --2.883674 54.063161 --2.880447 54.065801 --2.877807 54.069028 --2.873993 54.071375 --2.869299 54.073135 --2.862846 54.073722 --2.856978 54.074308 --2.851991 54.076068 --2.847884 54.078122 --2.843777 54.080469 --2.840257 54.083109 --2.835564 54.084576 --2.830283 54.086042 --2.823829 54.086336 --2.819136 54.088096 --2.814735 54.089856 --2.812389 54.093670 --2.813269 54.097190 --2.813269 54.101297 --2.811508 54.105697 --2.808575 54.108631 --2.805641 54.111271 --2.801828 54.114204 --2.799188 54.116845 --2.796841 54.120658 --2.799481 54.123592 --2.801534 54.125939 --2.805641 54.127992 --2.809748 54.130339 --2.812095 54.132979 --2.813269 54.137086 --2.815029 54.140313 --2.816789 54.143540 --2.819136 54.146767 --2.821776 54.149407 --2.825003 54.152047 --2.827643 54.154981 --2.831163 54.157621 --2.834390 54.159968 --2.837324 54.163195 --2.839671 54.165835 --2.842311 54.168768 --2.844658 54.171702 --2.846418 54.175222 --2.848178 54.178742 --2.847298 54.183143 --2.844071 54.186076 --2.839377 54.187543 --2.832923 54.187250 --2.826176 54.186076 --2.820309 54.187250 --2.817962 54.190770 --2.819722 54.194290 --2.822363 54.196930 --2.826763 54.199277 --2.833510 54.199864 --2.839964 54.199864 --2.845831 54.198691 --2.851698 54.197517 --2.856392 54.196050 --2.861965 54.194877 --2.868713 54.194584 --2.874873 54.194290 --2.879860 54.192530 --2.883674 54.189890 --2.887194 54.187543 --2.890714 54.184903 --2.895408 54.183143 --2.900688 54.181969 --2.905969 54.180503 --2.909782 54.178156 --2.913302 54.175516 --2.916529 54.172582 --2.917996 54.168475 --2.919463 54.164368 --2.921810 54.160848 --2.924450 54.157914 --2.928264 54.155274 --2.934131 54.154394 --2.938824 54.152634 --2.944691 54.152047 --2.951145 54.151460 --2.956719 54.150287 --2.962586 54.149407 --2.968746 54.148820 --2.976667 54.149407 --2.982827 54.150874 --2.987814 54.152634 --2.993095 54.154101 --2.996615 54.156741 --2.997202 54.160554 --2.997202 54.164661 --2.997202 54.168475 --2.998082 54.172582 --3.002482 54.174635 --3.007469 54.176396 --3.012750 54.178156 --3.015976 54.180503 --3.019497 54.183143 --3.022137 54.186076 --3.025070 54.189010 --3.027124 54.191943 --3.032404 54.193704 --3.037391 54.192237 --3.040618 54.189303 --3.043258 54.186076 --3.046485 54.183143 --3.049419 54.179916 --3.049419 54.175809 --3.049419 54.171702 --3.049419 54.167595 --3.051179 54.163488 --3.053233 54.159968 --3.056166 54.157034 --3.059686 54.154394 --3.063500 54.152047 --3.067314 54.149407 --3.069367 54.145887 --3.069367 54.141780 --3.069367 54.137379 --3.072301 54.134446 --3.075821 54.131806 --3.079634 54.129459 --3.081101 54.125645 --3.083741 54.121832 --3.086382 54.118898 --3.089902 54.116258 --3.094302 54.114498 --3.099582 54.112738 --3.103689 54.110978 --3.106623 54.107751 --3.106623 54.103644 --3.109850 54.100417 --3.115424 54.099830 --3.120117 54.098070 --3.125398 54.096603 --3.130091 54.095136 --3.135372 54.093670 --3.140065 54.092203 --3.145346 54.090443 --3.149453 54.088683 --3.153853 54.086629 --3.155320 54.082522 --3.151800 54.079882 --3.148279 54.077535 --3.145052 54.074895 --3.141532 54.072548 --3.139185 54.069321 --3.137425 54.066094 --3.138012 54.061694 --3.143879 54.061401 --3.147986 54.063748 --3.151506 54.066094 --3.154733 54.068735 --3.160307 54.070201 --3.165294 54.071961 --3.169401 54.074308 --3.172921 54.076655 --3.174681 54.079882 --3.175561 54.083989 --3.177321 54.087216 --3.180548 54.089856 --3.186122 54.091323 --3.190229 54.093670 --3.194336 54.095430 --3.202257 54.096016 --3.208710 54.095430 --3.214577 54.096016 --3.220738 54.097483 --3.226018 54.099243 --3.230419 54.101004 --3.233939 54.103644 --3.236286 54.106577 --3.238046 54.110098 --3.237166 54.114498 --3.237166 54.118605 --3.238339 54.122418 --3.239806 54.125939 --3.240979 54.129459 --3.239806 54.134153 --3.237459 54.137379 --3.234819 54.140606 --3.230712 54.142953 --3.228952 54.146767 --3.227192 54.150874 --3.228952 54.154101 --3.231592 54.157034 --3.235699 54.159088 --3.240393 54.161435 --3.245380 54.163195 --3.248900 54.165541 --3.245966 54.167595 --3.241566 54.169648 --3.235992 54.170529 --3.229832 54.171115 --3.222791 54.171115 --3.217511 54.172875 --3.213404 54.174635 --3.212524 54.179036 --3.213404 54.183143 --3.214871 54.186370 --3.214871 54.190477 --3.213697 54.193704 --3.211351 54.197224 --3.208710 54.200157 --3.206363 54.203678 --3.204017 54.207198 --3.202550 54.211305 --3.200790 54.215412 --3.199030 54.219519 --3.197856 54.223332 --3.198736 54.227146 --3.201083 54.230079 --3.204017 54.233013 --3.206363 54.235947 --3.209004 54.238880 --3.210470 54.242107 --3.211644 54.245921 --3.213404 54.249147 --3.213404 54.253254 --3.211644 54.257361 --3.207244 54.259415 --3.208710 54.261468 --3.214577 54.262642 --3.218978 54.260882 --3.221911 54.257655 --3.224845 54.254721 --3.226898 54.251201 --3.229245 54.247387 --3.230419 54.242987 --3.231005 54.238587 --3.231005 54.234480 --3.231005 54.230373 --3.232765 54.225972 --3.234232 54.222159 --3.236579 54.218639 --3.238926 54.215118 --3.239513 54.211305 --3.235699 54.208958 --3.232472 54.206318 --3.233059 54.202797 --3.235112 54.200451 --3.236872 54.198397 --3.240099 54.195170 --3.243620 54.192823 --3.248900 54.191357 --3.255647 54.192237 --3.262394 54.193117 --3.269435 54.193997 --3.277355 54.194584 --3.284396 54.194584 --3.289969 54.193704 --3.294370 54.191357 --3.298477 54.189303 --3.304931 54.189010 --3.311091 54.190183 --3.316078 54.191943 --3.319598 54.194584 --3.323412 54.196930 --3.326639 54.199571 --3.329572 54.202504 --3.331626 54.205144 --3.334559 54.208371 --3.337200 54.211011 --3.340426 54.213945 --3.343067 54.216585 --3.345707 54.219812 --3.348347 54.222452 --3.350694 54.225679 --3.353627 54.228319 --3.355974 54.231253 --3.359788 54.233893 --3.363015 54.236533 --3.366535 54.238880 --3.371815 54.240640 --3.376216 54.242694 --3.380323 54.244747 --3.382083 54.247974 --3.384723 54.251201 --3.386483 54.254428 --3.387950 54.257655 --3.390883 54.260882 --3.392644 54.264109 --3.396164 54.266749 --3.399391 54.269096 --3.402911 54.271736 --3.406431 54.274083 --3.409071 54.277016 --3.410832 54.280243 --3.411712 54.284057 --3.412005 54.287284 --3.412005 54.291391 --3.410245 54.295497 --3.409658 54.299898 --3.407311 54.303711 --3.405844 54.307818 --3.404964 54.312219 --3.404964 54.316326 --3.406725 54.319846 --3.408191 54.323073 --3.410245 54.326300 --3.412005 54.329820 --3.412885 54.333340 --3.412005 54.338034 --3.412298 54.342141 --3.417285 54.343901 --3.423446 54.345368 --3.429313 54.346248 --3.434007 54.348595 --3.437233 54.351235 --3.440460 54.353582 --3.443394 54.356809 --3.446621 54.359155 --3.450141 54.361796 --3.452781 54.364436 --3.455421 54.367369 --3.458355 54.370303 --3.460702 54.373236 --3.463342 54.376170 --3.465982 54.379103 --3.469502 54.381744 --3.472143 54.384677 --3.475663 54.387317 --3.478890 54.389664 --3.481530 54.392598 --3.484463 54.395531 --3.487690 54.398172 --3.490624 54.400812 --3.492971 54.403745 --3.496784 54.406385 --3.500011 54.409026 --3.503531 54.411372 --3.507052 54.414013 --3.510572 54.416359 --3.513799 54.419000 --3.517613 54.421347 --3.519959 54.424573 --3.524360 54.426627 --3.528173 54.429267 --3.531400 54.431614 --3.534920 54.434254 --3.538734 54.436601 --3.542841 54.438654 --3.546361 54.441001 --3.549588 54.443641 --3.553402 54.446282 --3.556922 54.448922 --3.559562 54.451562 --3.561909 54.454789 --3.564843 54.457429 --3.568069 54.460069 --3.572470 54.462123 --3.575990 54.464763 --3.579804 54.467110 --3.583031 54.469750 --3.585671 54.472684 --3.588311 54.475617 --3.591244 54.478551 --3.594471 54.481191 --3.598872 54.482951 --3.605032 54.484418 --3.609432 54.486471 --3.612659 54.489111 --3.615593 54.492045 --3.617940 54.494978 --3.620873 54.497912 --3.623220 54.500846 --3.627034 54.503192 --3.629674 54.506126 --3.632021 54.509059 --3.634074 54.512580 --3.633194 54.516100 --3.629674 54.518740 --3.624687 54.520207 --3.620287 54.522260 --3.615300 54.523727 --3.611779 54.526074 --3.609432 54.529594 --3.608552 54.534581 --3.606499 54.537808 --3.603565 54.540742 --3.599752 54.543675 --3.596231 54.546022 --3.592418 54.548662 --3.591244 54.552476 --3.590364 54.555996 --3.590364 54.560396 --3.589778 54.565090 --3.587137 54.568610 --3.585084 54.571837 --3.581857 54.575064 --3.578337 54.577411 --3.575697 54.580638 --3.575697 54.584745 --3.576577 54.587385 --3.577457 54.591492 --3.575697 54.595306 --3.573643 54.598826 --3.571590 54.602640 --3.569536 54.606160 --3.570416 54.609680 --3.571003 54.613494 --3.571883 54.617307 --3.571883 54.621414 --3.571296 54.625815 --3.571296 54.629921 --3.571296 54.634028 --3.570416 54.639015 --3.568950 54.642829 --3.565723 54.645763 --3.563082 54.648990 --3.559856 54.651923 --3.557215 54.654857 --3.554282 54.658084 --3.550468 54.660430 --3.547535 54.663657 --3.544601 54.666591 --3.541668 54.669818 --3.539321 54.673338 --3.537267 54.676565 --3.534040 54.679792 --3.530520 54.682139 --3.527587 54.685365 --3.523773 54.688006 --3.521133 54.691233 --3.518199 54.694166 --3.516732 54.697980 --3.514972 54.702087 --3.513212 54.706194 --3.511159 54.709714 --3.509105 54.713234 --3.505292 54.715874 --3.501771 54.718221 --3.497078 54.720275 --3.492971 54.722621 --3.488570 54.724382 --3.484170 54.726435 --3.480943 54.728195 --3.476250 54.729955 --3.472729 54.732596 --3.468329 54.734649 --3.464809 54.737289 --3.460702 54.739049 --3.456595 54.741690 --3.453075 54.744330 --3.450141 54.747263 --3.446914 54.750197 --3.444274 54.753424 --3.441047 54.756357 --3.438407 54.759584 --3.435767 54.763104 --3.434300 54.767211 --3.433713 54.771612 --3.432540 54.776012 --3.433713 54.780119 --3.434300 54.783639 --3.435180 54.787453 --3.436353 54.790973 --3.437233 54.795080 --3.438113 54.798600 --3.438113 54.802707 --3.438113 54.806814 --3.436060 54.809454 --3.433126 54.807401 --3.429313 54.810041 --3.426379 54.812975 --3.422859 54.815615 --3.419925 54.818548 --3.416405 54.821189 --3.413472 54.824122 --3.410245 54.827349 --3.407311 54.830283 --3.404084 54.833216 --3.400564 54.835856 --3.397924 54.838790 --3.394697 54.842017 --3.392644 54.845537 --3.389417 54.848471 --3.387363 54.851991 --3.386483 54.856684 --3.384723 54.860498 --3.383256 54.864605 --3.379736 54.867245 --3.376216 54.869592 --3.372109 54.872232 --3.368588 54.874579 --3.365068 54.877513 --3.360375 54.879566 --3.357441 54.882500 --3.353921 54.885140 --3.349520 54.886900 --3.345120 54.888953 --3.340426 54.891007 --3.335439 54.892474 --3.329866 54.893647 --3.323999 54.894820 --3.321358 54.891594 --3.324292 54.888660 --3.326639 54.885140 --3.324585 54.882793 --3.323119 54.882500 --3.323705 54.883673 --3.317545 54.882206 --3.310211 54.882206 --3.302584 54.881620 --3.297303 54.879859 --3.293490 54.877513 --3.289383 54.875166 --3.285569 54.872819 --3.281462 54.870765 --3.277062 54.868712 --3.272075 54.869299 --3.269141 54.872232 --3.267968 54.876633 --3.269141 54.880446 --3.270021 54.884260 --3.266208 54.886900 --3.261221 54.888367 --3.255354 54.889540 --3.250367 54.890714 --3.247140 54.893940 --3.245086 54.897461 --3.243326 54.901274 --3.246846 54.903914 --3.253300 54.903621 --3.258581 54.901861 --3.264154 54.900688 --3.271488 54.900688 --3.277355 54.902154 --3.282049 54.904501 --3.284689 54.907141 --3.287623 54.909488 --3.287036 54.913008 --3.284689 54.916529 --3.282929 54.920636 --3.279995 54.923569 --3.275595 54.925623 --3.270608 54.927089 --3.264741 54.927970 --3.260341 54.930316 --3.256527 54.932663 --3.253007 54.935303 --3.249193 54.937650 --3.244206 54.939117 --3.238339 54.940290 --3.232472 54.941757 --3.228072 54.943811 --3.223671 54.946451 --3.218684 54.947918 --3.212817 54.948798 --3.206070 54.949091 --3.199030 54.949091 --3.191989 54.948211 --3.186415 54.946744 --3.186415 54.942637 --3.185829 54.938824 --3.178201 54.938824 --3.172628 54.939704 --3.165587 54.938824 --3.159427 54.937357 --3.155026 54.935597 --3.148866 54.934130 --3.144466 54.932077 --3.140065 54.929730 --3.136252 54.927089 --3.131265 54.925329 --3.125104 54.925623 --3.119237 54.926796 --3.112783 54.926209 --3.107503 54.924449 --3.102223 54.922689 --3.095182 54.921809 --3.089315 54.922689 --3.084915 54.925036 --3.080514 54.927089 --3.076994 54.929436 --3.072594 54.931490 --3.068194 54.933250 --3.063500 54.935597 --3.059393 54.937357 --3.053233 54.938530 --3.046192 54.938530 --3.039151 54.938530 --3.032404 54.938824 --3.025951 54.939410 --3.022137 54.942051 --3.022137 54.946158 --3.025070 54.949091 --3.029177 54.951145 --3.037098 54.951731 --3.043552 54.951145 --3.049419 54.950264 --3.055579 54.949091 --3.060566 54.947918 --3.066140 54.946744 --3.073474 54.946744 --3.076114 54.949678 --3.074647 54.952905 --3.071714 54.955838 --3.068487 54.958772 --3.065553 54.961999 --3.062033 54.964345 --3.056166 54.965226 --3.049126 54.964345 --3.043845 54.962879 --3.036805 54.961999 --3.029764 54.960825 --3.022430 54.960825 --3.017150 54.962585 --3.013630 54.964932 --3.011283 54.968746 --3.009816 54.972559 --3.008936 54.976960 --3.008936 54.981067 --3.010696 54.984587 --3.015096 54.986640 --3.021844 54.987520 --3.029177 54.987520 --3.035338 54.986640 --3.040325 54.984880 --3.045312 54.983707 --3.050592 54.981947 --3.054993 54.979893 --3.059393 54.978133 --3.063500 54.976080 --3.068780 54.974320 --3.073767 54.973146 --3.080221 54.972559 --3.087848 54.972559 --3.095476 54.973146 --3.101929 54.972559 --3.107796 54.971386 --3.113077 54.969919 --3.118064 54.968746 --3.122464 54.966399 --3.127745 54.964932 --3.133612 54.963759 --3.140065 54.963465 --3.146226 54.964639 --3.151506 54.966399 --3.157373 54.967866 --3.164414 54.968746 --3.172628 54.969039 --3.180548 54.969626 --3.188469 54.970213 --3.195509 54.970213 --3.202257 54.969626 --3.208124 54.968746 --3.213111 54.967279 --3.218978 54.966106 --3.225138 54.965812 --3.231885 54.965226 --3.238339 54.964639 --3.243326 54.963172 --3.250073 54.962879 --3.257114 54.962879 --3.263274 54.963759 --3.267675 54.966106 --3.272075 54.968746 --3.277355 54.970213 --3.284396 54.971386 --3.292610 54.971679 --3.299357 54.972853 --3.305517 54.974026 --3.311678 54.975200 --3.317838 54.976666 --3.324879 54.977546 --3.329866 54.976080 --3.334559 54.974026 --3.339840 54.972559 --3.346000 54.971973 --3.353334 54.971973 --3.360668 54.971973 --3.368295 54.972559 --3.376509 54.973146 --3.383550 54.974026 --3.390297 54.974613 --3.395870 54.976373 --3.401151 54.978133 --3.406431 54.979893 --3.410832 54.981947 --3.415232 54.984294 --3.420219 54.985760 --3.425793 54.987520 --3.432833 54.988401 --3.440460 54.988987 --3.444861 54.986934 --3.447501 54.983414 --3.451021 54.980773 --3.456888 54.979600 --3.462169 54.981360 --3.468916 54.981360 --3.475076 54.980773 --3.478890 54.983414 --3.482117 54.985760 --3.487690 54.985760 --3.494144 54.986054 --3.497664 54.988694 --3.502358 54.990747 --3.508519 54.991041 --3.512332 54.988694 --3.511159 54.984880 --3.511159 54.980773 --3.516439 54.979307 --3.519959 54.976666 --3.521133 54.972266 --3.525240 54.970213 --3.531694 54.969626 --3.536387 54.970799 --3.539027 54.974026 --3.542548 54.976373 --3.545188 54.979307 --3.549001 54.981653 --3.551348 54.984587 --3.555749 54.986640 --3.560149 54.988987 --3.565429 54.990454 --3.571003 54.991334 --3.571883 54.986934 --3.573643 54.982827 --3.575110 54.978720 --3.577750 54.975493 --3.580390 54.972266 --3.580977 54.967572 --3.578337 54.964639 --3.575110 54.962292 --3.572176 54.959065 --3.570416 54.955838 --3.570416 54.951731 --3.571883 54.947918 --3.574230 54.944104 --3.575697 54.939997 --3.576577 54.935597 --3.578924 54.932077 --3.580390 54.927970 --3.577457 54.925036 --3.573350 54.922983 --3.568950 54.920929 --3.566016 54.917702 --3.567189 54.913302 --3.567776 54.908902 --3.567776 54.904795 --3.567776 54.900688 --3.568656 54.895701 --3.569536 54.891300 --3.573937 54.889540 --3.578924 54.887780 --3.583911 54.886313 --3.587724 54.883966 --3.590658 54.880739 --3.592711 54.877219 --3.595351 54.873699 --3.599752 54.871646 --3.606792 54.871646 --3.611193 54.873699 --3.615593 54.875752 --3.622047 54.877219 --3.628794 54.878099 --3.636128 54.878099 --3.643168 54.878099 --3.650209 54.877806 --3.656956 54.877513 --3.664290 54.877219 --3.671330 54.877219 --3.678371 54.878393 --3.683651 54.879859 --3.688931 54.881620 --3.695972 54.881620 --3.701252 54.879859 --3.706533 54.878686 --3.710640 54.876339 --3.714453 54.873992 --3.718854 54.871939 --3.722081 54.869299 --3.725894 54.866952 --3.730294 54.864605 --3.734695 54.862845 --3.738802 54.860498 --3.743202 54.858738 --3.748482 54.857271 --3.754936 54.856684 --3.762270 54.856684 --3.769311 54.856391 --3.775471 54.857858 --3.781631 54.859031 --3.787205 54.860791 --3.793366 54.861965 --3.800406 54.863138 --3.807447 54.862845 --3.811554 54.860791 --3.809207 54.858151 --3.808913 54.855218 --3.805100 54.854338 --3.807153 54.850817 --3.812140 54.849351 --3.817421 54.850231 --3.821821 54.852284 --3.823874 54.855511 --3.825635 54.859031 --3.827395 54.862258 --3.827395 54.866365 --3.825635 54.869885 --3.822994 54.873699 --3.819474 54.876046 --3.814781 54.875752 --3.811260 54.873406 --3.808327 54.871059 --3.808620 54.874579 --3.811847 54.876926 --3.815661 54.879566 --3.820941 54.878099 --3.822994 54.874579 --3.825928 54.871352 --3.827981 54.867832 --3.830328 54.864312 --3.836195 54.863432 --3.842356 54.862845 --3.846169 54.859911 --3.845289 54.856391 --3.842649 54.853458 --3.840889 54.850231 --3.842943 54.846710 --3.849690 54.846124 --3.855263 54.844950 --3.857610 54.842603 --3.852037 54.840550 --3.849396 54.837910 --3.847636 54.834389 --3.843823 54.832043 --3.837662 54.830576 --3.831795 54.829402 --3.827395 54.827349 --3.824755 54.824415 --3.825635 54.820895 --3.828862 54.817962 --3.833262 54.816202 --3.838249 54.814441 --3.844703 54.814148 --3.852037 54.813855 --3.858490 54.813268 --3.864064 54.812388 --3.867291 54.809454 --3.869344 54.805934 --3.874331 54.804174 --3.880199 54.803294 --3.884305 54.801240 --3.888999 54.799187 --3.893399 54.797133 --3.898387 54.795667 --3.904254 54.794493 --3.908361 54.792440 --3.913641 54.790973 --3.917161 54.788333 --3.920975 54.785693 --3.925375 54.783933 --3.929482 54.781586 --3.934469 54.780412 --3.939749 54.778652 --3.944150 54.776599 --3.947377 54.774252 --3.950017 54.770438 --3.953244 54.768091 --3.959111 54.766918 --3.964978 54.765745 --3.972312 54.765745 --3.979352 54.765745 --3.985513 54.766918 --3.991673 54.768385 --3.997834 54.769558 --4.000000 54.769829 -nan nan --1.588221 59.551821 --1.593501 59.550061 --1.599955 59.548888 --1.605235 59.546834 --1.608755 59.544194 --1.610516 59.540087 --1.610516 59.536860 --1.605822 59.534807 --1.599661 59.532753 --1.599661 59.529820 --1.606409 59.528646 --1.612276 59.527180 --1.615796 59.524246 --1.617849 59.520139 --1.621956 59.517792 --1.625477 59.514859 --1.628117 59.511339 --1.631930 59.508405 --1.639264 59.508112 --1.645131 59.509578 --1.645131 59.513099 --1.642198 59.516326 --1.645131 59.519552 --1.648065 59.522193 --1.650118 59.525420 --1.648065 59.529820 --1.645131 59.533047 --1.642198 59.536567 --1.639851 59.540381 --1.636918 59.543608 --1.634864 59.547421 --1.632224 59.551235 --1.626357 59.552408 --1.619023 59.552995 --1.613449 59.554462 --1.607582 59.555928 --1.600835 59.556808 --1.592621 59.556808 --1.585580 59.555342 --1.584700 59.552408 --1.588221 59.551821 -nan nan --2.372944 59.384023 --2.378811 59.382556 --2.384678 59.381089 --2.388785 59.378742 --2.391718 59.374929 --2.394065 59.371409 --2.396705 59.368182 --2.397879 59.364368 --2.395825 59.361141 --2.390838 59.358794 --2.387025 59.356447 --2.387905 59.353514 --2.394945 59.352927 --2.400812 59.351754 --2.406386 59.350287 --2.414013 59.349700 --2.417827 59.352340 --2.422521 59.354394 --2.430441 59.354394 --2.438068 59.354101 --2.442762 59.356154 --2.442175 59.359674 --2.438068 59.362315 --2.433668 59.364661 --2.430148 59.367888 --2.429268 59.372289 --2.429268 59.376396 --2.427214 59.380502 --2.423987 59.383729 --2.417240 59.384316 --2.409906 59.384903 --2.402572 59.385196 --2.397879 59.387250 --2.392598 59.389303 --2.388198 59.391650 --2.383211 59.393997 --2.378224 59.395757 --2.372357 59.394877 --2.368250 59.392530 --2.364436 59.389890 --2.366197 59.386663 --2.372944 59.384023 -nan nan --2.398466 59.279002 --2.405799 59.278709 --2.412547 59.279589 --2.419587 59.281055 --2.427508 59.282229 --2.432495 59.280175 --2.438068 59.278709 --2.445402 59.278415 --2.452443 59.277828 --2.459190 59.276655 --2.465057 59.275188 --2.468577 59.272255 --2.469164 59.268734 --2.469164 59.264334 --2.473564 59.262281 --2.479138 59.260521 --2.484418 59.258467 --2.486178 59.254653 --2.487939 59.250546 --2.491459 59.247613 --2.495566 59.244973 --2.496446 59.241453 --2.494686 59.237932 --2.495566 59.233532 --2.498793 59.230598 --2.504953 59.229132 --2.511994 59.229425 --2.515514 59.232359 --2.517567 59.235879 --2.517274 59.239986 --2.516394 59.244386 --2.515221 59.248786 --2.512874 59.252600 --2.511700 59.256120 --2.517274 59.256414 --2.521088 59.253773 --2.525488 59.251720 --2.529008 59.248493 --2.529302 59.244386 --2.529595 59.240866 --2.533995 59.238226 --2.540449 59.237346 --2.547783 59.237052 --2.554530 59.235879 --2.558637 59.233239 --2.561864 59.230305 --2.563037 59.225905 --2.567144 59.223265 --2.574185 59.223558 --2.577118 59.226785 --2.577118 59.230892 --2.574478 59.234412 --2.571251 59.237346 --2.567438 59.240279 --2.570958 59.242333 --2.577118 59.242333 --2.581812 59.240279 --2.585626 59.237346 --2.588853 59.234119 --2.596186 59.233825 --2.601173 59.235879 --2.607040 59.237639 --2.614081 59.237346 --2.620535 59.236172 --2.624935 59.233532 --2.627575 59.230305 --2.629335 59.226198 --2.633736 59.223558 --2.636963 59.220918 --2.639603 59.217104 --2.644003 59.214757 --2.648697 59.212704 --2.653684 59.210650 --2.656324 59.207130 --2.657204 59.202436 --2.660431 59.199796 --2.666591 59.200676 --2.671578 59.202436 --2.677739 59.203316 --2.680966 59.200090 --2.681259 59.195689 --2.680672 59.192169 --2.678326 59.188942 --2.680379 59.184835 --2.685953 59.184248 --2.689766 59.186595 --2.691527 59.190115 --2.692407 59.193929 --2.693580 59.197449 --2.692407 59.201850 --2.692407 59.206250 --2.692407 59.210357 --2.690646 59.214464 --2.686246 59.216811 --2.684486 59.220918 --2.680672 59.223265 --2.674512 59.224731 --2.668938 59.226491 --2.663071 59.227665 --2.658377 59.229718 --2.654271 59.232359 --2.651337 59.235879 --2.648697 59.239399 --2.646057 59.242919 --2.641070 59.244679 --2.636963 59.247320 --2.631976 59.249373 --2.628162 59.252013 --2.622882 59.253773 --2.617308 59.255240 --2.609974 59.255827 --2.602640 59.256120 --2.597066 59.257880 --2.597066 59.260814 --2.599707 59.263747 --2.599120 59.266681 --2.594133 59.268734 --2.593253 59.273135 --2.596480 59.275188 --2.599120 59.278122 --2.602934 59.280469 --2.607040 59.283109 --2.608801 59.286336 --2.605574 59.289563 --2.599707 59.291029 --2.592666 59.290443 --2.585626 59.291029 --2.578878 59.291909 --2.574771 59.294550 --2.566558 59.294550 --2.561277 59.296310 --2.559224 59.300123 --2.555410 59.303057 --2.549250 59.303937 --2.541622 59.304524 --2.534582 59.305110 --2.526368 59.305110 --2.520501 59.303057 --2.519328 59.299537 --2.523141 59.296310 --2.527835 59.294550 --2.533115 59.292496 --2.539569 59.291323 --2.543676 59.288976 --2.544556 59.285162 --2.546023 59.282229 --2.553357 59.281642 --2.559224 59.280175 --2.563331 59.277828 --2.566851 59.274602 --2.570078 59.271668 --2.573598 59.268734 --2.571545 59.265214 --2.565678 59.264334 --2.559810 59.266094 --2.554237 59.267561 --2.546023 59.266681 --2.539569 59.265214 --2.531942 59.265508 --2.527835 59.268441 --2.523141 59.270201 --2.517861 59.272255 --2.513167 59.274308 --2.508180 59.276068 --2.503486 59.278709 --2.498793 59.280469 --2.493806 59.282522 --2.488819 59.284869 --2.483832 59.286629 --2.478258 59.288096 --2.472978 59.289856 --2.465057 59.289856 --2.457136 59.289269 --2.450096 59.289563 --2.443349 59.290443 --2.438655 59.292496 --2.435135 59.295430 --2.433961 59.300123 --2.432788 59.304524 --2.429561 59.307457 --2.424574 59.309511 --2.419587 59.311564 --2.414307 59.313618 --2.407266 59.313911 --2.402279 59.312738 --2.399932 59.310391 --2.398759 59.306577 --2.397292 59.303350 --2.397292 59.299243 --2.399052 59.295136 --2.399932 59.291323 --2.396999 59.288683 --2.394065 59.285456 --2.390252 59.283109 --2.389958 59.279589 --2.396119 59.278415 --2.398466 59.279002 -nan nan --2.541329 59.116190 --2.545143 59.113550 --2.550423 59.111790 --2.552183 59.107390 --2.552477 59.103283 --2.549543 59.100642 --2.547490 59.097122 --2.542796 59.095069 --2.534875 59.093895 --2.526955 59.093895 --2.519034 59.093895 --2.514927 59.091255 --2.518447 59.088322 --2.521674 59.085681 --2.525781 59.082748 --2.529888 59.080401 --2.534875 59.078347 --2.541036 59.079228 --2.545729 59.081281 --2.553650 59.082161 --2.559517 59.080694 --2.563624 59.078347 --2.570078 59.077467 --2.577998 59.077467 --2.583865 59.075707 --2.589733 59.074534 --2.594426 59.072480 --2.598533 59.074241 --2.597653 59.078641 --2.595893 59.082748 --2.595893 59.086561 --2.596773 59.090668 --2.598240 59.093895 --2.601467 59.096535 --2.605280 59.099176 --2.612027 59.100642 --2.619948 59.101522 --2.625815 59.103283 --2.631682 59.105043 --2.638136 59.104163 --2.644003 59.102403 --2.648110 59.100056 --2.648697 59.097416 --2.646643 59.094189 --2.644590 59.090962 --2.644003 59.086855 --2.644883 59.082454 --2.646643 59.078347 --2.650750 59.075707 --2.656324 59.075414 --2.662191 59.076881 --2.668645 59.076001 --2.674512 59.074827 --2.682433 59.075414 --2.685366 59.078641 --2.685073 59.082454 --2.683313 59.086561 --2.680086 59.089788 --2.675979 59.092135 --2.672459 59.095362 --2.669818 59.098589 --2.667178 59.102109 --2.664538 59.105923 --2.661898 59.109150 --2.657791 59.111790 --2.649870 59.111790 --2.641950 59.110910 --2.634029 59.109736 --2.626109 59.109736 --2.620241 59.111497 --2.616134 59.113550 --2.615254 59.118244 --2.617015 59.121764 --2.618775 59.124991 --2.622002 59.127924 --2.627869 59.129684 --2.633736 59.131445 --2.637549 59.133791 --2.640190 59.137018 --2.640190 59.140832 --2.642243 59.144059 --2.646937 59.146406 --2.654271 59.147872 --2.660431 59.149046 --2.666591 59.150806 --2.663658 59.153153 --2.657791 59.154326 --2.649577 59.154326 --2.643123 59.155206 --2.637549 59.156966 --2.631976 59.158433 --2.626109 59.159607 --2.618188 59.159607 --2.613788 59.157260 --2.613201 59.153740 --2.614961 59.149339 --2.615841 59.145819 --2.609974 59.144059 --2.602053 59.143472 --2.593840 59.143179 --2.586799 59.143472 --2.578878 59.143472 --2.571251 59.142885 --2.571251 59.138485 --2.571545 59.140245 --2.577412 59.142299 --2.583572 59.141125 --2.588853 59.139072 --2.592079 59.136138 --2.595306 59.134085 --2.597653 59.130565 --2.598827 59.126164 --2.597360 59.122644 --2.593253 59.120004 --2.588266 59.117950 --2.581812 59.116777 --2.574185 59.117364 --2.567438 59.117950 --2.561864 59.119710 --2.555410 59.120591 --2.549250 59.121764 --2.542503 59.122644 --2.535462 59.121177 --2.534582 59.117364 --2.541329 59.116190 -nan nan --2.803881 59.079228 --2.805641 59.075414 --2.807402 59.071014 --2.811215 59.068080 --2.813562 59.064853 --2.816202 59.061040 --2.818549 59.057519 --2.821483 59.054292 --2.824709 59.051066 --2.823536 59.047252 --2.819722 59.044612 --2.812975 59.043732 --2.809162 59.040798 --2.807108 59.037571 --2.808868 59.033758 --2.810922 59.029651 --2.812389 59.025544 --2.815909 59.022610 --2.820896 59.020557 --2.827350 59.020557 --2.832043 59.022610 --2.835857 59.024957 --2.841724 59.027010 --2.848764 59.027304 --2.856685 59.028477 --2.864312 59.029064 --2.871646 59.028477 --2.877513 59.027304 --2.883380 59.028771 --2.888074 59.031117 --2.894234 59.032878 --2.900395 59.033758 --2.905969 59.031997 --2.910662 59.029944 --2.916823 59.029064 --2.924743 59.029944 --2.928850 59.032584 --2.928557 59.036691 --2.925623 59.039625 --2.922103 59.042852 --2.919463 59.046078 --2.918289 59.050772 --2.915943 59.054292 --2.914183 59.058399 --2.912129 59.062213 --2.907435 59.064266 --2.903328 59.066613 --2.900102 59.069840 --2.895995 59.071307 --2.895701 59.068373 --2.895701 59.064266 --2.893941 59.060746 --2.888074 59.058986 --2.879273 59.058693 --2.871059 59.058693 --2.862259 59.058106 --2.855218 59.057519 --2.848764 59.058693 --2.843191 59.059866 --2.839671 59.063093 --2.836444 59.066027 --2.835564 59.070427 --2.834390 59.075121 --2.832630 59.079228 --2.827643 59.080988 --2.822069 59.082748 --2.815615 59.083628 --2.808282 59.083041 --2.807402 59.079521 --2.803881 59.079228 -nan nan --2.687713 58.955432 --2.690940 58.952498 --2.694460 58.949565 --2.699154 58.947511 --2.702087 58.943991 --2.704727 58.940471 --2.707661 58.937537 --2.709715 58.933430 --2.708541 58.929617 --2.705901 58.926683 --2.700914 58.924630 --2.699154 58.921403 --2.702381 58.918469 --2.709715 58.917883 --2.716755 58.919056 --2.723209 58.920523 --2.731129 58.921403 --2.739930 58.921990 --2.746384 58.920816 --2.751077 58.918763 --2.758705 58.918469 --2.765452 58.918176 --2.771319 58.916416 --2.776306 58.914362 --2.781293 58.912602 --2.784813 58.909375 --2.787747 58.906442 --2.791267 58.903508 --2.793907 58.899988 --2.796254 58.896468 --2.800654 58.893828 --2.807108 58.892947 --2.811802 58.890894 --2.812975 58.886494 --2.812975 58.882093 --2.815615 58.878573 --2.820602 58.876813 --2.827056 58.875933 --2.832923 58.877400 --2.836737 58.880040 --2.840551 58.882387 --2.844071 58.885027 --2.848178 58.887374 --2.851991 58.890014 --2.856978 58.892361 --2.861965 58.894414 --2.867833 58.896174 --2.875460 58.897054 --2.882500 58.896761 --2.889247 58.895588 --2.894821 58.894121 --2.900395 58.892361 --2.906262 58.891187 --2.912422 58.890014 --2.918289 58.891774 --2.921516 58.894708 --2.923277 58.897935 --2.924157 58.901748 --2.927090 58.904682 --2.930904 58.907322 --2.935891 58.909375 --2.937651 58.912896 --2.939704 58.916122 --2.942638 58.918763 --2.946745 58.921403 --2.951439 58.923750 --2.953199 58.926977 --2.955252 58.930204 --2.954959 58.934310 --2.956132 58.938124 --2.956132 58.942231 --2.954372 58.946338 --2.952612 58.950152 --2.951439 58.954845 --2.954372 58.957779 --2.959066 58.960419 --2.965226 58.960419 --2.970507 58.958366 --2.975200 58.956312 --2.980187 58.954259 --2.984294 58.951618 --2.988401 58.949272 --2.993095 58.947218 --2.998375 58.944578 --3.003949 58.943404 --3.009816 58.941644 --3.015976 58.940764 --3.022430 58.939591 --3.029177 58.939004 --3.035338 58.937831 --3.042085 58.936657 --3.049126 58.936071 --3.057339 58.936071 --3.065847 58.936657 --3.073474 58.937831 --3.079928 58.936657 --3.079048 58.934017 --3.074061 58.931670 --3.071420 58.929030 --3.074354 58.925803 --3.078461 58.924923 --3.085501 58.924630 --3.091369 58.926390 --3.097236 58.928150 --3.103983 58.929323 --3.110143 58.928443 --3.115424 58.926390 --3.119531 58.923750 --3.119531 58.919643 --3.117477 58.916416 --3.120704 58.913189 --3.125984 58.914362 --3.132732 58.915829 --3.140652 58.917003 --3.148279 58.917003 --3.155026 58.915829 --3.160600 58.914069 --3.166467 58.912896 --3.172041 58.911429 --3.176735 58.913189 --3.183188 58.912602 --3.188469 58.910255 --3.194923 58.911722 --3.199910 58.913776 --3.204603 58.915829 --3.208710 58.918469 --3.212817 58.920816 --3.218684 58.922870 --3.222498 58.925216 --3.224551 58.928737 --3.226312 58.931964 --3.228365 58.935191 --3.230419 58.938711 --3.231005 58.942231 --3.232179 58.945751 --3.232179 58.949858 --3.231005 58.954845 --3.231005 58.958659 --3.233059 58.961886 --3.235992 58.965113 --3.238926 58.967753 --3.240099 58.971566 --3.238926 58.975967 --3.235699 58.979194 --3.231299 58.981541 --3.226898 58.983594 --3.222498 58.986528 --3.221618 58.989754 --3.222791 58.992688 --3.218978 58.995328 --3.214577 58.997675 --3.211351 59.000902 --3.207244 59.003249 --3.204603 59.006769 --3.207830 59.009703 --3.214577 59.011169 --3.219564 59.012929 --3.221325 59.016450 --3.221325 59.020557 --3.220445 59.025250 --3.222498 59.028477 --3.224551 59.031997 --3.230419 59.032584 --3.235992 59.031117 --3.240979 59.029064 --3.245086 59.026717 --3.248313 59.023490 --3.249193 59.019970 --3.246260 59.017036 --3.242446 59.014396 --3.239219 59.011756 --3.241859 59.007942 --3.248900 59.008236 --3.255060 59.009996 --3.260927 59.012049 --3.269435 59.012343 --3.275888 59.011463 --3.272955 59.008236 --3.267968 59.006476 --3.264154 59.003835 --3.261221 59.000902 --3.261221 58.996795 --3.264741 58.993568 --3.267675 58.990635 --3.271195 58.987701 --3.271782 58.985061 --3.267088 58.983594 --3.259461 58.984181 --3.253300 58.983301 --3.252420 58.979780 --3.254180 58.975673 --3.258287 58.973033 --3.261221 58.969806 --3.264154 58.966579 --3.267381 58.963646 --3.271488 58.961006 --3.279409 58.961006 --3.287036 58.960419 --3.291730 58.958659 --3.293196 58.954552 --3.290556 58.951618 --3.290556 58.947511 --3.296130 58.945751 --3.303464 58.946338 --3.308157 58.948391 --3.313144 58.950445 --3.316958 58.953085 --3.319598 58.956019 --3.323705 58.958659 --3.328692 58.960419 --3.334559 58.962179 --3.340133 58.963939 --3.345413 58.965993 --3.347174 58.969513 --3.349520 58.972740 --3.351281 58.975967 --3.352161 58.979780 --3.353334 58.983594 --3.354214 58.987114 --3.357148 58.990341 --3.361255 58.992688 --3.363015 58.996208 --3.363015 59.000315 --3.363895 59.003835 --3.365068 59.007356 --3.368002 59.010583 --3.368002 59.014690 --3.366242 59.018503 --3.364482 59.022903 --3.364482 59.027010 --3.363895 59.030531 --3.359788 59.033171 --3.355681 59.035518 --3.353921 59.039331 --3.354801 59.043438 --3.355974 59.046959 --3.350694 59.049305 --3.345413 59.050479 --3.341893 59.053706 --3.343947 59.056053 --3.346880 59.058986 --3.349814 59.061920 --3.351867 59.065147 --3.353041 59.068960 --3.353041 59.073067 --3.353041 59.077174 --3.353041 59.081281 --3.353041 59.085681 --3.351867 59.090082 --3.351867 59.094189 --3.350987 59.098589 --3.350987 59.102696 --3.350987 59.106803 --3.350401 59.110616 --3.344827 59.112083 --3.337493 59.112377 --3.331626 59.114137 --3.325759 59.115603 --3.322825 59.118537 --3.321065 59.122644 --3.321065 59.126751 --3.317545 59.129684 --3.311384 59.130858 --3.304637 59.132031 --3.299063 59.133205 --3.293196 59.134672 --3.287623 59.136432 --3.282636 59.138192 --3.277649 59.140245 --3.272075 59.142005 --3.265034 59.142592 --3.257407 59.142885 --3.251247 59.143765 --3.245380 59.145232 --3.238926 59.146406 --3.232472 59.147579 --3.225725 59.148753 --3.218978 59.148753 --3.210470 59.148753 --3.202550 59.148753 --3.195509 59.147872 --3.190522 59.145526 --3.185829 59.143472 --3.179962 59.141712 --3.172921 59.140245 --3.168227 59.138192 --3.163240 59.136138 --3.159427 59.133498 --3.153560 59.132031 --3.146519 59.130565 --3.138599 59.129684 --3.133905 59.127631 --3.130091 59.124991 --3.125104 59.122937 --3.120117 59.120884 --3.114250 59.119124 --3.108383 59.117364 --3.100169 59.116484 --3.094595 59.117950 --3.089608 59.120004 --3.084035 59.121471 --3.076994 59.122057 --3.073181 59.119417 --3.073181 59.115310 --3.071127 59.112083 --3.065260 59.110323 --3.059393 59.108563 --3.055579 59.106216 --3.052646 59.102989 --3.053233 59.099469 --3.057633 59.096829 --3.063793 59.096242 --3.067900 59.094482 --3.062913 59.092135 --3.057926 59.090082 --3.053819 59.087441 --3.052352 59.084215 --3.047365 59.082161 --3.043845 59.080988 --3.036218 59.080108 --3.028884 59.080694 --3.020964 59.080694 --3.015096 59.078934 --3.010696 59.077174 --3.005709 59.075414 --3.001895 59.072774 --2.998082 59.070134 --2.994855 59.067200 --3.002482 59.066613 --3.005416 59.064853 --3.001602 59.061920 --2.998962 59.059279 --2.995735 59.056053 --2.997202 59.053119 --3.003949 59.052239 --3.010403 59.051066 --3.016857 59.049892 --3.020377 59.046959 --3.019203 59.043438 --3.023310 59.040798 --3.030644 59.040211 --3.036511 59.041972 --3.040325 59.044612 --3.045312 59.046665 --3.051179 59.048425 --3.058220 59.048132 --3.063207 59.045785 --3.065847 59.042558 --3.064967 59.038745 --3.064967 59.034344 --3.067607 59.031117 --3.069367 59.027010 --3.073474 59.024370 --3.080514 59.023784 --3.087262 59.023197 --3.091075 59.020557 --3.094302 59.017623 --3.099582 59.015570 --3.103689 59.012636 --3.107796 59.010289 --3.110143 59.007062 --3.114250 59.004422 --3.120704 59.003249 --3.128038 59.002662 --3.133905 59.001489 --3.130091 58.998848 --3.125984 58.996502 --3.118064 58.995328 --3.110143 58.994448 --3.102223 58.994448 --3.094302 58.993568 --3.089608 58.991515 --3.083741 58.989754 --3.078754 58.987408 --3.073181 58.985941 --3.065260 58.985061 --3.057339 58.985061 --3.051472 58.986528 --3.046779 58.988288 --3.043258 58.991515 --3.042085 58.996208 --3.041498 59.000609 --3.040325 59.005009 --3.036805 59.007942 --3.031524 59.009409 --3.025364 59.011169 --3.018323 59.011756 --3.010989 59.012343 --3.002189 59.011756 --2.998375 59.009116 --2.994562 59.006769 --2.990455 59.003835 --2.987521 59.001195 --2.983708 58.998555 --2.979014 58.996502 --2.971973 58.995035 --2.964053 58.994155 --2.955252 58.993568 --2.949678 58.995328 --2.947038 58.998555 --2.946158 59.002955 --2.944985 59.007649 --2.942638 59.011463 --2.938531 59.008822 --2.934424 59.006182 --2.928557 59.005302 --2.922690 59.007062 --2.916529 59.007649 --2.911249 59.006769 --2.910369 59.002662 --2.909489 58.999142 --2.909782 58.995035 --2.908609 58.991515 --2.907729 58.987408 --2.902742 58.985647 --2.895701 58.986234 --2.890127 58.987408 --2.885140 58.989461 --2.879860 58.991515 --2.876927 58.989461 --2.877807 58.985941 --2.881914 58.983301 --2.884554 58.979780 --2.886020 58.976553 --2.883967 58.974793 --2.876046 58.973913 --2.871059 58.971566 --2.865192 58.970100 --2.858152 58.969513 --2.854925 58.972447 --2.852285 58.975967 --2.850525 58.980074 --2.847884 58.983594 --2.843777 58.982714 --2.839671 58.980367 --2.833803 58.978607 --2.827643 58.978607 --2.822656 58.980660 --2.817669 58.982714 --2.812975 58.984767 --2.807108 58.986234 --2.802121 58.987994 --2.796547 58.989754 --2.790094 58.990635 --2.782173 58.989754 --2.778653 58.987114 --2.778653 58.983007 --2.778653 58.978900 --2.779533 58.974500 --2.780706 58.970100 --2.783933 58.966873 --2.791560 58.967753 --2.799481 58.968633 --2.805348 58.967166 --2.811802 58.965993 --2.816789 58.964233 --2.822363 58.962766 --2.828816 58.961592 --2.834390 58.960419 --2.838497 58.957779 --2.839377 58.954259 --2.835564 58.951618 --2.830870 58.949565 --2.827643 58.946631 --2.823829 58.943991 --2.821189 58.941058 --2.814149 58.939591 --2.808575 58.941058 --2.803588 58.943404 --2.798894 58.945165 --2.794787 58.947805 --2.789507 58.949858 --2.783933 58.951032 --2.776893 58.951618 --2.769559 58.952205 --2.761345 58.952205 --2.755771 58.953672 --2.751664 58.956019 --2.749024 58.959832 --2.746677 58.963353 --2.742570 58.965699 --2.734356 58.965699 --2.727609 58.964526 --2.718808 58.963939 --2.712355 58.964819 --2.704434 58.964819 --2.698567 58.963059 --2.692407 58.961299 --2.687713 58.959246 --2.687713 58.955432 -nan nan --2.864606 58.846304 --2.868713 58.844837 --2.873700 58.842784 --2.879860 58.841610 --2.888661 58.842197 --2.897461 58.842784 --2.905382 58.843664 --2.913889 58.844251 --2.920343 58.843371 --2.926503 58.843077 --2.933544 58.843664 --2.940878 58.843077 --2.948505 58.843957 --2.953199 58.846011 --2.953199 58.850411 --2.948505 58.852171 --2.943518 58.854225 --2.937944 58.855691 --2.930024 58.855691 --2.921223 58.855398 --2.913302 58.855398 --2.910662 58.858625 --2.910662 58.862732 --2.907142 58.865959 --2.902155 58.867719 --2.896581 58.869479 --2.891008 58.870946 --2.884260 58.870653 --2.881914 58.867132 --2.884847 58.863612 --2.887194 58.860092 --2.888954 58.856865 --2.888954 58.852758 --2.883087 58.850998 --2.875166 58.850998 --2.869299 58.852465 --2.861672 58.852465 --2.861672 58.848358 --2.864606 58.846304 -nan nan --2.888074 58.816382 --2.894528 58.816382 --2.900688 58.815209 --2.904208 58.812568 --2.906555 58.808755 --2.908315 58.804648 --2.911836 58.801421 --2.916236 58.798781 --2.917996 58.794674 --2.916823 58.791154 --2.914183 58.787927 --2.911249 58.785286 --2.910369 58.781473 --2.914476 58.778833 --2.919170 58.777073 --2.924157 58.775019 --2.926503 58.771499 --2.926503 58.768272 --2.924450 58.765045 --2.920636 58.762405 --2.915943 58.760351 --2.910956 58.758004 --2.908902 58.754778 --2.908902 58.750671 --2.909195 58.746564 --2.910956 58.742457 --2.911836 58.738056 --2.913889 58.733949 --2.918289 58.731896 --2.925917 58.731309 --2.932664 58.731016 --2.939411 58.730136 --2.947918 58.730429 --2.952905 58.732483 --2.957892 58.734829 --2.961706 58.737176 --2.965520 58.739817 --2.970507 58.741870 --2.973147 58.744804 --2.976080 58.747737 --2.979894 58.750377 --2.982827 58.753311 --2.984881 58.756538 --2.985761 58.760351 --2.981654 58.762698 --2.976080 58.764165 --2.972853 58.767098 --2.974614 58.770619 --2.975494 58.774432 --2.976667 58.777953 --2.977547 58.782060 --2.979307 58.785286 --2.986348 58.786460 --2.993975 58.787633 --2.996908 58.790273 --2.997789 58.794087 --3.003656 58.795847 --3.010403 58.797607 --3.015096 58.799661 --3.017150 58.803181 --3.013923 58.806115 --3.007469 58.806115 --3.002776 58.803768 --2.994855 58.803181 --2.986934 58.803181 --2.980481 58.804061 --2.975494 58.806115 --2.970800 58.808168 --2.967573 58.811102 --2.969333 58.814329 --2.973147 58.816969 --2.981947 58.817555 --2.989281 58.816969 --2.994268 58.819022 --2.998962 58.821076 --3.006883 58.821076 --3.012456 58.819609 --3.018323 58.818435 --3.024777 58.817262 --3.031231 58.816382 --3.036805 58.818142 --3.033578 58.820782 --3.028884 58.823129 --3.023604 58.824889 --3.019203 58.826943 --3.014216 58.829290 --3.010109 58.831636 --3.004536 58.833103 --2.997202 58.832516 --2.991335 58.830756 --2.982827 58.830170 --2.978720 58.832810 --2.974614 58.835157 --2.967280 58.835743 --2.959066 58.835743 --2.953199 58.834277 --2.946745 58.832810 --2.940878 58.834570 --2.935304 58.835743 --2.928850 58.836917 --2.922396 58.837797 --2.916236 58.838970 --2.908022 58.838970 --2.899221 58.838384 --2.894234 58.836917 --2.890421 58.834570 --2.886314 58.831930 --2.883674 58.829290 --2.880447 58.826063 --2.877807 58.824303 --2.876633 58.820196 --2.880740 58.817849 --2.888074 58.817555 --2.888074 58.816382 -nan nan --3.043552 58.742163 --3.046485 58.738643 --3.050299 58.736003 --3.055286 58.734243 --3.060860 58.732483 --3.068194 58.731896 --3.069954 58.735416 --3.067607 58.738056 --3.062913 58.740110 --3.058806 58.742457 --3.054699 58.745097 --3.050592 58.747444 --3.043258 58.748030 --3.041498 58.744804 --3.043552 58.742163 -nan nan --3.104863 58.682026 --3.105450 58.678212 --3.107210 58.674105 --3.110143 58.670585 --3.113957 58.667945 --3.120411 58.667358 --3.127451 58.666771 --3.133025 58.665011 --3.141239 58.665011 --3.144759 58.667651 --3.141532 58.670878 --3.138012 58.673518 --3.136252 58.677919 --3.134198 58.681146 --3.129211 58.683199 --3.126278 58.687013 --3.125691 58.691413 --3.120117 58.692880 --3.116010 58.690240 --3.112197 58.687893 --3.110143 58.684373 --3.104863 58.682026 -nan nan --3.155026 58.878573 --3.150333 58.876520 --3.146226 58.873879 --3.145346 58.870359 --3.150333 58.868306 --3.158253 58.868306 --3.165001 58.869479 --3.169988 58.871533 --3.173801 58.874173 --3.175855 58.877400 --3.172921 58.881213 --3.166174 58.881507 --3.161187 58.879453 --3.155026 58.878573 -nan nan --3.155026 58.850411 --3.152973 58.846598 --3.151213 58.843664 --3.150333 58.839850 --3.151800 58.835743 --3.157373 58.834277 --3.165587 58.834277 --3.169401 58.836623 --3.172628 58.839850 --3.175268 58.842491 --3.176441 58.846304 --3.173801 58.849824 --3.169694 58.852171 --3.161774 58.852171 --3.155026 58.850411 -nan nan --3.077874 58.825476 --3.078754 58.820782 --3.078754 58.816675 --3.077874 58.813155 --3.082861 58.811102 --3.089022 58.811982 --3.095769 58.813155 --3.101929 58.812275 --3.107796 58.810515 --3.112783 58.811982 --3.121584 58.812568 --3.128331 58.813742 --3.135078 58.814915 --3.140945 58.816675 --3.143879 58.819609 --3.144759 58.823423 --3.146813 58.826649 --3.144172 58.830170 --3.140065 58.832810 --3.136252 58.835157 --3.132732 58.838384 --3.128625 58.840730 --3.124518 58.843371 --3.116304 58.843371 --3.109557 58.843957 --3.103983 58.845424 --3.096356 58.845717 --3.090782 58.847184 --3.084328 58.848358 --3.077874 58.849531 --3.072007 58.848651 --3.071714 58.845424 --3.075821 58.842784 --3.081688 58.841024 --3.087848 58.840144 --3.094302 58.839264 --3.101636 58.838970 --3.106330 58.836623 --3.108970 58.833397 --3.103983 58.831050 --3.096062 58.831050 --3.089022 58.831636 --3.081101 58.830463 --3.078168 58.827823 --3.077874 58.825476 -nan nan --3.194043 58.850118 --3.197270 58.848064 --3.200496 58.845131 --3.204017 58.841904 --3.206363 58.838384 --3.206363 58.835157 --3.199030 58.834863 --3.191109 58.834863 --3.184362 58.833690 --3.187002 58.829876 --3.189349 58.826356 --3.184362 58.824303 --3.175855 58.824009 --3.169694 58.823129 --3.169694 58.819609 --3.172921 58.816675 --3.177908 58.814622 --3.183188 58.813448 --3.190522 58.812862 --3.195509 58.810222 --3.199616 58.807875 --3.206070 58.806701 --3.212524 58.805528 --3.221031 58.806115 --3.229245 58.806115 --3.235112 58.804648 --3.238926 58.802301 --3.242153 58.799074 --3.245673 58.796141 --3.248020 58.792620 --3.248020 58.788220 --3.240979 58.787340 --3.235699 58.788513 --3.228658 58.789100 --3.221911 58.790273 --3.217218 58.792327 --3.213111 58.794674 --3.209004 58.797314 --3.203430 58.798487 --3.195216 58.798487 --3.188469 58.799074 --3.183188 58.801128 --3.177028 58.802301 --3.170281 58.803474 --3.163240 58.803474 --3.156200 58.804061 --3.149746 58.805235 --3.142119 58.805821 --3.136252 58.804061 --3.134785 58.800834 --3.137132 58.797314 --3.139772 58.793500 --3.137719 58.790273 --3.136839 58.786753 --3.141532 58.784700 --3.147986 58.783526 --3.154440 58.782646 --3.160307 58.781179 --3.168227 58.781179 --3.175268 58.780593 --3.180842 58.779126 --3.188762 58.779126 --3.194629 58.780886 --3.201670 58.782353 --3.210470 58.782646 --3.216044 58.781179 --3.220738 58.779126 --3.225725 58.777366 --3.231299 58.775606 --3.237166 58.776486 --3.245086 58.777366 --3.253007 58.777953 --3.261807 58.778539 --3.269141 58.777953 --3.275302 58.777366 --3.281756 58.776192 --3.288796 58.775606 --3.295837 58.776192 --3.300824 58.777953 --3.303757 58.781179 --3.305517 58.784406 --3.307571 58.787633 --3.310504 58.790567 --3.314318 58.792914 --3.317545 58.796141 --3.319305 58.799367 --3.320185 58.803181 --3.323412 58.806115 --3.327226 58.808755 --3.329866 58.811395 --3.329866 58.815502 --3.331919 58.819022 --3.335146 58.821956 --3.338960 58.824303 --3.343947 58.826356 --3.349814 58.828116 --3.354507 58.830170 --3.357441 58.833397 --3.360668 58.835157 --3.363601 58.838090 --3.366535 58.841024 --3.369469 58.843957 --3.372109 58.846891 --3.375336 58.850118 --3.377976 58.852758 --3.377976 58.856865 --3.375922 58.860385 --3.374749 58.865079 --3.377682 58.867719 --3.384430 58.869186 --3.390883 58.868012 --3.396457 58.866546 --3.403204 58.868012 --3.410245 58.869186 --3.417579 58.868599 --3.426379 58.869186 --3.431073 58.871533 --3.433126 58.874760 --3.433126 58.878866 --3.430486 58.882093 --3.427259 58.885320 --3.424032 58.888254 --3.421392 58.892067 --3.419632 58.895881 --3.418752 58.900575 --3.418165 58.904095 --3.415525 58.907615 --3.412298 58.910549 --3.407311 58.912896 --3.402911 58.915242 --3.397924 58.917296 --3.392057 58.918469 --3.385603 58.919056 --3.377976 58.919643 --3.372402 58.921403 --3.366828 58.922870 --3.361255 58.924336 --3.355974 58.925803 --3.349227 58.926977 --3.343947 58.927563 --3.335439 58.927563 --3.330746 58.925216 --3.329866 58.921696 --3.325759 58.919056 --3.318132 58.918469 --3.314025 58.915829 --3.315198 58.911135 --3.311384 58.908495 --3.305517 58.907029 --3.296717 58.906442 --3.290850 58.904682 --3.285863 58.902922 --3.279995 58.900868 --3.274128 58.899108 --3.269141 58.897054 --3.264448 58.895001 --3.260634 58.892361 --3.254767 58.890894 --3.247726 58.889427 --3.240099 58.888547 --3.233059 58.887080 --3.228365 58.885027 --3.225138 58.882093 --3.222498 58.879160 --3.218684 58.876813 --3.214577 58.874173 --3.216924 58.871533 --3.214871 58.868306 --3.211937 58.866252 --3.210764 58.862439 --3.209004 58.859212 --3.204897 58.856572 --3.198443 58.855398 --3.195216 58.852465 --3.194043 58.850118 -nan nan --3.266501 58.927857 --3.268848 58.924043 --3.274422 58.922870 --3.281756 58.922283 --3.289383 58.923163 --3.296423 58.924336 --3.302290 58.926097 --3.307277 58.928150 --3.309038 58.931377 --3.306397 58.934897 --3.300824 58.936364 --3.295837 58.935191 --3.290850 58.933430 --3.282929 58.932257 --3.274128 58.931964 --3.269435 58.929617 --3.266501 58.927857 -nan nan --2.964933 59.081281 --2.964053 59.078641 --2.963759 59.075414 --2.969333 59.073947 --2.975200 59.075414 --2.982241 59.076881 --2.990161 59.077761 --2.996028 59.079814 --2.999842 59.082161 --2.995735 59.084801 --2.989281 59.085681 --2.981947 59.085975 --2.974614 59.086561 --2.966693 59.086561 --2.964639 59.083334 --2.964933 59.081281 -nan nan --2.961413 59.169874 --2.967280 59.168407 --2.972853 59.166940 --2.979014 59.165180 --2.981947 59.162247 --2.981947 59.158433 --2.979894 59.154913 --2.978427 59.151686 --2.975200 59.148753 --2.972560 59.145819 --2.970507 59.142592 --2.969333 59.138485 --2.969333 59.134378 --2.973733 59.132031 --2.978720 59.129978 --2.983414 59.127924 --2.988988 59.126458 --2.994855 59.124991 --3.000429 59.123524 --3.007763 59.122937 --3.015096 59.122644 --3.023897 59.122937 --3.032698 59.123524 --3.040032 59.122937 --3.047952 59.122937 --3.053819 59.124697 --3.058806 59.127044 --3.063500 59.129098 --3.069367 59.130858 --3.075527 59.132618 --3.080221 59.134672 --3.085208 59.136725 --3.089022 59.139072 --3.091075 59.142592 --3.094302 59.145526 --3.097822 59.148166 --3.103983 59.149633 --3.110143 59.151393 --3.113957 59.154033 --3.114837 59.157847 --3.117770 59.160487 --3.121584 59.163127 --3.122464 59.166940 --3.122464 59.171047 --3.119237 59.174274 --3.115130 59.176621 --3.110143 59.178675 --3.105156 59.180435 --3.101929 59.183662 --3.097822 59.186009 --3.094302 59.189235 --3.089902 59.191582 --3.086968 59.194809 --3.083741 59.197743 --3.079928 59.200676 --3.074647 59.201263 --3.066727 59.200383 --3.058806 59.199503 --3.053819 59.197156 --3.052646 59.194516 --3.051766 59.190702 --3.051179 59.186889 --3.049712 59.184248 --3.047072 59.181315 --3.042085 59.179261 --3.035045 59.177795 --3.026244 59.177208 --3.019497 59.178381 --3.013043 59.179555 --3.007469 59.180728 --3.001602 59.182195 --2.996908 59.184542 --2.991041 59.185715 --2.986054 59.187769 --2.979601 59.188942 --2.973733 59.188062 --2.970800 59.185422 --2.965813 59.183075 --2.959946 59.181315 --2.956132 59.178968 --2.950852 59.177501 --2.952025 59.173101 --2.956719 59.171047 --2.961413 59.169874 -nan nan --2.909782 59.153153 --2.911249 59.149926 --2.914183 59.146406 --2.917116 59.143472 --2.920050 59.139952 --2.922396 59.136432 --2.924450 59.132618 --2.925037 59.128511 --2.928264 59.125871 --2.935011 59.124697 --2.937651 59.127924 --2.939704 59.131151 --2.939704 59.134965 --2.941758 59.138192 --2.943518 59.141712 --2.946745 59.144646 --2.947625 59.148459 --2.949385 59.151686 --2.949385 59.155793 --2.948505 59.160193 --2.944398 59.162834 --2.939118 59.164887 --2.932077 59.165474 --2.925917 59.165474 --2.917996 59.164300 --2.913009 59.162540 --2.910369 59.159313 --2.907142 59.156673 --2.909782 59.153153 -nan nan --2.952612 59.118244 --2.954079 59.115310 --2.956719 59.111790 --2.959946 59.108856 --2.966693 59.107683 --2.972853 59.108563 --2.977547 59.110616 --2.985174 59.111790 --2.991628 59.110616 --2.998375 59.109736 --3.004829 59.108563 --3.012750 59.108563 --3.018910 59.109443 --3.020964 59.112670 --3.016563 59.115310 --3.010403 59.116484 --3.003069 59.116777 --2.996322 59.117657 --2.990748 59.119124 --2.984881 59.120884 --2.979307 59.122351 --2.973733 59.123817 --2.966986 59.124697 --2.958479 59.124111 --2.953199 59.122351 --2.952612 59.118244 -nan nan --2.952612 59.345593 --2.958479 59.344127 --2.963466 59.342366 --2.967573 59.339726 --2.965226 59.336499 --2.962879 59.333272 --2.960533 59.330046 --2.960533 59.325939 --2.965520 59.323885 --2.972267 59.323005 --2.979307 59.322418 --2.985761 59.321245 --2.989868 59.318898 --2.989868 59.315671 --2.981947 59.314791 --2.976960 59.312738 --2.972267 59.310684 --2.964346 59.309804 --2.958479 59.310978 --2.952612 59.310391 --2.950558 59.306871 --2.947625 59.304230 --2.941464 59.303350 --2.934131 59.303644 --2.927090 59.302470 --2.924450 59.299537 --2.921516 59.296603 --2.915063 59.296603 --2.909489 59.298070 --2.903622 59.299830 --2.897168 59.299830 --2.893354 59.297190 --2.890127 59.295136 --2.891301 59.290443 --2.888074 59.287803 --2.881327 59.286336 --2.876340 59.284282 --2.875460 59.280469 --2.874580 59.276655 --2.874580 59.272841 --2.872820 59.269321 --2.865779 59.269028 --2.857565 59.269028 --2.849645 59.268148 --2.843777 59.266094 --2.838790 59.264041 --2.835857 59.261107 --2.833803 59.257880 --2.832923 59.254067 --2.832923 59.249960 --2.837910 59.248200 --2.845831 59.248786 --2.853165 59.249373 --2.858739 59.247906 --2.862846 59.245266 --2.866072 59.242333 --2.868126 59.238226 --2.869886 59.234119 --2.872526 59.230892 --2.877513 59.228545 --2.883967 59.228545 --2.887781 59.231185 --2.887781 59.235292 --2.885140 59.238812 --2.881620 59.242039 --2.879273 59.245266 --2.875753 59.248200 --2.873113 59.252013 --2.873113 59.256120 --2.876927 59.258467 --2.882794 59.260227 --2.888661 59.261987 --2.894528 59.263747 --2.899808 59.265801 --2.904502 59.268148 --2.909489 59.269908 --2.914476 59.272255 --2.918289 59.274602 --2.922983 59.276948 --2.927090 59.279589 --2.932077 59.281642 --2.936771 59.283696 --2.944691 59.284869 --2.951439 59.286336 --2.958479 59.287803 --2.965520 59.288096 --2.971973 59.287216 --2.976374 59.284869 --2.974027 59.281349 --2.967280 59.279882 --2.961413 59.278415 --2.958479 59.275188 --2.961119 59.271668 --2.969040 59.271668 --2.976960 59.272841 --2.983708 59.271668 --2.986054 59.268441 --2.988108 59.264041 --2.992215 59.261694 --2.999255 59.261107 --3.003362 59.263747 --3.005416 59.266974 --3.007176 59.270201 --3.010989 59.272841 --3.018030 59.274308 --3.025070 59.275482 --3.029764 59.277828 --3.030938 59.281349 --3.028297 59.284869 --3.028297 59.288976 --3.030351 59.292203 --3.030058 59.296310 --3.029177 59.301003 --3.030058 59.304817 --3.031818 59.308044 --3.035045 59.310978 --3.040032 59.313031 --3.047072 59.314498 --3.054699 59.315378 --3.061446 59.316551 --3.066727 59.318898 --3.070540 59.321245 --3.073474 59.324178 --3.075527 59.327405 --3.076407 59.331512 --3.071714 59.331512 --3.068487 59.330339 --3.062620 59.328579 --3.056166 59.328872 --3.048832 59.329165 --3.042965 59.327405 --3.037098 59.325939 --3.031524 59.324178 --3.025364 59.325645 --3.021257 59.327992 --3.015096 59.329165 --3.007763 59.327699 --3.002482 59.328285 --2.997202 59.330339 --2.993095 59.332686 --2.989868 59.335913 --2.988988 59.340606 --2.988988 59.344713 --2.988108 59.347940 --2.985174 59.351754 --2.980481 59.353514 --2.974614 59.355274 --2.968453 59.356154 --2.960239 59.355274 --2.954372 59.353514 --2.950265 59.352047 --2.945278 59.349700 --2.947038 59.346767 --2.952612 59.345593 -nan nan --2.869886 59.367888 --2.873406 59.365835 --2.877513 59.363195 --2.881620 59.360848 --2.883674 59.356741 --2.880153 59.353807 --2.878687 59.350580 --2.881033 59.347060 --2.883087 59.342953 --2.881033 59.339726 --2.879860 59.335913 --2.878100 59.332392 --2.876046 59.329165 --2.878687 59.325645 --2.883087 59.323298 --2.888661 59.321538 --2.889834 59.321245 --2.889834 59.321538 --2.896875 59.321245 --2.903915 59.322418 --2.906555 59.325645 --2.902448 59.327992 --2.895995 59.328872 --2.899808 59.329165 --2.907435 59.330339 --2.911249 59.332686 --2.912129 59.336499 --2.913302 59.340313 --2.913302 59.344127 --2.912129 59.348820 --2.909782 59.352340 --2.906849 59.355861 --2.903622 59.358794 --2.899515 59.361434 --2.895408 59.363781 --2.894528 59.367595 --2.896288 59.370822 --2.897461 59.374342 --2.895701 59.377862 --2.892181 59.380502 --2.886607 59.382263 --2.880447 59.381383 --2.875753 59.379036 --2.871646 59.376689 --2.868713 59.373755 --2.869886 59.367888 -nan nan --2.816789 59.219158 --2.815615 59.216517 --2.815615 59.212117 --2.814735 59.208597 --2.814735 59.204490 --2.817376 59.200970 --2.822363 59.198916 --2.819136 59.200970 --2.823829 59.203023 --2.828816 59.205370 --2.828816 59.209477 --2.827643 59.213877 --2.827056 59.218278 --2.825003 59.222384 --2.820309 59.223558 --2.816789 59.219158 -nan nan --2.726729 59.216811 --2.728489 59.212997 --2.732009 59.210064 --2.736996 59.208010 --2.741690 59.205957 --2.743744 59.201850 --2.746090 59.198329 --2.749317 59.195396 --2.753718 59.192756 --2.758998 59.190702 --2.761052 59.187475 --2.760171 59.183662 --2.759291 59.180141 --2.758705 59.176034 --2.757531 59.172514 --2.758705 59.168114 --2.759585 59.163420 --2.758998 59.159607 --2.756651 59.157260 --2.752838 59.154620 --2.744624 59.154620 --2.738757 59.154033 --2.736703 59.150513 --2.737290 59.146992 --2.740810 59.143765 --2.746677 59.142592 --2.753131 59.141419 --2.761052 59.141419 --2.767505 59.140539 --2.774252 59.139365 --2.779826 59.138192 --2.786280 59.137018 --2.788040 59.140245 --2.789214 59.143765 --2.790094 59.147872 --2.790094 59.151979 --2.790974 59.155500 --2.793907 59.158727 --2.797721 59.161073 --2.801534 59.163714 --2.807402 59.165180 --2.812389 59.167527 --2.819429 59.168994 --2.825296 59.170461 --2.827936 59.173394 --2.829110 59.177208 --2.827936 59.180728 --2.825589 59.184542 --2.826763 59.188062 --2.828523 59.191289 --2.824416 59.193929 --2.820309 59.191289 --2.816789 59.188942 --2.811508 59.186595 --2.805641 59.185128 --2.798308 59.185422 --2.792734 59.186889 --2.788627 59.189529 --2.785400 59.192462 --2.782760 59.195689 --2.781293 59.200676 --2.784520 59.203316 --2.788333 59.205957 --2.792147 59.208597 --2.794201 59.211824 --2.795374 59.215637 --2.794201 59.220038 --2.790974 59.222971 --2.792734 59.226491 --2.793614 59.230305 --2.791560 59.234119 --2.790974 59.237639 --2.790974 59.242039 --2.786867 59.244386 --2.781586 59.246440 --2.776013 59.248200 --2.770146 59.249373 --2.763105 59.249960 --2.759291 59.248200 --2.759585 59.244679 --2.763105 59.241746 --2.766625 59.238519 --2.766625 59.234412 --2.762812 59.232065 --2.754891 59.231185 --2.749024 59.232359 --2.741690 59.232945 --2.736996 59.230892 --2.733770 59.227958 --2.732303 59.224731 --2.730249 59.221504 --2.728196 59.217984 --2.726729 59.216811 -nan nan --2.722915 59.244386 --2.718808 59.242919 --2.716168 59.239692 --2.712941 59.236759 --2.713528 59.234119 --2.721742 59.234119 --2.729663 59.234999 --2.735530 59.236759 --2.740517 59.238812 --2.744330 59.241453 --2.744330 59.245559 --2.740810 59.248493 --2.734943 59.249960 --2.728196 59.248493 --2.722915 59.244386 -nan nan --1.774207 55.671623 --1.775967 55.667809 --1.778608 55.664289 --1.783008 55.662236 --1.789462 55.661942 --1.797089 55.662822 --1.802076 55.664582 --1.805596 55.667223 --1.811757 55.668689 --1.819677 55.669276 --1.827891 55.669863 --1.834932 55.670743 --1.841386 55.672210 --1.845786 55.674556 --1.848426 55.677197 --1.846373 55.681304 --1.841972 55.683357 --1.835812 55.684237 --1.829358 55.684824 --1.821437 55.684237 --1.813810 55.683944 --1.805890 55.683357 --1.798556 55.683357 --1.791515 55.682184 --1.785355 55.680717 --1.780955 55.678663 --1.777141 55.676023 --1.774207 55.671623 -nan nan -0.709918 52.977456 -0.715785 52.975696 -0.722532 52.974816 -0.729866 52.974229 -0.734853 52.972176 -0.736026 52.968949 -0.732506 52.966309 -0.726052 52.966015 -0.718718 52.966895 -0.711678 52.966895 -0.706984 52.968949 -0.699357 52.969829 -0.693196 52.969536 -0.687916 52.968069 -0.682342 52.968656 -0.678235 52.970709 -0.677062 52.974229 -0.679995 52.977163 -0.683222 52.978630 -0.689089 52.979510 -0.695837 52.979510 -0.701704 52.977750 -0.709918 52.977456 -nan nan -1.259077 51.880897 -1.256730 51.877084 -1.252917 51.875030 -1.248516 51.872977 -1.244409 51.871217 -1.239716 51.872977 -1.235902 51.875324 -1.235609 51.877084 -1.238542 51.880311 -1.242356 51.882364 -1.247343 51.883831 -1.253210 51.884124 -1.259077 51.883538 -1.259077 51.880897 -nan nan -0.997992 51.780277 -0.993005 51.778810 -0.987724 51.777930 -0.980977 51.778223 -0.975697 51.777637 -0.970123 51.776757 -0.965136 51.775290 -0.959856 51.774703 -0.954869 51.773236 -0.949882 51.772063 -0.944894 51.770596 -0.939614 51.769716 -0.934627 51.768249 -0.929933 51.767076 -0.924360 51.766489 -0.917906 51.766489 -0.912332 51.767956 -0.908225 51.770303 -0.907052 51.773530 -0.909985 51.776757 -0.914386 51.778517 -0.918493 51.780864 -0.923186 51.782917 -0.927293 51.784384 -0.932280 51.785851 -0.936387 51.787904 -0.941374 51.789078 -0.945481 51.790838 -0.951055 51.791718 -0.955749 51.793185 -0.961322 51.793771 -0.967483 51.794065 -0.971296 51.795238 -0.975990 51.795531 -0.982151 51.795825 -0.988898 51.795531 -0.996232 51.794651 -1.001805 51.793478 -1.006499 51.791424 -1.011193 51.789371 -1.014126 51.787024 -1.015593 51.783504 -1.011193 51.781744 -1.005912 51.780864 -1.000338 51.779984 -0.997992 51.780277 -nan nan --1.073677 50.677851 --1.077491 50.676678 --1.082184 50.675211 --1.086291 50.673451 --1.091572 50.672571 --1.096265 50.671104 --1.101252 50.669637 --1.106533 50.668757 --1.111813 50.667877 --1.116800 50.666997 --1.121787 50.665530 --1.127068 50.664357 --1.131175 50.662597 --1.135868 50.661130 --1.139095 50.658490 --1.143202 50.656730 --1.146136 50.653796 --1.149363 50.651449 --1.153176 50.648809 --1.155816 50.645875 --1.158750 50.642942 --1.161683 50.640008 --1.164324 50.637075 --1.166084 50.632968 --1.166964 50.628274 --1.166377 50.624754 --1.165790 50.620940 --1.165790 50.616833 --1.165204 50.613020 --1.164324 50.609500 --1.165790 50.604806 --1.168431 50.601872 --1.172538 50.600112 --1.177231 50.598352 --1.181925 50.596592 --1.186619 50.595419 --1.191312 50.593658 --1.196006 50.592192 --1.200700 50.590725 --1.205393 50.589551 --1.210674 50.588671 --1.215367 50.587205 --1.220941 50.586031 --1.225928 50.585151 --1.231208 50.584564 --1.236782 50.583391 --1.241769 50.582511 --1.247636 50.582218 --1.252917 50.581044 --1.258784 50.580751 --1.264944 50.579871 --1.270811 50.579577 --1.276678 50.579284 --1.282545 50.578991 --1.289293 50.578991 --1.295453 50.578991 --1.301613 50.579871 --1.307481 50.581338 --1.311294 50.583684 --1.315401 50.585738 --1.318041 50.588378 --1.321268 50.590725 --1.325082 50.593658 --1.328015 50.596005 --1.331242 50.598645 --1.335056 50.600699 --1.338869 50.603046 --1.343563 50.605393 --1.349137 50.606566 --1.352657 50.609500 --1.356764 50.611553 --1.359991 50.614193 --1.363511 50.616247 --1.367618 50.618594 --1.373192 50.620060 --1.377006 50.622114 --1.381699 50.623874 --1.387273 50.625341 --1.391967 50.626807 --1.397540 50.628568 --1.402821 50.630034 --1.407514 50.631794 --1.413088 50.632968 --1.418368 50.634435 --1.424236 50.635901 --1.429809 50.637368 --1.434503 50.639128 --1.438317 50.641475 --1.442717 50.642942 --1.446531 50.645289 --1.451518 50.647049 --1.456505 50.648809 --1.460025 50.651156 --1.463838 50.652916 --1.466479 50.656143 --1.469119 50.658490 --1.472932 50.660837 --1.478799 50.662303 --1.484080 50.663477 --1.488774 50.665530 --1.493467 50.667290 --1.499041 50.668757 --1.506375 50.669050 --1.512242 50.668757 --1.518109 50.668464 --1.523389 50.667584 --1.528083 50.666117 --1.533363 50.664944 --1.538057 50.663477 --1.543337 50.662890 --1.548618 50.662010 --1.553312 50.660250 --1.558592 50.659370 --1.563872 50.658490 --1.569153 50.657610 --1.570033 50.660543 --1.565926 50.662597 --1.561525 50.664357 --1.557712 50.666410 --1.554485 50.668757 --1.553605 50.672571 --1.550965 50.675211 --1.545978 50.676971 --1.541284 50.678438 --1.537177 50.680198 --1.535710 50.684305 --1.532483 50.686652 --1.529256 50.689292 --1.526030 50.692225 --1.523389 50.695159 --1.522509 50.699853 --1.519869 50.703080 --1.515175 50.704840 --1.508428 50.703960 --1.501681 50.703960 --1.495814 50.704546 --1.491120 50.705720 --1.485840 50.707187 --1.481146 50.708653 --1.475866 50.709533 --1.471172 50.710707 --1.466772 50.712467 --1.462078 50.713934 --1.457091 50.715400 --1.452398 50.716574 --1.447704 50.718041 --1.443890 50.720094 --1.439783 50.721854 --1.435676 50.723908 --1.432156 50.726255 --1.427462 50.727721 --1.421595 50.728308 --1.417488 50.726841 --1.418955 50.723028 --1.422475 50.720681 --1.424236 50.716574 --1.421889 50.713640 --1.416315 50.713054 --1.411328 50.714520 --1.406634 50.715694 --1.402234 50.717454 --1.396660 50.718334 --1.392260 50.719801 --1.388153 50.721561 --1.388153 50.725961 --1.389913 50.728895 --1.388740 50.731828 --1.384046 50.733295 --1.379646 50.733882 --1.375539 50.735935 --1.370845 50.737109 --1.366738 50.739162 --1.362925 50.741216 --1.358524 50.742976 --1.354417 50.745029 --1.350310 50.747083 --1.347083 50.749430 --1.343563 50.752070 --1.340923 50.755003 --1.338283 50.758230 --1.333296 50.759404 --1.327722 50.760284 --1.323322 50.761750 --1.319801 50.764097 --1.316281 50.766738 --1.313054 50.769084 --1.308947 50.771138 --1.302200 50.770844 --1.296920 50.772018 --1.291346 50.771431 --1.288119 50.768791 --1.285186 50.766151 --1.279025 50.766738 --1.275212 50.768498 --1.269931 50.767911 --1.267291 50.764977 --1.263184 50.762924 --1.258490 50.761164 --1.254677 50.758817 --1.249690 50.757350 --1.244996 50.755297 --1.240596 50.753537 --1.236782 50.751483 --1.232088 50.749430 --1.227101 50.747669 --1.222408 50.745909 --1.217714 50.744149 --1.211260 50.742976 --1.205980 50.741802 --1.199819 50.740629 --1.194246 50.739162 --1.188672 50.737695 --1.183098 50.736522 --1.177525 50.735055 --1.171071 50.733882 --1.164030 50.733295 --1.157576 50.733295 --1.150829 50.733002 --1.144375 50.733002 --1.139095 50.733882 --1.133815 50.734762 --1.129121 50.736229 --1.124427 50.737695 --1.117974 50.737402 --1.113867 50.735349 --1.111226 50.732708 --1.107119 50.730655 --1.103893 50.728015 --1.101252 50.725375 --1.097145 50.723321 --1.093919 50.720681 --1.095972 50.716574 --1.096559 50.711880 --1.091865 50.710413 --1.085998 50.709827 --1.081598 50.708067 --1.079251 50.705720 --1.076024 50.703373 --1.074557 50.700146 --1.072210 50.696919 --1.070744 50.693692 --1.067810 50.691052 --1.062236 50.689585 --1.059596 50.687532 --1.063703 50.684892 --1.067517 50.683132 --1.071917 50.681665 --1.073677 50.677851 -nan nan --3.243620 54.147354 --3.243620 54.142953 --3.245966 54.139433 --3.248020 54.136206 --3.248900 54.131512 --3.247140 54.127992 --3.248020 54.123592 --3.251247 54.120658 --3.251833 54.115965 --3.249193 54.113031 --3.246846 54.110098 --3.245966 54.106284 --3.245086 54.102470 --3.243326 54.099243 --3.240979 54.096310 --3.238046 54.093376 --3.236286 54.089856 --3.233939 54.087216 --3.230419 54.084869 --3.225138 54.082816 --3.218391 54.081935 --3.214577 54.079589 --3.214284 54.075775 --3.216631 54.072841 --3.217511 54.069908 --3.211351 54.068735 --3.209590 54.065214 --3.208124 54.061987 --3.204603 54.059347 --3.200203 54.057294 --3.194923 54.055534 --3.187295 54.054947 --3.179375 54.054654 --3.173508 54.053480 --3.170281 54.050840 --3.174975 54.049080 --3.181428 54.048493 --3.189056 54.049080 --3.196096 54.050253 --3.202257 54.051427 --3.209004 54.052600 --3.214871 54.053480 --3.219271 54.055827 --3.223671 54.058174 --3.226018 54.060814 --3.229832 54.063454 --3.232179 54.066388 --3.235112 54.069028 --3.237459 54.072255 --3.239219 54.075482 --3.241566 54.078415 --3.244500 54.081349 --3.245966 54.084869 --3.248607 54.087803 --3.250367 54.091029 --3.253007 54.093963 --3.255647 54.096897 --3.257994 54.099830 --3.259754 54.103057 --3.261807 54.106284 --3.262981 54.109804 --3.262981 54.113911 --3.264154 54.117725 --3.264154 54.121832 --3.265914 54.125352 --3.267088 54.128872 --3.267381 54.132686 --3.267381 54.136793 --3.266208 54.140900 --3.262981 54.143833 --3.260341 54.147060 --3.255060 54.148234 --3.248020 54.148234 --3.243620 54.147354 -nan nan --0.794697 60.837300 --0.799097 60.838767 --0.806138 60.840527 --0.814645 60.840821 --0.823739 60.841114 --0.831366 60.840821 --0.836647 60.838767 --0.838113 60.835247 --0.836060 60.831727 --0.834300 60.828206 --0.834887 60.824099 --0.834300 60.820286 --0.833713 60.816472 --0.835473 60.812072 --0.838700 60.808258 --0.842514 60.805325 --0.847207 60.802978 --0.851901 60.800631 --0.857475 60.798578 --0.861875 60.796231 --0.867742 60.794177 --0.870676 60.790950 --0.870969 60.786550 --0.873316 60.783323 --0.878596 60.781270 --0.884170 60.779803 --0.889157 60.779510 --0.890917 60.782736 --0.891504 60.786550 --0.892091 60.790657 --0.890331 60.795351 --0.888277 60.798284 --0.881823 60.799751 --0.876250 60.801218 --0.870382 60.802978 --0.865102 60.804738 --0.860995 60.807672 --0.857768 60.811485 --0.856008 60.815886 --0.855715 60.819992 --0.855421 60.824099 --0.855715 60.827913 --0.857768 60.831727 --0.859528 60.834954 --0.864222 60.837300 --0.869502 60.839647 --0.874196 60.841994 --0.878303 60.844341 --0.882997 60.842287 --0.886224 60.838474 --0.887690 60.833780 --0.887104 60.830260 --0.886517 60.826446 --0.886810 60.822339 --0.889451 60.817939 --0.894731 60.816472 --0.900305 60.814419 --0.905878 60.812365 --0.912332 60.811192 --0.918786 60.810312 --0.920839 60.807965 --0.918199 60.805031 --0.916439 60.801511 --0.921719 60.799751 --0.928173 60.798284 --0.933747 60.796524 --0.939027 60.794471 --0.938441 60.790657 --0.932280 60.788604 --0.927293 60.786257 --0.923480 60.783617 --0.922600 60.780096 --0.924360 60.775403 --0.925826 60.770709 --0.928467 60.766602 --0.930520 60.762495 --0.932867 60.758681 --0.932280 60.754868 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60.673315 --0.827846 60.674195 --0.824619 60.677422 --0.825499 60.681529 --0.823152 60.685636 --0.819632 60.688863 --0.824913 60.691503 --0.829020 60.693850 --0.834887 60.695904 --0.839580 60.697957 --0.845741 60.700011 --0.848674 60.702944 --0.849554 60.707051 --0.847794 60.711745 --0.843981 60.714385 --0.839580 60.717612 --0.835767 60.720545 --0.831953 60.723479 --0.828139 60.726412 --0.824032 60.729346 --0.820219 60.732573 --0.816405 60.735213 --0.811712 60.737853 --0.807311 60.740200 --0.802324 60.742840 --0.799391 60.746067 --0.803204 60.749001 --0.809071 60.750761 --0.817579 60.751934 --0.824619 60.753401 --0.826673 60.756041 --0.820512 60.757215 --0.812885 60.757801 --0.804964 60.758095 --0.804671 60.761028 --0.805258 60.765135 --0.807018 60.768655 --0.809658 60.771589 --0.810245 60.775403 --0.811125 60.779216 --0.811418 60.783030 --0.804964 60.782736 --0.796164 60.782736 --0.787363 60.782443 --0.779736 60.782736 --0.776216 60.784790 --0.773869 60.788897 --0.769175 60.791244 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60.587362 --0.759495 60.590589 --0.755681 60.593523 --0.753041 60.597630 --0.755094 60.601150 --0.757734 60.604084 --0.759495 60.607604 --0.764482 60.609951 --0.772695 60.611124 --0.780616 60.610831 --0.786776 60.609364 --0.789123 60.605257 --0.793524 60.602910 --0.802031 60.604084 --0.805845 60.606724 --0.807605 60.610244 --0.807311 60.614351 --0.806725 60.618751 --0.809365 60.621685 --0.816699 60.623445 --0.825793 60.624032 --0.834300 60.624032 --0.843101 60.624325 --0.851608 60.624618 --0.858648 60.624032 --0.863342 60.621392 --0.868036 60.618751 --0.874196 60.617578 --0.882703 60.617871 --0.887984 60.619045 --0.892091 60.621978 --0.895904 60.624325 --0.902065 60.626379 --0.910279 60.626672 --0.917613 60.625792 --0.924360 60.624912 --0.930520 60.623738 --0.936974 60.622272 --0.936094 60.619338 --0.933454 60.616405 --0.929347 60.613471 --0.926413 60.610537 --0.922600 60.607897 --0.919959 60.604670 --0.917026 60.601737 --0.914386 60.598510 --0.911452 60.595576 --0.908519 60.592643 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60.164345 --1.054902 60.163465 --1.061063 60.164639 --1.063116 60.168159 --1.062530 60.172266 --1.059303 60.175786 --1.059889 60.179600 --1.062823 60.182827 --1.068983 60.184587 --1.075144 60.183120 --1.077197 60.179307 --1.080131 60.176373 --1.088051 60.177840 --1.096265 60.179013 --1.105653 60.179307 --1.113867 60.179600 --1.120907 60.179013 --1.127361 60.177546 --1.127361 60.173439 --1.127068 60.169332 --1.122961 60.166986 --1.116800 60.164932 --1.111226 60.163172 --1.105946 60.160825 --1.102132 60.158185 --1.101546 60.154078 --1.103893 60.150264 --1.106239 60.146157 --1.108293 60.142344 --1.110053 60.137357 --1.111813 60.132663 --1.111813 60.128556 --1.110053 60.125329 --1.108293 60.121809 --1.105946 60.118582 --1.100959 60.116529 --1.095972 60.114182 --1.090985 60.111835 --1.085118 60.110075 --1.078957 60.108021 --1.071624 60.106261 --1.065757 60.104794 --1.059009 60.103034 --1.052849 60.104501 --1.048155 60.106848 --1.044928 60.110662 --1.044635 60.114769 --1.047569 60.117702 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60.452126 --1.312468 60.450659 --1.311001 60.455060 --1.311294 60.458873 --1.313641 60.462100 --1.313934 60.466207 --1.312761 60.469727 --1.309827 60.473248 --1.305134 60.475888 --1.301907 60.479115 --1.299853 60.483222 --1.297506 60.487622 --1.296040 60.491142 --1.303374 60.492609 --1.308947 60.490556 --1.313641 60.487915 --1.317455 60.485275 --1.320388 60.481755 --1.324202 60.478528 --1.331829 60.478235 --1.336816 60.480581 --1.335056 60.483515 --1.329775 60.485568 --1.326255 60.489089 --1.328309 60.492902 --1.327722 60.497009 --1.324788 60.500236 --1.319508 60.502290 --1.315988 60.505810 --1.315694 60.509917 --1.317455 60.513731 --1.320388 60.516664 --1.326255 60.518424 --1.332416 60.520184 --1.335643 60.523411 --1.328309 60.524291 --1.322148 60.525465 --1.316868 60.527518 --1.319801 60.529865 --1.328015 60.530745 --1.336523 60.531918 --1.339456 60.535145 --1.337989 60.538666 --1.331536 60.540132 --1.323322 60.539839 --1.315694 60.540132 --1.310707 60.542479 --1.307774 60.545999 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60.603790 --1.366151 60.604964 --1.372312 60.607017 --1.380526 60.608191 --1.389033 60.609071 --1.398127 60.609657 --1.404287 60.608191 --1.410448 60.607017 --1.416022 60.604964 --1.415142 60.602324 --1.409861 60.599977 --1.413088 60.596456 --1.416902 60.593230 --1.420715 60.590589 --1.421889 60.586776 --1.420422 60.583255 --1.416315 60.580615 --1.413675 60.577388 --1.416315 60.573868 --1.421889 60.572108 --1.426289 60.569761 --1.432156 60.567708 --1.437437 60.565948 --1.442717 60.563894 --1.448291 60.561841 --1.456798 60.562134 --1.458851 60.558027 --1.459145 60.554800 --1.457385 60.551280 --1.461492 60.548346 --1.466772 60.546293 --1.471466 60.543946 --1.476159 60.541306 --1.479680 60.538666 --1.473519 60.536612 --1.465599 60.535439 --1.458265 60.533972 --1.453278 60.531625 --1.450344 60.529865 --1.447117 60.526638 --1.444477 60.523705 --1.441543 60.520478 --1.437730 60.517837 --1.433916 60.514904 --1.428636 60.512850 --1.422769 60.510797 --1.415142 60.510210 --1.408394 60.511090 --1.402821 60.513144 --1.395780 60.514024 --1.388446 60.513437 --1.386686 60.509917 --1.388153 60.506397 --1.392553 60.503756 --1.398714 60.502583 --1.405754 60.501703 --1.413675 60.501410 --1.421889 60.501410 --1.430689 60.501703 --1.438610 60.502876 --1.445944 60.504050 --1.452984 60.505810 --1.459145 60.507863 --1.465305 60.509624 --1.470292 60.511970 --1.474106 60.514317 --1.479093 60.516957 --1.483200 60.519304 --1.488187 60.521651 --1.492000 60.524585 --1.496987 60.526638 --1.501094 60.529572 --1.501681 60.533092 --1.503441 60.536612 --1.504028 60.540426 --1.503735 60.544826 --1.504321 60.548346 --1.506081 60.551867 --1.511068 60.554213 --1.518989 60.553920 --1.525736 60.553040 --1.531897 60.551573 --1.539230 60.550693 --1.543631 60.548346 --1.545978 60.544239 --1.547444 60.539546 --1.546858 60.535732 --1.547151 60.531332 --1.547444 60.527225 --1.548031 60.523118 --1.549498 60.518718 --1.551551 60.514317 --1.554778 60.510797 --1.558592 60.507863 --1.563286 60.505517 --1.571793 60.505517 --1.578833 60.507277 --1.586167 60.508743 --1.592914 60.507863 --1.594381 60.503463 --1.594968 60.498769 --1.597901 60.495543 --1.602008 60.492609 --1.604649 60.488795 --1.607875 60.485275 --1.609929 60.481462 --1.611689 60.476768 --1.609636 60.474128 --1.601128 60.474128 --1.594674 60.475594 --1.588514 60.477061 --1.579420 60.476181 --1.572086 60.474714 --1.565046 60.472954 --1.558299 60.472954 --1.553605 60.475594 --1.551258 60.479701 --1.551258 60.483808 --1.545684 60.485862 --1.539524 60.484688 --1.536297 60.481755 --1.532483 60.479115 --1.526323 60.477355 --1.518696 60.477355 --1.513122 60.479408 --1.507842 60.481462 --1.501681 60.482635 --1.494641 60.483515 --1.487013 60.483808 --1.482026 60.481755 --1.482026 60.478235 --1.487600 60.476474 --1.493467 60.475008 --1.498748 60.472954 --1.502268 60.469727 --1.500214 60.466207 --1.498748 60.462687 --1.494641 60.460047 --1.490827 60.457406 --1.485840 60.455060 --1.478506 60.453593 --1.472639 60.455060 --1.469119 60.458580 --1.466479 60.462100 --1.464718 60.466794 --1.464425 60.470901 --1.459731 60.473248 --1.455038 60.475888 --1.452691 60.479995 --1.448291 60.482342 --1.443597 60.484688 --1.439490 60.482928 --1.441543 60.478821 --1.444770 60.475594 --1.447704 60.472074 --1.446824 60.467967 --1.446531 60.464447 --1.445944 60.460633 --1.444770 60.457406 --1.443010 60.454180 --1.441250 60.450953 --1.437437 60.448019 --1.432449 60.445966 --1.429809 60.442739 --1.430103 60.438632 --1.432449 60.434525 --1.434503 60.430418 --1.435970 60.426604 --1.433916 60.423377 --1.430983 60.420150 --1.424236 60.418684 --1.415728 60.417510 --1.408101 60.417804 --1.400181 60.418390 --1.391967 60.418097 --1.383753 60.416924 --1.384339 60.414283 --1.389033 60.411643 --1.394313 60.409590 --1.396660 60.405776 --1.397247 60.401376 --1.395193 60.398149 --1.396074 60.395215 --1.398420 60.391402 --1.398127 60.387588 --1.394900 60.384361 --1.389913 60.382308 --1.382873 60.380548 --1.375832 60.379081 --1.367912 60.378201 --1.366738 60.377614 --1.365858 60.377614 --1.364685 60.381134 --1.361751 60.384361 --1.357644 60.387588 --1.351777 60.388762 --1.344737 60.389642 --1.341803 60.386708 --1.341216 60.383188 --1.341803 60.378494 --1.346203 60.370574 --1.343856 60.372334 --1.341803 60.371747 --1.341216 60.368813 --1.333882 60.367347 --1.325668 60.366173 --1.317161 60.365880 --1.307774 60.365293 --1.299560 60.365000 --1.289879 60.364120 --1.281959 60.362946 --1.276972 60.360893 --1.271985 60.358546 --1.268171 60.355906 --1.263184 60.353559 --1.259077 60.350919 --1.259664 60.349159 --1.267584 60.348865 --1.274625 60.350332 --1.280492 60.352679 --1.287532 60.354146 --1.294866 60.355612 --1.304254 60.356493 --1.313641 60.357079 --1.320388 60.356493 --1.325668 60.354439 --1.326255 60.350332 --1.325668 60.346519 --1.322735 60.343292 --1.319801 60.340358 --1.318041 60.336838 --1.319215 60.334198 --1.326255 60.334784 --1.330362 60.337131 --1.334176 60.340065 --1.340336 60.341825 --1.345910 60.340065 --1.347670 60.335958 --1.351190 60.332144 --1.353831 60.328917 --1.357351 60.325397 --1.359404 60.321290 --1.360871 60.316596 --1.357937 60.313663 --1.354124 60.310729 --1.350310 60.308382 --1.342976 60.306622 --1.337109 60.304862 --1.339750 60.302222 --1.344443 60.299582 --1.348257 60.296648 --1.352070 60.294008 --1.355297 60.290194 --1.357937 60.286674 --1.361458 60.283447 --1.362925 60.286674 --1.364685 60.289901 --1.367912 60.293128 --1.369085 60.296648 --1.371138 60.299875 --1.372899 60.303395 --1.374365 60.306916 --1.377299 60.310143 --1.382286 60.312196 --1.388446 60.314250 --1.396367 60.315423 --1.405754 60.316010 --1.411035 60.317183 --1.412795 60.320703 --1.419249 60.321583 --1.426876 60.321290 --1.433916 60.320410 --1.440663 60.319823 --1.445944 60.318650 --1.444184 60.315423 --1.444477 60.311023 --1.442717 60.307502 --1.440957 60.304275 --1.441837 60.301342 --1.448877 60.302809 --1.455038 60.304862 --1.460612 60.305156 --1.460905 60.301049 --1.458265 60.298115 --1.455331 60.294888 --1.452398 60.291955 --1.450931 60.288434 --1.448877 60.284914 --1.447117 60.281687 --1.453571 60.280220 --1.459731 60.278754 --1.465892 60.277580 --1.467359 60.280807 --1.468239 60.284621 --1.467652 60.289021 --1.467359 60.293128 --1.467945 60.296942 --1.468825 60.300755 --1.469412 60.304569 --1.471172 60.308089 --1.472639 60.311316 --1.474693 60.315130 --1.479680 60.317183 --1.486427 60.317183 --1.491707 60.315423 --1.496987 60.313369 --1.503148 60.311903 --1.509308 60.310436 --1.516349 60.309849 --1.523096 60.308676 --1.531017 60.308382 --1.530137 60.305449 --1.525149 60.302809 --1.520162 60.300462 --1.522216 60.297528 --1.529843 60.296942 --1.535710 60.298995 --1.541871 60.300755 --1.550671 60.301049 --1.558005 60.300462 --1.556245 60.297235 --1.553605 60.294301 --1.550965 60.291075 --1.550965 60.287848 --1.557712 60.286968 --1.565632 60.286674 --1.571793 60.288728 --1.573260 60.291955 --1.575313 60.295181 --1.577660 60.298408 --1.581767 60.301049 --1.585580 60.303982 --1.589687 60.306329 --1.596728 60.308089 --1.605235 60.308089 --1.612276 60.307209 --1.619903 60.306916 --1.628410 60.307209 --1.635157 60.306036 --1.642198 60.305156 --1.648358 60.303982 --1.655399 60.303102 --1.661266 60.301635 --1.666840 60.299582 --1.671533 60.297235 --1.676520 60.295181 --1.681507 60.292835 --1.686788 60.290781 --1.691481 60.288434 --1.692655 60.284034 --1.692948 60.279634 --1.690015 60.278167 --1.682681 60.278754 --1.678280 60.278754 --1.676520 60.275527 --1.676520 60.271420 --1.678280 60.266726 --1.679747 60.262032 --1.680334 60.257632 --1.679454 60.254112 --1.678574 60.250298 --1.677987 60.246485 --1.676520 60.242964 --1.674467 60.239444 --1.671533 60.236511 --1.667720 60.233870 --1.664786 60.230937 --1.660092 60.228590 --1.655105 60.226243 --1.647772 60.224776 --1.639558 60.224483 --1.631637 60.225070 --1.629877 60.221256 --1.631050 60.217736 --1.631050 60.214509 --1.626063 60.212162 --1.619903 60.210402 --1.612862 60.209815 --1.604942 60.210109 --1.598195 60.210989 --1.592034 60.212162 --1.588807 60.215976 --1.583527 60.217736 --1.576780 60.218616 --1.570619 60.220083 --1.563579 60.221256 --1.557418 60.222430 --1.553605 60.225656 --1.550378 60.227417 --1.547444 60.224483 --1.544511 60.221256 --1.542751 60.218029 --1.540991 60.214509 --1.539524 60.210989 --1.539817 60.206882 --1.533657 60.207762 --1.533950 60.206882 --1.529843 60.208055 --1.524563 60.210109 --1.521043 60.211869 --1.516349 60.214509 --1.511068 60.216269 --1.509015 60.220669 --1.507255 60.225070 --1.505788 60.229763 --1.505201 60.233870 --1.504908 60.237977 --1.501094 60.241204 --1.495814 60.242964 --1.492880 60.240911 --1.491707 60.237977 --1.488774 60.235044 --1.486133 60.231817 --1.484373 60.228297 --1.484960 60.224190 --1.486427 60.219789 --1.485547 60.215976 --1.477919 60.215976 --1.469412 60.215976 --1.470292 60.213042 --1.475573 60.210989 --1.479386 60.208349 --1.478799 60.204535 --1.484667 60.203948 --1.493174 60.205122 --1.500508 60.204828 --1.508428 60.204535 --1.514589 60.203068 --1.519869 60.201015 --1.523389 60.198081 --1.526616 60.194561 --1.527790 60.190747 --1.527203 60.186934 --1.524269 60.184000 --1.520162 60.181360 --1.513122 60.179600 --1.504028 60.179307 --1.498748 60.176666 --1.496107 60.173733 --1.494347 60.170213 --1.490534 60.167866 --1.484667 60.165812 --1.478506 60.163759 --1.472639 60.161999 --1.465305 60.160532 --1.459438 60.158478 --1.456798 60.155545 --1.453571 60.152611 --1.448584 60.151144 --1.444477 60.154078 --1.441543 60.157598 --1.439490 60.161705 --1.438903 60.165812 --1.439783 60.169626 --1.440663 60.173733 --1.436263 60.176666 --1.430689 60.178133 --1.428343 60.181947 --1.425116 60.185467 --1.419249 60.183707 --1.418368 60.179600 --1.418662 60.175493 --1.416022 60.172559 --1.413088 60.169332 --1.408394 60.170506 --1.403701 60.173146 --1.399594 60.175786 --1.398127 60.180480 --1.398127 60.184587 --1.395487 60.188987 --1.394313 60.193388 --1.394607 60.197201 --1.395487 60.201015 --1.394900 60.205415 --1.394020 60.208935 --1.387860 60.210402 --1.382873 60.208055 --1.379939 60.205122 --1.376125 60.202188 --1.372018 60.199841 --1.367912 60.196908 --1.363218 60.194854 --1.358231 60.192507 --1.357351 60.196028 --1.355884 60.200721 --1.354124 60.205415 --1.352950 60.208935 --1.355884 60.211869 --1.358524 60.215096 --1.361458 60.218323 --1.363218 60.221550 --1.362925 60.225950 --1.363511 60.229763 --1.369378 60.231524 --1.375539 60.233284 --1.381699 60.235337 --1.387566 60.237097 --1.391380 60.240031 --1.393433 60.243258 --1.396074 60.246485 --1.403114 60.247951 --1.410155 60.249418 --1.414262 60.252058 --1.410155 60.254992 --1.403407 60.255872 --1.397247 60.254112 --1.392260 60.251765 --1.387566 60.249418 --1.380232 60.247951 --1.371138 60.247365 --1.362631 60.247071 --1.355591 60.245605 --1.350310 60.243258 --1.347670 60.240324 --1.347083 60.236511 --1.345323 60.232697 --1.342390 60.229763 --1.341803 60.226243 --1.340043 60.222430 --1.338283 60.219203 --1.336523 60.215976 --1.335936 60.211869 --1.334176 60.208349 --1.333589 60.204828 --1.331536 60.201015 --1.327722 60.201308 --1.324202 60.204535 --1.320975 60.207762 --1.318921 60.211869 --1.315694 60.215682 --1.310414 60.217443 --1.307481 60.220963 --1.308067 60.224776 --1.306600 60.229470 --1.305134 60.233870 --1.299853 60.235924 --1.294280 60.237684 --1.291346 60.241498 --1.286652 60.243844 --1.280492 60.245018 --1.274038 60.244138 --1.270225 60.241791 --1.269344 60.237684 --1.273451 60.234750 --1.277265 60.231524 --1.280199 60.228297 --1.282839 60.224190 --1.284892 60.220083 --1.287826 60.216269 --1.291053 60.213042 --1.293400 60.208935 --1.296333 60.205415 --1.299560 60.201895 --1.302493 60.198375 --1.305427 60.194854 --1.308654 60.191334 --1.310707 60.187227 --1.313054 60.183120 --1.315401 60.179307 --1.315694 60.174906 --1.315108 60.171093 --1.312174 60.168159 --1.309534 60.164932 --1.305134 60.163465 --1.302200 60.166692 --1.299560 60.170213 --1.296040 60.174026 --1.291346 60.176373 --1.288706 60.179600 --1.286359 60.184000 --1.283425 60.187520 --1.277852 60.189281 --1.273745 60.187520 --1.274038 60.183413 --1.275505 60.178720 --1.275798 60.174319 --1.277558 60.169919 --1.279612 60.165812 --1.282839 60.162292 --1.285186 60.158478 --1.286652 60.153491 --1.288119 60.149091 --1.289586 60.144397 --1.288999 60.140584 --1.287239 60.137357 --1.279025 60.136183 --1.269638 60.135303 --1.263771 60.133250 --1.261717 60.130903 --1.260837 60.127969 --1.260250 60.124156 --1.260837 60.120049 --1.261131 60.115942 --1.262597 60.111248 --1.263184 60.106848 --1.264357 60.102448 --1.266998 60.098341 --1.268464 60.093647 --1.270518 60.089833 --1.273451 60.086020 --1.275798 60.082206 --1.279025 60.078686 --1.280199 60.073992 --1.282839 60.069885 --1.284892 60.065778 --1.287239 60.061671 --1.289586 60.057858 --1.290759 60.053164 --1.292519 60.048470 --1.293986 60.043777 --1.295160 60.039376 --1.297506 60.035269 --1.299267 60.030576 --1.300440 60.026176 --1.301907 60.021482 --1.304547 60.017375 --1.305720 60.012681 --1.308067 60.008868 --1.311294 60.006521 --1.316281 60.008868 --1.322442 60.007401 --1.326255 60.004467 --1.329482 60.001240 --1.331536 59.996840 --1.331829 59.992733 --1.330362 59.989213 --1.328602 59.985693 --1.326842 59.982466 --1.325375 59.978945 --1.324495 59.975132 --1.328309 59.972198 --1.332709 59.973078 --1.337696 59.975132 --1.342683 59.974252 --1.346790 59.971318 --1.347083 59.966918 --1.344150 59.963984 --1.337109 59.962518 --1.329775 59.962811 --1.327722 59.959584 --1.326255 59.955770 --1.325668 59.952250 --1.324788 59.948437 --1.331536 59.948437 --1.337989 59.947557 --1.345323 59.946676 --1.350310 59.944623 --1.355004 59.942276 --1.357644 59.938756 --1.361164 59.935236 --1.360284 59.931422 --1.357644 59.928195 --1.355884 59.924675 --1.356177 59.920568 --1.355884 59.916754 --1.357351 59.912354 --1.365565 59.912354 --1.372605 59.913821 --1.375539 59.910301 --1.377886 59.906487 --1.378179 59.902087 --1.376419 59.898566 --1.373779 59.895339 --1.372018 59.891526 --1.367912 59.889179 --1.360578 59.889472 --1.353831 59.890352 --1.349724 59.888592 --1.347083 59.885659 --1.342976 59.882725 --1.338283 59.885365 --1.336229 59.889179 --1.333296 59.892699 --1.326255 59.893579 --1.318628 59.893873 --1.312761 59.892113 --1.308947 59.889472 --1.306014 59.886245 --1.302200 59.883605 --1.301907 59.881258 --1.305720 59.878325 --1.309534 59.875391 --1.312761 59.871578 --1.314228 59.867177 --1.313641 59.863364 --1.310707 59.860137 --1.306894 59.857497 --1.303374 59.859844 --1.300147 59.863364 --1.297506 59.866591 --1.292813 59.869231 --1.289293 59.866591 --1.286066 59.863657 --1.282545 59.860724 --1.279318 59.857790 --1.276972 59.854857 --1.271985 59.852510 --1.268758 59.851043 --1.265531 59.854857 --1.262597 59.858377 --1.260250 59.862190 --1.258784 59.866884 --1.258197 59.870991 --1.262304 59.873925 --1.268171 59.875978 --1.273158 59.878032 --1.271398 59.882432 --1.269051 59.886539 --1.266411 59.890352 --1.264944 59.894753 --1.263477 59.899446 --1.263184 59.903553 --1.262597 59.907660 --1.263184 59.911767 --1.265824 59.914701 --1.268758 59.917634 --1.271398 59.920861 --1.273158 59.924088 --1.269051 59.924968 --1.264357 59.922621 --1.259664 59.924968 --1.256730 59.928488 --1.254383 59.932889 --1.253797 59.936996 --1.252623 59.941396 --1.249396 59.944916 --1.247343 59.949023 --1.244996 59.953130 --1.243236 59.957824 --1.242062 59.962224 --1.240596 59.966918 --1.241182 59.970732 --1.242943 59.974252 --1.244703 59.977479 --1.246463 59.980999 --1.247930 59.984519 --1.248516 59.988920 --1.247930 59.993026 --1.243236 59.995667 --1.238542 59.993026 --1.235902 59.990093 --1.234142 59.986573 --1.229742 59.988333 --1.224461 59.990386 --1.219474 59.987746 --1.216541 59.984813 --1.213900 59.981586 --1.210380 59.979239 --1.202460 59.979532 --1.198646 59.982172 --1.196299 59.986279 --1.196006 59.990680 --1.194539 59.995373 --1.196299 59.998600 --1.200113 60.001534 --1.203926 60.004174 --1.207740 60.006521 --1.210674 60.009748 --1.213314 60.012681 --1.215074 60.016495 --1.217714 60.019428 --1.220648 60.022362 --1.221234 60.026176 --1.221821 60.029989 --1.220061 60.032923 --1.210674 60.032629 --1.201286 60.031749 --1.194539 60.032629 --1.187792 60.033216 --1.182512 60.035269 --1.176938 60.037323 --1.171657 60.039083 --1.166964 60.041723 --1.165497 60.046124 --1.164910 60.050524 --1.165790 60.054044 --1.174298 60.054338 --1.182512 60.054631 --1.189845 60.056098 --1.191312 60.059618 --1.190725 60.064018 --1.191606 60.067832 --1.193366 60.071059 --1.196886 60.073992 --1.200113 60.076926 --1.199526 60.081033 --1.197179 60.085140 --1.192486 60.087487 --1.188672 60.090420 --1.186325 60.091887 --1.192486 60.093647 --1.200700 60.095114 --1.206567 60.096581 --1.210674 60.099514 --1.212140 60.102741 --1.206567 60.104794 --1.200113 60.105675 --1.193072 60.106261 --1.188672 60.108901 --1.185445 60.112422 --1.187205 60.115942 --1.192192 60.118289 --1.194832 60.121516 --1.196593 60.124743 --1.194539 60.127676 --1.187205 60.127089 --1.182512 60.125036 --1.177231 60.122689 --1.173418 60.123276 --1.171364 60.126503 --1.172244 60.130316 --1.172538 60.134130 --1.170484 60.137357 --1.163150 60.137357 --1.158163 60.135303 --1.153176 60.132957 --1.146722 60.132076 --1.143789 60.135597 --1.146429 60.138530 --1.150243 60.141464 --1.149069 60.144984 --1.142615 60.144984 --1.135575 60.143224 --1.128534 60.144104 --1.125601 60.147918 --1.126188 60.151731 --1.130001 60.154078 --1.134988 60.156425 --1.139975 60.158772 --1.144669 60.161119 --1.150829 60.163172 --1.155816 60.165225 --1.157576 60.168746 --1.154056 60.172266 --1.150536 60.175200 --1.147602 60.178720 --1.143789 60.181653 --1.141442 60.185760 --1.141442 60.189281 --1.142029 60.192801 --1.143495 60.196321 --1.151416 60.196028 --1.157576 60.194854 --1.161390 60.191627 --1.166084 60.189281 --1.169017 60.185467 --1.173711 60.183413 --1.178991 60.181360 --1.184565 60.179307 --1.189845 60.177546 --1.195126 60.175493 --1.195419 60.177546 --1.194246 60.181067 --1.192486 60.185760 --1.187205 60.187814 --1.183685 60.190454 --1.179578 60.193681 --1.176351 60.197201 --1.173711 60.200428 --1.170191 60.204242 --1.168431 60.208349 --1.164910 60.211869 --1.162857 60.215976 --1.160510 60.220083 --1.166377 60.221550 --1.171951 60.220083 --1.175764 60.216856 --1.179578 60.213922 --1.183685 60.210695 --1.188085 60.208349 --1.192486 60.206002 --1.196593 60.203068 --1.201873 60.201015 --1.201286 60.205415 --1.199233 60.209522 --1.195419 60.212162 --1.191312 60.215389 --1.187792 60.218323 --1.183978 60.221256 --1.180458 60.225070 --1.180458 60.228003 --1.185445 60.230644 --1.194246 60.230644 --1.200700 60.229763 --1.208033 60.228883 --1.214781 60.228003 --1.220941 60.230057 --1.221821 60.232697 --1.218007 60.235924 --1.212727 60.237684 --1.204806 60.237977 --1.198059 60.238857 --1.191899 60.240324 --1.187205 60.242671 --1.183392 60.245898 --1.184565 60.248538 --1.189259 60.251178 --1.194246 60.253232 --1.198059 60.255872 --1.199819 60.259392 --1.200700 60.263206 --1.198939 60.267900 --1.195126 60.270833 --1.186912 60.269660 --1.184272 60.266726 --1.182512 60.262913 --1.174298 60.262032 --1.165790 60.262032 --1.164030 60.258219 --1.165497 60.253819 --1.166084 60.249418 --1.166377 60.245311 --1.163737 60.242084 --1.157576 60.240618 --1.149363 60.239151 --1.144669 60.241791 --1.142615 60.245898 --1.139388 60.249125 --1.134108 60.251472 --1.126188 60.251472 --1.118560 60.252058 --1.113280 60.253819 --1.108586 60.256165 --1.103893 60.258512 --1.098612 60.260566 --1.093332 60.262619 --1.092745 60.266726 --1.093625 60.270540 --1.097439 60.273473 --1.101252 60.275820 --1.107119 60.277874 --1.113573 60.278754 --1.119734 60.277580 --1.123547 60.274353 --1.127361 60.271420 --1.133815 60.269660 --1.134108 60.273473 --1.134988 60.277287 --1.138802 60.279927 --1.137922 60.282861 --1.135575 60.286674 --1.132641 60.290194 --1.129414 60.294008 --1.125601 60.296648 --1.121200 60.299288 --1.116800 60.300755 --1.108000 60.300462 --1.101252 60.301342 --1.096559 60.303982 --1.093625 60.307502 --1.090692 60.310729 --1.084238 60.312196 --1.078077 60.313663 --1.073677 60.316010 --1.073677 60.319530 --1.079544 60.321290 --1.085411 60.323344 --1.092452 60.324810 --1.099786 60.325984 --1.107119 60.326864 --1.113280 60.325690 --1.120027 60.324810 --1.127654 60.325397 --1.132348 60.328037 --1.137628 60.330384 --1.144375 60.331557 --1.151416 60.330971 --1.156990 60.328917 --1.159630 60.331851 --1.160217 60.335958 --1.162270 60.339478 --1.164617 60.342412 --1.168724 60.345052 --1.170484 60.347399 --1.163150 60.347692 --1.155230 60.347985 --1.146136 60.347399 --1.137922 60.346519 --1.129708 60.345345 --1.120320 60.344465 --1.111813 60.344172 --1.103893 60.344465 --1.097145 60.345345 --1.090105 60.346225 --1.084825 60.347985 --1.080131 60.350625 --1.075437 60.352972 --1.069863 60.355026 --1.066050 60.357959 --1.064583 60.362360 --1.064290 60.366760 --1.065757 60.370280 --1.066637 60.374094 --1.066050 60.378201 --1.063116 60.381721 --1.060769 60.385828 --1.062823 60.388468 --1.068983 60.390228 --1.078077 60.391108 --1.087465 60.391695 --1.095972 60.391988 --1.099199 60.388468 --1.101839 60.384948 --1.105359 60.381428 --1.107413 60.377321 --1.110053 60.373214 --1.114453 60.370867 --1.121787 60.372334 --1.123254 60.375854 --1.122667 60.379961 --1.121494 60.384361 --1.117387 60.387588 --1.113573 60.390522 --1.109760 60.393749 --1.105066 60.396095 --1.101252 60.399029 --1.097439 60.401962 --1.091865 60.404016 --1.086291 60.405776 --1.081011 60.407830 --1.076317 60.410176 --1.071624 60.412523 --1.067223 60.414870 --1.062530 60.417510 --1.058716 60.420444 --1.054022 60.423084 --1.051089 60.426311 --1.047275 60.429538 --1.043462 60.432471 --1.039941 60.435992 --1.037888 60.440099 --1.037301 60.444206 --1.041408 60.446846 --1.049035 60.446552 --1.055196 60.445379 --1.061356 60.443912 --1.066930 60.441859 --1.072210 60.440099 --1.076904 60.437458 --1.081598 60.435112 --1.085411 60.432178 --1.088345 60.428658 --1.090692 60.424551 --1.093038 60.420444 --1.095679 60.416337 --1.097732 60.414577 --1.098319 60.418684 --1.099199 60.422497 --1.103306 60.424257 --1.108586 60.422204 --1.111813 60.418684 --1.115040 60.415163 --1.119734 60.412817 --1.123547 60.409590 --1.123841 60.405483 --1.122081 60.402256 --1.127948 60.401669 --1.136455 60.401962 --1.140269 60.399029 --1.144082 60.395802 --1.145842 60.391402 --1.146136 60.387295 --1.147896 60.382601 --1.150536 60.385535 --1.151123 60.389348 --1.152003 60.393455 --1.151416 60.397562 --1.150829 60.401669 --1.152589 60.404896 --1.155523 60.408123 --1.162563 60.409590 --1.168724 60.408416 --1.174298 60.406363 --1.180458 60.404896 --1.186325 60.403723 --1.192779 60.402256 --1.200700 60.401962 --1.198646 60.404309 --1.195126 60.406950 --1.189552 60.409003 --1.184272 60.410763 --1.187205 60.413110 --1.195126 60.412817 --1.200700 60.410763 --1.205980 60.409003 --1.211847 60.407536 --1.218887 60.406656 --1.225928 60.405776 --1.231795 60.405189 --1.225635 60.406656 --1.220941 60.409296 --1.216247 60.411643 --1.211554 60.414283 --1.206860 60.416337 --1.202460 60.418977 --1.197766 60.421324 --1.192486 60.423377 --1.186325 60.424844 --1.179285 60.423377 --1.173124 60.421324 --1.166964 60.419564 --1.159337 60.418977 --1.154643 60.421031 --1.152589 60.425137 --1.155230 60.428364 --1.159337 60.431005 --1.164324 60.433351 --1.165204 60.435992 --1.162270 60.439805 --1.161097 60.442445 --1.166377 60.444792 --1.168431 60.447139 --1.165204 60.450953 --1.164030 60.454473 --1.166670 60.457406 --1.170484 60.460340 --1.177818 60.461807 --1.186325 60.461807 --1.189259 60.465034 --1.190432 60.466207 -nan nan --2.020038 60.132957 --2.021798 60.136770 --2.024732 60.139704 --2.027372 60.142637 --2.029132 60.146157 --2.029132 60.150264 --2.028546 60.154371 --2.032653 60.157305 --2.041747 60.158185 --2.051134 60.158478 --2.059348 60.158772 --2.065508 60.157305 --2.072549 60.156425 --2.077829 60.154371 --2.082523 60.152025 --2.086923 60.149384 --2.089857 60.145864 --2.091323 60.141464 --2.095137 60.138237 --2.098071 60.134717 --2.095137 60.132663 --2.089857 60.130610 --2.084870 60.128263 --2.079003 60.126503 --2.071669 60.124743 --2.065508 60.122982 --2.059348 60.121222 --2.053187 60.119169 --2.048494 60.116822 --2.043507 60.114769 --2.036173 60.114182 --2.032359 60.117115 --2.028839 60.120342 --2.026785 60.124156 --2.022679 60.127089 --2.019158 60.130316 --2.020038 60.132957 -nan nan --1.556538 60.201015 --1.558885 60.203068 --1.565926 60.204828 --1.575313 60.205415 --1.582940 60.205122 --1.587634 60.202481 --1.589687 60.198668 --1.587634 60.194854 --1.585287 60.191921 --1.577073 60.190747 --1.568859 60.189867 --1.560352 60.189867 --1.553312 60.190454 --1.548911 60.193094 --1.547444 60.197494 --1.549205 60.201015 --1.556538 60.201015 -nan nan --1.697642 60.343585 --1.702336 60.344465 --1.710549 60.344758 --1.718470 60.344172 --1.717883 60.340358 --1.714656 60.337425 --1.712310 60.334198 --1.708203 60.331557 --1.702922 60.329504 --1.698229 60.327157 --1.689721 60.326864 --1.682387 60.327744 --1.685028 60.323637 --1.684441 60.320117 --1.676227 60.318943 --1.670653 60.320703 --1.665373 60.322757 --1.658039 60.322170 --1.650412 60.322463 --1.648358 60.324810 --1.651292 60.327744 --1.649238 60.331557 --1.646892 60.335958 --1.647478 60.339771 --1.651292 60.342118 --1.659212 60.341825 --1.666253 60.341238 --1.674467 60.341531 --1.682094 60.341825 --1.691481 60.342412 --1.697642 60.343585 -nan nan --1.363218 60.332437 --1.366151 60.335664 --1.367912 60.338891 --1.373779 60.340945 --1.380819 60.340065 --1.384046 60.336251 --1.386980 60.332731 --1.387273 60.329504 --1.385513 60.325984 --1.381699 60.323637 --1.377886 60.320703 --1.371432 60.319823 --1.368792 60.323930 --1.366738 60.328037 --1.363218 60.332437 -nan nan --1.376419 60.371160 --1.381993 60.372627 --1.389033 60.374094 --1.397247 60.374974 --1.404287 60.376734 --1.410155 60.378494 --1.415142 60.380841 --1.420422 60.383188 --1.425409 60.385241 --1.430103 60.382894 --1.432743 60.379374 --1.438317 60.377614 --1.444477 60.376147 --1.448877 60.373507 --1.454744 60.371747 --1.454744 60.368227 --1.452691 60.365000 --1.451224 60.361480 --1.448291 60.358253 --1.446531 60.355026 --1.443597 60.351799 --1.440957 60.348865 --1.436850 60.348572 --1.431863 60.347105 --1.425996 60.347692 --1.418368 60.347985 --1.410448 60.348279 --1.402821 60.348572 --1.394900 60.349159 --1.389620 60.351212 --1.384046 60.352972 --1.380526 60.355906 --1.376125 60.358253 --1.372899 60.362066 --1.370552 60.365880 --1.373192 60.368813 --1.376419 60.371160 -nan nan --0.996525 60.724652 --1.005032 60.724946 --1.014419 60.725532 --1.023807 60.726412 --1.033194 60.727293 --1.040528 60.728466 --1.048742 60.729639 --1.056956 60.730813 --1.061356 60.729346 --1.063703 60.725239 --1.065757 60.721425 --1.068397 60.717318 --1.073677 60.719372 --1.075144 60.723186 --1.075437 60.726999 --1.077491 60.730226 --1.084825 60.731693 --1.092452 60.731399 --1.098612 60.729933 --1.104186 60.727879 --1.110053 60.725826 --1.112693 60.722305 --1.111226 60.718785 --1.110640 60.714972 --1.111226 60.710865 --1.113867 60.707344 --1.117094 60.703824 --1.120320 60.700304 --1.122374 60.696197 --1.122961 60.692090 --1.120027 60.688863 --1.117387 60.685930 --1.114453 60.682703 --1.111813 60.679769 --1.113280 60.675369 --1.114747 60.670675 --1.117094 60.666568 --1.120320 60.663048 --1.122374 60.658941 --1.122961 60.654834 --1.123547 60.650434 --1.125014 60.646033 --1.124134 60.642220 --1.123841 60.638406 --1.122081 60.634886 --1.120320 60.631366 --1.117387 60.628432 --1.113573 60.625792 --1.110933 60.622858 --1.107706 60.619631 --1.106239 60.616111 --1.106533 60.612004 --1.108000 60.607604 --1.111520 60.603790 --1.116800 60.604377 --1.117387 60.608191 --1.117974 60.612004 --1.120907 60.614938 --1.126188 60.617285 --1.132055 60.619045 --1.136162 60.621978 --1.139975 60.624325 --1.142615 60.627552 --1.142322 60.631952 --1.142029 60.636059 --1.139975 60.640460 --1.140855 60.644567 --1.144669 60.647207 --1.153176 60.648380 --1.159337 60.646913 --1.164617 60.644860 --1.169311 60.642513 --1.174298 60.639873 --1.177231 60.636646 --1.179578 60.632539 --1.180751 60.627845 --1.181338 60.623738 --1.180751 60.619925 --1.181045 60.615524 --1.181631 60.611418 --1.183098 60.607017 --1.183685 60.602910 --1.183098 60.598803 --1.182512 60.594990 --1.180458 60.591763 --1.179871 60.587656 --1.178405 60.584136 --1.176351 60.580909 --1.174591 60.577388 --1.173124 60.573868 --1.172538 60.570348 --1.171657 60.566534 --1.171071 60.562427 --1.171657 60.558320 --1.170777 60.554507 --1.170191 60.550693 --1.170484 60.546293 --1.171071 60.542186 --1.170191 60.538372 --1.168724 60.535145 --1.169897 60.531332 --1.170191 60.527225 --1.167844 60.524291 --1.164617 60.521064 --1.162270 60.518131 --1.159043 60.514904 --1.156403 60.511970 --1.154350 60.508450 --1.152003 60.505223 --1.148776 60.502290 --1.146136 60.499063 --1.144375 60.495836 --1.142909 60.492609 --1.139975 60.489382 --1.133815 60.487622 --1.127361 60.486449 --1.121494 60.487915 --1.112987 60.486742 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54.360916 --2.923863 54.357102 --2.925623 54.353288 --2.924450 54.349475 --2.925623 54.345074 --2.926503 54.340674 --2.929437 54.337447 --2.932370 54.334514 --2.934424 54.330700 --2.935304 54.327180 --2.934424 54.323366 --2.936184 54.319553 --2.939118 54.316326 --2.942345 54.313392 --2.944985 54.310165 --2.944985 54.306058 --2.944398 54.302538 --2.943225 54.298724 --2.942638 54.294911 --2.940878 54.291684 --2.939998 54.287870 --2.938531 54.286110 --2.942931 54.288164 --2.945865 54.291097 --2.948212 54.294031 --2.949972 54.297258 --2.951732 54.300485 --2.952612 54.304298 --2.953199 54.308112 --2.952612 54.312805 --2.950852 54.316619 --2.949092 54.320726 --2.947918 54.324833 --2.946158 54.328940 --2.943811 54.332460 --2.942638 54.336274 --2.941464 54.340967 --2.939704 54.345074 --2.938238 54.349181 --2.936477 54.352995 --2.935891 54.357689 --2.934131 54.361796 --2.932957 54.366196 --2.935011 54.369423 --2.936771 54.372650 --2.939118 54.375877 --2.940878 54.379103 --2.943518 54.382330 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unknown -% Source : unknown -% Format : ascii, c1: time c2: surface elevation -% Description : -% The wave data was used in one of WAFO predecessors, i.e. the Wave -% Analysis Toolbox version 1.1 (WAT) -% -% Hm0 = 1.9m, Tm02 = 4.0s, Tp2 = 11.5s Tp1=5.6s -% -% See also diff --git a/wafo/data/sfa89.dat b/wafo/data/sfa89.dat deleted file mode 100644 index 8411859..0000000 --- a/wafo/data/sfa89.dat +++ /dev/null @@ -1,144 +0,0 @@ - 0.0000000e+00 1.2400000e+01 2.0700000e+02 - 1.6666667e-01 1.1800000e+01 2.0480000e+02 - 3.3333333e-01 1.1300000e+01 1.9940000e+02 - 5.0000000e-01 1.1800000e+01 1.9560000e+02 - 6.6666667e-01 1.3000000e+01 1.9500000e+02 - 8.3333333e-01 1.3400000e+01 1.9550000e+02 - 1.0000000e+00 1.2000000e+01 1.9250000e+02 - 1.1666667e+00 1.3300000e+01 1.9250000e+02 - 1.3333333e+00 1.4900000e+01 1.9450000e+02 - 1.5000000e+00 1.4400000e+01 1.9790000e+02 - 1.6666667e+00 1.3600000e+01 1.9800000e+02 - 1.8333333e+00 1.2400000e+01 1.8510000e+02 - 2.0000000e+00 1.5100000e+01 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o+ruoyFozQm1Lh8hTHWQlShYeF1Bc4ESjtpuI3GMquvy4Njo6bLeNPNMhX7DM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\nQPH/x7b+U3K6ZM4AAAAASUVORK5CYII=\n" - } - ], - "prompt_number": 10 - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "Formation of 5 min maxima" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "yura = xn[:85500, 1]\n", - "yura = np.reshape(yura, (285, 300)).T\n", - "maxyura = yura.max(axis=0)\n", - "subplot(212)\n", - "plot(xn[299:85500:300, 0] / 3600, maxyura, '.')\n", - "xlabel('Time (h)')\n", - "ylabel('(m)')\n", - "title('Maximum 5 min water level')\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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- } - ], - "prompt_number": 11 - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "Estimation of GEV for yuramax" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "import wafo.stats as ws\n", - "phat = ws.genextreme.fit2(maxyura, method='ml')\n", - "phat.plotfitsummary()\n", - "show()\n", - "#disp('Block = 11, Last block')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stderr", - "text": [ - "c:\\pab\\workspace\\pywafo_svn\\pywafo\\src\\wafo\\stats\\estimation.py:1080: UserWarning: P-value is on the conservative side (i.e. too large) due to ties in the data!\n", - " warnings.warn('P-value is on the conservative side (i.e. too large) due to ties in the data!')\n" - ] - }, - { - "output_type": "display_data", - "png": 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WL14s1vVC/+cvXrxYzpgVKfgoMDCQDbgTEx0doGPH/88q3r1j9jH++WceM4J0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- } - ], - "prompt_number": 12 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/wafo/doc/tutorial_scripts/WAFO Chapter 2.ipynb b/wafo/doc/tutorial_scripts/WAFO Chapter 2.ipynb deleted file mode 100644 index 806de65..0000000 --- a/wafo/doc/tutorial_scripts/WAFO Chapter 2.ipynb +++ /dev/null @@ -1,706 +0,0 @@ -{ - "metadata": { - "name": "WAFO Chapter 2" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "CHAPTER2 Modelling random loads and stochastic waves\n", - "====================================================\n", - "\n", - "Chapter2 contains the commands used in Chapter 2 of the tutorial and present some tools for analysis of random functions with respect to their correlation, spectral and distributional properties. The presentation is divided into three examples: \n", - "\n", - "Example1 is devoted to estimation of different parameters in the model.\n", - "Example2 deals with spectral densities and\n", - "Example3 presents the use of WAFO to simulate samples of a Gaussian process.\n", - "\n", - "Some of the commands are edited for fast computation. \n", - "\n", - "Section 2.1 Introduction and preliminary analysis\n", - "=================================================\n", - "\n", - "Example 1: Sea data\n", - "-------------------\n", - "Observed crossings compared to the expected for Gaussian signals\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import wafo\n", - "import wafo.objects as wo\n", - "xx = wafo.data.sea()\n", - "me = xx[:, 1].mean()\n", - "sa = xx[:, 1].std()\n", - "xx[:, 1] -= me\n", - "ts = wo.mat2timeseries(xx)\n", - "tp = ts.turning_points()\n", - "\n", - "cc = tp.cycle_pairs()\n", - "lc = cc.level_crossings()\n", - "lc.plot()\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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FtVOrZelwrTbfQ5KSZEmDOXNYzoDshJ+fTBTnzhV6aJ06wK+/AoMHA0eOmCE2\nK8REYe3mzMm1v8SLFi+Wq1O5zSnZDTc3ubpu8GBZ6qMQr74qF3n36SMHuNPTzRCjFWGisGaXLwPf\nfSczQT6JQqsFVq2SpQyI7Mp77wHVqgFffaXX4V26yNpnSUlAYKDcDIkkDmZbK60WaNcO6NtXjsTl\nY9482aw+dMiMsRFZivh4uX3j77/L7ig9bdoEjBkjV3OXsKGv03Y3mG33C+6WLgU0mjxrOf3t6VNZ\nBmfFCvOFRWRRvL1li1utNui03r2BqlVtZ8yCC+7sVZ8+wJQpBS6KWLtWPjibg8hwc+YAmzfLPGMr\nmyAV9bPTane4s3sbN+p1yDvvmCEWIhs0ZgxQvjzQvbvc0mXlSvmzPbLaricq2LFjsh7/228rHQmR\ndXJykpWWY2Nl2Y+ZM5WOSDmFJorff/8913NHjx41STBkPDNnAl98ATg7Kx0JkXUrWxZYsABYsgS4\nfl3paJRRaKL4KI/dbcILmGVDynv+XM5y6tFD6UiILExmJvDZZ/IfiQFq1pQ1oYYNM/hUm5DvGMXx\n48dx7NgxJCcn45tvvtENgKSkpEBbwCpgMpFLl2TzII89Jl509ChQv36h5fmJ7I+TE3DhglyM969/\nGXTqmDGyO7dbNznlvFw5E8VogfJtUajVaqSkpECj0SAlJQWpqalITU1FhQoV8Msvv5gzRtJo5FaP\nBw7odfi6dcCbb5o4JiJrtWABMH9+rn22C1OypNwdr2pVuXrbnhQ6PTY+Ph7eFrbLjd1Nj12yRNYI\nP3y40GJN168Dr7wi/w1UqWKm+IiszTffAHv2AFFRBhdAu38fqFdPThgxYA2fRSjqZ2ehieLKlSv4\n6quvEB8fj6z/bl6uUqlwQM9vt6ZgV4ni/n2gQQNg3z4gIKDAQx89knsCf/gh8PHHZoqPyBplZgKN\nGwMzZhRpMG/FCrnh0bffAu++a4L4TMRkiSIgIADDhw9H06ZN4fDfbaBUKhVeVnAFil0livffl52h\n8+YVeFhGhiz6FxQkvywRUSEOHJCzPqZOLdLpZ88C/fsDzZsDP/xgHbvkmSxRvPzyyzh16lSRAzMF\nu0kUiYlyV5Xz54GKFfM9TKORC7VLlgR+/tm2atMQWbL0dKBrV/kFTc/ag4oyWa2nbt26YdGiRUhK\nSsLDhw91D1OJi4vD0KFD0bt3b5O9h9Vwd5cVYgtIEoCcvPHokVw5yiRBZD5lywJbtsgyOT//rHQ0\nplNoi8Kx6mrUAAAYJUlEQVTb2xuqPAZ74uLiTBYUAPTu3RubNm3K8zW7aVHoIS0N8PSUjQ49Zs4S\nkQns3QtMnAhYWOdLLiZrUcTHxyMuLi7XwxBDhgyBq6srGjVqlOP5qKgo+Pn5wdfXF7NnzzYscgIg\nyyG3bs0kQaSk114D7t2TX9hsUaFFAVetWpVni2LgwIF6v8ngwYPx0Ucf5ThHo9EgPDwc+/btg7u7\nO5o1a4bu3bujfv36el+XZJn9Ll2UjoLIBvz730DDhkDp0gaf6uAADBoku39tcTJJoS2KP/74Q/c4\nfPgwIiIisG3bNoPepE2bNnBxccnxXExMDHx8fODt7Q0nJyf069cPkZGRePjwIYYNG4azZ8/aZyvj\n2TODDr9wAXihoUZERTFjhpzvWkTvvSfHKWyxxEehLYqFCxfm+Pnx48fo27dvsd84MTERnp6eup89\nPDxw8uRJVK5cGd9//32h52ffhCM4OBjBwcHFjklxQgBvvCGLyujRTNBqgb/+KnBLCiLS11dfybmu\n770n99w2kI8PEBICtG8PbNggxw6VFh0dbZQN3gzej6Js2bJGGcjOqzvLEMXZrcli/forkJws/9r0\ncOOGnBD1QmONiIqibl1gyBBZNHD58iJdYvVqYO5coFkzuVd9p05GjtFAL36JnlrENSOFJopu3brp\n/lur1eLixYvo06dPkd4sO3d3dyQkJOh+TkhIgIc9j8hmZADjxgHLlgGO+uXv48fZ7URkVJMnAy+9\nBJw+DTRtavDpJUoAEybIjY769wdmzbKuldv5KfQT6ZP/Vr9SqVRwdHSEl5dXji6jogoKCkJsbCzi\n4+NRs2ZNbNiwAevWrdP7/IiICNvpcgLkyuuAADl9Qg+PHsk/SO6HTWREFSsC06bJ1dqRkUW+TNu2\nclv72bMtI1EUtwtKrz2z79y5gz/++AMqlQqvvPIKqlevbtCbhIaG4tChQ3jw4AGqV6+OadOmYfDg\nwdi9ezdGjx4NjUaDsLAwTJw4Ub+gbW0dRVKSbBqcOCE7OvXwj3/Ion/z55s4NiJ7o9EAT54Uu07/\ns2eAq6vsIraU7mGTlfDYuHEjxo8fj3bt2gEADh8+jLlz5yq6ctrmEkVqKnDkiN7zXDduBD7/HDhz\nRq4MJSLL1L070KEDMHq00pFIJi0KuG/fPl0rIjk5Ga+99hrOK7iyRKVSYcqUKbbV9aSnpCRZ9HL7\ndllOnIgs19WrQKtWwK5dcoBbKX93PU2dOtU0iaJRo0Y4f/68bpaSVqtFYGAg/vzzz6JFbAQ216LQ\nkxByd60mTeR+2ERk+bZsAcaOlev5qlZVNpaifnYWOpjduXNndOrUCf3794cQAhs2bEAXLgVWxM8/\nA7dvyz88IrIOvXrJ4cewsGKNjysq30QRGxuLu3fvYu7cudi8eTOOHj0KAGjZsiX69+9vtgDzY3Oz\nnvSwebNci1eypNKRENkJIeRiiCVLgNq1i3yZadPk5JO0NGX22jbZrKc33ngDM2fORMALu6qdP38e\nkydPxvbt24v8psVlE11PO3fKqXitW+t1uBBysejJk0CtWiaOjYj+Z+pUOdhQzDrir74qp8v+d16Q\nIoxePfbu3bu5kgQgB7dNXWLc5mVkACNGGHRKXJxczOPlZaKYiChvn3wCHDwoF+EVQ4sWcpGsNco3\nUTx+/DjfkzIyMkwSjN1YsECu+tSzNQHIPs4WLQzeB56Iiqt8ebk72KefyqZ9EbVqBRih7JIi8k0U\nQUFBWLp0aa7nly1bpuh+2X+LiIgwSrErs3vwAJgzR67tN8CZM4AF3HYi+xQWBty6JXcoKqIuXWTX\ncVKSEePSU3R0dLHq4+U7RnHnzh307NkTJUuW1CWGU6dO4fnz5/j111/hVoTqisZi1WMUY8YAajWw\naJFBp4WEyCl2nHBGpJCoKNlt3KNHkS8RFiZLSX36qRHjMoBJFtwJIXDw4EFcuHABKpUK/v7+6NCh\nQ7ECNQarTRRqtew/2rVLru3XkxBAtWrAn38WqfoxEVmI338Hhg4FLl1SphvZZCuzLZHVJgpAfuob\n+BcSHy9nTNy5Y5qQiMg8hJAtiiVL5L4V5mayPbMtldWOURiYJLRaOUFq0CATxUNEZqNSySHKfv2A\nY8fM974mG6OwZFbdojDQtGnAb78BBw4ATk5KR0NExhAVBQwcKDc66tzZfO9rdy0Ke7Bnj2yibtzI\nJEFkUdRqOYWpiDp3luU8Bg0CDNiGRzFMFOZQhAx+48b//og4gE1kYe7elVMQizFw2KIFsH+/LMuz\neLERYzMBJgpTu3dPLoDIzNT7lOfPgd695c6obduaMDYiKhpPT2DAAIPXQ72oYUO5Fc0338huZkvt\nUbfaRGE1g9nffiunLBnQdzRtGlCzpqwcQEQWauJE4KefgISEYl2mdm05bXbzZuCzz4wU2ws4mG3J\nHj4EfH2BU6cAb2+9Trl6FWjZEjh/XiYLIrJg//yn3MB+yZJiXyo5GQgOBvr3ByZPLn5oeeE6Cks0\ndaocbPjxR70OF0IOcnXqJFdhE5GFe/gQqFdP7kqk55fBgiQlye7mkSNNs32qyTYuoiJ6+hRYuNCg\nydK//gokJgIffWTCuIjIeCpXBo4eNVrtfzc3OcDdti1Qpgzw4YdGuWyxMVGYyu3b8muBr69eh6el\nyTJQq1dzKiyRVXnpJaNezstLJovgYJksBg406uWLhF1PFmLSJNlLVcy9UYjIRly6BLz2GvDdd3IW\npDGw68mKXb0KLFsGnDundCREZCnq1wd27wY6dgRKlwa6dVMuFqtNFLa0Z/bcubLbibOciCi7wEBg\nxw65zcC9e0DJkkW7jsn2zLZkttb1VKeO/GNo0EDpSIioWL7/Xi6wbdbMqJdt2lRujNmqVfGuw1pP\nliAzU852MkB8PJCeLpuZRGTltFq5YtbIOnSQhUGVwkRhTGvXymX9Bjh4UNal517YRDZgyBDg9Gn5\nMKL27eVnhVKYKIxFowG+/BIYNcqg0w4cUGYDEyIygdKl5T6nX3xh1Mu2aQPExMidWJXARGEsv/wC\nVKli0Ke+EPJbggXsLktExvL++8CJE7IOj5FUqCALCB4/brRLGoSJwhi0WmD6dFnRy4A+pGvX5OF1\n65owNiIyr7JlZennyEijXrZ9e+XGKax2eqxF2b5dLqfu0sWg0/7uduL4BJGNGTMGKGHc7+EdOsjy\ncUpgi8IYPD2B+fMN/sRntxORjTJykgDk1NizZ2W5H3NjojCGpk2B1q31PvzSJbluggPZRKSvsmWB\nJk3k3hXmZrVdT9a8MnvIEMDREejZ02hFJ4nIDgQFAX/+KbciMARXZlshLy+5/SGTBBEZIiJCzpYs\n6lgFV2ZbCa1W7sdeo4bSkRCRWezaZbRNZsqXB1JSjHIpgzBRFNX163LPCQM9eAA4OwOlSpkgJiKy\nPK++Kqs23LhR7Es5OwOpqUaIyUBMFEU1erTcks5At2+zSiyRXalcGfjgA2DWrGJfytmZLQrrceYM\ncOoUEBZm8KlJSXK7QyKyI2PHAhs2ALduFesyTBTW5Msv5crL0qUNPpUtCiI7VK2a/GI5Z06xLsNE\nYS0uXQIOHy7yrudsURDZqU8+AZ4/l9OWiqh8eY5RWIeZM2WF2HLlinQ6WxREdqpGDWDJkmLV7FGq\nRWG1C+4UM2lSsZoESUlcjU1ERcNEYS38/Ip1OlsURFRUHKOwExyjIKKiKldObp2s1Zr3fS2uRZGW\nloYRI0agVKlSCA4ORv/+/ZUOyWiEkKuymSiICM+eAWXKGHRKiRKyOGBammxdmIvFtSi2bNmCPn36\nYOnSpdi2bZvS4RjVgwfyG0ERZtUSkS25cAF4+eUiNQ2U6H4yS6IYMmQIXF1d0ahRoxzPR0VFwc/P\nD76+vpg9ezYAIDExEZ6engAABwcHc4RXuPXrjbL8nuMTRAQA8PeX3xqL8GXYZhPF4MGDERUVleM5\njUaD8PBwREVF4eLFi1i3bh0uXboEDw8PJCQkAAC05u6Iy8uDB8DIkUbZiITjE0QEQE6RnTABmD3b\n4HUVShQGNEuiaNOmDVxcXHI8FxMTAx8fH3h7e8PJyQn9+vVDZGQkevXqhc2bN2PEiBHo3r27OcIr\n2HffAb16yV3sioktCiLS6dkTSE4Gjh416DQlCgMqNpidvYsJADw8PHDy5EmULVsWP/74Y6HnR0RE\n6P7bZBsYPXkCLF4MnDxplMs1aAC4uhrlUkRk7RwcZCmgOXMM2iFz6FDAw0O/Y4u7YdHfFEsUqmKs\nTgRyJgqTWbQI6NIFqFvXKJdr3twolyEiWzFokCwUqNXq3b09YID+l3/xS/TUIu54pFiicHd3141F\nAEBCQgI89E2T5qDRAEuXyk1HiIhMoUwZYPp0paMolGLTY4OCghAbG4v4+Hio1Wps2LDBoDGJiIgI\nozSp8uXgAJw/L/uLiIisWHR0dLF6YcyyZ3ZoaCgOHTqEBw8eoHr16pg2bRoGDx6M3bt3Y/To0dBo\nNAgLC8PEiRP1up6175lNRKSEon52miVRGJtKpcKUKVNMN4hNRGRD/h7Unjp1qn0lCisMm4ioYMnJ\ncpMjEynqZ6fFlfAgIrJLFy4AzZoBWVlKR5ILE0V2Gg0weLAydXyJyL41bAi4uxeprIepWW2iMMms\np40bgWvX5Bp5IiJzGz0amDfP6Je1illPxmaSMQqtFggIAL7+GujUybjXJiLSR1YWUKcO8Ouvsrqs\nkXGMori2bpWLXzp2VDoSIrJXjo5AeLisMWdBrDZRGLXrSQi5OvKzz4q18TkRUbG9/77RWxPsejKG\n//xHVtrat88o5cSJiCyR3S24M3rYQrA1QUQ2jWMUxcUkQUSUJyYKIiIqkNUmCpNXjyUiUppGI7dj\nLiYOZhMR2apVq+Saiq1bjXI5DmYTEdma9HSgVi25HXOdOsW+HAeziYhsTdmyQFgYsGCBomGwRUFE\nZMkSEoDGjYG4OKBChWJdyu5aFBzMJiK74OkJvP46sGJFkS/BwWwiIlt35gxw8ybw1lvFugwHs4mI\nqEB21/VERETmwURBREQFYqIgIqICMVEQEVmT9HQgJcWsb2m1iYLTY4nILk2YAMyfb9ApnB5LRGRP\nzpwBuneXC/AcHQ06lbOeiIjsQZMmchHejh1me0smCiIiazNyJLBokdnejl1PRETW5vlzwMsLOHwY\neOklvU9j1xMRkb0oVQr46itArTbL27FFQURkJ9iiICIik2CiICKiAjFREBFRgaw2UXBlNhGRfrgy\nm4iI9MLBbCIiMgkmCiIiKhATBRERFYiJgoiICsREQUREBWKiICKiAjFREBFRgZgoiIioQEwURERU\nICYKIiIqkMUliri4OAwdOhS9e/dWOhQiIoIFJoratWvjhx9+UDoMo7CWooWM07isIU5riBFgnJbC\nZIliyJAhcHV1RaNGjXI8HxUVBT8/P/j6+mL27NmmenuLYC1/PIzTuKwhTmuIEWCclsJkiWLw4MGI\niorK8ZxGo0F4eDiioqJw8eJFrFu3DpcuXcJPP/2EMWPG4Pbt26YKh4iIishkiaJNmzZwcXHJ8VxM\nTAx8fHzg7e0NJycn9OvXD5GRkRgwYAC+/fZb1KxZEw8fPsSwYcNw9uxZm29xEBFZBWFCcXFxomHD\nhrqfN23aJIYOHar7+aeffhLh4eEGXxcAH3zwwQcfRXgUhSPMSKVSGeU6gpsWERGZjVlnPbm7uyMh\nIUH3c0JCAjw8PMwZAhERGcisiSIoKAixsbGIj4+HWq3Ghg0b0L17d3OGQEREBjJZoggNDUXLli1x\n9epVeHp6YsWKFXB0dMTChQvRqVMnNGjQAH379kX9+vULvdb48eNRv359BAYGolevXnjy5Emexyk9\n9XbTpk3w9/eHg4MDTp8+ne9x3t7eCAgIQJMmTfDKK6+YMUJJ3ziVvp8PHz5ESEgI6tWrh44dO+Lx\n48d5HqfE/dTn3nz88cfw9fVFYGAgzpw5Y5a4XlRYnNHR0ahYsSKaNGmCJk2aYPr06WaPMb+p9NlZ\nwr0sLE5LuJeA7Klp3749/P390bBhQ8yfPz/P4wy6p0Ua2TCzvXv3Co1GI4QQYsKECWLChAm5jsnK\nyhJ169YVcXFxQq1Wi8DAQHHx4kWzxnnp0iVx5coVERwcLE6dOpXvcd7e3uLBgwdmjCwnfeK0hPs5\nfvx4MXv2bCGEELNmzcrz/3chzH8/9bk3O3fuFF26dBFCCHHixAnRvHlzs8VnSJwHDx4U3bp1M3ts\n2R0+fFicPn06x8SX7CzhXgpReJyWcC+FECIpKUmcOXNGCCFESkqKqFevXrH/Pi1uZXZeQkJCUKKE\nDLV58+a4detWrmPym3prTn5+fqhXr55exwoFB+T1idMS7ue2bdswaNAgAMCgQYOwdevWfI815/3U\n595kj7158+Z4/Pgx7t69a7YY9Y0TUH5ySF5T6bOzhHsJFB4noPy9BIAaNWqgcePGAIDy5cujfv36\nudaoGXpPrSJRZPfjjz+ia9euuZ5PTEyEp6en7mcPDw8kJiaaMzS9qVQqvP766wgKCsKyZcuUDidP\nlnA/7969C1dXVwCAq6trvn/I5r6f+tybvI7J6wuOKekTp0qlwrFjxxAYGIiuXbvi4sWLZo1RH5Zw\nL/VhifcyPj4eZ86cQfPmzXM8b+g9Nev02IKEhITgzp07uZ7/8ssv0a1bNwDAjBkzULJkSfTv3z/X\nccaaelsYfeIszNGjR+Hm5obk5GSEhITAz88Pbdq0sag4lb6fM2bMyBVPfjGZ436+GIs+Xvx2aa57\nasj7NW3aFAkJCShbtix2796NHj164OrVq2aIzjBK30t9WNq9TE1NxTvvvIPvvvsO5cuXz/W6IffU\nYhLFb7/9VuDrK1euxK5du7B///48XzfX1NvC4tSHm5sbAKBatWro2bMnYmJijP7BVtw4LeF+urq6\n4s6dO6hRowaSkpJQvXr1PI8zx/3MTp978+Ixt27dgru7u8liyos+cTo7O+v+u0uXLhgxYgQePnyI\nypUrmy3OwljCvdSHJd3LzMxMvP3223j33XfRo0ePXK8bek+touspKioKc+fORWRkJEqXLp3nMZY2\n9Ta/vsr09HSkpKQAANLS0rB3794CZ3uYWn5xWsL97N69O1atWgUAWLVqVZ5/8ErcT33uTffu3bF6\n9WoAwIkTJ1CpUiVdN5q56BPn3bt3dX8DMTExEEJYVJIALONe6sNS7qUQAmFhYWjQoAFGjx6d5zEG\n31NjjbSbko+Pj/Dy8hKNGzcWjRs3FsOHDxdCCJGYmCi6du2qO27Xrl2iXr16om7duuLLL780e5xb\ntmwRHh4eonTp0sLV1VV07tw5V5zXr18XgYGBIjAwUPj7+1tsnEIofz8fPHggXnvtNeHr6ytCQkLE\no0ePcsWp1P3M6958//334vvvv9cdM3LkSFG3bl0REBBQ4Cw4JeNcuHCh8Pf3F4GBgaJFixbi+PHj\nZo+xX79+ws3NTTg5OQkPDw+xfPlyi7yXhcVpCfdSCCGOHDkiVCqVCAwM1H1m7tq1q1j3VCWEBQzT\nExGRxbKKriciIlIOEwURERWIiYKIiArEREFERAVioiDKQ14LlIwlIiICX3/9tcmuT2RsTBREeTDl\nyl9LXFVMVBAmCiI9Xb9+HV26dEFQUBDatm2LK1eu4MmTJ/D29tYdk5aWBi8vL2g0mjyPf9H8+fPh\n7++PwMBAhIaGmvG3IdKfxZTwILJ0H3zwAZYsWQIfHx+cPHkSI0aMwP79+9G4cWNER0cjODgYO3bs\nQOfOneHg4JDv8cD/WhWzZ89GfHw8nJyc8PTpUyV/PaJ8MVEQ6SE1NRXHjx9H7969dc+p1WoAQN++\nfbFhwwYEBwdj/fr1CA8PR2pqKo4dO5bn8dkFBASgf//+6NGjR54lSogsARMFkR60Wi0qVaqU505g\n3bp1w6RJk/Do0SOcPn0aHTp0QEpKClxcXPLdOezvggg7d+7E4cOHsX37dsyYMQN//vknHBwcTPq7\nEBmKYxREeqhQoQJq166NX375BYD8oD937hwAOUOqWbNm+Pjjj9GtWzeoVKo8jz9//nyOawohcPPm\nTQQHB2PWrFl48uQJ0tLSzPuLEemBiYIoD+np6fD09NQ95s2bh59//hnLly9H48aN0bBhQ2zfvl13\nfN++fbF27Vr07dtX99yLx2/btk33mkqlgkajwYABAxAQEICmTZti1KhRqFChgll/TyJ9sCggEREV\niC0KIiIqEBMFEREViImCiIgKxERBREQFYqIgIqICMVEQEVGB/h/cV8ENGKkrWAAAAABJRU5ErkJg\ngg==\n" - } - ], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Average number of upcrossings per time unit\n", - "----------------------------------------------\n", - "Next we compute the mean frequency as the average number of upcrossings per time unit of the mean level (= 0); this may require interpolation in the crossing intensity curve, as follows. \n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "T = xx[:, 0].max() - xx[:, 0].min()\n", - "f0 = np.interp(0, lc.args, lc.data, 0) / T #! zero up-crossing frequency \n", - "print('f0 = %g' % f0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "f0 = 0.224071\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Turningpoints and irregularity factor\n", - "----------------------------------------" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "fm = len(tp.data) / (2 * T) # frequency of maxima\n", - "alfa = f0 / fm # approx Tm24/Tm02\n", - "\n", - "print('fm = %g, alpha = %g, ' % (fm, alfa))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "fm = 0.456159, alpha = 0.491212, \n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Visually examine data\n", - "------------------------\n", - "We finish this section with some remarks about the quality of the measured data. Especially sea surface measurements can be of poor quality. We shall now check the quality of the dataset {\\tt xx}. It is always good practice to visually examine the data before the analysis to get an impression of the quality, \n", - "non-linearities and narrow-bandedness of the data.First we shall plot the data and zoom in on a specific region. A part of sea data is visualized with the following commands" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "ts.plot_wave('k-', tp, '*', nfig=1, nsub=1)\n", - "\n", - "axis([0, 2, -2, 2])\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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I5XKoVCrs3LkTGRkZANrDGltbW6FUKiGRSLB3717s37+fuUZYWBhqa2stnq0j76I93Hbb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\nHCkpKfDw8EBlZSXvuIMHD0Kj0WDatGlYv369zWMeMtzalFpTsgZrStb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ncOswAAAAAElF\nTkSuQmCC\n" - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finding possible spurious points\n", - "------------------------------------\n", - "However, if the amount of data is too large for visual examinations one could use the following criteria to find possible spurious points. One must be careful using the criteria for extremevalue analysis, because\n", - "it might remove extreme waves that are OK and not spurious." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import wafo.misc as wm\n", - "dt = ts.sampling_period()\n", - "# dt = np.diff(xx[:2,0])\n", - "dcrit = 5 * dt\n", - "ddcrit = 9.81 / 2 * dt * dt\n", - "zcrit = 0\n", - "inds, indg = wm.findoutliers(ts.data, zcrit, dcrit, ddcrit, verbose=True)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Found 0 spurious positive jumps of Dx\n", - "Found 0 spurious negative jumps of Dx\n", - "Found 37 spurious positive jumps of D^2x\n", - "Found 200 spurious negative jumps of D^2x\n", - "Found 244 consecutive equal values\n", - "Found the total of 1152 spurious points\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Section 2.2 Frequency Modeling of Load Histories\n", - "---------------------------------------------------\n", - "Periodogram: Raw spectrum" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "Lmax = 9500\n", - "S = ts.tospecdata(L=Lmax)\n", - "S.plot()\n", - "axis([0, 5, 0, 0.7])\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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dO9q2YJCcRurdu7lPJaOuCYJwX2S5uMzMTFz763XZ29sbaWlpmDlzJubOnYub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\nsvi81PM/e9bQM0oYncTHA99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2bVuN/V0UFxfDz88PlZWViI2NxbJlyxAbG6u2WaqxfPly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\nRU5ErkJggg==\n" - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Calculate moments \n", - "-------------------" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mom, text = S.moment(nr=4)\n", - "print('sigma = %g, m0 = %g' % (sa, sqrt(mom[0])))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "sigma = 0.472955, m0 = 0.472955\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Section 2.2.1 Random functions in Spectral Domain - Gaussian processes\n", - "--------------------------------------------------------------------------\n", - "Smoothing of spectral estimate \n", - "----------------------------------\n", - "By decreasing Lmax the spectrum estimate becomes smoother." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "Lmax0 = 200; Lmax1 = 50\n", - "S1 = ts.tospecdata(L=Lmax0)\n", - "S2 = ts.tospecdata(L=Lmax1)\n", - "S1.plot('-.')\n", - "S2.plot()\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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TyKRJk1AUhaFDh1JcXMyxY8eaI64WlZ6f3uylkEoBHQM4lHmoRZ4lhBDNrd42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\nWcjL0zqKptPbuzefT/6c+76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- } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " Estimated autocovariance\n", - "----------------------------\n", - "Obviously knowing the spectrum one can compute the covariance\n", - "function. The following code will compute the covariance for the \n", - "unimodal spectral density S1 and compare it with estimated \n", - "covariance of the signal xx." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "Lmax = 85\n", - "R1 = S1.tocovdata(nr=1) \n", - "Rest = ts.tocovdata(lag=Lmax)\n", - "R1.plot('.')\n", - "Rest.plot()\n", - "axis([0, 25, -0.1, 0.25])\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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So74nQghRRQpPILGxsbCzs4O1tTU0NTXh7++P8PBwiWV69eoFfX19AEDPnj3x9OnTeq9b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\nUAIhhBAiE0oghBBCZEIJhBBCiEz+H72XH4/yYkS0AAAAAElFTkSuQmCC\n" - } - ], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see in Figure below that the covariance function corresponding to the spectral density S2 significantly differs from the one estimated directly from data. It can be seen in Figure above that the covariance corresponding to S1 agrees much better with the estimated covariance function." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "R2 = S2.tocovdata(nr=1)\n", - "R2.plot('.')\n", - "Rest.plot()\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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sAmuH/1dlfbtauOKX8b/gpciXkJKTgneffrfOGzbv/30f03ZPg6G+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\nixEVFYXg4JbzqNmCggLk5+cDAB49eoT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- } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Section 2.2.2 Transformed Gaussian models\n", - "-------------------------------------------\n", - "We begin with computing skewness and kurtosis for the data set xx and compare it with the second order wave approximation proposed by Winterstein:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import wafo.stats as ws\n", - "rho3 = ws.skew(xx[:, 1])\n", - "rho4 = ws.kurtosis(xx[:, 1])\n", - "\n", - "sk, ku = S1.stats_nl(moments='sk')" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 13 - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "Comparisons of 3 transformations" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "import wafo.transform.models as wtm\n", - "gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku).trdata()\n", - "g = wtm.TrLinear(mean=me, sigma=sa).trdata() # Linear transformation \n", - "glc, gemp = lc.trdata(mean=me, sigma=sa)\n", - "\n", - "glc.plot('b-') #! Transf. estimated from level-crossings\n", - "gh.plot('b-.') #! Hermite Transf. estimated from moments\n", - "g.plot('r')\n", - "grid('on')\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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- } - ], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Test Gaussianity of a stochastic process\n", - "------------------------------------------\n", - "TESTGAUSSIAN simulates e(g(u)-u) = int (g(u)-u)^2 du for Gaussian processes given the spectral density, S. The result is plotted if test0 is given. This is useful for testing if the process X(t) is Gaussian.\n", - "If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.\n", - "\n", - "As we see from the figure below: none of the simulated values of test1 is above 1.00. Thus the data significantly departs from a Gaussian distribution. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "test0 = glc.dist2gauss()\n", - "# the following test takes time\n", - "N = len(xx)\n", - "test1 = S1.testgaussian(ns=N, cases=50, test0=test0)\n", - "is_gaussian = sum(test1 > test0) > 5 \n", - "print(is_gaussian)\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "False\n" - ] - }, - { - "output_type": "display_data", - "png": 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fP6SkpLi8XIVW2gIA9u3bh/79++PEiRPIzMxEXFycw/OdaQvFniF0Zh2D1oSG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\nY0it2QAAAABJRU5ErkJggg==\n" - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Normalplot of data xx\n", - "------------------------\n", - "indicates that the underlying distribution has a \"heavy\" upper tail and a \"light\" lower tail." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "import pylab\n", - "ws.probplot(ts.data.ravel(), dist='norm', plot=pylab)\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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+fJmbN29qH7dp0+beqqsBEg6isdBpLTjlwMgT0CQftrrCRavb7pZQEHdWI+c5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\nc/OmOdbWRcycOVS6k4SoBju7u1v/8/P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- } - ], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Section 2.2.3 Spectral densities of sea data\n", - "-----------------------------------------------\n", - "Example 2: Different forms of spectra" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import wafo.spectrum.models as wsm\n", - "clf()\n", - "Hm0 = 7; Tp = 11;\n", - "spec = wsm.Jonswap(Hm0=Hm0, Tp=Tp).tospecdata()\n", - "spec.plot()\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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RtGPHDri5ueG5555DixYt0KFDB7Rv3x4tWrTA7Nmz4enpiV27dskda4NmrE7r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\n" - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Directional spectrum and Encountered directional spectrum\n", - "=========================================================\n", - "Directional spectrum\n", - "---------------------" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "D = wsm.Spreading('cos2s')\n", - "Sd = D.tospecdata2d(spec)\n", - "Sd.plot()\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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JrbQYPJgNr7zCrVOnsvKJJ4iaOBF++R+ERpHDAdxozkFyaIKrdZ0/HYQOTWyr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\nRU5ErkJggg==\n" - } - ], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Encountered directional spectrum\n", - "--------------------------------- " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#clf()\n", - "#Se = spec2spec(Sd,'encdir',0,10);\n", - "#plotspec(Se), hold on\n", - "#plotspec(Sd,1,'--'), hold off\n", - "##!wafostamp('','(ER)')\n", - "#disp('Block = 17'),pause(pstate)\n", - "#\n", - "##!#! Frequency spectra\n", - "#clf\n", - "#Sd1 =spec2spec(Sd,'freq');\n", - "#Sd2 = spec2spec(Se,'enc');\n", - "#plotspec(spec), hold on\n", - "#plotspec(Sd1,1,'.'),\n", - "#plotspec(Sd2),\n", - "##!wafostamp('','(ER)')\n", - "#hold off\n", - "#disp('Block = 18'),pause(pstate)\n", - "#\n", - "##!#! Wave number spectrum\n", - "#clf\n", - "#Sk = spec2spec(spec,'k1d')\n", - "#Skd = spec2spec(Sd,'k1d')\n", - "#plotspec(Sk), hold on\n", - "#plotspec(Skd,1,'--'), hold off\n", - "##!wafostamp('','(ER)')\n", - "#disp('Block = 19'),pause(pstate)\n", - "#\n", - "##!#! Effect of waterdepth on spectrum\n", - "#clf\n", - "#plotspec(spec,1,'--'), hold on\n", - "#S20 = spec;\n", - "#S20.S = S20.S.*phi1(S20.w,20);\n", - "#S20.h = 20;\n", - "#plotspec(S20), hold off\n", - "##!wafostamp('','(ER)')\n", - "#disp('Block = 20'),pause(pstate)\n", - "#\n", - "##!#! Section 2.3 Simulation of transformed Gaussian process\n", - "##!#! Example 3: Simulation of random sea \n", - "##! The reconstruct function replaces the spurious points of seasurface by\n", - "##! simulated data on the basis of the remaining data and a transformed Gaussian\n", - "##! process. As noted previously one must be careful using the criteria \n", - "##! for finding spurious points when reconstructing a dataset, because\n", - "##! these criteria might remove the highest and steepest waves as we can see\n", - "##! in this plot where the spurious points is indicated with a '+' sign:\n", - "##!\n", - "#clf\n", - "#[y, grec] = reconstruct(xx,inds);\n", - "#waveplot(y,'-',xx(inds,:),'+',1,1)\n", - "#axis([0 inf -inf inf])\n", - "##!wafostamp('','(ER)')\n", - "#disp('Block = 21'),pause(pstate)\n", - "#\n", - "##! Compare transformation (grec) from reconstructed (y) \n", - "##! with original (glc) from (xx)\n", - "#clf\n", - "#trplot(g), hold on\n", - "#plot(gemp(:,1),gemp(:,2))\n", - "#plot(glc(:,1),glc(:,2),'-.')\n", - "#plot(grec(:,1),grec(:,2)), hold off \n", - "#disp('Block = 22'),pause(pstate)\n", - "#\n", - "##!#!\n", - "#clf\n", - "#L = 200;\n", - "#x = dat2gaus(y,grec);\n", - "#Sx = dat2spec(x,L);\n", - "#disp('Block = 23'),pause(pstate)\n", - "# \n", - "##!#!\n", - "#clf\n", - "#dt = spec2dt(Sx)\n", - "#Ny = fix(2*60/dt) #! = 2 minutes\n", - "#Sx.tr = grec;\n", - "#ysim = spec2sdat(Sx,Ny);\n", - "#waveplot(ysim,'-')\n", - "##!wafostamp('','(CR)')\n", - "#disp('Block = 24'),pause(pstate)\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Estimated spectrum compared to Torsethaugen spectrum\n", - "-------------------------------------------------------" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "clf()\n", - "fp = 1.1;dw = 0.01\n", - "H0 = S1.characteristic('Hm0')[0]\n", - "St = wsm.Torsethaugen(Hm0=H0,Tp=2*pi/fp).tospecdata(np.arange(0,5+dw/2,dw)) \n", - "S1.plot()\n", - "St.plot('-.')\n", - "axis([0, 6, 0, 0.4])\n", - "show()\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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WKHPmzBlGjhzJF198QVBQkEV1bVWhUsjCHQtLdFz9+ivccQc0bQpeXlCFPC6E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\ncQghhLCIJA4hhBAW+X/+nuw44UNfwAAAAABJRU5ErkJggg==\n" - } - ], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Transformed Gaussian model compared to Gaussian model\n", - "-------------------------------------------------------\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dt = St.sampling_period()\n", - "va, sk, ku = St.stats_nl(moments='vsk' )\n", - "#sa = sqrt(va)\n", - "gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa)\n", - " \n", - "ysim_t = St.sim(ns=240, dt=0.5)\n", - "xsim_t = ysim_t.copy()\n", - "xsim_t[:,1] = gh.gauss2dat(ysim_t[:,1])\n", - "\n", - "ts_y = wo.mat2timeseries(ysim_t)\n", - "ts_x = wo.mat2timeseries(xsim_t)\n", - "ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1)\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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7h8Eh9TSCkn+G+/m1MDQUenAX4wzx9bMP8FvyGzCZNU6u+HvaXMU+BGKK/lIs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\nH1OnTpXHbnneHhqqwLpDLvZgBLbbhuHla0swMgRYtgyoh0crzFdfAYs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- } - ], - "prompt_number": 20 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/wafo/doc/tutorial_scripts/WAFO Chapter 3.ipynb b/wafo/doc/tutorial_scripts/WAFO Chapter 3.ipynb deleted file mode 100644 index 8787457..0000000 --- a/wafo/doc/tutorial_scripts/WAFO Chapter 3.ipynb +++ /dev/null @@ -1,73 +0,0 @@ -{ - "metadata": { - "name": "WAFO Chapter 3" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "CHAPTER3 Demonstrates distributions of wave characteristics\n", - "=============================================================\n", - "\n", - "Chapter3 contains the commands used in Chapter3 in the tutorial.\n", - " \n", - "Some of the commands are edited for fast computation. \n", - "\n", - "Section 3.2 Estimation of wave characteristics from data\n", - "----------------------------------------------------------\n", - "Example 1\n", - "~~~~~~~~~~ " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "speed = 'fast'\n", - "#speed = 'slow'\n", - "\n", - "import wafo.data as wd\n", - "import wafo.misc as wm\n", - "import wafo.objects as wo\n", - "xx = wd.sea() \n", - "xx[:,1] = wm.detrendma(xx[:,1],len(xx))\n", - "ts = wo.mat2timeseries(xx)\n", - "Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8)\n", - "Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "AssertionError", - "evalue": "", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAssertionError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 8\u001b[0m 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\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2936\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0myp\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mAssertionError\u001b[0m: " - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/wafo/doc/tutorial_scripts/WAFO Chapter 4.ipynb b/wafo/doc/tutorial_scripts/WAFO Chapter 4.ipynb deleted file mode 100644 index 7ab36e8..0000000 --- a/wafo/doc/tutorial_scripts/WAFO Chapter 4.ipynb +++ /dev/null @@ -1,468 +0,0 @@ -{ - "metadata": { - "name": "WAFO Chapter 4" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Chapter 4 Fatigue load analysis and rain-flow cycles\n", - "=====================================================\n", - "\n", - "Section 4.3.1 Crossing intensity\n", - "--------------------------------\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import wafo.data as wd\n", - "import wafo.objects as wo\n", - "\n", - "printing=0\n", - "xx_sea = wd.sea() \n", - "ts = wo.mat2timeseries(xx_sea)\n", - "tp = ts.turning_points()\n", - "mM = tp.cycle_pairs(kind='min2max')\n", - "lc = mM.level_crossings(intensity=True)\n", - "T_sea = ts.args[-1]-ts.args[0]\n", - "\n", - "subplot(1,2,1)\n", - "lc.plot()\n", - "subplot(1,2,2)\n", - "lc.setplotter(plotmethod='step')\n", - "lc.plot()\n", - "show() \n", - " \n", - " \n", - "m_sea = ts.data.mean() \n", - "f0_sea = interp(m_sea, lc.args,lc.data)\n", - "extr_sea = len(tp.data)/(2*T_sea)\n", - "alfa_sea = f0_sea/extr_sea\n", - "print('alfa = %g ' % alfa_sea )" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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dywboLDA8PDxw6dIl1ePt27fDy5Kd5a0QEbB/P9C/v9SRWIlOncQFMg4dwogR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\nkT+tW9R/eaN3FgAAAABJRU5ErkJggg==\n" - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "alfa = 0.491212 \n" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Section 4.3.2 Extraction of rainflow cycles\n", - "-------------------------------------------\n", - "Min-max and rainflow cycle plots\n", - "---------------------------------" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mM_rfc = tp.cycle_pairs(h=0.3)\n", - " \n", - "clf()\n", - "subplot(122), \n", - "mM.plot() \n", - "title('min-max cycle pairs')\n", - "subplot(121), \n", - "mM_rfc.plot()\n", - "title('Rainflow filtered cycles')\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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nmzs3gFWhjY1llWgB5izXOl9X33NPqQ4rlUQI46mQtrSwC+Pdd927ufSUi8DX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\ncEQ6riUSiURiOVJJSCQSiUQXqSQkEolEootUEhKJRCLRRSo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- } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Min-max and rainflow cycle distributions\n", - "-------------------------------------------" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import wafo.misc as wm\n", - "ampmM_sea = mM.amplitudes()\n", - "ampRFC_sea = mM_rfc.amplitudes()\n", - "clf()\n", - "subplot(121) \n", - "wm.plot_histgrm(ampmM_sea,25)\n", - "ylim = gca().get_ylim()\n", - "title('min-max amplitude distribution')\n", - "subplot(122)\n", - "wm.plot_histgrm(ampRFC_sea,25)\n", - "gca().set_ylim(ylim)\n", - "title('Rainflow amplitude distribution')\n", - "show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "display_data", - "png": 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IAAsCERHpsCAQEREAFgQiItJhQSAiIgAsCEREpMOCQEREAFgQiIhIhwWBiIgA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\nx6QLb6asK1PjdmR9mRK3KVP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- } - ], - "prompt_number": 3 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#!#! Section 4.3.3 Simulation of rainflow cycles\n", - "#!#! Simulation of cycles in a Markov model\n", - "n=41; param_m=[-1, 1, n]; param_D=[1, n, n];\n", - "u_markov=levels(param_m);\n", - "G_markov=mktestmat(param_m,[-0.2, 0.2],0.15,1);\n", - "T_markov=5000;\n", - "#xxD_markov=mctpsim({G_markov [,]},T_markov);\n", - "#xx_markov=[(1:T_markov)' u_markov(xxD_markov)'];\n", - "#clf\n", - "#plot(xx_markov(1:50,1),xx_markov(1:50,2))\n", - "#title('Markov chain of turning points')\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 5'),pause(pstate)\n", - "#\n", - "#\n", - "##!#! Rainflow cycles in a transformed Gaussian model\n", - "##!#! Hermite transformed wave data and rainflow filtered turning points, h = 0.2.\n", - "#me = mean(xx_sea(:,2));\n", - "#sa = std(xx_sea(:,2));\n", - "#Hm0_sea = 4*sa;\n", - "#Tp_sea = 1/max(lc_sea(:,2));\n", - "#spec = jonswap([],[Hm0_sea Tp_sea]);\n", - "#\n", - "#[sk, ku] = spec2skew(spec);\n", - "#spec.tr = hermitetr([],[sa sk ku me]);\n", - "#param_h = [-1.5 2 51];\n", - "#spec_norm = spec;\n", - "#spec_norm.S = spec_norm.S/sa^2;\n", - "#xx_herm = spec2sdat(spec_norm,[2^15 1],0.1);\n", - "##! ????? PJ, JR 11-Apr-2001\n", - "##! NOTE, in the simulation program spec2sdat\n", - "##!the spectrum must be normalized to variance 1 \n", - "##! ?????\n", - "#h = 0.2;\n", - "#[dtp,u_herm,xx_herm_1]=dat2dtp(param_h,xx_herm,h);\n", - "#clf\n", - "#plot(xx_herm(:,1),xx_herm(:,2),'k','LineWidth',2); hold on;\n", - "#plot(xx_herm_1(:,1),xx_herm_1(:,2),'k--','Linewidth',2);\n", - "#axis([0 50 -1 1]), hold off;\n", - "#title('Rainflow filtered wave data')\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 6'),pause(pstate)\n", - "#\n", - "##!#! Rainflow cycles and rainflow filtered rainflow cycles in the transformed Gaussian process.\n", - "#tp_herm=dat2tp(xx_herm);\n", - "#RFC_herm=tp2rfc(tp_herm);\n", - "#mM_herm=tp2mm(tp_herm);\n", - "#h=0.2;\n", - "#[dtp,u,tp_herm_1]=dat2dtp(param_h,xx_herm,h);\n", - "#RFC_herm_1 = tp2rfc(tp_herm_1);\n", - "#clf\n", - "#subplot(121), ccplot(RFC_herm)\n", - "#title('h=0')\n", - "#subplot(122), ccplot(RFC_herm_1)\n", - "#title('h=0.2')\n", - "#if (printing==1), print -deps ../bilder/fatigue_8.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 7'),pause(pstate)\n", - "#\n", - "##!#! Section 4.3.4 Calculating the rainflow matrix\n", - "#\n", - "#\n", - "#Grfc_markov=mctp2rfm({G_markov []});\n", - "#clf\n", - "#subplot(121), cmatplot(u_markov,u_markov,G_markov), axis('square')\n", - "#subplot(122), cmatplot(u_markov,u_markov,Grfc_markov), axis('square')\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 8'),pause(pstate)\n", - "#\n", - "##!#! \n", - "#clf\n", - "#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},3) \n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 9'),pause(pstate)\t\n", - "#\n", - "##!#! Min-max-matrix and theoretical rainflow matrix for test Markov sequence.\n", - "#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},4)\n", - "#subplot(121), axis('square'), title('min2max transition matrix')\n", - "#subplot(122), axis('square'), title('Rainflow matrix')\n", - "#if (printing==1), print -deps ../bilder/fatigue_9.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 10'),pause(pstate)\n", - "#\n", - "##!#! Observed and theoretical rainflow matrix for test Markov sequence.\n", - "#n=length(u_markov);\n", - "#Frfc_markov=dtp2rfm(xxD_markov,n);\n", - "#clf\n", - "#cmatplot(u_markov,u_markov,{Frfc_markov Grfc_markov*T_markov/2},3) \n", - "#subplot(121), axis('square'), title('Observed rainflow matrix')\n", - "#subplot(122), axis('square'), title('Theoretical rainflow matrix')\n", - "#if (printing==1), print -deps ../bilder/fatigue_10.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 11'),pause(pstate)\n", - "#\n", - "##!#! Smoothed observed and calculated rainflow matrix for test Markov sequence.\n", - "#tp_markov=dat2tp(xx_markov);\n", - "#RFC_markov=tp2rfc(tp_markov);\n", - "#h=1;\n", - "#Frfc_markov_smooth=cc2cmat(param_m,RFC_markov,[],1,h);\n", - "#clf\n", - "#cmatplot(u_markov,u_markov,{Frfc_markov_smooth Grfc_markov*T_markov/2},4)\n", - "#subplot(121), axis('square'), title('Smoothed observed rainflow matrix')\n", - "#subplot(122), axis('square'), title('Theoretical rainflow matrix')\n", - "#if (printing==1), print -deps ../bilder/fatigue_11.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 12'),pause(pstate)\n", - "#\n", - "##!#! Rainflow matrix from spectrum\n", - "#clf\n", - "##!GmM3_herm=spec2mmtpdf(spec,[],'Mm',[],[],2);\n", - "#GmM3_herm=spec2cmat(spec,[],'Mm',[],param_h,2);\n", - "#pdfplot(GmM3_herm)\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 13'),pause(pstate)\n", - "#\n", - "#\n", - "##!#! Min-max matrix and theoretical rainflow matrix for Hermite-transformed Gaussian waves.\n", - "#Grfc_herm=mctp2rfm({GmM3_herm.f []});\n", - "#u_herm=levels(param_h);\n", - "#clf\n", - "#cmatplot(u_herm,u_herm,{GmM3_herm.f Grfc_herm},4)\n", - "#subplot(121), axis('square'), title('min-max matrix')\n", - "#subplot(122), axis('square'), title('Theoretical rainflow matrix')\n", - "#if (printing==1), print -deps ../bilder/fatigue_12.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 14'),pause(pstate)\n", - "#\n", - "##!#!\n", - "#clf\n", - "#Grfc_direct_herm=spec2cmat(spec,[],'rfc',[],[],2);\n", - "#subplot(121), pdfplot(GmM3_herm), axis('square'), hold on\n", - "#subplot(122), pdfplot(Grfc_direct_herm), axis('square'), hold off\n", - "#if (printing==1), print -deps ../bilder/fig_mmrfcjfr.eps\n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 15'),pause(pstate)\n", - "#\n", - "#\n", - "##!#! Observed smoothed and theoretical min-max matrix, \n", - "##!#! (and observed smoothed and theoretical rainflow matrix for Hermite-transformed Gaussian waves).\n", - "#tp_herm=dat2tp(xx_herm);\n", - "#RFC_herm=tp2rfc(tp_herm);\n", - "#mM_herm=tp2mm(tp_herm);\n", - "#h=0.2;\n", - "#FmM_herm_smooth=cc2cmat(param_h,mM_herm,[],1,h);\n", - "#Frfc_herm_smooth=cc2cmat(param_h,RFC_herm,[],1,h);\n", - "#T_herm=xx_herm(end,1)-xx_herm(1,1);\n", - "#clf\n", - "#cmatplot(u_herm,u_herm,{FmM_herm_smooth GmM3_herm.f*length(mM_herm) ; ...\n", - "# Frfc_herm_smooth Grfc_herm*length(RFC_herm)},4)\n", - "#subplot(221), axis('square'), title('Observed smoothed min-max matrix')\n", - "#subplot(222), axis('square'), title('Theoretical min-max matrix')\n", - "#subplot(223), axis('square'), title('Observed smoothed rainflow matrix')\n", - "#subplot(224), axis('square'), title('Theoretical rainflow matrix')\n", - "#if (printing==1), print -deps ../bilder/fatigue_13.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 16'),pause(pstate)\n", - "# \n", - "##!#! Section 4.3.5 Simulation from crossings and rainflow structure\n", - "#\n", - "##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)\n", - "##!#! for simulated process with irregularity factor 0.25.\n", - "#clf\n", - "#cross_herm=dat2lc(xx_herm);\n", - "#alpha1=0.25;\n", - "#alpha2=0.75;\n", - "#xx_herm_sim1=lc2sdat(cross_herm,500,alpha1);\n", - "#cross_herm_sim1=dat2lc(xx_herm_sim1);\n", - "#subplot(211)\n", - "#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2)))\n", - "#hold on\n", - "#stairs(cross_herm_sim1(:,1),...\n", - "# cross_herm_sim1(:,2)/max(cross_herm_sim1(:,2)))\n", - "#hold off\n", - "#title('Crossing intensity, \\alpha = 0.25')\n", - "#subplot(212)\n", - "#plot(xx_herm_sim1(:,1),xx_herm_sim1(:,2))\n", - "#title('Simulated load, \\alpha = 0.25')\n", - "#if (printing==1), print -deps ../bilder/fatigue_14_25.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 16'),pause(pstate)\n", - "#\n", - "##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)\n", - "##!#! for simulated process with irregularity factor 0.75.\n", - "#xx_herm_sim2=lc2sdat(cross_herm,500,alpha2);\n", - "#cross_herm_sim2=dat2lc(xx_herm_sim2);\n", - "#subplot(211)\n", - "#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2)))\n", - "#hold on\n", - "#stairs(cross_herm_sim2(:,1),...\n", - "# cross_herm_sim2(:,2)/max(cross_herm_sim2(:,2)))\n", - "#hold off\n", - "#title('Crossing intensity, \\alpha = 0.75')\n", - "#subplot(212)\n", - "#plot(xx_herm_sim2(:,1),xx_herm_sim2(:,2))\n", - "#title('Simulated load, \\alpha = 0.75')\n", - "#if (printing==1), print -deps ../bilder/fatigue_14_75.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 17'),pause(pstate)\n", - "#\n", - "##!#! Section 4.4 Fatigue damage and fatigue life distribution\n", - "##!#! Section 4.4.1 Introduction\n", - "#beta=3.2; gam=5.5E-10; T_sea=xx_sea(end,1)-xx_sea(1,1);\n", - "#d_beta=cc2dam(RFC_sea,beta)/T_sea;\n", - "#time_fail=1/gam/d_beta/3600 #!in hours of the specific storm\n", - "#disp('Block 18'),pause(pstate)\n", - "#\n", - "##!#! Section 4.4.2 Level crossings\n", - "##!#! Crossing intensity as calculated from the Markov matrix (solid curve) and from the observed rainflow matrix (dashed curve).\n", - "#clf\n", - "#mu_markov=cmat2lc(param_m,Grfc_markov);\n", - "#muObs_markov=cmat2lc(param_m,Frfc_markov/(T_markov/2));\n", - "#clf\n", - "#plot(mu_markov(:,1),mu_markov(:,2),muObs_markov(:,1),muObs_markov(:,2),'--')\n", - "#title('Theoretical and observed crossing intensity ')\n", - "#if (printing==1), print -deps ../bilder/fatigue_15.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 19'),pause(pstate)\n", - "#\n", - "##!#! Section 4.4.3 Damage\n", - "##!#! Distribution of damage from different RFC cycles, from calculated theoretical and from observed rainflow matrix.\n", - "#beta = 4;\n", - "#Dam_markov = cmat2dam(param_m,Grfc_markov,beta)\n", - "#DamObs1_markov = cc2dam(RFC_markov,beta)/(T_markov/2)\n", - "#DamObs2_markov = cmat2dam(param_m,Frfc_markov,beta)/(T_markov/2)\n", - "#disp('Block 20'),pause(pstate)\n", - "#\n", - "#Dmat_markov = cmat2dmat(param_m,Grfc_markov,beta);\n", - "#DmatObs_markov = cmat2dmat(param_m,Frfc_markov,beta)/(T_markov/2); \n", - "#clf\n", - "#subplot(121), cmatplot(u_markov,u_markov,Dmat_markov,4)\n", - "#title('Theoretical damage matrix') \n", - "#subplot(122), cmatplot(u_markov,u_markov,DmatObs_markov,4)\n", - "#title('Observed damage matrix') \n", - "#if (printing==1), print -deps ../bilder/fatigue_16.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 21'),pause(pstate)\n", - "#\n", - "#\n", - "##!#!\n", - "##!Damplus_markov = lc2dplus(mu_markov,beta)\n", - "#pause(pstate)\n", - "#\n", - "##!#! Section 4.4.4 Estimation of S-N curve\n", - "#\n", - "##!#! Load SN-data and plot in log-log scale.\n", - "#SN = load('sn.dat');\n", - "#s = SN(:,1);\n", - "#N = SN(:,2);\n", - "#clf\n", - "#loglog(N,s,'o'), axis([0 14e5 10 30])\n", - "##!if (printing==1), print -deps ../bilder/fatigue_?.eps end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 22'),pause(pstate)\n", - "#\n", - "#\n", - "##!#! Check of S-N-model on normal probability paper.\n", - "#\n", - "#normplot(reshape(log(N),8,5))\n", - "#if (printing==1), print -deps ../bilder/fatigue_17.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 23'),pause(pstate)\n", - "#\n", - "##!#! Estimation of S-N-model on linear scale.\n", - "#clf\n", - "#[e0,beta0,s20] = snplot(s,N,12);\n", - "#title('S-N-data with estimated N(s)','FontSize',20)\n", - "#set(gca,'FontSize',20)\n", - "#if (printing==1), print -deps ../bilder/fatigue_18a.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 24'),pause(pstate)\n", - "#\n", - "##!#! Estimation of S-N-model on log-log scale.\n", - "#clf\n", - "#[e0,beta0,s20] = snplot(s,N,14);\n", - "#title('S-N-data with estimated N(s)','FontSize',20)\n", - "#set(gca,'FontSize',20)\n", - "#if (printing==1), print -deps ../bilder/fatigue_18b.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 25'),pause(pstate)\n", - "#\n", - "##!#! Section 4.4.5 From S-N curve to fatigue life distribution\n", - "##!#! Damage intensity as function of $\\beta$\n", - "#beta = 3:0.1:8;\n", - "#DRFC = cc2dam(RFC_sea,beta);\n", - "#dRFC = DRFC/T_sea;\n", - "#plot(beta,dRFC), axis([3 8 0 0.25])\n", - "#title('Damage intensity as function of \\beta')\n", - "#if (printing==1), print -deps ../bilder/fatigue_19.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 26'),pause(pstate)\n", - "#\n", - "##!#! Fatigue life distribution with sea load.\n", - "#dam0 = cc2dam(RFC_sea,beta0)/T_sea;\n", - "#[t0,F0] = ftf(e0,dam0,s20,0.5,1);\n", - "#[t1,F1] = ftf(e0,dam0,s20,0,1);\n", - "#[t2,F2] = ftf(e0,dam0,s20,5,1);\n", - "#plot(t0,F0,t1,F1,t2,F2)\n", - "#title('Fatigue life distribution function')\n", - "#if (printing==1), print -deps ../bilder/fatigue_20.eps \n", - "#end\n", - "#wafostamp([],'(ER)')\n", - "#disp('Block 27, last block')" - ], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/wafo/doc/tutorial_scripts/WAFO Chapter 5.ipynb b/wafo/doc/tutorial_scripts/WAFO Chapter 5.ipynb deleted file mode 100644 index 5d0d96b..0000000 --- a/wafo/doc/tutorial_scripts/WAFO Chapter 5.ipynb +++ /dev/null @@ -1,11412 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib notebook\n", - "import numpy as np\n", - "import wafo.data as wd\n", - "import wafo.stats as ws\n", - "import matplotlib.pyplot as plt\n", - "# import mpld3\n", - "# mpld3.enable_notebook() # Enable interactive plots" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Chapter 5 Extreme value analysis\n", - "=================================\n", - "\n", - "Of particular interest in wave analysis is how to find extreme quantiles and extreme significant values for a wave series. Often this implies going outside the range of observed data, i.e. to predict, from a limited number of observations, how large the extreme values might be. Such analysis is\n", - "commonly known as Weibull analysis or Gumbel analysis, from the names of two familiar extreme value distributions. WAFO contains routines for fitting of such distributions, both for the Weibull and Gumbel distributions, and for two more general classes of distributions, the Generalized Pareto\n", - "Distribution (GPD) and the Generalized Extreme Value distribution (GEV).\n", - "\n", - "Section 5.1 Weibull and Gumbel papers\n", - "--------------------------------------\n", - "\n", - "Significant wave-height data on Weibull paper, on Gumbel paper and logarithm of data on Normal probability paper:\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
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');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width);\n", - " canvas.attr('height', height);\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "fig, axes = plt.subplots()\n", - "T=np.r_[1:100001]\n", - "#sT=gum.par[1] - gum.par[0]*log(-log(1-1./T));\n", - "sT = gum.isf(1./T)\n", - "plt.semilogx(T,sT)\n", - "plt.hold(True)\n", - "N=np.r_[1:len(Hs)+1]; \n", - "Nmax=max(N);\n", - "plt.plot(Nmax/N, sorted(Hs, reverse=True),'.')\n", - "plt.title('Return values in the Gumbel model')\n", - "plt.xlabel('Return period')\n", - "plt.ylabel('Return value') \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Section 5.2 Generalized Pareto and Extreme Value distributions\n", - "----------------------------------------------------------\n", - "Section 5.2.1 Generalized Extreme Value distribution\n", - "-------------------------------------------------\n", - "\n", - "Empirical distribution of significant wave-height with estimated Generalized Extreme Value distribution" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - " $(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " this.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width);\n", - " canvas.attr('height', height);\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import wafo.kdetools as wk\n", - "fig, axes = plt.subplots()\n", - "wk.TKDE(Hs, L2=0.5)(output='plot').plot('g--')\n", - "plt.hold(True)\n", - "gev.plotepdf() " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Analysis of yura87 wave data. \n", - " Wave data interpolated (spline) and organized in 5-minute intervals\n", - "Normalized to mean 0 and std = 1 to get stationary conditions. \n", - "maximum level over each 5-minute interval analysed by GEV" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
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');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width);\n", - " canvas.attr('height', height);\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:517: UserWarning: Upper bound is larger\n", - " warnings.warn('Upper bound is larger')\n" - ] - } - ], - "source": [ - "gpd3 = ws.genpareto.fit2(Hs[Hs>3],floc=3)\n", - "fig, axes = plt.subplots()\n", - "gpd3.plotesf()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Exceedances of significant wave-height data over level 7," - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - " $(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " this.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
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');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width);\n", - " canvas.attr('height', height);\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.34847708 1.19360282 -5.94834482])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:117: RuntimeWarning: divide by zero encountered in log\n", - " loglogP = log(-log(-expm1(logsf)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.34847789 1.19366352 -6.90775528])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.34847474 1.19359554 -6.90775528])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35499767 1.23279902 -1.15129255])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35494524 1.23277614 -2.110703 ])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35495493 1.23276739 -3.07011346])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35497638 1.23281073 -3.07011346])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35499767 1.23279902 -4.98893437])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35499767 1.23279902 -5.94834482])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n", - "c:\\pab\\workspace\\git_pywafo\\wafo\\stats\\estimation.py:343: UserWarning: The fitted parameters does not provide the optimum fit. Something wrong with fit (par = [ 0.35496599 1.23285957 -6.9060821 ])\n", - " 'Something wrong with fit (par = {})'.format(str(par)))\n" - ] - } - ], - "source": [ - "Rgev = ws.genextreme.rvs(0.3,1,2,size=100)\n", - "gp = ws.genextreme.fit2(Rgev,method='mps')\n", - "gm = ws.genextreme.fit2(Rgev,method='ml')\n", - "fig, axes = plt.subplots()\n", - "gp.plotesf()\n", - "plt.hold(True)\n", - "gm.plotesf('r--')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Similarly for the GPD distribution" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - " $(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " this.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width);\n", - " canvas.attr('height', height);\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "T = np.logspace(1, 5, 10)\n", - "sT = Y5gev.isf(1./T)\n", - "ci = []\n", - "t = []\n", - "for Ti, sTi in zip(T, sT):\n", - " try:\n", - " Lx = Y5gev.profile_quantile(sTi, i=2)\n", - " ci.append(Lx.get_bounds(alpha=0.05))\n", - " t.append(Ti)\n", - " except Exception:\n", - " pass\n", - "fig, axes = plt.subplots()\n", - "plt.semilogx(T,sT, t, ci,'r')\n", - "plt.hold(True)\n", - "N = np.r_[1:len(Y5M)+1]\n", - "Nmax = max(N)\n", - "plt.plot(Nmax/N, sorted(Y5M, reverse=True), '.')\n", - "plt.title('Return values in the GEV model')\n", - "plt.xlabel('Return period')\n", - "plt.ylabel('Return value') \n", - "plt.grid(True) " - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - " $(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " this.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width);\n", - " canvas.attr('height', height);\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "phat0_ci = [-0.87319166 -0.40162685]\n" - ] - } - ], - "source": [ - "# Better CI for phat.par[i=0] shape parameter\n", - "Lp0 = phat.profile(i=0, pmin=-1,pmax=1)\n", - "fig, axes = plt.subplots()\n", - "Lp0.plot()\n", - "phat0_ci = Lp0.get_bounds(alpha=0.1)\n", - "print('phat0_ci = {}'.format(phat0_ci))\n" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - " $(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " this.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
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CHAPTER1 demonstrates some applications of WAFO -#!================================================ -#! -#! CHAPTER1 gives an overview through examples some of the capabilities of -#! WAFO. WAFO is a toolbox of Matlab routines for statistical analysis and -#! simulation of random waves and loads. -#! -#! The commands are edited for fast computation. - - -#! Section 1.4 Some applications of WAFO -#!--------------------------------------- -#! Section 1.4.1 Simulation from spectrum, estimation of spectrum -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! Simulation of the sea surface from spectrum -#! The following code generates 200 seconds of data sampled with 10Hz from -#! the Torsethaugen spectrum -import wafo.spectrum.models as wsm -S = wsm.Torsethaugen(Hm0=6, Tp=8) -S1 = S.tospecdata() -S1.plot() -plt.show() - - -## -import wafo.objects as wo -xs = S1.sim(ns=2000, dt=0.1) -ts = wo.mat2timeseries(xs) -ts.plot_wave('-') -plt.show() - - -#! Estimation of spectrum -#!~~~~~~~~~~~~~~~~~~~~~~~ -#! A common situation is that one wants to estimate the spectrum for wave -#! measurements. The following code simulate 20 minutes signal sampled at 4Hz -#! and compare the spectral estimate with the original Torsethaugen spectum. -plt.clf() -Fs = 4 -xs = S1.sim(ns=np.fix(20 * 60 * Fs), dt=1. / Fs) -ts = wo.mat2timeseries(xs) -Sest = ts.tospecdata(L=400) -S1.plot() -Sest.plot('--') -plt.axis([0, 3, 0, 5]) -plt.show() - -#! Section 1.4.2 Probability distributions of wave characteristics. -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! Probability distribution of wave trough period: -#! WAFO gives the possibility of computing the exact probability -#! distributions for a number of characteristics given a spectral density. -#! In the following example we study the trough period extracted from the -#! time series and compared with the theoretical density computed with exact -#! spectrum, S1, and the estimated spectrum, Sest. -plt.clf() -import wafo.misc as wm -dtyex = S1.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3) -dtyest = Sest.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3) - -T, index = ts.wave_periods(vh=0, pdef='d2u') -bins = wm.good_bins(T, num_bins=25, odd=True) -wm.plot_histgrm(T, bins=bins, normed=True) - -dtyex.plot() -dtyest.plot('-.') -plt.axis([0, 10, 0, 0.35]) -plt.show() - -#! Section 1.4.3 Directional spectra -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! Here are a few lines of code, which produce directional spectra -#! with frequency independent and frequency dependent spreading. -plt.clf() -plotflag = 1 -Nt = 101 # number of angles -th0 = np.pi / 2 # primary direction of waves -Sp = 15 # spreading parameter - -D1 = wsm.Spreading(type='cos', theta0=th0, method=None) -D12 = wsm.Spreading(type='cos', theta0=0, method='mitsuyasu') - -SD1 = D1.tospecdata2d(S1) -SD12 = D12.tospecdata2d(S1) -SD1.plot() -SD12.plot() # linestyle='dashdot') -plt.show() - -#! 3D Simulation of the sea surface -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! The simulations show that frequency dependent spreading leads to -#! much more irregular surface so the orientation of waves is less -#! transparent compared to the frequency independent case. -# -#! Frequency independent spreading -#plotflag = 1; iseed = 1; -# -#Nx = 2 ^ 8;Ny = Nx;Nt = 1;dx = 0.5; dy = dx; dt = 0.25; fftdim = 2; -#randn('state', iseed) -#Y1 = seasim(SD1, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag); -#wafostamp('', '(ER)') -#axis('fill') -#disp('Block = 6'), pause(pstate) -# -### -## Frequency dependent spreading -#randn('state', iseed) -#Y12 = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag); -#wafostamp('', '(ER)') -#axis('fill') -#disp('Block = 7'), pause(pstate) -# -#! Estimation of directional spectrum -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! The figure is not shown in the Tutorial -# -# Nx = 3; Ny = 2; Nt = 2 ^ 12; dx = 10; dy = 10;dt = 0.5; -# F = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, 1, 0); -# Z = permute(F.Z, [3 1 2]); -# [X, Y] = meshgrid(F.x, F.y); -# N = Nx * Ny; -# types = repmat(sensortypeid('n'), N, 1); -# bfs = ones(N, 1); -# pos = [X(:), Y(:), zeros(N, 1)]; -# h = inf; -# nfft = 128; -# nt = 101; -# SDe = dat2dspec([F.t Z(:, :)], [pos types, bfs], h, nfft, nt); -#plotspec(SDe), hold on -#plotspec(SD12, '--'), hold off -#disp('Block = 8'), pause(pstate) - -#! Section 1.4.4 Fatigue, Load cycles and Markov models. -#! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! Switching Markow chain of turningpoints -#! In fatigue applications the exact sample path is not important, but -#! only the tops and bottoms of the load, called the sequence of turning -#! points (TP). From the turning points one can extract load cycles, from -#! which damage calculations and fatigue life predictions can be -#! performed. -#! -#! The commands below computes the intensity of rainflowcycles for -#! the Gaussian model with spectrum S1 using the Markov approximation. -#! The rainflow cycles found in the simulated load signal are shown in the -#! figure. - -#clf() -#paramu = [-6 6 61]; -#frfc = spec2cmat(S1, [], 'rfc', [], paramu); -#pdfplot(frfc); -#hold on -#tp = dat2tp(xs); -#rfc = tp2rfc(tp); -#plot(rfc(:, 2), rfc(:, 1), '.') -#wafostamp('', '(ER)') -#hold off -#disp('Block = 9'), pause(pstate) - -#! Section 1.4.5 Extreme value statistics -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -# Plot of yura87 data -plt.clf() -import wafo.data as wd -xn = wd.yura87() -#xn = load('yura87.dat'); -plt.subplot(211) -plt.plot(xn[::30, 0] / 3600, xn[::30, 1], '.') -plt.title('Water level') -plt.ylabel('(m)') - -#! Formation of 5 min maxima -yura = xn[:85500, 1] -yura = np.reshape(yura, (285, 300)).T -maxyura = yura.max(axis=0) -plt.subplot(212) -plt.plot(xn[299:85500:300, 0] / 3600, maxyura, '.') -plt.xlabel('Time (h)') -plt.ylabel('(m)') -plt.title('Maximum 5 min water level') -plt.show() - -#! Estimation of GEV for yuramax -plt.clf() -import wafo.stats as ws -phat = ws.genextreme.fit2(maxyura, method='ml') -phat.plotfitsummary() -plt.show() -#disp('Block = 11, Last block') diff --git a/wafo/doc/tutorial_scripts/chapter2.py b/wafo/doc/tutorial_scripts/chapter2.py deleted file mode 100644 index 03603c8..0000000 --- a/wafo/doc/tutorial_scripts/chapter2.py +++ /dev/null @@ -1,327 +0,0 @@ -import wafo.plotbackend.plotbackend as plt -import numpy as np - -# pyreport -o chapter2.html chapter2.py - -#! CHAPTER2 Modelling random loads and stochastic waves -#!======================================================= -#! -#! Chapter2 contains the commands used in Chapter 2 of the tutorial and -#! present some tools for analysis of random functions with -#! respect to their correlation, spectral and distributional properties. -#! The presentation is divided into three examples: -#! -#! Example1 is devoted to estimation of different parameters in the model. -#! Example2 deals with spectral densities and -#! Example3 presents the use of WAFO to simulate samples of a Gaussian -#! process. -#! -#! Some of the commands are edited for fast computation. -#! -#! Section 2.1 Introduction and preliminary analysis -#!==================================================== -#! Example 1: Sea data -#!---------------------- -#! Observed crossings compared to the expected for Gaussian signals - -import wafo -import wafo.objects as wo -xx = wafo.data.sea() -me = xx[:, 1].mean() -sa = xx[:, 1].std() -xx[:, 1] -= me -ts = wo.mat2timeseries(xx) -tp = ts.turning_points() - -cc = tp.cycle_pairs() -lc = cc.level_crossings() -lc.plot() -plt.show() - -#! Average number of upcrossings per time unit -#!---------------------------------------------- -#! Next we compute the mean frequency as the average number of upcrossings -#! per time unit of the mean level (= 0); this may require interpolation in the -#! crossing intensity curve, as follows. -T = xx[:, 0].max() - xx[:, 0].min() -f0 = np.interp(0, lc.args, lc.data, 0) / T # zero up-crossing frequency -print('f0 = %g' % f0) - -#! Turningpoints and irregularity factor -#!---------------------------------------- - -fm = len(tp.data) / (2 * T) # frequency of maxima -alfa = f0 / fm # approx Tm24/Tm02 - -print('fm = %g, alpha = %g, ' % (fm, alfa)) - -#! Visually examine data -#!------------------------ -#! We finish this section with some remarks about the quality -#! of the measured data. Especially sea surface measurements can be -#! of poor quality. We shall now check the quality of the dataset {\tt xx}. -#! It is always good practice to visually examine the data -#! before the analysis to get an impression of the quality, -#! non-linearities and narrow-bandedness of the data. -#! First we shall plot the data and zoom in on a specific region. -#! A part of sea data is visualized with the following commands -plt.clf() -ts.plot_wave('k-', tp, '*', nfig=1, nsub=1) - -plt.axis([0, 2, -2, 2]) -plt.show() - -#! Finding possible spurious points -#!------------------------------------ -#! However, if the amount of data is too large for visual examinations one -#! could use the following criteria to find possible spurious points. One -#! must be careful using the criteria for extremevalue analysis, because -#! it might remove extreme waves that are OK and not spurious. - -import wafo.misc as wm -dt = ts.sampling_period() -# dt = np.diff(xx[:2,0]) -dcrit = 5 * dt -ddcrit = 9.81 / 2 * dt * dt -zcrit = 0 -inds, indg = wm.findoutliers(ts.data, zcrit, dcrit, ddcrit, verbose=True) - -#! Section 2.2 Frequency Modeling of Load Histories -#!---------------------------------------------------- -#! Periodogram: Raw spectrum -#! -plt.clf() -Lmax = 9500 -S = ts.tospecdata(L=Lmax) -S.plot() -plt.axis([0, 5, 0, 0.7]) -plt.show() - -#! Calculate moments -#!------------------- -mom, text = S.moment(nr=4) -print('sigma = %g, m0 = %g' % (sa, np.sqrt(mom[0]))) - -#! Section 2.2.1 Random functions in Spectral Domain - Gaussian processes -#!-------------------------------------------------------------------------- -#! Smoothing of spectral estimate -#!---------------------------------- -#! By decreasing Lmax the spectrum estimate becomes smoother. - -plt.clf() -Lmax0 = 200 -Lmax1 = 50 -S1 = ts.tospecdata(L=Lmax0) -S2 = ts.tospecdata(L=Lmax1) -S1.plot('-.') -S2.plot() -plt.show() - -#! Estimated autocovariance -#!---------------------------- -#! Obviously knowing the spectrum one can compute the covariance -#! function. The following code will compute the covariance for the -#! unimodal spectral density S1 and compare it with estimated -#! covariance of the signal xx. -plt.clf() -Lmax = 85 -R1 = S1.tocovdata(nr=1) -Rest = ts.tocovdata(lag=Lmax) -R1.plot('.') -Rest.plot() -plt.axis([0, 25, -0.1, 0.25]) -plt.show() - -#! We can see in Figure below that the covariance function corresponding to -#! the spectral density S2 significantly differs from the one estimated -#! directly from data. -#! It can be seen in Figure above that the covariance corresponding to S1 -#! agrees much better with the estimated covariance function - -plt.clf() -R2 = S2.tocovdata(nr=1) -R2.plot('.') -Rest.plot() -plt.show() - -#! Section 2.2.2 Transformed Gaussian models -#!------------------------------------------- -#! We begin with computing skewness and kurtosis -#! for the data set xx and compare it with the second order wave approximation -#! proposed by Winterstein: -import wafo.stats as ws -rho3 = ws.skew(xx[:, 1]) -rho4 = ws.kurtosis(xx[:, 1]) - -sk, ku = S1.stats_nl(moments='sk') - -#! Comparisons of 3 transformations -plt.clf() -import wafo.transform.models as wtm -gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku).trdata() -g = wtm.TrLinear(mean=me, sigma=sa).trdata() # Linear transformation -glc, gemp = lc.trdata(mean=me, sigma=sa) - -glc.plot('b-') # Transf. estimated from level-crossings -gh.plot('b-.') # Hermite Transf. estimated from moments -g.plot('r') -plt.grid('on') -plt.show() - -#! Test Gaussianity of a stochastic process -#!------------------------------------------ -#! TESTGAUSSIAN simulates e(g(u)-u) = int (g(u)-u)^2 du for Gaussian processes -#! given the spectral density, S. The result is plotted if test0 is given. -#! This is useful for testing if the process X(t) is Gaussian. -#! If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level. -#! -#! As we see from the figure below: none of the simulated values of test1 is -#! above 1.00. Thus the data significantly departs from a Gaussian distribution. -plt.clf() -test0 = glc.dist2gauss() -#! the following test takes time -N = len(xx) -test1 = S1.testgaussian(ns=N, cases=50, test0=test0) -is_gaussian = sum(test1 > test0) > 5 -print(is_gaussian) -plt.show() - -#! Normalplot of data xx -#!------------------------ -#! indicates that the underlying distribution has a "heavy" upper tail and a -#! "light" lower tail. -plt.clf() -import pylab -ws.probplot(ts.data.ravel(), dist='norm', plot=pylab) -plt.show() -#! Section 2.2.3 Spectral densities of sea data -#!----------------------------------------------- -#! Example 2: Different forms of spectra -#! -import wafo.spectrum.models as wsm -plt.clf() -Hm0 = 7 -Tp = 11 -spec = wsm.Jonswap(Hm0=Hm0, Tp=Tp).tospecdata() -spec.plot() -plt.show() - -#! Directional spectrum and Encountered directional spectrum -#! Directional spectrum -plt.clf() -D = wsm.Spreading('cos2s') -Sd = D.tospecdata2d(spec) -Sd.plot() -plt.show() - - -##!Encountered directional spectrum -##!--------------------------------- -#clf() -#Se = spec2spec(Sd,'encdir',0,10); -#plotspec(Se), hold on -#plotspec(Sd,1,'--'), hold off -##!wafostamp('','(ER)') -#disp('Block = 17'),pause(pstate) -# -##!#! Frequency spectra -#clf -#Sd1 =spec2spec(Sd,'freq'); -#Sd2 = spec2spec(Se,'enc'); -#plotspec(spec), hold on -#plotspec(Sd1,1,'.'), -#plotspec(Sd2), -##!wafostamp('','(ER)') -#hold off -#disp('Block = 18'),pause(pstate) -# -##!#! Wave number spectrum -#clf -#Sk = spec2spec(spec,'k1d') -#Skd = spec2spec(Sd,'k1d') -#plotspec(Sk), hold on -#plotspec(Skd,1,'--'), hold off -##!wafostamp('','(ER)') -#disp('Block = 19'),pause(pstate) -# -##!#! Effect of waterdepth on spectrum -#clf -#plotspec(spec,1,'--'), hold on -#S20 = spec; -#S20.S = S20.S.*phi1(S20.w,20); -#S20.h = 20; -#plotspec(S20), hold off -##!wafostamp('','(ER)') -#disp('Block = 20'),pause(pstate) -# -##!#! Section 2.3 Simulation of transformed Gaussian process -##!#! Example 3: Simulation of random sea -##! The reconstruct function replaces the spurious points of seasurface by -##! simulated data on the basis of the remaining data and a transformed Gaussian -##! process. As noted previously one must be careful using the criteria -##! for finding spurious points when reconstructing a dataset, because -##! these criteria might remove the highest and steepest waves as we can see -##! in this plot where the spurious points is indicated with a '+' sign: -##! -#clf -#[y, grec] = reconstruct(xx,inds); -#waveplot(y,'-',xx(inds,:),'+',1,1) -#axis([0 inf -inf inf]) -##!wafostamp('','(ER)') -#disp('Block = 21'),pause(pstate) -# -##! Compare transformation (grec) from reconstructed (y) -##! with original (glc) from (xx) -#clf -#trplot(g), hold on -#plot(gemp(:,1),gemp(:,2)) -#plot(glc(:,1),glc(:,2),'-.') -#plot(grec(:,1),grec(:,2)), hold off -#disp('Block = 22'),pause(pstate) -# -##!#! -#clf -#L = 200; -#x = dat2gaus(y,grec); -#Sx = dat2spec(x,L); -#disp('Block = 23'),pause(pstate) -# -##!#! -#clf -#dt = spec2dt(Sx) -#Ny = fix(2*60/dt) #! = 2 minutes -#Sx.tr = grec; -#ysim = spec2sdat(Sx,Ny); -#waveplot(ysim,'-') -##!wafostamp('','(CR)') -#disp('Block = 24'),pause(pstate) -# -#! Estimated spectrum compared to Torsethaugen spectrum -#!------------------------------------------------------- - -plt.clf() -fp = 1.1 -dw = 0.01 -H0 = S1.characteristic('Hm0')[0] -St = wsm.Torsethaugen(Hm0=H0,Tp=2*np.pi/fp).tospecdata(np.arange(0,5+dw/2,dw)) -S1.plot() -St.plot('-.') -plt.axis([0, 6, 0, 0.4]) -plt.show() - - -#! Transformed Gaussian model compared to Gaussian model -#!-------------------------------------------------------- -dt = St.sampling_period() -va, sk, ku = St.stats_nl(moments='vsk') -#sa = sqrt(va) -gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa) - -ysim_t = St.sim(ns=240, dt=0.5) -xsim_t = ysim_t.copy() -xsim_t[:, 1] = gh.gauss2dat(ysim_t[:, 1]) - -ts_y = wo.mat2timeseries(ysim_t) -ts_x = wo.mat2timeseries(xsim_t) -ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1) -plt.show() diff --git a/wafo/doc/tutorial_scripts/chapter3.py b/wafo/doc/tutorial_scripts/chapter3.py deleted file mode 100644 index 8b159c2..0000000 --- a/wafo/doc/tutorial_scripts/chapter3.py +++ /dev/null @@ -1,615 +0,0 @@ -from wafo.plotbackend import plotbackend as plt -import numpy as np - -#! CHAPTER3 Demonstrates distributions of wave characteristics -#!============================================================= -#! -#! Chapter3 contains the commands used in Chapter3 in the tutorial. -#! -#! Some of the commands are edited for fast computation. -#! -#! Section 3.2 Estimation of wave characteristics from data -#!---------------------------------------------------------- -#! Example 1 -#!~~~~~~~~~~ - -speed = 'fast' -#speed = 'slow' -import scipy.signal as ss -import wafo.data as wd -import wafo.misc as wm -import wafo.objects as wo -import wafo.stats as ws -import wafo.spectrum.models as wsm -xx = wd.sea() -xx[:, 1] = ss.detrend(xx[:, 1]) -ts = wo.mat2timeseries(xx) -Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8) -Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8) - -#! Histogram of crestperiod compared to the kernel density estimate -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -import wafo.kdetools as wk -plt.clf() -print(Tc.mean()) -print(Tc.max()) - -t = np.linspace(0.01,8,200); -ftc = wk.TKDE(Tc, L2=0, inc=128) - -plt.plot(t,ftc.eval_grid(t), t, ftc.eval_grid_fast(t),'-.') -wm.plot_histgrm(Tc, normed=True) -plt.title('Kernel Density Estimates') -plt.xlabel('Tc [s]') -plt.axis([0, 8, 0, 0.5]) -plt.show() - -#! Extreme waves - model check: the highest and steepest wave -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -plt.clf() -S, H = ts.wave_height_steepness(kind=0) -indS = S.argmax() -indH = H.argmax() -ts.plot_sp_wave([indH, indS],'k.') -plt.show() - -#! Does the highest wave contradict a transformed Gaussian model? -#!---------------------------------------------------------------- - -# TODO: Fix this - -#clf -#inds1 = (5965:5974)'; #! points to remove -#Nsim = 10; -#[y1, grec1, g2, test, tobs, mu1o, mu1oStd] = ... -# reconstruct(xx,inds1,Nsim); -#spwaveplot(y1,indA-10) -#hold on -#plot(xx(inds1,1),xx(inds1,2),'+') -#lamb = 2.; -#muLstd = tranproc(mu1o-lamb*mu1oStd,fliplr(grec1)); -#muUstd = tranproc(mu1o+lamb*mu1oStd,fliplr(grec1)); -#plot (y1(inds1,1), [muLstd muUstd],'b-') -#axis([1482 1498 -1 3]), -#wafostamp([],'(ER)') -#disp('Block = 6'), -#pause(pstate) -# -##!#! Expected value (solid) compared to data removed -#clf -#plot(xx(inds1,1),xx(inds1,2),'+'), hold on -#mu = tranproc(mu1o,fliplr(grec1)); -#plot(y1(inds1,1), mu), hold off -#disp('Block = 7'), pause(pstate) - -#! Crest height PDF -#!------------------ -#! Transform data so that kde works better -plt.clf() -wave_data = ts.wave_parameters() -Ac = wave_data['Ac'] -L2 = 0.6 - -ws.probplot(Ac**L2, dist='norm', plot=plt) -plt.show() - -#!#! -plt.clf()# -fac = wk.TKDE(Ac,L2=L2)(np.linspace(0.01,3,200), output='plot') -fac.plot() -# wafostamp([],'(ER)') -print(fac.integrate(a=0.01, b=3)) -print(fac.integrate()) -print('Block = 8'), -# pause(pstate) - -#!#! Empirical crest height CDF -plt.clf() -Fac = fac.to_cdf() -Femp = ws.edf(Ac) -Fac.plot() -Femp.plot() -plt.axis([0, 2, 0, 1]) - -#wafostamp([],'(ER)') -#disp('Block = 9'), pause(pstate) - -#!#! Empirical crest height CDF compared to a Transformed Rayleigh approximation - -# facr = trraylpdf(fac.x{1},'Ac',grec1); -# Facr = cumtrapz(facr.x{1},facr.f); -# hold on -# plot(facr.x{1},Facr,'.') -# axis([1.25 2.25 0.95 1]) -# wafostamp([],'(ER)') -# disp('Block = 10'), pause(pstate) - -#!#! Joint pdf of crest period and crest amplitude -plt.clf() -Tcf = wave_data['Tcf'] -Tcb = wave_data['Tcb'] -Tc = Tcf + Tcb -fTcAc = wk.TKDE([Tc, Ac],L2=0.5, inc=256).eval_grid_fast(output='plot') -fTcAc.labels.labx = 'Tc [s]' -fTcAc.labels.laby = 'Ac [m]' -fTcAc.plot() -plt.hold(True) -plt.plot(Tc, Ac,'k.') -plt.hold(False) -plt.show() -#wafostamp([],'(ER)') -#disp('Block = 11'), pause(pstate) - -#!#! Example 4: Simple wave characteristics obtained from Jonswap spectrum -plt.clf() -S = wsm.Jonswap(Hm0=5, Tp=10).tospecdata() -m, mt = S.moment(nr=4, even=False) -print(m) -print(mt) -# disp('Block = 12'), pause(pstate) - -plt.clf() -S.bandwidth(['alpha']) -ch, Sa2, chtxt = S.characteristic(['Hm0', 'Tm02']) - -# disp('Block = 13'), pause(pstate) - -#!#! Section 3.3.2 Explicit form approximations of wave characteristic densities -#!#! Longuett-Higgins model for Tc and Ac -# plt.clf() -# t = np.linspace(0,15,100) -# h = np.linspace(0,6,100) -# flh = lh83pdf(t, h, [m[0],m[1], m[2]) -# #disp('Block = 14'), pause(pstate) -# -# #!#! Transformed Longuett-Higgins model for Tc and Ac -# clf -# [sk, ku ]=spec2skew(S); -# sa = sqrt(m(1)); -# gh = hermitetr([],[sa sk ku 0]); -# flhg = lh83pdf(t,h,[m(1),m(2),m(3)],gh); -# disp('Block = 15'), pause(pstate) - -#!#! Cavanie model for Tc and Ac -# clf -# t = np.linspace(0,10,100); -# h = np.linspace(0,7,100); -# fcav = cav76pdf(t,h,[m(1) m(2) m(3) m(5)],[]); -# disp('Block = 16'), pause(pstate) -# -# #!#! Example 5 Transformed Rayleigh approximation of crest- vs trough- amplitude -# clf -# xx = load('sea.dat'); -# x = xx; -# x(:,2) = detrend(x(:,2)); -# SS = dat2spec2(x); -# [sk, ku, me, si ] = spec2skew(SS); -# gh = hermitetr([],[si sk ku me]); -# Hs = 4*si; -# r = (0:0.05:1.1*Hs)'; -# fac_h = trraylpdf(r,'Ac',gh); -# fat_h = trraylpdf(r,'At',gh); -# h = (0:0.05:1.7*Hs)'; -# facat_h = trraylpdf(h,'AcAt',gh); -# pdfplot(fac_h) -# hold on -# pdfplot(fat_h,'--') -# hold off -# wafostamp([],'(ER)') -# disp('Block = 17'), pause(pstate) -# -# #!#! -# clf -# TC = dat2tc(xx, me); -# tc = tp2mm(TC); -# Ac = tc(:,2); -# At = -tc(:,1); -# AcAt = Ac+At; -# disp('Block = 18'), pause(pstate) -# -# #!#! -# clf -# Fac_h = [fac_h.x{1} cumtrapz(fac_h.x{1},fac_h.f)]; -# subplot(3,1,1) -# Fac = plotedf(Ac,Fac_h); -# hold on -# plot(r,1-exp(-8*r.^2/Hs^2),'.') -# axis([1. 2. 0.9 1]) -# title('Ac CDF') -# -# Fat_h = [fat_h.x{1} cumtrapz(fat_h.x{1},fat_h.f)]; -# subplot(3,1,2) -# Fat = plotedf(At,Fat_h); -# hold on -# plot(r,1-exp(-8*r.^2/Hs^2),'.') -# axis([1. 2. 0.9 1]) -# title('At CDF') -# -# Facat_h = [facat_h.x{1} cumtrapz(facat_h.x{1},facat_h.f)]; -# subplot(3,1,3) -# Facat = plotedf(AcAt,Facat_h); -# hold on -# plot(r,1-exp(-2*r.^2/Hs^2),'.') -# axis([1.5 3.5 0.9 1]) -# title('At+Ac CDF') -# -# wafostamp([],'(ER)') -# disp('Block = 19'), pause(pstate) -# -# #!#! Section 3.4 Exact wave distributions in transformed Gaussian Sea -# #!#! Section 3.4.1 Density of crest period, crest length or encountered crest period -# clf -# S1 = torsethaugen([],[6 8],1); -# D1 = spreading(101,'cos',pi/2,[15],[],0); -# D12 = spreading(101,'cos',0,[15],S1.w,1); -# SD1 = mkdspec(S1,D1); -# SD12 = mkdspec(S1,D12); -# disp('Block = 20'), pause(pstate) -# -# #!#! Crest period -# clf -# tic -# f_tc = spec2tpdf(S1,[],'Tc',[0 11 56],[],4); -# toc -# pdfplot(f_tc) -# wafostamp([],'(ER)') -# simpson(f_tc.x{1},f_tc.f) -# disp('Block = 21'), pause(pstate) -# -# #!#! Crest length -# -# if strncmpi(speed,'slow',1) -# opt1 = rindoptset('speed',5,'method',3); -# opt2 = rindoptset('speed',5,'nit',2,'method',0); -# else -# #! fast -# opt1 = rindoptset('speed',7,'method',3); -# opt2 = rindoptset('speed',7,'nit',2,'method',0); -# end -# -# -# clf -# if strncmpi(speed,'slow',1) -# NITa = 5; -# else -# disp('NIT=5 may take time, running with NIT=3 in the following') -# NITa = 3; -# end -# #!f_Lc = spec2tpdf2(S1,[],'Lc',[0 200 81],opt1); #! Faster and more accurate -# f_Lc = spec2tpdf(S1,[],'Lc',[0 200 81],[],NITa); -# pdfplot(f_Lc,'-.') -# wafostamp([],'(ER)') -# disp('Block = 22'), pause(pstate) -# -# -# f_Lc_1 = spec2tpdf(S1,[],'Lc',[0 200 81],1.5,NITa); -# #!f_Lc_1 = spec2tpdf2(S1,[],'Lc',[0 200 81],1.5,opt1); -# -# hold on -# pdfplot(f_Lc_1) -# wafostamp([],'(ER)') -# -# disp('Block = 23'), pause(pstate) -# #!#! -# clf -# simpson(f_Lc.x{1},f_Lc.f) -# simpson(f_Lc_1.x{1},f_Lc_1.f) -# -# disp('Block = 24'), pause(pstate) -# #!#! -# clf -# tic -# -# f_Lc_d1 = spec2tpdf(rotspec(SD1,pi/2),[],'Lc',[0 300 121],[],NITa); -# f_Lc_d12 = spec2tpdf(SD12,[],'Lc',[0 200 81],[],NITa); -# #! f_Lc_d1 = spec2tpdf2(rotspec(SD1,pi/2),[],'Lc',[0 300 121],opt1); -# #! f_Lc_d12 = spec2tpdf2(SD12,[],'Lc',[0 200 81],opt1); -# toc -# pdfplot(f_Lc_d1,'-.'), hold on -# pdfplot(f_Lc_d12), hold off -# wafostamp([],'(ER)') -# -# disp('Block = 25'), pause(pstate) -# -# #!#! -# -# -# clf -# opt1 = rindoptset('speed',5,'method',3); -# SD1r = rotspec(SD1,pi/2); -# if strncmpi(speed,'slow',1) -# f_Lc_d1_5 = spec2tpdf(SD1r,[], 'Lc',[0 300 121],[],5); -# pdfplot(f_Lc_d1_5), hold on -# else -# #! fast -# disp('Run the following example only if you want a check on computing time') -# disp('Edit the command file and remove #!') -# end -# f_Lc_d1_3 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],3); -# f_Lc_d1_2 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],2); -# f_Lc_d1_0 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],0); -# #!f_Lc_d1_n4 = spec2tpdf2(SD1r,[],'Lc',[0 400 161],opt1); -# -# pdfplot(f_Lc_d1_3), hold on -# pdfplot(f_Lc_d1_2) -# pdfplot(f_Lc_d1_0) -# #!pdfplot(f_Lc_d1_n4) -# -# #!simpson(f_Lc_d1_n4.x{1},f_Lc_d1_n4.f) -# -# disp('Block = 26'), pause(pstate) -# -# #!#! Section 3.4.2 Density of wave period, wave length or encountered wave period -# #!#! Example 7: Crest period and high crest waves -# clf -# tic -# xx = load('sea.dat'); -# x = xx; -# x(:,2) = detrend(x(:,2)); -# SS = dat2spec(x); -# si = sqrt(spec2mom(SS,1)); -# SS.tr = dat2tr(x); -# Hs = 4*si -# method = 0; -# rate = 2; -# [S, H, Ac, At, Tcf, Tcb, z_ind, yn] = dat2steep(x,rate,method); -# Tc = Tcf+Tcb; -# t = linspace(0.01,8,200); -# ftc1 = kde(Tc,{'L2',0},t); -# pdfplot(ftc1) -# hold on -# #! f_t = spec2tpdf(SS,[],'Tc',[0 8 81],0,4); -# f_t = spec2tpdf(SS,[],'Tc',[0 8 81],0,2); -# simpson(f_t.x{1},f_t.f) -# pdfplot(f_t,'-.') -# hold off -# wafostamp([],'(ER)') -# toc -# disp('Block = 27'), pause(pstate) -# -# #!#! -# clf -# tic -# -# if strncmpi(speed,'slow',1) -# NIT = 4; -# else -# NIT = 2; -# end -# #! f_t2 = spec2tpdf(SS,[],'Tc',[0 8 81],[Hs/2],4); -# tic -# f_t2 = spec2tpdf(SS,[],'Tc',[0 8 81],Hs/2,NIT); -# toc -# -# Pemp = sum(Ac>Hs/2)/sum(Ac>0) -# simpson(f_t2.x{1},f_t2.f) -# index = find(Ac>Hs/2); -# ftc1 = kde(Tc(index),{'L2',0},t); -# ftc1.f = Pemp*ftc1.f; -# pdfplot(ftc1) -# hold on -# pdfplot(f_t2,'-.') -# hold off -# wafostamp([],'(ER)') -# toc -# disp('Block = 28'), pause(pstate) -# -# #!#! Example 8: Wave period for high crest waves -# #! clf -# tic -# f_tcc2 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],-1); -# toc -# simpson(f_tcc2.x{1},f_tcc2.f) -# f_tcc3 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],3,5); -# #! f_tcc3 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],1,5); -# simpson(f_tcc3.x{1},f_tcc3.f) -# pdfplot(f_tcc2,'-.') -# hold on -# pdfplot(f_tcc3) -# hold off -# toc -# disp('Block = 29'), pause(pstate) -# -# #!#! -# clf -# [TC tc_ind v_ind] = dat2tc(yn,[],'dw'); -# N = length(tc_ind); -# t_ind = tc_ind(1:2:N); -# c_ind = tc_ind(2:2:N); -# Pemp = sum(yn(t_ind,2)<-Hs/2 & yn(c_ind,2)>Hs/2)/length(t_ind) -# ind = find(yn(t_ind,2)<-Hs/2 & yn(c_ind,2)>Hs/2); -# spwaveplot(yn,ind(2:4)) -# wafostamp([],'(ER)') -# disp('Block = 30'), pause(pstate) -# -# #!#! -# clf -# Tcc = yn(v_ind(1+2*ind),1)-yn(v_ind(1+2*(ind-1)),1); -# t = linspace(0.01,14,200); -# ftcc1 = kde(Tcc,{'kernel' 'epan','L2',0},t); -# ftcc1.f = Pemp*ftcc1.f; -# pdfplot(ftcc1,'-.') -# wafostamp([],'(ER)') -# disp('Block = 31'), pause(pstate) -# -# tic -# f_tcc22_1 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[Hs/2],-1); -# toc -# simpson(f_tcc22_1.x{1},f_tcc22_1.f) -# hold on -# pdfplot(f_tcc22_1) -# hold off -# wafostamp([],'(ER)') -# disp('Block = 32'), pause(pstate) -# -# disp('The rest of this chapter deals with joint densities.') -# disp('Some calculations may take some time.') -# disp('You could experiment with other NIT.') -# #!return -# -# #!#! Section 3.4.3 Joint density of crest period and crest height -# #!#! Example 9. Some preliminary analysis of the data -# clf -# tic -# yy = load('gfaksr89.dat'); -# SS = dat2spec(yy); -# si = sqrt(spec2mom(SS,1)); -# SS.tr = dat2tr(yy); -# Hs = 4*si -# v = gaus2dat([0 0],SS.tr); -# v = v(2) -# toc -# disp('Block = 33'), pause(pstate) -# -# #!#! -# clf -# tic -# [TC, tc_ind, v_ind] = dat2tc(yy,v,'dw'); -# N = length(tc_ind); -# t_ind = tc_ind(1:2:N); -# c_ind = tc_ind(2:2:N); -# v_ind_d = v_ind(1:2:N+1); -# v_ind_u = v_ind(2:2:N+1); -# T_d = ecross(yy(:,1),yy(:,2),v_ind_d,v); -# T_u = ecross(yy(:,1),yy(:,2),v_ind_u,v); -# -# Tc = T_d(2:end)-T_u(1:end); -# Tt = T_u(1:end)-T_d(1:end-1); -# Tcf = yy(c_ind,1)-T_u; -# Ac = yy(c_ind,2)-v; -# At = v-yy(t_ind,2); -# toc -# disp('Block = 34'), pause(pstate) -# -# #!#! -# clf -# tic -# t = linspace(0.01,15,200); -# kopt3 = kdeoptset('hs',0.25,'L2',0); -# ftc1 = kde(Tc,kopt3,t); -# ftt1 = kde(Tt,kopt3,t); -# pdfplot(ftt1,'k') -# hold on -# pdfplot(ftc1,'k-.') -# f_tc4 = spec2tpdf(SS,[],'Tc',[0 12 81],0,4,5); -# f_tc2 = spec2tpdf(SS,[],'Tc',[0 12 81],0,2,5); -# f_tc = spec2tpdf(SS,[],'Tc',[0 12 81],0,-1); -# pdfplot(f_tc,'b') -# hold off -# legend('kde(Tt)','kde(Tc)','f_{tc}') -# wafostamp([],'(ER)') -# toc -# disp('Block = 35'), pause(pstate) -# -# #!#! Example 10: Joint characteristics of a half wave: -# #!#! position and height of a crest for a wave with given period -# clf -# tic -# ind = find(4.4Hs/2); -# plot(Tc(ind), Ac(ind),'.'); -# hold on -# pdfplot(flh_g,'k-.') -# pdfplot(f_tcac_s) -# toc -# wafostamp([],'(ER)') -# disp('Block = 39'), pause(pstate) -# -# #!#! -# clf -# #! f_tcac = spec2thpdf(SS,[],'TcAc',[0 12 81],[0:0.2:8],opt1); -# #! pdfplot(f_tcac) -# disp('Block = 40'), pause(pstate) -# -# #!#! Section 3.4.4 Joint density of crest and trough height -# #!#! Section 3.4.5 Min-to-max distributions Markov method -# #!#! Example 11. (min-max problems with Gullfaks data) -# #!#! Joint density of maximum and the following minimum -# clf -# tic -# tp = dat2tp(yy); -# Mm = fliplr(tp2mm(tp)); -# fmm = kde(Mm); -# f_mM = spec2mmtpdf(SS,[],'mm',[],[-7 7 51],opt2); -# -# pdfplot(f_mM,'-.') -# hold on -# pdfplot(fmm,'k-') -# hold off -# wafostamp([],'(ER)') -# toc -# disp('Block = 41'), pause(pstate) -# -# #!#! The joint density of still water separated maxima and minima. -# clf -# tic -# ind = find(Mm(:,1)>v & Mm(:,2) easier to evaluate using cellmode evaluation. -#! revised pab Feb2004 -#! updated call to lc2sdat -#! Created by GL July 13, 2000 -#! from commands used in Chapter 4 -#! - -#! Chapter 4 Fatigue load analysis and rain-flow cycles -#!------------------------------------------------------ - -printing = 0 - - -#! Section 4.3.1 Crossing intensity -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -import numpy as np -from wafo.plotbackend import plotbackend as plt -import wafo.data as wd -import wafo.objects as wo - -xx_sea = wd.sea() -ts = wo.mat2timeseries(xx_sea) -tp = ts.turning_points() -mM = tp.cycle_pairs(kind='min2max') -lc = mM.level_crossings(intensity=True) -T_sea = ts.args[-1]-ts.args[0] - -plt.subplot(1,2,1) -lc.plot() -plt.subplot(1,2,2) -lc.setplotter(plotmethod='step') -lc.plot() -plt.show() - - -m_sea = ts.data.mean() -f0_sea = np.interp(m_sea, lc.args,lc.data) -extr_sea = len(tp.data)/(2*T_sea) -alfa_sea = f0_sea/extr_sea -print('alfa = %g ' % alfa_sea) - -#! Section 4.3.2 Extraction of rainflow cycles -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -#! Min-max and rainflow cycle plots -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -mM_rfc = tp.cycle_pairs(h=0.3) - -plt.clf() -plt.subplot(122), -mM.plot() -plt.title('min-max cycle pairs') -plt.subplot(121), -mM_rfc.plot() -plt.title('Rainflow filtered cycles') -plt.show() - -#! Min-max and rainflow cycle distributions -#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -import wafo.misc as wm -ampmM_sea = mM.amplitudes() -ampRFC_sea = mM_rfc.amplitudes() -plt.clf() -plt.subplot(121) -wm.plot_histgrm(ampmM_sea,25) -ylim = plt.gca().get_ylim() -plt.title('min-max amplitude distribution') -plt.subplot(122) -wm.plot_histgrm(ampRFC_sea,25) -plt.gca().set_ylim(ylim) -plt.title('Rainflow amplitude distribution') -plt.show() - -#!#! Section 4.3.3 Simulation of rainflow cycles -#!#! Simulation of cycles in a Markov model -# n = 41 -# param_m = [-1, 1, n] -# param_D = [1, n, n] -# u_markov=levels(param_m); -# G_markov=mktestmat(param_m,[-0.2, 0.2],0.15,1); -# T_markov=5000; -#xxD_markov=mctpsim({G_markov [,]},T_markov); -#xx_markov=[(1:T_markov)' u_markov(xxD_markov)']; -#clf -#plot(xx_markov(1:50,1),xx_markov(1:50,2)) -#title('Markov chain of turning points') -#wafostamp([],'(ER)') -#disp('Block 5'),pause(pstate) -# -# -##!#! Rainflow cycles in a transformed Gaussian model -##!#! Hermite transformed wave data and rainflow filtered turning points, h = 0.2. -#me = mean(xx_sea(:,2)); -#sa = std(xx_sea(:,2)); -#Hm0_sea = 4*sa; -#Tp_sea = 1/max(lc_sea(:,2)); -#spec = jonswap([],[Hm0_sea Tp_sea]); -# -#[sk, ku] = spec2skew(spec); -#spec.tr = hermitetr([],[sa sk ku me]); -#param_h = [-1.5 2 51]; -#spec_norm = spec; -#spec_norm.S = spec_norm.S/sa^2; -#xx_herm = spec2sdat(spec_norm,[2^15 1],0.1); -##! ????? PJ, JR 11-Apr-2001 -##! NOTE, in the simulation program spec2sdat -##!the spectrum must be normalized to variance 1 -##! ????? -#h = 0.2; -#[dtp,u_herm,xx_herm_1]=dat2dtp(param_h,xx_herm,h); -#clf -#plot(xx_herm(:,1),xx_herm(:,2),'k','LineWidth',2); hold on; -#plot(xx_herm_1(:,1),xx_herm_1(:,2),'k--','Linewidth',2); -#axis([0 50 -1 1]), hold off; -#title('Rainflow filtered wave data') -#wafostamp([],'(ER)') -#disp('Block 6'),pause(pstate) -# -##!#! Rainflow cycles and rainflow filtered rainflow cycles in the transformed Gaussian process. -#tp_herm=dat2tp(xx_herm); -#RFC_herm=tp2rfc(tp_herm); -#mM_herm=tp2mm(tp_herm); -#h=0.2; -#[dtp,u,tp_herm_1]=dat2dtp(param_h,xx_herm,h); -#RFC_herm_1 = tp2rfc(tp_herm_1); -#clf -#subplot(121), ccplot(RFC_herm) -#title('h=0') -#subplot(122), ccplot(RFC_herm_1) -#title('h=0.2') -#if (printing==1), print -deps ../bilder/fatigue_8.eps -#end -#wafostamp([],'(ER)') -#disp('Block 7'),pause(pstate) -# -##!#! Section 4.3.4 Calculating the rainflow matrix -# -# -#Grfc_markov=mctp2rfm({G_markov []}); -#clf -#subplot(121), cmatplot(u_markov,u_markov,G_markov), axis('square') -#subplot(122), cmatplot(u_markov,u_markov,Grfc_markov), axis('square') -#wafostamp([],'(ER)') -#disp('Block 8'),pause(pstate) -# -##!#! -#clf -#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},3) -#wafostamp([],'(ER)') -#disp('Block 9'),pause(pstate) -# -##!#! Min-max-matrix and theoretical rainflow matrix for test Markov sequence. -#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},4) -#subplot(121), axis('square'), title('min2max transition matrix') -#subplot(122), axis('square'), title('Rainflow matrix') -#if (printing==1), print -deps ../bilder/fatigue_9.eps -#end -#wafostamp([],'(ER)') -#disp('Block 10'),pause(pstate) -# -##!#! Observed and theoretical rainflow matrix for test Markov sequence. -#n=length(u_markov); -#Frfc_markov=dtp2rfm(xxD_markov,n); -#clf -#cmatplot(u_markov,u_markov,{Frfc_markov Grfc_markov*T_markov/2},3) -#subplot(121), axis('square'), title('Observed rainflow matrix') -#subplot(122), axis('square'), title('Theoretical rainflow matrix') -#if (printing==1), print -deps ../bilder/fatigue_10.eps -#end -#wafostamp([],'(ER)') -#disp('Block 11'),pause(pstate) -# -##!#! Smoothed observed and calculated rainflow matrix for test Markov sequence. -#tp_markov=dat2tp(xx_markov); -#RFC_markov=tp2rfc(tp_markov); -#h=1; -#Frfc_markov_smooth=cc2cmat(param_m,RFC_markov,[],1,h); -#clf -#cmatplot(u_markov,u_markov,{Frfc_markov_smooth Grfc_markov*T_markov/2},4) -#subplot(121), axis('square'), title('Smoothed observed rainflow matrix') -#subplot(122), axis('square'), title('Theoretical rainflow matrix') -#if (printing==1), print -deps ../bilder/fatigue_11.eps -#end -#wafostamp([],'(ER)') -#disp('Block 12'),pause(pstate) -# -##!#! Rainflow matrix from spectrum -#clf -##!GmM3_herm=spec2mmtpdf(spec,[],'Mm',[],[],2); -#GmM3_herm=spec2cmat(spec,[],'Mm',[],param_h,2); -#pdfplot(GmM3_herm) -#wafostamp([],'(ER)') -#disp('Block 13'),pause(pstate) -# -# -##!#! Min-max matrix and theoretical rainflow matrix for Hermite-transformed Gaussian waves. -#Grfc_herm=mctp2rfm({GmM3_herm.f []}); -#u_herm=levels(param_h); -#clf -#cmatplot(u_herm,u_herm,{GmM3_herm.f Grfc_herm},4) -#subplot(121), axis('square'), title('min-max matrix') -#subplot(122), axis('square'), title('Theoretical rainflow matrix') -#if (printing==1), print -deps ../bilder/fatigue_12.eps -#end -#wafostamp([],'(ER)') -#disp('Block 14'),pause(pstate) -# -##!#! -#clf -#Grfc_direct_herm=spec2cmat(spec,[],'rfc',[],[],2); -#subplot(121), pdfplot(GmM3_herm), axis('square'), hold on -#subplot(122), pdfplot(Grfc_direct_herm), axis('square'), hold off -#if (printing==1), print -deps ../bilder/fig_mmrfcjfr.eps -#end -#wafostamp([],'(ER)') -#disp('Block 15'),pause(pstate) -# -# -##!#! Observed smoothed and theoretical min-max matrix, -##!#! (and observed smoothed and theoretical rainflow matrix for Hermite-transformed Gaussian waves). -#tp_herm=dat2tp(xx_herm); -#RFC_herm=tp2rfc(tp_herm); -#mM_herm=tp2mm(tp_herm); -#h=0.2; -#FmM_herm_smooth=cc2cmat(param_h,mM_herm,[],1,h); -#Frfc_herm_smooth=cc2cmat(param_h,RFC_herm,[],1,h); -#T_herm=xx_herm(end,1)-xx_herm(1,1); -#clf -#cmatplot(u_herm,u_herm,{FmM_herm_smooth GmM3_herm.f*length(mM_herm) ; ... -# Frfc_herm_smooth Grfc_herm*length(RFC_herm)},4) -#subplot(221), axis('square'), title('Observed smoothed min-max matrix') -#subplot(222), axis('square'), title('Theoretical min-max matrix') -#subplot(223), axis('square'), title('Observed smoothed rainflow matrix') -#subplot(224), axis('square'), title('Theoretical rainflow matrix') -#if (printing==1), print -deps ../bilder/fatigue_13.eps -#end -#wafostamp([],'(ER)') -#disp('Block 16'),pause(pstate) -# -##!#! Section 4.3.5 Simulation from crossings and rainflow structure -# -##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve) -##!#! for simulated process with irregularity factor 0.25. -#clf -#cross_herm=dat2lc(xx_herm); -#alpha1=0.25; -#alpha2=0.75; -#xx_herm_sim1=lc2sdat(cross_herm,500,alpha1); -#cross_herm_sim1=dat2lc(xx_herm_sim1); -#subplot(211) -#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2))) -#hold on -#stairs(cross_herm_sim1(:,1),... -# cross_herm_sim1(:,2)/max(cross_herm_sim1(:,2))) -#hold off -#title('Crossing intensity, \alpha = 0.25') -#subplot(212) -#plot(xx_herm_sim1(:,1),xx_herm_sim1(:,2)) -#title('Simulated load, \alpha = 0.25') -#if (printing==1), print -deps ../bilder/fatigue_14_25.eps -#end -#wafostamp([],'(ER)') -#disp('Block 16'),pause(pstate) -# -##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve) -##!#! for simulated process with irregularity factor 0.75. -#xx_herm_sim2=lc2sdat(cross_herm,500,alpha2); -#cross_herm_sim2=dat2lc(xx_herm_sim2); -#subplot(211) -#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2))) -#hold on -#stairs(cross_herm_sim2(:,1),... -# cross_herm_sim2(:,2)/max(cross_herm_sim2(:,2))) -#hold off -#title('Crossing intensity, \alpha = 0.75') -#subplot(212) -#plot(xx_herm_sim2(:,1),xx_herm_sim2(:,2)) -#title('Simulated load, \alpha = 0.75') -#if (printing==1), print -deps ../bilder/fatigue_14_75.eps -#end -#wafostamp([],'(ER)') -#disp('Block 17'),pause(pstate) -# -##!#! Section 4.4 Fatigue damage and fatigue life distribution -##!#! Section 4.4.1 Introduction -#beta=3.2; gam=5.5E-10; T_sea=xx_sea(end,1)-xx_sea(1,1); -#d_beta=cc2dam(RFC_sea,beta)/T_sea; -#time_fail=1/gam/d_beta/3600 #!in hours of the specific storm -#disp('Block 18'),pause(pstate) -# -##!#! Section 4.4.2 Level crossings -##!#! Crossing intensity as calculated from the Markov matrix (solid curve) and from the observed rainflow matrix (dashed curve). -#clf -#mu_markov=cmat2lc(param_m,Grfc_markov); -#muObs_markov=cmat2lc(param_m,Frfc_markov/(T_markov/2)); -#clf -#plot(mu_markov(:,1),mu_markov(:,2),muObs_markov(:,1),muObs_markov(:,2),'--') -#title('Theoretical and observed crossing intensity ') -#if (printing==1), print -deps ../bilder/fatigue_15.eps -#end -#wafostamp([],'(ER)') -#disp('Block 19'),pause(pstate) -# -##!#! Section 4.4.3 Damage -##!#! Distribution of damage from different RFC cycles, from calculated theoretical and from observed rainflow matrix. -#beta = 4; -#Dam_markov = cmat2dam(param_m,Grfc_markov,beta) -#DamObs1_markov = cc2dam(RFC_markov,beta)/(T_markov/2) -#DamObs2_markov = cmat2dam(param_m,Frfc_markov,beta)/(T_markov/2) -#disp('Block 20'),pause(pstate) -# -#Dmat_markov = cmat2dmat(param_m,Grfc_markov,beta); -#DmatObs_markov = cmat2dmat(param_m,Frfc_markov,beta)/(T_markov/2); -#clf -#subplot(121), cmatplot(u_markov,u_markov,Dmat_markov,4) -#title('Theoretical damage matrix') -#subplot(122), cmatplot(u_markov,u_markov,DmatObs_markov,4) -#title('Observed damage matrix') -#if (printing==1), print -deps ../bilder/fatigue_16.eps -#end -#wafostamp([],'(ER)') -#disp('Block 21'),pause(pstate) -# -# -##!#! -##!Damplus_markov = lc2dplus(mu_markov,beta) -#pause(pstate) -# -##!#! Section 4.4.4 Estimation of S-N curve -# -##!#! Load SN-data and plot in log-log scale. -#SN = load('sn.dat'); -#s = SN(:,1); -#N = SN(:,2); -#clf -#loglog(N,s,'o'), axis([0 14e5 10 30]) -##!if (printing==1), print -deps ../bilder/fatigue_?.eps end -#wafostamp([],'(ER)') -#disp('Block 22'),pause(pstate) -# -# -##!#! Check of S-N-model on normal probability paper. -# -#normplot(reshape(log(N),8,5)) -#if (printing==1), print -deps ../bilder/fatigue_17.eps -#end -#wafostamp([],'(ER)') -#disp('Block 23'),pause(pstate) -# -##!#! Estimation of S-N-model on linear scale. -#clf -#[e0,beta0,s20] = snplot(s,N,12); -#title('S-N-data with estimated N(s)','FontSize',20) -#set(gca,'FontSize',20) -#if (printing==1), print -deps ../bilder/fatigue_18a.eps -#end -#wafostamp([],'(ER)') -#disp('Block 24'),pause(pstate) -# -##!#! Estimation of S-N-model on log-log scale. -#clf -#[e0,beta0,s20] = snplot(s,N,14); -#title('S-N-data with estimated N(s)','FontSize',20) -#set(gca,'FontSize',20) -#if (printing==1), print -deps ../bilder/fatigue_18b.eps -#end -#wafostamp([],'(ER)') -#disp('Block 25'),pause(pstate) -# -##!#! Section 4.4.5 From S-N curve to fatigue life distribution -##!#! Damage intensity as function of $\beta$ -#beta = 3:0.1:8; -#DRFC = cc2dam(RFC_sea,beta); -#dRFC = DRFC/T_sea; -#plot(beta,dRFC), axis([3 8 0 0.25]) -#title('Damage intensity as function of \beta') -#if (printing==1), print -deps ../bilder/fatigue_19.eps -#end -#wafostamp([],'(ER)') -#disp('Block 26'),pause(pstate) -# -##!#! Fatigue life distribution with sea load. -#dam0 = cc2dam(RFC_sea,beta0)/T_sea; -#[t0,F0] = ftf(e0,dam0,s20,0.5,1); -#[t1,F1] = ftf(e0,dam0,s20,0,1); -#[t2,F2] = ftf(e0,dam0,s20,5,1); -#plot(t0,F0,t1,F1,t2,F2) -#title('Fatigue life distribution function') -#if (printing==1), print -deps ../bilder/fatigue_20.eps -#end -#wafostamp([],'(ER)') -#disp('Block 27, last block') diff --git a/wafo/doc/tutorial_scripts/chapter5.py b/wafo/doc/tutorial_scripts/chapter5.py deleted file mode 100644 index 669ea4c..0000000 --- a/wafo/doc/tutorial_scripts/chapter5.py +++ /dev/null @@ -1,238 +0,0 @@ -## CHAPTER5 contains the commands used in Chapter 5 of the tutorial -# -# CALL: Chapter5 -# -# Some of the commands are edited for fast computation. -# Each set of commands is followed by a 'pause' command. -# - -# Tested on Matlab 5.3 -# History -# Added Return values by GL August 2008 -# Revised pab sept2005 -# Added sections -> easier to evaluate using cellmode evaluation. -# Created by GL July 13, 2000 -# from commands used in Chapter 5 -# - -## Chapter 5 Extreme value analysis - -## Section 5.1 Weibull and Gumbel papers -from __future__ import division -import numpy as np -import scipy.interpolate as si -from wafo.plotbackend import plotbackend as plt -import wafo.data as wd -import wafo.objects as wo -import wafo.stats as ws -import wafo.kdetools as wk -pstate = 'off' - -# Significant wave-height data on Weibull paper, - -fig = plt.figure() -ax = fig.add_subplot(111) -Hs = wd.atlantic() -wei = ws.weibull_min.fit(Hs) -tmp = ws.probplot(Hs, wei, ws.weibull_min, plot=ax) -plt.show() -#wafostamp([],'(ER)') -#disp('Block = 1'),pause(pstate) - -## -# Significant wave-height data on Gumbel paper, -plt.clf() -ax = fig.add_subplot(111) -gum = ws.gumbel_r.fit(Hs) -tmp1 = ws.probplot(Hs, gum, ws.gumbel_r, plot=ax) -#wafostamp([],'(ER)') -plt.show() -#disp('Block = 2'),pause(pstate) - -## -# Significant wave-height data on Normal probability paper, -plt.clf() -ax = fig.add_subplot(111) -phat = ws.norm.fit2(np.log(Hs)) -phat.plotresq() -#tmp2 = ws.probplot(np.log(Hs), phat, ws.norm, plot=ax) - -#wafostamp([],'(ER)') -plt.show() -#disp('Block = 3'),pause(pstate) - -## -# Return values in the Gumbel distribution -plt.clf() -T = np.r_[1:100000] -sT = gum[0] - gum[1] * np.log(-np.log1p(-1./T)) -plt.semilogx(T, sT) -plt.hold(True) -# ws.edf(Hs).plot() -Nmax = len(Hs) -N = np.r_[1:Nmax + 1] - -plt.plot(Nmax/N, sorted(Hs, reverse=True), '.') -plt.title('Return values in the Gumbel model') -plt.xlabel('Return period') -plt.ylabel('Return value') -#wafostamp([],'(ER)') -plt.show() -#disp('Block = 4'),pause(pstate) - -## Section 5.2 Generalized Pareto and Extreme Value distributions -## Section 5.2.1 Generalized Extreme Value distribution - -# Empirical distribution of significant wave-height with estimated -# Generalized Extreme Value distribution, -gev = ws.genextreme.fit2(Hs) -gev.plotfitsummary() -# wafostamp([],'(ER)') -# disp('Block = 5a'),pause(pstate) - -plt.clf() -x = np.linspace(0,14,200) -kde = wk.TKDE(Hs, L2=0.5)(x, output='plot') -kde.plot() -plt.hold(True) -plt.plot(x, gev.pdf(x),'--') -# disp('Block = 5b'),pause(pstate) - -# Analysis of yura87 wave data. -# Wave data interpolated (spline) and organized in 5-minute intervals -# Normalized to mean 0 and std = 1 to get stationary conditions. -# maximum level over each 5-minute interval analysed by GEV -xn = wd.yura87() -XI = np.r_[1:len(xn):0.25] - .99 -N = len(XI) -N = N - np.mod(N, 4*60*5) - -YI = si.interp1d(xn[:, 0], xn[:, 1], kind='linear')(XI) -YI = YI.reshape(4*60*5, N/(4*60*5)) # Each column holds 5 minutes of - # interpolated data. -Y5 = (YI - YI.mean(axis=0)) / YI.std(axis=0) -Y5M = Y5.maximum(axis=0) -Y5gev = ws.genextreme.fit2(Y5M,method='mps') -Y5gev.plotfitsummary() -#wafostamp([],'(ER)') -#disp('Block = 6'),pause(pstate) - -## Section 5.2.2 Generalized Pareto distribution - -# Exceedances of significant wave-height data over level 3, -gpd3 = ws.genpareto.fit2(Hs[Hs>3]-3, floc=0) -gpd3.plotfitsummary() -#wafostamp([],'(ER)') - -## -plt.figure() -# Exceedances of significant wave-height data over level 7, -gpd7 = ws.genpareto.fit2(Hs(Hs>7), floc=7) -gpd7.plotfitsummary() -# wafostamp([],'(ER)') -# disp('Block = 6'),pause(pstate) - -## -#Simulates 100 values from the GEV distribution with parameters (0.3, 1, 2), -# then estimates the parameters using two different methods and plots the -# estimated distribution functions together with the empirical distribution. -Rgev = ws.genextreme.rvs(0.3,1,2,size=100) -gp = ws.genextreme.fit2(Rgev, method='mps'); -gm = ws.genextreme.fit2(Rgev, *gp.par.tolist(), method='ml') -gm.plotfitsummary() - -gp.plotecdf() -plt.hold(True) -plt.plot(x, gm.cdf(x), '--') -plt.hold(False) -#wafostamp([],'(ER)') -#disp('Block =7'),pause(pstate) - -## -# ; -Rgpd = ws.genpareto.rvs(0.4,0, 1,size=100) -gp = ws.genpareto.fit2(Rgpd, method='mps') -gml = ws.genpareto.fit2(Rgpd, method='ml') - -gp.plotecdf() -x = sorted(Rgpd) -plt.hold(True) -plt.plot(x, gml.cdf(x)) -# gm = fitgenpar(Rgpd,'method','mom','plotflag',0); -# plot(x,cdfgenpar(x,gm),'g--') -#gw = fitgenpar(Rgpd,'method','pwm','plotflag',0); -#plot(x,cdfgenpar(x,gw),'g:') -#gml = fitgenpar(Rgpd,'method','ml','plotflag',0); -#plot(x,cdfgenpar(x,gml),'--') -#gmps = fitgenpar(Rgpd,'method','mps','plotflag',0); -#plot(x,cdfgenpar(x,gmps),'r-.') -plt.hold(False) -#wafostamp([],'(ER)') -#disp('Block = 8'),pause(pstate) - -## -# Return values for the GEV distribution -T = np.logspace(1, 5, 10); -#[sT, sTlo, sTup] = invgev(1./T,Y5gev,'lowertail',false,'proflog',true); - -#T = 2:100000; -#k=Y5gev.params(1); mu=Y5gev.params(3); sigma=Y5gev.params(2); -#sT1 = invgev(1./T,Y5gev,'lowertail',false); -#sT=mu + sigma/k*(1-(-log(1-1./T)).^k); -plt.clf() -#plt.semilogx(T,sT,T,sTlo,'r',T,sTup,'r') -#plt.hold(True) -#N = np.r_[1:len(Y5M)] -#Nmax = max(N); -#plot(Nmax./N, sorted(Y5M,reverse=True), '.') -#plt.title('Return values in the GEV model') -#plt.xlabel('Return priod') -#plt.ylabel('Return value') -#plt.grid(True) -#disp('Block = 9'),pause(pstate) - -## Section 5.3 POT-analysis - -# Estimated expected exceedance over level u as function of u. -plt.clf() - -mrl = ws.reslife(Hs,'umin',2,'umax',10,'Nu',200); -mrl.plot() -#wafostamp([],'(ER)') -#disp('Block = 10'),pause(pstate) - -## -# Estimated distribution functions of monthly maxima -#with the POT method (solid), -# fitting a GEV (dashed) and the empirical distribution. - -# POT- method -gpd7 = ws.genpareto.fit2(Hs(Hs>7)-7, method='mps', floc=0) -khat, loc, sigmahat = gpd7.par - -muhat = len(Hs[Hs>7])/(7*3*2) -bhat = sigmahat/muhat**khat -ahat = 7-(bhat-sigmahat)/khat -x = np.linspace(5,15,200); -plt.plot(x,ws.genextreme.cdf(x, khat,bhat,ahat)) -# disp('Block = 11'),pause(pstate) - -## -# Since we have data to compute the monthly maxima mm over -#42 months we can also try to fit a -# GEV distribution directly: -mm = np.zeros((1,41)) -for i in range(41): - mm[i] = max(Hs[((i-1)*14+1):i*14]) - - -gev = ws.genextreme.fit2(mm) - - -plt.hold(True) -gev.plotecdf() - -plt.hold(False) -#wafostamp([],'(ER)') -#disp('Block = 12, Last block'),pause(pstate) - diff --git a/wafo/doc/tutorial_scripts/rainflow_example.py b/wafo/doc/tutorial_scripts/rainflow_example.py deleted file mode 100644 index 75cac99..0000000 --- a/wafo/doc/tutorial_scripts/rainflow_example.py +++ /dev/null @@ -1,176 +0,0 @@ -from tutor_init import * -import itertools -# import sys -log = logging.getLogger(__name__) -log.setLevel(logging.DEBUG) - -MARKERS = ('o', 'x', '+', '.', '<', '>', '^', 'v') - - -def plot_varying_symbols(x, y, color='red', size=5): - """ - Create a plot with varying symbols - Parameters - ---------- - x : numpy array with x data of the points - y : numpy array with y data of the points - color : color of the symbols - - Returns - ------- - - """ - markers = itertools.cycle(MARKERS) - for q, p in zip(x, y): - plt.plot(q, p, marker=markers.next(), linestyle='', color=color, - markersize=size) - - -def damage_vs_S(S, beta, K): - """ - Calculate the damage 1/N for a given stress S - - Parameters - ---------- - S : Stress [Pa] - beta : coefficient, typically 3 - K : constant - - Returns - ------- - - """ - return K * np.power(S, beta) - -# Section 4.3.1 Crossing intensity -# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -import wafo.data as wd -import wafo.objects as wo -import wafo.misc as wm - -xx_sea = wd.sea() - -Tlength = xx_sea[-1, 0] - xx_sea[0, 0] -beta = 3 -K1 = 6.5e-31 -Np = 200 -Tp = Tlength / Np -A = 100e6 -log.info("setting sin wave with Tp={} and T={}".format(Tp, Tlength)) -Nc = 1.0 / damage_vs_S(A, beta, K1) -damage = float(Np) / float(Nc) -log.info("budget at S={} N={}: damage = {} ".format(A, Nc, damage)) -#xx_sea[:, 1] = A * np.cos(2 * np.pi * xx_sea[:, 0]/Tp) -xx_sea[:, 1] *= 500e6 - -log.info("loaded sea time series {}".format(xx_sea.shape)) -ts = wo.mat2timeseries(xx_sea) - -tp = ts.turning_points() -mM = tp.cycle_pairs(kind='min2max') -Mm = tp.cycle_pairs(kind='max2min') -lc = mM.level_crossings(intensity=True) -T_sea = ts.args[-1] - ts.args[0] - -# for i in dir(mM): -# print(i) - - -ts1 = wo.mat2timeseries(xx_sea[:, :]) -tp1 = ts1.turning_points() -sig_tp = ts.turning_points(h=0, wavetype='astm') -try: - sig_cp = sig_tp.cycle_astm() - log.info("Successfully used cycle_astm") -except AttributeError: - log.warning("Could use cycle_astm") - sig_cp = None -tp1 = ts1.turning_points() -tp2 = ts1.turning_points(wavetype='Mw') -mM1 = tp1.cycle_pairs(kind='min2max') -Mm1 = tp1.cycle_pairs(kind='max2min') - -tp_rfc = tp1.rainflow_filter(h=100e6) -mM_rfc = tp_rfc.cycle_pairs() -try: - mM_rfc_a = tp1.cycle_astm() -except AttributeError: - mM_rfc_a = None -tc1 = ts1.trough_crest() -min_to_max = True -rfc_plot = True -if min_to_max: - m1, M1 = mM1.get_minima_and_maxima() - i_min_start = 0 -else: - m1, M1 = Mm1.get_minima_and_maxima() - i_min_start = 2 - -m_rfc, M_rfc = mM_rfc.get_minima_and_maxima() -# m_rfc_a, M_rfc_a = mM_rfc_a.get_minima_and_maxima() -ts1.plot('b-') -if rfc_plot: - plot_varying_symbols(tp_rfc.args[0::2], m_rfc, color='red', size=10) - plot_varying_symbols(tp_rfc.args[1::2], M_rfc, color='green', size=10) -else: - plot_varying_symbols(tp.args[i_min_start::2], m1, color='red', size=10) - plot_varying_symbols(tp.args[1::2], M1, color='green', size=10) - -set_windows_title("Sea time series", log) - -plt.figure() -plt.subplot(122), -mM.plot() -plt.title('min-max cycle pairs') -plt.subplot(121), -mM_rfc.plot() - -title = 'Rainflow filtered cycles' -plt.title(title) -set_windows_title(title) - - -# Min-max and rainflow cycle distributions -#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -# import wafo.misc as wm -ampmM_sea = mM.amplitudes() -ampRFC_sea = mM_rfc.amplitudes() -plt.figure() -title = "s_n_curve" -set_windows_title(title) -S = np.linspace(1e6, 1000e6) -plt.loglog(S, damage_vs_S(S, beta, K1)) -plt.figure() -plt.subplot(121) -stress_range = (1, 1e9) -n_bins = 100 -wm.plot_histgrm(ampmM_sea, bins=n_bins, range=stress_range) -plt.xlim(stress_range) -ylim = plt.gca().get_ylim() -plt.title('min-max amplitude distribution') -plt.subplot(122) -if sig_cp is not None: - wm.plot_histgrm(sig_cp[:, 0], bins=n_bins, range=stress_range) - plt.gca().set_ylim(ylim) - title = 'Rainflow amplitude distribution' - plt.title(title) - plt.semilogy - set_windows_title(title) - - hist, bin_edges = np.histogram( - sig_cp[ - :, 0], bins=n_bins, range=stress_range) - - plt.figure() - title = "my_bins" - plt.title(title) - plt.title(title) - set_windows_title(title) - plt.semilogy - plt.bar(bin_edges[:-1], hist, width=stress_range[1] / n_bins) - - print("damage min/max : {}".format(mM_rfc.damage([beta], K1))) - - damage_rfc = K1 * np.sum(sig_cp[:, 0] ** beta) - print("damage rfc : {}".format(damage_rfc)) -plt.show('hold') diff --git a/wafo/doc/tutorial_scripts/tutor_init.py b/wafo/doc/tutorial_scripts/tutor_init.py deleted file mode 100644 index 849f589..0000000 --- a/wafo/doc/tutorial_scripts/tutor_init.py +++ /dev/null @@ -1,27 +0,0 @@ -import logging -import scipy as sp -import numpy as np -from numpy import pi, reshape -import matplotlib.pyplot as plt -import matplotlib -matplotlib.use('Qt4Agg') -from matplotlib import rcParams -rcParams.update({"font.size": 10}) - - -try: - from win32api import LoadResource -except ImportError: - pass - -log = logging.basicConfig( - format="%(asctime)s - %(name)s - %(levelname)s - %(message)s", - level=logging.DEBUG) - - -def set_windows_title(title, log=None): - if log is not None: - log.info("Set windows title {}".format(title)) - fig = plt.gcf() - fig.canvas.set_window_title(title) - plt.show() diff --git a/wafo/sg_filter/__init__.py b/wafo/sg_filter/__init__.py deleted file mode 100644 index eebc78c..0000000 --- a/wafo/sg_filter/__init__.py +++ /dev/null @@ -1,2 +0,0 @@ -from wafo.sg_filter._core import * # pylint: disable=wildcard-import -from wafo.sg_filter import demos diff --git a/wafo/sg_filter/_core.py b/wafo/sg_filter/_core.py deleted file mode 100644 index e1cb42c..0000000 --- a/wafo/sg_filter/_core.py +++ /dev/null @@ -1,1223 +0,0 @@ -from __future__ import absolute_import, division -import numpy as np -from numpy import (pi, linalg, concatenate, sqrt) -from scipy.sparse import spdiags -from scipy.sparse.linalg import spsolve -import scipy.optimize as optimize -from scipy.signal import _savitzky_golay -from scipy.ndimage import convolve1d -from scipy.ndimage.morphology import distance_transform_edt -import warnings -from wafo.dctpack import dctn, idctn - - -__all__ = ['SavitzkyGolay', 'Kalman', 'HodrickPrescott', 'smoothn', - 'HampelFilter', 'SmoothNd', 'noise'] - -# noise = np.random.randn(2**8)/10 -noise = [-0.0490483773397234, 0.07101522794824691, 0.043129450693516064, 0.07858516767729644, -0.04489848540755172, -0.012710090966021995, 0.022967442347004003, -0.1593564930543959, 0.14752458454255937, -0.1220055819473534, -0.030151822649201642, 0.009880871420067841, 0.0401050562035102, -0.10931262882008379, -0.14550620919429919, -0.06632845063372966, 0.07773893951749064, -0.009527784302072342, 0.06002486046176557, 0.11972670522904964, -0.14436696992162384, 0.06009486605688445, -0.05802790838575894, 0.16964239368289297, 0.09088881573238144, -0.003398259264109856, 0.059830811447018004, -0.08189024981767952, -0.05455483548325317, 0.056651518536760745, -0.05211609539593189, -0.07848323826083178, -0.03921692262168154, -0.04755275276447492, -0.05855172473750038, 0.06480280696345982, -0.05237889271019207, -0.05891912551792037, -0.04045907452295067, -0.09058522124919187, 0.1406515441218336, 0.15557979603588584, -0.09096515320242772, 0.1724190189462715, -0.04978942687488187, -0.0855435866249914, 0.09439718859306868, -0.14758639479507882, -0.07225230856508442, 0.008364508824556314, 0.06704423745152435, -0.01718113731784587, 0.07473943576290255, 0.028133087670974395, 0.026270590730899095, 0.13175770484080895, -0.01821821552644416, 0.11325945472394446, 0.04694754851273185, -0.23899404962137366, -0.1528175431702195, 0.151870532421663, -0.07353204927616248, 0.11604199430172217, -0.09111623325687843, -0.11887366073405607, -0.029872397510562025, 0.047672685028458936, -0.18340065977268627, 0.06896217941210328, 0.042997912112300564, 0.15416998299846174, -0.0386283794526545, 0.14070600624229804, 0.020984623041646142, -0.1892741373898864, 0.03253519397457513, -0.06182705494266229, -0.1326495728975159, 0.026234150321195537, 0.0550541170409239, 0.029275813927566702, 0.042742104678489906, -0.2170004668366198, -0.00035991761313413197, -0.0638872684868346, -0.11769436550364845, -0.017792813824766808, -0.022786402363044914, -0.10668279890162544, 0.05979507681729831, -0.1008100479486818, 0.0703474638610785, 0.1630534776572414, 0.06682406484481357, -0.0527228810042394, -0.046515310355062636, 0.04609515154732255, 0.11503753838360875, 0.11517599661346192, -0.05596425736274815, -0.06149119758833357, 0.10599964719188917, -0.012076380140185552, 0.0436828262270732, -0.03910174791470852, -0.03263251315745414, -0.012513843545007558, 0.004590611827089213, 0.0762719171282112, 0.06497715695411535, -0.003280826953794463, 0.13524154885565484, -0.020441364843140027, -0.09488214173137496, 0.1385755359902911, -0.23883052310744746, -0.10110537386421652, -0.1588981058869149, 0.06645444828058467, -0.2103306051703948, 0.15215327561190056, -0.03582175680076989, 0.013593833383013293, -0.11542058494732854, -0.05613268116816099, 0.012711037661355899, 0.04242805633100794, -0.011799315325220794, 0.12141794601099387, 0.054285270560662645, 0.07549385527022169, -0.04549437694653443, 0.11009856942530691, 0.05233482224379645, -0.042246830306136955, -0.1737197924666796, -0.10589427330127077, 0.04895472597843757, 0.06756519832636187, 0.083376600742245, -0.07502859751328732, -0.09493802498812245, -0.01058967186080922, -0.23759763247649018, 0.08439637862616411, -0.2021754550870607, 0.07365816800912013, 0.07435401663661081, 0.047992791325423556, -0.005250092450514997, 0.1693610927865244, 0.030338113772413154, -0.18010537945928004, 0.01744129379023785, 0.1902505975745975, -0.004598733688659104, 0.13663542585715657, -0.04100719174496187, -0.15406303185009937, -0.05297118247908407, 0.04435144348234146, 0.022377061632995063, 0.05491057192661079, -0.08473062163887303, -0.03907641665824873, 0.008686833182075315, -0.06053451866471732, -0.051735892949367854, -0.1902071038920444, 0.11508817132666356, 0.08903045262390544, -0.028537865059606825, -0.07160660523436188, 0.05994760363400714, 0.03637820115278829, 0.027604828657436364, 0.04168122074675033, -0.021707671111253164, 0.06770739385070886, -0.04848505599153394, -0.14377853380839264, 0.17448368721141166, -0.05972663746675887, -0.1615729579782888, -0.09508063624538736, -0.05501964872264433, -0.14370852991216054, -0.1025241548369181, -0.14751000180775747, -0.05402976681470177, -0.05847606145915367, 0.015603559358987138, 0.040327317968149784, 0.015596571983936361, 0.08721780106901023, 0.13669912032986667, -0.07070030973798198, 0.04821782065785363, 0.05266507025196321, -0.013775127999269254, 0.07032239356769251, 0.04685048562398681, 0.004648720572365418, -0.19364418622487742, 0.013662994215276983, 0.04703494294810789, 0.04863794676207257, -0.09883919097676001, -0.004798538894290822, -0.22183503742087135, 0.062096556899520906, 0.07098373434409047, -0.05335639719762188, -0.09150459514627822, -0.1329311651202703, -0.037376442133682145, 0.1238732233009325, -0.01232052797514208, 0.007151238520555889, -0.04772828461473576, -0.029830395387364726, -0.03277336781995001, 0.09964048194066656, 0.09306408040020697, -0.03761782769337173, 0.07059549032551317, -0.15490333414875848, 0.12599077783991805, 0.23520519946427365, 0.021640305946603107, 0.014851729969403227, -0.039035437601777224, -0.12087588583684257, -0.07207855860199022, -0.002800081649022032, 0.2543907308881692, -0.07966223382328289, -0.1014419766425384, -0.11243061225437859, -0.08744845956375621, -0.05540140267769189, -0.04995531421885231, -0.13274847220288336, 0.06435474943034288, 0.015640361472736924, -0.11210644205346465, -0.04080648821849449, -0.011452694652695428, 0.22044736923317904, 0.024322228245949113, 0.09622705616884256, 0.05793212184654495, -0.10620553812614748, 0.06762504431789758, 0.19135075519983785] # nopep8 - - -def _assert(cond, msg): - if not cond: - raise ValueError(msg) - - -class SavitzkyGolay(object): - r"""Smooth and optionally differentiate data with a Savitzky-Golay filter. - - The Savitzky-Golay filter removes high frequency noise from data. - It has the advantage of preserving the original shape and - features of the signal better than other types of filtering - approaches, such as moving averages techniques. - - Parameters - ---------- - n : int - the size of the smoothing window is 2*n+1. - degree : int - the degree of the polynomial used in the filtering. - Must be less than `window_size` - 1, i.e, less than 2*n. - diff_order : int - order of the derivative to compute (default = 0 means only smoothing) - 0 means that filter results in smoothing of function - 1 means that filter results in smoothing the first derivative of the - function and so on ... - delta : float, optional - The spacing of the samples to which the filter will be applied. - This is only used if deriv > 0. Default is 1.0. - axis : int, optional - The axis of the array `x` along which the filter is to be applied. - Default is -1. - mode : str, optional - Must be 'mirror', 'constant', 'nearest', 'wrap' or 'interp'. This - determines the type of extension to use for the padded signal to - which the filter is applied. When `mode` is 'constant', the padding - value is given by `cval`. See the Notes for more details on 'mirror', - 'constant', 'wrap', and 'nearest'. - When the 'interp' mode is selected (the default), no extension - is used. Instead, a degree `polyorder` polynomial is fit to the - last `window_length` values of the edges, and this polynomial is - used to evaluate the last `window_length // 2` output values. - cval : scalar, optional - Value to fill past the edges of the input if `mode` is 'constant'. - Default is 0.0. - - Notes - ----- - The Savitzky-Golay is a type of low-pass filter, particularly suited for - smoothing noisy data. The main idea behind this approach is to make for - each point a least-square fit with a polynomial of high order over a - odd-sized window centered at the point. - - Details on the `mode` options: - - 'mirror': - Repeats the values at the edges in reverse order. The value - closest to the edge is not included. - 'nearest': - The extension contains the nearest input value. - 'constant': - The extension contains the value given by the `cval` argument. - 'wrap': - The extension contains the values from the other end of the array. - - For example, if the input is [1, 2, 3, 4, 5, 6, 7, 8], and - `window_length` is 7, the following shows the extended data for - the various `mode` options (assuming `cval` is 0):: - - mode | Ext | Input | Ext - -----------+---------+------------------------+--------- - 'mirror' | 4 3 2 | 1 2 3 4 5 6 7 8 | 7 6 5 - 'nearest' | 1 1 1 | 1 2 3 4 5 6 7 8 | 8 8 8 - 'constant' | 0 0 0 | 1 2 3 4 5 6 7 8 | 0 0 0 - 'wrap' | 6 7 8 | 1 2 3 4 5 6 7 8 | 1 2 3 - - Examples - -------- - >>> import wafo.sg_filter as ws - >>> t = np.linspace(-4, 4, 500) - >>> noise = np.random.normal(0, 0.05, t.shape) - >>> noise = np.sqrt(0.05)*np.sin(100*t) - >>> y = np.exp( -t**2 ) + noise - >>> ysg = SavitzkyGolay(n=20, degree=2).smooth(y) - >>> np.allclose(ysg[:3], [ 0.01345312, 0.01164172, 0.00992839]) - True - >>> ysm = SavitzkyGolay(n=20, degree=2, mode='mirror').smooth(y) - >>> np.allclose(ysm[:3], [-0.01604804, -0.00592883, 0.0035858 ]) - True - >>> ysc = SavitzkyGolay(n=20, degree=2, mode='constant').smooth(y) - >>> np.allclose(ysc[:3], [-0.00279797, 0.00519541, 0.00666146]) - True - >>> ysn = SavitzkyGolay(n=20, degree=2, mode='nearest').smooth(y) - >>> np.allclose(ysn[:3], [ 0.08711171, 0.0846945 , 0.07587448]) - True - >>> ysw = SavitzkyGolay(n=20, degree=2, mode='wrap').smooth(y) - >>> np.allclose(ysw[:3], [-0.00208422, -0.00201491, 0.00201772]) - True - >>> np.allclose(SavitzkyGolay(n=20, degree=2).smooth_last(y), - ... 0.004921382626100505) - True - - import matplotlib.pyplot as plt - h = plt.plot(t, y, label='Noisy signal') - h1 = plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal') - h2 = plt.plot(t, ysg, 'r', label='Filtered signal') - h3 = plt.legend() - h4 = plt.title('Savitzky-Golay') - plt.show() - - References - ---------- - .. [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of - Data by Simplified Least Squares Procedures. Analytical - Chemistry, 1964, 36 (8), pp 1627-1639. - .. [2] Numerical Recipes 3rd Edition: The Art of Scientific Computing - W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery - Cambridge University Press ISBN-13: 9780521880688 - """ - - def __init__(self, n, degree=1, diff_order=0, delta=1.0, axis=-1, - mode='interp', cval=0.0): - self.n = n - self.degree = degree - self.diff_order = diff_order - self.mode = mode - self.cval = cval - self.axis = axis - self.delta = delta - window_length = 2 * n + 1 - self._coeff = _savitzky_golay.savgol_coeffs(window_length, - degree, deriv=diff_order, - delta=delta) - - def smooth_last(self, signal, k=1): - coeff = self._coeff - n = (np.size(coeff) - 1) // 2 - y = np.squeeze(signal) - if n == 0: - return y - if y.ndim > 1: - coeff.shape = (-1, 1) - first_vals = y[0] - np.abs(y[n:0:-1] - y[0]) - last_vals = y[-1] + np.abs(y[-2:-n - 2:-1] - y[-1]) - y = concatenate((first_vals, y, last_vals)) - return (y[-2 * n - 1 - k:-k] * coeff).sum(axis=0) - - def __call__(self, signal): - return self.smooth(signal) - - def smooth(self, signal): - dtype = np.result_type(signal, np.float) - x = np.asarray(signal, dtype=dtype) - - coeffs = self._coeff - mode, axis = self.mode, self.axis - if mode == "interp": - window_length, polyorder = self.n * 2 + 1, self.degree - deriv, delta = self.diff_order, self.delta - y = convolve1d(x, coeffs, axis=axis, mode="constant") - _savitzky_golay._fit_edges_polyfit(x, window_length, polyorder, - deriv, delta, axis, y) - else: - y = convolve1d(x, coeffs, axis=axis, mode=mode, cval=self.cval) - return y - - -def evar(y): - """Noise variance estimation. Assuming that the deterministic function Y - has additive Gaussian noise, EVAR(Y) returns an estimated variance of this - noise. - - Note: - ---- - A thin-plate smoothing spline model is used to smooth Y. It is assumed - that the model whose generalized cross-validation score is minimum can - provide the variance of the additive noise. A few tests showed that - EVAR works very well with "not too irregular" functions. - - Examples: - -------- - 1D signal - >>> n = 1e6 - >>> x = np.linspace(0,100,n); - >>> y = np.cos(x/10)+(x/50) - >>> var0 = 0.02 # noise variance - >>> yn = y + sqrt(var0)*np.random.randn(*y.shape) - >>> s = evar(yn) # estimated variance - >>> np.abs(s-var0)/var0 < 3.5/np.sqrt(n) - True - - 2D function - >>> xp = np.linspace(0,1,50) - >>> x, y = np.meshgrid(xp,xp) - >>> f = np.exp(x+y) + np.sin((x-2*y)*3) - >>> var0 = 0.04 # noise variance - >>> fn = f + sqrt(var0)*np.random.randn(*f.shape) - >>> s = evar(fn) # estimated variance - >>> np.abs(s-var0)/var0 < 3.5/np.sqrt(50) - True - - 3D function - >>> yp = np.linspace(-2,2,50) - >>> [x,y,z] = np.meshgrid(yp, yp, yp, sparse=True) - >>> f = x*np.exp(-x**2-y**2-z**2) - >>> var0 = 0.5 # noise variance - >>> fn = f + np.sqrt(var0)*np.random.randn(*f.shape) - >>> s = evar(fn) # estimated variance - >>> np.abs(s-var0)/var0 < 3.5/np.sqrt(50) - True - - Other example - ------------- - http://www.biomecardio.com/matlab/evar.html - - Note: - ---- - EVAR is only adapted to evenly-gridded 1-D to N-D data. - - See also - -------- - VAR, STD, SMOOTHN - - """ - - # Damien Garcia -- 2008/04, revised 2009/10 - y = np.atleast_1d(y) - d = y.ndim - sh0 = y.shape - - S = np.zeros(sh0) - sh1 = np.ones((d,), dtype=np.int64) - cos = np.cos - for i in range(d): - ni = sh0[i] - sh1[i] = ni - t = np.arange(ni).reshape(sh1) / ni - S += cos(pi * t) - sh1[i] = 1 - - S2 = 2 * (d - S).ravel() - # N-D Discrete Cosine Transform of Y - dcty2 = dctn(y).ravel() ** 2 - - def score_fun(L, S2, dcty2): - # Generalized cross validation score - M = 1 - 1. / (1 + 10 ** L * S2) - noisevar = (dcty2 * M ** 2).mean() - return noisevar / M.mean() ** 2 - # fun = lambda x : score_fun(x, S2, dcty2) - Lopt = optimize.fminbound(score_fun, -38, 38, args=(S2, dcty2)) - M = 1.0 - 1.0 / (1 + 10 ** Lopt * S2) - noisevar = (dcty2 * M ** 2).mean() - return noisevar - - -class _Filter(object): - def __init__(self, y, z0, weightstr, weights, s, robust, maxiter, tolz): - self.y = y - self.z0 = z0 - self.weightstr = weightstr - self.s = s - self.robust = robust - self.maxiter = maxiter - self.tolz = tolz - - self.auto_smooth = s is None - self.is_finite = np.isfinite(y) - self.nof = self.is_finite.sum() # number of finite elements - self.W = self._normalized_weights(weights, self.is_finite) - - self.gamma = self._gamma_fun(y) - - self.N = self._tensor_rank(y) - self.s_min, self.s_max = self._smoothness_limits(self.N) - - # Initialize before iterating - self.Wtot = self.W - self.is_weighted = (self.W < 1).any() # Weighted or missing data? - - self.z0 = self._get_start_condition(y, z0) - - self.y[~self.is_finite] = 0 # arbitrary values for missing y-data - - # Error on p. Smoothness parameter s = 10^p - self.errp = 0.1 - - # Relaxation factor RF: to speedup convergence - self.RF = 1.75 if self.is_weighted else 1.0 - - @staticmethod - def _tensor_rank(y): - """tensor rank of the y-array""" - return (np.array(y.shape) != 1).sum() - - @staticmethod - def _smoothness_par(h): - return (((1 + sqrt(1 + 8 * h)) / 4. / h) ** 2 - 1) / 16 - - def _smoothness_limits(self, n): - """ - Return upper and lower bound for the smoothness parameter - - The average leverage (h) is by definition in [0 1]. Weak smoothing - occurs if h is close to 1, while over-smoothing appears when h is - near 0. Upper and lower bounds for h are given to avoid under- or - over-smoothing. See equation relating h to the smoothness parameter - (Equation #12 in the referenced CSDA paper). - """ - h_min = 1e-6 ** (2. / n) - h_max = 0.99 ** (2. / n) - - s_min = self._smoothness_par(h_max) - s_max = self._smoothness_par(h_min) - return s_min, s_max - - @staticmethod - def _lambda_tensor(y): - """ - Return the Lambda tensor - - Lambda contains the eigenvalues of the difference matrix used in this - penalized least squares process. - """ - d = y.ndim - Lambda = np.zeros(y.shape) - shape0 = [1, ] * d - for i in range(d): - shape0[i] = y.shape[i] - Lambda = Lambda + \ - np.cos(pi * np.arange(y.shape[i]) / y.shape[i]).reshape(shape0) - shape0[i] = 1 - Lambda = -2 * (d - Lambda) - return Lambda - - def _gamma_fun(self, y): - Lambda = self._lambda_tensor(y) - - def gamma(s): - if s is None: - return 1.0 - return 1. / (1 + s * Lambda ** 2) - return gamma - - @staticmethod - def _initial_guess(y, I): - # Initial Guess with weighted/missing data - # nearest neighbor interpolation (in case of missing values) - z = y - if (1 - I).any(): - notI = ~I - z, L = distance_transform_edt(notI, return_indices=True) - z[notI] = y[L.flat[notI]] - - # coarse fast smoothing using one-tenth of the DCT coefficients - shape = z.shape - d = z.ndim - z = dctn(z) - for k in range(d): - z[int((shape[k] + 0.5) / 10) + 1::, ...] = 0 - z = z.reshape(np.roll(shape, -k)) - z = z.transpose(np.roll(range(d), -1)) - # z = shiftdim(z,1); - return idctn(z) - - def _get_start_condition(self, y, z0): - # Initial conditions for z - if self.is_weighted: - # With weighted/missing data - # An initial guess is provided to ensure faster convergence. For - # that purpose, a nearest neighbor interpolation followed by a - # coarse smoothing are performed. - if z0 is None: - z = self._initial_guess(y, self.is_finite) - else: - z = z0 # an initial guess (z0) has been provided - else: - z = np.zeros(y.shape) - return z - - @staticmethod - def _normalized_weights(weight, is_finite): - """ Return normalized weights. - - Zero weights are assigned to not finite values (Inf or NaN), - (Inf/NaN values = missing data). - """ - weights = weight * is_finite - _assert(np.all(0 <= weights), 'Weights must all be >=0') - return weights / weights.max() - - @staticmethod - def _studentized_residuals(r, I, h): - median_abs_deviation = np.median(np.abs(r[I] - np.median(r[I]))) - return np.abs(r / (1.4826 * median_abs_deviation) / sqrt(1 - h)) - - def robust_weights(self, r, I, h): - """Return weights for robust smoothing.""" - def bisquare(u): - c = 4.685 - return (1 - (u / c) ** 2) ** 2 * ((u / c) < 1) - - def talworth(u): - c = 2.795 - return u < c - - def cauchy(u): - c = 2.385 - return 1. / (1 + (u / c) ** 2) - - u = self._studentized_residuals(r, I, h) - - wfun = {'cauchy': cauchy, 'talworth': talworth}.get(self.weightstr, - bisquare) - weights = wfun(u) - - weights[np.isnan(weights)] = 0 - return weights - - @staticmethod - def _average_leverage(s, N): - h = sqrt(1 + 16 * s) - h = sqrt(1 + h) / sqrt(2) / h - return h ** N - - def check_smooth_parameter(self, s): - if self.auto_smooth: - if np.abs(np.log10(s) - np.log10(self.s_min)) < self.errp: - warnings.warn("""s = %g: the lower bound for s has been reached. - Put s as an input variable if required.""" % s) - elif np.abs(np.log10(s) - np.log10(self.s_max)) < self.errp: - warnings.warn("""s = %g: the Upper bound for s has been reached. - Put s as an input variable if required.""" % s) - - def gcv(self, p, aow, DCTy, y, Wtot): - # Search the smoothing parameter s that minimizes the GCV score - s = 10.0 ** p - gamma_s = self.gamma(s) - if aow > 0.9: - # aow = 1 means that all of the data are equally weighted - # very much faster: does not require any inverse DCT - residual = DCTy.ravel() * (gamma_s.ravel() - 1) - else: - # take account of the weights to calculate RSS: - is_finite = self.is_finite - yhat = idctn(gamma_s * DCTy) - residual = sqrt(Wtot[is_finite]) * (y[is_finite] - yhat[is_finite]) - - TrH = gamma_s.sum() - RSS = linalg.norm(residual)**2 # Residual sum-of-squares - GCVscore = RSS / self.nof / (1.0 - TrH / y.size) ** 2 - return GCVscore - - def _smooth(self, z, s): - auto_smooth = self.auto_smooth - norm = linalg.norm - y = self.y - Wtot = self.Wtot - gamma_s = self.gamma(s) - # "amount" of weights (see the function GCVscore) - aow = Wtot.sum() / y.size # 0 < aow <= 1 - for nit in range(self.maxiter): - DCTy = dctn(Wtot * (y - z) + z) - if auto_smooth and not np.remainder(np.log2(nit + 1), 1): - # The generalized cross-validation (GCV) method is used. - # We seek the smoothing parameter s that minimizes the GCV - # score i.e. s = Argmin(GCVscore). - # Because this process is time-consuming, it is performed from - # time to time (when nit is a power of 2) - log10s = optimize.fminbound( - self.gcv, np.log10(self.s_min), np.log10(self.s_max), - args=(aow, DCTy, y, Wtot), - xtol=self.errp, full_output=False, disp=False) - s = 10 ** log10s - gamma_s = self.gamma(s) - z0 = z - z = self.RF * idctn(gamma_s * DCTy) + (1 - self.RF) * z - # if no weighted/missing data => tol=0 (no iteration) - tol = norm(z0.ravel() - z.ravel()) / norm(z.ravel()) - converged = tol <= self.tolz or not self.is_weighted - if converged: - break - return z, s, converged - - def __call__(self, z, s): - z, s, converged = self._smooth(z, s) - if self.robust: - # -- Robust Smoothing: iteratively re-weighted process - h = self._average_leverage(s, self.N) - self.Wtot = self.W * self.robust_weights(self.y - z, - self.is_finite, h) - # re-initialize for another iterative weighted process - self.is_weighted = True - return z, s, converged - - -class SmoothNd(object): - def __init__(self, s=None, weight=None, robust=False, z0=None, tolz=1e-3, - maxiter=100, fulloutput=False): - self.s = s - self.weight = weight - self.robust = robust - self.z0 = z0 - self.tolz = tolz - self.maxiter = maxiter - self.fulloutput = fulloutput - - @property - def weightstr(self): - if isinstance(self._weight, str): - return self._weight.lower() - return 'bisquare' - - @property - def weight(self): - if self._weight is None or isinstance(self._weight, str): - return 1.0 - return self._weight - - @weight.setter - def weight(self, weight): - self._weight = weight - - def _init_filter(self, y): - return _Filter(y, self.z0, self.weightstr, self.weight, self.s, - self.robust, self.maxiter, self.tolz) - - @property - def num_steps(self): - return 3 if self.robust else 1 - - def __call__(self, data): - - y = np.atleast_1d(data) - if y.size < 2: - return data - - _filter = self._init_filter(y) - z = _filter.z0 - s = _filter.s - converged = False - for _i in range(self.num_steps): - z, s, converged = _filter(z, s) - - if not converged: - msg = """Maximum number of iterations (%d) has been exceeded. - Increase MaxIter option or decrease TolZ value.""" % (self.maxiter) - warnings.warn(msg) - - _filter.check_smooth_parameter(s) - - if self.fulloutput: - return z, s - return z - - -def smoothn(data, s=None, weight=None, robust=False, z0=None, tolz=1e-3, - maxiter=100, fulloutput=False): - """ - SMOOTHN fast and robust spline smoothing for 1-D to N-D data. - - Parameters - ---------- - data : array like - uniformly-sampled data array to smooth. Non finite values (NaN or Inf) - are treated as missing values. - s : real positive scalar - smooting parameter. The larger S is, the smoother the output will be. - Default value is automatically determined using the generalized - cross-validation (GCV) method. - weight : string or array weights - weighting array of real positive values, that must have the same size - as DATA. Note that a zero weight corresponds to a missing value. - robust : bool - If true carry out a robust smoothing that minimizes the influence of - outlying data. - tolz : real positive scalar - Termination tolerance on Z (default = 1e-3) - maxiter : scalar integer - Maximum number of iterations allowed (default = 100) - z0 : array-like - Initial value for the iterative process (default = original data) - - Returns - ------- - z : array like - smoothed data - - To be made - ---------- - Estimate the confidence bands (see Wahba 1983, Nychka 1988). - - Reference - --------- - Garcia D, Robust smoothing of gridded data in one and higher dimensions - with missing values. Computational Statistics & Data Analysis, 2010. - http://www.biomecardio.com/pageshtm/publi/csda10.pdf - - Examples: - -------- - - 1-D example - >>> import matplotlib.pyplot as plt - >>> import wafo.sg_filter as ws - >>> x = np.linspace(0, 100, 2**8) - >>> noise = np.random.randn(2**8)/10 - >>> noise = ws.noise - >>> y = np.cos(x/10)+(x/50)**2 + noise - >>> y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6]) - >>> y[181] = np.nan - >>> z = ws.smoothn(y) # Regular smoothing - >>> np.allclose(z[:3], [ 0.99517904, 0.99372346, 0.99079798]) - True - >>> zr = ws.smoothn(y,robust=True) # Robust smoothing - >>> np.allclose(zr[:3], [ 1.01190564, 1.00976197, 1.00513244]) - True - - h=plt.subplot(121), - h = plt.plot(x,y,'r.',x,z,'k',linewidth=2) - h=plt.title('Regular smoothing') - h=plt.subplot(122) - h=plt.plot(x,y,'r.',x,zr,'k',linewidth=2) - h=plt.title('Robust smoothing') - - 2-D example - >>> xp = np.r_[0:1:.02] - >>> [x,y] = np.meshgrid(xp,xp) - >>> f = np.exp(x+y) + np.sin((x-2*y)*3) - >>> fn = f + np.random.randn(*f.shape)*0.5 - >>> fs = smoothn(fn) - - h=plt.subplot(121), - h=plt.contourf(xp, xp, fn) - h=plt.subplot(122) - h=plt.contourf(xp, xp, fs) - - 2-D example with missing data - >>> import wafo.demos as wd - >>> n = 256 - >>> x0, y0, z0 = wd.peaks(n) - - z = z0 + rand(size(y0))*2 - I = randperm(n**2) - z[I(1:n^2*0.5)] = np.NaN; # lose 1/2 of data - z[40:90, 140:190] = np.NaN; # create a hole - zs = smoothn(z) - - plt.subplot(2,2,1) - plt.imagesc(y) # , axis equal off - plt.title('Noisy corrupt data') - plt.subplot(223) - plt.imagesc(z) # , axis equal off - plt.title('Recovered data ...') - plt.subplot(224) - plt.imagesc(y0) # , axis equal off - plt.title('... compared with original data') - - 3-D example - [x,y,z] = meshgrid(-2:.2:2); - xslice = [-0.8,1]; yslice = 2; zslice = [-2,0]; - vn = x.*exp(-x.^2-y.^2-z.^2) + randn(size(x))*0.06; - subplot(121), slice(x,y,z,vn,xslice,yslice,zslice,'cubic') - title('Noisy data') - v = smoothn(vn); - subplot(122), slice(x,y,z,v,xslice,yslice,zslice,'cubic') - title('Smoothed data') - - - Cellular vortical flow - [x,y] = meshgrid(linspace(0,1,24)); - Vx = cos(2*pi*x+pi/2).*cos(2*pi*y); - Vy = sin(2*pi*x+pi/2).*sin(2*pi*y); - Vx = Vx + sqrt(0.05)*randn(24,24); adding Gaussian noise - Vy = Vy + sqrt(0.05)*randn(24,24); adding Gaussian noise - I = randperm(numel(Vx)); - Vx(I(1:30)) = (rand(30,1)-0.5)*5; adding outliers - Vy(I(1:30)) = (rand(30,1)-0.5)*5; adding outliers - Vx(I(31:60)) = NaN; missing values - Vy(I(31:60)) = NaN; missing values - Vs = smoothn(complex(Vx,Vy),'robust'); automatic smoothing - subplot(121), quiver(x,y,Vx,Vy,2.5), axis square - title('Noisy velocity field') - subplot(122), quiver(x,y,real(Vs),imag(Vs)), axis square - title('Smoothed velocity field') - - See also - ------- - SmoothNd - - -- Damien Garcia -- 2009/03, revised 2010/11 - Visit - http://www.biomecardio.com/matlab/smoothn.html - for more details about SMOOTHN - """ - return SmoothNd(s, weight, robust, z0, tolz, maxiter, fulloutput)(data) - - -class HodrickPrescott(object): - - """Smooth data with a Hodrick-Prescott filter. - - The Hodrick-Prescott filter removes high frequency noise from data. - It has the advantage of preserving the original shape and - features of the signal better than other types of filtering - approaches, such as moving averages techniques. - - Parameter - --------- - w : real scalar - smooting parameter. Larger w means more smoothing. Values usually - in the [100, 20000] interval. As w approach infinity H-P will approach - a line. - - Examples - -------- - >>> import wafo.sg_filter as ws - >>> t = np.linspace(-4, 4, 500) - >>> y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape) - >>> ysg = ws.HodrickPrescott(w=10000)(y) - - import matplotlib.pyplot as plt - h = plt.plot(t, y, label='Noisy signal') - h1 = plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal') - h2 = plt.plot(t, ysg, 'r', label='Filtered signal') - h3 = plt.legend() - h4 = plt.title('Hodrick-Prescott') - plt.show() - - References - ---------- - .. [1] E. T. Whittaker, On a new method of graduation. In proceedings of - the Edinburgh Mathematical association., 1923, 78, pp 88-89. - .. [2] R. Hodrick and E. Prescott, Postwar U.S. business cycles: an - empirical investigation, - Journal of money, credit and banking, 1997, 29 (1), pp 1-16. - .. [3] Kim Hyeongwoo, Hodrick-Prescott filter, - 2004, www.auburn.edu/~hzk0001/hpfilter.pdf - """ - - def __init__(self, w=100): - self.w = w - - def _get_matrix(self, n): - w = self.w - diag_matrix = np.repeat( - np.atleast_2d([w, -4 * w, 6 * w + 1, -4 * w, w]).T, n, axis=1) - A = spdiags(diag_matrix, np.arange(-2, 2 + 1), n, n).tocsr() - A[0, 0] = A[-1, -1] = 1 + w - A[1, 1] = A[-2, -2] = 1 + 5 * w - A[0, 1] = A[1, 0] = A[-2, -1] = A[-1, -2] = -2 * w - return A - - def __call__(self, x): - x = np.atleast_1d(x).flatten() - n = len(x) - if n < 4: - return x.copy() - - A = self._get_matrix(n) - return spsolve(A, x) - - -class Kalman(object): - - """ - Kalman filter object - updates a system state vector estimate based upon an - observation, using a discrete Kalman filter. - - The Kalman filter is "optimal" under a variety of - circumstances. An excellent paper on Kalman filtering at - the introductory level, without detailing the mathematical - underpinnings, is: - - "An Introduction to the Kalman Filter" - Greg Welch and Gary Bishop, University of North Carolina - http://www.cs.unc.edu/~welch/kalman/kalmanIntro.html - - PURPOSE: - The purpose of each iteration of a Kalman filter is to update - the estimate of the state vector of a system (and the covariance - of that vector) based upon the information in a new observation. - The version of the Kalman filter in this function assumes that - observations occur at fixed discrete time intervals. Also, this - function assumes a linear system, meaning that the time evolution - of the state vector can be calculated by means of a state transition - matrix. - - USAGE: - filt = Kalman(R, x, P, A, B=0, Q, H) - x = filt(z, u=0) - - filt is a "system" object containing various fields used as input - and output. The state estimate "x" and its covariance "P" are - updated by the function. The other fields describe the mechanics - of the system and are left unchanged. A calling routine may change - these other fields as needed if state dynamics are time-dependent; - otherwise, they should be left alone after initial values are set. - The exceptions are the observation vector "z" and the input control - (or forcing function) "u." If there is an input function, then - "u" should be set to some nonzero value by the calling routine. - - System dynamics - --------------- - - The system evolves according to the following difference equations, - where quantities are further defined below: - - x = Ax + Bu + w meaning the state vector x evolves during one time - step by premultiplying by the "state transition - matrix" A. There is optionally (if nonzero) an input - vector u which affects the state linearly, and this - linear effect on the state is represented by - premultiplying by the "input matrix" B. There is also - gaussian process noise w. - z = Hx + v meaning the observation vector z is a linear function - of the state vector, and this linear relationship is - represented by premultiplication by "observation - matrix" H. There is also gaussian measurement - noise v. - where w ~ N(0,Q) meaning w is gaussian noise with covariance Q - v ~ N(0,R) meaning v is gaussian noise with covariance R - - VECTOR VARIABLES: - - s.x = state vector estimate. In the input struct, this is the - "a priori" state estimate (prior to the addition of the - information from the new observation). In the output struct, - this is the "a posteriori" state estimate (after the new - measurement information is included). - z = observation vector - u = input control vector, optional (defaults to zero). - - MATRIX VARIABLES: - - s.A = state transition matrix (defaults to identity). - s.P = covariance of the state vector estimate. In the input struct, - this is "a priori," and in the output it is "a posteriori." - (required unless autoinitializing as described below). - s.B = input matrix, optional (defaults to zero). - s.Q = process noise covariance (defaults to zero). - s.R = measurement noise covariance (required). - s.H = observation matrix (defaults to identity). - - NORMAL OPERATION: - - (1) define all state definition fields: A,B,H,Q,R - (2) define intial state estimate: x,P - (3) obtain observation and control vectors: z,u - (4) call the filter to obtain updated state estimate: x,P - (5) return to step (3) and repeat - - INITIALIZATION: - - If an initial state estimate is unavailable, it can be obtained - from the first observation as follows, provided that there are the - same number of observable variables as state variables. This "auto- - intitialization" is done automatically if s.x is absent or NaN. - - x = inv(H)*z - P = inv(H)*R*inv(H') - - This is mathematically equivalent to setting the initial state estimate - covariance to infinity. - - Example (Automobile Voltimeter): - ------- - >>> import wafo.sg_filter as ws - >>> V0 = 12 # Define the system as a constant of 12 volts - >>> h = 1 # voltimeter measure the voltage itself - >>> q = 1e-5 # variance of process noise s the car operates - >>> r = 0.1**2 # variance of measurement error - >>> b = 0 # no system input - >>> u = 0 # no system input - >>> filt = ws.Kalman(R=r, A=1, Q=q, H=h, B=b) - - # Generate random voltages and watch the filter operate. - >>> n = 50 - >>> truth = np.random.randn(n)*np.sqrt(q) + V0 - >>> z = truth + np.random.randn(n)*np.sqrt(r) # measurement - >>> x = np.zeros(n) - - >>> for i, zi in enumerate(z): - ... x[i] = filt(zi, u) # perform a Kalman filter iteration - - import matplotlib.pyplot as plt - hz = plt.plot(z,'r.', label='observations') - - # a-posteriori state estimates: - hx = plt.plot(x,'b-', label='Kalman output') - ht = plt.plot(truth,'g-', label='true voltage') - h = plt.legend() - h1 = plt.title('Automobile Voltimeter Example') - plt.show() - - """ - - def __init__(self, R, x=None, P=None, A=None, B=0, Q=None, H=None): - self.R = R # Estimated error in measurements. - self.x = x # Initial state estimate. - self.P = P # Initial covariance estimate. - self.A = A # State transition matrix. - self.B = B # Control matrix. - self.Q = Q # Estimated error in process. - self.H = H # Observation matrix. - self.reset() - - def reset(self): - self._filter = self._filter_first - - @staticmethod - def _none_or_atleast_2d(a): - if a is not None: - return np.atleast_2d(a) - return a - - @property - def A(self): - return self._a - - @A.setter - def A(self, a): - self._a = self._none_or_atleast_2d(a) - - def _set_A(self, n): - if self.A is None: - self.A = np.eye(n) - - @property - def Q(self): - return self._q - - @Q.setter - def Q(self, q): - self._q = self._none_or_atleast_2d(q) - - def _set_Q(self, n): - if self.Q is None: - self.Q = np.zeros((n, n)) - - @property - def H(self): - return self._h - - @H.setter - def H(self, h): - self._h = self._none_or_atleast_2d(h) - - def _set_H(self, n): - if self.H is None: - self.H = np.eye(n) - - @property - def P(self): - return self._p - - @P.setter - def P(self, p): - self._p = self._none_or_atleast_2d(p) - - def _set_P(self, HI): - if self.P is None: - self.P = np.dot(np.dot(HI, self.R), HI.T) - - def _init_first(self, n): - self._set_A(n) - self._set_Q(n) - self._set_H(n) - try: - HI = np.linalg.inv(self.H) - except Exception: - HI = np.eye(n) - self._set_P(HI) - return HI - - def _first_state(self, z): - n = np.size(z) - HI = self._init_first(n) - # initialize state estimate from first observation - x = np.dot(HI, z) - return x - - def _filter_first(self, z, u): - - self._filter = self._filter_main - - if self.x is None: - self.x = self._first_state(z) - return self.x - - n = np.size(self.x) - self._init_first(n) - return self._filter_main(z, u) - - def _predict_state(self, x, u): - return np.dot(self.A, x) + np.dot(self.B, u) - - def _predict_covariance(self, P): - A = self.A - return np.dot(np.dot(A, P), A.T) + self.Q - - def _compute_gain(self, P): - """Kalman gain factor.""" - H = self.H - PHT = np.dot(P, H.T) - innovation_covariance = np.dot(H, PHT) + self.R - # return np.linalg.solve(PHT, innovation_covariance) - return np.dot(PHT, np.linalg.inv(innovation_covariance)) - - def _update_state_from_observation(self, x, z, K): - innovation = z - np.dot(self.H, x) - return x + np.dot(K, innovation) - - def _update_covariance(self, P, K): - return P - np.dot(K, np.dot(self.H, P)) - # return np.dot(np.eye(len(P)) - K * self.H, P) - - def _filter_main(self, z, u): - """ This is the code which implements the discrete Kalman filter: - """ - P = self._predict_covariance(self.P) - x = self._predict_state(self.x, u) - - K = self._compute_gain(P) - - self.P = self._update_covariance(P, K) - self.x = self._update_state_from_observation(x, z, K) - - return self.x - - def __call__(self, z, u=0): - return self._filter(z, u) - - -class HampelFilter(object): - """Hampel Filter. - - HAMPEL(X,Y,DX,T,varargin) returns the Hampel filtered values of the - elements in Y. It was developed to detect outliers in a time series, - but it can also be used as an alternative to the standard median - filter. - - X,Y are row or column vectors with an equal number of elements. - The elements in Y should be Gaussian distributed. - - Parameters - ---------- - dx : positive scalar (default 3 * median(diff(X)) - which defines the half width of the filter window. Dx should be - dimensionally equivalent to the values in X. - t : positive scalar (default 3) - which defines the threshold value used in the equation - |Y - Y0| > T * S0. - adaptive: real scalar - if greater than 0 it uses an experimental adaptive Hampel filter. - If none it uses a standard Hampel filter - fulloutput: bool - if True also the vectors: outliers, Y0,LB,UB,ADX, which corresponds to - the mask of the replaced values, nominal data, lower and upper bounds - on the Hampel filter and the relative half size of the local window, - respectively. outliers.sum() gives the number of outliers detected. - - Examples - --------- - Hampel filter removal of outliers - >>> import numpy as np - >>> randint = np.random.randint - >>> Y = 5000 + np.random.randn(1000) - >>> outliers = randint(0,1000, size=(10,)) - >>> Y[outliers] = Y[outliers] + randint(1000, size=(10,)) - >>> YY, res = HampelFilter(fulloutput=True)(Y) - >>> YY1, res1 = HampelFilter(dx=1, t=3, adaptive=0.1, fulloutput=True)(Y) - >>> YY2, res2 = HampelFilter(dx=3, t=0, fulloutput=True)(Y) # Y0 = median - - X = np.arange(len(YY)) - plt.plot(X, Y, 'b.') # Original Data - plt.plot(X, YY, 'r') # Hampel Filtered Data - plt.plot(X, res['Y0'], 'b--') # Nominal Data - plt.plot(X, res['LB'], 'r--') # Lower Bounds on Hampel Filter - plt.plot(X, res['UB'], 'r--') # Upper Bounds on Hampel Filter - i = res['outliers'] - plt.plot(X[i], Y[i], 'ks') # Identified Outliers - plt.show('hold') - - References - ---------- - Chapters 1.4.2, 3.2.2 and 4.3.4 in Mining Imperfect Data: Dealing with - Contamination and Incomplete Records by Ronald K. Pearson. - - Acknowledgements - I would like to thank Ronald K. Pearson for the introduction to moving - window filters. Please visit his blog at: - http://exploringdatablog.blogspot.com/2012/01/moving-window-filters-and - -pracma.html - - """ - - def __init__(self, dx=None, t=3, adaptive=None, fulloutput=False): - self.dx = dx - self.t = t - self.adaptive = adaptive - self.fulloutput = fulloutput - - @staticmethod - def _check(dx): - _assert(np.isscalar(dx), 'DX must be a scalar.') - _assert(0 < dx, 'DX must be larger than zero.') - - @staticmethod - def localwindow(X, Y, DX, i): - mask = (X[i] - DX <= X) & (X <= X[i] + DX) - Y0 = np.median(Y[mask]) - # Calculate Local Scale of Natural Variation - S0 = 1.4826 * np.median(np.abs(Y[mask] - Y0)) - return Y0, S0 - - @staticmethod - def smgauss(X, V, DX): - Xj = X - Xk = np.atleast_2d(X).T - Wjk = np.exp(-((Xj - Xk) / (2 * DX)) ** 2) - G = np.dot(Wjk, V) / np.sum(Wjk, axis=0) - return G - - def _adaptive(self, Y, X, dx): - localwindow = self.localwindow - Y0, S0, ADX = self._init(Y, dx) - Y0Tmp = np.nan * np.zeros(Y.shape) - S0Tmp = np.nan * np.zeros(Y.shape) - DXTmp = np.arange(1, len(S0) + 1) * dx - # Integer variation of Window Half Size - # Calculate Initial Guess of Optimal Parameters Y0, S0, ADX - for i in range(len(Y)): - j = 0 - S0Rel = np.inf - while S0Rel > self.adaptive: - Y0Tmp[j], S0Tmp[j] = localwindow(X, Y, DXTmp[j], i) - if j > 0: - S0Rel = np.abs((S0Tmp[j - 1] - S0Tmp[j]) / - (S0Tmp[j - 1] + S0Tmp[j]) / 2) - j += 1 - - Y0[i] = Y0Tmp[j - 2] - S0[i] = S0Tmp[j - 2] - ADX[i] = DXTmp[j - 2] / dx - - # Gaussian smoothing of relevant parameters - DX = 2 * np.median(np.diff(X)) - ADX = self.smgauss(X, ADX, DX) - S0 = self.smgauss(X, S0, DX) - Y0 = self.smgauss(X, Y0, DX) - return Y0, S0, ADX - - def _init(self, Y, dx): - S0 = np.nan * np.zeros(Y.shape) - Y0 = np.nan * np.zeros(Y.shape) - ADX = dx * np.ones(Y.shape) - return Y0, S0, ADX - - def _fixed(self, Y, X, dx): - localwindow = self.localwindow - Y0, S0, ADX = self._init(Y, dx) - for i in range(len(Y)): - Y0[i], S0[i] = localwindow(X, Y, dx, i) - return Y0, S0, ADX - - def _filter(self, Y, X, dx): - if len(X) <= 1: - Y0, S0, ADX = self._init(Y, dx) - elif self.adaptive is None: - Y0, S0, ADX = self._fixed(Y, X, dx) - else: - Y0, S0, ADX = self._adaptive(Y, X, dx) # 'adaptive' - return Y0, S0, ADX - - def __call__(self, y, x=None): - Y = np.atleast_1d(y).ravel() - if x is None: - x = range(len(Y)) - X = np.atleast_1d(x).ravel() - - dx = 3 * np.median(np.diff(X)) if self.dx is None else self.dx - self._check(dx) - - Y0, S0, ADX = self._filter(Y, X, dx) - YY = Y.copy() - T = self.t - # Prepare Output - self.UB = Y0 + T * S0 - self.LB = Y0 - T * S0 - outliers = np.abs(Y - Y0) > T * S0 # possible outliers - np.putmask(YY, outliers, Y0) # YY[outliers] = Y0[outliers] - self.outliers = outliers - self.num_outliers = outliers.sum() - self.ADX = ADX - self.Y0 = Y0 - if self.fulloutput: - return YY, dict(outliers=outliers, Y0=Y0, - LB=self.LB, UB=self.UB, ADX=ADX) - return YY - - -if __name__ == '__main__': - from wafo.testing import test_docstrings - test_docstrings(__file__) diff --git a/wafo/sg_filter/demos.py b/wafo/sg_filter/demos.py deleted file mode 100644 index dfffda9..0000000 --- a/wafo/sg_filter/demos.py +++ /dev/null @@ -1,488 +0,0 @@ -import numpy as np -from scipy.sparse.linalg import expm -from scipy.signal import medfilt -from wafo.plotbackend import plotbackend as plt -from wafo.sg_filter._core import (SavitzkyGolay, smoothn, Kalman, - HodrickPrescott, HampelFilter) - - -def demo_savitzky_on_noisy_chirp(): - """ - Example - ------- - >>> demo_savitzky_on_noisy_chirp() - - >>> plt.close() - """ - plt.figure(figsize=(7, 12)) - - # generate chirp signal - tvec = np.arange(0, 6.28, .02) - true_signal = np.sin(tvec * (2.0 + tvec)) - true_d_signal = (2 + tvec) * np.cos(tvec * (2.0 + tvec)) - - # add noise to signal - noise = np.random.normal(size=true_signal.shape) - signal = true_signal + .15 * noise - - # plot signal - plt.subplot(311) - plt.plot(signal) - plt.title('signal') - - # smooth and plot signal - plt.subplot(312) - savgol = SavitzkyGolay(n=8, degree=4) - s_signal = savgol.smooth(signal) - s2 = smoothn(signal, robust=True) - plt.plot(s_signal) - plt.plot(s2) - plt.plot(true_signal, 'r--') - plt.title('smoothed signal') - - # smooth derivative of signal and plot it - plt.subplot(313) - savgol1 = SavitzkyGolay(n=8, degree=1, diff_order=1) - - dt = tvec[1] - tvec[0] - d_signal = savgol1.smooth(signal) / dt - - plt.plot(d_signal) - plt.plot(true_d_signal, 'r--') - plt.title('smoothed derivative of signal') - - -def demo_kalman_voltimeter(): - """ - Example - ------- - >>> demo_kalman_voltimeter() - - >>> plt.close() - """ - V0 = 12 - h = np.atleast_2d(1) # voltimeter measure the voltage itself - q = 1e-9 # variance of process noise as the car operates - r = 0.05 ** 2 # variance of measurement error - b = 0 # no system input - u = 0 # no system input - filt = Kalman(R=r, A=1, Q=q, H=h, B=b) - - # Generate random voltages and watch the filter operate. - n = 50 - truth = np.random.randn(n) * np.sqrt(q) + V0 - z = truth + np.random.randn(n) * np.sqrt(r) # measurement - x = np.zeros(n) - - for i, zi in enumerate(z): - x[i] = filt(zi, u) # perform a Kalman filter iteration - - _hz = plt.plot(z, 'r.', label='observations') - # a-posteriori state estimates: - _hx = plt.plot(x, 'b-', label='Kalman output') - _ht = plt.plot(truth, 'g-', label='true voltage') - plt.legend() - plt.title('Automobile Voltimeter Example') - - -def lti_disc(F, L=None, Q=None, dt=1): - """LTI_DISC Discretize LTI ODE with Gaussian Noise. - - Syntax: - [A,Q] = lti_disc(F,L,Qc,dt) - - In: - F - NxN Feedback matrix - L - NxL Noise effect matrix (optional, default identity) - Qc - LxL Diagonal Spectral Density (optional, default zeros) - dt - Time Step (optional, default 1) - - Out: - A - Transition matrix - Q - Discrete Process Covariance - - Description: - Discretize LTI ODE with Gaussian Noise. The original - ODE model is in form - - dx/dt = F x + L w, w ~ N(0,Qc) - - Result of discretization is the model - - x[k] = A x[k-1] + q, q ~ N(0,Q) - - Which can be used for integrating the model - exactly over time steps, which are multiples - of dt. - - """ - n = np.shape(F)[0] - if L is None: - L = np.eye(n) - - if Q is None: - Q = np.zeros((n, n)) - # Closed form integration of transition matrix - A = expm(F * dt) - - # Closed form integration of covariance - # by matrix fraction decomposition - - Phi = np.vstack((np.hstack((F, np.dot(np.dot(L, Q), L.T))), - np.hstack((np.zeros((n, n)), -F.T)))) - AB = np.dot(expm(Phi * dt), np.vstack((np.zeros((n, n)), np.eye(n)))) - # Q = AB[:n, :] / AB[n:(2 * n), :] - Q = np.linalg.solve(AB[n:(2 * n), :].T, AB[:n, :].T) - return A, Q - - -def demo_kalman_sine(): - """Kalman Filter demonstration with sine signal. - - Example - ------- - >>> demo_kalman_sine() - - >>> plt.close() - """ - sd = 0.5 - dt = 0.1 - w = 1 - T = np.arange(0, 30 + dt / 2, dt) - n = len(T) - X = 3 * np.sin(w * T) - Y = X + sd * np.random.randn(n) - - ''' Initialize KF to values - x = 0 - dx/dt = 0 - with great uncertainty in derivative - ''' - M = np.zeros((2, 1)) - P = np.diag([0.1, 2]) - R = sd ** 2 - H = np.atleast_2d([1, 0]) - q = 0.1 - F = np.atleast_2d([[0, 1], - [0, 0]]) - A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt) - - # Track and animate - m = M.shape[0] - _MM = np.zeros((m, n)) - _PP = np.zeros((m, m, n)) - '''In this demonstration we estimate a stationary sine signal from noisy - measurements by using the classical Kalman filter.' - ''' - filt = Kalman(R=R, x=M, P=P, A=A, Q=Q, H=H, B=0) - - # Generate random voltages and watch the filter operate. - # n = 50 - # truth = np.random.randn(n) * np.sqrt(q) + V0 - # z = truth + np.random.randn(n) * np.sqrt(r) # measurement - truth = X - z = Y - x = np.zeros((n, m)) - - for i, zi in enumerate(z): - x[i] = np.ravel(filt(zi, u=0)) - - _hz = plt.plot(z, 'r.', label='observations') - # a-posteriori state estimates: - _hx = plt.plot(x[:, 0], 'b-', label='Kalman output') - _ht = plt.plot(truth, 'g-', label='true voltage') - plt.legend() - plt.title('Automobile Voltimeter Example') - - -# for k in range(m): -# [M,P] = kf_predict(M,P,A,Q); -# [M,P] = kf_update(M,P,Y(k),H,R); -# -# MM(:,k) = M; -# PP(:,:,k) = P; -# -# % -# % Animate -# % -# if rem(k,10)==1 -# plot(T,X,'b--',... -# T,Y,'ro',... -# T(k),M(1),'k*',... -# T(1:k),MM(1,1:k),'k-'); -# legend('Real signal','Measurements','Latest estimate', -# 'Filtered estimate') -# title('Estimating a noisy sine signal with Kalman filter.'); -# drawnow; -# -# pause; -# end -# end -# -# clc; -# disp('In this demonstration we estimate a stationary sine signal ' -# 'from noisy measurements by using the classical Kalman filter.'); -# disp(' '); -# disp('The filtering results are now displayed sequantially for 10 time ' -# 'step at a time.'); -# disp(' '); -# disp('') -# pause; -# % -# % Apply Kalman smoother -# % -# SM = rts_smooth(MM,PP,A,Q); -# plot(T,X,'b--',... -# T,MM(1,:),'k-',... -# T,SM(1,:),'r-'); -# legend('Real signal','Filtered estimate','Smoothed estimate') -# title('Filtered and smoothed estimate of the original signal'); -# -# clc; -# disp('The filtered and smoothed estimates of the signal are now ' -# 'displayed.') -# disp(' '); -# disp('RMS errors:'); -# % -# % Errors -# % -# fprintf('KF = %.3f\nRTS = %.3f\n',... -# sqrt(mean((MM(1,:)-X(1,:)).^2)),... -# sqrt(mean((SM(1,:)-X(1,:)).^2))); - - -def demo_hampel(): - """ - Example - ------- - >>> demo_hampel() - - >>> plt.close() - """ - randint = np.random.randint - Y = 5000 + np.random.randn(1000) - outliers = randint(0, 1000, size=(10,)) - Y[outliers] = Y[outliers] + randint(1000, size=(10,)) - YY, res = HampelFilter(dx=3, t=3, fulloutput=True)(Y) - YY1, res1 = HampelFilter(dx=1, t=3, adaptive=0.1, fulloutput=True)(Y) - YY2, res2 = HampelFilter(dx=3, t=0, fulloutput=True)(Y) # median - plt.figure(1) - plot_hampel(Y, YY, res) - plt.title('Standard HampelFilter') - plt.figure(2) - plot_hampel(Y, YY1, res1) - plt.title('Adaptive HampelFilter') - plt.figure(3) - plot_hampel(Y, YY2, res2) - plt.title('Median filter') - - -def plot_hampel(Y, YY, res): - X = np.arange(len(YY)) - plt.plot(X, Y, 'b.') # Original Data - plt.plot(X, YY, 'r') # Hampel Filtered Data - plt.plot(X, res['Y0'], 'b--') # Nominal Data - plt.plot(X, res['LB'], 'r--') # Lower Bounds on Hampel Filter - plt.plot(X, res['UB'], 'r--') # Upper Bounds on Hampel Filter - i = res['outliers'] - plt.plot(X[i], Y[i], 'ks') # Identified Outliers - - -def demo_tide_filter(): - """ - Example - ------- - >>> demo_tide_filter() - - >>> plt.close() - """ - # import statsmodels.api as sa - import wafo.spectrum.models as sm - sd = 10 - Sj = sm.Jonswap(Hm0=4. * sd) - S = Sj.tospecdata() - - q = (0.1 * sd) ** 2 # variance of process noise s the car operates - r = (100 * sd) ** 2 # variance of measurement error - b = 0 # no system input - u = 0 # no system input - - from scipy.signal import butter, filtfilt, lfilter_zi # lfilter, - freq_tide = 1. / (12 * 60 * 60) - freq_wave = 1. / 10 - freq_filt = freq_wave / 10 - dt = 1. - freq = 1. / dt - fn = (freq / 2) - - P = 10 * np.diag([1, 0.01]) - R = r - H = np.atleast_2d([1, 0]) - - F = np.atleast_2d([[0, 1], - [0, 0]]) - A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt) - - t = np.arange(0, 60 * 12, 1. / freq) - w = 2 * np.pi * freq # 1 Hz - tide = 100 * np.sin(freq_tide * w * t + 2 * np.pi / 4) + 100 - y = tide + S.sim(len(t), dt=1. / freq)[:, 1].ravel() -# lowess = sa.nonparametric.lowess -# y2 = lowess(y, t, frac=0.5)[:,1] - - filt = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b) - filt2 = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b) - # y = tide + 0.5 * np.sin(freq_wave * w * t) - # Butterworth filter - b, a = butter(9, (freq_filt / fn), btype='low') - # y2 = [lowess(y[max(i-60,0):i + 1], t[max(i-60,0):i + 1], frac=.3)[-1,1] - # for i in range(len(y))] - # y2 = [lfilter(b, a, y[:i + 1])[i] for i in range(len(y))] - # y3 = filtfilt(b, a, y[:16]).tolist() + [filtfilt(b, a, y[:i + 1])[i] - # for i in range(16, len(y))] - # y0 = medfilt(y, 41) - _zi = lfilter_zi(b, a) - # y2 = lfilter(b, a, y)#, zi=y[0]*zi) # standard filter - y3 = filtfilt(b, a, y) # filter with phase shift correction - y4 = [] - y5 = [] - for _i, j in enumerate(y): - tmp = np.ravel(filt(j, u=u)) - tmp = np.ravel(filt2(tmp[0], u=u)) -# if i==0: -# print(filt.x) -# print(filt2.x) - y4.append(tmp[0]) - y5.append(tmp[1]) - _y0 = medfilt(y4, 41) - # print(filt.P) - # plot - - plt.plot(t, y, 'r.-', linewidth=2, label='raw data') - # plt.plot(t, y2, 'b.-', linewidth=2, label='lowess @ %g Hz' % freq_filt) - # plt.plot(t, y2, 'b.-', linewidth=2, label='filter @ %g Hz' % freq_filt) - plt.plot(t, y3, 'g.-', linewidth=2, label='filtfilt @ %g Hz' % freq_filt) - plt.plot(t, y4, 'k.-', linewidth=2, label='kalman') - # plt.plot(t, y5, 'k.', linewidth=2, label='kalman2') - plt.plot(t, tide, 'y-', linewidth=2, label='True tide') - plt.legend(frameon=False, fontsize=14) - plt.xlabel("Time [s]") - plt.ylabel("Amplitude") - - -def demo_savitzky_on_exponential(): - """ - Example - ------- - >>> demo_savitzky_on_exponential() - - >>> plt.close() - """ - t = np.linspace(-4, 4, 500) - y = np.exp(-t ** 2) + np.random.normal(0, 0.05, np.shape(t)) - n = 11 - ysg = SavitzkyGolay(n, degree=1, diff_order=0)(y) - plt.plot(t, y, t, ysg, '--') - - -def demo_smoothn_on_1d_cos(): - """ - Example - ------- - >>> demo_smoothn_on_1d_cos() - - >>> plt.close() - """ - x = np.linspace(0, 100, 2 ** 8) - y = np.cos(x / 10) + (x / 50) ** 2 + np.random.randn(np.size(x)) / 10 - y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6]) - z = smoothn(y) # Regular smoothing - zr = smoothn(y, robust=True) # Robust smoothing - _h0 = plt.subplot(121), - _h = plt.plot(x, y, 'r.', x, z, 'k', linewidth=2) - plt.title('Regular smoothing') - plt.subplot(122) - plt.plot(x, y, 'r.', x, zr, 'k', linewidth=2) - plt.title('Robust smoothing') - - -def demo_smoothn_on_2d_exp_sin(): - """ - Example - ------- - >>> demo_smoothn_on_2d_exp_sin() - - >>> plt.close() - """ - xp = np.arange(0, 1, 0.02) # np.r_[0:1:0.02] - [x, y] = np.meshgrid(xp, xp) - f = np.exp(x + y) + np.sin((x - 2 * y) * 3) - fn = f + np.random.randn(*f.shape) * 0.5 - _fs, s = smoothn(fn, fulloutput=True) - fs2 = smoothn(fn, s=2 * s) - _h = plt.subplot(131), - _h = plt.contourf(xp, xp, fn) - _h = plt.subplot(132), - _h = plt.contourf(xp, xp, fs2) - _h = plt.subplot(133), - _h = plt.contourf(xp, xp, f) - - -def _cardioid(n=1000): - t = np.linspace(0, 2 * np.pi, n) - x0 = 2 * np.cos(t) * (1 - np.cos(t)) - y0 = 2 * np.sin(t) * (1 - np.cos(t)) - x = x0 + np.random.randn(x0.size) * 0.1 - y = y0 + np.random.randn(y0.size) * 0.1 - return x, y, x0, y0 - - -def demo_smoothn_on_cardioid(): - """ - Example - ------- - >>> demo_smoothn_on_cardioid() - - >>> plt.close() - """ - x, y, x0, y0 = _cardioid() - z = smoothn(x + 1j * y, robust=False) - plt.plot(x0, y0, 'y', - x, y, 'r.', - np.real(z), np.imag(z), 'k', linewidth=2) - - -def demo_hodrick_on_cardioid(): - """ - Example - ------- - >>> demo_hodrick_on_cardioid() - - >>> plt.close() - """ - x, y, x0, y0 = _cardioid() - - smooth = HodrickPrescott(w=20000) - # smooth = HampelFilter(adaptive=50) - xs, ys = smooth(x), smooth(y) - plt.plot(x0, y0, 'y', - x, y, 'r.', - xs, ys, 'k', linewidth=2) - - -if __name__ == '__main__': - from wafo.testing import test_docstrings - test_docstrings(__file__) - # demo_savitzky_on_noisy_chirp() - # plt.show('hold') # show plot - # demo_kalman_sine() - # demo_tide_filter() - # demo_hampel() - # demo_kalman_voltimeter() - # demo_savitzky_on_exponential() -# plt.figure(1) -# demo_hodrick_on_cardioid() -# plt.figure(2) -# # demo_smoothn_on_1d_cos() -# demo_smoothn_on_cardioid() -# plt.show('hold') diff --git a/wafo/sg_filter/tests/__init__.py b/wafo/sg_filter/tests/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/wafo/sg_filter/tests/conftest.py b/wafo/sg_filter/tests/conftest.py deleted file mode 100644 index b267c86..0000000 --- a/wafo/sg_filter/tests/conftest.py +++ /dev/null @@ -1,11 +0,0 @@ -#!/usr/bin/env python -# -*- coding: utf-8 -*- -""" - Dummy conftest.py for wafo. - - If you don't know what this is for, just leave it empty. - Read more about conftest.py under: - https://pytest.org/latest/plugins.html -""" -from __future__ import print_function, absolute_import, division -import pytest # @UnusedImport diff --git a/wafo/sg_filter/tests/test_sg_filter.py b/wafo/sg_filter/tests/test_sg_filter.py deleted file mode 100644 index 3aa9797..0000000 --- a/wafo/sg_filter/tests/test_sg_filter.py +++ /dev/null @@ -1,80 +0,0 @@ -import unittest -import numpy as np -from wafo.sg_filter._core import HampelFilter, SavitzkyGolay, Kalman -from numpy.ma.testutils import assert_array_almost_equal - - -class Test(unittest.TestCase): - def test_kalman(self): - # V0 = 12 - h = np.atleast_2d(1) # voltimeter measure the voltage itself - q = 1e-9 # variance of process noise as the car operates - r = 0.05 ** 2 # variance of measurement error - b = 0 # no system input - u = 0 # no system input - filt = Kalman(R=r, A=1, Q=q, H=h, B=b) - - # Generate random voltages and watch the filter operate. - n = 50 - - # truth = np.random.randn(n) * np.sqrt(q) + V0 - truth = [12.0000146639, 12.0000065349, 12.0000032619, 11.9999884321, 11.9999738705, 11.9999717554, 12.000012208, 12.0000269596, 12.0000235391, 12.0000420788, 11.9999763588, 12.0000272251, 11.9999278487, 11.9999775611, 12.0000280208, 11.9999788802, 11.9999531533, 11.9999963402, 11.9999318055, 11.9999537065, 12.0000011098, 11.9999750291, 12.000012755, 11.9999355349, 11.9999960117, 12.0000033276, 12.0000100317, 11.9999962376, 12.0000527124, 12.000019087, 12.0000273276, 11.9999461331, 12.0000527385, 11.9999990413, 11.9999850764, 12.0000031025, 11.9999868222, 11.9999830042, 11.9999881952, 12.0000064122, 12.0000343455, 11.9999779108, 12.0000134648, 12.0000329604, 12.0000536949, 11.999990415, 11.9999935299, 11.9999850717, 12.0000048284, 12.000060395] # nopep8 - # print(', '.join(['{0}'.format(y) for y in truth])) - # noise = np.random.randn(n) * np.sqrt(r) - noise = [0.0621366489443, 0.0247330994998, 0.109271521369, -0.0567657373852, -0.0315244553453, -0.0025701462034, 0.00181288937042, 0.109022849782, 0.0241169949603, -0.0543790728855, 0.0380117839575, 0.0582078684346, -0.0734606815139, -0.0665977120387, 0.0270631615171, 0.0369150024436, 0.0788445252483, 0.0111006834355, 0.0169567513801, 0.057081645789, -0.0293106512335, 0.0120282068494, 0.0211769283138, -0.0703228625119, -0.0222740803259, 0.0636500853308, 0.0302268639638, 0.0823316446844, 0.0504871636818, -0.0295402185417, 0.0780534199429, -0.0275453184976, -0.0613567940452, -0.0416930336494, -0.0972202720552, 0.0367572628693, 0.0150242119742, -0.0269063072041, 0.0654834111234, 0.0281867030757, -0.0978716452136, -0.0209143055692, -0.0236015624104, 0.0215804707908, -0.0525669442916, -0.00999304544556, -0.120029281573, -0.0255283929591, -0.00426938028504, -0.0487170747831] # nopep8 - # print('noise') - # print(', '.join(['{0}'.format(y) for y in noise])) - z = np.array(truth) + np.array(noise) # measurement - x = np.zeros(n) - - for i, zi in enumerate(z): - x[i] = filt(zi, u) # perform a Kalman filter iteration - - # print(', '.join(['{0}'.format(y) for y in x])) - assert_array_almost_equal(x, [12.0621513128, 12.0434454699, 12.065388589, 12.0348470726, 12.0215675093, 12.0175398445, 12.0152948689, 12.0270143185, 12.0266950063, 12.0185917138, 12.0203550503, 12.0235117738, 12.0160466547, 12.0101417447, 12.0112717378, 12.0128731715, 12.0167512202, 12.0164370857, 12.0164608484, 12.0184896738, 12.0162133963, 12.0160220138, 12.0162467099, 12.0126366982, 12.0112399981, 12.01325607, 12.0138850472, 12.0163296762, 12.0175094638, 12.0159415984, 12.0179463317, 12.0165228489, 12.0141641309, 12.0125210028, 12.0093846209, 12.0101451843, 12.0102767167, 12.0092975878, 12.0107382282, 12.01117469, 12.0085152867, 12.0078138971, 12.0070834443, 12.0074137537, 12.0060816948, 12.0057319401, 12.0030552687, 12.0024592874, 12.0023220236, 12.0013021198]) # nopep8 - - def test_savitzky_golay(self): - t = np.linspace(-4, 4, 100) - # noise = np.random.normal(0, 0.05, t.shape) - noise = np.array([-0.0100738410948, 0.0434144660993, -0.00378151879776, 0.0113356386249, 0.00435077505515, -0.0477602072563, 0.0373494077292, -0.0133865881648, -0.058259106898, 0.0661995082581, -0.0302004598725, 0.0251073570423, 0.0504480752083, 0.00591197638959, -0.0936100824835, -0.0475801028574, 0.164260739963, 0.000309393717298, 0.0145265378376, 0.0451974209359, -0.0296464887607, 0.00113264461646, 0.0203243951278, 0.0250086489045, 0.0286663554031, 0.0162585459204, -0.0285237485127, 0.0841528003829, -0.0449728982279, 0.0549796633406, -0.0968901623365, 0.0306727572312, -0.06950957371, 0.00598396964893, 0.0583904237732, 0.0271856795988, 0.0503237614252, 0.179978222833, 0.0909965842309, -0.037723727536, 0.0766788834896, -0.135152061379, -0.0275445486266, 0.00437867535899, -0.0272885999582, -0.0167170993005, 0.0522077667657, -0.044618733434, -0.0323362657615, 0.0122726298648, 0.0311304227245, -0.106361849439, 0.0526578516171, 0.0600674983294, 0.0745276212563, -0.0488453979797, -0.000833273665862, 0.0232768529385, 0.0138869047145, -0.0581069396022, 0.0321001340163, -0.023975724861, -0.0281919023447, 0.0341550408589, -0.0128104984676, -0.0214928514613, -0.0930630211028, -0.086094936458, 0.0169055851217, -0.0106085935018, 0.0114499301052, 0.120823119533, 0.0401375561218, 0.0979979215035, -0.015930504967, 0.0730359376807, -0.0369380623571, 0.0628171477772, -0.0271592027456, -0.0805267873905, -0.047314352792, -0.00693573205681, -0.0276294819462, -0.00896110691771, 0.0248482543453, 0.0877066047642, -0.0325533337143, -0.0638923240986, 0.0512523528302, 0.0720952473332, 0.00555629231342, 0.0562912258368, 0.0518574742355, -0.0599288505845, 0.0129657160415, -0.0025435076237, -0.0136966498082, 0.0260013064028, 0.0315561663839, -0.0293194006299]) # nopep8 - # print(', '.join(['{0}'.format(y) for y in noise])) - y = np.exp(-t**2) + noise - ysg = SavitzkyGolay(n=20, degree=2).smooth(y) - # print(', '.join(['{0}'.format(y) for y in ysg])) - assert_array_almost_equal(ysg, [0.08136940307, 0.0628995512206, 0.0459066440291, 0.0303906814954, 0.0163516636196, 0.00378959040169, -0.00729553815838, -0.0169037220606, -0.0250349613049, -0.0316892558914, -0.03686660582, -0.0405670110908, -0.0427904717036, -0.0435369876586, -0.0428065589558, -0.0405991855951, -0.0369148675765, -0.0317536049001, -0.0251153975657, -0.0170002455736, -0.00740814892354, 0.00138883298422, 0.00903982318392, 0.0156981288342, 0.0262571138525, 0.038712235996, 0.0497401536595, 0.0708145615737, 0.0930139468092, 0.115399487253, 0.145859174356, 0.181612636791, 0.217133614374, 0.257717904903, 0.300137304571, 0.345750694351, 0.392370647909, 0.447698806473, 0.498669071812, 0.552242388661, 0.602481962016, 0.649961345551, 0.695325299394, 0.735374047294, 0.773010811455, 0.805919165272, 0.834865852047, 0.854796400219, 0.86842923705, 0.871717227059, 0.870973756546, 0.854091989437, 0.838398655214, 0.810673923439, 0.783634317013, 0.749908334726, 0.714315301461, 0.67175727743, 0.634614314389, 0.593943523363, 0.54497174327, 0.497539947485, 0.442464744684, 0.39039262486, 0.339641566641, 0.287962531039, 0.243889096129, 0.20650960823, 0.165038163827, 0.127423305227, 0.098217909507, 0.0723906956301, 0.0457840790019, 0.0325691800506, 0.0207065223098, 0.0137400799931, 0.00547944733578, -0.000268557810876, -0.00301934919753, -0.00213643706217, -0.0101846106787, -0.0170002602175, -0.0225833856784, -0.0269339870616, -0.030052064367, -0.0319376175946, -0.0325906467444, -0.0320111518164, -0.0301991328106, -0.0271545897271, -0.0228775225657, -0.0173679313266, -0.0106258160097, -0.00265117661497, 0.00655598685753, 0.0169956744078, 0.0286678860359, 0.0415726217417, 0.0557098815254, 0.0710796653868]) # nopep8 - - def test_hampelfilter(self): - - y = np.array([4979, 5002, 5004, 5000, 4987, 4989, 5008, 5013, 5000, 4996, 5026, 5000, 5003, 4988, 4991, 5017, 5013, 5004, 4990, 4997, 5010, 5007, 5001, 4970, 5002, 4986, 5032, 5003, 4994, 5001, 4988, 4998, 5002, 4996, 4988, 5009, 5003, 4986, 4996, 4994, 4997, 5003, 5012, 5002, 5001, 5006, 5006, 4986, 4998, 4978, 4995, 4999, 4987, 5015, 5009, 5016, 4995, 5007, 5013, 4996, 5018, 4992, 4989, 4994, 4991, 4995, 5018, 5007, 5008, 4990, 5010, 4986, 5009, 4999, 5008, 5000, 5001, 5000, 5004, 5032, 5009, 5005, 5014, 5000, 4992, 4994, 4991, 4993, 5000, 5005, 4993, 5003, 4995, 4980, 4995, 4999, 5007, 5000, 4988, 4982, 5030, 4997, 4993, 5009, 4993, 5020, 5010, 4997, 4987, 4999, 5006, 4984, 5000, 4987, 4986, 5006, 5002, 5001, 5003, 4996, 4994, 5002, 4989, 4998, 4996, 5007, 4993, 4998, 5001, 4989, 5012, 5001, 5010, 4996, 5004, 5008, 5002, 5024, 4997, 5001, 5010, 5023, 4996, 5018, 5002, 4990, 5009, 4997, 5016, 5000, 5013, 5008, 4990, 5011, 4996, 5010, 5004, 5023, 4999, 5004, 4996, 5011, 4998, 5000, 4988, 5000, 4993, 4998, 5000, 5006, 5010, 4988, 5000, 4997, 4995, 4996, 5005, 5003, 5009, 5009, 4997, 5010, 5014, 4990, 5013, 5015, 5011, 4987, 5004, 4999, 5030, 5000, 5000, 4999, 5013, 5012, 5001, 5012, 4995, 4997, 4995, 4985, 4989, 5007, 5010, 4997, 5011, 4995, 5000, 5011, 4998, 4991, 5021, 5003, 4985, 4991, 4995, 5018, 4979, 5003, 5011, 5009, 5001, 4998, 5008, 4994, 5016, 4992, 5008, 4993, 4983, 5010, 5023, 4975, 4987, 4994, 5002, 4984, 5005, 5006, 5005, 5000, 4996, 5000, 4999, 5004, 4994, 5000, 4981, 5001, 4994, 4993, 5000, 5004, 5001, 4992, 5002, 5006, 4997, 4987, 5001, 5008, 5011, 4995, 5006, 4976, 4999, 4989, 5008, 4996, 4997, 5006, 5005, 5007, 4990, 5010, 4996, 4998, 5000, 5014, 5002, 5001, 4996, 4997, 5000, 5003, 5000, 4986, 5013, 5001, 4990, 4990, 5010, 5000, 5021, 5000, 5006, 4995, 5012, 5019, 5000, 5006, 4999, 5007, 5014, 5000, 4994, 4991, 5010, 4985, 4988, 5007, 5005, 5000, 5005, 4997, 4995, 4987, 5000, 5000, 5009, 5000, 4999, 5011, 5018, 4994, 5000, 4995, 5000, 5008, 4994, 4992, 5000, 4998, 4992, 5006, 4996, 5000, 5018, 5000, 5022, 5002, 5007, 5000, 5012, 5014, 5010, 4997, 4996, 5014, 4995, 4991, 5006, 4992, 5008, 5004, 4995, 5016, 4974, 5005, 5000, 4985, 5002, 5000, 5009, 4991, 4995, 5004, 4987, 5014, 4986, 5008, 4985, 4995, 5010, 5000, 5001, 5013, 4988, 5001, 5002, 4986, 4985, 5001, 4995, 5004, 4998, 4998, 4992, 5003, 5000, 4991, 4998, 5002, 5011, 4986, 5013, 4997, 5000, 4997, 5003, 5014, 4998, 5002, 5006, 5015, 4992, 4992, 4995, 4998, 4994, 5007, 4977, 5004, 5005, 4990, 4991, 5001, 5010, 4991, 4990, 5006, 5004, 5004, 4997, 5001, 4992, 5000, 5000, 4996, 4987, 4993, 5001, 5006, 4999, 4993, 4999, 5001, 5001, 5014, 4985, 5010, 5006, 4989, 5002, 5011, 4999, 5010, 5005, 5002, 5010, 4990, 4994, 5000, 4985, 5010, 5000, 4999, 5000, 4977, 5007, 5005, 4990, 5000, 4985, 5003, 5009, 5012, 5012, 5000, 5018, 4997, 5002, 4992, 4999, 4997, 5005, 5009, 4989, 5005, 4988, 5001, 5000, 5018, 4999, 5005, 4997, 5015, 5001, 4988, 4983, 5013, 4992, 5002, 5012, 4999, 5013, 5000, 4988, 4989, 4996, 5000, 5002, 4999, 5021, 4991, 5009, 5005, 4994, 5000, 4994, 4985, 4999, 4980, 5013, 5014, 5000, 4996, 5008, 5028, 5002, 5004, 4999, 5012, 4992, 5002, 4987, 5004, 5009, 5004, 5013, 4989, 5027, 4992, 5016, 5007, 5003, 5013, 5003, 4983, 5000, 4987, 5001, 4998, 4994, 4998, 4997, 5023, 4971, 5001, 4990, 5025, 5003, 4996, 5006, 5005, 4995, 4994, 5023, 5003, 5005, 4991, 5001, 5028, 4996, 5001, 5005, 5001, 5001, 5028, 4983, 5000, 5005, 5001, 4999, 5003, 4982, 5000, 5012, 5011, 5008, 5000, 4998, 4994, 4988, 5013, 4998, 5017, 4991, 5007, 5016, 5007, 4997, 4974, 4997, 5006, 5003, 5010, 5003, 4997, 4997, 4994, 4998, 4987, 5004, 4974, 5009, 5006, 5009, 4984, 5010, 5023, 5000, 5008, 4992, 5008, 4993, 5010, 5012, 4989, 5002, 4993, 5007, 4985, 4990, 4988, 4997, 5000, 4994, 5004, 4981, 5000, 4999, 5003, 4988, 5006, 5019, 5003, 4992, 4977, 4998, 4987, 4995, 4987, 5000, 4986, 4998, 4996, 5008, 5011, 5009, 5000, 4999, 5010, 4999, 5009, 5010, 4992, 4998, 4994, 5009, 4998, 5013, 5011, 4997, 5016, 4995, 5003, 4986, 5010, 4995, 4986, 5025, 4990, 5010, 4990, 4996, 5000, 5002, 4994, 5002, 5000, 5020, 4995, 5003, 5006, 5000, 4997, 4996, 5010, 4992, 5013, 4998, 4988, 4999, 5004, 5004, 5002, 5002, 5001, 4986, 5011, 5012, 4988, 5000, 5000, 5012, 5004, 5004, 4984, 5012, 4998, 5005, 5005, 5005, 4995, 4971, 5006, 5000, 5008, 5015, 4999, 4999, 4996, 5000, 4992, 5019, 5020, 4999, 4991, 5020, 5000, 5002, 5000, 5003, 4985, 4990, 5011, 5012, 4997, 4989, 4999, 5006, 4997, 4992, 4999, 4985, 4999, 5012, 5003, 4989, 5010, 5010, 5012, 4990, 4986, 5014, 5000, 4994, 5017, 4995, 5005, 5003, 5000, 5000, 4988, 5018, 5007, 5009, 5002, 5004, 4999, 5026, 4987, 4986, 5000, 4994, 5012, 5022, 4996, 5002, 4986, 4990, 4989, 5030, 4997, 5002, 5004, 4999, 5000, 4992, 4977, 4997, 4998, 5000, 4987, 5032, 4998, 5014, 4978, 5001, 4988, 5006, 5003, 5005, 5021, 5005, 5000, 5003, 4990, 4991, 4990, 5016, 5006, 4981, 5002, 4998, 4989, 4995, 5007, 5004, 5019, 5001, 5004, 5000, 4996, 4988, 5022, 5003, 5009, 4998, 5003, 4991, 5000, 4988, 5004, 5002, 4991, 4998, 4996, 4991, 5013, 5007, 5010, 5004, 5006, 5007, 4993, 5000, 5002, 4992, 4999, 4992, 5001, 4989, 4992, 5015, 5011, 5008, 5004, 4990, 4995, 4993, 5004, 4995, 4982, 5008, 5000, 4993, 5000, 5000, 4991, 5005, 5008, 5003, 4994, 4997, 5012, 4995, 5009, 5020, 5010, 5019, 4979, 5013, 4990, 5002, 5000, 5015, 4989, 5009, 4998, 5004, 5010, 4988, 4994, 5004, 4985, 4998, 4991, 4985, 4994, 4986, 5010, 4990, 5002, 5005, 5008, 5004, 4988, 4980, 5005, 4994, 5004, 4998, 4990, 5010, 5003, 5011, 4992, 5009, 5003, 5013, 4996, 4997, 4989, 4992, 5002, 4992, 4996, 4999, 5000, 5009, 4990, 4992, 5020, 4981, 5011, 5000, 5008, 4997, 4994, 4982, 5014, 5013, 4996, 5002, 5011, 5003, 5000, 5015, 4999, 5001, 5002, 5018, 4984, 5022, 5009, 5006, 5009, 5000, 4974, 4991, 5020, 5000, 4987, 5003, 4987, 5003, 5002, 5016, 4997, 5022, 5005, 4998, 4999, 5001, 5000, 5008, 5000, 5001, 4994, 4991, 4997, 4990, 4991, 4995, 5008, 5007, 4994, 5000, 5007, 4988, 5014, 5003, 4998, 4995, 5000, 5000, 5004], dtype=float) # nopep8 - # randint = np.random.randint - # y = 5000 + np.int_(10*np.random.randn(1000)) - # outliers = randint(0, 1000, size=(10,)) - outliers = np.array([470, 795, 399, 614, 864, 37, 815, 112, 69, 16]) - # noise = randint(1000, size=(10,)) - noise = np.array([932, 286, 736, 427, 858, 63, 243, 264, 668, 844]) - y[outliers] = y[outliers] + noise - yy, res = HampelFilter(fulloutput=True)(y) - yy1 = HampelFilter(dx=1, t=3, adaptive=0.1, fulloutput=False)(y) - yy2 = HampelFilter(dx=3, t=0, fulloutput=False)(y) - # print(', '.join(['{0:d}'.format(yj) for yj in y])) - # print(', '.join(['{0:d}'.format(int(yj)) for yj in yy2])) - - self.assert_(sum(res['outliers'] == True) == 76) - valid_names = set(('Y0', 'outliers', 'LB', 'ADX', 'UB')) - for name in res: - self.assert_(name in valid_names) - assert_array_almost_equal(yy[outliers], [5002, 5000, 5003, 5008, 5000, - 4997, 4998, 4999, 5009, 4997]) - - true_yy = [5001, 5002, 5004, 5000, 4987, 4989, 5008, 5013, 5000, 4996, 5000, 5000, 5003, 4988, 4991, 5017, 4997, 5004, 4990, 4997, 5010, 5007, 5001, 4970, 5002, 4986, 5032, 5003, 4994, 5001, 4988, 4998, 5002, 4996, 4988, 5009, 5003, 4997, 4996, 4994, 4997, 5003, 5012, 5002, 5001, 5006, 5006, 4986, 4998, 4978, 4995, 4999, 4987, 5015, 5009, 5016, 4995, 5007, 5013, 4996, 5018, 4992, 4989, 4994, 4991, 4995, 5018, 5007, 5008, 5009, 5010, 5008, 5009, 4999, 5000, 5000, 5001, 5000, 5004, 5005, 5009, 5005, 5014, 5000, 4992, 4994, 4991, 4993, 5000, 5005, 4993, 5003, 4995, 4980, 4995, 4999, 5007, 5000, 4988, 4982, 5030, 4997, 4993, 5009, 4993, 5020, 5010, 4997, 4987, 4999, 5006, 4984, 4999, 4987, 4986, 5006, 5002, 5001, 5003, 4996, 4994, 5002, 4989, 4998, 4996, 5007, 4993, 4998, 5001, 4989, 5012, 5001, 5010, 4996, 5004, 5008, 5002, 5004, 4997, 5001, 5010, 5023, 4996, 5018, 5002, 4990, 5009, 4997, 5016, 5000, 5013, 5008, 4990, 5011, 4996, 5010, 5004, 5023, 4999, 5004, 4996, 5011, 4998, 5000, 4998, 5000, 4993, 4998, 5000, 5006, 5010, 4988, 5000, 4997, 4995, 4996, 5005, 5003, 5009, 5009, 4997, 5010, 5014, 5011, 5013, 5015, 5011, 4987, 5004, 4999, 5000, 5000, 5000, 4999, 5001, 5012, 5001, 5012, 4995, 4997, 4995, 4985, 4989, 5007, 5010, 4997, 5011, 4995, 5000, 5011, 4998, 4991, 5021, 5003, 4985, 4991, 4995, 5018, 4979, 5003, 5011, 5009, 5001, 4998, 5008, 4994, 5016, 4992, 5008, 4993, 4983, 5010, 5023, 4975, 4987, 4994, 5002, 5002, 5005, 5006, 5005, 5000, 4996, 5000, 4999, 5004, 5000, 5000, 4981, 5001, 4994, 4993, 5000, 5004, 5001, 4992, 5002, 5006, 4997, 4987, 5001, 5008, 5011, 4995, 5006, 4976, 4999, 4989, 5008, 4996, 4997, 5006, 5005, 5007, 4990, 5010, 4996, 4998, 5000, 5000, 5002, 5001, 4996, 4997, 5000, 5003, 5000, 5000, 5013, 5001, 4990, 4990, 5010, 5000, 5021, 5000, 5006, 4995, 5012, 5019, 5000, 5006, 4999, 5007, 5014, 5000, 4994, 4991, 5010, 4985, 4988, 5007, 5005, 5000, 5005, 4997, 4995, 4987, 5000, 5000, 5000, 5000, 4999, 5011, 5018, 4994, 5000, 4995, 5000, 5008, 4994, 4992, 5000, 4998, 4992, 5006, 4996, 5000, 5018, 5000, 5002, 5002, 5007, 5000, 5012, 5014, 5010, 4997, 4996, 5014, 4995, 4991, 5006, 4992, 5008, 5004, 4995, 5016, 5000, 5005, 5000, 4985, 5002, 5000, 5009, 4991, 4995, 5004, 4987, 5014, 4986, 5008, 4985, 4995, 5010, 5000, 5001, 5001, 5001, 5001, 5002, 4986, 5001, 5001, 4995, 5004, 4998, 4998, 4992, 5003, 5000, 4991, 4998, 5002, 5011, 5000, 5013, 4997, 5000, 5003, 5003, 5014, 4998, 5002, 5006, 5015, 4992, 4992, 4995, 4998, 4994, 5007, 4977, 5004, 5005, 4990, 4991, 4991, 4991, 4991, 5004, 5006, 5004, 5004, 4997, 5001, 4992, 5000, 5000, 4996, 4987, 4993, 5001, 5006, 4999, 4993, 4999, 5001, 5001, 5014, 4985, 5010, 5006, 4989, 5002, 5011, 4999, 5010, 5005, 5002, 5010, 4990, 4994, 5000, 4985, 5000, 5000, 4999, 5000, 5000, 5007, 5005, 4990, 5000, 4985, 5003, 5009, 5012, 5012, 5000, 5002, 4997, 5002, 4992, 4999, 4997, 5005, 5009, 4989, 5005, 4988, 5001, 5000, 5000, 4999, 5005, 4997, 5015, 5001, 4988, 4983, 5013, 4992, 5002, 5012, 4999, 5013, 5000, 4988, 4989, 4996, 5000, 5002, 4999, 5002, 4991, 5009, 5005, 4994, 5000, 4994, 4985, 4999, 4980, 5013, 5014, 5000, 4996, 5008, 5002, 5002, 5004, 4999, 5012, 4992, 5002, 4987, 5004, 5009, 5004, 5013, 4989, 5027, 4992, 5016, 5007, 5003, 5013, 5003, 5001, 5000, 4987, 5001, 4998, 4994, 4998, 4997, 4997, 4971, 5001, 4990, 5001, 5003, 4996, 5006, 5005, 4995, 5005, 5023, 5003, 5005, 4991, 5001, 5001, 4996, 5001, 5005, 5001, 5001, 5001, 5001, 5000, 5005, 5001, 4999, 5003, 5001, 5000, 5012, 5011, 5008, 5000, 4998, 4994, 4988, 5013, 4998, 5017, 4991, 5007, 5016, 5007, 4997, 5003, 4997, 5006, 5003, 5010, 5003, 4997, 4997, 4994, 4998, 4987, 5004, 5004, 5009, 5006, 5009, 5009, 5010, 5023, 5000, 5008, 5008, 5008, 4993, 5010, 5012, 4989, 5002, 4993, 4990, 4985, 4990, 4988, 4997, 5000, 4994, 5004, 5000, 5000, 4999, 5003, 5003, 5006, 5019, 5003, 4992, 4977, 4998, 4987, 4995, 4987, 5000, 4986, 4998, 4996, 5008, 5011, 5009, 5000, 5009, 5010, 4999, 5009, 5010, 4992, 4998, 4994, 5009, 4998, 5013, 5011, 4997, 5016, 4995, 5003, 4986, 5010, 4995, 4986, 5025, 4990, 5010, 4990, 4996, 5000, 5002, 4994, 5002, 5000, 5002, 4995, 5003, 5006, 5000, 4997, 4996, 4998, 4992, 5013, 4998, 4988, 4999, 5004, 5004, 5002, 5002, 5001, 4986, 5011, 5012, 4988, 5000, 5000, 5012, 5004, 5004, 4984, 5004, 5005, 5005, 5005, 5005, 5005, 5005, 5006, 5000, 5008, 5015, 4999, 4999, 4996, 5000, 4992, 5019, 5020, 4999, 4991, 5000, 5000, 5002, 5000, 5003, 4985, 4990, 5011, 5012, 4997, 4989, 4999, 4997, 4997, 4992, 4999, 4985, 4999, 5012, 5003, 5010, 5010, 5010, 5012, 5010, 4986, 5014, 5000, 4994, 5017, 4995, 5005, 5003, 5000, 5000, 4988, 5018, 5007, 5009, 5002, 5004, 4999, 5000, 4987, 4986, 5000, 4994, 5012, 5022, 4996, 5002, 4986, 4990, 4989, 4997, 4997, 5002, 5004, 4999, 5000, 4992, 4998, 4997, 4998, 5000, 5000, 5032, 4998, 5014, 4978, 5001, 5003, 5006, 5003, 5005, 5005, 5005, 5000, 5003, 4990, 4991, 4990, 5016, 5006, 4981, 4998, 4998, 4989, 4995, 5007, 5004, 5004, 5001, 5004, 5000, 4996, 4988, 5000, 5003, 5009, 4998, 5003, 4991, 5000, 4988, 5004, 5002, 4991, 4998, 4996, 4991, 5013, 5007, 5010, 5004, 5006, 5007, 4993, 5000, 5002, 4992, 4999, 4992, 5001, 4989, 4992, 5015, 5011, 5008, 5004, 4990, 4995, 4993, 5004, 5000, 4982, 5008, 5000, 4993, 5000, 5000, 4991, 5005, 5008, 5003, 4994, 4997, 5012, 4995, 5009, 5020, 5010, 5019, 4979, 5013, 4990, 5002, 5000, 5015, 4989, 5009, 4998, 5004, 5010, 4988, 4994, 5004, 4985, 4998, 4991, 4985, 4994, 4986, 5010, 4990, 5002, 5005, 5008, 5004, 4988, 5004, 5005, 4994, 5004, 4998, 4990, 5010, 5003, 5011, 4992, 5009, 5003, 5013, 4996, 4997, 4989, 4992, 5002, 4992, 4996, 4999, 5000, 5009, 4990, 4992, 5020, 4981, 5011, 5000, 5008, 4997, 4994, 4982, 5014, 5013, 4996, 5002, 5011, 5003, 5000, 5002, 4999, 5001, 5002, 5018, 4984, 5022, 5009, 5006, 5009, 5000, 4974, 4991, 5020, 5000, 4987, 5003, 5002, 5003, 5002, 5016, 4997, 5002, 5005, 4998, 4999, 5001, 5000, 5000, 5000, 5001, 4994, 4991, 4997, 4990, 4991, 4995, 5008, 5007, 4994, 5000, 5007, 4988, 5014, 5003, 4998, 4995, 5000, 5000, 5004] # nopep8 - true_yy1 = [4999, 5002, 5004, 5000, 4987, 4989, 5008, 5013, 5000, 4996, 5026, 5000, 5003, 4988, 4991, 5017, 5003, 5004, 4990, 4997, 5010, 5007, 5001, 4970, 5002, 4986, 5032, 5003, 4994, 5001, 4988, 4998, 5002, 4996, 4988, 5009, 5003, 5001, 4996, 4994, 4997, 5003, 5012, 5002, 5001, 5006, 5006, 4986, 4998, 4978, 4995, 4999, 4987, 5015, 5009, 5016, 4995, 5007, 5013, 4996, 5018, 4992, 4989, 4994, 4991, 4995, 5018, 5007, 5008, 5006, 5010, 4986, 5009, 4999, 5008, 5000, 5001, 5000, 5004, 5004, 5009, 5005, 5014, 5000, 4992, 4994, 4991, 4993, 5000, 5005, 4993, 5003, 4995, 4980, 4995, 4999, 5007, 5000, 4988, 4982, 5030, 4997, 4993, 5009, 4993, 5020, 5010, 4997, 4987, 4999, 5006, 4984, 4998, 4987, 4986, 5006, 5002, 5001, 5003, 4996, 4994, 5002, 4989, 4998, 4996, 5007, 4993, 4998, 5001, 4989, 5012, 5001, 5010, 4996, 5004, 5008, 5002, 5024, 4997, 5001, 5010, 5023, 4996, 5018, 5002, 4990, 5009, 4997, 5016, 5000, 5013, 5008, 4990, 5011, 4996, 5010, 5004, 5023, 4999, 5004, 4996, 5011, 4998, 5000, 4988, 5000, 4993, 4998, 5000, 5006, 5010, 4988, 5000, 4997, 4995, 4996, 5005, 5003, 5009, 5009, 4997, 5010, 5014, 5009, 5013, 5015, 5011, 5005, 5004, 4999, 5002, 5000, 5000, 4999, 5013, 5012, 5001, 5012, 4995, 4997, 4995, 4985, 4989, 5007, 5010, 4997, 5011, 4995, 5000, 5011, 4998, 4991, 5021, 5003, 4985, 4991, 4995, 5018, 4979, 5003, 5011, 5009, 5001, 4998, 5008, 4994, 5016, 4992, 5008, 4993, 4983, 5010, 5023, 4975, 4987, 4994, 5002, 4984, 5005, 5006, 5005, 5000, 4996, 5000, 4999, 5004, 4994, 5000, 4981, 5001, 4994, 4993, 5000, 5004, 5001, 4992, 5002, 5006, 4997, 4987, 5001, 5008, 5011, 4995, 5006, 4976, 4999, 4989, 5008, 4996, 4997, 5006, 5005, 5007, 4990, 5010, 4996, 4998, 5000, 5000, 5002, 5001, 4996, 4997, 5000, 5003, 5000, 4986, 5013, 5001, 4990, 4990, 5010, 5000, 5021, 5000, 5006, 4995, 5012, 5019, 5000, 5006, 4999, 5007, 5014, 5000, 4994, 4991, 5010, 4985, 4988, 5007, 5005, 5000, 5005, 4997, 4995, 4999, 5000, 5000, 5009, 5000, 4999, 5011, 5018, 4994, 5000, 4995, 5000, 5008, 4994, 4992, 5000, 4998, 4992, 5006, 4996, 5000, 5018, 5000, 5022, 5002, 5007, 5000, 5012, 5014, 5010, 4997, 4996, 5014, 4995, 4991, 5006, 4992, 5008, 5004, 4995, 5016, 5000, 5005, 5000, 4985, 5002, 5000, 5009, 4991, 4995, 5004, 4987, 5014, 4986, 5008, 4985, 4995, 5010, 5000, 5001, 5013, 4988, 5001, 5002, 4986, 4985, 5001, 4995, 5004, 4998, 4998, 4992, 5003, 5000, 4991, 4998, 5002, 5011, 4986, 5013, 4997, 5000, 5002, 5003, 5014, 4998, 5002, 5006, 5015, 4992, 4992, 4995, 4998, 4994, 5007, 4977, 5004, 5005, 4990, 4991, 5001, 5010, 4991, 4990, 5006, 5004, 5004, 4997, 5001, 4992, 5000, 5000, 4996, 4987, 4993, 5001, 5006, 4999, 4993, 4999, 5001, 5001, 5014, 4985, 5010, 5006, 4989, 5002, 5011, 4999, 5010, 5005, 5002, 5010, 4990, 4994, 5000, 4985, 5010, 5000, 4999, 5000, 4977, 5007, 5005, 4990, 5000, 4985, 5003, 5009, 5012, 5012, 5000, 5003, 4997, 5002, 4992, 4999, 4997, 5005, 5009, 4989, 5005, 4988, 5001, 5000, 5000, 4999, 5005, 4997, 5015, 5001, 4988, 4983, 5013, 4992, 5002, 5012, 4999, 5013, 5000, 4988, 4989, 4996, 5000, 5002, 4999, 5021, 4991, 5009, 5005, 4994, 5000, 4994, 4985, 4999, 4980, 5013, 5014, 5000, 4996, 5008, 5028, 5002, 5004, 4999, 5012, 4992, 5002, 4987, 5004, 5009, 5004, 5013, 4989, 5027, 4992, 5016, 5007, 5003, 5013, 5003, 4999, 5000, 4987, 5001, 4998, 4994, 4998, 4997, 4998, 4998, 5001, 4990, 5025, 5003, 4996, 5006, 5005, 4995, 4994, 5023, 5003, 5005, 4991, 5001, 5001, 4996, 5001, 5005, 5001, 5001, 5000, 5000, 5000, 5005, 5001, 4999, 5003, 4982, 5000, 5012, 5011, 5008, 5000, 4998, 4994, 4988, 5013, 4998, 5017, 4991, 5007, 5016, 5007, 4997, 4974, 4997, 5006, 5003, 5010, 5003, 4997, 4997, 4994, 4998, 4987, 5004, 5001, 5009, 5006, 5009, 4984, 5010, 5023, 5000, 5008, 5007, 5008, 4993, 5010, 5012, 4989, 5002, 4993, 5007, 4985, 4990, 4988, 4997, 5000, 4994, 5004, 4981, 5000, 4999, 5003, 4988, 5006, 5019, 5003, 4992, 4977, 4998, 4987, 4995, 4987, 5000, 4986, 4998, 4996, 5008, 5011, 5009, 5000, 4999, 5010, 4999, 5009, 5010, 4992, 4998, 4994, 5009, 4998, 5013, 5011, 4997, 5016, 4995, 5003, 4986, 5010, 4995, 4986, 5025, 4990, 5010, 4990, 4996, 5000, 5002, 4994, 5002, 5000, 5001, 4995, 5003, 5006, 5000, 4997, 4996, 5010, 4992, 5013, 4998, 4988, 4999, 5004, 5004, 5002, 5002, 5001, 4986, 5011, 5012, 4988, 5000, 5000, 5012, 5004, 5004, 4984, 5012, 4998, 5005, 5005, 5005, 4995, 5004, 5006, 5000, 5008, 5015, 4999, 4999, 4996, 5000, 4992, 5019, 5020, 4999, 4991, 5020, 5000, 5002, 5000, 5003, 4985, 4990, 5011, 5012, 4997, 4989, 4999, 5006, 4997, 4992, 4999, 4985, 4999, 5012, 5003, 4989, 5010, 5010, 5012, 4990, 4986, 5014, 5000, 4994, 5017, 4995, 5005, 5003, 5000, 5000, 4988, 5018, 5007, 5009, 5002, 5004, 4999, 5026, 4987, 4986, 5000, 4994, 5012, 5022, 4996, 5002, 4986, 4990, 4989, 4997, 4997, 5002, 5004, 4999, 5000, 4992, 4999, 4997, 4998, 5000, 5002, 5032, 4998, 5014, 4978, 5001, 4988, 5006, 5003, 5005, 5002, 5005, 5000, 5003, 4990, 4991, 4990, 5016, 5006, 4981, 4999, 4998, 4989, 4995, 5007, 5004, 5019, 5001, 5004, 5000, 4996, 4988, 5001, 5003, 5009, 4998, 5003, 4991, 5000, 4988, 5004, 5002, 4991, 4998, 4996, 4991, 5013, 5007, 5010, 5004, 5006, 5007, 4993, 5000, 5002, 4992, 4999, 4992, 5001, 4989, 4992, 5015, 5011, 5008, 5004, 4990, 4995, 4993, 5004, 5000, 4982, 5008, 5000, 4993, 5000, 5000, 4991, 5005, 5008, 5003, 4994, 4997, 5012, 4995, 5009, 5020, 5010, 5019, 4979, 5013, 4990, 5002, 5000, 5015, 4989, 5009, 4998, 5004, 5010, 4988, 4994, 5004, 4985, 4998, 4991, 4985, 4994, 4986, 5010, 4990, 5002, 5005, 5008, 5004, 4988, 4980, 5005, 4994, 5004, 4998, 4990, 5010, 5003, 5011, 4992, 5009, 5003, 5013, 4996, 4997, 4989, 4992, 5002, 4992, 4996, 4999, 5000, 5009, 4990, 4992, 5020, 4981, 5011, 5000, 5008, 4997, 4994, 4982, 5014, 5013, 4996, 5002, 5011, 5003, 5000, 5015, 4999, 5001, 5002, 5018, 4984, 5022, 5009, 5006, 5009, 5000, 4974, 4991, 5020, 5000, 4987, 5003, 4987, 5003, 5002, 5016, 4997, 5022, 5005, 4998, 4999, 5001, 5000, 4999, 5000, 5001, 4994, 4991, 4997, 4990, 4991, 4995, 5008, 5007, 4994, 5000, 5007, 4988, 5014, 5003, 4998, 4995, 5000, 5000, 5004] # nopep8 - true_yy2 = [5001, 5000, 4994, 5000, 5002, 5000, 5000, 5000, 5000, 5003, 5000, 5000, 5000, 5003, 5003, 5003, 4997, 5004, 5007, 5004, 5001, 5001, 5001, 5002, 5002, 5001, 5001, 5001, 4998, 5001, 4998, 4996, 4998, 4998, 5002, 5002, 4996, 4997, 5003, 5003, 5002, 5001, 5002, 5003, 5003, 5002, 5001, 4998, 4998, 4995, 4995, 4998, 4999, 4999, 5007, 5009, 5009, 5009, 5007, 4996, 4996, 4994, 4994, 4994, 4994, 4995, 5007, 5008, 5008, 5009, 5008, 5008, 5008, 5001, 5000, 5001, 5001, 5004, 5004, 5005, 5005, 5005, 5005, 5000, 4994, 4994, 4994, 4993, 4994, 4995, 4995, 4995, 4995, 4995, 4999, 4995, 4995, 4999, 4999, 4997, 4997, 4993, 4997, 5009, 4997, 4997, 4999, 4999, 4999, 4999, 4997, 4987, 4999, 5002, 5001, 5002, 5001, 5001, 5002, 5001, 4998, 4996, 4996, 4996, 4998, 4998, 4998, 4998, 5001, 5001, 5001, 5001, 5004, 5004, 5004, 5004, 5002, 5004, 5008, 5002, 5010, 5002, 5002, 5009, 5002, 5002, 5002, 5002, 5008, 5008, 5008, 5008, 5008, 5008, 5008, 5004, 5004, 5004, 5004, 5004, 5000, 4999, 5000, 4998, 4998, 4998, 5000, 5000, 5000, 5000, 5000, 5000, 4997, 4997, 4997, 5000, 5003, 5003, 5005, 5009, 5009, 5009, 5010, 5011, 5011, 5011, 5004, 5011, 5004, 5000, 5000, 5000, 5000, 5001, 5001, 5001, 5001, 5001, 4997, 4995, 4995, 4995, 4997, 4997, 4997, 5000, 5007, 5000, 4998, 5000, 5000, 5000, 4998, 4995, 4995, 4995, 4995, 4995, 5003, 5003, 5003, 5003, 5003, 5008, 5001, 5001, 4998, 4994, 4994, 5008, 4993, 4993, 4993, 4994, 4994, 4994, 4994, 5002, 5002, 5002, 5000, 5000, 5000, 5000, 5000, 4999, 5000, 4999, 4994, 4994, 5000, 5000, 5000, 5000, 5001, 5001, 5001, 5001, 5001, 5002, 5001, 5001, 5001, 5001, 4999, 4999, 4996, 4997, 4997, 4999, 5005, 5005, 5005, 5005, 5005, 5000, 5000, 5000, 5001, 5000, 5000, 5000, 5001, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5001, 5000, 5000, 5000, 5006, 5006, 5006, 5006, 5006, 5006, 5007, 5006, 5000, 5000, 5000, 5000, 4994, 4994, 4994, 5000, 5005, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 4995, 5000, 4998, 4998, 4998, 4996, 4998, 5000, 5000, 5000, 5002, 5002, 5002, 5007, 5007, 5010, 5007, 5007, 5010, 5010, 4997, 4997, 4996, 4996, 5004, 4995, 5004, 5004, 5004, 5004, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 4995, 4995, 4995, 4995, 4995, 5000, 5000, 5001, 5000, 5001, 5001, 5001, 5001, 5001, 4995, 5001, 4998, 4998, 4998, 4998, 4998, 4998, 4998, 4998, 5000, 5000, 5000, 4998, 5000, 5002, 5003, 5003, 5003, 5002, 5003, 5006, 5003, 5002, 4998, 4998, 4995, 4995, 4994, 4995, 4998, 4998, 4994, 5001, 5001, 5001, 4991, 4991, 5001, 5004, 5004, 5001, 5001, 5001, 5000, 5000, 4997, 4996, 4996, 5000, 4999, 4996, 4999, 4999, 5001, 5001, 4999, 5001, 5001, 5001, 5002, 5006, 5002, 5006, 5005, 5002, 5005, 5005, 5002, 5002, 5000, 5000, 5000, 4999, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5003, 5003, 5003, 5003, 5009, 5009, 5009, 5002, 5000, 4999, 4999, 4999, 4999, 4999, 4999, 5001, 5001, 5001, 5000, 5001, 5000, 5001, 5001, 5001, 4999, 5001, 4997, 5001, 5001, 4999, 5002, 5002, 5000, 5000, 4999, 4999, 5000, 4999, 4999, 4999, 5000, 5002, 5002, 5000, 5000, 4994, 4999, 4994, 4994, 4999, 4999, 4999, 5000, 5008, 5008, 5004, 5002, 5004, 5004, 5002, 5002, 5002, 5002, 5004, 5004, 5004, 5004, 5004, 5009, 5007, 5007, 5007, 5007, 5003, 5003, 5003, 5001, 5000, 4998, 4998, 4998, 4998, 4998, 4998, 4997, 4998, 5001, 5001, 5001, 5003, 5003, 5003, 5003, 5003, 5005, 5003, 5001, 5003, 5003, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5001, 5000, 5000, 5001, 5001, 5003, 5003, 5000, 5000, 5000, 5000, 4998, 4998, 4998, 4998, 5007, 5007, 5007, 5007, 4997, 5006, 5003, 5003, 5003, 5003, 5003, 5003, 4998, 4997, 4997, 4997, 4997, 4998, 5004, 5004, 5006, 5009, 5009, 5008, 5009, 5008, 5008, 5008, 5008, 5008, 5008, 5002, 5002, 5002, 4993, 4990, 4993, 4993, 4994, 4994, 4994, 4997, 4999, 5000, 4999, 5000, 5000, 5003, 5003, 5003, 4998, 4998, 4995, 4992, 4992, 4987, 4995, 4995, 4996, 4998, 5000, 5000, 5000, 5008, 5008, 5009, 5009, 5000, 4999, 4999, 4999, 4998, 4998, 4998, 4998, 5009, 5009, 5003, 5003, 5003, 4997, 4995, 4995, 4995, 4995, 4995, 4995, 4996, 5000, 4996, 5000, 5000, 5000, 5000, 5002, 5002, 5002, 5000, 5000, 5000, 5000, 5000, 4998, 4997, 4998, 4999, 4999, 5002, 5002, 5002, 5002, 5002, 5002, 5002, 5001, 5000, 5000, 5004, 5004, 5000, 5004, 5004, 5004, 5004, 5005, 5005, 5005, 5005, 5005, 5005, 5005, 5000, 5000, 5000, 5000, 4999, 4999, 4999, 4999, 4999, 5000, 5000, 5002, 5000, 5000, 5000, 5000, 5000, 5002, 5000, 4997, 4997, 4999, 4999, 4997, 4997, 4997, 4999, 4999, 4999, 4999, 4999, 5003, 5010, 5010, 5003, 5010, 5010, 5000, 5000, 4995, 5000, 5003, 5000, 5000, 5000, 5000, 5003, 5003, 5002, 5004, 5004, 5007, 5004, 5002, 5000, 4999, 4999, 5000, 4996, 5000, 5000, 4996, 4996, 4996, 4996, 4997, 4997, 4999, 5000, 5000, 4999, 4999, 4998, 4998, 4998, 4998, 4998, 5000, 5000, 5001, 5001, 5001, 5001, 5003, 5003, 5005, 5005, 5005, 5003, 5003, 5000, 5000, 5000, 4991, 4991, 4998, 4998, 4998, 4998, 4998, 5004, 5001, 5004, 5004, 5004, 5001, 5001, 5001, 5003, 5000, 5003, 5003, 5003, 5000, 5000, 5000, 5000, 4998, 4998, 4996, 4998, 4998, 4998, 5004, 5006, 5007, 5007, 5006, 5004, 5002, 5000, 4999, 4999, 4999, 4992, 4992, 4999, 5001, 5004, 5004, 5004, 5004, 5004, 5004, 4995, 4995, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5003, 5003, 5003, 5003, 5009, 5010, 5010, 5010, 5010, 5010, 5002, 5002, 5000, 5002, 5000, 5002, 5004, 5004, 4998, 5004, 4998, 4998, 4994, 4991, 4994, 4991, 4991, 4991, 4991, 4994, 5002, 5004, 5004, 5002, 5004, 5004, 5004, 4998, 4994, 4998, 5003, 5003, 5003, 5003, 5003, 5009, 5003, 5003, 4997, 4997, 4997, 4996, 4996, 4996, 4996, 4999, 4999, 4996, 4999, 4999, 5000, 5000, 5000, 5000, 5000, 4997, 5000, 5000, 4997, 4997, 5002, 5003, 5003, 5003, 5002, 5002, 5002, 5002, 5001, 5002, 5002, 5006, 5009, 5009, 5006, 5006, 5006, 5000, 5000, 5000, 4991, 5000, 5002, 5002, 5002, 5003, 5003, 5003, 5002, 5001, 5000, 5001, 5000, 5000, 5000, 5000, 5000, 4997, 4994, 4994, 4994, 4995, 4995, 4995, 5000, 5000, 5007, 5003, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000] # nopep8 - - assert_array_almost_equal(np.int_(yy), true_yy) - assert_array_almost_equal(np.int_(yy1), true_yy1) - assert_array_almost_equal(np.int_(yy2), true_yy2) - - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.test_hampelfilter'] - unittest.main() diff --git a/wafo/source/c_library/build_all.py b/wafo/source/c_library/build_all.py deleted file mode 100644 index 49ee1eb..0000000 --- a/wafo/source/c_library/build_all.py +++ /dev/null @@ -1,25 +0,0 @@ -""" -f2py c_library.pyf c_functions.c -c - -See also http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW -""" -import os -import sys -from wafo.f2py_tools import f2py_call_str - -def compile_all(): - f2py_call = f2py_call_str() - print '=' * 75 - print 'compiling c_codes' - print '=' * 75 - - compile_format = f2py_call + ' %s %s -c' - - pyfs = ('c_library.pyf',) - files = ('c_functions.c',) - - for pyf, file_ in zip(pyfs, files): - os.system(compile_format % (pyf, file_)) - -if __name__ == '__main__': - compile_all() diff --git a/wafo/source/c_library/c_functions.c b/wafo/source/c_library/c_functions.c deleted file mode 100644 index 8f2c2a2..0000000 --- a/wafo/source/c_library/c_functions.c +++ /dev/null @@ -1,779 +0,0 @@ -#include "math.h" -/* -* Install gfortran and run the following to build the module on windows: - * f2py c_library.pyf c_functions.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - */ - -/* - * findrfc.c - - * - * Returns indices to RFC turningpoints of a vector - * of turningpoints - * - * 1998 by Per Andreas Brodtkorb. - */ - -void findrfc(double *y1,double hmin, int *ind, int n,int *info) { - double xminus, xplus, Tpl, Tmi, *y, Tstart; - int i, j, ix=0, NC, iy; - info[0] = 0; - if (*(y1+0)> *(y1+1)){ - /* if first is a max , ignore the first max*/ - y=&(*(y1+1)); - NC=floor((n-1)/2); - Tstart=1; - } - else { - y=y1; - NC=floor(n/2); - Tstart=0; - } - - if (NC<1){ - return; /* No RFC cycles*/ - } - - - if (( *(y+0) > *(y+1)) && ( *(y+1) > *(y+2)) ){ - info[0] = -1; - return; /*This is not a sequence of turningpoints, exit */ - } - if ((*(y+0) < *(y+1)) && (*(y+1)< *(y+2))){ - info[0]=-1; - return; /*This is not a sequence of turningpoints, exit */ - } - - - for (i=0; i=0) && (*(y+2*j+1)<=*(y+2*i+1))){ - if( (*(y+2*j)= xplus){ - if ( (*(y+2*i+1)-xminus) >= hmin){ - *(ind+ix)=Tmi; - ix++; - *(ind+ix)=(Tstart+2*i+1); - ix++; - } /*if*/ - goto L180; - } - - j=i+1; - while((j= *(y+2*i+1)) goto L170; - if( (*(y+2*j+2) <= xplus) ){ - xplus=*(y+2*j+2); - Tpl=(Tstart+2*j+2); - }/*if*/ - j++; - } /*while*/ - - - if ( (*(y+2*i+1)-xminus) >= hmin) { - *(ind+ix)=Tmi; - ix++; - *(ind+ix)=(Tstart+2*i+1); - ix++; - - } /*if*/ - goto L180; - L170: - if (xplus <= xminus ) { - if ( (*(y+2*i+1)-xminus) >= hmin){ - *(ind+ix)=Tmi; - ix++; - *(ind+ix)=(Tstart+2*i+1); - ix++; - } /*if*/ - /*goto L180;*/ - } - else{ - if ( (*(y+2*i+1)-xplus) >= hmin) { - *(ind+ix)=(Tstart+2*i+1); - ix++; - *(ind+ix)=Tpl; - ix++; - } /*if*/ - } /*elseif*/ - L180: - iy=i; - } /* for i */ - info[0] = ix; - return ; -} - - - -/* - * findcross.c - - * - * Returns indices to level v crossings of argument vector - * - * 1998 by Per Andreas Brodtkorb. last modified 23.06-98 - */ - - -void findcross(double *y, double v, int *ind, int n, int *info) -{ int i,start, ix=0,dcross=0; - start=0; - if ( y[0]< v){ - dcross=-1; /* first is a up-crossing*/ - } - else if ( y[0]> v){ - dcross=1; /* first is a down-crossing*/ - } - else if ( y[0]== v){ - /* Find out what type of crossing we have next time.. */ - for (i=1; i v){ - ind[ix] = i-1; /* first crossing is a up-crossing*/ - ix++; - dcross=1; /*The next crossing is a down-crossing*/ - goto L120; - } - } - } - L120: - for (i=start; i v) ) || ((dcross==1 ) && (y[i]>=v) && (y[i+1] < v) ) ) { - - ind[ix] = i; - ix++; - dcross=-dcross; - } - } - info[0] = ix; - return; -} - - -/* - * DISUFQ Is an internal function to spec2nlsdat - * - * CALL: disufq(rvec,ivec,rA,iA, w,kw,h,g,nmin,nmax,m,n) - * - * rvec, ivec = real and imaginary parts of the resultant (size m X n). - * rA, iA = real and imaginary parts of the amplitudes (size m X n). - * w = vector with angular frequencies (w>=0) - * kw = vector with wavenumbers (kw>=0) - * h = water depth (h >=0) - * g = constant acceleration of gravity - * nmin = minimum index where rA(:,nmin) and iA(:,nmin) is - * greater than zero. - * nmax = maximum index where rA(:,nmax) and iA(:,nmax) is - * greater than zero. - * m = size(rA,1),size(iA,1) - * n = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2) - * - * DISUFQ returns the summation of difference frequency and sum - * frequency effects in the vector vec = rvec +sqrt(-1)*ivec. - * The 2'nd order contribution to the Stokes wave is then calculated by - * a simple 1D Fourier transform, real(FFT(vec)). - * - * Install gfortran and run the following to build the module: - * f2py diffsumfunq.pyf disufq1.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - * - * by Per Andreas Brodtkorb 15.08.2001 - * revised pab 14.03.2002, 01.05.2002 22.07.2002, oct 2008 - */ - -void disufq(double *rvec, double *ivec, - double *rA, double *iA, - double *w, double *kw, - double h, double g, - int nmin, int nmax, - int m, int n) -{ - double Epij, Edij; - double tmp1, tmp2, tmp3, tmp4, kfact; - double w1, w2, kw1, kw2, Cg; - double rrA, iiA, riA, irA; - int i,jy,ix,iz1,iv1,ixi,jyi; - //int iz2, iv2; - //Initialize rvec and ivec to zero - for (ix=0;ix10000){ /* deep water /Inifinite water depth */ - for (ix = nmin-1;ix=0) - * kw = vector with wavenumbers (kw>=0) - * h = water depth (h >=0) - * g = constant acceleration of gravity - * nmin = minimum index where rA(:,nmin) and iA(:,nmin) is - * greater than zero. - * nmax = maximum index where rA(:,nmax) and iA(:,nmax) is - * greater than zero. - * m = size(rA,1),size(iA,1) - * n = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2) - * - * DISUFQ2 returns the summation of sum and difference frequency - * frequency effects in the vectors svec = rsvec +sqrt(-1)*isvec and - * dvec = rdvec +sqrt(-1)*idvec. - * The 2'nd order contribution to the Stokes wave is then calculated by - * a simple 1D Fourier transform, real(FFT(svec+dvec)). - * - * - * This is a MEX-file for MATLAB. - * by Per Andreas Brodtkorb 15.08.2001 - * revised pab 14.03.2002, 01.05.2002 - */ - -void disufq2(double *rsvec, double *isvec, - double *rdvec, double *idvec, - double *rA, double *iA, - double *w, double *kw, - double h, double g, - int nmin, int nmax, - int m, int n) -{ - double Epij, Edij; - double tmp1, tmp2, tmp3, tmp4, kfact; - double w1, w2, kw1, kw2, Cg; - double rrA, iiA, riA, irA; - int i,jy,ix,iz1,iv1,ixi,jyi; - //int iz2,iv2 - - //Initialize rvec and ivec to zero - for (ix=0;ix10000){ /* deep water /Inifinite water depth */ - for (ix = nmin-1;ix= 2) && (fabs(a[j-1]-a[j-2]) <= fabs(a[j]-a[j-1])) ) { - ampl=fabs( (a[j-1]-a[j-2])/2 ); - switch(j) { - case 0: { break; } - case 1: { break; } - case 2: { - mean=(a[0]+a[1])/2; - a[0]=a[1]; - a[1]=a[2]; - j=1; - if (ampl > 0) { - *po++=ampl; - *po++=mean; - *po++=0.50; - } - break; - } - default: { - mean=(a[j-1]+a[j-2])/2; - a[j-2]=a[j]; - j=j-2; - if (ampl > 0) { - *po++=ampl; - *po++=mean; - *po++=1.00; - cNr1++; - } - break; - } - } - } - } - cNr2 = 1; - for (index=0; index 0){ - *po++=ampl; - *po++=mean; - *po++=0.50; - cNr2++; - } - } - // array of ints nout is outputted - nout[0] = cNr1; - nout[1] = cNr2; -} -/* ++++++++++ END RF3 */ - - -// ++ BEGIN RF5 [ampl ampl_mean nr_of_cycle cycle_begin_time cycle_period_time] -/* ++++++++++ Rain flow with time analysis */ -//By Adam Nieslony -//Visit the MATLAB Central File Exchange for latest version -//http://www.mathworks.com/matlabcentral/fileexchange/3026 -void -findrfc5_astm(double *array_ext, double *array_t, double *array_out, int n, int *nout) { - double *pr, *pt, *po, a[16384], t[16384], ampl, mean, period, atime; - int tot_num, index, j, cNr1, cNr2; - - -// tot_num = mxGetM(array_ext) * mxGetN(array_ext); - tot_num = n; - - // pointers to the first element of the arrays - pr = &array_ext[0]; - pt = &array_t[0]; - po = &array_out[0]; - -// array_out = mxCreateDoubleMatrix(5, tot_num-1, mxREAL); - - // The original rainflow counting by Nieslony, unchanged - j = -1; - cNr1 = 1; - for (index=0; index= 2) && (fabs(a[j-1]-a[j-2]) <= fabs(a[j]-a[j-1])) ) { - ampl=fabs( (a[j-1]-a[j-2])/2 ); - switch(j) -{ - case 0: { break; } - case 1: { break; } - case 2: { - mean=(a[0]+a[1])/2; - period=(t[1]-t[0])*2; - atime=t[0]; - a[0]=a[1]; - a[1]=a[2]; - t[0]=t[1]; - t[1]=t[2]; - j=1; - if (ampl > 0) { - *po++=ampl; - *po++=mean; - *po++=0.50; - *po++=atime; - *po++=period; - } - break; - } - default: { - mean=(a[j-1]+a[j-2])/2; - period=(t[j-1]-t[j-2])*2; - atime=t[j-2]; - a[j-2]=a[j]; - t[j-2]=t[j]; - j=j-2; - if (ampl > 0) { - *po++=ampl; - *po++=mean; - *po++=1.00; - *po++=atime; - *po++=period; - cNr1++; - } - break; - } - } - } - } - cNr2 = 1; - for (index=0; index 0){ - *po++=ampl; - *po++=mean; - *po++=0.50; - *po++=atime; - *po++=period; - cNr2++; - } - } -// /* free the memeory !!!*/ -// mxSetN(array_out, tot_num - cNr); - nout[0] = cNr1; - nout[1] = cNr2; -} -/* ++++++++++ END RF5 */ diff --git a/wafo/source/c_library/c_library rf3 rf5 license.txt b/wafo/source/c_library/c_library rf3 rf5 license.txt deleted file mode 100644 index 420c520..0000000 --- a/wafo/source/c_library/c_library rf3 rf5 license.txt +++ /dev/null @@ -1,24 +0,0 @@ -Copyright (c) 2003, Adam Niesłony -All rights reserved. - -Redistribution and use in source and binary forms, with or without -modification, are permitted provided that the following conditions are -met: - - * Redistributions of source code must retain the above copyright - notice, this list of conditions and the following disclaimer. - * Redistributions in binary form must reproduce the above copyright - notice, this list of conditions and the following disclaimer in - the documentation and/or other materials provided with the distribution - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" -AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE -LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR -CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF -SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS -INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN -CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) -ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -POSSIBILITY OF SUCH DAMAGE. diff --git a/wafo/source/c_library/c_library.pyf b/wafo/source/c_library/c_library.pyf deleted file mode 100644 index 5e58404..0000000 --- a/wafo/source/c_library/c_library.pyf +++ /dev/null @@ -1,86 +0,0 @@ -! File c_code.pyf -python module c_library -interface - subroutine findrfc(y1, hmin, ind, n, info) - intent(c) findrfc ! findrfc is a C function - intent(c) ! all findrfc arguments are considered as C based - integer intent(hide), depend(y1) :: n=len(y1) - double precision dimension(n), intent(in) :: y1 ! input array - double precision intent(in) :: hmin - integer dimension(n), intent(out) :: ind ! output array, - integer dimension(1), intent(out) :: info - end subroutine findrfc - subroutine findcross(y, v, ind, n, info) - intent(c) findcross ! findcross is a C function - intent(c) ! all findcross arguments are considered as C based - integer intent(hide), depend(y) :: n=len(y) - double precision dimension(n), intent(in) :: y ! input array - double precision intent(in) :: v - integer dimension(n), intent(out) :: ind ! output array, - integer dimension(1),intent(out) :: info - end subroutine findcross - subroutine disufq(rvec, ivec, rA, iA, w, kw, h, g,nmin,nmax, m, n) - intent(c) disufq ! disufq is a C function - intent(c) ! all disufq arguments are considered as C based - !integer intent(hide), depend(rA),check(n*m==len(iA)) :: n=len(rA)/m - !integer intent(hide), depend(rA), check(m==shape(iA,1)) :: m=shape(rA,1) - double precision dimension(n*m), intent(in) :: rA, iA ! input array - double precision dimension(n/2+1), intent(in) :: w, kw ! input array - double precision intent(in) :: h, g - integer intent(in) :: nmin, nmax - double precision dimension(n*m), intent(out) :: rvec, ivec ! output array, - end subroutine disufq - subroutine disufq2(rsvec, isvec,rdvec, idvec, rA, iA, w, kw, h, g,nmin,nmax, m, n) - intent(c) disufq2 ! disufq2 is a C function - intent(c) ! all disufq2 arguments are considered as C based - !integer intent(hide), depend(rA),check(n*m==len(iA)) :: n=len(rA)/m - !integer intent(hide), depend(rA), check(m==shape(iA,1)) :: m=shape(rA,1) - double precision dimension(n*m), intent(in) :: rA, iA ! input array - double precision dimension(n/2+1), intent(in) :: w, kw ! input array - double precision intent(in) :: h, g - integer intent(in) :: nmin, nmax - double precision dimension(n*m), intent(out) :: rsvec, isvec, rdvec, idvec ! output array, - end subroutine disufq2 - - ! ===== START NIESLONY RAINFLOW FUNCTIONS - ! RAINFLOW Revision: 1.1 - ! by Adam Nieslony, 2009 - subroutine findrfc3_astm(array_ext, array_out, n, nout) - intent(c) findrfc3_astm ! rf3 is a C function - intent(c) ! all rf3 arguments are - ! considered as C based - - ! n is the length of the input array array_ext - integer intent(hide), depend(array_ext) :: n=len(array_ext) - - ! of input array x - double precision intent(in) :: array_ext(n) - - ! the output array - double precision intent(out) :: array_out(n,3) - - ! nout array, to output additional ints - integer dimension(2), intent(out) :: nout - end subroutine findrfc3_astm - - subroutine findrfc5_astm(array_ext, array_t, array_out, n, nout) - intent(c) findrfc5_astm ! rf5 is a C function - intent(c) ! all rf5 arguments are - ! considered as C based - - ! n is the length of the input array array_ext - integer intent(hide), depend(array_ext) :: n=len(array_ext) - - ! of input array x - double precision intent(in) :: array_ext(n), array_t(n) - - ! the output array - double precision intent(out) :: array_out(n,5) - - ! nout array, to output additional ints - integer dimension(2), intent(out) :: nout - end subroutine findrfc5_astm - ! ===== END NIESLONY RAINFLOW FUNCTIONS - -end interface -end python module c_library \ No newline at end of file diff --git a/wafo/source/c_library/c_librarymodule.c b/wafo/source/c_library/c_librarymodule.c deleted file mode 100644 index efacace..0000000 --- a/wafo/source/c_library/c_librarymodule.c +++ /dev/null @@ -1,1359 +0,0 @@ -/* File: c_librarymodule.c - * This file is auto-generated with f2py (version:2). - * f2py is a Fortran to Python Interface Generator (FPIG), Second Edition, - * written by Pearu Peterson . - * See http://cens.ioc.ee/projects/f2py2e/ - * Generation date: Thu Jan 29 22:06:57 2015 - * $Revision:$ - * $Date:$ - * Do not edit this file directly unless you know what you are doing!!! - */ -#ifdef __cplusplus -extern "C" { -#endif - -/*********************** See f2py2e/cfuncs.py: includes ***********************/ -#include "Python.h" -#include -#include "fortranobject.h" -#include - -/**************** See f2py2e/rules.py: mod_rules['modulebody'] ****************/ -static PyObject *c_library_error; -static PyObject *c_library_module; - -/*********************** See f2py2e/cfuncs.py: typedefs ***********************/ -/*need_typedefs*/ - -/****************** See f2py2e/cfuncs.py: typedefs_generated ******************/ -/*need_typedefs_generated*/ - -/********************** See f2py2e/cfuncs.py: cppmacros **********************/ -#define rank(var) var ## _Rank -#define shape(var,dim) var ## _Dims[dim] -#define old_rank(var) (((PyArrayObject *)(capi_ ## var ## _tmp))->nd) -#define old_shape(var,dim) (((PyArrayObject *)(capi_ ## var ## _tmp))->dimensions[dim]) -#define fshape(var,dim) shape(var,rank(var)-dim-1) -#define len(var) shape(var,0) -#define flen(var) fshape(var,0) -#define old_size(var) PyArray_SIZE((PyArrayObject *)(capi_ ## var ## _tmp)) -/* #define index(i) capi_i ## i */ -#define slen(var) capi_ ## var ## _len -#define size(var, ...) f2py_size((PyArrayObject *)(capi_ ## var ## _tmp), ## __VA_ARGS__, -1) - -#ifdef DEBUGCFUNCS -#define CFUNCSMESS(mess) fprintf(stderr,"debug-capi:"mess); -#define CFUNCSMESSPY(mess,obj) CFUNCSMESS(mess) \ - PyObject_Print((PyObject *)obj,stderr,Py_PRINT_RAW);\ - fprintf(stderr,"\n"); -#else -#define CFUNCSMESS(mess) -#define CFUNCSMESSPY(mess,obj) -#endif - -#ifndef max -#define max(a,b) ((a > b) ? (a) : (b)) -#endif -#ifndef min -#define min(a,b) ((a < b) ? (a) : (b)) -#endif -#ifndef MAX -#define MAX(a,b) ((a > b) ? (a) : (b)) -#endif -#ifndef MIN -#define MIN(a,b) ((a < b) ? (a) : (b)) -#endif - -#define CHECKSCALAR(check,tcheck,name,show,var)\ - if (!(check)) {\ - char errstring[256];\ - sprintf(errstring, "%s: "show, "("tcheck") failed for "name, var);\ - PyErr_SetString(c_library_error,errstring);\ - /*goto capi_fail;*/\ - } else -#if defined(PREPEND_FORTRAN) -#if defined(NO_APPEND_FORTRAN) -#if defined(UPPERCASE_FORTRAN) -#define F_FUNC(f,F) _##F -#else -#define F_FUNC(f,F) _##f -#endif -#else -#if defined(UPPERCASE_FORTRAN) -#define F_FUNC(f,F) _##F##_ -#else -#define F_FUNC(f,F) _##f##_ -#endif -#endif -#else -#if defined(NO_APPEND_FORTRAN) -#if defined(UPPERCASE_FORTRAN) -#define F_FUNC(f,F) F -#else -#define F_FUNC(f,F) f -#endif -#else -#if defined(UPPERCASE_FORTRAN) -#define F_FUNC(f,F) F##_ -#else -#define F_FUNC(f,F) f##_ -#endif -#endif -#endif -#if defined(UNDERSCORE_G77) -#define F_FUNC_US(f,F) F_FUNC(f##_,F##_) -#else -#define F_FUNC_US(f,F) F_FUNC(f,F) -#endif - - -/************************ See f2py2e/cfuncs.py: cfuncs ************************/ -static int f2py_size(PyArrayObject* var, ...) -{ - npy_int sz = 0; - npy_int dim; - npy_int rank; - va_list argp; - va_start(argp, var); - dim = va_arg(argp, npy_int); - if (dim==-1) - { - sz = PyArray_SIZE(var); - } - else - { - rank = PyArray_NDIM(var); - if (dim>=1 && dim<=rank) - sz = PyArray_DIM(var, dim-1); - else - fprintf(stderr, "f2py_size: 2nd argument value=%d fails to satisfy 1<=value<=%d. Result will be 0.\n", dim, rank); - } - va_end(argp); - return sz; -} - -static int double_from_pyobj(double* v,PyObject *obj,const char *errmess) { - PyObject* tmp = NULL; - if (PyFloat_Check(obj)) { -#ifdef __sgi - *v = PyFloat_AsDouble(obj); -#else - *v = PyFloat_AS_DOUBLE(obj); -#endif - return 1; - } - tmp = PyNumber_Float(obj); - if (tmp) { -#ifdef __sgi - *v = PyFloat_AsDouble(tmp); -#else - *v = PyFloat_AS_DOUBLE(tmp); -#endif - Py_DECREF(tmp); - return 1; - } - if (PyComplex_Check(obj)) - tmp = PyObject_GetAttrString(obj,"real"); - else if (PyString_Check(obj) || PyUnicode_Check(obj)) - /*pass*/; - else if (PySequence_Check(obj)) - tmp = PySequence_GetItem(obj,0); - if (tmp) { - PyErr_Clear(); - if (double_from_pyobj(v,tmp,errmess)) {Py_DECREF(tmp); return 1;} - Py_DECREF(tmp); - } - { - PyObject* err = PyErr_Occurred(); - if (err==NULL) err = c_library_error; - PyErr_SetString(err,errmess); - } - return 0; -} - -static int int_from_pyobj(int* v,PyObject *obj,const char *errmess) { - PyObject* tmp = NULL; - if (PyInt_Check(obj)) { - *v = (int)PyInt_AS_LONG(obj); - return 1; - } - tmp = PyNumber_Int(obj); - if (tmp) { - *v = PyInt_AS_LONG(tmp); - Py_DECREF(tmp); - return 1; - } - if (PyComplex_Check(obj)) - tmp = PyObject_GetAttrString(obj,"real"); - else if (PyString_Check(obj) || PyUnicode_Check(obj)) - /*pass*/; - else if (PySequence_Check(obj)) - tmp = PySequence_GetItem(obj,0); - if (tmp) { - PyErr_Clear(); - if (int_from_pyobj(v,tmp,errmess)) {Py_DECREF(tmp); return 1;} - Py_DECREF(tmp); - } - { - PyObject* err = PyErr_Occurred(); - if (err==NULL) err = c_library_error; - PyErr_SetString(err,errmess); - } - return 0; -} - - -/********************* See f2py2e/cfuncs.py: userincludes *********************/ -/*need_userincludes*/ - -/********************* See f2py2e/capi_rules.py: usercode *********************/ - - -/* See f2py2e/rules.py */ -extern void findrfc(double*,double,int*,int,int*); -extern void findcross(double*,double,int*,int,int*); -extern void disufq(double*,double*,double*,double*,double*,double*,double,double,int,int,int,int); -extern void disufq2(double*,double*,double*,double*,double*,double*,double*,double*,double,double,int,int,int,int); -extern void findrfc3_astm(double*,double*,int,int*); -extern void findrfc5_astm(double*,double*,double*,int,int*); -/*eof externroutines*/ - -/******************** See f2py2e/capi_rules.py: usercode1 ********************/ - - -/******************* See f2py2e/cb_rules.py: buildcallback *******************/ -/*need_callbacks*/ - -/*********************** See f2py2e/rules.py: buildapi ***********************/ - -/********************************** findrfc **********************************/ -static char doc_f2py_rout_c_library_findrfc[] = "\ -ind,info = findrfc(y1,hmin)\n\nWrapper for ``findrfc``.\ -\n\nParameters\n----------\n" -"y1 : input rank-1 array('d') with bounds (n)\n" -"hmin : input float\n" -"\nReturns\n-------\n" -"ind : rank-1 array('i') with bounds (n)\n" -"info : rank-1 array('i') with bounds (1)"; -/* extern void findrfc(double*,double,int*,int,int*); */ -static PyObject *f2py_rout_c_library_findrfc(const PyObject *capi_self, - PyObject *capi_args, - PyObject *capi_keywds, - void (*f2py_func)(double*,double,int*,int,int*)) { - PyObject * volatile capi_buildvalue = NULL; - volatile int f2py_success = 1; -/*decl*/ - - double *y1 = NULL; - npy_intp y1_Dims[1] = {-1}; - const int y1_Rank = 1; - PyArrayObject *capi_y1_tmp = NULL; - int capi_y1_intent = 0; - PyObject *y1_capi = Py_None; - double hmin = 0; - PyObject *hmin_capi = Py_None; - int *ind = NULL; - npy_intp ind_Dims[1] = {-1}; - const int ind_Rank = 1; - PyArrayObject *capi_ind_tmp = NULL; - int capi_ind_intent = 0; - int n = 0; - int *info = NULL; - npy_intp info_Dims[1] = {-1}; - const int info_Rank = 1; - PyArrayObject *capi_info_tmp = NULL; - int capi_info_intent = 0; - static char *capi_kwlist[] = {"y1","hmin",NULL}; - -/*routdebugenter*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_clock(); -#endif - if (!PyArg_ParseTupleAndKeywords(capi_args,capi_keywds,\ - "OO:c_library.findrfc",\ - capi_kwlist,&y1_capi,&hmin_capi)) - return NULL; -/*frompyobj*/ - /* Processing variable info */ - info_Dims[0]=1; - capi_info_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_info_tmp = array_from_pyobj(NPY_INT,info_Dims,info_Rank,capi_info_intent,Py_None); - if (capi_info_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `info' of c_library.findrfc to C/Fortran array" ); - } else { - info = (int *)(capi_info_tmp->data); - - /* Processing variable y1 */ - ; - capi_y1_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_y1_tmp = array_from_pyobj(NPY_DOUBLE,y1_Dims,y1_Rank,capi_y1_intent,y1_capi); - if (capi_y1_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 1st argument `y1' of c_library.findrfc to C/Fortran array" ); - } else { - y1 = (double *)(capi_y1_tmp->data); - - /* Processing variable hmin */ - f2py_success = double_from_pyobj(&hmin,hmin_capi,"c_library.findrfc() 2nd argument (hmin) can't be converted to double"); - if (f2py_success) { - /* Processing variable n */ - n = len(y1); - /* Processing variable ind */ - ind_Dims[0]=n; - capi_ind_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_ind_tmp = array_from_pyobj(NPY_INT,ind_Dims,ind_Rank,capi_ind_intent,Py_None); - if (capi_ind_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `ind' of c_library.findrfc to C/Fortran array" ); - } else { - ind = (int *)(capi_ind_tmp->data); - -/*end of frompyobj*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_call_clock(); -#endif -/*callfortranroutine*/ - (*f2py_func)(y1,hmin,ind,n,info); -if (PyErr_Occurred()) - f2py_success = 0; -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_call_clock(); -#endif -/*end of callfortranroutine*/ - if (f2py_success) { -/*pyobjfrom*/ -/*end of pyobjfrom*/ - CFUNCSMESS("Building return value.\n"); - capi_buildvalue = Py_BuildValue("NN",capi_ind_tmp,capi_info_tmp); -/*closepyobjfrom*/ -/*end of closepyobjfrom*/ - } /*if (f2py_success) after callfortranroutine*/ -/*cleanupfrompyobj*/ - } /*if (capi_ind_tmp == NULL) ... else of ind*/ - /* End of cleaning variable ind */ - /* End of cleaning variable n */ - } /*if (f2py_success) of hmin*/ - /* End of cleaning variable hmin */ - if((PyObject *)capi_y1_tmp!=y1_capi) { - Py_XDECREF(capi_y1_tmp); } - } /*if (capi_y1_tmp == NULL) ... else of y1*/ - /* End of cleaning variable y1 */ - } /*if (capi_info_tmp == NULL) ... else of info*/ - /* End of cleaning variable info */ -/*end of cleanupfrompyobj*/ - if (capi_buildvalue == NULL) { -/*routdebugfailure*/ - } else { -/*routdebugleave*/ - } - CFUNCSMESS("Freeing memory.\n"); -/*freemem*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_clock(); -#endif - return capi_buildvalue; -} -/******************************* end of findrfc *******************************/ - -/********************************* findcross *********************************/ -static char doc_f2py_rout_c_library_findcross[] = "\ -ind,info = findcross(y,v)\n\nWrapper for ``findcross``.\ -\n\nParameters\n----------\n" -"y : input rank-1 array('d') with bounds (n)\n" -"v : input float\n" -"\nReturns\n-------\n" -"ind : rank-1 array('i') with bounds (n)\n" -"info : rank-1 array('i') with bounds (1)"; -/* extern void findcross(double*,double,int*,int,int*); */ -static PyObject *f2py_rout_c_library_findcross(const PyObject *capi_self, - PyObject *capi_args, - PyObject *capi_keywds, - void (*f2py_func)(double*,double,int*,int,int*)) { - PyObject * volatile capi_buildvalue = NULL; - volatile int f2py_success = 1; -/*decl*/ - - double *y = NULL; - npy_intp y_Dims[1] = {-1}; - const int y_Rank = 1; - PyArrayObject *capi_y_tmp = NULL; - int capi_y_intent = 0; - PyObject *y_capi = Py_None; - double v = 0; - PyObject *v_capi = Py_None; - int *ind = NULL; - npy_intp ind_Dims[1] = {-1}; - const int ind_Rank = 1; - PyArrayObject *capi_ind_tmp = NULL; - int capi_ind_intent = 0; - int n = 0; - int *info = NULL; - npy_intp info_Dims[1] = {-1}; - const int info_Rank = 1; - PyArrayObject *capi_info_tmp = NULL; - int capi_info_intent = 0; - static char *capi_kwlist[] = {"y","v",NULL}; - -/*routdebugenter*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_clock(); -#endif - if (!PyArg_ParseTupleAndKeywords(capi_args,capi_keywds,\ - "OO:c_library.findcross",\ - capi_kwlist,&y_capi,&v_capi)) - return NULL; -/*frompyobj*/ - /* Processing variable info */ - info_Dims[0]=1; - capi_info_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_info_tmp = array_from_pyobj(NPY_INT,info_Dims,info_Rank,capi_info_intent,Py_None); - if (capi_info_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `info' of c_library.findcross to C/Fortran array" ); - } else { - info = (int *)(capi_info_tmp->data); - - /* Processing variable y */ - ; - capi_y_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_y_tmp = array_from_pyobj(NPY_DOUBLE,y_Dims,y_Rank,capi_y_intent,y_capi); - if (capi_y_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 1st argument `y' of c_library.findcross to C/Fortran array" ); - } else { - y = (double *)(capi_y_tmp->data); - - /* Processing variable v */ - f2py_success = double_from_pyobj(&v,v_capi,"c_library.findcross() 2nd argument (v) can't be converted to double"); - if (f2py_success) { - /* Processing variable n */ - n = len(y); - /* Processing variable ind */ - ind_Dims[0]=n; - capi_ind_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_ind_tmp = array_from_pyobj(NPY_INT,ind_Dims,ind_Rank,capi_ind_intent,Py_None); - if (capi_ind_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `ind' of c_library.findcross to C/Fortran array" ); - } else { - ind = (int *)(capi_ind_tmp->data); - -/*end of frompyobj*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_call_clock(); -#endif -/*callfortranroutine*/ - (*f2py_func)(y,v,ind,n,info); -if (PyErr_Occurred()) - f2py_success = 0; -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_call_clock(); -#endif -/*end of callfortranroutine*/ - if (f2py_success) { -/*pyobjfrom*/ -/*end of pyobjfrom*/ - CFUNCSMESS("Building return value.\n"); - capi_buildvalue = Py_BuildValue("NN",capi_ind_tmp,capi_info_tmp); -/*closepyobjfrom*/ -/*end of closepyobjfrom*/ - } /*if (f2py_success) after callfortranroutine*/ -/*cleanupfrompyobj*/ - } /*if (capi_ind_tmp == NULL) ... else of ind*/ - /* End of cleaning variable ind */ - /* End of cleaning variable n */ - } /*if (f2py_success) of v*/ - /* End of cleaning variable v */ - if((PyObject *)capi_y_tmp!=y_capi) { - Py_XDECREF(capi_y_tmp); } - } /*if (capi_y_tmp == NULL) ... else of y*/ - /* End of cleaning variable y */ - } /*if (capi_info_tmp == NULL) ... else of info*/ - /* End of cleaning variable info */ -/*end of cleanupfrompyobj*/ - if (capi_buildvalue == NULL) { -/*routdebugfailure*/ - } else { -/*routdebugleave*/ - } - CFUNCSMESS("Freeing memory.\n"); -/*freemem*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_clock(); -#endif - return capi_buildvalue; -} -/****************************** end of findcross ******************************/ - -/*********************************** disufq ***********************************/ -static char doc_f2py_rout_c_library_disufq[] = "\ -rvec,ivec = disufq(rA,iA,w,kw,h,g,nmin,nmax,m,[n])\n\nWrapper for ``disufq``.\ -\n\nParameters\n----------\n" -"rA : input rank-1 array('d') with bounds (n*m)\n" -"iA : input rank-1 array('d') with bounds (n*m)\n" -"w : input rank-1 array('d') with bounds (0.5 * n + 1.0)\n" -"kw : input rank-1 array('d') with bounds (0.5 * n + 1.0)\n" -"h : input float\n" -"g : input float\n" -"nmin : input int\n" -"nmax : input int\n" -"m : input int\n" -"\nOther Parameters\n----------------\n" -"n : input int, optional\n Default: (len(w)-1.0)/(0.5)\n" -"\nReturns\n-------\n" -"rvec : rank-1 array('d') with bounds (n*m)\n" -"ivec : rank-1 array('d') with bounds (n*m)"; -/* extern void disufq(double*,double*,double*,double*,double*,double*,double,double,int,int,int,int); */ -static PyObject *f2py_rout_c_library_disufq(const PyObject *capi_self, - PyObject *capi_args, - PyObject *capi_keywds, - void (*f2py_func)(double*,double*,double*,double*,double*,double*,double,double,int,int,int,int)) { - PyObject * volatile capi_buildvalue = NULL; - volatile int f2py_success = 1; -/*decl*/ - - double *rvec = NULL; - npy_intp rvec_Dims[1] = {-1}; - const int rvec_Rank = 1; - PyArrayObject *capi_rvec_tmp = NULL; - int capi_rvec_intent = 0; - double *ivec = NULL; - npy_intp ivec_Dims[1] = {-1}; - const int ivec_Rank = 1; - PyArrayObject *capi_ivec_tmp = NULL; - int capi_ivec_intent = 0; - double *rA = NULL; - npy_intp rA_Dims[1] = {-1}; - const int rA_Rank = 1; - PyArrayObject *capi_rA_tmp = NULL; - int capi_rA_intent = 0; - PyObject *rA_capi = Py_None; - double *iA = NULL; - npy_intp iA_Dims[1] = {-1}; - const int iA_Rank = 1; - PyArrayObject *capi_iA_tmp = NULL; - int capi_iA_intent = 0; - PyObject *iA_capi = Py_None; - double *w = NULL; - npy_intp w_Dims[1] = {-1}; - const int w_Rank = 1; - PyArrayObject *capi_w_tmp = NULL; - int capi_w_intent = 0; - PyObject *w_capi = Py_None; - double *kw = NULL; - npy_intp kw_Dims[1] = {-1}; - const int kw_Rank = 1; - PyArrayObject *capi_kw_tmp = NULL; - int capi_kw_intent = 0; - PyObject *kw_capi = Py_None; - double h = 0; - PyObject *h_capi = Py_None; - double g = 0; - PyObject *g_capi = Py_None; - int nmin = 0; - PyObject *nmin_capi = Py_None; - int nmax = 0; - PyObject *nmax_capi = Py_None; - int m = 0; - PyObject *m_capi = Py_None; - int n = 0; - PyObject *n_capi = Py_None; - static char *capi_kwlist[] = {"rA","iA","w","kw","h","g","nmin","nmax","m","n",NULL}; - -/*routdebugenter*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_clock(); -#endif - if (!PyArg_ParseTupleAndKeywords(capi_args,capi_keywds,\ - "OOOOOOOOO|O:c_library.disufq",\ - capi_kwlist,&rA_capi,&iA_capi,&w_capi,&kw_capi,&h_capi,&g_capi,&nmin_capi,&nmax_capi,&m_capi,&n_capi)) - return NULL; -/*frompyobj*/ - /* Processing variable nmax */ - f2py_success = int_from_pyobj(&nmax,nmax_capi,"c_library.disufq() 8th argument (nmax) can't be converted to int"); - if (f2py_success) { - /* Processing variable g */ - f2py_success = double_from_pyobj(&g,g_capi,"c_library.disufq() 6th argument (g) can't be converted to double"); - if (f2py_success) { - /* Processing variable h */ - f2py_success = double_from_pyobj(&h,h_capi,"c_library.disufq() 5th argument (h) can't be converted to double"); - if (f2py_success) { - /* Processing variable m */ - f2py_success = int_from_pyobj(&m,m_capi,"c_library.disufq() 9th argument (m) can't be converted to int"); - if (f2py_success) { - /* Processing variable w */ - ; - capi_w_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_w_tmp = array_from_pyobj(NPY_DOUBLE,w_Dims,w_Rank,capi_w_intent,w_capi); - if (capi_w_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 3rd argument `w' of c_library.disufq to C/Fortran array" ); - } else { - w = (double *)(capi_w_tmp->data); - - /* Processing variable nmin */ - f2py_success = int_from_pyobj(&nmin,nmin_capi,"c_library.disufq() 7th argument (nmin) can't be converted to int"); - if (f2py_success) { - /* Processing variable n */ - if (n_capi == Py_None) n = (len(w)-1.0)/(0.5); else - f2py_success = int_from_pyobj(&n,n_capi,"c_library.disufq() 1st keyword (n) can't be converted to int"); - if (f2py_success) { - CHECKSCALAR((len(w)-1.0)/(0.5)>=n,"(len(w)-1.0)/(0.5)>=n","1st keyword n","disufq:n=%d",n) { - /* Processing variable kw */ - kw_Dims[0]=0.5 * n + 1.0; - capi_kw_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_kw_tmp = array_from_pyobj(NPY_DOUBLE,kw_Dims,kw_Rank,capi_kw_intent,kw_capi); - if (capi_kw_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 4th argument `kw' of c_library.disufq to C/Fortran array" ); - } else { - kw = (double *)(capi_kw_tmp->data); - - /* Processing variable rA */ - rA_Dims[0]=n*m; - capi_rA_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_rA_tmp = array_from_pyobj(NPY_DOUBLE,rA_Dims,rA_Rank,capi_rA_intent,rA_capi); - if (capi_rA_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 1st argument `rA' of c_library.disufq to C/Fortran array" ); - } else { - rA = (double *)(capi_rA_tmp->data); - - /* Processing variable iA */ - iA_Dims[0]=n*m; - capi_iA_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_iA_tmp = array_from_pyobj(NPY_DOUBLE,iA_Dims,iA_Rank,capi_iA_intent,iA_capi); - if (capi_iA_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 2nd argument `iA' of c_library.disufq to C/Fortran array" ); - } else { - iA = (double *)(capi_iA_tmp->data); - - /* Processing variable ivec */ - ivec_Dims[0]=n*m; - capi_ivec_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_ivec_tmp = array_from_pyobj(NPY_DOUBLE,ivec_Dims,ivec_Rank,capi_ivec_intent,Py_None); - if (capi_ivec_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `ivec' of c_library.disufq to C/Fortran array" ); - } else { - ivec = (double *)(capi_ivec_tmp->data); - - /* Processing variable rvec */ - rvec_Dims[0]=n*m; - capi_rvec_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_rvec_tmp = array_from_pyobj(NPY_DOUBLE,rvec_Dims,rvec_Rank,capi_rvec_intent,Py_None); - if (capi_rvec_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `rvec' of c_library.disufq to C/Fortran array" ); - } else { - rvec = (double *)(capi_rvec_tmp->data); - -/*end of frompyobj*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_call_clock(); -#endif -/*callfortranroutine*/ - (*f2py_func)(rvec,ivec,rA,iA,w,kw,h,g,nmin,nmax,m,n); -if (PyErr_Occurred()) - f2py_success = 0; -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_call_clock(); -#endif -/*end of callfortranroutine*/ - if (f2py_success) { -/*pyobjfrom*/ -/*end of pyobjfrom*/ - CFUNCSMESS("Building return value.\n"); - capi_buildvalue = Py_BuildValue("NN",capi_rvec_tmp,capi_ivec_tmp); -/*closepyobjfrom*/ -/*end of closepyobjfrom*/ - } /*if (f2py_success) after callfortranroutine*/ -/*cleanupfrompyobj*/ - } /*if (capi_rvec_tmp == NULL) ... else of rvec*/ - /* End of cleaning variable rvec */ - } /*if (capi_ivec_tmp == NULL) ... else of ivec*/ - /* End of cleaning variable ivec */ - if((PyObject *)capi_iA_tmp!=iA_capi) { - Py_XDECREF(capi_iA_tmp); } - } /*if (capi_iA_tmp == NULL) ... else of iA*/ - /* End of cleaning variable iA */ - if((PyObject *)capi_rA_tmp!=rA_capi) { - Py_XDECREF(capi_rA_tmp); } - } /*if (capi_rA_tmp == NULL) ... else of rA*/ - /* End of cleaning variable rA */ - if((PyObject *)capi_kw_tmp!=kw_capi) { - Py_XDECREF(capi_kw_tmp); } - } /*if (capi_kw_tmp == NULL) ... else of kw*/ - /* End of cleaning variable kw */ - } /*CHECKSCALAR((len(w)-1.0)/(0.5)>=n)*/ - } /*if (f2py_success) of n*/ - /* End of cleaning variable n */ - } /*if (f2py_success) of nmin*/ - /* End of cleaning variable nmin */ - if((PyObject *)capi_w_tmp!=w_capi) { - Py_XDECREF(capi_w_tmp); } - } /*if (capi_w_tmp == NULL) ... else of w*/ - /* End of cleaning variable w */ - } /*if (f2py_success) of m*/ - /* End of cleaning variable m */ - } /*if (f2py_success) of h*/ - /* End of cleaning variable h */ - } /*if (f2py_success) of g*/ - /* End of cleaning variable g */ - } /*if (f2py_success) of nmax*/ - /* End of cleaning variable nmax */ -/*end of cleanupfrompyobj*/ - if (capi_buildvalue == NULL) { -/*routdebugfailure*/ - } else { -/*routdebugleave*/ - } - CFUNCSMESS("Freeing memory.\n"); -/*freemem*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_clock(); -#endif - return capi_buildvalue; -} -/******************************* end of disufq *******************************/ - -/********************************** disufq2 **********************************/ -static char doc_f2py_rout_c_library_disufq2[] = "\ -rsvec,isvec,rdvec,idvec = disufq2(rA,iA,w,kw,h,g,nmin,nmax,m,[n])\n\nWrapper for ``disufq2``.\ -\n\nParameters\n----------\n" -"rA : input rank-1 array('d') with bounds (n*m)\n" -"iA : input rank-1 array('d') with bounds (n*m)\n" -"w : input rank-1 array('d') with bounds (0.5 * n + 1.0)\n" -"kw : input rank-1 array('d') with bounds (0.5 * n + 1.0)\n" -"h : input float\n" -"g : input float\n" -"nmin : input int\n" -"nmax : input int\n" -"m : input int\n" -"\nOther Parameters\n----------------\n" -"n : input int, optional\n Default: (len(w)-1.0)/(0.5)\n" -"\nReturns\n-------\n" -"rsvec : rank-1 array('d') with bounds (n*m)\n" -"isvec : rank-1 array('d') with bounds (n*m)\n" -"rdvec : rank-1 array('d') with bounds (n*m)\n" -"idvec : rank-1 array('d') with bounds (n*m)"; -/* extern void disufq2(double*,double*,double*,double*,double*,double*,double*,double*,double,double,int,int,int,int); */ -static PyObject *f2py_rout_c_library_disufq2(const PyObject *capi_self, - PyObject *capi_args, - PyObject *capi_keywds, - void (*f2py_func)(double*,double*,double*,double*,double*,double*,double*,double*,double,double,int,int,int,int)) { - PyObject * volatile capi_buildvalue = NULL; - volatile int f2py_success = 1; -/*decl*/ - - double *rsvec = NULL; - npy_intp rsvec_Dims[1] = {-1}; - const int rsvec_Rank = 1; - PyArrayObject *capi_rsvec_tmp = NULL; - int capi_rsvec_intent = 0; - double *isvec = NULL; - npy_intp isvec_Dims[1] = {-1}; - const int isvec_Rank = 1; - PyArrayObject *capi_isvec_tmp = NULL; - int capi_isvec_intent = 0; - double *rdvec = NULL; - npy_intp rdvec_Dims[1] = {-1}; - const int rdvec_Rank = 1; - PyArrayObject *capi_rdvec_tmp = NULL; - int capi_rdvec_intent = 0; - double *idvec = NULL; - npy_intp idvec_Dims[1] = {-1}; - const int idvec_Rank = 1; - PyArrayObject *capi_idvec_tmp = NULL; - int capi_idvec_intent = 0; - double *rA = NULL; - npy_intp rA_Dims[1] = {-1}; - const int rA_Rank = 1; - PyArrayObject *capi_rA_tmp = NULL; - int capi_rA_intent = 0; - PyObject *rA_capi = Py_None; - double *iA = NULL; - npy_intp iA_Dims[1] = {-1}; - const int iA_Rank = 1; - PyArrayObject *capi_iA_tmp = NULL; - int capi_iA_intent = 0; - PyObject *iA_capi = Py_None; - double *w = NULL; - npy_intp w_Dims[1] = {-1}; - const int w_Rank = 1; - PyArrayObject *capi_w_tmp = NULL; - int capi_w_intent = 0; - PyObject *w_capi = Py_None; - double *kw = NULL; - npy_intp kw_Dims[1] = {-1}; - const int kw_Rank = 1; - PyArrayObject *capi_kw_tmp = NULL; - int capi_kw_intent = 0; - PyObject *kw_capi = Py_None; - double h = 0; - PyObject *h_capi = Py_None; - double g = 0; - PyObject *g_capi = Py_None; - int nmin = 0; - PyObject *nmin_capi = Py_None; - int nmax = 0; - PyObject *nmax_capi = Py_None; - int m = 0; - PyObject *m_capi = Py_None; - int n = 0; - PyObject *n_capi = Py_None; - static char *capi_kwlist[] = {"rA","iA","w","kw","h","g","nmin","nmax","m","n",NULL}; - -/*routdebugenter*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_clock(); -#endif - if (!PyArg_ParseTupleAndKeywords(capi_args,capi_keywds,\ - "OOOOOOOOO|O:c_library.disufq2",\ - capi_kwlist,&rA_capi,&iA_capi,&w_capi,&kw_capi,&h_capi,&g_capi,&nmin_capi,&nmax_capi,&m_capi,&n_capi)) - return NULL; -/*frompyobj*/ - /* Processing variable nmax */ - f2py_success = int_from_pyobj(&nmax,nmax_capi,"c_library.disufq2() 8th argument (nmax) can't be converted to int"); - if (f2py_success) { - /* Processing variable g */ - f2py_success = double_from_pyobj(&g,g_capi,"c_library.disufq2() 6th argument (g) can't be converted to double"); - if (f2py_success) { - /* Processing variable m */ - f2py_success = int_from_pyobj(&m,m_capi,"c_library.disufq2() 9th argument (m) can't be converted to int"); - if (f2py_success) { - /* Processing variable w */ - ; - capi_w_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_w_tmp = array_from_pyobj(NPY_DOUBLE,w_Dims,w_Rank,capi_w_intent,w_capi); - if (capi_w_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 3rd argument `w' of c_library.disufq2 to C/Fortran array" ); - } else { - w = (double *)(capi_w_tmp->data); - - /* Processing variable h */ - f2py_success = double_from_pyobj(&h,h_capi,"c_library.disufq2() 5th argument (h) can't be converted to double"); - if (f2py_success) { - /* Processing variable nmin */ - f2py_success = int_from_pyobj(&nmin,nmin_capi,"c_library.disufq2() 7th argument (nmin) can't be converted to int"); - if (f2py_success) { - /* Processing variable n */ - if (n_capi == Py_None) n = (len(w)-1.0)/(0.5); else - f2py_success = int_from_pyobj(&n,n_capi,"c_library.disufq2() 1st keyword (n) can't be converted to int"); - if (f2py_success) { - CHECKSCALAR((len(w)-1.0)/(0.5)>=n,"(len(w)-1.0)/(0.5)>=n","1st keyword n","disufq2:n=%d",n) { - /* Processing variable rdvec */ - rdvec_Dims[0]=n*m; - capi_rdvec_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_rdvec_tmp = array_from_pyobj(NPY_DOUBLE,rdvec_Dims,rdvec_Rank,capi_rdvec_intent,Py_None); - if (capi_rdvec_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `rdvec' of c_library.disufq2 to C/Fortran array" ); - } else { - rdvec = (double *)(capi_rdvec_tmp->data); - - /* Processing variable idvec */ - idvec_Dims[0]=n*m; - capi_idvec_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_idvec_tmp = array_from_pyobj(NPY_DOUBLE,idvec_Dims,idvec_Rank,capi_idvec_intent,Py_None); - if (capi_idvec_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `idvec' of c_library.disufq2 to C/Fortran array" ); - } else { - idvec = (double *)(capi_idvec_tmp->data); - - /* Processing variable isvec */ - isvec_Dims[0]=n*m; - capi_isvec_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_isvec_tmp = array_from_pyobj(NPY_DOUBLE,isvec_Dims,isvec_Rank,capi_isvec_intent,Py_None); - if (capi_isvec_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `isvec' of c_library.disufq2 to C/Fortran array" ); - } else { - isvec = (double *)(capi_isvec_tmp->data); - - /* Processing variable rsvec */ - rsvec_Dims[0]=n*m; - capi_rsvec_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_rsvec_tmp = array_from_pyobj(NPY_DOUBLE,rsvec_Dims,rsvec_Rank,capi_rsvec_intent,Py_None); - if (capi_rsvec_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `rsvec' of c_library.disufq2 to C/Fortran array" ); - } else { - rsvec = (double *)(capi_rsvec_tmp->data); - - /* Processing variable kw */ - kw_Dims[0]=0.5 * n + 1.0; - capi_kw_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_kw_tmp = array_from_pyobj(NPY_DOUBLE,kw_Dims,kw_Rank,capi_kw_intent,kw_capi); - if (capi_kw_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 4th argument `kw' of c_library.disufq2 to C/Fortran array" ); - } else { - kw = (double *)(capi_kw_tmp->data); - - /* Processing variable rA */ - rA_Dims[0]=n*m; - capi_rA_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_rA_tmp = array_from_pyobj(NPY_DOUBLE,rA_Dims,rA_Rank,capi_rA_intent,rA_capi); - if (capi_rA_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 1st argument `rA' of c_library.disufq2 to C/Fortran array" ); - } else { - rA = (double *)(capi_rA_tmp->data); - - /* Processing variable iA */ - iA_Dims[0]=n*m; - capi_iA_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_iA_tmp = array_from_pyobj(NPY_DOUBLE,iA_Dims,iA_Rank,capi_iA_intent,iA_capi); - if (capi_iA_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 2nd argument `iA' of c_library.disufq2 to C/Fortran array" ); - } else { - iA = (double *)(capi_iA_tmp->data); - -/*end of frompyobj*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_call_clock(); -#endif -/*callfortranroutine*/ - (*f2py_func)(rsvec,isvec,rdvec,idvec,rA,iA,w,kw,h,g,nmin,nmax,m,n); -if (PyErr_Occurred()) - f2py_success = 0; -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_call_clock(); -#endif -/*end of callfortranroutine*/ - if (f2py_success) { -/*pyobjfrom*/ -/*end of pyobjfrom*/ - CFUNCSMESS("Building return value.\n"); - capi_buildvalue = Py_BuildValue("NNNN",capi_rsvec_tmp,capi_isvec_tmp,capi_rdvec_tmp,capi_idvec_tmp); -/*closepyobjfrom*/ -/*end of closepyobjfrom*/ - } /*if (f2py_success) after callfortranroutine*/ -/*cleanupfrompyobj*/ - if((PyObject *)capi_iA_tmp!=iA_capi) { - Py_XDECREF(capi_iA_tmp); } - } /*if (capi_iA_tmp == NULL) ... else of iA*/ - /* End of cleaning variable iA */ - if((PyObject *)capi_rA_tmp!=rA_capi) { - Py_XDECREF(capi_rA_tmp); } - } /*if (capi_rA_tmp == NULL) ... else of rA*/ - /* End of cleaning variable rA */ - if((PyObject *)capi_kw_tmp!=kw_capi) { - Py_XDECREF(capi_kw_tmp); } - } /*if (capi_kw_tmp == NULL) ... else of kw*/ - /* End of cleaning variable kw */ - } /*if (capi_rsvec_tmp == NULL) ... else of rsvec*/ - /* End of cleaning variable rsvec */ - } /*if (capi_isvec_tmp == NULL) ... else of isvec*/ - /* End of cleaning variable isvec */ - } /*if (capi_idvec_tmp == NULL) ... else of idvec*/ - /* End of cleaning variable idvec */ - } /*if (capi_rdvec_tmp == NULL) ... else of rdvec*/ - /* End of cleaning variable rdvec */ - } /*CHECKSCALAR((len(w)-1.0)/(0.5)>=n)*/ - } /*if (f2py_success) of n*/ - /* End of cleaning variable n */ - } /*if (f2py_success) of nmin*/ - /* End of cleaning variable nmin */ - } /*if (f2py_success) of h*/ - /* End of cleaning variable h */ - if((PyObject *)capi_w_tmp!=w_capi) { - Py_XDECREF(capi_w_tmp); } - } /*if (capi_w_tmp == NULL) ... else of w*/ - /* End of cleaning variable w */ - } /*if (f2py_success) of m*/ - /* End of cleaning variable m */ - } /*if (f2py_success) of g*/ - /* End of cleaning variable g */ - } /*if (f2py_success) of nmax*/ - /* End of cleaning variable nmax */ -/*end of cleanupfrompyobj*/ - if (capi_buildvalue == NULL) { -/*routdebugfailure*/ - } else { -/*routdebugleave*/ - } - CFUNCSMESS("Freeing memory.\n"); -/*freemem*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_clock(); -#endif - return capi_buildvalue; -} -/******************************* end of disufq2 *******************************/ - -/******************************* findrfc3_astm *******************************/ -static char doc_f2py_rout_c_library_findrfc3_astm[] = "\ -array_out,nout = findrfc3_astm(array_ext)\n\nWrapper for ``findrfc3_astm``.\ -\n\nParameters\n----------\n" -"array_ext : input rank-1 array('d') with bounds (n)\n" -"\nReturns\n-------\n" -"array_out : rank-2 array('d') with bounds (n,3)\n" -"nout : rank-1 array('i') with bounds (2)"; -/* extern void findrfc3_astm(double*,double*,int,int*); */ -static PyObject *f2py_rout_c_library_findrfc3_astm(const PyObject *capi_self, - PyObject *capi_args, - PyObject *capi_keywds, - void (*f2py_func)(double*,double*,int,int*)) { - PyObject * volatile capi_buildvalue = NULL; - volatile int f2py_success = 1; -/*decl*/ - - double *array_ext = NULL; - npy_intp array_ext_Dims[1] = {-1}; - const int array_ext_Rank = 1; - PyArrayObject *capi_array_ext_tmp = NULL; - int capi_array_ext_intent = 0; - PyObject *array_ext_capi = Py_None; - double *array_out = NULL; - npy_intp array_out_Dims[2] = {-1, -1}; - const int array_out_Rank = 2; - PyArrayObject *capi_array_out_tmp = NULL; - int capi_array_out_intent = 0; - int n = 0; - int *nout = NULL; - npy_intp nout_Dims[1] = {-1}; - const int nout_Rank = 1; - PyArrayObject *capi_nout_tmp = NULL; - int capi_nout_intent = 0; - static char *capi_kwlist[] = {"array_ext",NULL}; - -/*routdebugenter*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_clock(); -#endif - if (!PyArg_ParseTupleAndKeywords(capi_args,capi_keywds,\ - "O:c_library.findrfc3_astm",\ - capi_kwlist,&array_ext_capi)) - return NULL; -/*frompyobj*/ - /* Processing variable array_ext */ - ; - capi_array_ext_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_array_ext_tmp = array_from_pyobj(NPY_DOUBLE,array_ext_Dims,array_ext_Rank,capi_array_ext_intent,array_ext_capi); - if (capi_array_ext_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 1st argument `array_ext' of c_library.findrfc3_astm to C/Fortran array" ); - } else { - array_ext = (double *)(capi_array_ext_tmp->data); - - /* Processing variable nout */ - nout_Dims[0]=2; - capi_nout_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_nout_tmp = array_from_pyobj(NPY_INT,nout_Dims,nout_Rank,capi_nout_intent,Py_None); - if (capi_nout_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `nout' of c_library.findrfc3_astm to C/Fortran array" ); - } else { - nout = (int *)(capi_nout_tmp->data); - - /* Processing variable n */ - n = len(array_ext); - /* Processing variable array_out */ - array_out_Dims[0]=n,array_out_Dims[1]=3; - capi_array_out_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_array_out_tmp = array_from_pyobj(NPY_DOUBLE,array_out_Dims,array_out_Rank,capi_array_out_intent,Py_None); - if (capi_array_out_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `array_out' of c_library.findrfc3_astm to C/Fortran array" ); - } else { - array_out = (double *)(capi_array_out_tmp->data); - -/*end of frompyobj*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_call_clock(); -#endif -/*callfortranroutine*/ - (*f2py_func)(array_ext,array_out,n,nout); -if (PyErr_Occurred()) - f2py_success = 0; -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_call_clock(); -#endif -/*end of callfortranroutine*/ - if (f2py_success) { -/*pyobjfrom*/ -/*end of pyobjfrom*/ - CFUNCSMESS("Building return value.\n"); - capi_buildvalue = Py_BuildValue("NN",capi_array_out_tmp,capi_nout_tmp); -/*closepyobjfrom*/ -/*end of closepyobjfrom*/ - } /*if (f2py_success) after callfortranroutine*/ -/*cleanupfrompyobj*/ - } /*if (capi_array_out_tmp == NULL) ... else of array_out*/ - /* End of cleaning variable array_out */ - /* End of cleaning variable n */ - } /*if (capi_nout_tmp == NULL) ... else of nout*/ - /* End of cleaning variable nout */ - if((PyObject *)capi_array_ext_tmp!=array_ext_capi) { - Py_XDECREF(capi_array_ext_tmp); } - } /*if (capi_array_ext_tmp == NULL) ... else of array_ext*/ - /* End of cleaning variable array_ext */ -/*end of cleanupfrompyobj*/ - if (capi_buildvalue == NULL) { -/*routdebugfailure*/ - } else { -/*routdebugleave*/ - } - CFUNCSMESS("Freeing memory.\n"); -/*freemem*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_clock(); -#endif - return capi_buildvalue; -} -/**************************** end of findrfc3_astm ****************************/ - -/******************************* findrfc5_astm *******************************/ -static char doc_f2py_rout_c_library_findrfc5_astm[] = "\ -array_out,nout = findrfc5_astm(array_ext,array_t)\n\nWrapper for ``findrfc5_astm``.\ -\n\nParameters\n----------\n" -"array_ext : input rank-1 array('d') with bounds (n)\n" -"array_t : input rank-1 array('d') with bounds (n)\n" -"\nReturns\n-------\n" -"array_out : rank-2 array('d') with bounds (n,5)\n" -"nout : rank-1 array('i') with bounds (2)"; -/* extern void findrfc5_astm(double*,double*,double*,int,int*); */ -static PyObject *f2py_rout_c_library_findrfc5_astm(const PyObject *capi_self, - PyObject *capi_args, - PyObject *capi_keywds, - void (*f2py_func)(double*,double*,double*,int,int*)) { - PyObject * volatile capi_buildvalue = NULL; - volatile int f2py_success = 1; -/*decl*/ - - double *array_ext = NULL; - npy_intp array_ext_Dims[1] = {-1}; - const int array_ext_Rank = 1; - PyArrayObject *capi_array_ext_tmp = NULL; - int capi_array_ext_intent = 0; - PyObject *array_ext_capi = Py_None; - double *array_t = NULL; - npy_intp array_t_Dims[1] = {-1}; - const int array_t_Rank = 1; - PyArrayObject *capi_array_t_tmp = NULL; - int capi_array_t_intent = 0; - PyObject *array_t_capi = Py_None; - double *array_out = NULL; - npy_intp array_out_Dims[2] = {-1, -1}; - const int array_out_Rank = 2; - PyArrayObject *capi_array_out_tmp = NULL; - int capi_array_out_intent = 0; - int n = 0; - int *nout = NULL; - npy_intp nout_Dims[1] = {-1}; - const int nout_Rank = 1; - PyArrayObject *capi_nout_tmp = NULL; - int capi_nout_intent = 0; - static char *capi_kwlist[] = {"array_ext","array_t",NULL}; - -/*routdebugenter*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_clock(); -#endif - if (!PyArg_ParseTupleAndKeywords(capi_args,capi_keywds,\ - "OO:c_library.findrfc5_astm",\ - capi_kwlist,&array_ext_capi,&array_t_capi)) - return NULL; -/*frompyobj*/ - /* Processing variable nout */ - nout_Dims[0]=2; - capi_nout_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_nout_tmp = array_from_pyobj(NPY_INT,nout_Dims,nout_Rank,capi_nout_intent,Py_None); - if (capi_nout_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `nout' of c_library.findrfc5_astm to C/Fortran array" ); - } else { - nout = (int *)(capi_nout_tmp->data); - - /* Processing variable array_ext */ - ; - capi_array_ext_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_array_ext_tmp = array_from_pyobj(NPY_DOUBLE,array_ext_Dims,array_ext_Rank,capi_array_ext_intent,array_ext_capi); - if (capi_array_ext_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 1st argument `array_ext' of c_library.findrfc5_astm to C/Fortran array" ); - } else { - array_ext = (double *)(capi_array_ext_tmp->data); - - /* Processing variable n */ - n = len(array_ext); - /* Processing variable array_t */ - array_t_Dims[0]=n; - capi_array_t_intent |= F2PY_INTENT_C|F2PY_INTENT_IN; - capi_array_t_tmp = array_from_pyobj(NPY_DOUBLE,array_t_Dims,array_t_Rank,capi_array_t_intent,array_t_capi); - if (capi_array_t_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting 2nd argument `array_t' of c_library.findrfc5_astm to C/Fortran array" ); - } else { - array_t = (double *)(capi_array_t_tmp->data); - - /* Processing variable array_out */ - array_out_Dims[0]=n,array_out_Dims[1]=5; - capi_array_out_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_C|F2PY_INTENT_OUT; - capi_array_out_tmp = array_from_pyobj(NPY_DOUBLE,array_out_Dims,array_out_Rank,capi_array_out_intent,Py_None); - if (capi_array_out_tmp == NULL) { - if (!PyErr_Occurred()) - PyErr_SetString(c_library_error,"failed in converting hidden `array_out' of c_library.findrfc5_astm to C/Fortran array" ); - } else { - array_out = (double *)(capi_array_out_tmp->data); - -/*end of frompyobj*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_start_call_clock(); -#endif -/*callfortranroutine*/ - (*f2py_func)(array_ext,array_t,array_out,n,nout); -if (PyErr_Occurred()) - f2py_success = 0; -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_call_clock(); -#endif -/*end of callfortranroutine*/ - if (f2py_success) { -/*pyobjfrom*/ -/*end of pyobjfrom*/ - CFUNCSMESS("Building return value.\n"); - capi_buildvalue = Py_BuildValue("NN",capi_array_out_tmp,capi_nout_tmp); -/*closepyobjfrom*/ -/*end of closepyobjfrom*/ - } /*if (f2py_success) after callfortranroutine*/ -/*cleanupfrompyobj*/ - } /*if (capi_array_out_tmp == NULL) ... else of array_out*/ - /* End of cleaning variable array_out */ - if((PyObject *)capi_array_t_tmp!=array_t_capi) { - Py_XDECREF(capi_array_t_tmp); } - } /*if (capi_array_t_tmp == NULL) ... else of array_t*/ - /* End of cleaning variable array_t */ - /* End of cleaning variable n */ - if((PyObject *)capi_array_ext_tmp!=array_ext_capi) { - Py_XDECREF(capi_array_ext_tmp); } - } /*if (capi_array_ext_tmp == NULL) ... else of array_ext*/ - /* End of cleaning variable array_ext */ - } /*if (capi_nout_tmp == NULL) ... else of nout*/ - /* End of cleaning variable nout */ -/*end of cleanupfrompyobj*/ - if (capi_buildvalue == NULL) { -/*routdebugfailure*/ - } else { -/*routdebugleave*/ - } - CFUNCSMESS("Freeing memory.\n"); -/*freemem*/ -#ifdef F2PY_REPORT_ATEXIT -f2py_stop_clock(); -#endif - return capi_buildvalue; -} -/**************************** end of findrfc5_astm ****************************/ -/*eof body*/ - -/******************* See f2py2e/f90mod_rules.py: buildhooks *******************/ -/*need_f90modhooks*/ - -/************** See f2py2e/rules.py: module_rules['modulebody'] **************/ - -/******************* See f2py2e/common_rules.py: buildhooks *******************/ - -/*need_commonhooks*/ - -/**************************** See f2py2e/rules.py ****************************/ - -static FortranDataDef f2py_routine_defs[] = { - {"findrfc",-1,{{-1}},0,(char *)findrfc,(f2py_init_func)f2py_rout_c_library_findrfc,doc_f2py_rout_c_library_findrfc}, - {"findcross",-1,{{-1}},0,(char *)findcross,(f2py_init_func)f2py_rout_c_library_findcross,doc_f2py_rout_c_library_findcross}, - {"disufq",-1,{{-1}},0,(char *)disufq,(f2py_init_func)f2py_rout_c_library_disufq,doc_f2py_rout_c_library_disufq}, - {"disufq2",-1,{{-1}},0,(char *)disufq2,(f2py_init_func)f2py_rout_c_library_disufq2,doc_f2py_rout_c_library_disufq2}, - {"findrfc3_astm",-1,{{-1}},0,(char *)findrfc3_astm,(f2py_init_func)f2py_rout_c_library_findrfc3_astm,doc_f2py_rout_c_library_findrfc3_astm}, - {"findrfc5_astm",-1,{{-1}},0,(char *)findrfc5_astm,(f2py_init_func)f2py_rout_c_library_findrfc5_astm,doc_f2py_rout_c_library_findrfc5_astm}, - -/*eof routine_defs*/ - {NULL} -}; - -static PyMethodDef f2py_module_methods[] = { - - {NULL,NULL} -}; - -#if PY_VERSION_HEX >= 0x03000000 -static struct PyModuleDef moduledef = { - PyModuleDef_HEAD_INIT, - "c_library", - NULL, - -1, - f2py_module_methods, - NULL, - NULL, - NULL, - NULL -}; -#endif - -#if PY_VERSION_HEX >= 0x03000000 -#define RETVAL m -PyMODINIT_FUNC PyInit_c_library(void) { -#else -#define RETVAL -PyMODINIT_FUNC initc_library(void) { -#endif - int i; - PyObject *m,*d, *s; -#if PY_VERSION_HEX >= 0x03000000 - m = c_library_module = PyModule_Create(&moduledef); -#else - m = c_library_module = Py_InitModule("c_library", f2py_module_methods); -#endif - Py_TYPE(&PyFortran_Type) = &PyType_Type; - import_array(); - if (PyErr_Occurred()) - {PyErr_SetString(PyExc_ImportError, "can't initialize module c_library (failed to import numpy)"); return RETVAL;} - d = PyModule_GetDict(m); - s = PyString_FromString("$Revision: $"); - PyDict_SetItemString(d, "__version__", s); -#if PY_VERSION_HEX >= 0x03000000 - s = PyUnicode_FromString( -#else - s = PyString_FromString( -#endif - "This module 'c_library' is auto-generated with f2py (version:2).\nFunctions:\n" -" ind,info = findrfc(y1,hmin)\n" -" ind,info = findcross(y,v)\n" -" rvec,ivec = disufq(rA,iA,w,kw,h,g,nmin,nmax,m,n=(len(w)-1.0)/(0.5))\n" -" rsvec,isvec,rdvec,idvec = disufq2(rA,iA,w,kw,h,g,nmin,nmax,m,n=(len(w)-1.0)/(0.5))\n" -" array_out,nout = findrfc3_astm(array_ext)\n" -" array_out,nout = findrfc5_astm(array_ext,array_t)\n" -"."); - PyDict_SetItemString(d, "__doc__", s); - c_library_error = PyErr_NewException ("c_library.error", NULL, NULL); - Py_DECREF(s); - for(i=0;f2py_routine_defs[i].name!=NULL;i++) - PyDict_SetItemString(d, f2py_routine_defs[i].name,PyFortranObject_NewAsAttr(&f2py_routine_defs[i])); - - - - - - -/*eof initf2pywraphooks*/ -/*eof initf90modhooks*/ - -/*eof initcommonhooks*/ - - -#ifdef F2PY_REPORT_ATEXIT - if (! PyErr_Occurred()) - on_exit(f2py_report_on_exit,(void*)"c_library"); -#endif - - return RETVAL; -} -#ifdef __cplusplus -} -#endif diff --git a/wafo/source/c_library/setup.py b/wafo/source/c_library/setup.py deleted file mode 100644 index d6d9242..0000000 --- a/wafo/source/c_library/setup.py +++ /dev/null @@ -1,18 +0,0 @@ -''' -python setup.py build_src build_ext --inplace - -See also http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW -''' -# File setup.py - - -def configuration(parent_package='', top_path=None): - from numpy.distutils.misc_util import Configuration - config = Configuration('', parent_package, top_path) - - config.add_extension('c_library', - sources=['c_library.pyf', 'c_functions.c']) - return config -if __name__ == "__main__": - from numpy.distutils.core import setup - setup(**configuration(top_path='').todict()) diff --git a/wafo/source/cov2XXXpdf/bounds/cov2acdfb.f b/wafo/source/cov2XXXpdf/bounds/cov2acdfb.f deleted file mode 100644 index b6a85b4..0000000 --- a/wafo/source/cov2XXXpdf/bounds/cov2acdfb.f +++ /dev/null @@ -1,450 +0,0 @@ - PROGRAM sp2Acdf1 -C*********************************************************************** -C This program computes upper and lower bounds for: * -C * -C density of T_i, for Ac <=h, in a gaussian process i.e. * -C * -C half wavelength (up-crossing to downcrossing) for crests h * -C I.R. 27 Dec. 1999 * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansrup - double precision, dimension(:,:),allocatable :: ansrlo - double precision, dimension(: ),allocatable :: ex,CY - double precision, dimension(:,:),allocatable :: xc,fxind - double precision, dimension(: ),allocatable :: h - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size,icy - integer ::it1,it2,status - double precision :: ds,dT ! lag spacing for covariances -! f90 sp2Acdf1.f rind50.f - - CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,Nx,dT) - !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - if (abs(def).GT.1) THEN - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - !CALL INIT_AMPLITUDES(h,def,Nx) - endif - allocate(h(1:Nx)) - CALL INIT_AMPLITUDES(h,def,Nx) - CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - - NI=4; Nd=2 - Nc=3; Mb=2 - - Nj=0 - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - - allocate(CY(1:Nx)) - do icy=1,Nx - CY(icy)=exp(-0.5*h(icy)*h(icy)/100)/(10*sqrt(twopi)) - enddo - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate BIG' - end if - allocate(ex(1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate ex' - end if - allocate(ansrup(1:Ntime,1:Nx)) - allocate(ansrlo(1:Ntime,1:Nx)) - ansrup=0.d0 - ansrlo=0.d0 - allocate(fxind(1:Nx,1:2)) - fxind=0.d0 !this is not needed - allocate(xc(1:Nc,1:Nx)) - - - allocate(a_up(Mb,NI-1)) - allocate(a_lo(Mb,NI-1)) - a_up=0.d0 - a_lo=0.d0 - xc(1,1:Nx)=h(1:Nx) - xc(2,1:Nx)=u - xc(3,1:Nx)=u - - if (def.GT.0) then - a_up(1,1)=0.d0 - a_lo(1,1)=u - a_up(1,2)=XdInf - a_lo(1,3)=-XdInf - a_up(2,1)=1.d0 - else - a_up(1,1)=u - a_lo(1,1)=0.d0 - a_lo(1,2)=-XdInf - a_up(1,3)= XdInf - a_lo(2,1)=1.d0 - endif - !print *,'Nstart',Nstart - Nstart=MAX(3,Nstart) - - - if (SCIS.GT.0) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - - !print *,'loop starts' - do Ntd=Nstart,Ntime - - Ntdc=Ntd+Nc - ex=0.d0 - BIG=0.d0 - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period - - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - !print *,'test',fxind/CY(1:Nx) - - do icy=1,Nx - ansrup(Ntd,icy)=fxind(icy,1)*CC/CY(icy) - ansrlo(Ntd,icy)=fxind(icy,2)*CC/CY(icy) - enddo - if (SCIS.GT.0) then - write(11,*) COV(1) ! save coefficient of variation - endif - if((Nx.gt.4).or.NIT.gt.4) print *,'Ready: ',Ntd,' of ',Ntime - enddo - goto 300 - 300 open (unit=11, file='dens.out', STATUS='unknown') - - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansrup(ts,ph),ansrlo(ts,ph) - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 continue - deallocate(BIG) - deallocate(ex) - deallocate(fxind) - deallocate(ansrup) - deallocate(ansrlo) - deallocate(xc) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - - if (allocated(R3)) then - deallocate(R3) - deallocate(R4) - deallocate(h) - ENDIF - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,def,Ntime,Nstart,NIT,speed,Nx,dT) - IMPLICIT NONE - integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) def - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - - if (abs(def).GT.1) then - READ (14,*) dT - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - else - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - endif - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,def,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: def - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - !if (def.LT.0) THEN - ! H=-H - !endif - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime,def - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - if (abs(def).GT.1) then - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(4,*) R3(i) - read(5,*) R4(i) - enddo - - close(4) - close(5) - endif - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,shft,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! For ts>1: -! X(t2)..X(ts),..X(tn-1) X''(ts) X'(t1) X'(tn) X(ts) X(t1) X(tn) X'(ts) -! = [Xt Xd Xc] -! -! For ts<=1: -! X(t2)..,..X(tn-1) X'(t1) X'(tn) Y X(t1) X(tn) -! = [Xt Xd Xc] -!Add Y Condition : Y=h - -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - - if (ts.LE.1) THEN - Ntd1=tn - N=Ntd1+Nc; - shft=0 ! def=1 want only crest period Tc - else - Ntd1=tn+1 - N=Ntd1+4 - shft=1 ! def=2 or 3 want Tc Ac or Tcf, Ac - endif - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1+shft) = 0.d0 !cov(X(ti+1),Y) - BIG(i ,Ntd1+2+shft) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+3+shft) = R0(i+1) !cov(X(t.. ),X(tn)) - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X' (t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X' (tn)) - enddo - !call echo(big(1:tn,1:tn),tn) -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - -!cov(Xc) - !print *,'t' - BIG(Ntd1+1+shft,Ntd1+1+shft) = 100.d0!100.d0 ! cov(Y,Y) - BIG(Ntd1+1+shft,Ntd1+2+shft) = 0.d0 - BIG(Ntd1+1+shft,Ntd1+3+shft) = 0.d0 - BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+2+shft,Ntd1+3+shft) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+3+shft,Ntd1+3+shft) = R0(1) ! cov(X(tn),X (tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1+shft) = 0.d0 !cov(X'(tn),Y) - BIG(Ntd1 ,Ntd1+2+shft) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+3+shft) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+1+shft) = 0.d0 !cov(X'(t1),Y) - BIG(Ntd1-1,Ntd1+2+shft) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+3+shft) =-R1(tn) !cov(X'(t1),X(tn)) - - - !call echo(big(1:N,1:N),N) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - BIG(i,j)=tmp - enddo - !call echo(big(1:N,1:N),N) - enddo - !if (tn.eq.3) then - !do j=1,N - ! do i=j,N - ! print *,'test',j,i,BIG(j,i) - ! enddo - !call echo(big(1:N,1:N),N) - !enddo - !endif - !call echo(big(1:N,1:N),N) - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2Acdf1 - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/bounds/cov2mmpdfb.f b/wafo/source/cov2XXXpdf/bounds/cov2mmpdfb.f deleted file mode 100644 index 2d9aee7..0000000 --- a/wafo/source/cov2XXXpdf/bounds/cov2mmpdfb.f +++ /dev/null @@ -1,356 +0,0 @@ - PROGRAM sp2mM1 -C*********************************************************************************** -C Computes upper lower bounds for density of maximum and the following minimum * -C*********************************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansrup - double precision, dimension(:,:),allocatable :: ansrlo - double precision, dimension(: ),allocatable :: ex,h - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(:,:),allocatable :: fxind - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nstart,Ntime,tn,ts,speed,seed1,seed_size - integer :: status,i,j,ij,Nx1 - double precision :: ds,dT ! lag spacing for covariances - -! f90 sp2AmM1.f rind52.f - - CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,Nx1,dT) - Nx=Nx1*(Nx1-1)/2 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - - CALL INITDATA(speed) - - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - allocate(h(1:Nx1)) - - CALL INIT_AMPLITUDES(h,Nx1) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! Y= X'(t2)...X'(tn-1)||X''(t1) X''(tn)||X(t1) X(tn) X'(t1) X'(tn) !! -! = [ Xt Xd Xc ] !! -! !! -! Nt=tn-2, Nd=2, Nc=4 !! -! !! -! Xt= contains Nt time points in the indicator function !! -! Xd= " Nd derivatives !! -! Xc= " Nc variables to condition on !! -! !! -! There are 3 ( NI=4) regions with constant bariers: !! -! (indI(1)=0); for i\in (indI(1),indI(2)] Y(i)<0. !! -! (indI(2)=Nt) ; for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) !! -! (indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn)) !! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - - NI=4; Nd=2 - Nc=4; Mb=1 - - Nj=0 - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(R4(1)) - XtInf=10.d0*SQRT(-R2(1)) - ! normalizing constant - CC=TWOPI*SQRT(-R2(1)/R4(1)) - - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate BIG' - end if - allocate(ex(1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate ex' - end if - allocate(ansrup(1:Nx1,1:Nx1)) - ansrup=0.d0 - allocate(ansrlo(1:Nx1,1:Nx1)) - ansrlo=0.d0 - allocate(fxind(1:Nx,1:2)) - fxind=0.d0 !this is not needed - allocate(xc(1:Nc,1:Nx)) - - - allocate(a_up(Mb,NI-1)) - allocate(a_lo(Mb,NI-1)) - - a_up=0.d0 - a_lo=0.d0 - - ij=0 - do i=2,Nx1 - do j=1,i-1 - ij=ij+1 - xc(1,ij)=h(i) - xc(2,ij)=h(j) - enddo - enddo - xc(3,1:Nx)=0.d0 - xc(4,1:Nx)=0.d0 - - a_lo(1,1)=-Xtinf - a_lo(1,2)=-XdInf - a_up(1,3)=+XdInf - - - Nstart=MAX(2,Nstart) - - - if (SCIS.GT.0) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - - do Ntd=Nstart,Ntime - - Ntdc=Ntd+Nc - ex=0.d0 - BIG=0.d0 - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,R0,R1,R2,R3,R4) ! positive wave period - - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - ij=0 - do i=2,Nx1 - do j=1,i-1 - ij=ij+1 - ansrup(i,j)=ansrup(i,j)+fxind(ij,1)*CC*dt - ansrlo(i,j)=ansrlo(i,j)+fxind(ij,2)*CC*dt - enddo - enddo - - if (SCIS.GT.0) then - write(11,*) COV(1) ! save coefficient of variation - endif - print *,'Ready: ',Ntd,' of ',Ntime - enddo - goto 300 - 300 open (unit=11, file='dens.out', STATUS='unknown') - do i=1,Nx1 - do j=1,Nx1 - write(11,*) ansrup(i,j),ansrlo(i,j) - enddo - enddo - close(11) - 900 continue - deallocate(BIG) - deallocate(ex) - deallocate(fxind) - deallocate(ansrup) - deallocate(ansrlo) - deallocate(xc) - deallocate(R0) - deallocate(R1) - deallocate(R2) - deallocate(R3) - deallocate(R4) - deallocate(h) - - if (allocated(COV) ) then - deallocate(COV) - endif - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (Ntime,Nstart,NIT,speed,Nx,dT) - IMPLICIT NONE - integer, intent(out):: Ntime,Nstart,NIT,speed,Nx - double precision ,intent(out) :: dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - READ (14,*) dT - - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - read(4,*) R3(i) - read(5,*) R4(i) - enddo - close(1) - close(2) - close(3) - close(3) - close(5) - return - END SUBROUTINE INIT_COVARIANCES - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn - integer :: i,j,N - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X(t1),X(tn),X'(t1),X'(tn) -! = [ Xt | Xd | Xc ] -! -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - N=tn+4 - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,tn+1) = R1(i+1) !cov(X'(ti+1),X(t1)) - BIG(tn-1-i ,tn+2) = -R1(i+1) !cov(X'(ti+1),X(tn)) - BIG(i ,tn+3) = -R2(i+1) !cov(X'(ti+1),X'(t1)) - BIG(tn-1-i ,tn+4) = -R2(i+1) !cov(X'(ti+1),X'(tn)) - !Cov(Xt,Xd) - BIG(i,tn-1) = R3(i+1) !cov(X'(ti+1),X''(t1)) - BIG(tn-1-i,tn) =-R3(i+1) !cov(X'(ti+1),X''(tn)) - enddo - -!cov(Xd) - BIG(tn-1 ,tn-1 ) = R4(1) - BIG(tn-1,tn ) = R4(tn) !cov(X''(t1),X''(tn)) - BIG(tn ,tn ) = R4(1) - -!cov(Xc) - BIG(tn+1,tn+1) = R0(1) ! cov(X(t1),X(t1)) - BIG(tn+1,tn+2) = R0(tn) ! cov(X(t1),X(tn)) - BIG(tn+1,tn+3) = 0.d0 ! cov(X(t1),X'(t1)) - BIG(tn+1,tn+4) = R1(tn) ! cov(X(t1),X'(tn)) - BIG(tn+2,tn+2) = R0(1) ! cov(X(tn),X(tn)) - BIG(tn+2,tn+3) =-R1(tn) ! cov(X(tn),X'(t1)) - BIG(tn+2,tn+4) = 0.d0 ! cov(X(tn),X'(tn)) - BIG(tn+3,tn+3) =-R2(1) ! cov(X'(t1),X'(t1)) - BIG(tn+3,tn+4) =-R2(tn) ! cov(X'(t1),X'(tn)) - BIG(tn+4,tn+4) =-R2(1) ! cov(X'(tn),X'(tn)) -!Xc=X(t1),X(tn),X'(t1),X'(tn) -!Xd=X''(t1),X''(tn) -!cov(Xd,Xc) - BIG(tn-1 ,tn+1) = R2(1) !cov(X''(t1),X(t1)) - BIG(tn-1 ,tn+2) = R2(tn) !cov(X''(t1),X(tn)) - BIG(tn-1 ,tn+3) = 0.d0 !cov(X''(t1),X'(t1)) - BIG(tn-1 ,tn+4) = R3(tn) !cov(X''(t1),X'(tn)) - BIG(tn ,tn+1) = R2(tn) !cov(X''(tn),X(t1)) - BIG(tn ,tn+2) = R2(1) !cov(X''(tn),X(tn)) - BIG(tn ,tn+3) =-R3(tn) !cov(X''(tn),X'(t1)) - BIG(tn ,tn+4) = 0.d0 !cov(X''(tn),X'(tn)) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - BIG(i,j)=tmp - enddo - enddo - RETURN - END SUBROUTINE COV_INPUT - - - END PROGRAM sp2mM1 - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/bounds/cov2tccpdfb.f b/wafo/source/cov2XXXpdf/bounds/cov2tccpdfb.f deleted file mode 100644 index 9f77d29..0000000 --- a/wafo/source/cov2XXXpdf/bounds/cov2tccpdfb.f +++ /dev/null @@ -1,504 +0,0 @@ - PROGRAM sp2tccpdf1 -C*********************************************************************** -C This program computes upper and lower bounds for the: * -C * -C density of T= T_1+T_2 in a gaussian process i.e. * -C * -C wavelengthes for crests

h2 * -C * -C Sylvie and Igor 7 dec. 1999 * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - & NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansrup - double precision, dimension(:,:),allocatable :: ansrlo - double precision, dimension(: ),allocatable :: ex,CY1,CY2 - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(:,:),allocatable ::fxind - double precision, dimension(: ),allocatable :: h1,h2 - double precision, dimension(: ),allocatable :: hh1,hh2 - double precision, dimension(: ),allocatable :: R0,R1,R2 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Ntime,N0,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2 - integer :: icy,icy2 - double precision :: ds,dT ! lag spacing for covariances -! DIGITAL: -! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf.exe rind48.f sp2tthpdf.f -! SOLARIS: -!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind48.f sp2tthpdf.f - - !print *,'enter sp2thpdf' - CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - - !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT - !Nx1=1 - !Nx2=1 - - Nx=Nx1*Nx2 - !print *,'NN',Nx1,Nx2,Nx - - - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - - allocate(h1(1:Nx1)) - allocate(h2(1:Nx2)) - CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2) - - - allocate(hh1(1:Nx)) - allocate(hh2(1:Nx)) - !h transformation - do icy=1,Nx1 - do icy2=1,Nx2 - hh1((icy-1)*Nx2+icy2)=h1(icy); - hh2((icy-1)*Nx2+icy2)=h2(icy2); - enddo - enddo - - Nj=0 - indI(1)=0 - -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - !h1(1)=XtInf - !h2(1)=XtInf - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - allocate(CY1(1:Nx)) - allocate(CY2(1:Nx)) - do icy=1,Nx - CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi)) - CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi)) - enddo - !print *,CY1 - allocate(ansrup(1:Ntime,1:Nx)) - allocate(ansrlo(1:Ntime,1:Nx)) - ansrup=0.d0 - ansrlo=0.d0 - allocate(fxind(1:Nx,1:2)) - !fxind=0.d0 this is not needed - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !! -! = [Xt Xd Xc] !! -! !! -! Nt=tn-2, Nd=3, Nc=2+3 !! -! !! -! Xt= contains Nt time points in the indicator function !! -! Xd= " Nd derivatives !! -! Xc= " Nc variables to condition on !! -! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd !! -! !! -! There are 6 ( NI=7) regions with constant bariers: !! -! (indI(1)=0); for i\in (indI(1),indI(2)] u0 (deriv. X'(t1)) !! -! (indI(6)=Nt+2); for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn)) !! -! (indI(7)=Nt+3); NI=7. !! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - - NI=7; Nd=3 - Nc=5; Mb=3 - allocate(a_up(1:Mb,1:(NI-1))) - allocate(a_lo(1:Mb,1:(NI-1))) - a_up=0.d0 - a_lo=0.d0 - allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) - ALLOCATE(xc(1:Nc,1:Nx)) - allocate(ex(1:(Ntime+Nc+1))) - !print *,size(ex),Ntime - ex=0.d0 - !print *,size(ex),ex - xc(1,1:Nx)=hh1(1:Nx) - xc(2,1:Nx)=hh2(1:Nx) - xc(3,1:Nx)=u - xc(4,1:Nx)=u - xc(5,1:Nx)=u - ! upp- down- upp-crossings at t1,ts,tn - - a_lo(1,1)=u - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(1,3)=u - - - a_lo(1,4)=-XdInf - a_up(1,5)= XdInf - a_up(1,6)= XdInf - - a_up(2,1)=1.d0 - a_lo(3,3)=1.d0 !signe a voir!!!!!! -! print *,a_up -! print *,a_lo - do tn=N0,Ntime,1 -! do tn=Ntime,Ntime,1 - Ntd=tn+1 - Nt=Ntd-Nd - Ntdc=Ntd+Nc - indI(4)=Nt - indI(5)=Nt+1 - indI(6)=Nt+2 - indI(7)=Ntd - if (SCIS.gt.0) then - if (SCIS.EQ.2) then - Nj=max(Nt,0) - else - Nj=min(max(Nt-5, 0),0) - endif - endif - do ts=3,tn-2 - !print *,'ts,tn' ,ts,tn,Ntdc - CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period - indI(2)=ts-2 - indI(3)=ts-1 - - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - - ds=dt - do icy=1,Nx - ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2) - ansrup(tn,icy)=ansrup(tn,icy)+fxind(icy,1)*CC*ds - & /(CY1(icy)*CY2(icy)) - ansrlo(tn,icy)=ansrlo(tn,icy)+fxind(icy,2)*CC*ds - & /(CY1(icy)*CY2(icy)) - enddo - enddo ! ts - print *,'Ready: ',tn,' of ',Ntime - - enddo !tn - - 300 open (unit=11, file='dens.out', STATUS='unknown') - - do ts=1,Ntime - do ph=1,Nx - !write(11,*) ansrup(ts,ph),ansrlo(ts,ph) - write(11,111) ansrup(ts,ph),ansrlo(ts,ph) - enddo - enddo - 111 FORMAT(2x,F12.8,2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansrup) - deallocate(ansrlo) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - deallocate(h1) - deallocate(h2) - deallocate(hh1) - deallocate(hh2) - deallocate(a_up) - deallocate(a_lo) - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - IMPLICIT NONE - integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1 - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) Ntime - READ (14,*) N0 - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - - - READ (14,*) Nx1,Nx2 - READ (14,*) dT - if (Ntime.lt.5) then - print *,'The number of wavelength points is too small, stop' - stop - end if - - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h1,h2 - integer, intent(in) :: Nx1,Nx2 - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx1 - READ (4,*) H1(ix) - enddo - do ix=1,Nx2 - READ (4,*) H2(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - integer ,intent(in) :: tn,ts - integer :: i,j,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! -! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| -! = [Xt Xd Xc] -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - Ntd1=tn+1 - N=Ntd1+Nc - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1) = 0.d0 !cov(X(ti+1),Y1) - BIG(i ,Ntd1+2) = 0.d0 !cov(X(ti+1),Y2) - BIG(i ,Ntd1+4) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+5) = R0(i+1) !cov(X(t.. ),X(tn)) - - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X'(t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X'(tn)) - enddo -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - BIG(Ntd1-2,Ntd1-1) = -R2(ts) !cov(X'(ts),X'(t1)) - BIG(Ntd1-2,Ntd1-2) = -R2(1) - BIG(Ntd1-2,Ntd1 ) = -R2(tn+1-ts) !cov(X'(ts),X'(tn)) - -!cov(Xc) - BIG(Ntd1+1,Ntd1+1) = 100.d0 ! cov(Y1 Y1) - BIG(Ntd1+1,Ntd1+2) = 0.d0 ! cov(Y1 Y2) - BIG(Ntd1+1,Ntd1+3) = 0.d0 ! cov(Y1 X(ts)) - BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(Y1 X(t1)) - BIG(Ntd1+1,Ntd1+5) = 0.d0 ! cov(Y1 X(tn)) - BIG(Ntd1+2,Ntd1+2) = 100.d0 ! cov(Y2 Y2) - BIG(Ntd1+2,Ntd1+3) = 0.d0 ! cov(Y2 X(ts)) - BIG(Ntd1+2,Ntd1+4) = 0.d0 ! cov(Y2 X(t1)) - BIG(Ntd1+2,Ntd1+5) = 0.d0 ! cov(Y2 X(tn)) - - BIG(Ntd1+3,Ntd1+3) = R0(1) ! cov(X(ts),X (ts) - BIG(Ntd1+3,Ntd1+4) = R0(ts) ! cov(X(ts),X (t1)) - BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts) ! cov(X(ts),X (tn)) - BIG(Ntd1+4,Ntd1+4) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+4,Ntd1+5) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+5,Ntd1+5) = R0(1) ! cov(X(tn),X (tn)) - - -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1) = 0.d0 !cov(X'(tn),Y1) - BIG(Ntd1 ,Ntd1+2) = 0.d0 !cov(X'(tn),Y2) - BIG(Ntd1-1 ,Ntd1+1) = 0.d0 !cov(X'(t1),Y1) - BIG(Ntd1-1 ,Ntd1+2) = 0.d0 !cov(X'(t1),Y2) - BIG(Ntd1-2 ,Ntd1+1) = 0.d0 !cov(X'(ts),Y1) - BIG(Ntd1-2 ,Ntd1+2) = 0.d0 !cov(X'(ts),Y2) - - BIG(Ntd1 ,Ntd1+4) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+5) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+4) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+5) =-R1(tn) !cov(X'(t1),X(tn)) - BIG(Ntd1 ,Ntd1+3) = R1(tn+1-ts) !cov(X'(tn),X (ts)) - BIG(Ntd1-1,Ntd1+3) =-R1(ts) !cov(X'(t1),X (ts)) - BIG(Ntd1-2,Ntd1+3) = 0.d0 !cov(X'(ts),X (ts) - BIG(Ntd1-2,Ntd1+4) = R1(ts) !cov(X'(ts),X (t1)) - BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts) !cov(X'(ts),X (tn)) - - - do i=1,tn-2 - j=abs(i+1-ts) -!cov(Xt,Xc) - BIG(i,Ntd1+3) = R0(j+1) !cov(X(ti+1),X(ts)) -!Cov(Xt,Xd) - if ((i+1-ts).lt.0) then - BIG(i,Ntd1-2) = R1(j+1) - else !cov(X(ti+1),X'(ts)) - BIG(i,Ntd1-2) = -R1(j+1) - endif - enddo - -! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - - BIG(i,j)=tmp - enddo - enddo - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2tccpdf1 - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/bounds/cov2tthpdfb.f b/wafo/source/cov2XXXpdf/bounds/cov2tthpdfb.f deleted file mode 100644 index c925525..0000000 --- a/wafo/source/cov2XXXpdf/bounds/cov2tthpdfb.f +++ /dev/null @@ -1,497 +0,0 @@ - PROGRAM sp2tthpdf1 -C*********************************************************************** -C This program computes: * -C * -C density of T= T_1+T_2 in a gaussian process i.e. * -C * -C wavelengthes for crests

h2 * -C * -C Sylvie and Igor 7 dec. 1999 * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - & NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex,CY1,CY2 - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h1,h2 - double precision, dimension(: ),allocatable :: hh1,hh2 - double precision, dimension(: ),allocatable :: R0,R1,R2 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Ntime,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2,N0 - integer :: icy,icy2 - double precision :: ds,dT ! lag spacing for covariances -! DIGITAL: -! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf1.exe rind49.f sp2tthpdf1.f -! SOLARIS: -!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind49.f sp2tthpdf1.f - - !print *,'enter sp2thpdf' - CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - - !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT - !Nx1=1 - !Nx2=1 - - Nx=Nx1*Nx2 - !print *,'NN',Nx1,Nx2,Nx - - - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - - allocate(h1(1:Nx1)) - allocate(h2(1:Nx2)) - CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2) - - - allocate(hh1(1:Nx)) - allocate(hh2(1:Nx)) - !h transformation - do icy=1,Nx1 - do icy2=1,Nx2 - hh1((icy-1)*Nx2+icy2)=h1(icy); - hh2((icy-1)*Nx2+icy2)=h2(icy2); - enddo - enddo - - Nj=0 - indI(1)=0 - -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - !h1(1)=XtInf - !h2(1)=XtInf - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - allocate(CY1(1:Nx)) - allocate(CY2(1:Nx)) - do icy=1,Nx - CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi)) - CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi)) - enddo - !print *,CY1 - allocate(ansr(1:Ntime,1:Nx)) - ansr=0.d0 - allocate(fxind(1:Nx)) - fxind=0.d0 - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !! -! = [Xt Xd Xc] !! -! !! -! Nt=tn-2, Nd=3, Nc=2+3 !! -! !! -! Xt= contains Nt time points in the indicator function !! -! Xd= " Nd derivatives !! -! Xc= " Nc variables to condition on !! -! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd !! -! !! -! There are 6 ( NI=7) regions with constant bariers: !! -! (indI(1)=0); for i\in (indI(1),indI(2)] u0 (deriv. X'(t1)) !! -! (indI(6)=Nt+2); for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn)) !! -! (indI(7)=Nt+3); NI=7. !! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - - NI=7; Nd=3 - Nc=5; Mb=3 - allocate(a_up(1:Mb,1:(NI-1))) - allocate(a_lo(1:Mb,1:(NI-1))) - a_up=0.d0 - a_lo=0.d0 - allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) - ALLOCATE(xc(1:Nc,1:Nx)) - allocate(ex(1:(Ntime+Nc+1))) - !print *,size(ex),Ntime - ex=0.d0 - !print *,size(ex),ex - xc(1,1:Nx)=hh1(1:Nx) - xc(2,1:Nx)=hh2(1:Nx) - xc(3,1:Nx)=u - xc(4,1:Nx)=u - xc(5,1:Nx)=u - ! upp- down- upp-crossings at t1,ts,tn - - a_lo(1,1)=u - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(1,3)=u - - - a_lo(1,4)=-XdInf - a_up(1,5)= XdInf - a_up(1,6)= XdInf - - a_up(2,1)=1.d0 - a_lo(3,3)=1.d0 !signe a voir!!!!!! -! print *,a_up -! print *,a_lo - do tn=N0,Ntime,1 -! do tn=Ntime,Ntime,1 - Ntd=tn+1 - Nt=Ntd-Nd - Ntdc=Ntd+Nc - indI(4)=Nt - indI(5)=Nt+1 - indI(6)=Nt+2 - indI(7)=Ntd - if (SCIS.gt.0) then - if (SCIS.EQ.2) then - Nj=max(Nt,0) - else - Nj=min(max(Nt-5, 0),0) - endif - endif - do ts=3,tn-2 - !print *,'ts,tn' ,ts,tn,Ntdc - CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period - indI(2)=ts-2 - indI(3)=ts-1 - - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - - ds=dt - do icy=1,Nx - ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2) - ansr(tn,icy)=ansr(tn,icy)+fxind(icy)*CC*ds/(CY1(icy)*CY2(icy)) - enddo - enddo ! ts - print *,'Ready: ',tn,' of ',Ntime - - enddo !tn - !print *,'ansr',ansr - 300 open (unit=11, file='dens.out', STATUS='unknown') - !print *, ansr - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansr(ts,ph),hh1(ph),hh2(ph) - ! write(11,111) ansr(ts,ph) - - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - deallocate(h1) - deallocate(h2) - deallocate(hh1) - deallocate(hh2) - deallocate(a_up) - deallocate(a_lo) - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - IMPLICIT NONE - integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1 - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) Ntime - READ (14,*) N0 - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - - - READ (14,*) Nx1,Nx2 - READ (14,*) dT - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h1,h2 - integer, intent(in) :: Nx1,Nx2 - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx1 - READ (4,*) H1(ix) - enddo - do ix=1,Nx2 - READ (4,*) H2(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - integer ,intent(in) :: tn,ts - integer :: i,j,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! -! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| -! = [Xt Xd Xc] -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - Ntd1=tn+1 - N=Ntd1+Nc - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1) = 0.d0 !cov(X(ti+1),Y1) - BIG(i ,Ntd1+2) = 0.d0 !cov(X(ti+1),Y2) - BIG(i ,Ntd1+4) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+5) = R0(i+1) !cov(X(t.. ),X(tn)) - - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X'(t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X'(tn)) - enddo -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - BIG(Ntd1-2,Ntd1-1) = -R2(ts) !cov(X'(ts),X'(t1)) - BIG(Ntd1-2,Ntd1-2) = -R2(1) - BIG(Ntd1-2,Ntd1 ) = -R2(tn+1-ts) !cov(X'(ts),X'(tn)) - -!cov(Xc) - BIG(Ntd1+1,Ntd1+1) = 100.d0 ! cov(Y1 Y1) - BIG(Ntd1+1,Ntd1+2) = 0.d0 ! cov(Y1 Y2) - BIG(Ntd1+1,Ntd1+3) = 0.d0 ! cov(Y1 X(ts)) - BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(Y1 X(t1)) - BIG(Ntd1+1,Ntd1+5) = 0.d0 ! cov(Y1 X(tn)) - BIG(Ntd1+2,Ntd1+2) = 100.d0 ! cov(Y2 Y2) - BIG(Ntd1+2,Ntd1+3) = 0.d0 ! cov(Y2 X(ts)) - BIG(Ntd1+2,Ntd1+4) = 0.d0 ! cov(Y2 X(t1)) - BIG(Ntd1+2,Ntd1+5) = 0.d0 ! cov(Y2 X(tn)) - - BIG(Ntd1+3,Ntd1+3) = R0(1) ! cov(X(ts),X (ts) - BIG(Ntd1+3,Ntd1+4) = R0(ts) ! cov(X(ts),X (t1)) - BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts) ! cov(X(ts),X (tn)) - BIG(Ntd1+4,Ntd1+4) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+4,Ntd1+5) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+5,Ntd1+5) = R0(1) ! cov(X(tn),X (tn)) - - -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1) = 0.d0 !cov(X'(tn),Y1) - BIG(Ntd1 ,Ntd1+2) = 0.d0 !cov(X'(tn),Y2) - BIG(Ntd1-1 ,Ntd1+1) = 0.d0 !cov(X'(t1),Y1) - BIG(Ntd1-1 ,Ntd1+2) = 0.d0 !cov(X'(t1),Y2) - BIG(Ntd1-2 ,Ntd1+1) = 0.d0 !cov(X'(ts),Y1) - BIG(Ntd1-2 ,Ntd1+2) = 0.d0 !cov(X'(ts),Y2) - - BIG(Ntd1 ,Ntd1+4) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+5) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+4) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+5) =-R1(tn) !cov(X'(t1),X(tn)) - BIG(Ntd1 ,Ntd1+3) = R1(tn+1-ts) !cov(X'(tn),X (ts)) - BIG(Ntd1-1,Ntd1+3) =-R1(ts) !cov(X'(t1),X (ts)) - BIG(Ntd1-2,Ntd1+3) = 0.d0 !cov(X'(ts),X (ts) - BIG(Ntd1-2,Ntd1+4) = R1(ts) !cov(X'(ts),X (t1)) - BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts) !cov(X'(ts),X (tn)) - - - do i=1,tn-2 - j=abs(i+1-ts) -!cov(Xt,Xc) - BIG(i,Ntd1+3) = R0(j+1) !cov(X(ti+1),X(ts)) -!Cov(Xt,Xd) - if ((i+1-ts).lt.0) then - BIG(i,Ntd1-2) = R1(j+1) - else !cov(X(ti+1),X'(ts)) - BIG(i,Ntd1-2) = -R1(j+1) - endif - enddo - -! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - - BIG(i,j)=tmp - enddo - enddo - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2tthpdf1 - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2acdf.f b/wafo/source/cov2XXXpdf/cov2acdf.f deleted file mode 100644 index 2877fec..0000000 --- a/wafo/source/cov2XXXpdf/cov2acdf.f +++ /dev/null @@ -1,445 +0,0 @@ - PROGRAM sp2Acdf -C*********************************************************************** -C This program computes: * -C * -C density of T_i, for Ac <=h, in a gaussian process i.e. * -C * -C half wavelength (up-crossing to downcrossing) for crests h * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex,CY - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size,icy - integer ::it1,it2,status - double precision :: ds,dT ! lag spacing for covariances -! f90 sp2Acdf.f rind51.f - - CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,Nx,dT) - !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - if (abs(def).GT.1) THEN - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - !CALL INIT_AMPLITUDES(h,def,Nx) - endif - allocate(h(1:Nx)) - CALL INIT_AMPLITUDES(h,def,Nx) - CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - - NI=4; Nd=2 - Nc=3; Mb=2 - - Nj=0 - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - - allocate(CY(1:Nx)) - do icy=1,Nx - CY(icy)=exp(-0.5*h(icy)*h(icy)/100)/(10*sqrt(twopi)) - enddo - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate BIG' - end if - allocate(ex(1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate ex' - end if - allocate(ansr(1:Ntime,1:Nx)) - ansr=0.d0 - allocate(fxind(1:Nx)) - fxind=0.d0 !this is not needed - allocate(xc(1:Nc,1:Nx)) - - - allocate(a_up(Mb,NI-1)) - allocate(a_lo(Mb,NI-1)) - a_up=0.d0 - a_lo=0.d0 - xc(1,1:Nx)=h(1:Nx) - xc(2,1:Nx)=u - xc(3,1:Nx)=u - - if (def.GT.0) then - a_up(1,1)=0.d0 - a_lo(1,1)=u - a_up(1,2)=XdInf - a_lo(1,3)=-XdInf - a_up(2,1)=1.d0 - else - a_up(1,1)=u - a_lo(1,1)=0.d0 - a_lo(1,2)=-XdInf - a_up(1,3)= XdInf - a_lo(2,1)=1.d0 - endif - !print *,'Nstart',Nstart - Nstart=MAX(3,Nstart) - - - if (SCIS.GT.0) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - - !print *,'loop starts' - do Ntd=Nstart,Ntime - - Ntdc=Ntd+Nc - ex=0.d0 - BIG=0.d0 - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period -C CALL ECHO(BIG(1:2,1:2)) - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - !print *,'test',fxind/CY(1:Nx) - - do icy=1,Nx - ansr(Ntd,icy)=fxind(icy)*CC/CY(icy) - enddo - if (SCIS.GT.0) then - write(11,*) COV(1) ! save coefficient of variation - endif - if((Nx.gt.4).or.NIT.gt.5) print *,'Ready: ',Ntd,' of ',Ntime - enddo - goto 300 - 300 open (unit=11, file='dens.out', STATUS='unknown') - - !print *, ansr - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansr(ts,ph) - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 continue - deallocate(BIG) - deallocate(ex) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - - if (allocated(R3)) then - deallocate(R3) - deallocate(R4) - deallocate(h) - ENDIF - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,def,Ntime,Nstart,NIT,speed,Nx,dT) - IMPLICIT NONE - integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) def - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - - if (abs(def).GT.1) then - READ (14,*) dT - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - else - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - endif - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,def,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: def - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - !if (def.LT.0) THEN - ! H=-H - !endif - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime,def - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - if (abs(def).GT.1) then - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(4,*) R3(i) - read(5,*) R4(i) - enddo - - close(4) - close(5) - endif - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,shft,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! For ts>1: -! X(t2)..X(ts),..X(tn-1) X''(ts) X'(t1) X'(tn) X(ts) X(t1) X(tn) X'(ts) -! = [Xt Xd Xc] -! -! For ts<=1: -! X(t2)..,..X(tn-1) X'(t1) X'(tn) Y X(t1) X(tn) -! = [Xt Xd Xc] -!Add Y Condition : Y=h - -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - - if (ts.LE.1) THEN - Ntd1=tn - N=Ntd1+Nc; - shft=0 ! def=1 want only crest period Tc - else - Ntd1=tn+1 - N=Ntd1+4 - shft=1 ! def=2 or 3 want Tc Ac or Tcf, Ac - endif - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1+shft) = 0.d0 !cov(X(ti+1),Y) - BIG(i ,Ntd1+2+shft) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+3+shft) = R0(i+1) !cov(X(t.. ),X(tn)) - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X' (t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X' (tn)) - enddo - !call echo(big(1:tn,1:tn),tn) -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - -!cov(Xc) - !print *,'t' - BIG(Ntd1+1+shft,Ntd1+1+shft) = 100.d0!100.d0 ! cov(Y,Y) - BIG(Ntd1+1+shft,Ntd1+2+shft) = 0.d0 - BIG(Ntd1+1+shft,Ntd1+3+shft) = 0.d0 - BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+2+shft,Ntd1+3+shft) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+3+shft,Ntd1+3+shft) = R0(1) ! cov(X(tn),X (tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1+shft) = 0.d0 !cov(X'(tn),Y) - BIG(Ntd1 ,Ntd1+2+shft) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+3+shft) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+1+shft) = 0.d0 !cov(X'(t1),Y) - BIG(Ntd1-1,Ntd1+2+shft) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+3+shft) =-R1(tn) !cov(X'(t1),X(tn)) - - - !call echo(big(1:N,1:N),N) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - BIG(i,j)=tmp - enddo - !call echo(big(1:N,1:N),N) - enddo - !if (tn.eq.3) then - !do j=1,N - ! do i=j,N - ! print *,'test',j,i,BIG(j,i) - ! enddo - !call echo(big(1:N,1:N),N) - !enddo - !endif - !call echo(big(1:N,1:N),N) - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2Acdf - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2mmpdf.f b/wafo/source/cov2XXXpdf/cov2mmpdf.f deleted file mode 100644 index 6046c5a..0000000 --- a/wafo/source/cov2XXXpdf/cov2mmpdf.f +++ /dev/null @@ -1,357 +0,0 @@ - PROGRAM cov2mmpdf -C******************************************************************************* -C This program computes joint density of maximum and the following minimum * -C******************************************************************************* - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nstart,Ntime,tn,ts,speed,seed1,seed_size - integer :: status,i,j,ij,Nx1 - double precision :: ds,dT ! lag spacing for covariances - -! f90 cov2mmpdf.f rind51.f - - CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,Nx1,dT) - Nx=Nx1*(Nx1-1)/2 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - - CALL INITDATA(speed) - - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - allocate(h(1:Nx1)) - - CALL INIT_AMPLITUDES(h,Nx1) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! Y= X'(t2)...X'(tn-1)||X''(t1) X''(tn)|| X'(t1) X'(tn) X(t1) X(tn) !! -! = [ Xt Xd Xc ] !! -! !! -! Nt=tn-2, Nd=2, Nc=4 !! -! !! -! Xt= contains Nt time points in the indicator function !! -! Xd= " Nd derivatives !! -! Xc= " Nc variables to condition on !! -! !! -! There are 3 ( NI=4) regions with constant bariers: !! -! (indI(1)=0); for i\in (indI(1),indI(2)] Y(i)<0. !! -! (indI(2)=Nt) ; for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) !! -! (indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn)) !! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - - NI=4; Nd=2 - Nc=4; Mb=1 - - Nj=0 - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(R4(1)) - XtInf=10.d0*SQRT(-R2(1)) - ! normalizing constant - CC=TWOPI*SQRT(-R2(1)/R4(1)) - - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate BIG' - end if - allocate(ex(1:Ntime+Nc),stat=status) - if (status.ne.0) then - print *,'can not allocate ex' - end if - if (Nx.gt.1) then - allocate(ansr(1:Nx1,1:Nx1)) - else - allocate(ansr(1,1:Ntime)) - end if - ansr=0.d0 - allocate(fxind(1:Nx)) - fxind=0.d0 !this is not needed - allocate(xc(1:Nc,1:Nx)) - - - allocate(a_up(Mb,NI-1)) - allocate(a_lo(Mb,NI-1)) - - a_up=0.d0 - a_lo=0.d0 - - ij=0 - do i=2,Nx1 - do j=1,i-1 - ij=ij+1 - xc(3,ij)=h(i) - xc(4,ij)=h(j) - enddo - enddo - xc(1,1:Nx)=0.d0 - xc(2,1:Nx)=0.d0 - - a_lo(1,1)=-Xtinf - a_lo(1,2)=-XdInf - a_up(1,3)=+XdInf - - - Nstart=MAX(2,Nstart) - - - if (SCIS.GT.0) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - - do Ntd=Nstart,Ntime - - Ntdc=Ntd+Nc - ex=0.d0 - BIG=0.d0 - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,R0,R1,R2,R3,R4) ! positive wave period - - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - ij=0 - if (Nx .gt. 1) then - do i=2,Nx1 - do j=1,i-1 - ij=ij+1 - ansr(i,j)=ansr(i,j)+fxind(ij)*CC*dt - enddo - enddo - else - ansr(1,Ntd)=fxind(1)*CC - end if - - if (SCIS.GT.0) then - write(11,*) COV(1) ! save coefficient of variation - endif - print *,'Ready: ',Ntd,' of ',Ntime - enddo - goto 300 - 300 open (unit=11, file='dens.out', STATUS='unknown') - if (Nx.gt.1) then - do i=1,Nx1 - do j=1,Nx1 - write(11,*) ansr(i,j) - enddo - enddo - else - do j=1,Ntime - write(11,*) ansr(1,j) - enddo - end if - close(11) - 900 continue - deallocate(BIG) - deallocate(ex) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(R0) - deallocate(R1) - deallocate(R2) - deallocate(R3) - deallocate(R4) - deallocate(h) - - if (allocated(COV) ) then - deallocate(COV) - endif - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (Ntime,Nstart,NIT,speed,Nx,dT) - IMPLICIT NONE - integer, intent(out):: Ntime,Nstart,NIT,speed,Nx - double precision ,intent(out) :: dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - READ (14,*) dT - - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - read(4,*) R3(i) - read(5,*) R4(i) - enddo - close(1) - close(2) - close(3) - close(3) - close(5) - return - END SUBROUTINE INIT_COVARIANCES - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn - integer :: i,j,N - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn) -! = [ Xt | Xd | Xc ] -! -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - N=tn+4 - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,tn+3) = R1(i+1) !cov(X'(ti+1),X(t1)) - BIG(tn-1-i ,tn+4) = -R1(i+1) !cov(X'(ti+1),X(tn)) - BIG(i ,tn+1) = -R2(i+1) !cov(X'(ti+1),X'(t1)) - BIG(tn-1-i ,tn+2) = -R2(i+1) !cov(X'(ti+1),X'(tn)) - !Cov(Xt,Xd) - BIG(i,tn-1) = R3(i+1) !cov(X'(ti+1),X''(t1)) - BIG(tn-1-i,tn) =-R3(i+1) !cov(X'(ti+1),X''(tn)) - enddo - -!cov(Xd) - BIG(tn-1 ,tn-1 ) = R4(1) - BIG(tn-1,tn ) = R4(tn) !cov(X''(t1),X''(tn)) - BIG(tn ,tn ) = R4(1) - -!cov(Xc) - BIG(tn+3,tn+3) = R0(1) ! cov(X(t1),X(t1)) - BIG(tn+3,tn+4) = R0(tn) ! cov(X(t1),X(tn)) - BIG(tn+1,tn+3) = 0.d0 ! cov(X(t1),X'(t1)) - BIG(tn+2,tn+3) = R1(tn) ! cov(X(t1),X'(tn)) - BIG(tn+4,tn+4) = R0(1) ! cov(X(tn),X(tn)) - BIG(tn+1,tn+4) =-R1(tn) ! cov(X(tn),X'(t1)) - BIG(tn+2,tn+4) = 0.d0 ! cov(X(tn),X'(tn)) - BIG(tn+1,tn+1) =-R2(1) ! cov(X'(t1),X'(t1)) - BIG(tn+1,tn+2) =-R2(tn) ! cov(X'(t1),X'(tn)) - BIG(tn+2,tn+2) =-R2(1) ! cov(X'(tn),X'(tn)) -!Xc=X(t1),X(tn),X'(t1),X'(tn) -!Xd=X''(t1),X''(tn) -!cov(Xd,Xc) - BIG(tn-1 ,tn+3) = R2(1) !cov(X''(t1),X(t1)) - BIG(tn-1 ,tn+4) = R2(tn) !cov(X''(t1),X(tn)) - BIG(tn-1 ,tn+1) = 0.d0 !cov(X''(t1),X'(t1)) - BIG(tn-1 ,tn+2) = R3(tn) !cov(X''(t1),X'(tn)) - BIG(tn ,tn+3) = R2(tn) !cov(X''(tn),X(t1)) - BIG(tn ,tn+4) = R2(1) !cov(X''(tn),X(tn)) - BIG(tn ,tn+1) =-R3(tn) !cov(X''(tn),X'(t1)) - BIG(tn ,tn+2) = 0.d0 !cov(X''(tn),X'(tn)) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - BIG(i,j)=tmp - enddo - enddo - RETURN - END SUBROUTINE COV_INPUT - - - END PROGRAM cov2mmpdf - \ No newline at end of file diff --git a/wafo/source/cov2XXXpdf/cov2mmtpdf.f b/wafo/source/cov2XXXpdf/cov2mmtpdf.f deleted file mode 100644 index 6cf7c9a..0000000 --- a/wafo/source/cov2XXXpdf/cov2mmtpdf.f +++ /dev/null @@ -1,769 +0,0 @@ - PROGRAM sp2mmt -C******************************************************************************* -C This program computes joint density of the maximum and the following * -C minimum or level u separated maxima and minima + period/wavelength * -C******************************************************************************* - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:), allocatable :: BIG - double precision, dimension(:,:,:),allocatable :: ansr - double precision, dimension(: ), allocatable :: ex - double precision, dimension(:,:), allocatable :: xc - double precision, dimension(: ), allocatable :: fxind,h - double precision, dimension(: ), allocatable :: R0,R1,R2,R3,R4 - double precision :: CC,U,XdInf,XtInf - double precision, dimension(1,4) :: a_up,a_lo ! size Mb X NI-1 - integer , dimension(: ), allocatable :: seed - integer ,dimension(5) :: indI = 0 ! length NI - integer :: Nstart,Ntime,ts,tn,speed,seed1,seed_size - integer :: status,i,j,ij,Nx0,Nx1,DEF,isOdd !,TMP - LOGICAL :: SYMMETRY=.FALSE. - double precision :: dT ! lag spacing for covariances - -! f90 -gline -fieee -Nl126 -C -o intmodule.f rind60.f sp2mmt.f - - CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,SCIS,SEED1,Nx1,dT,u,def) - CALL INITDATA(speed) - - if (SCIS.GT.0) then - !allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - if (ALLOCATED(COV)) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - endif - - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - - Nx0 = Nx1 ! just plain Mm - IF (def.GT.1) Nx0=2*Nx1 ! level v separated max2min densities wanted - - - allocate(h(1:Nx0)) - - CALL INIT_AMPLITUDES(h,Nx0) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) -! For DEF = 0,1 : (Maxima, Minima and period/wavelength) -! = 2,3 : (Level v separated Maxima and Minima and period/wavelength between them) -! If Nx==1 then the conditional density for period/wavelength between Maxima and Minima -! given the Max and Min is returned -!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -! Y= X'(t2)..X'(ts)..X'(tn-1)||X''(t1) X''(tn)|| X'(t1) X'(tn) X(t1) X(tn) -! = [ Xt Xd Xc ] -! -! Nt = tn-2, Nd = 2, Nc = 4 -! -! Xt= contains Nt time points in the indicator function -! Xd= " Nd derivatives in Jacobian -! Xc= " Nc variables to condition on -! -! There are 3 (NI=4) regions with constant barriers: -! (indI(1)=0); for i\in (indI(1),indI(2)] Y(i)<0. -! (indI(2)=Nt) ; for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) -! (indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn)) -! -! -! For DEF = 4,5 (Level v separated Maxima and Minima and period/wavelength from Max to crossing) -! If Nx==1 then the conditional joint density for period/wavelength between Maxima, Minima and Max to -! level v crossing given the Max and the min is returned -!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -! Y= X'(t2)..X'(ts)..X'(tn-1)||X''(t1) X''(tn) X'(ts)|| X'(t1) X'(tn) X(t1) X(tn) X(ts) -! = [ Xt Xd Xc ] -! -! Nt = tn-2, Nd = 3, Nc = 5 -! -! Xt= contains Nt time points in the indicator function -! Xd= " Nd derivatives -! Xc= " Nc variables to condition on -! -! There are 4 (NI=5) regions with constant barriers: -! (indI(1)=0); for i\in (indI(1),indI(2)] Y(i)<0. -! (indI(2)=Nt) ; for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) -! (indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn)) -! (indI(4)=Nt+2); for i\in (indI(4)+1,indI(5)], Y(i)<0 (deriv. X'(ts)) -! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! -!Revised pab 22.04.2000 -! - added mean separated min/max + (Tdm, TMd) period distributions -! - added scis - - -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf = 10.d0*SQRT(R4(1)) - XtInf = 10.d0*SQRT(-R2(1)) - - Nc = 4 - NI=4; Nd=2; - Mb=1 ; - Nj = 0 - indI(1) = 0 - Nstart=MAX(2,Nstart) - - isOdd = MOD(Nx1,2) - IF (def.LE.1) THEN ! just plain Mm - Nx = Nx1*(Nx1-1)/2 - IJ = (Nx1+isOdd)/2 - IF (H(1)+H(Nx1).EQ.0.AND. - & (H(IJ).EQ.0.OR.H(IJ)+H(IJ+1).EQ.0) ) THEN - SYMMETRY=.FALSE. - PRINT *,' Integration region symmetric' - ! May save Nx1-isOdd integrations in each time step - ! This is not implemented yet. - !Nx = Nx1*(Nx1-1)/2-Nx1+isOdd - ENDIF - - CC = TWOPI*SQRT(-R2(1)/R4(1)) ! normalizing constant = 1/ expected number of zero-up-crossings of X' - - ELSE ! level u separated Mm - Nx = (Nx1-1)*(Nx1-1) - IF ( ABS(u).LE.1D-8.AND.H(1)+H(Nx1+1).EQ.0.AND. - & (H(Nx1)+H(2*Nx1).EQ.0) ) THEN - SYMMETRY=.FALSE. - PRINT *,' Integration region symmetric' - ! Not implemented for DEF <= 3 - !IF (DEF.LE.3) Nx = (Nx1-1)*(Nx1-2)/2 - ENDIF - - IF (DEF.GT.3) THEN - Nstart = MAX(Nstart,3) - Nc = 5 - NI=5; Nd=3; - ENDIF - CC = TWOPI*SQRT(-R0(1)/R2(1))*exp(0.5D0*u*u/R0(1)) ! normalizing constant= 1/ expected number of u-up-crossings of X - ENDIF - - !print *,'def',def - IF (Nx.GT.1) THEN - IF ((DEF.EQ.0.OR.DEF.EQ.2)) THEN ! (M,m) or (M,m)v distribution wanted - allocate(ansr(Nx1,Nx1,1),stat=status) - ELSE ! (M,m,TMm), (M,m,TMm)v (M,m,TMd)v or (M,M,Tdm)v distributions wanted - allocate(ansr(Nx1,Nx1,Ntime),stat=status) - ENDIF - ELSEIF (DEF.GT.3) THEN ! Conditional distribution for (TMd,TMm)v or (Tdm,TMm)v given (M,m) wanted - allocate(ansr(1,Ntime,Ntime),stat=status) - ELSE ! Conditional distribution for (TMm) or (TMm)v given (M,m) wanted - allocate(ansr(1,1,Ntime),stat=status) - ENDIF - if (status.ne.0) print *,'can not allocate ansr' - allocate(BIG(Ntime+Nc+1,Ntime+Nc+1),stat=status) - if (status.ne.0) print *,'can not allocate BIG' - allocate(ex(1:Ntime+Nc+1),stat=status) - if (status.ne.0) print *,'can not allocate ex' - allocate(fxind(Nx),xc(Nc,Nx)) - - -! Initialization -!~~~~~~~~~~~~~~~~~ - - BIG = 0.d0 - ex = 0.d0 - ansr = 0.d0 - a_up = 0.d0 - a_lo = 0.d0 - - xc(:,:) = 0.d0 - !xc(:,1:Nx) = 0.d0 - !xc(2,1:Nx) = 0.d0 - - a_lo(1,1) = -Xtinf - a_lo(1,2) = -XdInf - a_up(1,3) = +XdInf - a_lo(1,4) = -Xtinf - ij = 0 - IF (DEF.LE.1) THEN ! Max2min and period/wavelength - do I=2,Nx1 - J = IJ+I-1 - xc(3,IJ+1:J) = h(I) - xc(4,IJ+1:J) = h(1:I-1) - IJ = J - enddo - ELSE - ! Level u separated Max2min - xc(Nc,:) = u - ! H(1) = H(Nx1+1)= u => start do loop at I=2 since by definition we must have: minimum u - xc(4,IJ+1:J) = h(Nx1+2:2*Nx1) ! Min < u - IJ = J - enddo - - !CALL ECHO(transpose(xc(3:5,:))) - if (DEF.GT.3) GOTO 200 - ENDIF - do Ntd = Nstart,Ntime - !Ntd=tn - Ntdc = Ntd+Nc - Nt = Ntd-Nd; - indI(2) = Nt; - indI(3) = Nt+1; - indI(4) = Ntd; - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,0,R0,R1,R2,R3,R4) ! positive wave period - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - IF (Nx.LT.2) THEN -! Density of TMm given the Max and the Min. Note that the density is not scaled to unity - ansr(1,1,Ntd) = fxind(1)*CC - GOTO 100 - ENDIF - IJ = 0 - SELECT CASE (DEF) - CASE(:0) -! joint density of (M,m) -!~~~~~~~~~~~~~~~~~~~~~~~~ - do i = 2, Nx1 - J = IJ+i-1 - ansr(1:i-1,i,1) = ansr(1:i-1,i,1)+fxind(ij+1:J)*CC*dt - IJ=J - enddo - CASE (1) -! joint density of (M,m,TMm) - do i = 2, Nx1 - J = IJ+i-1 - ansr(1:i-1,i,Ntd) = fxind(ij+1:J)*CC - IJ = J - enddo - CASE (2) - ! joint density of level v separated (M,m)v - do i = 2,Nx1 - J = IJ+Nx1-1 - ansr(2:Nx1,i,1) = ansr(2:Nx1,i,1)+fxind(ij+1:J)*CC*dt - IJ = J - enddo - CASE (3:) - ! joint density of level v separated (M,m,TMm)v - do i = 2,Nx1 - J = IJ+Nx1-1 - ansr(2:Nx1,i,Ntd) = ansr(2:Nx1,i,Ntd)+fxind(ij+1:J)*CC - IJ = J - enddo - END SELECT - - 100 if (ALLOCATED(COV)) then - write(11,*) COV(:) ! save coefficient of variation - endif - print *,'Ready: ',Ntd,' of ',Ntime - enddo - - goto 800 - - 200 do tn = Nstart,Ntime - Ntd = tn+1 - Ntdc = Ntd + Nc - Nt = Ntd - Nd; - indI(2) = Nt; - indI(3) = Nt + 1; - indI(4) = Nt + 2; - indI(5) = Ntd; - !CALL COV_INPUT2(BIG(1:Ntdc,1:Ntdc),tn,-2,R0,R1,R2,R3,R4) ! positive wave period - IF (SYMMETRY) GOTO 300 - - do ts = 2,tn-1 - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period - !print *,'Big=' - !CALL ECHO(BIG(1:Ntdc,1:MIN(Ntdc,10))) - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - - SELECT CASE (def) - CASE (:4) - IF (Nx.EQ.1) THEN -! Joint density (TMd,TMm) given the Max and the min. Note the density is not scaled to unity - ansr(1,ts,tn) = fxind(1)*CC - - ELSE -! 4, gives level u separated Max2min and wave period from Max to the crossing of level u (M,m,TMd). - ij = 0 - do i = 2,Nx1 - J = IJ+Nx1-1 - ansr(2:Nx1,i,ts) = ansr(2:Nx1,i,ts)+ - & fxind(ij+1:J)*CC*dt - IJ = J - enddo - ENDIF - CASE (5:) - IF (Nx.EQ.1) THEN -! Joint density (Tdm,TMm) given the Max and the min. Note the density is not scaled to unity - ansr(1,tn-ts+1,tn) = fxind(1)*CC - ELSE - -! 5, gives level u separated Max2min and wave period from the crossing of level u to the min (M,m,Tdm). - ij = 0 - do i = 2,Nx1 - J = IJ+Nx1-1 - ansr(2:Nx1,i,tn-ts+1)=ansr(2:Nx1,i,tn-ts+1)+ - & fxind(ij+1:J)*CC*dt - IJ = J - enddo - ENDIF - END SELECT - if (ALLOCATED(COV)) then - write(11,*) COV(:) ! save coefficient of variation - endif - enddo - GOTO 400 - 300 do ts = 2,FLOOR(DBLE(Ntd)/2.d0) ! Using the symmetry since U = 0 and the transformation is linear - CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period - !print *,'Big=' - !CALL ECHO(BIG(1:Ntdc,1:Ntdc)) - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) - IF (Nx.EQ.1) THEN -! Joint density of (TMd,TMm),(Tdm,TMm) given the max and the min. Note that the density is not scaled to unity - ansr(1,ts,tn) = fxind(1)*CC - IF (ts.LT.tn-ts+1) THEN - ansr(1,tn-ts+1,tn) = fxind(1)*CC - ENDIF - GOTO 350 - ENDIF - IJ = 0 - SELECT CASE (def) - CASE (:4) - -! 4, gives level u separated Max2min and wave period from Max to the crossing of level u (M,m,TMd). - do i = 2,Nx1 - j = ij+Nx1-1 - ansr(2:Nx1,i,ts) = ansr(2:Nx1,i,ts)+ - & fxind(ij+1:J)*CC*dt - IF (ts.LT.tn-ts+1) THEN - ansr(i,2:Nx1,tn-ts+1) = - & ansr(i,2:Nx1,tn-ts+1)+fxind(ij+1:J)*CC*dt ! exploiting the symmetry - ENDIF - IJ = J - enddo - CASE (5:) -! 5, gives level u separated Max2min and wave period from the crossing of level u to min (M,m,Tdm). - do i = 2,Nx1 - J = IJ+Nx1-1 - - ansr(2:Nx1,i,tn-ts+1)=ansr(2:Nx1,i,tn-ts+1)+ - & fxind(ij+1:J)*CC*dt - IF (ts.LT.tn-ts+1) THEN - ansr(i,2:Nx1,ts) = ansr(i,2:Nx1,ts)+ - & fxind(ij+1:J)*CC*dt ! exploiting the symmetry - ENDIF - IJ = J - enddo - END SELECT - 350 enddo - 400 print *,'Ready: ',tn,' of ',Ntime - enddo - - - - - 800 open (unit=11, file='dens.out', STATUS='unknown') - !print *,'ans, IJ,def', shape(ansr),IJ,DEF - if (Nx.GT.1) THEN - ij = 1 - IF (DEF.GT.2.OR.DEF.EQ.1) IJ = Ntime - !print *,'ans, IJ,def', size(ansr),IJ,DEF - do ts = 1,ij - do j=1,Nx1 - do i=1,Nx1 - write(11,*) ansr(i,j,ts) - enddo - enddo - enddo - ELSE - ij = 1 - IF (DEF.GT.3) IJ = Ntime - !print *,'ans, IJ,def', size(ansr),IJ,DEF - do ts = 1,Ntime - do j = 1,ij - write(11,*) ansr(1,j,ts) - enddo - enddo - ENDIF - close(11) - 900 continue - deallocate(BIG) - deallocate(ex) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(R0) - deallocate(R1) - deallocate(R2) - deallocate(R3) - deallocate(R4) - deallocate(h) - - if (allocated(COV) ) then - deallocate(COV) - endif - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (Ntime,Nstart,NIT,speed,SCIS,SEED1,Nx,dT,u,def) - IMPLICIT NONE - integer, intent(out):: Ntime,Nstart,NIT,speed,Nx,DEF,SCIS,SEED1 - double precision ,intent(out) :: dT,U - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - READ (14,*) dT - READ (14,*) U - READ (14,*) DEF - - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - read(4,*) R3(i) - read(5,*) R4(i) - enddo - close(1) - close(2) - close(3) - close(3) - close(5) - return - END SUBROUTINE INIT_COVARIANCES - -C********************************************************************** - - SUBROUTINE COV_INPUT2(BIG,tn,ts,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,N,shft -! the order of the variables in the covariance matrix -! are organized as follows: -! for ts <= 1: -! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn) -! = [ Xt | Xd | Xc ] -! -! for ts > =2: -! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn) X(ts) -! = [ Xt | Xd | Xc ] -! -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - if (ts.GT.1) THEN - ! Assumption: a previous call to covinput has been made - ! need only to update the last row and column of big: - N=tn+5 - !Cov(Xt,Xc) - do i=1,tn-2 - j=abs(i+1-ts) - BIG(i,N) = -sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X'(ti+1),X(ts)) - enddo - !Cov(Xc) - BIG(N ,N) = R0(1) ! cov(X(ts),X(ts)) - BIG(tn+3 ,N) = R0(ts) ! cov(X(t1),X(ts)) - BIG(tn+4 ,N) = R0(tn-ts+1) ! cov(X(tn),X(ts)) - BIG(tn+1 ,N) = -R1(ts) ! cov(X'(t1),X(ts)) - BIG(tn+2 ,N) = R1(tn-ts+1) ! cov(X'(tn),X(ts)) - !Cov(Xd,Xc) - BIG(tn-1 ,N) = R2(ts) !cov(X''(t1),X(ts)) - BIG(tn ,N) = R2(tn-ts+1) !cov(X''(tn),X(ts)) - - ! make lower triangular part equal to upper - do j=1,N-1 - BIG(N,j) = BIG(j,N) - enddo - return - endif - IF (ts.LT.0) THEN - shft = 1 - N=tn+5; - ELSE - shft = 0 - N=tn+4; - ENDIF - - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,tn+3) = R1(i+1) !cov(X'(ti+1),X(t1)) - BIG(tn-1-i ,tn+4) = -R1(i+1) !cov(X'(ti+1),X(tn)) - BIG(i ,tn+1) = -R2(i+1) !cov(X'(ti+1),X'(t1)) - BIG(tn-1-i ,tn+2) = -R2(i+1) !cov(X'(ti+1),X'(tn)) - !Cov(Xt,Xd) - BIG(i,tn-1) = R3(i+1) !cov(X'(ti+1),X''(t1)) - BIG(tn-1-i,tn) =-R3(i+1) !cov(X'(ti+1),X''(tn)) - enddo - -!cov(Xd) - BIG(tn-1 ,tn-1 ) = R4(1) - BIG(tn-1 ,tn ) = R4(tn) !cov(X''(t1),X''(tn)) - BIG(tn ,tn ) = R4(1) - -!cov(Xc) - BIG(tn+3 ,tn+3) = R0(1) ! cov(X(t1),X(t1)) - BIG(tn+3 ,tn+4) = R0(tn) ! cov(X(t1),X(tn)) - BIG(tn+1 ,tn+3) = 0.d0 ! cov(X(t1),X'(t1)) - BIG(tn+2 ,tn+3) = R1(tn) ! cov(X(t1),X'(tn)) - BIG(tn+4 ,tn+4) = R0(1) ! cov(X(tn),X(tn)) - BIG(tn+1 ,tn+4) =-R1(tn) ! cov(X(tn),X'(t1)) - BIG(tn+2 ,tn+4) = 0.d0 ! cov(X(tn),X'(tn)) - BIG(tn+1 ,tn+1) =-R2(1) ! cov(X'(t1),X'(t1)) - BIG(tn+1 ,tn+2) =-R2(tn) ! cov(X'(t1),X'(tn)) - BIG(tn+2 ,tn+2) =-R2(1) ! cov(X'(tn),X'(tn)) -!Xc=X(t1),X(tn),X'(t1),X'(tn) -!Xd=X''(t1),X''(tn) -!cov(Xd,Xc) - BIG(tn-1 ,tn+3) = R2(1) !cov(X''(t1),X(t1)) - BIG(tn-1 ,tn+4) = R2(tn) !cov(X''(t1),X(tn)) - BIG(tn-1 ,tn+1) = 0.d0 !cov(X''(t1),X'(t1)) - BIG(tn-1 ,tn+2) = R3(tn) !cov(X''(t1),X'(tn)) - BIG(tn ,tn+3) = R2(tn) !cov(X''(tn),X(t1)) - BIG(tn ,tn+4) = R2(1) !cov(X''(tn),X(tn)) - BIG(tn ,tn+1) =-R3(tn) !cov(X''(tn),X'(t1)) - BIG(tn ,tn+2) = 0.d0 !cov(X''(tn),X'(tn)) - - - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - BIG(i,j) = BIG(j,i) - enddo - enddo - RETURN - END SUBROUTINE COV_INPUT2 - - SUBROUTINE COV_INPUT(BIG,tn,ts,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,N,shft, tnold = 0 -! the order of the variables in the covariance matrix -! are organized as follows: -! for ts <= 1: -! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn) -! = [ Xt | Xd | Xc ] -! -! for ts > =2: -! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(ts) X'(t1),X'(tn),X(t1),X(tn) X(ts) -! = [ Xt | Xd | Xc ] -! -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s)) = r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - SAVE tnold - - if (ts.GT.1) THEN - shft = 1 - N=tn+5+shft - !Cov(Xt,Xc) - do i=1,tn-2 - j=abs(i+1-ts) - BIG(i,N) = -sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X'(ti+1),X(ts)) - enddo - !Cov(Xc) - BIG(N ,N) = R0(1) ! cov(X(ts),X(ts)) - BIG(tn+shft+3 ,N) = R0(ts) ! cov(X(t1),X(ts)) - BIG(tn+shft+4 ,N) = R0(tn-ts+1) ! cov(X(tn),X(ts)) - BIG(tn+shft+1 ,N) = -R1(ts) ! cov(X'(t1),X(ts)) - BIG(tn+shft+2 ,N) = R1(tn-ts+1) ! cov(X'(tn),X(ts)) - !Cov(Xd,Xc) - BIG(tn-1 ,N) = R2(ts) !cov(X''(t1),X(ts)) - BIG(tn ,N) = R2(tn-ts+1) !cov(X''(tn),X(ts)) - - !ADD a level u crossing at ts - - !Cov(Xt,Xd) - do i = 1,tn-2 - j = abs(i+1-ts) - BIG(i,tn+shft) = -R2(j+1) !cov(X'(ti+1),X'(ts)) - enddo - !Cov(Xd) - BIG(tn+shft,tn+shft) = -R2(1) !cov(X'(ts),X'(ts)) - BIG(tn-1 ,tn+shft) = R3(ts) !cov(X''(t1),X'(ts)) - BIG(tn ,tn+shft) = -R3(tn-ts+1) !cov(X''(tn),X'(ts)) - - !Cov(Xd,Xc) - BIG(tn+shft ,N ) = 0.d0 !cov(X'(ts),X(ts)) - BIG(tn+shft,tn+shft+3) = R1(ts) ! cov(X'(ts),X(t1)) - BIG(tn+shft,tn+shft+4) = -R1(tn-ts+1) ! cov(X'(ts),X(tn)) - BIG(tn+shft,tn+shft+1) = -R2(ts) ! cov(X'(ts),X'(t1)) - BIG(tn+shft,tn+shft+2) = -R2(tn-ts+1) ! cov(X'(ts),X'(tn)) - - - - IF (tnold.EQ.tn) THEN ! A previous call to covinput with tn==tnold has been made - ! need only to update row and column N and tn+1 of big: - ! make lower triangular part equal to upper and then return - do j=1,tn+shft - BIG(N,j) = BIG(j,N) - BIG(tn+shft,j) = BIG(j,tn+shft) - enddo - do j=tn+shft+1,N-1 - BIG(N,j) = BIG(j,N) - BIG(j,tn+shft) = BIG(tn+shft,j) - enddo - return - ENDIF - tnold = tn - ELSE - N = tn+4 - shft = 0 - endif - - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,tn+shft+3) = R1(i+1) !cov(X'(ti+1),X(t1)) - BIG(tn-1-i ,tn+shft+4) = -R1(i+1) !cov(X'(ti+1),X(tn)) - BIG(i ,tn+shft+1) = -R2(i+1) !cov(X'(ti+1),X'(t1)) - BIG(tn-1-i ,tn+shft+2) = -R2(i+1) !cov(X'(ti+1),X'(tn)) - !Cov(Xt,Xd) - BIG(i,tn-1) = R3(i+1) !cov(X'(ti+1),X''(t1)) - BIG(tn-1-i,tn) =-R3(i+1) !cov(X'(ti+1),X''(tn)) - enddo - -!cov(Xd) - BIG(tn-1 ,tn-1 ) = R4(1) - BIG(tn-1 ,tn ) = R4(tn) !cov(X''(t1),X''(tn)) - BIG(tn ,tn ) = R4(1) - -!cov(Xc) - BIG(tn+shft+3 ,tn+shft+3) = R0(1) ! cov(X(t1),X(t1)) - BIG(tn+shft+3 ,tn+shft+4) = R0(tn) ! cov(X(t1),X(tn)) - BIG(tn+shft+1 ,tn+shft+3) = 0.d0 ! cov(X(t1),X'(t1)) - BIG(tn+shft+2 ,tn+shft+3) = R1(tn) ! cov(X(t1),X'(tn)) - BIG(tn+shft+4 ,tn+shft+4) = R0(1) ! cov(X(tn),X(tn)) - BIG(tn+shft+1 ,tn+shft+4) =-R1(tn) ! cov(X(tn),X'(t1)) - BIG(tn+shft+2 ,tn+shft+4) = 0.d0 ! cov(X(tn),X'(tn)) - BIG(tn+shft+1 ,tn+shft+1) =-R2(1) ! cov(X'(t1),X'(t1)) - BIG(tn+shft+1 ,tn+shft+2) =-R2(tn) ! cov(X'(t1),X'(tn)) - BIG(tn+shft+2 ,tn+shft+2) =-R2(1) ! cov(X'(tn),X'(tn)) -!Xc=X(t1),X(tn),X'(t1),X'(tn) -!Xd=X''(t1),X''(tn) -!cov(Xd,Xc) - BIG(tn-1 ,tn+shft+3) = R2(1) !cov(X''(t1),X(t1)) - BIG(tn-1 ,tn+shft+4) = R2(tn) !cov(X''(t1),X(tn)) - BIG(tn-1 ,tn+shft+1) = 0.d0 !cov(X''(t1),X'(t1)) - BIG(tn-1 ,tn+shft+2) = R3(tn) !cov(X''(t1),X'(tn)) - BIG(tn ,tn+shft+3) = R2(tn) !cov(X''(tn),X(t1)) - BIG(tn ,tn+shft+4) = R2(1) !cov(X''(tn),X(tn)) - BIG(tn ,tn+shft+1) =-R3(tn) !cov(X''(tn),X'(t1)) - BIG(tn ,tn+shft+2) = 0.d0 !cov(X''(tn),X'(tn)) - - - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - BIG(i,j) = BIG(j,i) - enddo - enddo - RETURN - END SUBROUTINE COV_INPUT - END PROGRAM sp2mmt - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2tccpdf.f b/wafo/source/cov2XXXpdf/cov2tccpdf.f deleted file mode 100644 index 3582432..0000000 --- a/wafo/source/cov2XXXpdf/cov2tccpdf.f +++ /dev/null @@ -1,498 +0,0 @@ - PROGRAM sp2tccpdf -C*********************************************************************** -C This program computes: * -C * -C density of T= T_1+T_2 in a gaussian process i.e. * -C * -C wavelengthes for crests

h2 * -C * -C Sylvie and Igor 7 dec. 1999 * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - & NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex,CY1,CY2 - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h1,h2 - double precision, dimension(: ),allocatable :: hh1,hh2 - double precision, dimension(: ),allocatable :: R0,R1,R2 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Ntime,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2,N0 - integer :: icy,icy2 - double precision :: ds,dT ! lag spacing for covariances -! DIGITAL: -! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf1.exe rind49.f sp2tthpdf1.f -! SOLARIS: -!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind49.f sp2tthpdf1.f - - !print *,'enter sp2thpdf' - CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - - !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT - !Nx1=1 - !Nx2=1 - - Nx=Nx1*Nx1 - !print *,'NN',Nx1,Nx2,Nx - - - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - - allocate(h1(1:Nx1)) - allocate(h2(1:Nx2)) - CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2) - - - allocate(hh1(1:Nx)) - allocate(hh2(1:Nx)) - !h transformation - do icy=1,Nx1 - do icy2=1,Nx2 - hh1((icy-1)*Nx2+icy2)=h1(icy); - hh2((icy-1)*Nx2+icy2)=h2(icy2); - enddo - enddo - - Nj=0 - indI(1)=0 - -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - !h1(1)=XtInf - !h2(1)=XtInf - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - allocate(CY1(1:Nx)) - allocate(CY2(1:Nx)) - do icy=1,Nx - CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi)) - CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi)) - enddo - !print *,CY1 - allocate(ansr(1:Ntime,1:Nx)) - ansr=0.d0 - allocate(fxind(1:Nx)) - fxind=0.d0 - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !! -! = [Xt Xd Xc] !! -! !! -! Nt=tn-2, Nd=3, Nc=2+3 !! -! !! -! Xt= contains Nt time points in the indicator function !! -! Xd= " Nd derivatives !! -! Xc= " Nc variables to condition on !! -! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd !! -! !! -! There are 6 ( NI=7) regions with constant bariers: !! -! (indI(1)=0); for i\in (indI(1),indI(2)] u0 (deriv. X'(t1)) !! -! (indI(6)=Nt+2); for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn)) !! -! (indI(7)=Nt+3); NI=7. !! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - - NI=7; Nd=3 - Nc=5; Mb=3 - allocate(a_up(1:Mb,1:(NI-1))) - allocate(a_lo(1:Mb,1:(NI-1))) - a_up=0.d0 - a_lo=0.d0 - allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) - ALLOCATE(xc(1:Nc,1:Nx)) - allocate(ex(1:(Ntime+Nc+1))) - !print *,size(ex),Ntime - ex=0.d0 - !print *,size(ex),ex - xc(1,1:Nx)=hh1(1:Nx) - xc(2,1:Nx)=hh2(1:Nx) - xc(3,1:Nx)=u - xc(4,1:Nx)=u - xc(5,1:Nx)=u - ! upp- down- upp-crossings at t1,ts,tn - - a_lo(1,1)=u - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(1,3)=u - - - a_lo(1,4)=-XdInf - a_up(1,5)= XdInf - a_up(1,6)= XdInf - - a_up(2,1)=1.d0 - a_lo(3,3)=1.d0 !signe a voir!!!!!! -! print *,a_up -! print *,a_lo - do tn=N0,Ntime,1 -! do tn=Ntime,Ntime,1 - Ntd=tn+1 - Nt=Ntd-Nd - Ntdc=Ntd+Nc - indI(4)=Nt - indI(5)=Nt+1 - indI(6)=Nt+2 - indI(7)=Ntd - if (SCIS.gt.0) then - if (SCIS.EQ.2) then - Nj=max(Nt,0) - else - Nj=min(max(Nt-5, 0),0) - endif - endif - do ts=3,tn-2 - !print *,'ts,tn' ,ts,tn,Ntdc - CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period - indI(2)=ts-2 - indI(3)=ts-1 - - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - - ds=dt - do icy=1,Nx - ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2) - ansr(tn,icy)=ansr(tn,icy)+fxind(icy)*CC*ds/(CY1(icy)*CY2(icy)) - enddo - enddo ! ts - print *,'Ready: ',tn,' of ',Ntime - - enddo !tn - !print *,'ansr',ansr - 300 open (unit=11, file='dens.out', STATUS='unknown') - !print *, ansr - do ts=1,Ntime - do ph=1,Nx - !write(11,*) ansr(ts,ph),hh1(ph),hh2(ph) - write(11,111) ansr(ts,ph) - - enddo - enddo - 111 FORMAT(2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - deallocate(h1) - deallocate(h2) - deallocate(hh1) - deallocate(hh2) - deallocate(a_up) - deallocate(a_lo) - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - IMPLICIT NONE - integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1 - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - - READ (14,*) U - READ (14,*) Ntime - READ (14,*) N0 - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - - - READ (14,*) Nx1,Nx2 - READ (14,*) dT - if (Ntime.lt.5) then - print *,'The number of wavelength points is too small, stop' - stop - end if - - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h1,h2 - integer, intent(in) :: Nx1,Nx2 - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx1 - READ (4,*) H1(ix) - enddo - do ix=1,Nx2 - READ (4,*) H2(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - integer ,intent(in) :: tn,ts - integer :: i,j,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! -! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| -! = [Xt Xd Xc] -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - Ntd1=tn+1 - N=Ntd1+Nc - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1) = 0.d0 !cov(X(ti+1),Y1) - BIG(i ,Ntd1+2) = 0.d0 !cov(X(ti+1),Y2) - BIG(i ,Ntd1+4) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+5) = R0(i+1) !cov(X(t.. ),X(tn)) - - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X'(t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X'(tn)) - enddo -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - BIG(Ntd1-2,Ntd1-1) = -R2(ts) !cov(X'(ts),X'(t1)) - BIG(Ntd1-2,Ntd1-2) = -R2(1) - BIG(Ntd1-2,Ntd1 ) = -R2(tn+1-ts) !cov(X'(ts),X'(tn)) - -!cov(Xc) - BIG(Ntd1+1,Ntd1+1) = 100.d0 ! cov(Y1 Y1) - BIG(Ntd1+1,Ntd1+2) = 0.d0 ! cov(Y1 Y2) - BIG(Ntd1+1,Ntd1+3) = 0.d0 ! cov(Y1 X(ts)) - BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(Y1 X(t1)) - BIG(Ntd1+1,Ntd1+5) = 0.d0 ! cov(Y1 X(tn)) - BIG(Ntd1+2,Ntd1+2) = 100.d0 ! cov(Y2 Y2) - BIG(Ntd1+2,Ntd1+3) = 0.d0 ! cov(Y2 X(ts)) - BIG(Ntd1+2,Ntd1+4) = 0.d0 ! cov(Y2 X(t1)) - BIG(Ntd1+2,Ntd1+5) = 0.d0 ! cov(Y2 X(tn)) - - BIG(Ntd1+3,Ntd1+3) = R0(1) ! cov(X(ts),X (ts) - BIG(Ntd1+3,Ntd1+4) = R0(ts) ! cov(X(ts),X (t1)) - BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts) ! cov(X(ts),X (tn)) - BIG(Ntd1+4,Ntd1+4) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+4,Ntd1+5) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+5,Ntd1+5) = R0(1) ! cov(X(tn),X (tn)) - - -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1) = 0.d0 !cov(X'(tn),Y1) - BIG(Ntd1 ,Ntd1+2) = 0.d0 !cov(X'(tn),Y2) - BIG(Ntd1-1 ,Ntd1+1) = 0.d0 !cov(X'(t1),Y1) - BIG(Ntd1-1 ,Ntd1+2) = 0.d0 !cov(X'(t1),Y2) - BIG(Ntd1-2 ,Ntd1+1) = 0.d0 !cov(X'(ts),Y1) - BIG(Ntd1-2 ,Ntd1+2) = 0.d0 !cov(X'(ts),Y2) - - BIG(Ntd1 ,Ntd1+4) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+5) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+4) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+5) =-R1(tn) !cov(X'(t1),X(tn)) - BIG(Ntd1 ,Ntd1+3) = R1(tn+1-ts) !cov(X'(tn),X (ts)) - BIG(Ntd1-1,Ntd1+3) =-R1(ts) !cov(X'(t1),X (ts)) - BIG(Ntd1-2,Ntd1+3) = 0.d0 !cov(X'(ts),X (ts) - BIG(Ntd1-2,Ntd1+4) = R1(ts) !cov(X'(ts),X (t1)) - BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts) !cov(X'(ts),X (tn)) - - - do i=1,tn-2 - j=abs(i+1-ts) -!cov(Xt,Xc) - BIG(i,Ntd1+3) = R0(j+1) !cov(X(ti+1),X(ts)) -!Cov(Xt,Xd) - if ((i+1-ts).lt.0) then - BIG(i,Ntd1-2) = R1(j+1) - else !cov(X(ti+1),X'(ts)) - BIG(i,Ntd1-2) = -R1(j+1) - endif - enddo - -! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - - BIG(i,j)=tmp - enddo - enddo - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2tccpdf - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2tcpdf.f b/wafo/source/cov2XXXpdf/cov2tcpdf.f deleted file mode 100644 index 094e339..0000000 --- a/wafo/source/cov2XXXpdf/cov2tcpdf.f +++ /dev/null @@ -1,440 +0,0 @@ - PROGRAM sp2tcpdf -C*********************************************************************** -C This program computes: * -C * -C density of T_i, for Ac <=h, in a gaussian process i.e. * -C * -C half wavelength (up-crossing to downcrossing) for crests h * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex,CY - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(2,6) :: a_up=0.d0,a_lo=0.d0 - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size,icy - integer ::it1,it2 - double precision :: ds,dT ! lag spacing for covariances -! DIGITAL: -! f90 -o ~/WAT/V1/sp2tcpdf.exe rind44.f sp2tcpdf.f - - !print *,'enter sp2thpdf' - CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,Nx,dT) - !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - if (abs(def).GT.1) THEN - !allocate(h(1:Nx)) - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - !CALL INIT_AMPLITUDES(h,def,Nx) - endif - allocate(h(1:Nx)) - CALL INIT_AMPLITUDES(h,def,Nx) - CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - - print *,'Nx',Nx - - Nj=0 - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - print *,'XdInf,XtInf' - print *,XdInf,XtInf - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - !fy(h) - allocate(CY(1:Nx)) - do icy=1,Nx - CY(icy)=exp(-0.5*h(icy)*h(icy)/100)/(10*sqrt(twopi)) - enddo - - allocate(ansr(1:Ntime,1:Nx)) - ansr=0.d0 - allocate(fxind(1:Nx)) - fxind=0.d0 !this is not needed - - NI=4; Nd=2 - Nc=3; Mb=2 - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc)) - allocate(xc(1:Nc,1:Nx)) - allocate(ex(1:Ntime+Nc)) - ex=0.d0 - !print *,'nc',Nc,Nx - xc(1,1:Nx)=h(1:Nx) - print *,'xc',h(1) - print *,'test',def; - xc(2,1:Nx)=u - xc(3,1:Nx)=u - if (def.GT.0) then - a_up(1,1)=u !+XtInf - a_lo(1,1)=u - a_up(1,2)=XdInf - a_lo(1,3)=-XdInf - a_up(2,1)=1.d0 - else - a_up(1,1)=u - a_lo(1,1)=u !-XtInf - a_lo(1,2)=-XdInf - a_up(1,3)= XdInf - a_lo(2,1)=1.d0 - print *,'a_lo',a_lo(2,1) - endif - !print *,'Nstart',Nstart - Nstart=MAX(3,Nstart) - !print *,'Nstart',Nstart - if (SCIS.GT.0) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - do Ntd=Nstart,Ntime - !CALL COV_INPUT2(BIG,Ntd, R0,R1,R2) - Ntdc=Ntd+Nc; - CALL COV_INPUT(BIG,Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - !Ntdc=Ntd+Nc; - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - ! print *,'test',fxind/CY(1:Nx) - do icy=1,Nx - ansr(Ntd,icy)=fxind(icy)*CC/CY(icy) - enddo - if (SCIS.GT.0) then - write(11,*) COV(1) ! save coefficient of variation - endif - print *,'Ready: ',Ntd,' of ',Ntime - enddo - goto 300 - 300 open (unit=11, file='dens.out', STATUS='unknown') - - !print *, ansr - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansr(ts,ph) - ! write(11,111) ansr(ts,ph) - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - - if (allocated(R3)) then - deallocate(R3) - deallocate(R4) - deallocate(h) - ENDIF - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,def,Ntime,Nstart,NIT,speed,Nx,dT) - IMPLICIT NONE - integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) def - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - print *,'def',def - if (abs(def).GT.1) then - READ (14,*) dT - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - else - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - endif - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,def,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: def - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - !if (def.LT.0) THEN - ! H=-H - !endif - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime,def - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - if (abs(def).GT.1) then - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(4,*) R3(i) - read(5,*) R4(i) - enddo - - close(4) - close(5) - endif - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,shft,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! For ts>1: -! X(t2)..X(ts),..X(tn-1) X''(ts) X'(t1) X'(tn) X(ts) X(t1) X(tn) X'(ts) -! = [Xt Xd Xc] -! -! For ts<=1: -! X(t2)..,..X(tn-1) X'(t1) X'(tn) Y X(t1) X(tn) -! = [Xt Xd Xc] -!Add Y Condition : Y=h - -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - - if (ts.LE.1) THEN - Ntd1=tn - N=Ntd1+Nc; - shft=0 ! def=1 want only crest period Tc - else - Ntd1=tn+1 - N=Ntd1+4 - shft=1 ! def=2 or 3 want Tc Ac or Tcf, Ac - endif - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1+shft) = 0.d0 !cov(X(ti+1),Y) - BIG(i ,Ntd1+2+shft) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+3+shft) = R0(i+1) !cov(X(t.. ),X(tn)) - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X' (t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X' (tn)) - enddo - !call echo(big(1:tn,1:tn),tn) -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - -!cov(Xc) - !print *,'t' - BIG(Ntd1+1+shft,Ntd1+1+shft) = 100.d0!100.d0 ! cov(Y,Y) - BIG(Ntd1+1+shft,Ntd1+2+shft) = 0.d0 - BIG(Ntd1+1+shft,Ntd1+3+shft) = 0.d0 - BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+2+shft,Ntd1+3+shft) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+3+shft,Ntd1+3+shft) = R0(1) ! cov(X(tn),X (tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1+shft) = 0.d0 !cov(X'(tn),Y) - BIG(Ntd1 ,Ntd1+2+shft) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+3+shft) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+1+shft) = 0.d0 !cov(X'(t1),Y) - BIG(Ntd1-1,Ntd1+2+shft) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+3+shft) =-R1(tn) !cov(X'(t1),X(tn)) - - - !call echo(big(1:N,1:N),N) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - BIG(i,j)=tmp - enddo - !call echo(big(1:N,1:N),N) - enddo - !if (tn.eq.3) then - !do j=1,N - ! do i=j,N - ! print *,'test',j,i,BIG(j,i) - ! enddo - !call echo(big(1:N,1:N),N) - !enddo - !endif - !call echo(big(1:N,1:N),N) - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2tcpdf - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2thpdf.f b/wafo/source/cov2XXXpdf/cov2thpdf.f deleted file mode 100644 index 8d6f01a..0000000 --- a/wafo/source/cov2XXXpdf/cov2thpdf.f +++ /dev/null @@ -1,569 +0,0 @@ - PROGRAM sp2thpdf -!*********************************************************************** -! This program computes: * -! * -! density of S_i,Hi,T_i in a gaussian process i.e. * -! * -! quart wavelength (up-crossing to crest) and crest amplitude * -! -! def = 1, gives half wave period, Tc (default). -! -1, gives half wave period, Tt. -! 2, gives half wave period and wave crest amplitude (Tc,Ac). -! -2, gives half wave period and wave trough amplitude (Tt,At). -! 3, gives crest front period and wave crest amplitude (Tcf,Ac). -! -3, gives trough back period and wave trough amplitude (Ttb,At). -! 4, gives minimum of crest front/back period and wave crest -! amplitude (max(Tcf,Tcb),Ac). -! -4, gives minimum of trough front/back period and wave trough -! amplitude (max(Ttf,Ttb),At). -!*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - & NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(2,6) :: a_up=0.d0,a_lo=0.d0 - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size - double precision :: ds,dT ! lag spacing for covariances -! DIGITAL: -! f90 -g2 -C -automatic -o ../wave/alpha/sp2thpdf.exe rind44.f sp2thpdf.f -! SOLARIS: -!f90 -g -O -w3 -Bdynamic -fixed -o ../wave/sol2/sp2thpdf.exe rind44.f sp2thpdf.f -! linux: -! f90 -gline -Nl126 -C -o sp2thpdf.exe rind45.f sp2thpdf.f -! HP700 -!f90 -g -C -o ../exec/hp700/sp2thpdf.exe rind45.f sp2thpdf.f -!f90 -g -C +check=all +FPVZID -o ../exec/hp700/sp2thpdf2.exe rind45.f sp2thpdf.f - - - !print *,'enter sp2thpdf' - CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT) - !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT - - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - if (abs(def).GT.1) THEN - allocate(h(1:Nx)) - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - - CALL INIT_AMPLITUDES(h,def,Nx) - endif - CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - - !print *,'Nx',Nx - - Nj=0 - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - !print *,'XdInf,XtInf' - !print *,XdInf,XtInf - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - if (abs(def).EQ.4) CC=2.d0*CC - allocate(ansr(1:Ntime,1:Nx)) - ansr=0.d0 - allocate(fxind(1:Nx)) - !fxind=0.d0 this is not needed - - if (abs(def).GT.1) then - GOTO 200 - endif - NI=4; Nd=2 - Nc=2; Mb=1 - Nx=1 - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc)) - allocate(xc(1:Nc,1:Nx)) - allocate(ex(1:Ntime+Nc)) - ex=0.d0 - xc(1,1)=u - xc(2,1)=u - - if (def.GT.0) then - a_up(1,1)=u+XtInf - a_lo(1,1)=u - a_up(1,2)=XdInf - a_lo(1,3)=-XdInf - else - a_up(1,1)=u - a_lo(1,1)=u-XtInf - a_lo(1,2)=-XdInf - a_up(1,3)= XdInf - endif - !print *,'Nstart',Nstart - Nstart=MAX(2,Nstart) - !print *,'Nstart',Nstart - if (SCIS.GT.0) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - do Ntd=Nstart,Ntime - !CALL COV_INPUT2(BIG,Ntd, R0,R1,R2) - CALL COV_INPUT(BIG,Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - Ntdc=Ntd+Nc; - !if (SCIS.gt.0) then - ! if (SCIS.EQ.2) then - ! Nj=max(Nt,0) - ! else - ! Nj=min(max(Nt-5, 0),0) - ! endif - !endif - !Ex=0.d0 - !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc) - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - ansr(Ntd,1)=fxind(1)*CC - if (SCIS.GT.0) then - write(11,*) COV(1) ! save coefficient of variation - endif - print *,'Ready: ',Ntd,' of ',Ntime - enddo - if (SCIS.GT.0) then - close(11) - endif - goto 300 -200 continue - XddInf=10.d0*SQRT(R4(1)) - NI=7; Nd=3 - Nc=4; Mb=2 - allocate(BIG(1:Ntime+Nc+1,1:Ntime+Nc+1)) - ALLOCATE(xc(1:Nc,1:Nx)) - allocate(ex(1:Ntime+Nc+1)) - - ex=0.d0 - xc(1,1:Nx)=h - xc(2,1:Nx)=u - xc(3,1:Nx)=u - xc(4,1:Nx)=0.d0 - - if (def.GT.0) then - a_up(2,1)=1.d0 !*h - a_lo(1,1)=u - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(2,2)=1.d0 ! *h - a_lo(2,2)=1.d0 ! *h - a_up(2,3)=1.d0 !*h - a_lo(1,3)=u - - a_lo(1,4)=-XddInf - a_up(1,5)= XdInf - a_lo(1,6)=-XdInf - else !def<0 - a_up(1,1)=u - a_lo(2,1)=1.d0 !*h - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(2,2)=1.d0 ! *h - a_lo(2,2)=1.d0 ! *h - a_up(1,3)=u - a_lo(2,3)=1.d0 !*h - - a_up(1,4)=XddInf - a_lo(1,5)=-XdInf - a_up(1,6)=XdInf - endif - - Nstart=MAX(Nstart,3) - do tn=Nstart,Ntime,1 - Ntd=tn+1 - Nt=Ntd-Nd - Ntdc=Ntd+Nc - indI(4)=Nt - indI(5)=Nt+1 - indI(6)=Nt+2 - indI(7)=Ntd - if (SCIS.gt.0) then - if (SCIS.EQ.2) then - Nj=max(Nt,0) - else - Nj=min(max(Nt-5, 0),0) - endif - endif - do ts=2,FLOOR(DBLE(tn+1)/2.d0) - !print *,'ts,tn' ,ts,tn - CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period - indI(2)=ts-2 - indI(3)=ts-1 - !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc) - !print *,'sp call rind' - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc) - !print *,'sp rind finished',fxind - !goto 900 - if (abs(def).LT.3) THEN - if (ts .EQ.tn-ts+1) then - ds=dt - else - ds=2.d0*dt - endif - ansr(tn,1:Nx)=ansr(tn,1:Nx)+fxind*CC*ds - else - ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*dT - if ((ts.LT.tn-ts+1).and. (abs(def).lt.4)) THEN - ansr(tn-ts+1,1:Nx)=ansr(tn-ts+1,1:Nx)+fxind*CC*dT ! exploiting the symmetry - endif - endif - enddo ! ts - print *,'Ready: ',tn,' of ',Ntime - - enddo !tn - !print *,'ansr',ansr - 300 open (unit=11, file='dens.out', STATUS='unknown') - !print *, ansr - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansr(ts,ph) - ! write(11,111) ansr(ts,ph) - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - if (allocated(R3)) then - deallocate(R3) - deallocate(R4) - deallocate(h) - ENDIF - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT) - IMPLICIT NONE - integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx,SCIS,seed1 - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) def - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - - if (abs(def).GT.1) then - READ (14,*) Nx - READ (14,*) dT - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - else - Nx=1 - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - endif - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,def,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: def - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - !if (def.LT.0) THEN - ! H=-H - !endif - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime,def - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - if (abs(def).GT.1) then - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(4,*) R3(i) - read(5,*) R4(i) - enddo - - close(4) - close(5) - endif - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,shft,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! For ts>1: -! ||X(t2)..X(ts),..X(tn-1)||X''(ts) X'(t1) X'(tn)||X(ts) X(t1) X(tn) X'(ts)|| -! = [Xt Xd Xc] -! -! For ts<=1: -! ||X(t2)..,..X(tn-1)||X'(t1) X'(tn)||X(t1) X(tn)|| -! = [Xt Xd Xc] - -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - - if (ts.LE.1) THEN - Ntd1=tn - N=Ntd1+2; - shft=0 ! def=1 want only crest period Tc - else - Ntd1=tn+1 - N=Ntd1+4 - shft=1 ! def=2 or 3 want Tc Ac or Tcf, Ac - endif - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1+shft) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+2+shft) = R0(i+1) !cov(X(t.. ),X(tn)) - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X' (t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X' (tn)) - enddo - !call echo(big(1:tn,1:tn),tn) -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - -!cov(Xc) - BIG(Ntd1+1+shft,Ntd1+1+shft) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+1+shft,Ntd1+2+shft) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1) ! cov(X(tn),X (tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1+shft) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+2+shft) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+1+shft) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+2+shft) =-R1(tn) !cov(X'(t1),X(tn)) - - - if (ts.GT.1) then - -! -!cov(Xc) - BIG(Ntd1+1,Ntd1+1) = R0(1) ! cov(X(ts),X (ts) - BIG(Ntd1+1,Ntd1+2) = R0(ts) ! cov(X(ts),X (t1)) - BIG(Ntd1+1,Ntd1+3) = R0(tn+1-ts) ! cov(X(ts),X (tn)) - BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(X(ts),X'(ts)) - - BIG(Ntd1+2,Ntd1+4) = R1(ts) ! cov(X(t1),X'(ts)) - BIG(Ntd1+3,Ntd1+4) = -R1(tn+1-ts) !cov(X(tn),X'(ts)) - BIG(Ntd1+4,Ntd1+4) = -R2(1) ! cov(X'(ts),X'(ts)) - -!cov(Xd) - BIG(Ntd1-2,Ntd1-1) = -R3(ts) !cov(X''(ts),X'(t1)) - BIG(Ntd1-2,Ntd1-2) = R4(1) - BIG(Ntd1-2,Ntd1 ) = R3(tn+1-ts) !cov(X''(ts),X'(tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+4) =-R2(tn+1-ts) !cov(X'(tn),X'(ts)) - BIG(Ntd1 ,Ntd1+1) = R1(tn+1-ts) !cov(X'(tn),X (ts)) - - BIG(Ntd1-1,Ntd1+4) =-R2(ts) !cov(X'(t1),X'(ts)) - BIG(Ntd1-1,Ntd1+1) =-R1(ts) !cov(X'(t1),X (ts)) - - BIG(Ntd1-2,Ntd1+1) = R2(1) !cov(X''(ts),X (ts) - BIG(Ntd1-2,Ntd1+2) = R2(ts) !cov(X''(ts),X (t1)) - BIG(Ntd1-2,Ntd1+3) = R2(tn+1-ts) !cov(X''(ts),X (tn)) - BIG(Ntd1-2,Ntd1+4) = 0.d0 !cov(X''(ts),X'(ts)) -!cov(Xt,Xc) - do i=1,tn-2 - j=abs(i+1-ts) - BIG(i,Ntd1+1) = R0(j+1) !cov(X(ti+1),X(ts)) - BIG(i,Ntd1+4) = sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X(ti+1),X'(ts)) ! check this - -!Cov(Xt,Xd)=cov(X(ti+1),X(ts)) - BIG(i,Ntd1-2) = R2(j+1) !cov(X(ti+1),X''(ts)) - enddo - endif ! ts>1 - - !call echo(big(1:N,1:N),N) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - - BIG(i,j)=tmp - enddo - !call echo(big(1:N,1:N),N) - - enddo - !call echo(big(1:N,1:N),N) - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2thpdf - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2thpdfalan.f b/wafo/source/cov2XXXpdf/cov2thpdfalan.f deleted file mode 100644 index 95e8c22..0000000 --- a/wafo/source/cov2XXXpdf/cov2thpdfalan.f +++ /dev/null @@ -1,632 +0,0 @@ - PROGRAM sp2thpdf -!*********************************************************************** -! This program computes: * -! * -! density of S_i,Hi,T_i in a gaussian process i.e. * -! * -! quart wavelength (up-crossing to crest) and crest amplitude * -! -! def = 1, gives half wave period, Tc (default). -! -1, gives half wave period, Tt. -! 2, gives half wave period and wave crest amplitude (Tc,Ac). -! -2, gives half wave period and wave trough amplitude (Tt,At). -! 3, gives crest front period and wave crest amplitude (Tcf,Ac). -! -3, gives trough back period and wave trough amplitude (Ttb,At). -! 4, gives minimum of crest front/back period and wave crest -! amplitude (min(Tcf,Tcb),Ac). -! -4, gives minimum of trough front/back period and wave trough -! amplitude (min(Ttf,Ttb),At). -!*********************************************************************** -!History: -! revised Per A. Brodtkorb 04.04.2000 -! - -! revised Per A. Brodtkorb 23.11.99 -! - fixed a bug in calculating pdf for def = +/- 4 -! revised Per A. Brodtkorb 03.11.99 -! - added def = +/-4 -! revised Per A. Brodtkorb 23.09.99 -! - minor changes to covinput -! - removed the calculation of the transformation to spec2thpdf.m -! by Igor Rychlik - - - use GLOBALDATA, only : rateLHD,SCIS,NSIMmax,COV,ABSEPS - use globalconst - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansr - double precision, dimension(: ),allocatable :: ex - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(: ),allocatable :: fxind,h - double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(2,6) :: a_up=0.d0,a_lo=0.d0 - integer, dimension(6) :: INFIN=2 - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Nx,Nt,Nc,Nd,NI,Mb,Ntd, Ntdc - integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size - double precision :: dT, EPSOLD ! lag spacing for covariances - LOGICAL :: init=.TRUE. -! DIGITAL: -! f90 -g2 -C -automatic -o ../wave/alpha/sp2thpdf.exe rind44.f sp2thpdf.f -! SOLARIS: -!f90 -g -O -w3 -Bdynamic -fixed -o ../wave/sol2/sp2thpdf.exe rind44.f sp2thpdf.f -! linux: -! f90 -gline -Nl126 -C -o ../exec/lnx86/sp2thpdf8.exe intmodule.f rind60.f sp2thpdf.f -! f90 -gline -Nl126 -C -o sp2thpdf.exe rind45.f sp2thpdf.f -! f90 -gline -Nl126 -C -o ../exec/lnx86/sp2thpdf3.exe adaptmodule.f krbvrcmod.f krobovmod.f rcrudemod.f rind55.f sp2thpdf.f -! HP700 -!f90 -g -C -o ../exec/hp700/sp2thpdf.exe rind45.f sp2thpdf.f -!f90 -g -C +check=all +FPVZID -o ../exec/hp700/sp2thpdf.exe rind45.f sp2thpdf.f -! f90 +gprof +extend_source +Oall +Odataprefetch +Ofastaccess +Oinfo +Oprocelim -C +check=all -o ../exec/hp700/sp2thpdf.exe rind48.f sp2thpdf.f - - !print *,'enter sp2thpdf' - - CALL INIT_LEVELS(U,def,Ntime,Nstart,speed,SCIS,seed1, - & Nx,dT,rateLHD) - !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT - - - if (SCIS.GT.0) then - !allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - if (abs(def).GT.1) THEN - allocate(h(1:Nx)) - allocate(R3(1:Ntime+1)) - allocate(R4(1:Ntime+1)) - CALL INIT_AMPLITUDES(h,def,Nx) - endif - CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - - !print *,'Nx',Nx - - - indI(1)=0 -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - !print *,'XdInf,XtInf' - !print *,XdInf,XtInf - ! normalizing constant - CC=TWPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - allocate(ansr(1:Ntime,1:Nx)) - ansr=0.d0 - allocate(fxind(1:Nx)) - !fxind=0.d0 this is not needed - - if (abs(def).GT.1) GOTO 200 - - NI=4; Nd=2 - Nc=2; Mb=1 - Nx=1 - allocate(BIG(1:Ntime+Nc,1:Ntime+Nc)) - allocate(xc(1:Nc,1:Nx)) - allocate(ex(1:Ntime+Nc)) - ex=0.d0 - xc(1,1)=u - xc(2,1)=u -! INFIN = INTEGER, array of integration limits flags: size 1 x Nb (in) -! if INFIN(I) < 0, Ith limits are (-infinity, infinity); -! if INFIN(I) = 0, Ith limits are (-infinity, Hup(I)]; -! if INFIN(I) = 1, Ith limits are [Hlo(I), infinity); -! if INFIN(I) = 2, Ith limits are [Hlo(I), Hup(I)]. - - if (def.GT.0) then - INFIN(1:2) = 1 - INFIN(3) = 0 - a_up(1,1)= u+XtInf - a_lo(1,1)= u - a_up(1,2)= XdInf - a_lo(1,3)=-XdInf - else - INFIN(1:2) = 0 - INFIN(3) = 1 - a_up(1,1)=u - a_lo(1,1)=u-XtInf - a_lo(1,2)=-XdInf - a_up(1,3)= XdInf - endif - !print *,'Nstart',Nstart - Nstart=MAX(2,Nstart) - !print *,'Nstart',Nstart - if (ALLOCATED(COV)) then - open (unit=11, file='COV.out', STATUS='unknown') - write(11,*) 0.d0 - endif - do Ntd=Nstart,Ntime - !CALL COV_INPUT2(BIG,Ntd, R0,R1,R2) - CALL COV_INPUT(BIG,Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period - Nt=Ntd-Nd; - indI(2)=Nt; - indI(3)=Nt+1; - indI(4)=Ntd; - Ntdc=Ntd+Nc; -! IF (Ntd.GT.5.AND.(INIT)) THEN -! INIT=.FALSE. -! CALL INITDATA(speed) -! ENDIF - !if (SCIS.gt.1) Nj=Nt - !if (SCIS.gt.0) then - ! if (SCIS.EQ.2) then - ! Nj=max(Nt,0) - ! else - ! Nj=min(max(Nt-5, 0),0) - ! endif - !endif - !Ex=0.d0 - !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc) - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),xc, - & Nt,indI(1:NI),a_lo(1:Mb,1:NI-1),a_up(1:Mb,1:NI-1), - & INFIN(1:NI-1)) - ansr(Ntd,1)=fxind(1)*CC - if (ALLOCATED(COV)) then !SCIS.GT.0 - write(11,*) COV(1) ! save coefficient of variation - endif - print *,'Ready: ',Ntd,' of ',Ntime - enddo - if (ALLOCATED(COV)) then - close(11) - endif - goto 300 -200 continue - XddInf=10.d0*SQRT(R4(1)) - NI=7; Nd=3 - Nc=4; Mb=2 - allocate(BIG(1:Ntime+Nc+1,1:Ntime+Nc+1)) - ALLOCATE(xc(1:Nc,1:Nx)) - allocate(ex(1:Ntime+Nc+1)) - - ex=0.d0 - xc(1,1:Nx)=h(1:Nx) - xc(2,1:Nx)=u - xc(3,1:Nx)=u - xc(4,1:Nx)=0.d0 - -! INFIN = INTEGER, array of integration limits flags: size 1 x Nb (in) -! if INFIN(I) < 0, Ith limits are (-infinity, infinity); -! if INFIN(I) = 0, Ith limits are (-infinity, Hup(I)]; -! if INFIN(I) = 1, Ith limits are [Hlo(I), infinity); -! if INFIN(I) = 2, Ith limits are [Hlo(I), Hup(I)]. - if (def.GT.0) then - INFIN(2)=-1 - INFIN(4)=0 - INFIN(5)=1 - INFIN(6)=0 - a_up(2,1)=1.d0 !*h - a_lo(1,1)=u - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(2,2)=1.d0 ! *h - a_lo(2,2)=1.d0 ! *h - a_up(2,3)=1.d0 !*h - a_lo(1,3)=u - - a_lo(1,4)=-XddInf - a_up(1,5)= XdInf - a_lo(1,6)=-XdInf - else !def<0 - INFIN(2)=-1 - INFIN(4)=1 - INFIN(5)=0 - INFIN(6)=1 - a_up(1,1)=u - a_lo(2,1)=1.d0 !*h - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(2,2)=1.d0 ! *h - a_lo(2,2)=1.d0 ! *h - a_up(1,3)=u - a_lo(2,3)=1.d0 !*h - a_up(1,4)=XddInf - a_lo(1,5)=-XdInf - a_up(1,6)=XdInf - endif - EPSOLD=ABSEPS - Nstart=MAX(Nstart,3) - do tn=Nstart,Ntime,1 - Ntd=tn+1 - Nt=Ntd-Nd - Ntdc=Ntd+Nc - indI(4)=Nt - indI(5)=Nt+1 - indI(6)=Nt+2 - indI(7)=Ntd -! IF (Ntd.GT.5.AND.INIT) THEN -! INIT=.FALSE. -! CALL INITDATA(speed) -! ENDIF - !if (SCIS.gt.1) Nj=Nt - !if (SCIS.gt.0) then - ! if (SCIS.EQ.2) then - ! Nj=max(Nt,0) - ! else - ! Nj=min(max(Nt-5, 0),0) - ! endif - !endif - ABSEPS=MIN(SQRT(DBLE(tn))*EPSOLD*0.5D0,0.1D0) - do ts=2,FLOOR(DBLE(tn+1)/2.d0) - !print *,'ts,tn' ,ts,tn - CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period - indI(2)=ts-2 - indI(3)=ts-1 - !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc) - !print *,'sp call rind' - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),xc, - & Nt,indI(1:NI),a_lo(1:Mb,1:NI-1),a_up(1:Mb,1:NI-1), - & INFIN(1:NI-1)) - !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc) - !print *,'sp rind finished',fxind - !goto 900 - SELECT CASE (ABS(def)) - CASE (:2) -! 2, gives half wave period and wave crest amplitude (Tc,Ac). -! -2, gives half wave period and wave trough amplitude (Tt,At). - if (ts .EQ.tn-ts+1) then - ansr(tn,1:Nx)=ansr(tn,1:Nx)+fxind*CC*dt - else - ansr(tn,1:Nx)=ansr(tn,1:Nx)+fxind*CC*2.d0*dt - endif - CASE (3) -! 3, gives crest front period and wave crest amplitude (Tcf,Ac). -! -3, gives trough back period and wave trough amplitude (Ttb,At). - ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*dT - if ((ts.LT.tn-ts+1)) THEN - ansr(tn-ts+1,1:Nx)=ansr(tn-ts+1,1:Nx)+fxind*CC*dT ! exploiting the symmetry - endif - CASE (4:) -! 4, gives minimum of crest front/back period and wave crest amplitude (min(Tcf,Tcb),Ac). -! -4, gives minimum of trough front/back period and wave trough amplitude (min(Ttf,Ttb),At). - if (ts .EQ.tn-ts+1) then - ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*dt - else - ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*2.0*dt - endif - end select - enddo ! ts - print *,'Ready: ',tn,' of ',Ntime, ' ABSEPS = ', ABSEPS - - enddo !tn - !print *,'ansr',ansr - 300 open (unit=11, file='dens.out', STATUS='unknown') - !print *, ansr - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansr(ts,ph) - ! write(11,111) ansr(ts,ph) - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansr) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - if (allocated(R3)) then - deallocate(R3) - deallocate(R4) - deallocate(h) - ENDIF - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,def,Ntime,Nstart,speed,SCIS,seed1,Nx,dT,rateLHD) - IMPLICIT NONE - integer, intent(out):: def,Ntime,Nstart,speed,Nx,SCIS,seed1, - & rateLHD - double precision ,intent(out) :: U,dT - double precision :: XSPLT - integer :: NIT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) def - READ (14,*) Ntime - READ (14,*) Nstart - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - READ (14,*) Nx - READ (14,*) dT - READ (14,*) rateLHD - READ (14,*) XSPLT - if (abs(def).GT.1) then - - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - else - Nx=1 - if (Ntime.lt.2) then - print *,'The number of wavelength points is too small, stop' - stop - end if - endif - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h,def,Nx) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h - integer, intent(in) :: def - integer, intent(in) :: Nx - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx - READ (4,*) H(ix) - enddo - CLOSE(UNIT=4) - !if (def.LT.0) THEN - ! H=-H - !endif - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - double precision, dimension(:),intent(out) :: R3,R4 - integer,intent(in) :: Ntime,def - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - if (abs(def).GT.1) then - open (unit=4, file='Cd3.in',STATUS='unknown') - open (unit=5, file='Cd4.in',STATUS='unknown') - - do i=1,Ntime - read(4,*) R3(i) - read(5,*) R4(i) - enddo - - close(4) - close(5) - endif - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - double precision, dimension(:),intent(in) :: R3,R4 - integer ,intent(in) :: tn,ts - integer :: i,j,shft,Ntd1,N !=Ntdc -! the order of the variables in the covariance matrix -! are organized as follows: -! For ts>1: -! ||X(t2)..X(ts),..X(tn-1)||X''(ts) X'(t1) X'(tn)||X(ts) X(t1) X(tn) X'(ts)|| -! = [Xt Xd Xc] -! -! For ts<=1: -! ||X(t2)..,..X(tn-1)||X'(t1) X'(tn)||X(t1) X(tn)|| -! = [Xt Xd Xc] - -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - - if (ts.LE.1) THEN - Ntd1=tn - N=Ntd1+2; - shft=0 ! def=1 want only crest period Tc - else - Ntd1=tn+1 - N=Ntd1+4 - shft=1 ! def=2 or 3 want Tc Ac or Tcf, Ac - endif - - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1+shft) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+2+shft) = R0(i+1) !cov(X(t.. ),X(tn)) - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X' (t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X' (tn)) - enddo - !call echo(big(1:tn,1:tn),tn) -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - -!cov(Xc) - BIG(Ntd1+1+shft,Ntd1+1+shft) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+1+shft,Ntd1+2+shft) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1) ! cov(X(tn),X (tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1+shft) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+2+shft) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+1+shft) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+2+shft) =-R1(tn) !cov(X'(t1),X(tn)) - - - if (ts.GT.1) then - -! -!cov(Xc) - BIG(Ntd1+1,Ntd1+1) = R0(1) ! cov(X(ts),X (ts) - BIG(Ntd1+1,Ntd1+2) = R0(ts) ! cov(X(ts),X (t1)) - BIG(Ntd1+1,Ntd1+3) = R0(tn+1-ts) ! cov(X(ts),X (tn)) - BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(X(ts),X'(ts)) - - BIG(Ntd1+2,Ntd1+4) = R1(ts) ! cov(X(t1),X'(ts)) - BIG(Ntd1+3,Ntd1+4) = -R1(tn+1-ts) !cov(X(tn),X'(ts)) - BIG(Ntd1+4,Ntd1+4) = -R2(1) ! cov(X'(ts),X'(ts)) - -!cov(Xd) - BIG(Ntd1-2,Ntd1-1) = -R3(ts) !cov(X''(ts),X'(t1)) - BIG(Ntd1-2,Ntd1-2) = R4(1) - BIG(Ntd1-2,Ntd1 ) = R3(tn+1-ts) !cov(X''(ts),X'(tn)) -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+4) =-R2(tn+1-ts) !cov(X'(tn),X'(ts)) - BIG(Ntd1 ,Ntd1+1) = R1(tn+1-ts) !cov(X'(tn),X (ts)) - - BIG(Ntd1-1,Ntd1+4) =-R2(ts) !cov(X'(t1),X'(ts)) - BIG(Ntd1-1,Ntd1+1) =-R1(ts) !cov(X'(t1),X (ts)) - - BIG(Ntd1-2,Ntd1+1) = R2(1) !cov(X''(ts),X (ts) - BIG(Ntd1-2,Ntd1+2) = R2(ts) !cov(X''(ts),X (t1)) - BIG(Ntd1-2,Ntd1+3) = R2(tn+1-ts) !cov(X''(ts),X (tn)) - BIG(Ntd1-2,Ntd1+4) = 0.d0 !cov(X''(ts),X'(ts)) -!cov(Xt,Xc) - do i=1,tn-2 - j=abs(i+1-ts) - BIG(i,Ntd1+1) = R0(j+1) !cov(X(ti+1),X(ts)) - BIG(i,Ntd1+4) = sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X(ti+1),X'(ts)) ! check this - -!Cov(Xt,Xd)=cov(X(ti+1),X(ts)) - BIG(i,Ntd1-2) = R2(j+1) !cov(X(ti+1),X''(ts)) - enddo - endif ! ts>1 - - !call echo(big(1:N,1:N),N) - ! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - BIG(i,j) =BIG(j,i) - enddo - !call echo(big(1:N,1:N),N) - enddo - !call echo(big(1:N,1:N),N) - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - END PROGRAM sp2thpdf - - - - - - - - - diff --git a/wafo/source/cov2XXXpdf/cov2tthpdf.f b/wafo/source/cov2XXXpdf/cov2tthpdf.f deleted file mode 100644 index c0230de..0000000 --- a/wafo/source/cov2XXXpdf/cov2tthpdf.f +++ /dev/null @@ -1,505 +0,0 @@ - PROGRAM sp2tthpdf -C*********************************************************************** -C This program computes upper and lower bounds for the: * -C * -C density of T= T_1+T_2 in a gaussian process i.e. * -C * -C wavelengthes for crests

h2 * -C * -C Sylvie and Igor 7 dec. 1999 * -C*********************************************************************** - use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, - & NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV - use rind - IMPLICIT NONE - double precision, dimension(:,:),allocatable :: BIG - double precision, dimension(:,:),allocatable :: ansrup - double precision, dimension(:,:),allocatable :: ansrlo - double precision, dimension(: ),allocatable :: ex,CY1,CY2 - double precision, dimension(:,:),allocatable :: xc - double precision, dimension(:,:),allocatable ::fxind - double precision, dimension(: ),allocatable :: h1,h2 - double precision, dimension(: ),allocatable :: hh1,hh2 - double precision, dimension(: ),allocatable :: R0,R1,R2 - double precision ::CC,U,XddInf,XdInf,XtInf - double precision, dimension(:,:),allocatable :: a_up,a_lo - integer , dimension(: ),allocatable :: seed - integer ,dimension(7) :: indI - integer :: Ntime,N0,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2 - integer :: icy,icy2 - double precision :: ds,dT ! lag spacing for covariances -! DIGITAL: -! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf.exe rind48.f sp2tthpdf.f -! SOLARIS: -!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind48.f sp2tthpdf.f - - !print *,'enter sp2thpdf' - CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - - !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT' - !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT - !Nx1=1 - !Nx2=1 - - Nx=Nx1*Nx2 - !print *,'NN',Nx1,Nx2,Nx - - - !XSPLT=1.5d0 - if (SCIS.GT.0) then - allocate(COV(1:Nx)) - call random_seed(SIZE=seed_size) - allocate(seed(seed_size)) - call random_seed(GET=seed(1:seed_size)) ! get current seed - seed(1)=seed1 ! change seed - call random_seed(PUT=seed(1:seed_size)) - deallocate(seed) - endif - CALL INITDATA(speed) - !print *,ntime,speed,u,NIT - allocate(R0(1:Ntime+1)) - allocate(R1(1:Ntime+1)) - allocate(R2(1:Ntime+1)) - - allocate(h1(1:Nx1)) - allocate(h2(1:Nx2)) - CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - CALL INIT_COVARIANCES(Ntime,R0,R1,R2) - - - allocate(hh1(1:Nx)) - allocate(hh2(1:Nx)) - !h transformation - do icy=1,Nx1 - do icy2=1,Nx2 - hh1((icy-1)*Nx2+icy2)=h1(icy); - hh2((icy-1)*Nx2+icy2)=h2(icy2); - enddo - enddo - - Nj=0 - indI(1)=0 - -C ***** The bound 'infinity' is set to 10*sigma ***** - XdInf=10.d0*SQRT(-R2(1)) - XtInf=10.d0*SQRT(R0(1)) - !h1(1)=XtInf - !h2(1)=XtInf - ! normalizing constant - CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) - allocate(CY1(1:Nx)) - allocate(CY2(1:Nx)) - do icy=1,Nx - CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi)) - CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi)) - enddo - !print *,CY1 - allocate(ansrup(1:Ntime,1:Nx)) - allocate(ansrlo(1:Ntime,1:Nx)) - ansrup=0.d0 - ansrlo=0.d0 - allocate(fxind(1:Nx,1:2)) - !fxind=0.d0 this is not needed - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !! -! = [Xt Xd Xc] !! -! !! -! Nt=tn-2, Nd=3, Nc=2+3 !! -! !! -! Xt= contains Nt time points in the indicator function !! -! Xd= " Nd derivatives !! -! Xc= " Nc variables to condition on !! -! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd !! -! !! -! There are 6 ( NI=7) regions with constant bariers: !! -! (indI(1)=0); for i\in (indI(1),indI(2)] u0 (deriv. X'(t1)) !! -! (indI(6)=Nt+2); for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn)) !! -! (indI(7)=Nt+3); NI=7. !! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - - NI=7; Nd=3 - Nc=5; Mb=3 - allocate(a_up(1:Mb,1:(NI-1))) - allocate(a_lo(1:Mb,1:(NI-1))) - a_up=0.d0 - a_lo=0.d0 - allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) - ALLOCATE(xc(1:Nc,1:Nx)) - allocate(ex(1:(Ntime+Nc+1))) - !print *,size(ex),Ntime - ex=0.d0 - !print *,size(ex),ex - xc(1,1:Nx)=hh1(1:Nx) - xc(2,1:Nx)=hh2(1:Nx) - xc(3,1:Nx)=u - xc(4,1:Nx)=u - xc(5,1:Nx)=u - ! upp- down- upp-crossings at t1,ts,tn - - a_lo(1,1)=u - a_up(1,2)=XtInf ! X(ts) is redundant - a_lo(1,2)=-Xtinf - a_up(1,3)=u - - - a_lo(1,4)=-XdInf - a_up(1,5)= XdInf - a_up(1,6)= XdInf - - a_up(2,1)=1.d0 - a_lo(3,3)=1.d0 !signe a voir!!!!!! -! print *,a_up -! print *,a_lo - do tn=N0,Ntime,1 -! do tn=Ntime,Ntime,1 - Ntd=tn+1 - Nt=Ntd-Nd - Ntdc=Ntd+Nc - indI(4)=Nt - indI(5)=Nt+1 - indI(6)=Nt+2 - indI(7)=Ntd - if (SCIS.gt.0) then - if (SCIS.EQ.2) then - Nj=max(Nt,0) - else - Nj=min(max(Nt-5, 0),0) - endif - endif - do ts=3,tn-2 - !print *,'ts,tn' ,ts,tn,Ntdc - CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period - indI(2)=ts-2 - indI(3)=ts-1 - - - CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), - & xc,indI,a_lo,a_up) - - ds=dt - do icy=1,Nx - ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2) - ansrup(tn,icy)=ansrup(tn,icy)+fxind(icy,1)*CC*ds - & /(CY1(icy)*CY2(icy)) - ansrlo(tn,icy)=ansrlo(tn,icy)+fxind(icy,2)*CC*ds - & /(CY1(icy)*CY2(icy)) - enddo - enddo ! ts - print *,'Ready: ',tn,' of ',Ntime - - enddo !tn - - 300 open (unit=11, file='dens.out', STATUS='unknown') - - do ts=1,Ntime - do ph=1,Nx - write(11,*) ansrup(ts,ph),ansrlo(ts,ph)!,hh1(ph),hh2(ph) - ! write(11,111) ansrup(ts,ph),ansrlo(ts,ph) - - enddo - enddo - !111 FORMAT(2x,F12.8) - close(11) - 900 deallocate(big) - deallocate(fxind) - deallocate(ansrup) - deallocate(ansrlo) - deallocate(xc) - deallocate(ex) - deallocate(R0) - deallocate(R1) - deallocate(R2) - if (allocated(COV) ) then - deallocate(COV) - endif - deallocate(h1) - deallocate(h2) - deallocate(hh1) - deallocate(hh2) - deallocate(a_up) - deallocate(a_lo) - stop - !return - - CONTAINS - - - - SUBROUTINE INIT_LEVELS - & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) - IMPLICIT NONE - integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1 - double precision ,intent(out) :: U,dT - - - OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') - READ (14,*) U - READ (14,*) Ntime - READ (14,*) N0 - READ (14,*) NIT - READ (14,*) speed - READ (14,*) SCIS - READ (14,*) seed1 - - - READ (14,*) Nx1,Nx2 - READ (14,*) dT - if (Ntime.lt.3) then - print *,'The number of wavelength points is too small, stop' - stop - end if - - CLOSE(UNIT=14) - - RETURN - END SUBROUTINE INIT_LEVELS - -C****************************************************** - SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2) - IMPLICIT NONE - double precision, dimension(:), intent(out) :: h1,h2 - integer, intent(in) :: Nx1,Nx2 - integer :: ix - - - OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') - -C -C Reading in amplitudes -C - do ix=1,Nx1 - READ (4,*) H1(ix) - enddo - do ix=1,Nx2 - READ (4,*) H2(ix) - enddo - CLOSE(UNIT=4) - - RETURN - END SUBROUTINE INIT_AMPLITUDES - -C************************************************** - -C*********************************************************************** -C*********************************************************************** - - SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:),intent(out) :: R0,R1,R2 - integer,intent(in) :: Ntime - integer :: i - open (unit=1, file='Cd0.in',STATUS='unknown') - open (unit=2, file='Cd1.in',STATUS='unknown') - open (unit=3, file='Cd2.in',STATUS='unknown') - - do i=1,Ntime - read(1,*) R0(i) - read(2,*) R1(i) - read(3,*) R2(i) - enddo - close(1) - close(2) - close(3) - - return - END SUBROUTINE INIT_COVARIANCES - -C*********************************************************************** -C*********************************************************************** - -C********************************************************************** - - SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:),intent(inout) :: BIG - double precision, dimension(:),intent(in) :: R0,R1,R2 - integer ,intent(in) :: tn,ts - integer :: i,j,Ntd1,N !=Ntdc - double precision :: tmp -! the order of the variables in the covariance matrix -! are organized as follows: -! -! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| -! = [Xt Xd Xc] -! where -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), -! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have -! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). -! -! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) -! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) -! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) -! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) -! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) - - Ntd1=tn+1 - N=Ntd1+Nc - do i=1,tn-2 - !cov(Xt) - do j=i,tn-2 - BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) - enddo - !cov(Xt,Xc) - BIG(i ,Ntd1+1) = 0.d0 !cov(X(ti+1),Y1) - BIG(i ,Ntd1+2) = 0.d0 !cov(X(ti+1),Y2) - BIG(i ,Ntd1+4) = R0(i+1) !cov(X(ti+1),X(t1)) - BIG(tn-1-i ,Ntd1+5) = R0(i+1) !cov(X(t.. ),X(tn)) - - !Cov(Xt,Xd)=cov(X(ti+1),x(tj) - BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X'(t1)) - BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X'(tn)) - enddo -!cov(Xd) - BIG(Ntd1 ,Ntd1 ) = -R2(1) - BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn)) - BIG(Ntd1-1,Ntd1-1) = -R2(1) - BIG(Ntd1-2,Ntd1-1) = -R2(ts) !cov(X'(ts),X'(t1)) - BIG(Ntd1-2,Ntd1-2) = -R2(1) - BIG(Ntd1-2,Ntd1 ) = -R2(tn+1-ts) !cov(X'(ts),X'(tn)) - -!cov(Xc) - BIG(Ntd1+1,Ntd1+1) = 100.d0 ! cov(Y1 Y1) - BIG(Ntd1+1,Ntd1+2) = 0.d0 ! cov(Y1 Y2) - BIG(Ntd1+1,Ntd1+3) = 0.d0 ! cov(Y1 X(ts)) - BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(Y1 X(t1)) - BIG(Ntd1+1,Ntd1+5) = 0.d0 ! cov(Y1 X(tn)) - BIG(Ntd1+2,Ntd1+2) = 100.d0 ! cov(Y2 Y2) - BIG(Ntd1+2,Ntd1+3) = 0.d0 ! cov(Y2 X(ts)) - BIG(Ntd1+2,Ntd1+4) = 0.d0 ! cov(Y2 X(t1)) - BIG(Ntd1+2,Ntd1+5) = 0.d0 ! cov(Y2 X(tn)) - - BIG(Ntd1+3,Ntd1+3) = R0(1) ! cov(X(ts),X (ts) - BIG(Ntd1+3,Ntd1+4) = R0(ts) ! cov(X(ts),X (t1)) - BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts) ! cov(X(ts),X (tn)) - BIG(Ntd1+4,Ntd1+4) = R0(1) ! cov(X(t1),X (t1)) - BIG(Ntd1+4,Ntd1+5) = R0(tn) ! cov(X(t1),X (tn)) - BIG(Ntd1+5,Ntd1+5) = R0(1) ! cov(X(tn),X (tn)) - - -!cov(Xd,Xc) - BIG(Ntd1 ,Ntd1+1) = 0.d0 !cov(X'(tn),Y1) - BIG(Ntd1 ,Ntd1+2) = 0.d0 !cov(X'(tn),Y2) - BIG(Ntd1-1 ,Ntd1+1) = 0.d0 !cov(X'(t1),Y1) - BIG(Ntd1-1 ,Ntd1+2) = 0.d0 !cov(X'(t1),Y2) - BIG(Ntd1-2 ,Ntd1+1) = 0.d0 !cov(X'(ts),Y1) - BIG(Ntd1-2 ,Ntd1+2) = 0.d0 !cov(X'(ts),Y2) - - BIG(Ntd1 ,Ntd1+4) = R1(tn) !cov(X'(tn),X(t1)) - BIG(Ntd1 ,Ntd1+5) = 0.d0 !cov(X'(tn),X(tn)) - BIG(Ntd1-1,Ntd1+4) = 0.d0 !cov(X'(t1),X(t1)) - BIG(Ntd1-1,Ntd1+5) =-R1(tn) !cov(X'(t1),X(tn)) - BIG(Ntd1 ,Ntd1+3) = R1(tn+1-ts) !cov(X'(tn),X (ts)) - BIG(Ntd1-1,Ntd1+3) =-R1(ts) !cov(X'(t1),X (ts)) - BIG(Ntd1-2,Ntd1+3) = 0.d0 !cov(X'(ts),X (ts) - BIG(Ntd1-2,Ntd1+4) = R1(ts) !cov(X'(ts),X (t1)) - BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts) !cov(X'(ts),X (tn)) - - - do i=1,tn-2 - j=abs(i+1-ts) -!cov(Xt,Xc) - BIG(i,Ntd1+3) = R0(j+1) !cov(X(ti+1),X(ts)) -!Cov(Xt,Xd) - if ((i+1-ts).lt.0) then - BIG(i,Ntd1-2) = R1(j+1) - else !cov(X(ti+1),X'(ts)) - BIG(i,Ntd1-2) = -R1(j+1) - endif - enddo - -! make lower triangular part equal to upper - do j=1,N-1 - do i=j+1,N - tmp =BIG(j,i) - - BIG(i,j)=tmp - enddo - enddo - -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT - - SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) - IMPLICIT NONE - double precision, dimension(:,:), intent(out) :: BIG - double precision, dimension(:), intent(in) :: R0,R1,R2 - integer :: pt,i,j -! the order of the variables in the covariance matrix -! are organized as follows; -! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] -! -! where Xd is the derivatives -! -! Xt= time points in the indicator function -! Xd= derivatives -! Xc=variables to condition on - -!cov(Xc) - BIG(pt+2,pt+2) = R0(1) - BIG(pt+1,pt+1) = R0(1) - BIG(pt+1,pt+2) = R0(pt) -!cov(Xd) - BIG(pt,pt) = -R2(1) - BIG(pt-1,pt-1) = -R2(1) - BIG(pt-1,pt) = -R2(pt) -!cov(Xd,Xc) - BIG(pt,pt+2) = 0.d0 - BIG(pt,pt+1) = R1(pt) - BIG(pt-1,pt+2) = -R1(pt) - BIG(pt-1,pt+1) = 0.d0 - - if (pt.GT.2) then -!cov(Xt) - do i=1,pt-2 - do j=i,pt-2 - BIG(i,j) = R0(j-i+1) - enddo - enddo -!cov(Xt,Xc) - do i=1,pt-2 - BIG(i,pt+1) = R0(i+1) - BIG(pt-1-i,pt+2) = R0(i+1) - enddo -!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) - do i=1,pt-2 - BIG(i,pt-1) = -R1(i+1) - BIG(pt-1-i,pt)= R1(i+1) - enddo - endif - - - ! make lower triangular part equal to upper - do j=1,pt+1 - do i=j+1,pt+2 - BIG(i,j)=BIG(j,i) - enddo - enddo -C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) -C 10 format(6F8.4) - RETURN - END SUBROUTINE COV_INPUT2 - - - END PROGRAM sp2tthpdf - - - - - - - - - diff --git a/wafo/source/mreg/build_all.py b/wafo/source/mreg/build_all.py deleted file mode 100644 index 335ccdc..0000000 --- a/wafo/source/mreg/build_all.py +++ /dev/null @@ -1,30 +0,0 @@ -""" -f2py c_library.pyf c_functions.c -c - -gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -c dsvdc.f mregmodule.f - -""" -import os -import sys -from wafo.f2py_tools import f2py_call_str - - -def compile_all(): - f2py_call = f2py_call_str() - print '=' * 75 - print 'compiling cov2mod' - print '=' * 75 - - files = ['dsvdc', 'mregmodule', 'intfcmod'] - compile1_format = 'gfortran -fPIC -c %s.f' - format1 = '%s.o ' * len(files) - for file_ in files: - os.system(compile1_format % file_) - file_objects = format1 % tuple(files) - - os.system(f2py_call + ' -m cov2mod -c %s cov2mmpdfreg_intfc.f' % - file_objects) - - -if __name__ == '__main__': - compile_all() diff --git a/wafo/source/mreg/cov2mmpdfreg.f b/wafo/source/mreg/cov2mmpdfreg.f deleted file mode 100644 index da529bf..0000000 --- a/wafo/source/mreg/cov2mmpdfreg.f +++ /dev/null @@ -1,651 +0,0 @@ -C Version 1994-X-18 - -C This is a new version of WAMP program computing crest-trough wavelength -C and amplitude density. -C -C revised pab 2007 -C -moved all common blocks into modules -C -renamed from minmax to sp2mmpdfreg + fixed some bugs -C revised pab July 2007 -! -renamed from sp2mmpdfreg to cov2mmpdfreg - - PROGRAM cov2mmpdfreg - USE SIZEMOD - USE EPSMOD - USE CHECKMOD - USE MREGMOD - IMPLICIT NONE - real*8 Q0,SQ0,Q1,SQ1, AA, BB, DAI, AI , U,V,VV, XL0, XL2, XL4 - REAL*8 VDERI, CDER,SDER, DER, CONST, F, HHHH,FM, VALUE -C INTEGER, PARAMETER :: MMAX = 5, NMAX = 101, RDIM = 10201 - REAL*8, DIMENSION(NMAX) :: HHT,T,Ulev,Vlev,VT,UT,Vdd,Udd - REAL*8, DIMENSION(RDIM) :: R,R1,R2,R3 - REAL*8, DIMENSION(5*NMAX) :: COV - REAL*8, DIMENSION(NMAX,NMAX) :: UVdens -C DIMENSION UVdens(NMAX,NMAX),HHT(NMAX) -C DIMENSION T(NMAX),Ulev(NMAX),Vlev(NMAX) -C DIMENSION VT(NMAX),UT(NMAX),Vdd(NMAX),Udd(NMAX) -C DIMENSION COV(5*NMAX),R(RDIM),R1(RDIM),R2(RDIM),R3(RDIM) - DIMENSION AA(MMAX-2,MMAX-2),BB(MMAX+1),DAI(MMAX),AI((MMAX+1)*NMAX) - -C -C The program computes the joint density of maximum the following minimum -C and the distance between Max and min for a zero-mean stationary -C Gaussian process with covariance function defined explicitely with 4 -C derivatives. The process should be normalized so that the first and -C the second spectral moments are equal to 1. The values of Max are taken -C as the nodes at Hermite-Quadrature and then integrated out so that -C the output is a joint density of wavelength T and amplitude H=Max-min. -C The Max values are defined by subroutine Gauss_M with the accuracy -C input epsu. The principle is that the integral of the marginal density -C of f_Max is computed with sufficient accuracy. -C - REAL*8, DIMENSION(NMAX) :: B0,DB0,DDB0,B1,DB1,DDB1,DB2,DDB2 - REAL*8, DIMENSION(NMAX) :: Q,SQ,VDER,DBI,BI -C DIMENSION B0(NMAX),DB0(NMAX),DDB0(NMAX) -C DIMENSION B1(NMAX),DB1(NMAX),DDB1(NMAX) -C DIMENSION DB2(NMAX),DDB2(NMAX) -C DIMENSION Q(NMAX),SQ(NMAX),VDER(NMAX),DBI(NMAX),BI(NMAX) - INTEGER :: J,I,I1,I2,I3,IU, IV, NU,NV,NG,N,NIT, NNIT, INF - INTEGER :: fffff -C REAL*8 EPS0 -C INTEGER III01,III11,III21,III31,III41,III51 -C *,III61,III71,III81,III91,III101 , III0 -C COMMON/CHECK1/III01,III11,III21,III31,III41,III51 -C *,III61,III71,III81,III91,III101 -C COMMON/CHECKQ/III0 -C COMMON /EPS/ EPS,EPSS,CEPSS - -C -C Initiation of all constants and integration nodes 'INITINTEG' -C - CALL INITINTEG(NIT) -c -c OBS. we are using the variables R,R1,R2 R3 as a temporary storage -C for transformation g of the process. - - - -c - CALL INITLEVELS(Ulev,NU,Vlev,NV,T,HHT,N,R1,R2,NG) - IF( R1(1) .gt. R1(ng)) then - do 13 I=1,ng - R3(I)=R1(I) - R(I) =R2(I) -13 continue - do 17 i=1,ng - R1(i) = R3(ng-i+1) - R2(i) = R(ng-i+1) -17 continue - end if - if(abs(R1(ng)-R1(1))*abs(R2(ng)-R2(1)).lt.0.01d0) then - print *,'The transformation g is singular, stop' - stop - end if - DO 14 IV=1,Nv - V=Vlev(IV) - CALL TRANSF(NG,V,R2,R1,VALUE,DER) - VT(IV)=VALUE - Vdd(IV)=DER -14 continue - DO 16 IU=1,Nu - U = Ulev(IU) - CALL TRANSF(NG,U,R2,R1,VALUE,DER) - UT(IU) = VALUE - Udd(IU) = DER - do 16 IV=1,Nv - UVdens(IU,IV)=0.0d0 -16 CONTINUE - - - CALL COVG(XL0,XL2,XL4,COV,R1,R2,R3,T,N) - - - Q0=XL4 - IF (Q0.le.1.0D0+EPS) then - Print *,'Covariance structure is singular, stop.' - stop - end if - SQ0 = SQRT(Q0) - Q1 = XL0-XL2*XL2/XL4 - IF (Q1.le.eps) then - Print *,'Covariance structure is singular, stop.' - stop - end if - SQ1 = SQRT(Q1) - DO 10 I=1,N - B0(I) =-COV(I+2*N) - DB0(I) =-COV(I+3*N) - DDB0(I)=-COV(I+4*N) - - B1(I) =COV(I)+COV(I+2*N)*(XL2/XL4) - DB1(I) =COV(I+N)+COV(I+3*N)*(XL2/XL4) - DDB1(I)=COV(I+2*N)+XL2*(COV(I+4*N)/XL4) -C -C Q(I) contains Var(X(T(i))|X'(0),X''(0),X(0)) -C VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0)) -C - Q(I)=XL0 - COV(I+N)*(COV(I+N)/XL2) - B0(I)*(B0(I)/Q0) - 1 -B1(I)*(B1(I)/Q1) - VDER(I)=XL4 - (COV(I+3*N)*COV(I+3*N))/XL2 - (DDB0(I)*DDB0(I))/Q0 - 1 - (DDB1(I)*DDB1(I))/Q1 - - -C -C DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0)) -C - DDB2(I)=-XL2 - (COV(I+N)*COV(I+3*N))/XL2 - DDB0(I)*(B0(I)/Q0) - 1 -DDB1(I)*(B1(I)/Q1) - IF(Q(I).LE.eps) then - SQ(i) =0.0d0 - DDB2(i)=0.0d0 - else - SQ(I)=SQRT(Q(I)) -C -C VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0),X(T(i)) -C - - VDER(I)=VDER(I) - (DDB2(I)*DDB2(I))/Q(I) - end if - -10 CONTINUE - DO 15 I=1,N - DO 15 J=1,N -C -C R1 contains Cov(X(T(I)),X'(T(J))|X'(0),X''(0),X(0)) -C - R1(J+(I-1)*N)=R1(J+(I-1)*N) - COV(I+N)*(COV(J+2*N)/XL2) - 1 - (B0(I)*DB0(J)/Q0) - (B1(I)*DB1(J)/Q1) - -C -C R2 contains Cov(X'(T(I)),X'(T(J))|X'(0),X''(0),X(0)) -C - R2(J+(I-1)*N) = -R2(J+(I-1)*N) - COV(I+2*N)*(COV(J+2*N)/XL2) - 1 - DB0(I)*DB0(J)/Q0 - DB1(I)*(DB1(J)/Q1) -C -C R3 contains Cov(X''(T(I)),X'(T(J))|X'(0),X''(0),X(0)) -C - R3(J+(I-1)*N) = R3(J+(I-1)*N) - COV(I+3*N)*(COV(J+2*N)/XL2) - 1 - DB0(J)*(DDB0(I)/Q0) - DDB1(I)*(DB1(J)/Q1) -15 CONTINUE - -C The initiations are finished and we are beginning with 3 loops -C on T=T(I), U=Ulevels(IU), V=Ulevels(IV), U>V. - - DO 20 I=1,N - - NNIT=NIT - IF (Q(I).LE.EPS) GO TO 20 - - DO 30 I1=1,I - DB2(I1)=R1(I1+(I-1)*N) - -C Cov(X'(T(I1)),X(T(i))|X'(0),X''(0),X(0)) -C DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0)) - - 30 CONTINUE - - DO 50 I3=1,I - DBI(I3) = R3(I3+(I-1)*N) - (DDB2(I)*DB2(I3)/Q(I)) - BI(I3) = R2(I3+(I-1)*N) - (DB2(I)*DB2(I3)/Q(I)) - 50 CONTINUE - DO 51 I3=1,I-1 - AI(I3)=0.0d0 - AI(I3+I-1)=DB0(I3)/SQ0 - AI(I3+2*(I-1))=DB1(I3)/SQ1 - AI(I3+3*(I-1))=DB2(I3)/SQ(I) - 51 CONTINUE - VDERI=VDER(I) - DAI(1)=0.0d0 - DAI(2)=DDB0(I)/SQ0 - DAI(3)=DDB1(I)/SQ1 - DAI(4)=DDB2(I)/SQ(I) - AA(1,1)=DB0(I)/SQ0 - AA(1,2)=DB1(I)/SQ1 - AA(1,3)=DB2(I)/SQ(I) - AA(2,1)=XL2/SQ0 - AA(2,2)=SQ1 - AA(2,3)=0.0d0 - AA(3,1)=B0(I)/SQ0 - AA(3,2)=B1(I)/SQ1 - AA(3,3)=SQ(I) - IF (BI(I).LE.EPS) NNIT=0 - IF (NNIT.GT.1) THEN - IF(I.LT.1) GO TO 41 - DO 40 I1=1,I-1 - DO 40 I2=1,I-1 - -C R contains Cov(X'(T(I1)),X'(T(I2))|X'(0),X''(0),X(0),X(I)) - - R(I2+(I1-1)*(I-1))=R2(I2+(I1-1)*N)-(DB2(I1)*DB2(I2)/Q(I)) - - 40 CONTINUE - 41 CONTINUE - END IF - -C Here the covariance of the problem would be innitiated - - INF=0 - Print *,' Laps to go:',N-I+1 - DO 80 IV=1,Nv - V=VT(IV) -! IF (ABS(V).GT.5.0D0) GO TO 80 - IF (Vdd(IV).LT.EPS0) GO TO 80 - DO 60 IU=1,Nu - U=UT(IU) - IF (U.LE.V) go to 60 -! IF (ABS(U).GT.5.0D0) GO TO 60 - IF (Udd(IU).LT.EPS0) GO TO 60 - BB(1)=0.0d0 - BB(2)=U - BB(3)=V -! if (IV.EQ.2.AND.IU.EQ.1) THEN -! fffff = 10 -! endif - - CALL MREG(F,R,BI,DBI,AA,BB,AI,DAI,VDERI,3,I-1,NNIT,INF) - INF=1 - UVdens(IU,IV) = UVdens(IU,IV) + Udd(IU)*Vdd(IV)*HHT(I)*F -! if (F.GT.0.01.AND.U.GT.2.AND.V.LT.-2) THEN -! if (N-I+1 .eq. 38.and.IV.EQ.26.AND.IU.EQ.16) THEN -! if (IV.EQ.32.AND.IU.EQ.8.and.I.eq.11) THEN -! PRINT * ,' R:', R(1:I) -! PRINT * ,' BI:', BI(1:I) -! PRINT * ,' DBI:', DBI(1:I) -! PRINT * ,' DB2:', DB2(1:I) -! PRINT * ,' DB0(1):', DB0(1) -! PRINT * ,' DB1(1):', DB1(1) -! PRINT * ,' DAI:', DAI -! PRINT * ,' BB:', BB -! PRINT * ,' VDERI:', VDERI -! PRINT * ,' F :', F -! PRINT * ,' UVDENS :', UVdens(IU,IV) -! fffff = 10 -! endif - - 60 CONTINUE - 80 continue - 20 CONTINUE - hhhh=0.0d0 - do 90 Iu=1,Nu - do 90 Iv=1,Nv - WRITE(10,300) Ulev(iu),Vlev(iv),UVdens(iu,iv) - hhhh=hhhh+UVdens(iu,iv) - 90 continue - if (nu.gt.1.and.nv.gt.1) then - write(11,*) 'SumSum f_uv *du*dv=' - 1,(Ulev(2)-Ulev(1))*(Vlev(2)-Vlev(1))*hhhh - end if - -C sder=sqrt(XL4-XL2*XL2/XL0) -C cder=-XL2/sqrt(XL0) -C const=1/sqrt(XL0*XL4) -C DO 95 IU=1,NU -C U=UT(IU) -C FM=Udd(IU)*const*exp(-0.5*U*U/XL0)*PMEAN(-cder*U,sder) -C WRITE(9,300) Ulev(IU),FM -C 95 continue -C DO 105 IV=1,NV -C V=VT(IV) -C VV=cder*V -C Fm=Vdd(IV)*const*exp(-0.5*V*V/XL0)*PMEAN(VV,sder) -C WRITE(8,300) Vlev(IV),Fm -C 105 continue - if (III0.eq.0) III0=1 - - write(11,*) 'Rate of calls RINDT0:',float(iii01)/float(III0) - write(11,*) 'Rate of calls RINDT1:',float(iii11)/float(III0) - write(11,*) 'Rate of calls RINDT2:',float(iii21)/float(III0) - write(11,*) 'Rate of calls RINDT3:',float(iii31)/float(III0) - write(11,*) 'Rate of calls RINDT4:',float(iii41)/float(III0) - write(11,*) 'Rate of calls RINDT5:',float(iii51)/float(III0) - write(11,*) 'Rate of calls RINDT6:',float(iii61)/float(III0) - write(11,*) 'Rate of calls RINDT7:',float(iii71)/float(III0) - write(11,*) 'Rate of calls RINDT8:',float(iii81)/float(III0) - write(11,*) 'Rate of calls RINDT9:',float(iii91)/float(III0) - write(11,*) 'Rate of calls RINDT10:',float(iii101)/float(III0) - write(11,*) 'Number of calls of RINDT*',III0 - - CLOSE(UNIT=8) - CLOSE(UNIT=9) - CLOSE(UNIT=10) - CLOSE(UNIT=11) - - 300 FORMAT(4(3X,F10.6)) - STOP - END - - SUBROUTINE INITLEVELS(ULEVELS,NU,Vlevels,Nv,T,HT,N,TG,XG,NG) - USE TBRMOD - USE SIZEMOD - IMPLICIT NONE -C INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201 -C DIMENSION ULEVELS(1),Vlevels(1),T(1),HT(1),TG(1),XG(1),HH(101) - REAL*8, DIMENSION(NMAX), intent(inout) :: ULEVELS,Vlevels,T,HT - REAL*8, DIMENSION(RDIM), intent(inout) :: TG,XG - INTEGER, intent(inout) :: NG - REAL*8 :: UMIN,UMAX,VMIN,VMAX, HU,HV - integer :: N, I, NU, NV -C REAL*8, DIMENSION(NMAX) :: HH -C COMMON/TBR/HH - OPEN(UNIT=2,FILE='transf.in') - OPEN(UNIT=4,FILE='Mm.in') - OPEN(UNIT=3,FILE='t.in') - - - NG=1 - 12 READ (2,*,END=11) TG(NG),XG(NG) - NG=NG+1 - GO TO 12 - 11 CONTINUE - NG=NG-1 - IF (NG.GT.501) THEN - PRINT *,'Vector defining transformation of data > 501, stop' - STOP - END IF - - - N=1 - 32 READ (3,*,END=31) T(N) - N=N+1 - GO TO 32 - 31 CONTINUE - N=N-1 - - CLOSE(UNIT=3) - - IF(N.ge.NMAX) then - print *,'The number of wavelength points >',NMAX-1, ' stop' - stop - end if - IF(N.lt.2) then - print *,'The number of wavelength points < 2, stop' - stop - end if - - HT(1)=0.5d0*(T(2)-T(1)) - HT(N)=0.5d0*(T(N)-T(N-1)) - HH(1)=-100.0d0 - HH(N)=-100.0d0 - DO 10 I=2,N-1 - HT(I)=0.5d0*(T(I+1)-T(I-1)) - HH(I)=-100.0d0 -10 CONTINUE - - - - READ(4,*) Umin,Umax,NU - READ(4,*) Vmin,Vmax,NV - - IF(NU.gt.NMAX) then - print *,'The number of maxima >',NMAX,' stop' - stop - end if - IF(NV.gt.NMAX) then - print *,'The number of minima >',NMAX,' stop' - stop - end if - - IF(NU.LT.1) Then - print *,'The number of maxima < 1, stop' - stop - end if - IF(NV.LT.1) Then - print *,'The number of minima < 1, stop' - stop - end if - - Ulevels(1)=Umax - IF (NU.lt.2) go to 25 - HU=(Umax-Umin)/DBLE(NU-1) - DO 20 I=1,NU-1 - ULEVELS(I+1)=Umax-DBLE(I)*HU -20 CONTINUE - - 25 continue - Vlevels(1)=Vmax - IF (NV.lt.2) go to 35 - HV=(Vmax-Vmin)/DBLE(NV-1) - DO 30 I=1,Nv-1 - VLEVELS(I+1)=Vmax-DBLE(I)*HV -30 CONTINUE -35 continue - CLOSE(UNIT=4) - RETURN - END - - - SUBROUTINE TRANSF(N,T,A,TIMEV,VALUE,DER) -C -C N number of data points -C TIMEV vector of time points -C A a vector of values of a function G(TIME) -C T independent time point -C VALUE is a value of a function at T, i.e. VALUE=G(T). -c DER=G'(t) -C - USE SIZEMOD - IMPLICIT NONE - REAL*8, intent(inout):: VALUE, DER,T -C INTEGER, PARAMETER :: RDIM = 10201 - REAL*8, DIMENSION(RDIM), intent(in) :: A,TIMEV - integer, intent(in) :: N - REAL*8:: T1 - integer :: I - - IF (T.LT.TIMEV(1)) then - der=(A(2)-A(1))/(TIMEV(2)-TIMEV(1)) - T1=T-TIMEV(1) - VALUE=A(1)+T1*DER - return - end if - IF (T.GT.TIMEV(N)) then - der = (A(N)-A(N-1))/(TIMEV(N)-TIMEV(N-1)) - T1 = T-TIMEV(N) - VALUE=A(N)+T1*DER - return - end if - DO 5 I=2,N - IF (T.LT.TIMEV(I)) GO TO 10 -5 CONTINUE -10 I=I-1 - T1=T-TIMEV(I) - DER=(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I)) - VALUE=A(I)+T1*DER - RETURN - END - - REAL*8 FUNCTION SPLE(N,T,A,TIMEV) -C -C N number of data points -C TIME vector of time points -C A a vector of values of a function G(TIME) -C T independent time point -C SPLE is a value of a function at T, i.e. SPLE=G(T). -C - USE SIZEMOD - IMPLICIT NONE - INTEGER, INTENT(IN):: N - - REAL*8, INTENT(IN) :: T - REAL*8, DIMENSION(5*NMAX), INTENT(IN) :: A,TIMEV - REAL*8 :: T1 - INTEGER :: I - SPLE=-9.9d0 - IF (T.LT.TIMEV(1) .OR. T.GT.TIMEV(N)) RETURN - DO 5 I=2,N - IF (T.LT.TIMEV(I)) GO TO 10 -5 CONTINUE -10 I=I-1 - T1=T-TIMEV(I) - SPLE=A(I)+T1*(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I)) - RETURN - END - - - - SUBROUTINE COVG(XL0,XL2,XL4,COV,COV1,COV2,COV3,T,N) -C -C COVG evaluates: -C -C XL0,XL2,XL4 - spectral moments. -C -C Covariance function and its four derivatives for a vector T of length N. -C It is saved in a vector COV; COV(1,...,N)=r(T), COV(N+1,...,2N)=r'(T), etc. -C The vector COV should be of the length 5*N. -C -C Covariance matrices COV1=r'(T-T), COV2=r''(T-T) and COV3=r'''(T-T) -C Dimension of COV1, COV2 should be N*N. -C - USE SIZEMOD -! IMPLICIT NONE -C INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201 - REAL*8, PARAMETER:: ZERO = 0.0d0 - REAL*8, intent(inout) :: XL0,XL2,XL4 - REAL*8, DIMENSION(5*NMAX), intent(inout) :: COV - REAL*8, DIMENSION(5*NMAX) :: A, TIMEV - REAL*8, DIMENSION(RDIM), intent(inout) :: COV1,COV2,COV3 - REAL*8, DIMENSION(NMAX), intent(in) :: T - INTEGER, intent(in) :: N - integer :: NT, I, J, II - REAL*8 :: TT, T0 - OPEN(UNIT=32,FILE='Cd0.in') - OPEN(UNIT=33,FILE='Cd1.in') - OPEN(UNIT=34,FILE='Cd2.in') - OPEN(UNIT=35,FILE='Cd3.in') - OPEN(UNIT=36,FILE='Cd4.in') -C -C COV(Y(T),Y(0)) -C - - NT=1 - 12 READ (32,*,END=11) TIMEV(NT),A(NT) - NT=NT+1 - GO TO 12 - 11 CONTINUE - NT=NT-1 - - - XL0=SPLE(NT,ZERO,A,TIMEV) - - DO 10 I=1,N - COV(I)=SPLE(NT,T(I),A,TIMEV) -10 CONTINUE - -C -C DERIVATIVE COV(Y(T),Y(0)) -C - - NT=1 - 22 READ (33,*,END=21) TIMEV(NT),A(NT) - NT=NT+1 - GO TO 22 - 21 CONTINUE - NT=NT-1 - - II=0 - DO 20 I=1,N - COV(I+N)=SPLE(NT,T(I),A,TIMEV) - DO 20 J=1,N - II=II+1 - T0=T(J)-T(I) - TT=ABS(T0) - COV1(II)=SPLE(NT,TT,A,TIMEV) - IF (T0.LT.0.0d0) COV1(II)=-COV1(II) -20 CONTINUE - -C 2-DERIVATIVE COV(Y(T),Y(0)) - - NT=1 - 32 READ (34,*,END=31) TIMEV(NT),A(NT) - NT=NT+1 - GO TO 32 - 31 CONTINUE - NT=NT-1 - - II=0 - XL2=-SPLE(NT,ZERO,A,TIMEV) - - DO 30 I=1,N - COV(I+2*N)=SPLE(NT,T(I),A,TIMEV) - DO 30 J=1,N - II=II+1 - TT=ABS(T(J)-T(I)) - COV2(II)=SPLE(NT,TT,A,TIMEV) -30 CONTINUE - -C 3-DERIVATIVE COV(Y(T),Y(0)) - - NT=1 - 42 READ (35,*,END=41) TIMEV(NT),A(NT) - NT=NT+1 - GO TO 42 - 41 CONTINUE - NT=NT-1 - - - II=0 - DO 40 I=1,N - COV(I+3*N)=SPLE(NT,T(I),A,TIMEV) - DO 40 J=1,N - II=II+1 - T0=T(J)-T(I) - TT=ABS(T0) - COV3(II)=SPLE(NT,TT,A,TIMEV) - IF (T0.LT.0.0d0) COV3(II)=-COV3(II) -40 CONTINUE - - - -C 4-DERIVATIVE COV(Y(T),Y(0)) - - NT=1 - 52 READ (36,*,END=51) TIMEV(NT),A(NT) - NT=NT+1 - GO TO 52 - 51 CONTINUE - NT=NT-1 - - XL4=SPLE(NT,ZERO,A,TIMEV) - - DO 50 I=1,N - COV(I+4*N)=SPLE(NT,T(I),A,TIMEV) -50 CONTINUE - CLOSE(UNIT=32) - CLOSE(UNIT=33) - CLOSE(UNIT=34) - CLOSE(UNIT=35) - CLOSE(UNIT=36) - RETURN - END - - SUBROUTINE INITINTEG(NIT) - USE RINTMOD - USE EPSMOD - USE INFCMOD - USE MREGMOD -! IMPLICIT NONE - INTEGER, intent(inout) :: NIT -! INTEGER ISQ1 -C dimension INF(10),INFO(10) - -C COMMON /RINT/ C,FC -C COMMON /EPS/ EPS,EPSS,CEPSS -C COMMON /INFC/ ISQ,INF,INFO - OPEN(UNIT=1,FILE='accur.in') - OPEN(UNIT=8,FILE='min.out') - OPEN(UNIT=9,FILE='Max.out') - OPEN(UNIT=10,FILE='Maxmin.out') - OPEN(UNIT=11,FILE='Maxmin.log') - - READ(1,*) NIT,IAC,ISQ - READ(1,*) EPS,EPSS,EPS0 - - CLOSE (UNIT=1) - - FC=FI(C)-FI(-C) - CEPSS=1.0d0-EPSS - - RETURN - END - diff --git a/wafo/source/mreg/cov2mmpdfreg_intfc.f b/wafo/source/mreg/cov2mmpdfreg_intfc.f deleted file mode 100644 index 445d617..0000000 --- a/wafo/source/mreg/cov2mmpdfreg_intfc.f +++ /dev/null @@ -1,370 +0,0 @@ -C Version 1994-X-18 - -C This is a new version of WAMP program computing crest-trough wavelength -C and amplitude density. -C -C revised pab 2007 -C -moved all common blocks into modules -C -renamed from minmax to sp2mmpdfreg + fixed some bugs -C revised pab July 2007 -! -renamed from sp2mmpdfreg to cov2mmpdfreg -! gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -c dsvdc.f mregmodule.f cov2mmpdfreg.f - - SUBROUTINE INITINTEG(EPS_,EPSS_,EPS0_,C_,IAC_,ISQ_) -! Initiation of all constants and integration nodes 'INITINTEG' - USE RINTMOD - USE EPSMOD - USE INFCMOD - USE MREGMOD - REAL*8 :: EPS_,EPSS_,EPS0_,C_ - INTEGER :: IAC_,ISQ_ -Cf2py real*8, optional :: EPS_ = 0.01 -Cf2py real*8, optional :: EPSS_ = 0.00005 -Cf2py real*8, optional :: EPS0_ = 0.00005 -Cf2py real*8, optional :: C_ = 4.5 -Cf2py integer, optional :: IAC_ = 1 -Cf2py integer, optional :: ISQ_ = 0 -! IMPLICIT NONE -C COMMON /RINT/ C,FC -C COMMON /EPS/ EPS,EPSS,CEPSS -C COMMON /INFC/ ISQ,INF,INFO - - IAC = IAC_ - ISQ = ISQ_ - EPS = EPS_ - EPSS = EPSS_ - EPS0 = EPS0_ - C = C_ - - FC = FI(C)-FI(-C) -! CEPSS = 1.0d0-EPSS - RETURN - END SUBROUTINE INITINTEG - - subroutine cov2mmpdfreg(UVdens,t,COV,ULev,VLev,Tg,Xg,Nt,Nu,Nv,Ng, - & NIT) - USE SIZEMOD - USE EPSMOD - USE CHECKMOD - USE MREGMOD - USE INTFCMOD - IMPLICIT NONE - INTEGER, INTENT(IN) :: Nt, Nu, Nv, Ng, NIT - REAL*8, DIMENSION(Nt,5), intent(in):: COV - REAL*8, DIMENSION(Nu,Nv), intent(out):: UVdens - REAL*8, DIMENSION(Nu), intent(in):: ULev - REAL*8, DIMENSION(Nv), intent(in):: VLev - REAL*8, DIMENSION(Ng), intent(in):: Tg, Xg - REAL*8, dimension(Nt), intent(in):: T -Cf2py integer, intent(hide), depend(t) :: Nt = len(t) -Cf2py integer, intent(hide), depend(Ulev) :: Nu = len(Ulev) -Cf2py integer, intent(hide), depend(Vlev) :: Nv = len(Vlev) -Cf2py integer, intent(hide), depend(Tg) :: Ng = len(Tg) -Cf2py integer, optional :: NIT = 2 -Cf2py real*8, intent(out), depend(Nu,Nv) :: UVdens -Cf2py depend(Ng) Xg -Cf2py depend(Nt,5) COV - real*8 Q0,SQ0,Q1,SQ1, U,V, XL0, XL2, XL4 - REAL*8 VDERI, DER, F, HHHH, VALUE -C REAL*8 VV, CDER,SDER, CONST1, FM -C INTEGER, PARAMETER :: MMAX = 5, NMAX = 101, RDIM = 10201 - REAL*8, DIMENSION(NMAX) :: HHT,VT,UT,Vdd,Udd - REAL*8, DIMENSION(RDIM) :: R,R1,R2,R3 - REAL*8:: AA(MMAX-2,MMAX-2),AI((MMAX+1)*NMAX) - REAL*8, DIMENSION(MMAX+1) :: BB, DAI -C DIMENSION UVdens(NMAX,NMAX),HHT(NMAX) -C DIMENSION T(NMAX),Ulev(NMAX),Vlev(NMAX) -C DIMENSION VT(NMAX),UT(NMAX),Vdd(NMAX),Udd(NMAX) -C DIMENSION COV(5*NMAX),R(RDIM),R1(RDIM),R2(RDIM),R3(RDIM) - - -C -C The program computes the joint density of maximum the following minimum -C and the distance between Max and min for a zero-mean stationary -C Gaussian process with covariance function defined explicitely with 4 -C derivatives. The process should be normalized so that the first and -C the second spectral moments are equal to 1. The values of Max are taken -C as the nodes at Hermite-Quadrature and then integrated out so that -C the output is a joint density of wavelength T and amplitude H=Max-min. -C The Max values are defined by subroutine Gauss_M with the accuracy -C input epsu. The principle is that the integral of the marginal density -C of f_Max is computed with sufficient accuracy. -C - REAL*8, DIMENSION(NMAX) :: B0,DB0,DDB0,B1,DB1,DDB1,DB2,DDB2 - REAL*8, DIMENSION(NMAX) :: Q,SQ,VDER,DBI,BI -C DIMENSION B0(NMAX),DB0(NMAX),DDB0(NMAX) -C DIMENSION B1(NMAX),DB1(NMAX),DDB1(NMAX) -C DIMENSION DB2(NMAX),DDB2(NMAX) -C DIMENSION Q(NMAX),SQ(NMAX),VDER(NMAX),DBI(NMAX),BI(NMAX) - INTEGER :: J,I,I1,I2,I3,IU, IV,N, NNIT, INF -C INTEGER :: fffff -C REAL*8 EPS0 -C INTEGER III01,III11,III21,III31,III41,III51 -C *,III61,III71,III81,III91,III101 , III0 -C COMMON/CHECK1/III01,III11,III21,III31,III41,III51 -C *,III61,III71,III81,III91,III101 -C COMMON/CHECKQ/III0 -C COMMON /EPS/ EPS,EPSS,CEPSS - -C -C Initiation of all constants and integration nodes 'INITINTEG' -C -! CALL INITINTEG() - -! OPEN(UNIT=8,FILE='min.out') -! OPEN(UNIT=9,FILE='Max.out') -! OPEN(UNIT=10,FILE='Maxmin.out') -! OPEN(UNIT=11,FILE='Maxmin.log') -c -c OBS. we are using the variables R,R1,R2 R3 as a temporary storage -C for transformation g of the process. - - N = Nt - CALL INITLEVELS(T,HHT,Nt,NU,Nv) -C CALL INITLEVELS(Ulev,NU,Vlev,NV,T,HHT,Nt,R1,R2,NG) - IF( Tg(1) .gt. Tg(ng)) then - print *,'Error Tg must be strictly increasing' - return - end if - if(abs(Tg(ng)-Tg(1))*abs(Xg(ng)-Xg(1)).lt.0.01d0) then - print *,'The transformation g is singular, stop' - return - end if - -! do IV=1,Nt -! print *, 'Cov', COV(IV,:) -! end do - - DO IV=1,Nv - V=Vlev(IV) - CALL TRANSF(NG,V,Xg,Tg,VALUE,DER) - VT(IV)=VALUE - Vdd(IV)=DER - enddo - DO IU=1,Nu - U = Ulev(IU) - CALL TRANSF(NG,U,Xg,Tg,VALUE,DER) - UT(IU) = VALUE - Udd(IU) = DER - do IV=1,Nv - UVdens(IU,IV)=0.0d0 - enddo - enddo - - CALL COVG(XL0,XL2,XL4,R1,R2,R3,COV,T,Nt) - - - Q0=XL4 - IF (Q0.le.1.0D0+EPS) then - Print *,'Covariance structure is singular, stop.' - return - end if - SQ0 = SQRT(Q0) - Q1 = XL0-XL2*XL2/XL4 - IF (Q1.le.EPS) then - Print *,'Covariance structure is singular, stop.' - return - end if - SQ1 = SQRT(Q1) - DO I=1,Nt - B0(I) =-COV(I,3) - DB0(I) =-COV(I,4) - DDB0(I)=-COV(I,5) - - B1(I) =COV(I,1)+COV(I,3)*(XL2/XL4) - DB1(I) =COV(I,2)+COV(I,4)*(XL2/XL4) - DDB1(I)=COV(I,3)+XL2*(COV(I,5)/XL4) -C -C Q(I) contains Var(X(T(i))|X'(0),X''(0),X(0)) -C VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0)) -C - Q(I)=XL0 - COV(I,2)*(COV(I,2)/XL2) - B0(I)*(B0(I)/Q0) - 1 -B1(I)*(B1(I)/Q1) - VDER(I)=XL4 - (COV(I,4)*COV(I,4))/XL2 - (DDB0(I)*DDB0(I))/Q0 - 1 - (DDB1(I)*DDB1(I))/Q1 - - -C -C DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0)) -C - DDB2(I)=-XL2 - (COV(I,2)*COV(I,4))/XL2 - DDB0(I)*(B0(I)/Q0) - 1 -DDB1(I)*(B1(I)/Q1) - IF(Q(I).LE.eps) then - SQ(i) =0.0d0 - DDB2(i)=0.0d0 - else - SQ(I)=SQRT(Q(I)) -C -C VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0),X(T(i)) -C - - VDER(I)=VDER(I) - (DDB2(I)*DDB2(I))/Q(I) - end if - -c10 CONTINUE - enddo - DO I=1,Nt - DO J=1,Nt -C -C R1 contains Cov(X(T(I)),X'(T(J))|X'(0),X''(0),X(0)) -C - R1(J+(I-1)*N) = R1(J+(I-1)*N) - COV(I,2)*(COV(J,3)/XL2) - 1 - (B0(I)*DB0(J)/Q0) - (B1(I)*DB1(J)/Q1) - -C -C R2 contains Cov(X'(T(I)),X'(T(J))|X'(0),X''(0),X(0)) -C - R2(J+(I-1)*N) = -R2(J+(I-1)*N) - COV(I,3)*(COV(J,3)/XL2) - 1 - DB0(I)*DB0(J)/Q0 - DB1(I)*(DB1(J)/Q1) -C -C R3 contains Cov(X''(T(I)),X'(T(J))|X'(0),X''(0),X(0)) -C - R3(J+(I-1)*N) = R3(J+(I-1)*N) - COV(I,4)*(COV(J,3)/XL2) - 1 - DB0(J)*(DDB0(I)/Q0) - DDB1(I)*(DB1(J)/Q1) -c15 CONTINUE - enddo - enddo - -C The initiations are finished and we are beginning with 3 loops -C on T=T(I), U=Ulevels(IU), V=Ulevels(IV), U>V. - - DO I=1,Nt - - NNIT=NIT - IF (Q(I).LE.EPS) GO TO 20 - - DO I1=1,I - DB2(I1)=R1(I1+(I-1)*N) - -C Cov(X'(T(I1)),X(T(i))|X'(0),X''(0),X(0)) -C DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0)) - - enddo - - DO I3=1,I - DBI(I3) = R3(I3+(I-1)*N) - (DDB2(I)*DB2(I3)/Q(I)) - BI(I3) = R2(I3+(I-1)*N) - (DB2(I)*DB2(I3)/Q(I)) - enddo - DO I3=1,I-1 - AI(I3)=0.0d0 - AI(I3+I-1)=DB0(I3)/SQ0 - AI(I3+2*(I-1))=DB1(I3)/SQ1 - AI(I3+3*(I-1))=DB2(I3)/SQ(I) - enddo - VDERI=VDER(I) - DAI(1)=0.0d0 - DAI(2)=DDB0(I)/SQ0 - DAI(3)=DDB1(I)/SQ1 - DAI(4)=DDB2(I)/SQ(I) - AA(1,1)=DB0(I)/SQ0 - AA(1,2)=DB1(I)/SQ1 - AA(1,3)=DB2(I)/SQ(I) - AA(2,1)=XL2/SQ0 - AA(2,2)=SQ1 - AA(2,3)=0.0d0 - AA(3,1)=B0(I)/SQ0 - AA(3,2)=B1(I)/SQ1 - AA(3,3)=SQ(I) - IF (BI(I).LE.EPS) NNIT=0 - IF (NNIT.GT.1) THEN - IF(I.LT.1) GO TO 41 - DO I1=1,I-1 - DO I2=1,I-1 -C R contains Cov(X'(T(I1)),X'(T(I2))|X'(0),X''(0),X(0),X(I)) - R(I2+(I1-1)*(I-1))=R2(I2+(I1-1)*N)-(DB2(I1)*DB2(I2)/Q(I)) - - enddo - enddo - 41 CONTINUE - END IF - -C Here the covariance of the problem would be initiated - - INF=0 - Print *,' Laps to go:',Nt-I+1 - DO IV=1,Nv - V=VT(IV) -! IF (ABS(V).GT.5.0D0) GO TO 80 - IF (Vdd(IV).LT.EPS0) GO TO 80 - DO IU=1,Nu - U=UT(IU) - IF (U.LE.V) go to 60 -! IF (ABS(U).GT.5.0D0) GO TO 60 - IF (Udd(IU).LT.EPS0) GO TO 60 - BB(1)=0.0d0 - BB(2)=U - BB(3)=V -! if (IV.EQ.2.AND.IU.EQ.1) THEN -! fffff = 10 -! endif - - CALL MREG(F,R,BI,DBI,AA,BB,AI,DAI,VDERI,3,I-1,NNIT,INF) - INF=1 - UVdens(IU,IV) = UVdens(IU,IV) + Udd(IU)*Vdd(IV)*HHT(I)*F - -! if (F.GT.0.01.AND.U.GT.2.AND.V.LT.-2) THEN -! if (N-I+1 .eq. 38.and.IV.EQ.26.AND.IU.EQ.16) THEN -! if (IV.EQ.32.AND.IU.EQ.8.and.I.eq.11) THEN -! PRINT * ,' R:', R(1:I) -! PRINT * ,' BI:', BI(1:I) -! PRINT * ,' DBI:', DBI(1:I) -! PRINT * ,' DB2:', DB2(1:I) -! PRINT * ,' DB0(1):', DB0(1) -! PRINT * ,' DB1(1):', DB1(1) -! PRINT * ,' DAI:', DAI -! PRINT * ,' BB:', BB -! PRINT * ,' VDERI:', VDERI -! PRINT * ,' F :', F -! PRINT * ,' UVDENS :', UVdens(IU,IV) -! fffff = 10 -! endif - - 60 CONTINUE - enddo - 80 continue - enddo - 20 CONTINUE - enddo - - hhhh=0.0d0 - do Iu=1,Nu - do Iv=1,Nv -! WRITE(10,300) Ulev(iu),Vlev(iv),UVdens(iu,iv) - hhhh=hhhh+UVdens(iu,iv) - enddo - enddo - if (nu.gt.1.and.nv.gt.1) then - VALUE = (Ulev(2)-Ulev(1))*(Vlev(2)-Vlev(1))*hhhh - print *,'SumSum f_uv *du*dv=', VALUE - end if - -C sder=sqrt(XL4-XL2*XL2/XL0) -C cder=-XL2/sqrt(XL0) -C const1=1/sqrt(XL0*XL4) -C DO 95 IU=1,NU -C U=UT(IU) -C FM=Udd(IU)*const1*exp(-0.5*U*U/XL0)*PMEAN(-cder*U,sder) -C WRITE(9,300) Ulev(IU),FM -C 95 continue -C DO 105 IV=1,NV -C V=VT(IV) -C VV=cder*V -C Fm=Vdd(IV)*const1*exp(-0.5*V*V/XL0)*PMEAN(VV,sder) -C WRITE(8,300) Vlev(IV),Fm -C 105 continue - if (III0.eq.0) III0=1 - - PRINT *, 'Rate of calls RINDT0:',float(iii01)/float(III0) - PRINT *, 'Rate of calls RINDT1:',float(iii11)/float(III0) - PRINT *, 'Rate of calls RINDT2:',float(iii21)/float(III0) - PRINT *, 'Rate of calls RINDT3:',float(iii31)/float(III0) - PRINT *, 'Rate of calls RINDT4:',float(iii41)/float(III0) - PRINT *, 'Rate of calls RINDT5:',float(iii51)/float(III0) - PRINT *, 'Rate of calls RINDT6:',float(iii61)/float(III0) - PRINT *, 'Rate of calls RINDT7:',float(iii71)/float(III0) - PRINT *, 'Rate of calls RINDT8:',float(iii81)/float(III0) - PRINT *, 'Rate of calls RINDT9:',float(iii91)/float(III0) - PRINT *, 'Rate of calls RINDT10:',float(iii101)/float(III0) - PRINT *, 'Number of calls of RINDT*',III0 - return - END subroutine cov2mmpdfreg diff --git a/wafo/source/mreg/dsvdc.f b/wafo/source/mreg/dsvdc.f deleted file mode 100644 index 9330beb..0000000 --- a/wafo/source/mreg/dsvdc.f +++ /dev/null @@ -1,613 +0,0 @@ - MODULE SVD - IMPLICIT NONE - INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(12, 60) - -! Based upon routines from the NSWC (Naval Surface Warfare Center), -! which were based upon LAPACK routines. - -! Code converted using TO_F90 by Alan Miller -! Date: 2003-11-11 Time: 17:50:44 -! Revised pab 2007 -! Converted to fixed form - - - CONTAINS - - - SUBROUTINE drotg(da, db, dc, ds) - -! DESIGNED BY C.L.LAWSON, JPL, 1977 SEPT 08 -! -! CONSTRUCT THE GIVENS TRANSFORMATION -! -! ( DC DS ) -! G = ( ) , DC**2 + DS**2 = 1 , -! (-DS DC ) -! -! WHICH ZEROS THE SECOND ENTRY OF THE 2-VECTOR (DA,DB)**T . -! -! THE QUANTITY R = (+/-)SQRT(DA**2 + DB**2) OVERWRITES DA IN -! STORAGE. THE VALUE OF DB IS OVERWRITTEN BY A VALUE Z WHICH -! ALLOWS DC AND DS TO BE RECOVERED BY THE FOLLOWING ALGORITHM: -! IF Z=1 SET DC=0.D0 AND DS=1.D0 -! IF DABS(Z) < 1 SET DC=SQRT(1-Z**2) AND DS=Z -! IF DABS(Z) > 1 SET DC=1/Z AND DS=SQRT(1-DC**2) -! -! NORMALLY, THE SUBPROGRAM DROT(N,DX,INCX,DY,INCY,DC,DS) WILL -! NEXT BE CALLED TO APPLY THE TRANSFORMATION TO A 2 BY N MATRIX. -! -! ------------------------------------------------------------------ - - REAL (dp), INTENT(IN OUT) :: da - REAL (dp), INTENT(IN OUT) :: db - REAL (dp), INTENT(OUT) :: dc - REAL (dp), INTENT(OUT) :: ds - - REAL (dp) :: u, v, r - IF (ABS(da) <= ABS(db)) GO TO 10 - -! *** HERE ABS(DA) > ABS(DB) *** - - u = da + da - v = db / u - -! NOTE THAT U AND R HAVE THE SIGN OF DA - - r = SQRT(.25D0 + v**2) * u - -! NOTE THAT DC IS POSITIVE - - dc = da / r - ds = v * (dc + dc) - db = ds - da = r - RETURN - -! *** HERE ABS(DA) <= ABS(DB) *** - - 10 IF (db == 0.d0) GO TO 20 - u = db + db - v = da / u - -! NOTE THAT U AND R HAVE THE SIGN OF DB -! (R IS IMMEDIATELY STORED IN DA) - - da = SQRT(.25D0 + v**2) * u - -! NOTE THAT DS IS POSITIVE - - ds = db / da - dc = v * (ds + ds) - IF (dc == 0.d0) GO TO 15 - db = 1.d0 / dc - RETURN - 15 db = 1.d0 - RETURN - -! *** HERE DA = DB = 0.D0 *** - - 20 dc = 1.d0 - ds = 0.d0 - RETURN - - END SUBROUTINE drotg - - - SUBROUTINE dswap1 (n, dx, dy) -! INTERCHANGES TWO VECTORS. -! USES UNROLLED LOOPS FOR INCREMENTS EQUAL ONE. -! JACK DONGARRA, LINPACK, 3/11/78. -! This version is for increments = 1. - - INTEGER, INTENT(IN) :: n - REAL (dp), INTENT(IN OUT) :: dx(*) - REAL (dp), INTENT(IN OUT) :: dy(*) - - REAL (dp) :: dtemp - INTEGER :: i, m, mp1 - - IF(n <= 0) RETURN - -! CODE FOR BOTH INCREMENTS EQUAL TO 1 -! -! CLEAN-UP LOOP - - m = MOD(n,3) - IF( m == 0 ) GO TO 40 - DO i = 1,m - dtemp = dx(i) - dx(i) = dy(i) - dy(i) = dtemp - END DO - IF( n < 3 ) RETURN - 40 mp1 = m + 1 - DO i = mp1,n,3 - dtemp = dx(i) - dx(i) = dy(i) - dy(i) = dtemp - dtemp = dx(i + 1) - dx(i + 1) = dy(i + 1) - dy(i + 1) = dtemp - dtemp = dx(i + 2) - dx(i + 2) = dy(i + 2) - dy(i + 2) = dtemp - END DO - RETURN - END SUBROUTINE dswap1 - - - SUBROUTINE drot1 (n, dx, dy, c, s) -! APPLIES A PLANE ROTATION. -! JACK DONGARRA, LINPACK, 3/11/78. -! This version is for increments = 1. - - INTEGER, INTENT(IN) :: n - REAL (dp), INTENT(IN OUT) :: dx(*) - REAL (dp), INTENT(IN OUT) :: dy(*) - REAL (dp), INTENT(IN) :: c - REAL (dp), INTENT(IN) :: s - - REAL (dp) :: dtemp - INTEGER :: i - - IF(n <= 0) RETURN -! CODE FOR BOTH INCREMENTS EQUAL TO 1 - - DO i = 1,n - dtemp = c*dx(i) + s*dy(i) - dy(i) = c*dy(i) - s*dx(i) - dx(i) = dtemp - END DO - RETURN - END SUBROUTINE drot1 - - - SUBROUTINE dsvdc(x, n, p, s, e, u, v, job, info) - - INTEGER, INTENT(IN) :: n - INTEGER, INTENT(IN) :: p - REAL (dp), INTENT(IN OUT) :: x(:,:) - REAL (dp), INTENT(OUT) :: s(:) - REAL (dp), INTENT(OUT) :: e(:) - REAL (dp), INTENT(OUT) :: u(:,:) - REAL (dp), INTENT(OUT) :: v(:,:) - INTEGER, INTENT(IN) :: job - INTEGER, INTENT(OUT) :: info - -! DSVDC IS A SUBROUTINE TO REDUCE A DOUBLE PRECISION NXP MATRIX X -! BY ORTHOGONAL TRANSFORMATIONS U AND V TO DIAGONAL FORM. THE -! DIAGONAL ELEMENTS S(I) ARE THE SINGULAR VALUES OF X. THE -! COLUMNS OF U ARE THE CORRESPONDING LEFT SINGULAR VECTORS, -! AND THE COLUMNS OF V THE RIGHT SINGULAR VECTORS. -! -! ON ENTRY -! -! X DOUBLE PRECISION(LDX,P), WHERE LDX.GE.N. -! X CONTAINS THE MATRIX WHOSE SINGULAR VALUE -! DECOMPOSITION IS TO BE COMPUTED. X IS -! DESTROYED BY DSVDC. -! -! LDX INTEGER. -! LDX IS THE LEADING DIMENSION OF THE ARRAY X. -! -! N INTEGER. -! N IS THE NUMBER OF ROWS OF THE MATRIX X. -! -! P INTEGER. -! P IS THE NUMBER OF COLUMNS OF THE MATRIX X. -! -! LDU INTEGER. -! LDU IS THE LEADING DIMENSION OF THE ARRAY U. -! (SEE BELOW). -! -! LDV INTEGER. -! LDV IS THE LEADING DIMENSION OF THE ARRAY V. -! (SEE BELOW). -! -! JOB INTEGER. -! JOB CONTROLS THE COMPUTATION OF THE SINGULAR -! VECTORS. IT HAS THE DECIMAL EXPANSION AB -! WITH THE FOLLOWING MEANING -! -! A.EQ.0 DO NOT COMPUTE THE LEFT SINGULAR VECTORS. -! A.EQ.1 RETURN THE N LEFT SINGULAR VECTORS IN U. -! A.GE.2 RETURN THE FIRST MIN(N,P) SINGULAR -! VECTORS IN U. -! B.EQ.0 DO NOT COMPUTE THE RIGHT SINGULAR VECTORS. -! B.EQ.1 RETURN THE RIGHT SINGULAR VECTORS IN V. -! -! ON RETURN -! -! S DOUBLE PRECISION(MM), WHERE MM=MIN(N+1,P). -! THE FIRST MIN(N,P) ENTRIES OF S CONTAIN THE SINGULAR -! VALUES OF X ARRANGED IN DESCENDING ORDER OF MAGNITUDE. -! -! E DOUBLE PRECISION(P). -! E ORDINARILY CONTAINS ZEROS. HOWEVER SEE THE -! DISCUSSION OF INFO FOR EXCEPTIONS. -! -! U DOUBLE PRECISION(LDU,K), WHERE LDU.GE.N. IF -! JOBA.EQ.1 THEN K.EQ.N, IF JOBA.GE.2 -! THEN K.EQ.MIN(N,P). -! U CONTAINS THE MATRIX OF LEFT SINGULAR VECTORS. -! U IS NOT REFERENCED IF JOBA.EQ.0. IF N.LE.P -! OR IF JOBA.EQ.2, THEN U MAY BE IDENTIFIED WITH X -! IN THE SUBROUTINE CALL. -! -! V DOUBLE PRECISION(LDV,P), WHERE LDV.GE.P. -! V CONTAINS THE MATRIX OF RIGHT SINGULAR VECTORS. -! V IS NOT REFERENCED IF JOB.EQ.0. IF P.LE.N, -! THEN V MAY BE IDENTIFIED WITH X IN THE -! SUBROUTINE CALL. -! -! INFO INTEGER. -! THE SINGULAR VALUES (AND THEIR CORRESPONDING SINGULAR -! VECTORS) S(INFO+1),S(INFO+2),...,S(M) ARE CORRECT -! (HERE M=MIN(N,P)). THUS IF INFO.EQ.0, ALL THE -! SINGULAR VALUES AND THEIR VECTORS ARE CORRECT. -! IN ANY EVENT, THE MATRIX B = TRANS(U)*X*V IS THE -! BIDIAGONAL MATRIX WITH THE ELEMENTS OF S ON ITS DIAGONAL -! AND THE ELEMENTS OF E ON ITS SUPER-DIAGONAL (TRANS(U) -! IS THE TRANSPOSE OF U). THUS THE SINGULAR VALUES -! OF X AND B ARE THE SAME. -! -! LINPACK. THIS VERSION DATED 03/19/79 . -! G.W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB. -! -! DSVDC USES THE FOLLOWING FUNCTIONS AND SUBPROGRAMS. -! -! EXTERNAL DROT -! BLAS DAXPY,DDOT,DSCAL,DSWAP,DNRM2,DROTG -! FORTRAN DABS,DMAX1,MAX0,MIN0,MOD,DSQRT - -! INTERNAL VARIABLES - - INTEGER :: iter, j, jobu, k, kase, kk, l, ll, lls, lm1, lp1, ls, - & lu, m, maxit,mm, mm1, mp1, nct, nctp1, ncu, nrt, nrtp1 - REAL (dp) :: t, work(n) - REAL (dp) :: b, c, cs, el, emm1, f, g, scale, shift, sl, sm, sn, - & smm1, t1, test, ztest - LOGICAL :: wantu, wantv - -! SET THE MAXIMUM NUMBER OF ITERATIONS. - - maxit = 30 - -! DETERMINE WHAT IS TO BE COMPUTED. - - wantu = .false. - wantv = .false. - jobu = MOD(job,100)/10 - ncu = n - IF (jobu > 1) ncu = MIN(n,p) - IF (jobu /= 0) wantu = .true. - IF (MOD(job,10) /= 0) wantv = .true. - -! REDUCE X TO BIDIAGONAL FORM, STORING THE DIAGONAL ELEMENTS -! IN S AND THE SUPER-DIAGONAL ELEMENTS IN E. - - info = 0 - nct = MIN(n-1, p) - s(1:nct+1) = 0.0_dp - nrt = MAX(0, MIN(p-2,n)) - lu = MAX(nct,nrt) - IF (lu < 1) GO TO 170 - DO l = 1, lu - lp1 = l + 1 - IF (l > nct) GO TO 20 - -! COMPUTE THE TRANSFORMATION FOR THE L-TH COLUMN AND -! PLACE THE L-TH DIAGONAL IN S(L). - - s(l) = SQRT( SUM( x(l:n,l)**2 ) ) - IF (s(l) == 0.0D0) GO TO 10 - IF (x(l,l) /= 0.0D0) s(l) = SIGN(s(l), x(l,l)) - x(l:n,l) = x(l:n,l) / s(l) - x(l,l) = 1.0D0 + x(l,l) - - 10 s(l) = -s(l) - - 20 IF (p < lp1) GO TO 50 - DO j = lp1, p - IF (l > nct) GO TO 30 - IF (s(l) == 0.0D0) GO TO 30 - -! APPLY THE TRANSFORMATION. - - t = -DOT_PRODUCT(x(l:n,l), x(l:n,j)) / x(l,l) - x(l:n,j) = x(l:n,j) + t * x(l:n,l) - -! PLACE THE L-TH ROW OF X INTO E FOR THE -! SUBSEQUENT CALCULATION OF THE ROW TRANSFORMATION. - - 30 e(j) = x(l,j) - END DO - - 50 IF (.NOT.wantu .OR. l > nct) GO TO 70 - -! PLACE THE TRANSFORMATION IN U FOR SUBSEQUENT BACK MULTIPLICATION. - - u(l:n,l) = x(l:n,l) - - 70 IF (l > nrt) CYCLE - -! COMPUTE THE L-TH ROW TRANSFORMATION AND PLACE THE -! L-TH SUPER-DIAGONAL IN E(L). - - e(l) = SQRT( SUM( e(lp1:p)**2 ) ) - IF (e(l) == 0.0D0) GO TO 80 - IF (e(lp1) /= 0.0D0) e(l) = SIGN(e(l), e(lp1)) - e(lp1:lp1+p-l-1) = e(lp1:p) / e(l) - e(lp1) = 1.0D0 + e(lp1) - - 80 e(l) = -e(l) - IF (lp1 > n .OR. e(l) == 0.0D0) GO TO 120 - -! APPLY THE TRANSFORMATION. - - work(lp1:n) = 0.0D0 - DO j = lp1, p - work(lp1:lp1+n-l-1) = work(lp1:lp1+n-l-1) + e(j) * - & x(lp1:lp1+n-l-1,j) - END DO - DO j = lp1, p - x(lp1:lp1+n-l-1,j) = x(lp1:lp1+n-l-1,j) - (e(j)/e(lp1)) * - & work(lp1:lp1+n-l-1) - END DO - - 120 IF (.NOT.wantv) CYCLE - -! PLACE THE TRANSFORMATION IN V FOR SUBSEQUENT -! BACK MULTIPLICATION. - - v(lp1:p,l) = e(lp1:p) - END DO - -! SET UP THE FINAL BIDIAGONAL MATRIX OF ORDER M. - - 170 m = MIN(p,n+1) - nctp1 = nct + 1 - nrtp1 = nrt + 1 - IF (nct < p) s(nctp1) = x(nctp1,nctp1) - IF (n < m) s(m) = 0.0D0 - IF (nrtp1 < m) e(nrtp1) = x(nrtp1,m) - e(m) = 0.0D0 - -! IF REQUIRED, GENERATE U. - - IF (.NOT.wantu) GO TO 300 - IF (ncu < nctp1) GO TO 200 - DO j = nctp1, ncu - u(1:n,j) = 0.0_dp - u(j,j) = 1.0_dp - END DO - - 200 DO ll = 1, nct - l = nct - ll + 1 - IF (s(l) == 0.0D0) GO TO 250 - lp1 = l + 1 - IF (ncu < lp1) GO TO 220 - DO j = lp1, ncu - t = -DOT_PRODUCT(u(l:n,l), u(l:n,j)) / u(l,l) - u(l:n,j) = u(l:n,j) + t * u(l:n,l) - END DO - - 220 u(l:n,l) = -u(l:n,l) - u(l,l) = 1.0D0 + u(l,l) - lm1 = l - 1 - IF (lm1 < 1) CYCLE - u(1:lm1,l) = 0.0_dp - CYCLE - - 250 u(1:n,l) = 0.0_dp - u(l,l) = 1.0_dp - END DO - -! IF IT IS REQUIRED, GENERATE V. - - 300 IF (.NOT.wantv) GO TO 350 - DO ll = 1, p - l = p - ll + 1 - lp1 = l + 1 - IF (l > nrt) GO TO 320 - IF (e(l) == 0.0D0) GO TO 320 - DO j = lp1, p - t = -DOT_PRODUCT(v(lp1:lp1+p-l-1,l), - & v(lp1:lp1+p-l-1,j)) / v(lp1,l) - v(lp1:lp1+p-l-1,j) = v(lp1:lp1+p-l-1,j) + t * v(lp1:lp1+p-l-1,l) - END DO - - 320 v(1:p,l) = 0.0D0 - v(l,l) = 1.0D0 - END DO - -! MAIN ITERATION LOOP FOR THE SINGULAR VALUES. - - 350 mm = m - iter = 0 - -! QUIT IF ALL THE SINGULAR VALUES HAVE BEEN FOUND. - -! ...EXIT - 360 IF (m == 0) GO TO 620 - -! IF TOO MANY ITERATIONS HAVE BEEN PERFORMED, SET FLAG AND RETURN. - - IF (iter < maxit) GO TO 370 - info = m -! ......EXIT - GO TO 620 - -! THIS SECTION OF THE PROGRAM INSPECTS FOR NEGLIGIBLE ELEMENTS -! IN THE S AND E ARRAYS. ON COMPLETION -! THE VARIABLES KASE AND L ARE SET AS FOLLOWS. -! -! KASE = 1 IF S(M) AND E(L-1) ARE NEGLIGIBLE AND L < M -! KASE = 2 IF S(L) IS NEGLIGIBLE AND L < M -! KASE = 3 IF E(L-1) IS NEGLIGIBLE, L < M, AND -! S(L), ..., S(M) ARE NOT NEGLIGIBLE (QR STEP). -! KASE = 4 IF E(M-1) IS NEGLIGIBLE (CONVERGENCE). - - 370 DO ll = 1, m - l = m - ll -! ...EXIT - IF (l == 0) EXIT - test = ABS(s(l)) + ABS(s(l+1)) - ztest = test + ABS(e(l)) - IF (ztest /= test) CYCLE - e(l) = 0.0D0 -! ......EXIT - EXIT - END DO - - IF (l /= m - 1) GO TO 410 - kase = 4 - GO TO 480 - - 410 lp1 = l + 1 - mp1 = m + 1 - DO lls = lp1, mp1 - ls = m - lls + lp1 -! ...EXIT - IF (ls == l) EXIT - test = 0.0D0 - IF (ls /= m) test = test + ABS(e(ls)) - IF (ls /= l + 1) test = test + ABS(e(ls-1)) - ztest = test + ABS(s(ls)) - IF (ztest /= test) CYCLE - s(ls) = 0.0D0 -! ......EXIT - EXIT - END DO - - IF (ls /= l) GO TO 450 - kase = 3 - GO TO 480 - - 450 IF (ls /= m) GO TO 460 - kase = 1 - GO TO 480 - - 460 kase = 2 - l = ls - 480 l = l + 1 - -! PERFORM THE TASK INDICATED BY KASE. - - SELECT CASE ( kase ) - CASE ( 1) - GO TO 490 - CASE ( 2) - GO TO 520 - CASE ( 3) - GO TO 540 - CASE ( 4) - GO TO 570 - END SELECT - -! DEFLATE NEGLIGIBLE S(M). - - 490 mm1 = m - 1 - f = e(m-1) - e(m-1) = 0.0D0 - DO kk = l, mm1 - k = mm1 - kk + l - t1 = s(k) - CALL drotg(t1, f, cs, sn) - s(k) = t1 - IF (k == l) GO TO 500 - f = -sn*e(k-1) - e(k-1) = cs*e(k-1) - - 500 IF (wantv) CALL drot1(p, v(1:,k), v(1:,m), cs, sn) - END DO - GO TO 610 - -! SPLIT AT NEGLIGIBLE S(L). - - 520 f = e(l-1) - e(l-1) = 0.0D0 - DO k = l, m - t1 = s(k) - CALL drotg(t1, f, cs, sn) - s(k) = t1 - f = -sn*e(k) - e(k) = cs*e(k) - IF (wantu) CALL drot1(n, u(1:,k), u(1:,l-1), cs, sn) - END DO - GO TO 610 - -! PERFORM ONE QR STEP. -! -! CALCULATE THE SHIFT. - - 540 scale = MAX(ABS(s(m)),ABS(s(m-1)),ABS(e(m-1)),ABS(s(l)),ABS(e(l))) - sm = s(m)/scale - smm1 = s(m-1)/scale - emm1 = e(m-1)/scale - sl = s(l)/scale - el = e(l)/scale - b = ((smm1 + sm)*(smm1 - sm) + emm1**2)/2.0D0 - c = (sm*emm1)**2 - shift = 0.0D0 - IF (b == 0.0D0 .AND. c == 0.0D0) GO TO 550 - shift = SQRT(b**2+c) - IF (b < 0.0D0) shift = -shift - shift = c/(b + shift) - - 550 f = (sl + sm)*(sl - sm) - shift - g = sl*el - -! CHASE ZEROS. - - mm1 = m - 1 - DO k = l, mm1 - CALL drotg(f, g, cs, sn) - IF (k /= l) e(k-1) = f - f = cs*s(k) + sn*e(k) - e(k) = cs*e(k) - sn*s(k) - g = sn*s(k+1) - s(k+1) = cs*s(k+1) - IF (wantv) CALL drot1(p, v(1:,k), v(1:,k+1), cs, sn) - CALL drotg(f, g, cs, sn) - s(k) = f - f = cs*e(k) + sn*s(k+1) - s(k+1) = -sn*e(k) + cs*s(k+1) - g = sn*e(k+1) - e(k+1) = cs*e(k+1) - IF (wantu .AND. k < n) CALL drot1(n, u(1:,k), u(1:,k+1), cs, sn) - END DO - e(m-1) = f - iter = iter + 1 - GO TO 610 - -! CONVERGENCE. - -! MAKE THE SINGULAR VALUE POSITIVE. - - 570 IF (s(l) >= 0.0D0) GO TO 590 - s(l) = -s(l) - IF (wantv) v(1:p,l) = -v(1:p,l) - -! ORDER THE SINGULAR VALUE. - - 590 IF (l == mm) GO TO 600 -! ...EXIT - IF (s(l) >= s(l+1)) GO TO 600 - t = s(l) - s(l) = s(l+1) - s(l+1) = t - IF (wantv .AND. l < p) CALL dswap1(p, v(1:,l), v(1:,l+1)) - IF (wantu .AND. l < n) CALL dswap1(n, u(1:,l), u(1:,l+1)) - l = l + 1 - GO TO 590 - - 600 iter = 0 - m = m - 1 - - 610 GO TO 360 - - 620 RETURN - END SUBROUTINE dsvdc - - END MODULE SVD diff --git a/wafo/source/mreg/intfcmod.f b/wafo/source/mreg/intfcmod.f deleted file mode 100644 index 927dd3e..0000000 --- a/wafo/source/mreg/intfcmod.f +++ /dev/null @@ -1,189 +0,0 @@ - MODULE INTFCMOD - IMPLICIT NONE - PUBLIC :: INITLEVELS, TRANSF, COVG - - CONTAINS - SUBROUTINE INITLEVELS(T,HT,N,NU,Nv) - USE TBRMOD - USE SIZEMOD - IMPLICIT NONE -C INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201 -C DIMENSION ULEVELS(1),Vlevels(1),T(1),HT(1),TG(1),XG(1),HH(101) - REAL*8, DIMENSION(:), intent(in) :: T - REAL*8, DIMENSION(:), intent(out) :: HT -C INTEGER, intent(in) :: NG - REAL*8 :: UMIN,UMAX,VMIN,VMAX, HU,HV - integer :: N, I, NU, NV -C REAL*8, DIMENSION(NMAX) :: HH -C COMMON/TBR/HH - -C IF (NG.GT.501) THEN -C PRINT *,'Vector defining transformation of data > 501, stop' -C STOP -C END IF - - - IF(N.ge.NMAX) then - print *,'The number of wavelength points >',NMAX-1, ' stop' - stop - end if - IF(N.lt.2) then - print *,'The number of wavelength points < 2, stop' - stop - end if - - HT(1)=0.5d0*(T(2)-T(1)) - HT(N)=0.5d0*(T(N)-T(N-1)) - HH(1)=-100.0d0 - HH(N)=-100.0d0 - DO I=2,N-1 - HT(I)=0.5d0*(T(I+1)-T(I-1)) - HH(I)=-100.0d0 -c10 CONTINUE - enddo - - - IF(NU.gt.NMAX) then - print *,'The number of maxima >',NMAX,' stop' - stop - end if - IF(NV.gt.NMAX) then - print *,'The number of minima >',NMAX,' stop' - stop - end if - - IF(NU.LT.1) Then - print *,'The number of maxima < 1, stop' - stop - end if - IF(NV.LT.1) Then - print *,'The number of minima < 1, stop' - stop - end if - - RETURN - END SUBROUTINE INITLEVELS - - - SUBROUTINE TRANSF(N,T,A,TIMEV,VALUE,DER) -C -C N number of data points -C TIMEV vector of time points -C A a vector of values of a function G(TIME) -C T independent time point -C VALUE is a value of a function at T, i.e. VALUE=G(T). -c DER=G'(t) -C - USE SIZEMOD - IMPLICIT NONE - REAL*8, intent(inout):: VALUE, DER,T -C INTEGER, PARAMETER :: RDIM = 10201 - REAL*8, DIMENSION(:), intent(in) :: A,TIMEV - integer, intent(in) :: N - REAL*8:: T1 - integer :: I - - IF (T.LT.TIMEV(1)) then - der=(A(2)-A(1))/(TIMEV(2)-TIMEV(1)) - T1=T-TIMEV(1) - VALUE=A(1)+T1*DER - return - end if - IF (T.GT.TIMEV(N)) then - der = (A(N)-A(N-1))/(TIMEV(N)-TIMEV(N-1)) - T1 = T-TIMEV(N) - VALUE=A(N)+T1*DER - return - end if - DO I=2,N - IF (T.LT.TIMEV(I)) GO TO 10 - ENDDO - 10 I=I-1 - T1=T-TIMEV(I) - DER=(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I)) - VALUE=A(I)+T1*DER - RETURN - END SUBROUTINE TRANSF - - REAL*8 FUNCTION SPLE(N,T,A,TIMEV) -C -C N number of data points -C TIME vector of time points -C A a vector of values of a function G(TIME) -C T independent time point -C SPLE is a value of a function at T, i.e. SPLE=G(T). -C - USE SIZEMOD - IMPLICIT NONE - INTEGER, INTENT(IN):: N - - REAL*8, INTENT(IN) :: T - REAL*8, DIMENSION(:), INTENT(IN) :: A,TIMEV - REAL*8 :: T1 - INTEGER :: I - SPLE=-9.9d0 - IF (T.LT.TIMEV(1) .OR. T.GT.TIMEV(N)) RETURN - DO I=2,N - IF (T.LT.TIMEV(I)) GO TO 10 - ENDDO - 10 I=I-1 - T1=T-TIMEV(I) - SPLE=A(I)+T1*(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I)) - RETURN - END FUNCTION SPLE - - SUBROUTINE COVG(XL0,XL2,XL4,COV1,COV2,COV3,COV,T,N) -C -C Covariance function and its four derivatives for a vector T of length N -C is assumed in a vector COV; COV(1,...,N,1)=r(T), COV(1,...,N, 2)=r'(T), etc. -C The vector COV should be of the shape N x 5. -C -C COVG Returns: -C XL0,XL2,XL4 - spectral moments. -C -C Covariance matrices COV1=r'(T-T), COV2=r''(T-T) and COV3=r'''(T-T) -C Dimension of COV1, COV2 should be atleast N*N. -C - USE SIZEMOD -! IMPLICIT NONE -C INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201 - REAL*8, PARAMETER:: ZERO = 0.0d0 - REAL*8, intent(inout) :: XL0,XL2,XL4 - REAL*8, DIMENSION(N,5), intent(in) :: COV - REAL*8, DIMENSION(N), intent(in) :: T - REAL*8, DIMENSION(RDIM), intent(inout) :: COV1,COV2,COV3 - INTEGER, intent(in) :: N - integer :: I, J, II - REAL*8 :: TT, T0 -C -C COV(Y(T),Y(0)) = COV(:,1) -C DERIVATIVE COV(Y(T),Y(0)) = COV(:,2) -C 2-DERIVATIVE COV(Y(T),Y(0)) = COV(:,3) -C 3-DERIVATIVE COV(Y(T),Y(0)) = COV(:,4) -C 4-DERIVATIVE COV(Y(T),Y(0)) = COV(:,5) - - XL0 = COV(1,1) - XL2 = -COV(1,3) - XL4 = COV(1,5) -! XL0 = SPLE(NT, ZERO, COV(:,1), T) -! XL2 = -SPLE(NT, ZERO, COV(:,3), T) -! XL4 = SPLE(NT, ZERO, COV(:,5), T) - - II=0 - DO I=1,N - DO J=1,N - II = II+1 - T0 = T(J)-T(I) - TT = ABS(T0) - COV1(II) = SPLE(N, TT, COV(:,2), T) - COV2(II) = SPLE(N, TT, COV(:,3), T) - COV3(II) = SPLE(N, TT, COV(:,4), T) - IF (T0.LT.0.0d0) then - COV1(II)=-COV1(II) - COV3(II)=-COV3(II) - endif - enddo - enddo - RETURN - END SUBROUTINE COVG - END module intfcmod diff --git a/wafo/source/mreg/mregmodule.f b/wafo/source/mreg/mregmodule.f deleted file mode 100644 index 8a779f4..0000000 --- a/wafo/source/mreg/mregmodule.f +++ /dev/null @@ -1,3044 +0,0 @@ -C Version July 2007 -C -C The MREG module provide 3 programs. -C -C 1) MREG -C 2) RIND -C 3) FI - normal CDF -C -C MREG and RIND are explained in the following: -C -C -C CALL MREG(F,R,B,DB,AA,BB,A,DA,VDER,M,N,NIT,INFR) -C -C F = expectation -C R = Covariance R(i+(j-1)*N) = Cov( Delta(T(i)), Delta(T(j)), length RDIM (in) -C B = Covariance B(i) = Cov(Delta(T(i)), XN), B(N+1)=Var(XN) length NMAX (in) -C DB = Covariance DB(i) = Cov(Delta(T(i)), Y0), DB(N+1)=Cov(XN,Y0) length NMAX (in) -C AA = Regression matrix coefficients size MMAX x MMAX -C BB = Regression vector coefficients length MMax + 1 -C A = Slepian model coefficients, length (MMax + 1) * NMAX -C DA = Slepian model coefficients, length MMax + 1 -C VDER = variance of Y0, Var(Y0) -C M = Number of regressors ( 0 < M < MMAX) -C N = dimension of the problem ( N < NMAX) -C NIT = 0,1,2..., maximum # of iterations/integrations done by quadrature -C to calculate the indicator function -C INFR = 1 means all input are the same as in the previous call except BB, A and DA -C 0 indicate new input -C -C The program MREG computes the following problem: -C -C We consider a process X(I)=X(T(I)) at the grid of N points T(1),...,T(N), -C -C X(I) = -A(I) + Z*A(I+N) + Sum Xj*A(I+(j+1)*N) + Delta(I), j=1,...,M-1 -C -C where the sum disappears if M=1. We assume that Z,Xj are independent -C standard Rayleigh, Gaussian distributed rv. and independent of the zero -C mean Gaussian residual process, with covariance structure given in R, -C -C R(i+(j-1)N) = Cov (Delta(T(i)), Delta(T(j))). -C -C Additionally we have a zero mean Gaussian variable XN, -C independent of Z,Xj with covariance structure defined by -C B(i)= Cov (Delta(T(i)),XN), i=1,...,N, B(N+1)=Var(XN). -C Furthermore XN and Z,Xj satisfies the following equation system -C -C (BB + (XN,0,...,0)^T = AA*(Z,X1,...,Xm-1)^T (***) -C -C where AA is (M,M) matrix, BB is M-vector. We rewrite this equation, by -C introducing a variable Xm=XN/SQRT(Var(XN)) and construct new matrix AA1 -c by adding the column (SQRT(Var(XN)),0,...,0) and the row with only zeros. -C The equations (***) writtes -C -C (BB,0)^T = AA1*(Z,X1,...,Xm-1,Xm)^T (****) -C -C where AA1 is (M+1,M+1) matrix, We assume that the rank of AA1 is M, -C otherwise the density is singular and we give a output F=0.CC -C -C Let Y0 be a zero-mean Gaussian variable independent of Z,Xj -C with covariance structure defined by -C DB(i)= Cov (Delta(T(i)),Y0), i=1,...,N, DB(N+1)=Cov(XN,Y0), Var(Y0)=VDER. -C Let Y be defined by -C -C Y=-DA(1) + Z*DA(2) + Sum Xj*DA(2+j) +Y0, j=1,...,M-1. -C -C The MREG program computes: -C -C F = E[ Y^+ *1{ HH0 defines integration region for X. -C In the simplest case NIT=0 we define (Delta(1),...,Delta(N),Y1)=0.0d0 -C For NIT=1 only (Delta(1),...,Delta(N))=0, i.e. we have to compute -C a one dimensional integral. Finally by conditioning on X the problem is -C put in the format of RIND-problem. -C -C INF indicates whether one -C has already called the subroutine before and ONLY! inputs BB, DA or A -C was changed. -C -C Observe the limitations are : N mreg and rind publicly available -! - All commonblocks are replaced with a corresponding module - -! References -! Rychlik, I and Lindgren, G (1993) -! "CROSSREG - A Technique for First Passage and Wave Density Analysis" -! Probability in the Engineering and Informational Sciences, Vol 7, pp 125--148 -! -! Lindgren, G and Rychlik, I (1991) -! "Slepian Models and Regression Approximations in Crossing and xtreme value Theory", -! International Statistical Review, Vol 59, 2, pp 195--225 - - - MODULE SIZEMOD - IMPLICIT NONE - INTEGER, PARAMETER :: MMAX = 6, NMAX = 201 - INTEGER, PARAMETER :: RDIM = NMAX*NMAX - END MODULE SIZEMOD - - MODULE EPSMOD - IMPLICIT NONE - ! Constants determining accuracy of integration - !----------------------------------------------- - !if the conditional variance are less than: -C DOUBLE PRECISION :: EPS2=1.d-4 !- EPS2, the variable is - ! considered deterministic - DOUBLE PRECISION :: EPS = 1.d-2 ! SQRT(EPS2) -C DOUBLE PRECISION :: XCEPS2=1.d-16 ! if Var(Xc) is less return NaN - DOUBLE PRECISION :: EPSS = 5.d-5 ! accuracy of Indicator -C DOUBLE PRECISION :: CEPSS=0.99995d0 ! accuracy of Indicator - DOUBLE PRECISION :: EPS0 = 5.d-5 ! used in GAUSSLE1 to implicitly - ! determ. # nodes - -C DOUBLE PRECISION :: fxcEpss=1.d-20 ! if less do not compute E(...|Xc) -C DOUBLE PRECISION :: xCutOff=5.d0 ! upper/lower truncation limit of the - ! normal CDF -C DOUBLE PRECISION :: FxCutOff = 0.99999942669686d0 -C DOUBLE PRECISION :: CFxCutOff = 5.733031438470704d-7 ! 1-FxCutOff, - - END MODULE EPSMOD - - MODULE RINTMOD - DOUBLE PRECISION, save :: C = 4.5d0 - DOUBLE PRECISION, save :: FC = 0.999993204653751d0 -C COMMON /RINT/ C,FC - END MODULE RINTMOD - - MODULE TBRMOD - USE SIZEMOD - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(NMAX) :: HH - END MODULE TBRMOD - - MODULE EXPACCMOD - DOUBLE PRECISION,PARAMETER:: PMAX = 40.0d0 -C COMMON /EXPACC/ PMAX - END MODULE EXPACCMOD - - MODULE INFCMOD - IMPLICIT NONE - INTEGER, save :: ISQ = 0, IAC=1 - INTEGER, DIMENSION(10) :: INF,INFO -C DOUBLE PRECISION, DIMENSION(10):: -C COMMON /INFC/ ISQ,INF,INFO - END MODULE INFCMOD - MODULE CHECKMOD - IMPLICIT NONE -C III01,III11,... - variables,counts how many times one calls -C subroutine RIND0,RIND1,..., III*1 are also modified in the -C subroutines RIND*. This gives us statistics over the complexity of -C numerical calculations. - INTEGER :: III01,III11,III21,III31,III41,III51 - INTEGER :: III61,III71,III81,III91,III101 - INTEGER :: III0 - END MODULE CHECKMOD - - - MODULE QUADRMOD - IMPLICIT NONE ! Quadratures available: Legendre - INTEGER :: I - -C BLOCK DATA inithermite - - INTEGER, PARAMETER :: NNW = 13 - INTEGER, DIMENSION(25) :: NN - REAL*8 Z(126),H(126) - - -C COMMON /QUADR/ Z,H,NN,NNW -c COMMON /EXPACC/ PMAX -C COMMON /RINT/ C,FC - -C DATA NNW /13/ - DATA (NN(I),I=1,NNW)/2,3,4,5,6,7,8,9,10,12,16,20,24/ -C DATA PMAX/40./ -C DATA C/4.5/ - DATA (H(I),I=1,61)/1.0d0,1.0d0,0.555555555555556d0, - * 0.888888888888889d0, - * 0.555555555555556d0,0.347854845137454d0,0.652145154862546d0, - * 0.652145154862546d0,0.347854845137454d0,0.236926885056189d0, - * 0.478628670499366d0,0.568888888888889d0,0.478628670499366d0, - * 0.236926885056189d0,0.171324492379170d0,0.360761573048139d0, - * 0.467913934572691d0,0.467913934572691d0,0.360761573048139d0, - * 0.171324492379170d0,0.129484966168870d0,0.279705391489277d0, - * 0.381830050505119d0,0.417959183673469d0,0.381830050505119d0, - * 0.279705391489277d0,0.129484966168870d0,0.101228536290376d0, - * 0.222381034453374d0,0.313706645877887d0,0.362683783378362d0, - * 0.362683783378362d0,0.313706645877887d0,0.222381034453374d0, - * 0.101228536290376d0,0.081274388361574d0,0.180648160694857d0, - * 0.260610696402935d0,0.312347077040003d0,0.330239355001260d0, - * 0.312347077040003d0,0.260610696402935d0,0.180648160694857d0, - * 0.081274388361574d0,0.066671344308688d0,0.149451349150581d0, - * 0.219086362515982d0,0.269266719309996d0,0.295524224714753d0, - * 0.295524224714753d0,0.269266719309996d0,0.219086362515982d0, - * 0.149451349150581d0,0.066671344308688d0,0.047175336386512d0, - * 0.106939325995318d0,0.160078328543346d0,0.203167426723066d0, - * 0.233492536538355d0,0.249147048513403d0,0.249147048513403d0/ - DATA (H(I),I=62,101)/0.233492536538355d0,0.203167426723066d0, - * 0.160078328543346d0,0.106939325995318d0, - * 0.047175336386512d0,0.027152459411754094852d0, - * 0.062253523938647892863d0,0.095158511682492784810d0, - * 0.124628971255533872052d0,0.149595988816576732081d0, - * 0.169156519395002538189d0,0.182603415044923588867d0, - * 0.189450610455068496285d0,0.189450610455068496285d0, - * 0.182603415044923588867d0,0.169156519395002538189d0, - * 0.149595988816576732081d0,0.124628971255533872052d0, - * 0.095158511682492784810d0,0.062253523938647892863d0, - * 0.027152459411754094852d0,0.017614007139152118312d0, - * 0.040601429800386941331d0,0.062672048334109063570d0, - * 0.083276741576704748725d0,0.101930119817240435037d0, - * 0.118194531961518417312d0,0.131688638449176626898d0, - * 0.142096109318382051329d0,0.149172986472603746788d0, - * 0.152753387130725850698d0,0.152753387130725850698d0, - * 0.149172986472603746788d0,0.142096109318382051329d0, - * 0.131688638449176626898d0,0.118194531961518417312d0, - * 0.101930119817240435037d0,0.083276741576704748725d0, - * 0.062672048334109063570d0,0.040601429800386941331d0/ - DATA (H(I),I=102,126)/0.017614007139152118312d0, - * 0.012341229799987199547d0, 0.028531388628933663181d0, - * 0.044277438817419806169d0, 0.059298584915436780746d0, - * 0.073346481411080305734d0, 0.086190161531953275917d0, - * 0.097618652104113888270d0, 0.107444270115965634783d0, - * 0.115505668053725601353d0, 0.121670472927803391204d0, - * 0.125837456346828296121d0, 0.127938195346752156974d0, - * 0.127938195346752156974d0, 0.125837456346828296121d0, - * 0.121670472927803391204d0, 0.115505668053725601353d0, - * 0.107444270115965634783d0, 0.097618652104113888270d0, - * 0.086190161531953275917d0, 0.073346481411080305734d0, - * 0.059298584915436780746d0, 0.044277438817419806169d0, - * 0.028531388628933663181d0, 0.012341229799987199547d0/ - - DATA (Z(I),I=1,58)/-0.577350269189626d0,0.577350269189626d0, - * -0.774596669241483d0,0.0d0, - * 0.774596669241483d0, -0.861136311594053d0, -0.339981043584856d0, - * 0.339981043584856d0, 0.861136311594053d0, -0.906179845938664d0, - * -0.538469310105683d0,0.0d0, - * 0.538469310105683d0, 0.906179845938664d0, -0.932469514203152d0, - * -0.661209386466265d0, -0.238619186083197d0, 0.238619186083197d0, - * 0.661209386466265d0, 0.932469514203152d0, -0.949107912342759d0, - * -0.741531185599394d0, -0.405845151377397d0, 0.0d0, - * 0.405845151377397d0, 0.741531185599394d0, 0.949107912342759d0, - * -0.960289856497536d0, -0.796666477413627d0, -0.525532409916329d0, - * -0.183434642495650d0, 0.183434642495650d0, 0.525532409916329d0, - * 0.796666477413627d0, 0.960289856497536d0, -0.968160239507626d0, - * -0.836031107326636d0, -0.613371432700590d0, -0.324253423403809d0, - * 0.0d0, - * 0.324253423403809d0, 0.613371432700590d0, 0.836031107326636d0, - * 0.968160239507626d0, -0.973906528517172d0, -0.865063366688985d0, - * -0.679409568299024d0, -0.433395394129247d0, -0.148874338981631d0, - * 0.148874338981631d0, 0.433395394129247d0, 0.679409568299024d0, - * 0.865063366688985d0, 0.973906528517172d0, -0.981560634246719d0, - * -0.904117256370475d0, -0.769902674194305d0, -0.587317954286617d0/ - DATA (Z(I),I=59,99)/-0.367831498198180d0, -0.125233408511469d0, - * 0.125233408511469d0, 0.367831498198180d0, - * 0.587317954286617d0, 0.769902674194305d0, - * 0.904117256370475d0, 0.981560634246719d0, - * -0.989400934991649932596d0, - * -0.944575023073232576078d0, -0.865631202387831743880d0, - * -0.755404408355003033895d0, -0.617876244402643748447d0, - * -0.458016777657227386342d0, -0.281603550779258913230d0, - * -0.095012509837637440185d0, 0.095012509837637440185d0, - * 0.281603550779258913230d0, 0.458016777657227386342d0, - * 0.617876244402643748447d0, 0.755404408355003033895d0, - * 0.865631202387831743880d0, 0.944575023073232576078d0, - * 0.989400934991649932596d0, -0.993128599185094924786d0, - * -0.963971927277913791268d0, -0.912234428251325905868d0, - * -0.839116971822218823395d0, -0.746331906460150792614d0, - * -0.636053680726515025453d0, -0.510867001950827098004d0, - * -0.373706088715419560673d0, -0.227785851141645078080d0, - * -0.076526521133497333755d0, 0.076526521133497333755d0, - * 0.227785851141645078080d0, 0.373706088715419560673d0, - * 0.510867001950827098004d0, 0.636053680726515025453d0, - * 0.746331906460150792614d0, 0.839116971822218823395d0/ - DATA (Z(I),I=100,126)/0.912234428251325905868d0, - * 0.963971927277913791268d0, 0.993128599185094924786d0, - * -0.995187219997021360180d0, -0.974728555971309498198d0, - * -0.938274552002732758524d0, -0.886415527004401034213d0, - * -0.820001985973902921954d0, -0.740124191578554364244d0, - * -0.648093651936975569252d0, -0.545421471388839535658d0, - * -0.433793507626045138487d0, -0.315042679696163374387d0, - * -0.191118867473616309159d0, -0.064056892862605626085d0, - * 0.064056892862605626085d0, 0.191118867473616309159d0, - * 0.315042679696163374387d0, 0.433793507626045138487d0, - * 0.545421471388839535658d0, 0.648093651936975569252d0, - * 0.740124191578554364244d0, 0.820001985973902921954d0, - * 0.886415527004401034213d0, 0.938274552002732758524d0, - * 0.974728555971309498198d0, 0.995187219997021360180d0/ - END MODULE QUADRMOD - - -C - MODULE MREGMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: RIND, MREG, FI - - INTERFACE RIND - MODULE PROCEDURE RIND - END INTERFACE - - INTERFACE MREG - MODULE PROCEDURE MREG - END INTERFACE - - INTERFACE FI - MODULE PROCEDURE FI - END INTERFACE - - INTERFACE C1_C2 - MODULE PROCEDURE C1_C2 - END INTERFACE - - INTERFACE GAUSS1 - MODULE PROCEDURE GAUSS1 - END INTERFACE - - INTERFACE GAUSINT - MODULE PROCEDURE GAUSINT - END INTERFACE - - INTERFACE PYTHAG - MODULE PROCEDURE PYTHAG - END INTERFACE - - - CONTAINS - - - SUBROUTINE RIND(XIND,R,BU,DBUN,DB,SQ,VDER,NIT,N,INFR) - USE TBRMOD - USE INFCMOD - USE CHECKMOD - USE EPSMOD - USE SIZEMOD - IMPLICIT NONE - REAL*8, intent(inout) :: XIND,DBUN,VDER - REAL*8, DIMENSION(RDIM), intent(inout) :: R - REAL*8, DIMENSION(NMAX), intent(inout) :: BU,DB, SQ - INTEGER, intent(in) :: NIT,N,INFR - REAL*8 SDER - INTEGER, save :: NNIT - INTEGER I,III -C DIMENSION R(1),BU(1),SQ(1),DB(1) -C DIMENSION INF(10),INFO(10),HH(101) -C COMMON /TBR/ HH -C COMMON /INFC/ ISQ,INF,INFO -C COMMON /CHECK1/ III01,III11,III21,III31,III41,III51 -C *,III61,III71,III81,III91,III101 -C COMMON /EPS/ EPS,EPSS,CEPSS -C -C III01,III11,... - variables,counts how many times one calls -C subroutine RIND0,RIND1,..., III*1 are also modified in the -C subroutines RIND*. This gives us statistics over the complexity of -C numerical calculations. -C - XIND=0.0d0 - IF (N.lt.1) go to 99 - - IF (INFR.EQ.0) THEN - NNIT=MIN(NIT,N) - if (NNIT.gt.10) NNIT=10 - DO I=1,10 - INF(I)=0 - INFO(I)=0 - enddo - III=0 - DO I=1,N - IF (SQ(I).GT.EPS) then - III=1 - else - IF(BU(I).GT.0.0d0) THEN - RETURN - END IF - IF(BU(I).LT.HH(I)) THEN - RETURN - END IF - END IF - enddo - END IF - IF (III.eq.0) go to 99 - -! GO TO (10,20,30,40,50,60,70,80,90,100) NNIT - SELECT CASE (NNIT) - CASE (1) - CALL RIND1(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii11=iii11+1 - CASE(2) - CALL RIND2(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii21=iii21+1 - CASE(3) - CALL RIND3(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii31=iii31+1 - CASE(4) - CALL RIND4(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii41=iii41+1 - CASE(5) - CALL RIND5(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii51=iii51+1 - CASE(6) - CALL RIND6(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii61=iii61+1 - CASE(7) - CALL RIND7(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii71=iii71+1 - CASE(8) - CALL RIND8(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii81=iii81+1 - CASE (9) - CALL RIND9(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii91=iii91+1 - CASE (10) - CALL RIND10(XIND,R,BU,DBUN,DB,SQ,VDER,N) - iii101=iii101+1 - CASE DEFAULT - CALL RIND0(XIND,BU,DBUN,VDER,N) - iii01=iii01+1 - END SELECT - RETURN - - 99 continue - SDER=0.0d0 - IF(VDER.GT.EPS) SDER=SQRT(VDER) - XIND=PMEAN(DBUN,SDER) - return - END SUBROUTINE RIND - - SUBROUTINE RIND0(XIND,BU,DBUN,VDER,N) - USE TBRMOD - USE EPSMOD - USE SIZEMOD - IMPLICIT NONE - INTEGER, intent(in) :: N - REAL*8, intent(inout) :: XIND,DBUN,VDER - REAL*8, DIMENSION(NMAX), intent(inout) :: BU - REAL*8 SDER - INTEGER I -! DIMENSION BU(NMAX) -C DIMENSION HH(101) -C COMMON /EPS/ EPS,EPSS,CEPSS -C COMMON /TBR/ HH - - IF (N.LT.1) GO TO 20 - XIND=0.0d0 - IF(DBUN.LT.0.0d0) THEN - RETURN - END IF - DO I=1,N - IF(BU(I).GT.0.0d0) THEN - RETURN - END IF - IF(BU(I).LT.HH(I)) THEN - RETURN - END IF - enddo -20 CONTINUE - SDER=0.0d0 - IF(VDER.GT.EPS) SDER=SQRT(VDER) - XIND=PMEAN(DBUN,SDER) - RETURN - END SUBROUTINE RIND0 - - SUBROUTINE RIND1(XIND,R,BU,DBUN,DB,SQ,VDER,N) - USE SIZEMOD - USE TBRMOD - USE INFCMOD - USE CHECKMOD - USE EPSMOD - USE RINTMOD - IMPLICIT NONE - REAL*8, intent(inout) :: XIND,DBUN,VDER - REAL*8, DIMENSION(RDIM), intent(inout) :: R - REAL*8, DIMENSION(NMAX), intent(inout) :: BU,DB,SQ - INTEGER, intent(in) :: N - REAL*8, DIMENSION(NMAX), save :: B1,SQ1 - REAL*8, DIMENSION(24) :: XX1, H1 - REAL*8 XMI,XMA,DER,SDER - REAL*8, save :: DB1N,SDER1,VDER1, SS0 - REAL*8 XFF,XF,X,XH, SQ0, HHB - INTEGER I,III,J,II0,N1 -! INTEGER IAC,N -! real*8 XIND,R,BU,DBUN,DB,SQ,VDER -! REAL*8 XX1,H1, B1,SQ1,XMI,XMA, SDER,DB1N , DER, SDER1 -! REAL*8 XFF,X, XH, SQ0, HHB, SS0, VDER1, XF -! INTEGER I,J,III,II0,N1 -C DIMENSION R(1),BU(1),SQ(1),DB(1),B1(NMAX),SQ1(NMAX) -! DIMENSION R(RDIM),BU(NMAX),SQ(NMAX),DB(NMAX) ,B1(NMAX),SQ1(NMAX) -! DIMENSION XX1(24),H1(24) -C DIMENSION HH(101),INF(10),INFO(10) - -C COMMON /EPS/ EPS,EPSS,CEPSS -C COMMON /RINT/ C,FC -C COMMON /TBR/ HH -C COMMON /INFC/ ISQ,INF,INFO -C COMMON /CHECK1/ III01,III11,III21,III31,III41,III51 -C *,III61,III71,III81,III91,III101 - -c print *,'Topp of R1:',sq(1),sq(2),sq(3) - XIND=0.0d0 - -C Choice of the time for conditioning, two methods -C -C ISQ=1; INF(1)=II0 is the point where the SQ(I) obtaines its maximum, SQ0 -C is the maximal st. deviation of the residual. -C -C ISQ=0; INF(1) is the time point when the probability P(hhXMA or X(INF(1))EPS) THEN - XR1=R1(I+(I-1)*N) -c IF(XR1.LT.0.0d0) CALL ERROR(I,N,-1) - SQ1(I)=0.0d0 - IF (XR1.GT.EPS) SQ1(I)=SQRT(XR1) - ENDIF - ENDDO - DO I=1,N - B1(I)=B1(I)/SQ0 - ENDDO -99 CONTINUE -C -C *********************************************************** -C -C We shall condition on the values of X, XMIEPS) THEN - - XR1=R1(I+(I-1)*N) -c IF(XR1.LT.0.0d0) CALL ERROR(I,N,-1) - SQ1(I)=0.0d0 - IF (XR1.GT.EPS) SQ1(I)=SQRT(XR1) - ENDIF - ENDDO - DO I=1,N - B1(I)=B1(I)/SQ0 - ENDDO -99 CONTINUE -C -C *********************************************************** -C -C We shall condition on the values of X, XMI0 or -C -C b) BU(I)+x*B1(I)+C*SQ(I)XMAX in GAUSS1 - stop!' -C STOP - END IF - NNN=0 - DO I=1,NNW - N=NN(I) - DO J=1,N - XX1(J)=0.5d0*(Z(NNN+J)*(XMA-XMI)+XMA+XMI) - Z1(J)=XX1(J)*XX1(J) - H1(J)=0.5d0*SP*(XMA-XMI)*H(NNN+J)*EXP(-0.5d0*Z1(J)) - ENDDO - NNN=NNN+N - SDOT=GAUSINT(XMI,XMA,0.0d0,1.0d0,0.0d0,1.0d0) - SDOT1=0.d0 - DO I1=1,N - SDOT1=SDOT1+Z1(I1)*H1(I1) - ENDDO - DIFF1=ABS(SDOT-SDOT1) - IF(EPS0.LT.DIFF1) GO TO 10 - III0=III0+N -C PRINT *,'N. of nodes',III0 - RETURN -10 CONTINUE - ENDDO - END SUBROUTINE GAUSS1 - - - SUBROUTINE M_COND(Syy_cd,Syyii,Syx_cd,Syy,Syx,ii,N) -C -C INPUT: -C -C ii IS THE INDEX OF THE TIME ON WHICH WE ARE CONDITIONING. -C N number of variables in covariance matrix Syy -C -C Covariance matrix Syy(I+(J-1)*N)=Cov(Yi,Yj) (is unchanged) -C Covariance vector Syx(I)=Cov(Yi,X) (is unchanged) -C -C OUTPUT: -C -C Covariance matrix Syy_cd(I+(J-1)*N)=Cov(Xi,Xj|Xii) -C Covariance vector Syyii(I)=Cov(Xi,Xii) -C Covariance vector Syx_cd(I)=Cov(Xi,Y|Xii) -C Variance Q1=Var(Xii)=Syyii(ii) -c Obs. If Q1 -C 4.5. Under we have a table with -C exact values of FIFUNK. -C -C x FIFUNK(x) -C -C -5.0 0.00000005233 -C -4.5 0.00000069515 -C -4.0 0.00000711075 -C 4.0 4.00000700000 -C 4.5 4.50000100000 -C -C Obviously the tresholds -4.5 and 4.5 can be increased. -C -C - IMPLICIT NONE - REAL*8, intent(in) :: XX, SS - REAL*8 X,Y,W,Z - REAL*8, parameter :: SP = 0.398942280401433d0 - IF(XX.LT.4.5d0*SS) GO TO 1 - PMEAN=XX - RETURN -1 IF(XX.GT.-4.5d0*SS) GO TO 3 - PMEAN=0.0d0 - RETURN -3 continue - if (SS .LT. 0.0000001d0) then - PMEAN=0.0d0 - RETURN - end if - - X=XX/SS - - IF(X==0) goto 8 - Y=0.5d0*ABS(X) - IF(Y<1.0d0) then - W=Y*Y - Z=((((((((0.000124818987d0*W-0.001075204047d0)*W - 1 +0.005198775019d0)*W-0.019198292d0)*W+0.05905403564d0)*W - 2 -0.15196875136d0)*W+0.3191529327d0)*W-0.5319230073d0)*W - 3 +0.7978845606d0)*Y*2.0d0 - else - Y=Y-2.0d0 - Z=(((((((((((((-0.000045255659d0*Y+0.00015252929d0)*Y - * -0.000019538132d0)*Y-0.000676904986d0)*Y - 1 +0.001390604284d0)*Y-0.000794620820d0)*Y - 2 -0.002034254874d0)*Y+0.006549791214d0)*Y-0.010557625006d0)*Y+ - 3 0.011630447319d0)*Y-0.009279453341d0)*Y+0.005353579108d0)*Y- - 4 0.002141268741d0)*Y+0.000535310849d0)*Y+0.9999366575d0 - endif - IF(X.GT.0.0d0) PMEAN=SS*SP*EXP(-0.5d0*X*X)+XX*0.5d0*(Z+1.0d0) - IF(X.LT.0.0d0) PMEAN=SS*SP*EXP(-0.5d0*X*X)+XX*0.5d0*(1.0d0-Z) - RETURN -8 PMEAN=SS*SP - RETURN - END FUNCTION PMEAN - - - REAL*8 FUNCTION FI(XX) -C -C Algorithm 209 from CACAM. -C FI(xx) is a distribution functions of N(0,1) variable. -C - IMPLICIT NONE - REAL*8, intent(in) :: XX - REAL*8 X, Y,Z, W - X=XX - IF(X==0) then - FI=0.5d0 - RETURN - endif - Y=0.5d0*ABS(X) - IF(Y>3.0d0) then - IF(X.GT.0.0d0) FI=1.0d0 - IF(X.LT.0.0d0) FI=0.0d0 - RETURN - endif - IF (Y<1.0d0) then - W=Y*Y - Z=((((((((0.000124818987d0*W-0.001075204047d0)*W - 1 +0.005198775019d0)*W-0.019198292d0)*W+0.05905403564d0)*W - 2 -0.15196875136d0)*W+0.3191529327d0)*W-0.5319230073d0)*W - 3 +0.7978845606d0)*Y*2.0d0 - ELSE - Y=Y-2.0d0 - Z=(((((((((((((-0.000045255659d0*Y+0.00015252929d0)*Y - 1 -0.000019538132d0)*Y-0.000676904986d0)*Y+0.001390604284d0)*Y - 2 -0.000794620820d0)*Y-0.002034254874d0)*Y+0.006549791214d0)*Y - 3 -0.010557625006d0)*Y+0.011630447319d0)*Y-0.009279453341d0)*Y - 4 +0.005353579108d0)*Y-0.002141268741d0)*Y+0.000535310849d0)*Y - 5 +0.9999366575d0 - endif -100 IF(X.GT.0.0d0) FI=0.5d0*(Z+1.0d0) - IF(X.LT.0.0d0) FI=0.5d0*(1.0d0-Z) - RETURN - END FUNCTION FI - -C Version 1991-XII-14 - -C The MREG program. -C -C -C We consider a process X(I)=X(T(I)) at the grid of N points T(1),...,T(N), -C -C X(I) = -A(I) + Z*A(I+N) + Sum Xj*A(I+(j+1)*N) + Delta(I), -C -C the sum disapears if M=1, j=1,...,M-1. We assume that Z,Xj are independend -C standart Rayleigh, Gaussian distributed rv. and independent of the zero -C mean Gaussian residual process, with covariance structure given in R, -C -C R(i+(j-1)N) = Cov (Delta(T(i)), Delta(T(j))). -C -C Additionally we have a zero mean Gaussian variable XN, -C independent of Z,Xj with covariance structure defined by -C B(i)= Cov (Delta(T(i)),XN), i=1,...,N, B(N+1)=Var(XN). -C Furthermore XN and Z,Xj satisfies the following equation system -C -C (BB + (XN,0,...,0)^T = AA*(Z,X1,...,Xm-1)^T (***) -C -C where AA is (M,M) matrix, BB is M-vector. We rewrite this equation, by -C introducing a variable X_M=XN/SQRT(XN) and construct new matrix AA1 -c by adding the column (SQRT(Var(XN)),0,...,0) and the row with only zeros. -C The equations (***) writtes -C -C (BB,0)^T = AA1*(Z,X1,...,Xm-1,Xm)^T (****) -C -C where AA1 is (M+1,M+1) matrix, We assume that the rank of AA1 is M, -C otherwise the density is singular and we give a output F=0.CC -C -C Let Y0 be a zero-mean Gaussian variable independent of Z,Xj -C with covariance structure defined by -C DB(i)= Cov (Delta(T(i)),Y0), i=1,...,N, DB(N+1)=Cov(XN,Y0), Var(Y0)=VDER. -C Let Y be defined by -C -C Y=-DA(1) + Z*DA(2) + Sum Xj*DA(2+j) +Y0, -C -C j=1,...,M-1. The program computes: -C -C F = E[ Y^+ *1{ HH0 defines integration region for X. -C In the simplest case NIT=0 we define (Delta(1),...,Delta(N),Y1)=0.0d0 -C For NIT=1 only (Delta(1),...,Delta(N))=0, i.e. we have to compute -C a one dimensional integral. Finally by conditioning on X the problem is -C put in the format of RIND-problem. -C -C INF indicates whether one -C has already called the subroutine before and ONLY! inputs BB, DA or A -C was changed. -C -C Observe the limitations are : N<=100, 00 -c - IF (NNIT.GT.1) THEN - DO I=1,N - XR1=R(I+(I-1)*N)-B(I)*(B(I)/QD) - IF(XR1.GT.EPS) THEN - SQ(I)=SQRT(XR1) - ENDIF - ENDDO - - DO I=1,N - DO J=1,N - R1(J+(I-1)*N)=R(J+(I-1)*N)-B(I)*(B(J)/QD) - ENDDO - ENDDO - - - END IF - - -105 CONTINUE - if (idet.gt.1) return -C -C Renormalization is done -C - CALL R_ORT(CC,PC,PD,U1,V1,W1,AO,BB,A1,A0,B0,DA0,D0,DET1,M+1,N) - IF(CC.LT.0.0d0) RETURN - XMI=-C - XMA= C - IF(ABS(PD).LE.EPS.AND.PC.LT.0.0d0) RETURN - IF(ABS(PD).LE.EPS) GO TO 102 - X=-PC/PD - IF(PD.GT.0.0d0.AND.XMI.LT.X) XMI=X - IF(PD.LT.0.0d0.AND.XMA.GT.X) XMA=X -102 CONTINUE -c PRINT *,'XMI,XMA',XMI,XMA - IF(NNIT.eq.1.AND.IAC.LT.1.OR.NNIT.eq.0.OR.XMI.GE.XMA) THEN - CALL C1_C2(XMI,XMA,A0,B0,D0(1),D0(2),0.0d0,SQ,N) -c PRINT *,'XMI,XMA',XMI,XMA - F=GAUSINT(XMI,XMA,D0(1),D0(2),PC,PD)*CC -c print *,'return',f,cc - RETURN - END IF -C -C *********************************************************** -C -C We shall condition on the values of X, XMI eps, all maxpts used - integer n, d, infin(d), maxpts, inform, tmpinf - double precision lower(d), upper(d), releps, abseps, - & error, value, stdev(d), rho(d*(d-1)/2), - & covar(d,d), - & nlower(d), nupper(d), means(d,n), tmpval - integer i, j - - do i=1,d - stdev(i) = dsqrt(covar(i,i)) - infin(i) = 2 - end do - do i=1,d - do j=1,i-1 - rho(j+(i-2)*(i-1)/2) = covar(i,j)/stdev(i)/stdev(j) - end do - end do - value = 0d0 - - inform = 0 - - do i=1,n - do j=1,d - nlower(j) = (lower(j) - means(j,i))/stdev(j) - nupper(j) = (upper(j) - means(j,i))/stdev(j) - end do - call mvndst(d,nlower,nupper,infin,rho,maxpts,abseps,releps, - & error,tmpval,tmpinf) - value = value + tmpval - if (tmpinf .eq. 1) then - inform = 1 - end if - end do - - value = value / n - - END - - SUBROUTINE MVNDST( N, LOWER, UPPER, INFIN, CORREL, MAXPTS, - & ABSEPS, RELEPS, ERROR, VALUE, INFORM ) -* -* A subroutine for computing multivariate normal probabilities. -* This subroutine uses an algorithm given in the paper -* "Numerical Computation of Multivariate Normal Probabilities", in -* J. of Computational and Graphical Stat., 1(1992), pp. 141-149, by -* Alan Genz -* Department of Mathematics -* Washington State University -* Pullman, WA 99164-3113 -* Email : AlanGenz@wsu.edu -* -* Parameters -* -* N INTEGER, the number of variables. -* LOWER REAL, array of lower integration limits. -* UPPER REAL, array of upper integration limits. -* INFIN INTEGER, array of integration limits flags: -* if INFIN(I) < 0, Ith limits are (-infinity, infinity); -* if INFIN(I) = 0, Ith limits are (-infinity, UPPER(I)]; -* if INFIN(I) = 1, Ith limits are [LOWER(I), infinity); -* if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)]. -* CORREL REAL, array of correlation coefficients; the correlation -* coefficient in row I column J of the correlation matrix -* should be stored in CORREL( J + ((I-2)*(I-1))/2 ), for J < I. -* THe correlation matrix must be positive semidefinite. -* MAXPTS INTEGER, maximum number of function values allowed. This -* parameter can be used to limit the time. A sensible -* strategy is to start with MAXPTS = 1000*N, and then -* increase MAXPTS if ERROR is too large. -* ABSEPS REAL absolute error tolerance. -* RELEPS REAL relative error tolerance. -* ERROR REAL estimated absolute error, with 99% confidence level. -* VALUE REAL estimated value for the integral -* INFORM INTEGER, termination status parameter: -* if INFORM = 0, normal completion with ERROR < EPS; -* if INFORM = 1, completion with ERROR > EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* if INFORM = 2, N > 500 or N < 1. -* - EXTERNAL MVNDFN - INTEGER N, INFIN(*), MAXPTS, INFORM, INFIS, IVLS - DOUBLE PRECISION CORREL(*), LOWER(*), UPPER(*), RELEPS, ABSEPS, - & ERROR, VALUE, E, D, MVNDNT, MVNDFN - COMMON /DKBLCK/IVLS - IF ( N .GT. 500 .OR. N .LT. 1 ) THEN - INFORM = 2 - VALUE = 0 - ERROR = 1 - ELSE - INFORM = INT(MVNDNT(N, CORREL, LOWER, UPPER, INFIN, INFIS, - & D, E)) - IF ( N-INFIS .EQ. 0 ) THEN - VALUE = 1 - ERROR = 0 - ELSE IF ( N-INFIS .EQ. 1 ) THEN - VALUE = E - D - ERROR = 2D-16 - ELSE -* -* Call the lattice rule integration subroutine -* - IVLS = 0 - CALL DKBVRC( N-INFIS-1, IVLS, MAXPTS, MVNDFN, - & ABSEPS, RELEPS, ERROR, VALUE, INFORM ) - ENDIF - ENDIF - END - DOUBLE PRECISION FUNCTION MVNDFN( N, W ) -* -* Integrand subroutine -* - INTEGER N, INFIN(*), INFIS, NL - DOUBLE PRECISION W(*), LOWER(*), UPPER(*), CORREL(*), D, E - PARAMETER ( NL = 500 ) - DOUBLE PRECISION COV(NL*(NL+1)/2), A(NL), B(NL), Y(NL) - INTEGER INFI(NL), I, J, IJ, IK, INFA, INFB - DOUBLE PRECISION SUM, AI, BI, DI, EI, PHINVS, BVNMVN, MVNDNT - SAVE A, B, INFI, COV - MVNDFN = 1 - INFA = 0 - INFB = 0 - IK = 1 - IJ = 0 - DO I = 1, N+1 - SUM = 0 - DO J = 1, I-1 - IJ = IJ + 1 - IF ( J .LT. IK ) SUM = SUM + COV(IJ)*Y(J) - END DO - IF ( INFI(I) .NE. 0 ) THEN - IF ( INFA .EQ. 1 ) THEN - AI = MAX( AI, A(I) - SUM ) - ELSE - AI = A(I) - SUM - INFA = 1 - END IF - END IF - IF ( INFI(I) .NE. 1 ) THEN - IF ( INFB .EQ. 1 ) THEN - BI = MIN( BI, B(I) - SUM ) - ELSE - BI = B(I) - SUM - INFB = 1 - END IF - END IF - IJ = IJ + 1 - IF ( I .EQ. N+1 .OR. COV(IJ+IK+1) .GT. 0 ) THEN - CALL MVNLMS( AI, BI, 2*INFA+INFB-1, DI, EI ) - IF ( DI .GE. EI ) THEN - MVNDFN = 0 - RETURN - ELSE - MVNDFN = MVNDFN*( EI - DI ) - IF ( I .LE. N ) Y(IK) = PHINVS( DI + W(IK)*( EI - DI ) ) - IK = IK + 1 - INFA = 0 - INFB = 0 - END IF - END IF - END DO - RETURN -* -* Entry point for intialization. -* - ENTRY MVNDNT( N, CORREL, LOWER, UPPER, INFIN, INFIS, D, E ) - MVNDNT = 0 -* -* Initialization and computation of covariance Cholesky factor. -* - CALL COVSRT( N, LOWER,UPPER,CORREL,INFIN,Y, INFIS,A,B,COV,INFI ) - IF ( N - INFIS .EQ. 1 ) THEN - CALL MVNLMS( A(1), B(1), INFI(1), D, E ) - ELSE IF ( N - INFIS .EQ. 2 ) THEN - IF ( ABS( COV(3) ) .GT. 0 ) THEN - D = SQRT( 1 + COV(2)**2 ) - IF ( INFI(2) .NE. 0 ) A(2) = A(2)/D - IF ( INFI(2) .NE. 1 ) B(2) = B(2)/D - E = BVNMVN( A, B, INFI, COV(2)/D ) - D = 0 - ELSE - IF ( INFI(1) .NE. 0 ) THEN - IF ( INFI(2) .NE. 0 ) A(1) = MAX( A(1), A(2) ) - ELSE - IF ( INFI(2) .NE. 0 ) A(1) = A(2) - END IF - IF ( INFI(1) .NE. 1 ) THEN - IF ( INFI(2) .NE. 1 ) B(1) = MIN( B(1), B(2) ) - ELSE - IF ( INFI(2) .NE. 1 ) B(1) = B(2) - END IF - IF ( INFI(1) .NE. INFI(2) ) INFI(1) = 2 - CALL MVNLMS( A(1), B(1), INFI(1), D, E ) - END IF - INFIS = INFIS + 1 - END IF - END - SUBROUTINE MVNLMS( A, B, INFIN, LOWER, UPPER ) - DOUBLE PRECISION A, B, LOWER, UPPER, MVNPHI - INTEGER INFIN - LOWER = 0 - UPPER = 1 - IF ( INFIN .GE. 0 ) THEN - IF ( INFIN .NE. 0 ) LOWER = MVNPHI(A) - IF ( INFIN .NE. 1 ) UPPER = MVNPHI(B) - ENDIF - UPPER = MAX( UPPER, LOWER ) - END - SUBROUTINE COVSRT( N, LOWER, UPPER, CORREL, INFIN, Y, - & INFIS, A, B, COV, INFI ) -* -* Subroutine to sort integration limits and determine Cholesky factor. -* - INTEGER N, INFI(*), INFIN(*), INFIS - DOUBLE PRECISION - & A(*), B(*), COV(*), LOWER(*), UPPER(*), CORREL(*), Y(*) - INTEGER I, J, K, L, M, II, IJ, IL, JMIN - DOUBLE PRECISION SUMSQ, AJ, BJ, SUM, SQTWPI, EPS, D, E - DOUBLE PRECISION CVDIAG, AMIN, BMIN, DMIN, EMIN, YL, YU - PARAMETER ( SQTWPI = 2.506628274631001D0, EPS = 1D-10 ) - AMIN = 0 - BMIN = 0 - IJ = 0 - II = 0 - INFIS = 0 - DO I = 1, N - A(I) = 0 - B(I) = 0 - INFI(I) = INFIN(I) - IF ( INFI(I) .LT. 0 ) THEN - INFIS = INFIS + 1 - ELSE - IF ( INFI(I) .NE. 0 ) A(I) = LOWER(I) - IF ( INFI(I) .NE. 1 ) B(I) = UPPER(I) - ENDIF - DO J = 1, I-1 - IJ = IJ + 1 - II = II + 1 - COV(IJ) = CORREL(II) - END DO - IJ = IJ + 1 - COV(IJ) = 1 - END DO -* -* First move any doubly infinite limits to innermost positions. -* - IF ( INFIS .LT. N ) THEN - DO I = N, N-INFIS+1, -1 - IF ( INFI(I) .GE. 0 ) THEN - DO J = 1,I-1 - IF ( INFI(J) .LT. 0 ) THEN - CALL RCSWP( J, I, A, B, INFI, N, COV ) - GO TO 10 - ENDIF - END DO - ENDIF - 10 END DO -* -* Sort remaining limits and determine Cholesky factor. -* - II = 0 - DO I = 1, N-INFIS -* -* Determine the integration limits for variable with minimum -* expected probability and interchange that variable with Ith. -* - DMIN = 0 - EMIN = 1 - JMIN = I - CVDIAG = 0 - IJ = II - DO J = I, N-INFIS - IF ( COV(IJ+J) .GT. EPS ) THEN - SUMSQ = SQRT( COV(IJ+J) ) - SUM = 0 - DO K = 1, I-1 - SUM = SUM + COV(IJ+K)*Y(K) - END DO - AJ = ( A(J) - SUM )/SUMSQ - BJ = ( B(J) - SUM )/SUMSQ - CALL MVNLMS( AJ, BJ, INFI(J), D, E ) - IF ( EMIN + D .GE. E + DMIN ) THEN - JMIN = J - AMIN = AJ - BMIN = BJ - DMIN = D - EMIN = E - CVDIAG = SUMSQ - ENDIF - ENDIF - IJ = IJ + J - END DO - IF ( JMIN .GT. I ) CALL RCSWP( I, JMIN, A,B, INFI, N, COV ) - COV(II+I) = CVDIAG -* -* Compute Ith column of Cholesky factor. -* Compute expected value for Ith integration variable and -* scale Ith covariance matrix row and limits. -* - IF ( CVDIAG .GT. 0 ) THEN - IL = II + I - DO L = I+1, N-INFIS - COV(IL+I) = COV(IL+I)/CVDIAG - IJ = II + I - DO J = I+1, L - COV(IL+J) = COV(IL+J) - COV(IL+I)*COV(IJ+I) - IJ = IJ + J - END DO - IL = IL + L - END DO - IF ( EMIN .GT. DMIN + EPS ) THEN - YL = 0 - YU = 0 - IF ( INFI(I) .NE. 0 ) YL = -EXP( -AMIN**2/2 )/SQTWPI - IF ( INFI(I) .NE. 1 ) YU = -EXP( -BMIN**2/2 )/SQTWPI - Y(I) = ( YU - YL )/( EMIN - DMIN ) - ELSE - IF ( INFI(I) .EQ. 0 ) Y(I) = BMIN - IF ( INFI(I) .EQ. 1 ) Y(I) = AMIN - IF ( INFI(I) .EQ. 2 ) Y(I) = ( AMIN + BMIN )/2 - END IF - DO J = 1, I - II = II + 1 - COV(II) = COV(II)/CVDIAG - END DO - A(I) = A(I)/CVDIAG - B(I) = B(I)/CVDIAG - ELSE - IL = II + I - DO L = I+1, N-INFIS - COV(IL+I) = 0 - IL = IL + L - END DO -* -* If the covariance matrix diagonal entry is zero, -* permute limits and/or rows, if necessary. -* -* - DO J = I-1, 1, -1 - IF ( ABS( COV(II+J) ) .GT. EPS ) THEN - A(I) = A(I)/COV(II+J) - B(I) = B(I)/COV(II+J) - IF ( COV(II+J) .LT. 0 ) THEN - CALL DKSWAP( A(I), B(I) ) - IF ( INFI(I) .NE. 2 ) INFI(I) = 1 - INFI(I) - END IF - DO L = 1, J - COV(II+L) = COV(II+L)/COV(II+J) - END DO - DO L = J+1, I-1 - IF( COV((L-1)*L/2+J+1) .GT. 0 ) THEN - IJ = II - DO K = I-1, L, -1 - DO M = 1, K - CALL DKSWAP( COV(IJ-K+M), COV(IJ+M) ) - END DO - CALL DKSWAP( A(K), A(K+1) ) - CALL DKSWAP( B(K), B(K+1) ) - M = INFI(K) - INFI(K) = INFI(K+1) - INFI(K+1) = M - IJ = IJ - K - END DO - GO TO 20 - END IF - END DO - GO TO 20 - END IF - COV(II+J) = 0 - END DO - 20 II = II + I - Y(I) = 0 - END IF - END DO - ENDIF - END -* - SUBROUTINE DKSWAP( X, Y ) - DOUBLE PRECISION X, Y, T - T = X - X = Y - Y = T - END -* - SUBROUTINE RCSWP( P, Q, A, B, INFIN, N, C ) -* -* Swaps rows and columns P and Q in situ, with P <= Q. -* - DOUBLE PRECISION A(*), B(*), C(*) - INTEGER INFIN(*), P, Q, N, I, J, II, JJ - CALL DKSWAP( A(P), A(Q) ) - CALL DKSWAP( B(P), B(Q) ) - J = INFIN(P) - INFIN(P) = INFIN(Q) - INFIN(Q) = J - JJ = ( P*( P - 1 ) )/2 - II = ( Q*( Q - 1 ) )/2 - CALL DKSWAP( C(JJ+P), C(II+Q) ) - DO J = 1, P-1 - CALL DKSWAP( C(JJ+J), C(II+J) ) - END DO - JJ = JJ + P - DO I = P+1, Q-1 - CALL DKSWAP( C(JJ+P), C(II+I) ) - JJ = JJ + I - END DO - II = II + Q - DO I = Q+1, N - CALL DKSWAP( C(II+P), C(II+Q) ) - II = II + I - END DO - END -* - SUBROUTINE DKBVRC( NDIM, MINVLS, MAXVLS, FUNCTN, ABSEPS, RELEPS, - & ABSERR, FINEST, INFORM ) -* -* Automatic Multidimensional Integration Subroutine -* -* AUTHOR: Alan Genz -* Department of Mathematics -* Washington State University -* Pulman, WA 99164-3113 -* Email: AlanGenz@wsu.edu -* -* Last Change: 1/15/03 -* -* KRBVRC computes an approximation to the integral -* -* 1 1 1 -* I I ... I F(X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -* -* DKBVRC uses randomized Korobov rules for the first 100 variables. -* The primary references are -* "Randomization of Number Theoretic Methods for Multiple Integration" -* R. Cranley and T.N.L. Patterson, SIAM J Numer Anal, 13, pp. 904-14, -* and -* "Optimal Parameters for Multidimensional Integration", -* P. Keast, SIAM J Numer Anal, 10, pp.831-838. -* If there are more than 100 variables, the remaining variables are -* integrated using the rules described in the reference -* "On a Number-Theoretical Integration Method" -* H. Niederreiter, Aequationes Mathematicae, 8(1972), pp. 304-11. -* -*************** Parameters ******************************************** -****** Input parameters -* NDIM Number of variables, must exceed 1, but not exceed 40 -* MINVLS Integer minimum number of function evaluations allowed. -* MINVLS must not exceed MAXVLS. If MINVLS < 0 then the -* routine assumes a previous call has been made with -* the same integrand and continues that calculation. -* MAXVLS Integer maximum number of function evaluations allowed. -* FUNCTN EXTERNALly declared user defined function to be integrated. -* It must have parameters (NDIM,Z), where Z is a real array -* of dimension NDIM. -* -* ABSEPS Required absolute accuracy. -* RELEPS Required relative accuracy. -****** Output parameters -* MINVLS Actual number of function evaluations used. -* ABSERR Estimated absolute accuracy of FINEST. -* FINEST Estimated value of integral. -* INFORM INFORM = 0 for normal exit, when -* ABSERR <= MAX(ABSEPS, RELEPS*ABS(FINEST)) -* and -* INTVLS <= MAXCLS. -* INFORM = 1 If MAXVLS was too small to obtain the required -* accuracy. In this case a value FINEST is returned with -* estimated absolute accuracy ABSERR. -************************************************************************ - EXTERNAL FUNCTN - INTEGER NDIM, MINVLS, MAXVLS, INFORM, NP, PLIM, NLIM, KLIM, KLIMI, - & SAMPLS, I, INTVLS, MINSMP - PARAMETER ( PLIM = 28, NLIM = 1000, KLIM = 100, MINSMP = 8 ) - INTEGER P(PLIM), C(PLIM,KLIM-1) - DOUBLE PRECISION FUNCTN, ABSEPS, RELEPS, FINEST, ABSERR, DIFINT, - & FINVAL, VARSQR, VAREST, VARPRD, VALUE - DOUBLE PRECISION X(2*NLIM), VK(NLIM), ONE - PARAMETER ( ONE = 1 ) - SAVE P, C, SAMPLS, NP, VAREST - INFORM = 1 - INTVLS = 0 - KLIMI = KLIM - IF ( MINVLS .GE. 0 ) THEN - FINEST = 0 - VAREST = 0 - SAMPLS = MINSMP - DO I = MIN( NDIM, 10), PLIM - NP = I - IF ( MINVLS .LT. 2*SAMPLS*P(I) ) GO TO 10 - END DO - SAMPLS = MAX( MINSMP, MINVLS/( 2*P(NP) ) ) - ENDIF - 10 VK(1) = ONE/P(NP) - DO I = 2, NDIM - IF ( I .LE. KLIM ) THEN - VK(I) = MOD( C(NP, MIN(NDIM-1,KLIM-1))*VK(I-1), ONE ) - ELSE - VK(I) = INT( P(NP)*2**(DBLE(I-KLIM)/(NDIM-KLIM+1)) ) - VK(I) = MOD( VK(I)/P(NP), ONE ) - END IF - END DO - FINVAL = 0 - VARSQR = 0 - DO I = 1, SAMPLS - CALL DKSMRC( NDIM, KLIMI, VALUE, P(NP), VK, FUNCTN, X ) - DIFINT = ( VALUE - FINVAL )/I - FINVAL = FINVAL + DIFINT - VARSQR = ( I - 2 )*VARSQR/I + DIFINT**2 - END DO - INTVLS = INTVLS + 2*SAMPLS*P(NP) - VARPRD = VAREST*VARSQR - FINEST = FINEST + ( FINVAL - FINEST )/( 1 + VARPRD ) - IF ( VARSQR .GT. 0 ) VAREST = ( 1 + VARPRD )/VARSQR - ABSERR = 7*SQRT( VARSQR/( 1 + VARPRD ) )/2 - IF ( ABSERR .GT. MAX( ABSEPS, ABS(FINEST)*RELEPS ) ) THEN - IF ( NP .LT. PLIM ) THEN - NP = NP + 1 - ELSE - SAMPLS = MIN( 3*SAMPLS/2, ( MAXVLS - INTVLS )/( 2*P(NP) ) ) - SAMPLS = MAX( MINSMP, SAMPLS ) - ENDIF - IF ( INTVLS + 2*SAMPLS*P(NP) .LE. MAXVLS ) GO TO 10 - ELSE - INFORM = 0 - ENDIF - MINVLS = INTVLS -* -* Optimal Parameters for Lattice Rules -* - DATA P( 1),(C( 1,I),I = 1,99)/ 31, 12, 2*9, 13, 8*12, 3*3, 12, - & 2*7, 9*12, 3*3, 12, 2*7, 9*12, 3*3, 12, 2*7, 9*12, 3*3, 12, 2*7, - & 8*12, 7, 3*3, 3*7, 21*3/ - DATA P( 2),(C( 2,I),I = 1,99)/ 47, 13, 11, 17, 10, 6*15, - & 22, 2*15, 3*6, 2*15, 9, 13, 3*2, 13, 2*11, 10, 9*15, 3*6, 2*15, - & 9, 13, 3*2, 13, 2*11, 10, 9*15, 3*6, 2*15, 9, 13, 3*2, 13, 2*11, - & 2*10, 8*15, 6, 2, 3, 2, 3, 12*2/ - DATA P( 3),(C( 3,I),I = 1,99)/ 73, 27, 28, 10, 2*11, 20, - & 2*11, 28, 2*13, 28, 3*13, 16*14, 2*31, 3*5, 31, 13, 6*11, 7*13, - & 16*14, 2*31, 3*5, 11, 13, 7*11, 2*13, 11, 13, 4*5, 14, 13, 8*5/ - DATA P( 4),(C( 4,I),I = 1,99)/ 113, 35, 2*27, 36, 22, 2*29, - & 20, 45, 3*5, 16*21, 29, 10*17, 12*23, 21, 27, 3*3, 24, 2*27, - & 17, 3*29, 17, 4*5, 16*21, 3*17, 6, 2*17, 6, 3, 2*6, 5*3/ - DATA P( 5),(C( 5,I),I = 1,99)/ 173, 64, 66, 2*28, 2*44, 55, - & 67, 6*10, 2*38, 5*10, 12*49, 2*38, 31, 2*4, 31, 64, 3*4, 64, - & 6*45, 19*66, 11, 9*66, 45, 11, 7, 3, 3*2, 27, 5, 2*3, 2*5, 7*2/ - DATA P( 6),(C( 6,I),I = 1,99)/ 263, 111, 42, 54, 118, 20, - & 2*31, 72, 17, 94, 2*14, 11, 3*14, 94, 4*10, 7*14, 3*11, 7*8, - & 5*18, 113, 2*62, 2*45, 17*113, 2*63, 53, 63, 15*67, 5*51, 12, - & 51, 12, 51, 5, 2*3, 2*2, 5/ - DATA P( 7),(C( 7,I),I = 1,99)/ 397, 163, 154, 83, 43, 82, - & 92, 150, 59, 2*76, 47, 2*11, 100, 131, 6*116, 9*138, 21*101, - & 6*116, 5*100, 5*138, 19*101, 8*38, 5*3/ - DATA P( 8),(C( 8,I),I = 1,99)/ 593, 246, 189, 242, 102, - & 2*250, 102, 250, 280, 118, 196, 118, 191, 215, 2*121, - & 12*49, 34*171, 8*161, 17*14, 6*10, 103, 4*10, 5/ - DATA P( 9),(C( 9,I),I = 1,99)/ 907, 347, 402, 322, 418, - & 215, 220, 3*339, 337, 218, 4*315, 4*167, 361, 201, 11*124, - & 2*231, 14*90, 4*48, 23*90, 10*243, 9*283, 16, 283, 16, 2*283/ - DATA P(10),(C(10,I),I = 1,99)/ 1361, 505, 220, 601, 644, - & 612, 160, 3*206, 422, 134, 518, 2*134, 518, 652, 382, - & 206, 158, 441, 179, 441, 56, 2*559, 14*56, 2*101, 56, - & 8*101, 7*193, 21*101, 17*122, 4*101/ - DATA P(11),(C(11,I),I = 1,99)/ 2053, 794, 325, 960, 528, - & 2*247, 338, 366, 847, 2*753, 236, 2*334, 461, 711, 652, - & 3*381, 652, 7*381, 226, 7*326, 126, 10*326, 2*195, 19*55, - & 7*195, 11*132, 13*387/ - DATA P(12),(C(12,I),I = 1,99)/ 3079, 1189, 888, 259, 1082, 725, - & 811, 636, 965, 2*497, 2*1490, 392, 1291, 2*508, 2*1291, 508, - & 1291, 2*508, 4*867, 934, 7*867, 9*1284, 4*563, 3*1010, 208, - & 838, 3*563, 2*759, 564, 2*759, 4*801, 5*759, 8*563, 22*226/ - DATA P(13),(C(13,I),I = 1,99)/ 4621, 1763, 1018, 1500, 432, - & 1332, 2203, 126, 2240, 1719, 1284, 878, 1983, 4*266, - & 2*747, 2*127, 2074, 127, 2074, 1400, 10*1383, 1400, 7*1383, - & 507, 4*1073, 5*1990, 9*507, 17*1073, 6*22, 1073, 6*452, 318, - & 4*301, 2*86, 15/ - DATA P(14),(C(14,I),I = 1,99)/ 6947, 2872, 3233, 1534, 2941, - & 2910, 393, 1796, 919, 446, 2*919, 1117, 7*103, 2311, 3117, 1101, - & 2*3117, 5*1101, 8*2503, 7*429, 3*1702, 5*184, 34*105, 13*784/ - DATA P(15),(C(15,I),I = 1,99)/ 10427, 4309, 3758, 4034, 1963, - & 730, 642, 1502, 2246, 3834, 1511, 2*1102, 2*1522, 2*3427, - & 3928, 2*915, 4*3818, 3*4782, 3818, 4782, 2*3818, 7*1327, 9*1387, - & 13*2339, 18*3148, 3*1776, 3*3354, 925, 2*3354, 5*925, 8*2133/ - DATA P(16),(C(16,I),I = 1,99)/ 15641, 6610, 6977, 1686, 3819, - & 2314, 5647, 3953, 3614, 5115, 2*423, 5408, 7426, 2*423, - & 487, 6227, 2660, 6227, 1221, 3811, 197, 4367, 351, - & 1281, 1221, 3*351, 7245, 1984, 6*2999, 3995, 4*2063, 1644, - & 2063, 2077, 3*2512, 4*2077, 19*754, 2*1097, 4*754, 248, 754, - & 4*1097, 4*222, 754,11*1982/ - DATA P(17),(C(17,I),I = 1,99)/ 23473, 9861, 3647, 4073, 2535, - & 3430, 9865, 2830, 9328, 4320, 5913, 10365, 8272, 3706, 6186, - & 3*7806, 8610, 2563, 2*11558, 9421, 1181, 9421, 3*1181, 9421, - & 2*1181, 2*10574, 5*3534, 3*2898, 3450, 7*2141, 15*7055, 2831, - & 24*8204, 3*4688, 8*2831/ - DATA P(18),(C(18,I),I = 1,99)/ 35221, 10327, 7582, 7124, 8214, - & 9600, 10271, 10193, 10800, 9086, 2365, 4409, 13812, - & 5661, 2*9344, 10362, 2*9344, 8585, 11114, 3*13080, 6949, - & 3*3436, 13213, 2*6130, 2*8159, 11595, 8159, 3436, 18*7096, - & 4377, 7096, 5*4377, 2*5410, 32*4377, 2*440, 3*1199/ - DATA P(19),(C(19,I),I = 1,99)/ 52837, 19540, 19926, 11582, - & 11113, 24585, 8726, 17218, 419, 3*4918, 15701, 17710, - & 2*4037, 15808, 11401, 19398, 2*25950, 4454, 24987, 11719, - & 8697, 5*1452, 2*8697, 6436, 21475, 6436, 22913, 6434, 18497, - & 4*11089, 2*3036, 4*14208, 8*12906, 4*7614, 6*5021, 24*10145, - & 6*4544, 4*8394/ - DATA P(20),(C(20,I),I = 1,99)/ 79259, 34566, 9579, 12654, - & 26856, 37873, 38806, 29501, 17271, 3663, 10763, 18955, - & 1298, 26560, 2*17132, 2*4753, 8713, 18624, 13082, 6791, - & 1122, 19363, 34695, 4*18770, 15628, 4*18770, 33766, 6*20837, - & 5*6545, 14*12138, 5*30483, 19*12138, 9305, 13*11107, 2*9305/ - DATA P(21),(C(21,I),I = 1,99)/118891, 31929, 49367, 10982, 3527, - & 27066, 13226, 56010, 18911, 40574, 2*20767, 9686, 2*47603, - & 2*11736, 41601, 12888, 32948, 30801, 44243, 2*53351, 16016, - & 2*35086, 32581, 2*2464, 49554, 2*2464, 2*49554, 2464, 81, 27260, - & 10681, 7*2185, 5*18086, 2*17631, 3*18086, 37335, 3*37774, - & 13*26401, 12982, 6*40398, 3*3518, 9*37799, 4*4721, 4*7067/ - DATA P(22),(C(22,I),I = 1,99)/178349, 40701, 69087, 77576, 64590, - & 39397, 33179, 10858, 38935, 43129, 2*35468, 5279, 2*61518, 27945, - & 2*70975, 2*86478, 2*20514, 2*73178, 2*43098, 4701, - & 2*59979, 58556, 69916, 2*15170, 2*4832, 43064, 71685, 4832, - & 3*15170, 3*27679, 2*60826, 2*6187, 5*4264, 45567, 4*32269, - & 9*62060, 13*1803, 12*51108, 2*55315, 5*54140, 13134/ - DATA P(23),(C(23,I),I = 1,99)/267523, 103650, 125480, 59978, - & 46875, 77172, 83021, 126904, 14541, 56299, 43636, 11655, - & 52680, 88549, 29804, 101894, 113675, 48040, 113675, - & 34987, 48308, 97926, 5475, 49449, 6850, 2*62545, 9440, - & 33242, 9440, 33242, 9440, 33242, 9440, 62850, 3*9440, - & 3*90308, 9*47904, 7*41143, 5*36114, 24997, 14*65162, 7*47650, - & 7*40586, 4*38725, 5*88329/ - DATA P(24),(C(24,I),I = 1,99)/401287, 165843, 90647, 59925, - & 189541, 67647, 74795, 68365, 167485, 143918, 74912, - & 167289, 75517, 8148, 172106, 126159,3*35867, 121694, - & 52171, 95354, 2*113969, 76304, 2*123709, 144615, 123709, - & 2*64958, 32377, 2*193002, 25023, 40017, 141605, 2*189165, - & 141605, 2*189165, 3*141605, 189165, 20*127047, 10*127785, - & 6*80822, 16*131661, 7114, 131661/ - DATA P(25),(C(25,I),I = 1,99)/601942, 130365, 236711, 110235, - & 125699, 56483, 93735, 234469, 60549, 1291, 93937, - & 245291, 196061, 258647, 162489, 176631, 204895, 73353, - & 172319, 28881, 136787,2*122081, 275993, 64673, 3*211587, - & 2*282859, 211587, 242821, 3*256865, 122203, 291915, 122203, - & 2*291915, 122203, 2*25639, 291803, 245397, 284047, - & 7*245397, 94241, 2*66575, 19*217673, 10*210249, 15*94453/ - DATA P(26),(C(26,I),I = 1,99)/902933, 333459, 375354, 102417, - & 383544, 292630, 41147, 374614, 48032, 435453, 281493, 358168, - & 114121, 346892, 238990, 317313, 164158, 35497, 2*70530, 434839, - & 3*24754, 393656, 2*118711, 148227, 271087, 355831, 91034, - & 2*417029, 2*91034, 417029, 91034, 2*299843, 2*413548, 308300, - & 3*413548, 3*308300, 413548, 5*308300, 4*15311, 2*176255, 6*23613, - & 172210, 4* 204328, 5*121626, 5*200187, 2*121551, 12*248492, - & 5*13942/ - DATA P(27), (C(27,I), I = 1,99)/ 1354471, 500884, 566009, 399251, - & 652979, 355008, 430235, 328722, 670680, 2*405585, 424646, - & 2*670180, 641587, 215580, 59048, 633320, 81010, 20789, 2*389250, - & 2*638764, 2*389250, 398094, 80846, 2*147776, 296177, 2*398094, - & 2*147776, 396313, 3*578233, 19482, 620706, 187095, 620706, - & 187095, 126467, 12*241663, 321632, 2*23210, 3*394484, 3*78101, - & 19*542095, 3*277743, 12*457259/ - DATA P(28), (C(28,I), I = 1, 99)/ 2031713, 858339, 918142, 501970, - & 234813, 460565, 31996, 753018, 256150, 199809, 993599, 245149, - & 794183, 121349, 150619, 376952, 2*809123, 804319, 67352, 969594, - & 434796, 969594, 804319, 391368, 761041, 754049, 466264, 2*754049, - & 466264, 2*754049, 282852, 429907, 390017, 276645, 994856, 250142, - & 144595, 907454, 689648, 4*687580, 978368, 687580, 552742, 105195, - & 942843, 768249, 4*307142, 7*880619, 11*117185, 11*60731, - & 4*178309, 8*74373, 3*214965/ -* - END -* - SUBROUTINE DKSMRC( NDIM, KLIM, SUMKRO, PRIME, VK, FUNCTN, X ) - EXTERNAL FUNCTN - INTEGER NDIM, NK, KLIM, PRIME, K, J, JP - DOUBLE PRECISION SUMKRO, VK(*), FUNCTN, X(*), ONE, XT, MVNUNI - PARAMETER ( ONE = 1 ) - SUMKRO = 0 - NK = MIN( NDIM, KLIM ) - DO J = 1, NK - 1 - JP = J + INT(MVNUNI()*( NK + 1 - J )) - XT = VK(J) - VK(J) = VK(JP) - VK(JP) = XT - END DO - DO J = 1, NDIM - X(NDIM+J) = MVNUNI() - END DO - DO K = 1, PRIME - DO J = 1, NDIM - X(J) = ABS( 2*MOD( K*VK(J) + X(NDIM+J), ONE ) - 1 ) - END DO - SUMKRO = SUMKRO + ( FUNCTN(NDIM,X) - SUMKRO )/( 2*K - 1 ) - DO J = 1, NDIM - X(J) = 1 - X(J) - END DO - SUMKRO = SUMKRO + ( FUNCTN(NDIM,X) - SUMKRO )/( 2*K ) - END DO - END -* - DOUBLE PRECISION FUNCTION MVNPHI( Z ) -* -* Normal distribution probabilities accurate to 1.e-15. -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7, - * Z, P, EXPNTL, CUTOFF, ROOTPI, ZABS - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = .70038 30644 43688 1D0, - * P6 = .035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = .088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 -* - IF ( ZABS .GT. 37 ) THEN - P = 0 - ELSE -* -* |Z| <= 37 -* - EXPNTL = EXP( -ZABS**2/2 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS .LT. CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1/( ZABS + 2/( ZABS + 3/( ZABS - * + 4/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0 ) P = 1 - P - MVNPHI = P - END - DOUBLE PRECISION FUNCTION PHINVS(P) -* -* ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3 -* -* Produces the normal deviate Z corresponding to a given lower -* tail area of P. -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, - * A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - * C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - * E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - * P, Q, R - PARAMETER ( SPLIT1 = 0.425, SPLIT2 = 5, - * CONST1 = 0.180625D0, CONST2 = 1.6D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( 2*P - 1 )/2 - IF ( ABS(Q) .LE. SPLIT1 ) THEN - R = CONST1 - Q*Q - PHINVS = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + 1 ) - ELSE - R = MIN( P, 1 - P ) - IF ( R .GT. 0 ) THEN - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - PHINVS = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + 1 ) - ELSE - R = R - SPLIT2 - PHINVS = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + 1 ) - END IF - ELSE - PHINVS = 9 - END IF - IF ( Q .LT. 0 ) PHINVS = - PHINVS - END IF - END - DOUBLE PRECISION FUNCTION BVNMVN( LOWER, UPPER, INFIN, CORREL ) -* -* A function for computing bivariate normal probabilities. -* -* Parameters -* -* LOWER REAL, array of lower integration limits. -* UPPER REAL, array of upper integration limits. -* INFIN INTEGER, array of integration limits flags: -* if INFIN(I) = 0, Ith limits are (-infinity, UPPER(I)]; -* if INFIN(I) = 1, Ith limits are [LOWER(I), infinity); -* if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)]. -* CORREL REAL, correlation coefficient. -* - DOUBLE PRECISION LOWER(*), UPPER(*), CORREL, BVU - INTEGER INFIN(*) - IF ( INFIN(1) .EQ. 2 .AND. INFIN(2) .EQ. 2 ) THEN - BVNMVN = BVU ( LOWER(1), LOWER(2), CORREL ) - + - BVU ( UPPER(1), LOWER(2), CORREL ) - + - BVU ( LOWER(1), UPPER(2), CORREL ) - + + BVU ( UPPER(1), UPPER(2), CORREL ) - ELSE IF ( INFIN(1) .EQ. 2 .AND. INFIN(2) .EQ. 1 ) THEN - BVNMVN = BVU ( LOWER(1), LOWER(2), CORREL ) - + - BVU ( UPPER(1), LOWER(2), CORREL ) - ELSE IF ( INFIN(1) .EQ. 1 .AND. INFIN(2) .EQ. 2 ) THEN - BVNMVN = BVU ( LOWER(1), LOWER(2), CORREL ) - + - BVU ( LOWER(1), UPPER(2), CORREL ) - ELSE IF ( INFIN(1) .EQ. 2 .AND. INFIN(2) .EQ. 0 ) THEN - BVNMVN = BVU ( -UPPER(1), -UPPER(2), CORREL ) - + - BVU ( -LOWER(1), -UPPER(2), CORREL ) - ELSE IF ( INFIN(1) .EQ. 0 .AND. INFIN(2) .EQ. 2 ) THEN - BVNMVN = BVU ( -UPPER(1), -UPPER(2), CORREL ) - + - BVU ( -UPPER(1), -LOWER(2), CORREL ) - ELSE IF ( INFIN(1) .EQ. 1 .AND. INFIN(2) .EQ. 0 ) THEN - BVNMVN = BVU ( LOWER(1), -UPPER(2), -CORREL ) - ELSE IF ( INFIN(1) .EQ. 0 .AND. INFIN(2) .EQ. 1 ) THEN - BVNMVN = BVU ( -UPPER(1), LOWER(2), -CORREL ) - ELSE IF ( INFIN(1) .EQ. 1 .AND. INFIN(2) .EQ. 1 ) THEN - BVNMVN = BVU ( LOWER(1), LOWER(2), CORREL ) - ELSE IF ( INFIN(1) .EQ. 0 .AND. INFIN(2) .EQ. 0 ) THEN - BVNMVN = BVU ( -UPPER(1), -UPPER(2), CORREL ) - END IF - END - DOUBLE PRECISION FUNCTION BVU( SH, SK, R ) -* -* A function for computing bivariate normal probabilities. -* -* Yihong Ge -* Department of Computer Science and Electrical Engineering -* Washington State University -* Pullman, WA 99164-2752 -* and -* Alan Genz -* Department of Mathematics -* Washington State University -* Pullman, WA 99164-3113 -* Email : alangenz@wsu.edu -* -* BVN - calculate the probability that X is larger than SH and Y is -* larger than SK. -* -* Parameters -* -* SH REAL, integration limit -* SK REAL, integration limit -* R REAL, correlation coefficient -* LG INTEGER, number of Gauss Rule Points and Weights -* - DOUBLE PRECISION BVN, SH, SK, R, ZERO, TWOPI - INTEGER I, LG, NG - PARAMETER ( ZERO = 0, TWOPI = 6.283185307179586D0 ) - DOUBLE PRECISION X(10,3), W(10,3), AS, A, B, C, D, RS, XS - DOUBLE PRECISION MVNPHI, SN, ASR, H, K, BS, HS, HK - SAVE X, W -* Gauss Legendre Points and Weights, N = 6 - DATA ( W(I,1), X(I,1), I = 1,3) / - * 0.1713244923791705D+00,-0.9324695142031522D+00, - * 0.3607615730481384D+00,-0.6612093864662647D+00, - * 0.4679139345726904D+00,-0.2386191860831970D+00/ -* Gauss Legendre Points and Weights, N = 12 - DATA ( W(I,2), X(I,2), I = 1,6) / - * 0.4717533638651177D-01,-0.9815606342467191D+00, - * 0.1069393259953183D+00,-0.9041172563704750D+00, - * 0.1600783285433464D+00,-0.7699026741943050D+00, - * 0.2031674267230659D+00,-0.5873179542866171D+00, - * 0.2334925365383547D+00,-0.3678314989981802D+00, - * 0.2491470458134029D+00,-0.1252334085114692D+00/ -* Gauss Legendre Points and Weights, N = 20 - DATA ( W(I,3), X(I,3), I = 1,10) / - * 0.1761400713915212D-01,-0.9931285991850949D+00, - * 0.4060142980038694D-01,-0.9639719272779138D+00, - * 0.6267204833410906D-01,-0.9122344282513259D+00, - * 0.8327674157670475D-01,-0.8391169718222188D+00, - * 0.1019301198172404D+00,-0.7463319064601508D+00, - * 0.1181945319615184D+00,-0.6360536807265150D+00, - * 0.1316886384491766D+00,-0.5108670019508271D+00, - * 0.1420961093183821D+00,-0.3737060887154196D+00, - * 0.1491729864726037D+00,-0.2277858511416451D+00, - * 0.1527533871307259D+00,-0.7652652113349733D-01/ - IF ( ABS(R) .LT. 0.3 ) THEN - NG = 1 - LG = 3 - ELSE IF ( ABS(R) .LT. 0.75 ) THEN - NG = 2 - LG = 6 - ELSE - NG = 3 - LG = 10 - ENDIF - H = SH - K = SK - HK = H*K - BVN = 0 - IF ( ABS(R) .LT. 0.925 ) THEN - HS = ( H*H + K*K )/2 - ASR = ASIN(R) - DO I = 1, LG - SN = SIN(ASR*( X(I,NG)+1 )/2) - BVN = BVN + W(I,NG)*EXP( ( SN*HK - HS )/( 1 - SN*SN ) ) - SN = SIN(ASR*(-X(I,NG)+1 )/2) - BVN = BVN + W(I,NG)*EXP( ( SN*HK - HS )/( 1 - SN*SN ) ) - END DO - BVN = BVN*ASR/(2*TWOPI) + MVNPHI(-H)*MVNPHI(-K) - ELSE - IF ( R .LT. 0 ) THEN - K = -K - HK = -HK - ENDIF - IF ( ABS(R) .LT. 1 ) THEN - AS = ( 1 - R )*( 1 + R ) - A = SQRT(AS) - BS = ( H - K )**2 - C = ( 4 - HK )/8 - D = ( 12 - HK )/16 - BVN = A*EXP( -(BS/AS + HK)/2 ) - + *( 1 - C*(BS - AS)*(1 - D*BS/5)/3 + C*D*AS*AS/5 ) - IF ( HK .GT. -160 ) THEN - B = SQRT(BS) - BVN = BVN - EXP(-HK/2)*SQRT(TWOPI)*MVNPHI(-B/A)*B - + *( 1 - C*BS*( 1 - D*BS/5 )/3 ) - ENDIF - A = A/2 - DO I = 1, LG - XS = ( A*(X(I,NG)+1) )**2 - RS = SQRT( 1 - XS ) - BVN = BVN + A*W(I,NG)* - + ( EXP( -BS/(2*XS) - HK/(1+RS) )/RS - + - EXP( -(BS/XS+HK)/2 )*( 1 + C*XS*( 1 + D*XS ) ) ) - XS = AS*(-X(I,NG)+1)**2/4 - RS = SQRT( 1 - XS ) - BVN = BVN + A*W(I,NG)*EXP( -(BS/XS + HK)/2 ) - + *( EXP( -HK*(1-RS)/(2*(1+RS)) )/RS - + - ( 1 + C*XS*( 1 + D*XS ) ) ) - END DO - BVN = -BVN/TWOPI - ENDIF - IF ( R .GT. 0 ) BVN = BVN + MVNPHI( -MAX( H, K ) ) - IF ( R .LT. 0 ) BVN = -BVN + MAX( ZERO, MVNPHI(-H)-MVNPHI(-K) ) - ENDIF - BVU = BVN - END - DOUBLE PRECISION FUNCTION MVNUNI() -* -* Uniform (0,1) random number generator -* -* Reference: -* L'Ecuyer, Pierre (1996), -* "Combined Multiple Recursive Random Number Generators" -* Operations Research 44, pp. 816-822. -* -* - INTEGER A12, A13, A21, A23, P12, P13, P21, P23 - INTEGER Q12, Q13, Q21, Q23, R12, R13, R21, R23 - INTEGER X10, X11, X12, X20, X21, X22, Z, M1, M2, H - DOUBLE PRECISION INVMP1 - PARAMETER ( M1 = 2147483647, M2 = 2145483479 ) - PARAMETER ( A12 = 63308, Q12 = 33921, R12 = 12979 ) - PARAMETER ( A13 = -183326, Q13 = 11714, R13 = 2883 ) - PARAMETER ( A21 = 86098, Q21 = 24919, R21 = 7417 ) - PARAMETER ( A23 = -539608, Q23 = 3976, R23 = 2071 ) - PARAMETER ( INVMP1 = 4.656612873077392578125D-10 ) -* INVMP1 = 1/(M1+1) - SAVE X10, X11, X12, X20, X21, X22 - DATA X10, X11, X12, X20, X21, X22 - & / 15485857, 17329489, 36312197, 55911127, 75906931, 96210113 / -* -* Component 1 -* - H = X10/Q13 - P13 = -A13*( X10 - H*Q13 ) - H*R13 - H = X11/Q12 - P12 = A12*( X11 - H*Q12 ) - H*R12 - IF ( P13 .LT. 0 ) P13 = P13 + M1 - IF ( P12 .LT. 0 ) P12 = P12 + M1 - X10 = X11 - X11 = X12 - X12 = P12 - P13 - IF ( X12 .LT. 0 ) X12 = X12 + M1 -* -* Component 2 -* - H = X20/Q23 - P23 = -A23*( X20 - H*Q23 ) - H*R23 - H = X22/Q21 - P21 = A21*( X22 - H*Q21 ) - H*R21 - IF ( P23 .LT. 0 ) P23 = P23 + M2 - IF ( P21 .LT. 0 ) P21 = P21 + M2 - X20 = X21 - X21 = X22 - X22 = P21 - P23 - IF ( X22 .LT. 0 ) X22 = X22 + M2 -* -* Combination -* - Z = X12 - X22 - IF ( Z .LE. 0 ) Z = Z + M1 - MVNUNI = Z*INVMP1 - END diff --git a/wafo/source/mvnprd/build_all.py b/wafo/source/mvnprd/build_all.py deleted file mode 100644 index e89b68c..0000000 --- a/wafo/source/mvnprd/build_all.py +++ /dev/null @@ -1,25 +0,0 @@ -"""builds mvnprdmod.pyd.""" -import os -import sys -from wafo.f2py_tools import f2py_call_str - - -def compile_all(): - f2py_call = f2py_call_str() - print '=' * 75 - print 'compiling mvnprd' - print '=' * 75 - - files = ['mvnprd', 'mvnprodcorrprb'] - compile1_format = 'gfortran -fPIC -c %s.f' - for file_ in files: - os.system(compile1_format % file_) - file_objects = '%s.o %s.o' % tuple(files) - - # os.system('f2py.py -m mvnprdmod -c %s mvnprd_interface.f - # --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71' % file_objects) - os.system(f2py_call + ' -m mvnprdmod -c %s mvnprd_interface.f ' % - file_objects) - -if __name__ == '__main__': - compile_all() diff --git a/wafo/source/mvnprd/mvnprd.dsp b/wafo/source/mvnprd/mvnprd.dsp deleted file mode 100644 index 3843b97..0000000 --- a/wafo/source/mvnprd/mvnprd.dsp +++ /dev/null @@ -1,93 +0,0 @@ -# Microsoft Developer Studio Project File - Name="mvnprd" - Package Owner=<4> -# Microsoft Developer Studio Generated Build File, Format Version 6.00 -# ** DO NOT EDIT ** - -# TARGTYPE "Win32 (x86) Console Application" 0x0103 - -CFG=mvnprd - Win32 Debug -!MESSAGE This is not a valid makefile. To build this project using NMAKE, -!MESSAGE use the Export Makefile command and run -!MESSAGE -!MESSAGE NMAKE /f "mvnprd.mak". -!MESSAGE -!MESSAGE You can specify a configuration when running NMAKE -!MESSAGE by defining the macro CFG on the command line. For example: -!MESSAGE -!MESSAGE NMAKE /f "mvnprd.mak" CFG="mvnprd - Win32 Debug" -!MESSAGE -!MESSAGE Possible choices for configuration are: -!MESSAGE -!MESSAGE "mvnprd - Win32 Release" (based on "Win32 (x86) Console Application") -!MESSAGE "mvnprd - Win32 Debug" (based on "Win32 (x86) Console Application") -!MESSAGE - -# Begin Project -# PROP AllowPerConfigDependencies 0 -# PROP Scc_ProjName "" -# PROP Scc_LocalPath "" -CPP=cl.exe -F90=df.exe -RSC=rc.exe - -!IF "$(CFG)" == "mvnprd - Win32 Release" - -# PROP BASE Use_MFC 0 -# PROP BASE Use_Debug_Libraries 0 -# PROP BASE Output_Dir "Release" -# PROP BASE Intermediate_Dir "Release" -# PROP BASE Target_Dir "" -# PROP Use_MFC 0 -# PROP Use_Debug_Libraries 0 -# PROP Output_Dir "Release" -# PROP Intermediate_Dir "Release" -# PROP Target_Dir "" -# ADD BASE F90 /compile_only /nologo /warn:nofileopt -# ADD F90 /compile_only /nologo /warn:nofileopt -# ADD BASE CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c -# ADD CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c -# ADD BASE RSC /l 0x414 /d "NDEBUG" -# ADD RSC /l 0x414 /d "NDEBUG" -BSC32=bscmake.exe -# ADD BASE BSC32 /nologo -# ADD BSC32 /nologo -LINK32=link.exe -# ADD BASE LINK32 kernel32.lib /nologo /subsystem:console /machine:I386 -# ADD LINK32 kernel32.lib /nologo /subsystem:console /machine:I386 - -!ELSEIF "$(CFG)" == "mvnprd - Win32 Debug" - -# PROP BASE Use_MFC 0 -# PROP BASE Use_Debug_Libraries 1 -# PROP BASE Output_Dir "Debug" -# PROP BASE Intermediate_Dir "Debug" -# PROP BASE Target_Dir "" -# PROP Use_MFC 0 -# PROP Use_Debug_Libraries 1 -# PROP Output_Dir "Debug" -# PROP Intermediate_Dir "Debug" -# PROP Target_Dir "" -# ADD BASE F90 /check:bounds /compile_only /debug:full /nologo /traceback /warn:argument_checking /warn:nofileopt -# ADD F90 /check:bounds /compile_only /debug:full /nologo /traceback /warn:argument_checking /warn:nofileopt -# ADD BASE CPP /nologo /W3 /Gm /GX /ZI /Od /D "WIN32" /D "_DEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /GZ /c -# ADD CPP /nologo /W3 /Gm /GX /ZI /Od /D "WIN32" /D "_DEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /GZ /c -# ADD BASE RSC /l 0x414 /d "_DEBUG" -# ADD RSC /l 0x414 /d "_DEBUG" -BSC32=bscmake.exe -# ADD BASE BSC32 /nologo -# ADD BSC32 /nologo -LINK32=link.exe -# ADD BASE LINK32 kernel32.lib /nologo /subsystem:console /debug /machine:I386 /pdbtype:sept -# ADD LINK32 kernel32.lib /nologo /subsystem:console /debug /machine:I386 /pdbtype:sept - -!ENDIF - -# Begin Target - -# Name "mvnprd - Win32 Release" -# Name "mvnprd - Win32 Debug" -# Begin Source File - -SOURCE=.\mvnprd.f -# End Source File -# End Target -# End Project diff --git a/wafo/source/mvnprd/mvnprd.dsw b/wafo/source/mvnprd/mvnprd.dsw deleted file mode 100644 index 10861ae..0000000 --- a/wafo/source/mvnprd/mvnprd.dsw +++ /dev/null @@ -1,29 +0,0 @@ -Microsoft Developer Studio Workspace File, Format Version 6.00 -# WARNING: DO NOT EDIT OR DELETE THIS WORKSPACE FILE! - -############################################################################### - -Project: "mvnprd"=.\mvnprd.dsp - Package Owner=<4> - -Package=<5> -{{{ -}}} - -Package=<4> -{{{ -}}} - -############################################################################### - -Global: - -Package=<5> -{{{ -}}} - -Package=<3> -{{{ -}}} - -############################################################################### - diff --git a/wafo/source/mvnprd/mvnprd.f b/wafo/source/mvnprd/mvnprd.f deleted file mode 100644 index d9d2a61..0000000 --- a/wafo/source/mvnprd/mvnprd.f +++ /dev/null @@ -1,1099 +0,0 @@ -C -C f2py -m mvnprd -h mvnprd.pyf mvnprd.f only: mvnprd -C edit mvnprd.pyf with input and output and then -C f2py mvnprd.pyf mvnprd.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C -C f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m mvnprd -c mvnprd.f - -C Altarnative: compile mvnprd and link to it through mvnprd_interface.f -C -C gfortran -fPIC -c mvnprd.f -C f2py -m mvnprdmod -c mvnprd.o mvnprd_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C -C df -c mvnprd.f -C f2py -m mvnprdmod -c mvnprd.obj mvnprd_interface.f --fcompiler=compaqv --compiler=mingw32 -lmsvcr71 - -! This is a MEX-file for MATLAB. -! and contains a mex-interface to Charles W. Dunnett's programs -! ,MVNPRD and MVSTUD subroutines for computing multivariate normal -! or student T probabilities with product correlation structure. The -! file should compile without errors on (Fortran77) standard Fortran -! compilers. -* -* The mex-interface was written by -* Per Andreas Brodtkorb -* Norwegian Defence Research Establishment -* P.O. Box 115m -* N-3191 Horten -* Norway -* Email: Per.Brodtkorb@ffi.no -* -* Charles Dunnett -C Dept. of Mathematics and Statistics -C McMaster University -C Hamilton, Ontario L8S 4K1 -C Canada -C E-mail: dunnett@mcmaster.ca -C Tel.: (905) 525-9140 (Ext. 27104) -* -* MVNPRDMEX Computes multivariate normal or student T probability -* with product correlation structure. - -* -* CALL [value,bound,inform] = mvnprdmex(RHO,A,B,D,NDF,abseps,IERC,HNC) -* -* RHO REAL, array of coefficients defining the correlation -* coefficient by: -* correlation(I,J) = RHO(I)*RHO(J) for J/=I -* where -* 1 < RHO(I) < 1 -* A REAL, array of lower integration limits. -* B REAL, array of upper integration limits. -* NOTE: any values greater the 37, are considered as -* infinite values. -* D Real array of means -* NDF Degrees of freedom, NDF<=0 gives normal probabilities -* ABSEPS REAL absolute error tolerance. -* IERC INTEGER 1 if strict error control based on fourth -* derivative -* 0 if intuitive error control based on halving the -* intervals -* HINC REAL start interval width of simpson rule -* -* OUTPUT: -* VALUE REAL estimated value for the integral -* BOUND REAL bound on the error of the approximation -* INFORM INTEGER, termination status parameter: -* 0, if normal completion with ERROR < EPS; -* 1, if N > 100 or N < 1. -* 2, IF any abs(rho)>=1 -* 4, if ANY(B(I)<=A(i)) -* 5, if number of terms computed exceeds maximum number of -* evaluation points -* 6, if fault accurs in normal subroutines -* 7, if subintervals are too narrow or too many -* 8, if bounds exceeds abseps -* -* -* MVNPRDMEX calculates multivariate normal or student T probability -* with product correlation structure for rectangular regions. -* The accuracy is up to around single precision, i.e., about 1e-7. -* -* This file was successfully compiled for matlab 5.3 -* using Compaq Visual Fortran 6.1, and Windows 2000. -* The example here uses Fortran77 source. -* First, you will need to modify your mexopts.bat file. -* To find it, issue the command prefdir(1) from the Matlab command line, -* the directory it answers with will contain your mexopts.bat file. -* Open it for editing. The first section will look like: -* -*rem ******************************************************************** -*rem General parameters -*rem ******************************************************************** -*set MATLAB=%MATLAB% -*set DF_ROOT=C:\Program Files\Microsoft Visual Studio -*set VCDir=%DF_ROOT%\VC98 -*set MSDevDir=%DF_ROOT%\Common\msdev98 -*set DFDir=%DF_ROOT%\DF98 -*set PATH=%MSDevDir%\bin;%DFDir%\BIN;%VCDir%\BIN;%PATH% -*set INCLUDE=%DFDir%\INCLUDE;%DFDir%\IMSL\INCLUDE;%INCLUDE% -*set LIB=%DFDir%\LIB;%VCDir%\LIB -* -* then you are ready to compile this file at the matlab prompt using the -* following command: -* mex -O mvnprdmex.f - - - -C The rest of this file contains: -C 1. A Readme file provided by Charles Dunnett, the author of AS 251. -C 2. The published algorithm AS 251 together with the two other AS algorithms -C which it calls (AS 66 and AS 241). -C 3. A driver program (MVTIN) for either multivariate normal or t. -C 4. MVSTUD for calculating multivariate t probabilities. -C *************************************************************************** - -C Date: Mon, 10 Apr 1995 16:49:10 +0059 (EDT) -C From: "Charles W. Dunnett" -C Subject: Readme for AS251 (extended version incl. multivariate t) - -C MVTIN is a driver program for computing multivariate normal or t -C probability integrals over arbitrary rectangular regions. The -C correlation structure is assumed to be of product form, rho_ij = -C b_i x b_j, where -1 < b_i < +1. - -C It requires the following:- - -C 1. MVNPRD (published as algorithm AS 251 in Applied -C Statistics (1989), 38: 564-579; see also the correction -C note in Applied Statistics (1993), 42: 709), - -C 2. ALNORM and PPND7 (published as algorithms AS 66 and -C AS 241, respectively, in Applied Statistics, and - -C 3. MVSTUD ( which Studentizes MVNPRD). - - - - SUBROUTINE MVNPRD(A, B, BPD, EPS, N, INF, IERC, HINC, PROB, BOUND, - * IFAULT) - implicit none -C -C ALGORITHM AS 251.1 APPL.STATIST. (1989), VOL.38, NO.3 -C -C FOR A MULTIVARIATE NORMAL VECTOR WITH CORRELATION STRUCTURE -C DEFINED BY RHO(I,J) = BPD(I) * BPD(J), COMPUTES THE PROBABILITY -C THAT THE VECTOR FALLS IN A RECTANGLE IN N-SPACE WITH ERROR -C LESS THAN EPS. -C - INTEGER NN - PARAMETER (NN = 100) - DOUBLE PRECISION A(*), B(*), BPD(*), ESTT(22), FV(5), FD(5), - & F1T(22), F2T(22), F3T(22), G1T(22), G3T(22), PSUM(22), H(NN) - $ , HL(NN),BB(NN) - INTEGER INF(*), INFT(NN), LDIR(22) - DOUBLE PRECISION ZERO, HALF, ONE, TWO, FOUR, SIX, PT1, PT24, - * SMALL, DXMIN, SQRT2, PROB, ERRL, BI, START, - * Z, HINC, ADDN, EPS2, EPS1, EPS, ZU, Z2, Z3, Z4, Z5, ZZ, - * ERFAC, EL, EL1, BOUND, PART0, PART2, PART3, FUNC0, FUNC2, - * FUNCN, WT, CONTRB, DLG, DX, DA, ESTL, ESTR, TSUM, EXCESS, ERROR, - * PROB1, SAFE, ONEP5,X2880 - INTEGER N, IERC, IFAULT, I, NTM, NMAX, LVL, NR, NDIM - DOUBLE PRECISION ALNORM, PPND7 - EXTERNAL ALNORM, PPND7 - DATA ZERO, HALF, ONE, TWO, FOUR, SIX /0.0, 0.5, 1.0, 2.0, - * 4.0, 6.0/ - DATA PT1, PT24, ONEP5, X2880 /0.1, 0.24, 1.5, 2880.0/ - DATA SMALL, DXMIN, SQRT2 /1.0E-10, 0.0000001, 1.41421356237310/ -C -C CHECK FOR INPUT VALUES OUT OF RANGE. -C - PROB = ZERO - BOUND = ZERO - IFAULT = 1 - IF (N .LT. 1 .OR. N .GT. NN) RETURN - DO 10 I = 1, N - BI = ABS(BPD(I)) - IFAULT = 2 - IF (BI .GE. ONE) RETURN - IFAULT = 3 - IF (INF(I) .LT. 0 .OR. INF(I) .GT. 2) RETURN - IFAULT = 4 - IF (INF(I) .EQ. 2 .AND. A(I) .LE. B(I)) RETURN - 10 CONTINUE - IFAULT = 0 - PROB = ONE -C -C CHECK WHETHER ANY BPD(I) = 0. -C - NDIM = 0 - DO 20 I = 1, N - IF (BPD(I) .NE. ZERO) THEN - NDIM = NDIM + 1 - H(NDIM) = A(I) - HL(NDIM) = B(I) - BB(NDIM) = BPD(I) - INFT(NDIM) = INF(I) - ELSE -C -C IF ANY BPD(I) = 0, THE CONTRIBUTION TO PROB FOR THAT -C VARIABLE IS COMPUTED FROM A UNIVARIATE NORMAL. -C - IF (INF(I) .LT. 1) THEN - PROB = PROB * (ONE - ALNORM(B(I), .FALSE.)) - ELSE IF (INF(I) .EQ. 1) THEN - PROB = PROB * ALNORM(A(I), .FALSE.) - ELSE - PROB = PROB * (ALNORM(A(I), .FALSE.) - - * ALNORM(B(I), .FALSE.)) - END IF - IF (PROB .LE. SMALL) PROB = ZERO - END IF - 20 CONTINUE - IF (NDIM .EQ. 0 .OR. PROB .EQ. ZERO) RETURN -C -C IF NOT ALL BPD(I) = 0, PROB IS COMPUTED BY SIMPSON'S RULE. -C BUT FIRST, INITIALIZE THE VARIABLES. -C - Z = ZERO - IF (HINC .LE. ZERO) HINC = PT24 - ADDN = -ONE - DO 30 I = 1, NDIM - IF (INFT(I) .EQ. 2 .OR. - * (INFT(I) .NE. INFT(1) .AND. BB(I) * BB(1) .GT. ZERO) .OR. - * (INFT(I) .EQ. INFT(1) .AND. BB(I) * BB(1) .LT. ZERO)) - * ADDN = ZERO - 30 CONTINUE -C -C THE VALUE OF ADDN IS TO BE ADDED TO THE PRODUCT EXPRESSIONS IN -C THE INTEGRAND TO INSURE THAT THE LIMITING VALUE IS ZERO. -C - PROB1 = ZERO - NTM = 0 - NMAX = 400 - IF (IERC .EQ. 0) NMAX = NMAX * 2 - CALL PFUNC (Z, H, HL, BB, NDIM, INFT, ADDN, SAFE, FUNC0, NTM, - * IERC, PART0) - EPS2 = EPS * PT1 * HALF -C -C SET UPPER BOUND ON Z AND APPORTION EPS. -C - ZU = -PPND7(EPS2, IFAULT) / SQRT2 - IF (IFAULT .NE. 0) THEN - IFAULT = 6 - RETURN - END IF - !NR = IFIX(ZU / HINC) + 1 - NR = NINT(ZU / HINC) + 1 - ERFAC = ONE - IF (IERC .NE. 0) ERFAC = X2880 / HINC ** 5 - EL = (EPS - EPS2) / FLOAT(NR) * ERFAC - EL1 = EL -C -C START COMPUTATIONS FOR THE INTERVAL (Z, Z + HINC). -C - 40 ERROR = ZERO - LVL = 0 - FV(1) = PART0 - FD(1) = SAFE - START = Z - DA = HINC - Z3 = START + HALF * DA - CALL PFUNC(Z3, H, HL, BB, NDIM, INFT, ADDN, FD(3), FUNCN, NTM, - * IERC, FV(3)) - Z5 = START + DA - CALL PFUNC(Z5, H, HL, BB, NDIM, INFT, ADDN, FD(5), FUNC2, NTM, - * IERC, FV(5)) - PART2 = FV(5) - SAFE = FD(5) - WT = DA / SIX - CONTRB = WT * (FV(1) + FOUR * FV(3) + FV(5)) - DLG = ZERO - IF (IERC .NE. 0) THEN - CALL WMAX(FD(1), FD(3), FD(5), DLG) - IF (DLG .LE. EL) GO TO 90 - DX = DA - GO TO 60 - END IF - LVL = 1 - LDIR(LVL) = 2 - PSUM(LVL) = ZERO -C -C BISECT INTERVAL. IF IERC = 1, COMPUTE ESTIMATE ON LEFT -C HALF; IF IERC = 0, ON BOTH HALVES. -C - 50 DX = HALF * DA - WT = DX / SIX - Z2 = START + HALF * DX - CALL PFUNC(Z2, H, HL, BB, NDIM, INFT, ADDN, FD(2), FUNCN, NTM, - * IERC,FV(2)) - ESTL = WT * (FV(1) + FOUR * FV(2) + FV(3)) - IF (IERC .EQ. 0) THEN - Z4 = START + ONEP5 * DX - CALL PFUNC(Z4, H, HL, BB, NDIM, INFT, ADDN, FD(4), FUNCN, - * NTM, IERC, FV(4)) - ESTR = WT * (FV(3) + FOUR * FV(4) + FV(5)) - TSUM = ESTL + ESTR - DLG = ABS(CONTRB - TSUM) - EPS1 = EL / TWO ** (LVL - 1) - ERRL = DLG - ELSE - FV(3) = FV(2) - FD(3) = FD(2) - CALL WMAX(FD(1), FD(3), FD(5), DLG) - ERRL = DLG / TWO ** (5 * LVL) - TSUM = ESTL - EPS1 = EL * (TWO ** LVL) ** 4 - END IF -C -C STOP SUBDIVIDING INTERVAL WHEN ACCURACY IS SUFFICIENT, -C OR IF INTERVAL TOO NARROW OR SUBDIVIDED TOO OFTEN. -C - IF (DLG .LE. EPS1 .OR. DLG .LT. SMALL) GO TO 70 - IF (IFAULT .EQ. 0 .AND. NTM .GE. NMAX) IFAULT = 5 - IF (ABS(DX) .LE. DXMIN .OR. LVL .GT. 21) IFAULT = 7 - IF (IFAULT .NE. 0) GO TO 70 -C -C RAISE LEVEL. STORE INFORMATION FOR RIGHT HALF AND APPLY -C SIMPSON'S RULE TO LEFT HALF. -C - 60 LVL = LVL + 1 - LDIR(LVL) = 1 - F1T(LVL) = FV(3) - F3T(LVL) = FV(5) - DA = DX - FV(5) = FV(3) - IF (IERC .EQ. 0) THEN - F2T(LVL) = FV(4) - ESTT(LVL) = ESTR - CONTRB = ESTL - FV(3) = FV(2) - ELSE - G1T(LVL) = FD(3) - G3T(LVL) = FD(5) - FD(5) = FD(3) - END IF - GO TO 50 -C -C ACCEPT APPROXIMATE VALUE FOR INTERVAL. -C RESTORE SAVED INFORMATION TO PROCESS -C RIGHT HALF INTERVAL. -C - 70 ERROR = ERROR + ERRL - 80 IF (LDIR(LVL) .EQ. 1) THEN - PSUM(LVL) = TSUM - LDIR(LVL) = 2 - IF (IERC .EQ. 0) DX = DX * TWO - START = START + DX - DA = HINC / TWO ** (LVL - 1) - FV(1) = F1T(LVL) - IF (IERC .EQ. 0) THEN - FV(3) = F2T(LVL) - CONTRB = ESTT(LVL) - ELSE - FV(3) = F3T(LVL) - FD(1) = G1T(LVL) - FD(5) = G3T(LVL) - END IF - FV(5) = F3T(LVL) - GO TO 50 - END IF - TSUM = TSUM + PSUM(LVL) - LVL = LVL - 1 - IF (LVL .GT. 0) GO TO 80 - CONTRB = TSUM - LVL = 1 - DLG = ERROR - 90 PROB1 = PROB1 + CONTRB - BOUND = BOUND + DLG - EXCESS = EL - DLG - EL = EL1 - IF (EXCESS .GT. ZERO) EL = EL1 + EXCESS - IF ((FUNC0 .GT. ZERO .AND. FUNC2 .LE. FUNC0) .OR. - * (FUNC0 .LT. ZERO .AND. FUNC2 .GE. FUNC0)) THEN - ZZ = -SQRT2 * Z5 - PART3 = ABS(FUNC2) * ALNORM(ZZ, .FALSE.) + BOUND / ERFAC - IF (PART3 .LE. EPS .OR. NTM .GE. NMAX .OR. Z5 .GE. ZU) GOTO 100 - END IF - Z = Z5 - PART0 = PART2 - FUNC0 = FUNC2 - IF (Z .LT. ZU .AND. NTM .LT. NMAX) GO TO 40 - 100 PROB = (PROB1 - ADDN * HALF) * PROB - BOUND = PART3 - IF (NTM .GE. NMAX .AND. IFAULT .EQ. 0) IFAULT = 5 - IF (BOUND .GT. EPS .AND. IFAULT .EQ. 0) IFAULT = 8 - RETURN - END - SUBROUTINE PFUNC(Z, A, B, BPD, N, INF, ADDN, DERIV, FUNCN, NTM, - * IERC, RESULT) - implicit none -C -C ALGORITHM AS 251.2 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C COMPUTE FUNCTION IN INTEGRAND AND ITS 4TH DERIVATIVE. -C - INTEGER NN - PARAMETER (NN = 100) - DOUBLE PRECISION A(*), B(*), BPD(*), FOU(NN), FOU1(4, NN), TMP(4), - & GOU(NN), GOU1(4, NN), FF(4), GF(4), TERM(4), GERM(4) - INTEGER INF(*) - DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, SIX, EIGHT, TWELVE, - & SIXTN, SMALL, Z, U, U1, U2, BI, HI, HLI, BP, ADDN, DERIV, - $ FUNCN,RESULT, RSLT1, RSLT2, DEN, SQRT2, SQRTPI, PHI, PHI1, - $ PHI2,PHI3, PHI4, FRM, GRM - INTEGER N, NTM, IERC, INFI, I, J, K, M, L, IK - DOUBLE PRECISION ALNORM - EXTERNAL ALNORM - DATA ZERO, ONE, TWO, THREE, FOUR, SIX, EIGHT, TWELVE, SIXTN, - * SMALL /0.0, 1.0, 2.0, 3.0, 4.0, 6.0, 8.0, 12.0, 16.0, 0.1E-12/ - DATA SQRT2, SQRTPI /1.41421356237310, 1.77245385090552/ - DERIV = ZERO - NTM = NTM + 1 - RSLT1 = ONE - RSLT2 = ONE - BI = ONE - HI = A(1) + ONE - HLI = B(1) + ONE - INFI = -1 - DO 60 I = 1, N - IF (BPD(I) .EQ. BI .AND. A(I) .EQ. HI .AND. B(I) .EQ. HLI .AND. - * INF(I) .EQ. INFI) THEN - FOU(I) = FOU(I - 1) - GOU(I) = GOU(I - 1) - DO 10 IK = 1, 4 - FOU1(IK, I) = FOU1(IK, I - 1) - GOU1(IK, I) = GOU1(IK, I - 1) - 10 CONTINUE - ELSE - BI = BPD(I) - HI = A(I) - HLI = B(I) - INFI = INF(I) - IF (BI .EQ. ZERO) THEN - IF (INFI .LT. 1) THEN - FOU(I) = ONE - ALNORM(HLI, .FALSE.) - ELSE IF (INFI .EQ. 1) THEN - FOU(I) = ALNORM(HI, .FALSE.) - ELSE - FOU(I) = ALNORM(HI, .FALSE.) - ALNORM(HLI, .FALSE.) - END IF - GOU(I) = FOU(I) - DO 20 IK = 1, 4 - FOU1(IK, I) = ZERO - GOU1(IK, I) = ZERO - 20 CONTINUE - ELSE - DEN = SQRT(ONE - BI * BI) - BP = BI * SQRT2 / DEN - IF (INFI .LT. 1) THEN - U = -HLI / DEN + Z * BP - FOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, FOU1(1, I)) - BP = -BP - U = -HLI / DEN + Z * BP - GOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, GOU1(1, I)) - ELSE IF (INFI .EQ. 1) THEN - U = HI / DEN + Z * BP - GOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, GOU1(1, I)) - BP = -BP - U = HI / DEN + Z * BP - FOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, FOU1(1, I)) - ELSE - U2 = -HLI / DEN + Z * BP - CALL ASSIGN (U2, BP, FOU1(1, I)) - BP = -BP - U1 = HI / DEN + Z * BP - CALL ASSIGN (U1, BP, TMP(1)) - FOU(I) = ALNORM(U1, .FALSE.) + ALNORM(U2, .FALSE.) - ONE - DO 30 IK = 1, 4 - FOU1(IK, I) = FOU1(IK, I) + TMP(IK) - 30 CONTINUE - IF (-HLI .EQ. HI) THEN - GOU(I) = FOU(I) - DO 40 IK = 1, 4 - GOU1(IK, I) = FOU1(IK, I) - 40 CONTINUE - ELSE - U2 = -HLI / DEN + Z * BP - CALL ASSIGN (U2, BP, GOU1(1, I)) - BP = -BP - U1 = HI / DEN + Z * BP - GOU(I) = ALNORM(U1, .FALSE.) + ALNORM(U2, .FALSE.)-ONE - CALL ASSIGN (U1, BP, TMP(1)) - DO 50 IK = 1, 4 - GOU1(IK, I) = GOU1(IK, I) + TMP(IK) - 50 CONTINUE - END IF - END IF - END IF - END IF - RSLT1 = RSLT1 * FOU(I) - RSLT2 = RSLT2 * GOU(I) - IF (RSLT1 .LE. SMALL) RSLT1 = ZERO - IF (RSLT2 .LE. SMALL) RSLT2 = ZERO - 60 CONTINUE - FUNCN = RSLT1 + RSLT2 + ADDN - RESULT = FUNCN * EXP(-Z * Z) / SQRTPI -C -C IF 4TH DERIVATIVE IS NOT WANTED, STOP HERE. -C OTHERWISE, PROCEED TO COMPUTE 4TH DERIVATIVE. -C - IF (IERC .EQ. 0) RETURN - DO 70 IK = 1, 4 - FF(IK) = ZERO - GF(IK) = ZERO - 70 CONTINUE - DO 100 I = 1, N - FRM = ONE - GRM = ONE - DO 80 J = 1, N - IF (J .EQ. 1) GO TO 80 - FRM = FRM * FOU(J) - GRM = GRM * GOU(J) - IF (FRM .LE. SMALL) FRM = ZERO - IF (GRM .LE. SMALL) GRM = ZERO - 80 CONTINUE - DO 90 IK = 1, 4 - FF(IK) = FF(IK) + FRM * FOU1(IK, I) - GF(IK) = GF(IK) + GRM * GOU1(IK, I) - 90 CONTINUE - 100 CONTINUE - IF (N .LE. 2) GO TO 230 - DO 130 I = 1, N - DO 120 J = I + 1, N - TERM(2) = FOU1(1, I) * FOU1(1, J) - GERM(2) = GOU1(1, I) * GOU1(1, J) - TERM(3) = FOU1(2, I) * FOU1(1, J) - GERM(3) = GOU1(2, I) * GOU1(1, J) - TERM(4) = FOU1(3, I) * FOU1(1, J) - GERM(4) = GOU1(3, I) * GOU1(1, J) - TERM(1) = FOU1(2, I) * FOU1(2, J) - GERM(1) = GOU1(2, I) * GOU1(2, J) - DO 110 K = 1, N - IF (K .EQ. I .OR. K .EQ. J) GO TO 110 - CALL TOOSML (1, TERM, FOU(K)) - CALL TOOSML (1, GERM, GOU(K)) - 110 CONTINUE - FF(2) = FF(2) + TWO * TERM(2) - FF(3) = FF(3) + TWO * TERM(3) * THREE - FF(4) = FF(4) + TWO * (TERM(4) * FOUR + TERM(1) * THREE) - GF(2) = GF(2) + TWO * GERM(2) - GF(3) = GF(3) + TWO * GERM(3) * THREE - GF(4) = GF(4) + TWO * (GERM(4) * FOUR + GERM(1) * THREE) - 120 CONTINUE - 130 CONTINUE - DO 170 I = 1, N - DO 160 J = I + 1, N - DO 150 K = J + 1, N - TERM(3) = FOU1(1, I) * FOU1(1, J) * FOU1(1, K) - TERM(4) = FOU1(2, I) * FOU1(1, J) * FOU1(1, K) - GERM(3) = GOU1(1, I) * GOU1(1, J) * GOU1(1, K) - GERM(4) = GOU1(2, I) * GOU1(1, J) * GOU1(1, K) - IF (N .GT. 3) THEN - DO 140 M = 1, N - IF (M .EQ. I .OR. M .EQ. J .OR. M .EQ. K) GO TO 140 - CALL TOOSML (3, TERM, FOU(M)) - CALL TOOSML (3, GERM, GOU(M)) - 140 CONTINUE - END IF - FF(3) = FF(3) + SIX * TERM(3) - FF(4) = FF(4) + SIX * TERM(4) * SIX - GF(3) = GF(3) + SIX * GERM(3) - GF(4) = GF(4) + SIX * GERM(4) * SIX - 150 CONTINUE - 160 CONTINUE - 170 CONTINUE - IF (N .LE. 3) GO TO 230 - DO 220 I = 1, N - DO 210 J = I + 1, N - DO 200 K = J + 1, N - DO 190 M = K + 1, N - TERM(4) = FOU1(1, I) * FOU1(1, J) * FOU1(1, K) * FOU1(1, M) - GERM(4) = GOU1(1, I) * GOU1(1, J) * GOU1(1, K) * GOU1(1, M) - IF (N .GT. 4) THEN - DO 180 L = 1, N - IF (L .EQ. I .OR. L .EQ. J .OR. L .EQ. K .OR. L .EQ. M)GOTO 180 - CALL TOOSML (4, TERM, FOU(L)) - CALL TOOSML (4, GERM, GOU(L)) - 180 CONTINUE - END IF - FF(4) = FF(4) + FOUR * SIX * TERM(4) - GF(4) = GF(4) + FOUR * SIX * GERM(4) - 190 CONTINUE - 200 CONTINUE - 210 CONTINUE - 220 CONTINUE -C - 230 CONTINUE - PHI = EXP(-Z * Z) / SQRTPI - PHI1 = -TWO * Z * PHI - PHI2 = (FOUR * Z ** 2 - TWO) * PHI - PHI3 = (-EIGHT * Z ** 3 + TWELVE * Z) * PHI - PHI4 = (SIXTN * Z ** 2 * (Z ** 2 - THREE) + TWELVE) * PHI - DERIV = PHI * (FF(4) + GF(4)) + FOUR * PHI1 * (FF(3) + GF(3)) - * + SIX * PHI2 * (FF(2) + GF(2)) + FOUR * PHI3 * (FF(1) + GF(1)) - * + PHI4 * FUNCN - RETURN - END - SUBROUTINE ASSIGN (U, BP, FF) - implicit none -C -C ALGORITHM AS 251.3 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C COMPUTE DERIVATIVES OF NORMAL CDF'S. -C - DOUBLE PRECISION FF(4) - DOUBLE PRECISION U, U2, BP, HALF, ONE, THREE, SQ2PI, T1, T2, T3 - $ ,ZERO, UMAX, SMALL - INTEGER I - DATA HALF, ONE, THREE, SQ2PI /0.5, 1.0, 3.0, 2.50662827463100/ - DATA ZERO, UMAX, SMALL /0.0, 8.0, 0.1E-07/ - IF (ABS(U) .GT. UMAX) THEN - DO 10 I = 1, 4 - FF(I) = ZERO - 10 CONTINUE - ELSE - U2 = U * U - T1 = BP * EXP(-HALF * U2) / SQ2PI - T2 = BP * T1 - T3 = BP * T2 - FF(1) = T1 - FF(2) = -U * T2 - FF(3) = (U2 - ONE) * T3 - FF(4) = (THREE - U2) * U * BP * T3 - DO 20 I = 1, 4 - IF(ABS(FF(I)) .LT. SMALL) FF(I) = ZERO - 20 CONTINUE - END IF - RETURN - END - SUBROUTINE WMAX(W1, W2, W3, DLG) - implicit none -C -C ALGORITHM AS 251.4 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C LARGEST ABSOLUTE VALUE OF QUADRATIC FUNCTION FITTED -C TO THREE POINTS. -C - DOUBLE PRECISION W1, W2, W3, DLG, QUAD, QLIM, QMIN, ONE, TWO, B2C - DATA ONE, TWO, QMIN /1.0, 2.0, 0.00001/ - DLG = MAX( ABS(W1), ABS(W3) ) - QUAD = W1 - W2 * TWO + W3 - QLIM = MAX( ABS(W1 - W3) / TWO , QMIN) - IF (ABS(QUAD) .LE. QLIM) RETURN - B2C = (W1 - W3) / QUAD / TWO - IF (ABS(B2C) .GE. ONE) RETURN - DLG = MAX( DLG, ABS(W2 - B2C * QUAD * B2C / TWO) ) - RETURN - END - SUBROUTINE TOOSML (N, FF, F) - implicit none -C -C ALGORITHM AS 251.5 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C MULTIPLY FF(I) BY F FOR I = N TO 4. SET TO ZERO IF TOO SMALL. -C - DOUBLE PRECISION FF(4), F, ZERO, SMALL - INTEGER N, I - DATA ZERO, SMALL /0.0, 0.1E-12/ - DO 10 I = N, 4 - FF(I) = FF(I) * F - IF (ABS(FF(I)) .LE. SMALL) FF(I) = ZERO - 10 CONTINUE - RETURN - END - DOUBLE PRECISION FUNCTION ALNORM(X, UPPER) - implicit none -C -C ALGORITHM AS 66 APPL. STATIST. (1973) VOL.22, P.424 -C -C EVALUATES THE TAIL AREA OF THE STANDARDIZED NORMAL CURVE -C FROM X TO INFINITY IF UPPER IS .TRUE. OR -C FROM MINUS INFINITY TO X IF UPPER IS .FALSE. -C - DOUBLE PRECISION LTONE, UTZERO, ZERO, HALF, ONE, CON, A1, A2, A3, - $ A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, B8, B9, - $ B10, B11, B12, X, Y, Z, ZEXP - LOGICAL UPPER, UP -C -C LTONE AND UTZERO MUST BE SET TO SUIT THE PARTICULAR COMPUTER -C (SEE INTRODUCTORY TEXT) -C - DATA LTONE, UTZERO /7.0, 18.66/ - DATA ZERO, HALF, ONE, CON /0.0, 0.5, 1.0, 1.28/ - DATA A1, A2, A3, - $ A4, A5, A6, - $ A7 - $ /0.398942280444, 0.399903438504, 5.75885480458, - $ 29.8213557808, 2.62433121679, 48.6959930692, - $ 5.92885724438/ - DATA B1, B2, B3, - $ B4, B5, B6, - $ B7, B8, B9, - $ B10, B11, B12 - $ /0.398942280385, 3.8052E-8, 1.00000615302, - $ 3.98064794E-4, 1.98615381364, 0.151679116635, - $ 5.29330324926, 4.8385912808, 15.1508972451, - $ 0.742380924027, 30.789933034, 3.99019417011/ -C - ZEXP(Z) = EXP(Z) -C - UP = UPPER - Z = X - IF (Z .GE. ZERO) GOTO 10 - UP = .NOT. UP - Z = -Z - 10 IF (Z .LE. LTONE .OR. UP .AND. Z .LE. UTZERO) GOTO 20 - ALNORM = ZERO - GOTO 40 - 20 Y = HALF * Z * Z - IF (Z .GT. CON) GOTO 30 -C - ALNORM = HALF - Z * (A1 - A2 * Y / (Y + A3 - A4 / (Y + A5 + - $ A6 / (Y + A7)))) - GOTO 40 -C - 30 ALNORM = B1 * ZEXP(-Y) / (Z - B2 + B3 / (Z + B4 + B5 / (Z - - $ B6 + B7 / (Z + B8 - B9 / (Z + B10 + B11 / (Z + B12)))))) -C - 40 IF (.NOT. UP) ALNORM = ONE - ALNORM - RETURN - END - DOUBLE PRECISION FUNCTION PPND7 (P, IFAULT) - implicit none -C -C ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3 -C -C PRODUCES THE NORMAL DEVIATE Z CORRESPONDING TO A GIVEN LOWER -C TAIL AREA OF P; Z IS ACCURATE TO ABOUT 1 PART IN 10**7. -C -C THE HASH SUMS BELOW ARE THE SUMS OF THE MANTISSAS OF THE -C COEFFICIENTS. THEY ARE INCLUDED FOR USE IN CHECKING -C TRANSCRIPTION. -C - INTEGER IFAULT - DOUBLE PRECISION ZERO, ONE, HALF, SPLIT1, SPLIT2, CONST1, CONST2, - * A0, A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, D1, D2, - * E0, E1, E2, E3, F1, F2, P, Q, R - PARAMETER (ZERO = 0.0E0, ONE = 1.0E0, HALF = 0.5E0, - * SPLIT1 = 0.425E0, SPLIT2 = 5.0E0, - * CONST1 = 0.180625E0, CONST2 = 1.6E0) -C -C COEFFICIENTS FOR P CLOSE TO 1/2 - PARAMETER (A0 = 3.3871327179D0, - * A1 = 5.0434271938D1, - * A2 = 1.5929113202D2, - * A3 = 5.9109374720D1, - * B1 = 1.7895169469D1, - * B2 = 7.8757757664D1, - * B3 = 6.7187563600D1) -C HASH SUM AB 32.3184577772 -C -C COEFFICIENTS FOR P NEITHER CLOSE TO 1/2 NOR 0 OR 1 - PARAMETER (C0 = 1.4234372777D0, - * C1 = 2.7568153900D0, - * C2 = 1.3067284816D0, - * C3 = 1.7023821103D-1, - * D1 = 7.3700164250D-1, - * D2 = 1.2021132975D-1) -C HASH SUM CD 15.7614929821 -C -C COEFFICIENTS FOR P NEAR 0 OR 1 - PARAMETER (E0 = 6.6579051150E0, - * E1 = 3.0812263860E0, - * E2 = 4.2868294337E-1, - * E3 = 1.7337203997E-2, - * F1 = 2.4197894225E-1, - * F2 = 1.2258202635E-2) -C HASH SUM EF 19.4052910204 -C - IFAULT = 0 - Q = P - HALF - IF (ABS(Q) .LE. SPLIT1) THEN - R = CONST1 - Q * Q - PPND7 = Q * (((A3 * R + A2) * R + A1) * R + A0) / - * (((B3 * R + B2) * R + B1) * R + ONE) - RETURN - ELSE - IF (Q .LT. 0) THEN - R = P - ELSE - R = ONE - P - ENDIF - IF (R .LE. ZERO) THEN - IFAULT = 1 - PPND7 = ZERO - RETURN - ENDIF - R = SQRT(-LOG(R)) - IF (R .LE. SPLIT2) THEN - R = R - CONST2 - PPND7 = (((C3 * R + C2) * R + C1) * R + C0) / - * ((D2 * R + D1) * R + ONE) - ELSE - R = R - SPLIT2 - PPND7 = (((E3 * R + E2) * R + E1) * R + E0) / - * ((F2 * R + F1) * R + ONE) - ENDIF - IF (Q .LT. 0) PPND7 = -PPND7 - RETURN - ENDIF - END - SUBROUTINE MVSTUD(NDF,A,B,BPD,ERRB,N,INF,D,IERC,HNC,PROB, - * BND,IFLT) - implicit none -C -C COMPUTE MULTIVARIATE STUDENT INTEGRAL, -C USING MVNPRD (DUNNETT, APPL. STAT., 1989) -C IF RHO(I,J) = BPD(I)*BPD(J). -C -C IF RHO(I,J) HAS GENERAL STRUCTURE, USE -C MULNOR (SCHERVISH, APPL. STAT., 1984) AND REPLACE -C CALL MVNPRD(A,B,BPD,EPS,N,INF,IERC,HNC,PROB,BND,IFLT) -C BY CALL MULNOR(A,B,SIG,EPS,N,INF,PROB,BND,IFLT). -C -C AUTHOR: C.W. DUNNETT, MCMASTER UNVERSITY -C -C BASED ON ADAPTIVE SIMPSON'S RULE ALGORITHM -C DESCRIBED IN SHAMPINE & ALLEN: "NUMERICAL -C COMPUTING", (1974), PAGE 240. -C -C PARAMETERS ARE SAME AS IN ALGORITHM AS 251 -C IN APPL. STAT. (1989), VOL. 38: 564-579 -C WITH THE FOLLOWING ADDITIONS: -C NDF INTEGER INPUT DEGREES OF FREEDOM -C D REAL ARRAY INPUT NON-CENTRALITY VECTOR -C (PUT NDF = 0 FOR INFINITE D.F.) -C - DOUBLE PRECISION :: HNC,PROB,BND - INTEGER :: NN, MAXDF,I,IERC,NDF,N,IFLT - PARAMETER (NN=100, MAXDF = 150) - integer :: INF(*) - DOUBLE PRECISION :: A(*),B(*),BPD(*),D(*),F(3), - & AA(NN),BB(NN) - DOUBLE PRECISION :: ERB2, ERRB, AX,BX,XX - DOUBLE PRECISION,SAVE :: ZERO,HALF,TWO,THREE,FOUR - INTEGER :: NF - !DIMENSION A(*),B(*),BPD(*),INF(*),D(*),F(3),AA(NN),BB(NN) - DATA ZERO,HALF,TWO,THREE,FOUR / 0.0, 0.5, 2.0, 3.0, 4.0 / - !external float - DO 10 I = 1, N - AA(I) = A(I) - D(I) - BB(I) = B(I) - D(I) - 10 CONTINUE - IF (NDF .LE. 0) THEN - CALL MVNPRD(AA,BB,BPD,ERRB,N,INF,IERC,HNC,PROB,BND,IFLT) - RETURN - ENDIF - BND = ZERO - IFLT = 0 - - ERB2 = ERRB -C -C CHECK IF D.F. EXCEED MAXDF; IF YES, THEN PROB -C IS COMPUTED BY QUADRATIC INTERPOLATION ON 1./D.F. -C - IF (NDF .LE. MAXDF) GO TO 20 - CALL MVNPRD(AA,BB,BPD,ERB2,N,INF,IERC,HNC,F(1),BND,IFLT) - NF = MAXDF / 2 - CALL SIMPSN(NF,A,B,BPD,ERB2,N,INF,D,IERC,HNC,F(3),BND,IFLT) - NF = NF * 2 - CALL SIMPSN(NF,A,B,BPD,ERB2,N,INF,D,IERC,HNC,F(2),BND,IFLT) - XX = DBLE(NF) / DBLE(NDF) - AX = F(3) - F(2)*TWO + F(1) - BX = F(2)*FOUR - F(3) - F(1)*THREE - PROB = F(1) + XX * (AX * XX + BX) * HALF - RETURN - 20 CALL SIMPSN (NDF,A,B,BPD,ERB2,N,INF,D,IERC,HNC,PROB,BND,IFLT) - RETURN - END - SUBROUTINE SIMPSN (NDF,A,B,BPD,ERRB,N,INF,D,IERC,HNC,PROB, - * BND,IFLT) - implicit none -C -C STUDENTIZES A MULTIVARIATE INTEGRAL USING SIMPSON'S RULE. -C - double precision :: A,B,BPD,D, - * FV,F1T,F2T,F3T, - * LDIR,PSUM,ESTT,ERRR,GV,G1T,G2T, - * G3T,GSUM - double precision :: PROB, BOUNDA, BOUNDG,sTART, DAX, ERB2,ERRB, - $ EPS1, F0,G0, HNC, ERROR,DA,Z3,WT, CONTRG,DX,Z2,Z4,ESTL,ESTR, - $ ESTGL,ESTGR,CONTRB,TSUM,SUMG,DLG,ERRL,EXCESS,BND - double precision :: ZERO,HALF,ONE,ONEP5,TWO,FOUR,SIX,DXMIN - INTEGER :: IFLAG, IER, NDF,N, INF, IERC,LVL,IFLT - DIMENSION A(*),B(*),BPD(*),INF(*),D(*), - * FV(5),F1T(30),F2T(30),F3T(30), - * LDIR(30),PSUM(30),ESTT(30),ERRR(30),GV(5),G1T(30),G2T(30), - * G3T(30),GSUM(30) - DATA ZERO,HALF,ONE,ONEP5,TWO,FOUR,SIX,DXMIN /0.0,0.5,1.0,1.5, - * 2.0,4.0,6.0,0.000004/ - PROB = ZERO - BOUNDA = ZERO - BOUNDG = ZERO - IFLAG = 0 - IER = 0 - START = -ONE - DAX = ONE - ERB2 = ERRB * HALF - EPS1 = ERB2 * HALF - CALL FUN (ZERO,NDF,A,B,BPD,ERB2,N,INF,D,F0,G0,IERC,HNC,IER) - 10 FV(1) = ZERO - GV(1) = ZERO - ERROR = ZERO - DA = DAX - LVL = 1 - Z3 = START + HALF*DA - CALL FUN(Z3,NDF,A,B,BPD,ERB2,N,INF,D,FV(3),GV(3),IERC,HNC,IER) - FV(5) = F0 - GV(5) = G0 - WT = ABS(DA) / SIX - CONTRB = WT * (FV(1) + FOUR * FV(3) + FV(5)) - CONTRG = WT * (GV(1) + FOUR * GV(3) + GV(5)) - LDIR(LVL) = 2 - PSUM(LVL) = ZERO - GSUM(LVL) = ZERO -C -C BISECT INTERVAL; COMPUTE ESTIMATES FOR EACH HALF. -C - 20 DX = HALF * DA - WT = ABS(DX) / SIX - Z2 = START + HALF * DX - CALL FUN(Z2,NDF,A,B,BPD,ERB2,N,INF,D,FV(2),GV(2),IERC,HNC,IER) - Z4 = START + ONEP5 * DX - CALL FUN(Z4,NDF,A,B,BPD,ERB2,N,INF,D,FV(4),GV(4),IERC,HNC,IER) - ESTL = WT * (FV(1) + FOUR * FV(2) + FV(3)) - ESTR = WT * (FV(3) + FOUR * FV(4) + FV(5)) - ESTGL = WT * (GV(1) + FOUR * GV(2) + GV(3)) - ESTGR = WT * (GV(3) + FOUR * GV(4) + GV(5)) - TSUM = ESTL + ESTR - SUMG = ESTGL + ESTGR - DLG = ABS(CONTRB - TSUM) - ERRL = DLG -C -C STOP BISECTING WHEN ACCURACY SUFFICIENT, OR IF -C INTERVAL TOO NARROW OR BISECTED TOO OFTEN. -C - 30 IF (DLG .LE. EPS1) GO TO 50 - IF (ABS(DX) .LE. DXMIN .OR. LVL .GE. 30) GO TO 40 -C -C RAISE LEVEL. STORE INFORMATION FOR RIGHT HALF -C AND APPLY SIMPSON'S RULE TO LEFT HALF. -C - LVL = LVL + 1 - LDIR(LVL) = 1 - F1T(LVL) = FV(3) - F2T(LVL) = FV(4) - F3T(LVL) = FV(5) - G1T(LVL) = GV(3) - G2T(LVL) = GV(4) - G3T(LVL) = GV(5) - DA = DX - FV(5) = FV(3) - FV(3) = FV(2) - GV(5) = GV(3) - GV(3) = GV(2) - ESTT(LVL) = ESTR - CONTRB = ESTL - CONTRG = ESTGL - EPS1 = EPS1 * HALF - ERRR(LVL) = EPS1 - GO TO 20 -C -C ACCEPT APPROXIMATE VALUE FOR INTERVAL. -C - 40 IFLAG = 11 - 50 ERROR = ERROR + ERRL - 60 IF (LDIR(LVL) .EQ. 1) GO TO 70 - TSUM = TSUM + PSUM(LVL) - SUMG = SUMG + GSUM(LVL) - LVL = LVL - 1 - IF (LVL .GT. 0) GO TO 60 - CONTRB = TSUM - CONTRG = SUMG - LVL = 1 - DLG = ERROR - GO TO 80 -C -C RESTORE SAVED INFORMATION TO PROCESS RIGHT HALF. -C - 70 PSUM(LVL) = TSUM - GSUM(LVL) = SUMG - LDIR(LVL) = 2 - DA = DAX / TWO**(LVL-1) - START = START + DX * TWO - FV(1) = F1T(LVL) - FV(3) = F2T(LVL) - FV(5) = F3T(LVL) - GV(1) = G1T(LVL) - GV(3) = G2T(LVL) - GV(5) = G3T(LVL) - CONTRB = ESTT(LVL) - EXCESS = EPS1 - DLG - EPS1 = ERRR(LVL) - IF (EXCESS .GT. ZERO) EPS1 = EPS1 + EXCESS - GO TO 20 - 80 PROB = PROB + CONTRB - BOUNDG = BOUNDG + CONTRG - BOUNDA = BOUNDA + DLG - IF (Z4 .LE. ZERO) GO TO 90 - IF (IFLT .EQ. 0) IFLT = IER - IF (IFLT .EQ. 0) IFLT = IFLAG - BOUNDA = BOUNDA + BOUNDG - IF (BND .LT. BOUNDA) BND = BOUNDA - RETURN - 90 EPS1 = ERB2 * HALF - EXCESS = EPS1 - BND - IF (EXCESS .GT. ZERO) EPS1 = EPS1 + EXCESS - START = ONE - DAX = -ONE - GO TO 10 - END - DOUBLE PRECISION FUNCTION SDIST(Y,N) - implicit none -C -C COMPUTE Y**(N/2 - 1) EXP(-Y) / GAMMA(N/2) -C -C (Revised: 1994-01-19) -C - DOUBLE PRECISION :: Y,XN,TEST, ZERO, HALF, ONE, X23,SQRTPI - INTEGER :: N,JJ,JK,JKP,J - DATA ZERO, HALF, ONE, X23 / 0.0, 0.5, 1.0, -23.0 / - DATA SQRTPI / 1.77245385090552 / - SDIST = ZERO - IF (Y .LE. ZERO) RETURN - JJ = N/2 - 1 - JK = 2 * JJ - N + 2 - JKP = JJ - JK - SDIST = ONE - IF (JK .LT. 0) SDIST = SDIST / SQRT(Y) / SQRTPI - IF (JKP .EQ. 0) GO TO 20 - XN = DBLE(N) * HALF - TEST = LOG(Y) - Y / DBLE(JKP) - IF ( TEST .LT. X23 ) THEN - SDIST = ZERO - RETURN - ENDIF - SDIST = LOG ( SDIST ) - DO 10 J = 1, JKP - XN = XN - ONE - SDIST = SDIST + TEST - LOG(XN) - 10 CONTINUE - IF ( SDIST .LT. X23 ) THEN - SDIST = ZERO - ELSE - SDIST = EXP( SDIST ) - ENDIF - RETURN - 20 SDIST = SDIST * EXP(-Y) - RETURN - END - SUBROUTINE FUN (Z,NDF,H,HL,BPD,ERB2,N,INF,D,F0,G0,IERC - * ,HNC,IER) - implicit none - double precision :: ZERO, ONE, TWO, SMALL, Z, arg, term , f0, g0 - $ ,df,ERB2,HNC,BND,PROB - INTEGER NN,NDF,N, I, IER,IERC,IFLT - PARAMETER (NN=100) - DOUBLE precision :: A,B,H,HL,BPD,D, SDIST - integer :: INF - DIMENSION A(NN),B(NN),H(*),HL(*),BPD(*),INF(*),D(*) - DATA ZERO, ONE, TWO, SMALL / 0.0, 1.0, 2.0, 1.0E-08 / - external SDIST - F0 = ZERO - G0 = ZERO - IF (Z .LE. -ONE .OR. Z .GE. ONE) RETURN - DF = DBLE(NDF) - ARG = (ONE + Z) / (ONE - Z) - TERM = ARG * DF * TWO / (ONE-Z)**2 * SDIST(DF/TWO*ARG*ARG,NDF) - IF (TERM .LE. SMALL) RETURN - DO 10 I = 1, N - A(I) = ARG * H(I) - D(I) - B(I) = ARG * HL(I) - D(I) - 10 CONTINUE - CALL MVNPRD (A,B,BPD,ERB2,N,INF,IERC,HNC,PROB,BND,IFLT) - IF (IER .EQ. 0) IER = IFLT - G0 = TERM * BND - F0 = TERM * PROB - RETURN - END - -C * * * * * * * * * * * * * * * * * * * * * * * * * * * * -C Charles Dunnett -C Dept. of Mathematics and Statistics -C McMaster University -C Hamilton, Ontario L8S 4K1 -C Canada -C E-mail: dunnett@mcmaster.ca -C Tel.: (905) 525-9140 (Ext. 27104) -C * * * * * * * * * * * * * * * * * * * * * * * * * * * * - - diff --git a/wafo/source/mvnprd/mvnprd.pyf b/wafo/source/mvnprd/mvnprd.pyf deleted file mode 100644 index 2398238..0000000 --- a/wafo/source/mvnprd/mvnprd.pyf +++ /dev/null @@ -1,23 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - -python module mvnprd ! in - interface ! in :mvnprd - subroutine mvnprd(a,b,bpd,eps,n,inf,ierc,hinc,prob,bound,ifault) ! in :mvnprd:mvnprd.f - double precision dimension(*) :: a - double precision dimension(*) :: b - double precision dimension(*) :: bpd - double precision :: eps - integer :: n - integer dimension(*) :: inf - integer :: ierc - double precision :: hinc - double precision :: prob - double precision :: bound - integer :: ifault - end subroutine mvnprd - end interface -end python module mvnprd - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/mvnprd/mvnprd_interface.f b/wafo/source/mvnprd/mvnprd_interface.f deleted file mode 100644 index ab89396..0000000 --- a/wafo/source/mvnprd/mvnprd_interface.f +++ /dev/null @@ -1,88 +0,0 @@ - - subroutine prbnormtndpc(rho,a,b,NDF,N,abseps,IERC,HNC,PRB,BOUND, - * IFAULT) - double precision A(N),B(N),rho(N),D(N) - integer INFIN(N) - integer NDF,N,IERC - integer IFAULT - double precision HNC -C double precision EPS - double precision PRB, BOUND - double precision, parameter :: infinity = 37.0d0 -Cf2py integer, intent(hide), depend(rho) :: N = len(rho) -Cf2py depend(N) a -Cf2py depend(N) b -Cf2py integer, optional :: NDF = 0 -Cf2py double precision, optional :: abseps = 0.001 -Cf2py double precision, optional :: HNC = 0.24 -Cf2py integer, optional :: IERC =0 -Cf2py double precision, intent(out) :: PRB -Cf2py double precision, intent(out) :: BOUND -Cf2py integer, intent(out) :: IFAULT - -CCf2py intent(in) N,IERC -CCf2py intent(in) HINC,EPS -CCf2py intent(in) INF -CCf2py intent(in) A,B,rho - - - -* Set INFIN INTEGER, array of integration limits flags: -* if INFIN(I) < 0, Ith limits are (-infinity, infinity); -* if INFIN(I) = 0, Ith limits are [LOWER(I), infinity); -* if INFIN(I) = 1, Ith limits are (-infinity, UPPER(I)]; -* if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)]. - Ndim = 0 - DO K = 1,N - Ndim = Ndim + 1 - INFIN(Ndim) = 2 - D(k) = 0.0 - if (A(K)-D(K).LE.-INFINITY) THEN - if (B(K)-D(K) .GE. INFINITY) THEN - Ndim = Ndim - 1 - !INFIN(K) = -1 - else - INFIN(Ndim) = 1 - endif - else if (B(K)-D(K).GE.INFINITY) THEN - INFIN(Ndim) = 0 - endif - if (ndim EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* -* MVNPRODCORRPRB calculates multivariate normal probability -* with product correlation structure for rectangular regions. -* The accuracy is up to almost double precision, i.e., about 1e-14. -* -* This file was successfully compiled for matlab 5.3 -* using Compaq Visual Fortran 6.1, and Windows 2000. -* The example here uses Fortran77 source. -* First, you will need to modify your mexopts.bat file. -* To find it, issue the command prefdir(1) from the Matlab command line, -* the directory it answers with will contain your mexopts.bat file. -* Open it for editing. The first section will look like: -* -*rem ******************************************************************** -*rem General parameters -*rem ******************************************************************** -*set MATLAB=%MATLAB% -*set DF_ROOT=C:\Program Files\Microsoft Visual Studio -*set VCDir=%DF_ROOT%\VC98 -*set MSDevDir=%DF_ROOT%\Common\msdev98 -*set DFDir=%DF_ROOT%\DF98 -*set PATH=%MSDevDir%\bin;%DFDir%\BIN;%VCDir%\BIN;%PATH% -*set INCLUDE=%DFDir%\INCLUDE;%DFDir%\IMSL\INCLUDE;%INCLUDE% -*set LIB=%DFDir%\LIB;%VCDir%\LIB -* -* then you are ready to compile this file at the matlab prompt using the -* following command: -* mex -O mvnprodcorrprbmex.f - MODULE ERFCOREMOD - IMPLICIT NONE - - INTERFACE CALERF - MODULE PROCEDURE CALERF - END INTERFACE - - INTERFACE DERF - MODULE PROCEDURE DERF - END INTERFACE - - INTERFACE DERFC - MODULE PROCEDURE DERFC - END INTERFACE - - INTERFACE DERFCX - MODULE PROCEDURE DERFCX - END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C Revised pab Dec 2008 -C updated parameter statements in CALERF so that it works when -C compiling with gfortran. -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- -C DOUBLE PRECISION, DIMENSION(5) :: A, Q -C DOUBLE PRECISION, DIMENSION(4) :: B -C DOUBLE PRECISION, DIMENSION(9) :: C -C DOUBLE PRECISION, DIMENSION(8) :: D -C DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER, DIMENSION(5) :: - & A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/) - DOUBLE PRECISION, PARAMETER, DIMENSION(4) :: - & B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - DOUBLE PRECISION, DIMENSION(9) :: - & C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/) - DOUBLE PRECISION, DIMENSION(8) :: - & D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - DOUBLE PRECISION, parameter, - & DIMENSION(6) :: P =(/3.05326634961232344D-1, - & 3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/) - DOUBLE PRECISION, parameter, - & DIMENSION(5) :: Q =(/2.56852019228982242D00, - & 1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/) -C------------------------------------------------------------------ - - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD - module functionInterface - INTERFACE - FUNCTION F(Z) result (VAL) - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - END FUNCTION F - END INTERFACE - end module functionInterface - module AdaptiveGaussKronrod - implicit none - private - public :: dqagpe,dqagp - - INTERFACE dqagpe - MODULE PROCEDURE dqagpe - END INTERFACE - - INTERFACE dqagp - MODULE PROCEDURE dqagp - END INTERFACE - - INTERFACE dqelg - MODULE PROCEDURE dqelg - END INTERFACE - - INTERFACE dqpsrt - MODULE PROCEDURE dqpsrt - END INTERFACE - - INTERFACE dqk21 - MODULE PROCEDURE dqk21 - END INTERFACE - - INTERFACE dqk15 - MODULE PROCEDURE dqk15 - END INTERFACE - - INTERFACE dqk9 - MODULE PROCEDURE dqk9 - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - - contains - subroutine dea3(E0,E1,E2,abserr,result) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result = E2 - abserr = err1 + err2 + E2*small*ten - else - result = E1 + one/ss - abserr = err1 + err2 + abs(result-E2) - endif - endif - end subroutine dea3 - subroutine dqagp(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier) -! use functionInterface - implicit none - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result1,abserr - integer, intent(out) :: neval,ier - double precision :: f -!Locals - double precision,dimension(limit) :: alist, blist, rlist, elist - double precision,dimension(npts+2) :: pts - integer, dimension(limit) :: iord, level - integer, dimension(npts+2) :: ndin - integer ::last - external f - CALL dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin - $ ,last) - end subroutine dqagp - subroutine dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin, - * last) -! use functionInterface - implicit none -c***begin prologue dqagpe -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a2a1 -c***keywords automatic integrator, general-purpose, -! singularities at user specified points, -! extrapolation, globally adaptive. -c***author piessens,robert ,appl. math. & progr. div. - k.u.leuven -! de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose the routine calculates an approximation result to a given -! definite integral i = integral of f over (a,b), hopefully -! satisfying following claim for accuracy abs(i-result).le. -! max(epsabs,epsrel*abs(i)). break points of the integration -! interval, where local difficulties of the integrand may -! occur(e.g. singularities,discontinuities),provided by user. -c***description -! -! computation of a definite integral -! standard fortran subroutine -! double precision version -! -! parameters -! on entry -! f - double precision -! function subprogram defining the integrand -! function f(x). the actual name for f needs to be -! declared e x t e r n a l in the driver program. -! -! a - double precision -! lower limit of integration -! -! b - double precision -! upper limit of integration -! -! npts2 - integer -! number equal to two more than the number of -! user-supplied break points within the integration -! range, npts2.ge.2. -! if npts2.lt.2, the routine will end with ier = 6. -! -! points - double precision -! vector of dimension npts2, the first (npts2-2) -! elements of which are the user provided break -! points. if these points do not constitute an -! ascending sequence there will be an automati! -! sorting. -! -! epsabs - double precision -! absolute accuracy requested -! epsrel - double precision -! relative accuracy requested -! if epsabs.le.0 -! and epsrel.lt.max(50*rel.mach.acc.,0.5d-28), -! the routine will end with ier = 6. -! -! limit - integer -! gives an upper bound on the number of subintervals -! in the partition of (a,b), limit.ge.npts2 -! if limit.lt.npts2, the routine will end with -! ier = 6. -! -! on return -! result - double precision -! approximation to the integral -! -! abserr - double precision -! estimate of the modulus of the absolute error, -! which should equal or exceed abs(i-result) -! -! neval - integer -! number of integrand evaluations -! -! ier - integer -! ier = 0 normal and reliable termination of the -! routine. it is assumed that the requested -! accuracy has been achieved. -! ier.gt.0 abnormal termination of the routine. -! the estimates for integral and error are -! less reliable. it is assumed that the -! requested accuracy has not been achieved. -! error messages -! ier = 1 maximum number of subdivisions allowed -! has been achieved. one can allow more -! subdivisions by increasing the value of -! limit (and taking the according dimension -! adjustments into account). however, if -! this yields no improvement it is advised -! to analyze the integrand in order to -! determine the integration difficulties. if -! the position of a local difficulty can be -! determined (i.e. singularity, -! discontinuity within the interval), it -! should be supplied to the routine as an -! element of the vector points. if necessary -! an appropriate special-purpose integrator -! must be used, which is designed for -! handling the type of difficulty involved. -! = 2 the occurrence of roundoff error is -! detected, which prevents the requested -! tolerance from being achieved. -! the error may be under-estimated. -! = 3 extremely bad integrand behaviour occurs -! at some points of the integration -! interval. -! = 4 the algorithm does not converge. -! roundoff error is detected in the -! extrapolation table. it is presumed that -! the requested tolerance cannot be -! achieved, and that the returned result is -! the best which can be obtained. -! = 5 the integral is probably divergent, or -! slowly convergent. it must be noted that -! divergence can occur with any other value -! of ier.gt.0. -! = 6 the input is invalid because -! npts2.lt.2 or -! break points are specified outside -! the integration range or -! (epsabs.le.0 and -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) -! or limit.lt.npts2. -! result, abserr, neval, last, rlist(1), -! and elist(1) are set to zero. alist(1) and -! blist(1) are set to a and b respectively. -! -! alist - double precision -! vector of dimension at least limit, the first -! last elements of which are the left end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! blist - double precision -! vector of dimension at least limit, the first -! last elements of which are the right end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! rlist - double precision -! vector of dimension at least limit, the first -! last elements of which are the integral -! approximations on the subintervals -! -! elist - double precision -! vector of dimension at least limit, the first -! last elements of which are the moduli of the -! absolute error estimates on the subintervals -! -! pts - double precision -! vector of dimension at least npts2, containing the -! integration limits and the break points of the -! interval in ascending sequence. -! -! level - integer -! vector of dimension at least limit, containing the -! subdivision levels of the subinterval, i.e. if -! (aa,bb) is a subinterval of (p1,p2) where p1 as -! well as p2 is a user-provided break point or -! integration limit, then (aa,bb) has level l if -! abs(bb-aa) = abs(p2-p1)*2**(-l). -! -! ndin - integer -! vector of dimension at least npts2, after first -! integration over the intervals (pts(i)),pts(i+1), -! i = 0,1, ..., npts2-2, the error estimates over -! some of the intervals may have been increased -! artificially, in order to put their subdivision -! forward. if this happens for the subinterval -! numbered k, ndin(k) is put to 1, otherwise -! ndin(k) = 0. -! -! iord - integer -! vector of dimension at least limit, the first k -! elements of which are pointers to the -! error estimates over the subintervals, -! such that elist(iord(1)), ..., elist(iord(k)) -! form a decreasing sequence, with k = last -! if last.le.(limit/2+2), and k = limit+1-last -! otherwise -! -! last - integer -! number of subintervals actually produced in the -! subdivisions process -! -c***references (none) -c***routines called d1mach,dqelg,dqk21,dqpsrt -c***end prologue dqagpe - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result,abserr - integer, intent(out) :: neval,ier - double precision,dimension(limit), intent(out) :: alist, blist - double precision,dimension(limit), intent(out) :: rlist, elist - double precision,dimension(npts+2),intent(out) :: pts - integer, dimension(limit), intent(out) :: iord, level - integer, dimension(npts+2), intent(out) :: ndin - integer ::last - double precision :: f -! locals - double precision :: area,area1,area12,area2,a1, - * a2,b1,b2,correc,abseps,defabs,defab1,defab2, - * dres,epmach,erlarg,erlast,errbnd, - * errmax,error1,erro12,error2,errsum,ertest,oflow, - * resa,resabs,reseps,sign,temp,uflow, hSplit - double precision, dimension(3) :: res3la(3) - double precision, dimension(52) :: rlist2(52) - integer :: i,id,ierro,ind1,ind2,ip1,iroff1,iroff2,iroff3,j, - * jlow,jupbnd,k,ksgn,ktmin,levcur,levmax,maxerr, - * nint,nintp1,npts2,nres,nrmax,numrl2 - logical :: extrap,noext - external f -! -! - -! -! -! the dimension of rlist2 is determined by the value of -! limexp in subroutine epsalg (rlist2 should be of dimension -! (limexp+2) at least). -! -! -! list of major variables -! ----------------------- -! -! alist - list of left end points of all subintervals -! considered up to now -! blist - list of right end points of all subintervals -! considered up to now -! rlist(i) - approximation to the integral over -! (alist(i),blist(i)) -! rlist2 - array of dimension at least limexp+2 -! containing the part of the epsilon table which -! is still needed for further computations -! elist(i) - error estimate applying to rlist(i) -! maxerr - pointer to the interval with largest error -! estimate -! errmax - elist(maxerr) -! erlast - error on the interval currently subdivided -! (before that subdivision has taken place) -! area - sum of the integrals over the subintervals -! errsum - sum of the errors over the subintervals -! errbnd - requested accuracy max(epsabs,epsrel* -! abs(result)) -! *****1 - variable for the left subinterval -! *****2 - variable for the right subinterval -! last - index for subdivision -! nres - number of calls to the extrapolation routine -! numrl2 - number of elements in rlist2. if an appropriate -! approximation to the compounded integral has -! been obtained, it is put in rlist2(numrl2) after -! numrl2 has been increased by one. -! erlarg - sum of the errors over the intervals larger -! than the smallest interval considered up to now -! extrap - logical variable denoting that the routine -! is attempting to perform extrapolation. i.e. -! before subdividing the smallest interval we -! try to decrease the value of erlarg. -! noext - logical variable denoting that extrapolation is -! no longer allowed (true-value) -! -! machine dependent constants -! --------------------------- -! -! epmach is the largest relative spacing. -! uflow is the smallest positive magnitude. -! oflow is the largest positive magnitude. -! -c***first executable statement dqagpe - epmach = d1mach(4) - uflow = d1mach(1) - oflow = d1mach(2) -! -! test on validity of parameters -! ----------------------------- -! - hSplit = 0.2D0 - ier = 0 - neval = 0 - last = 0 - result = 0.0d+00 - abserr = 0.0d+00 - alist(1) = a - blist(1) = b - rlist(1) = 0.0d+00 - elist(1) = 0.0d+00 - iord(1) = 0 - level(1) = 0 - npts2 = npts+2 - if((npts2.lt.2).or.(limit.le.npts).or. - & ((epsabs.le.0.0d+00).and. - & (epsrel.lt.dmax1(0.5d+02*epmach,0.5d-28)))) then - ier = 6 - go to 999 - endif - - sign = 1.0d+00 - if(a.gt.b) then - go to 999 - endif - if (npts>0) then - if(any(points(1:npts)<=a).or.any(b<=points(1:npts))) then - ier = 6 - go to 999 - endif - endif -! -! if any break points are provided, sort them into an -! ascending sequence. -! - pts(1) = a - pts(npts+2) = b - do i = 1,npts - pts(i+1) = minval(points(i:npts)) - enddo -! -! compute first integral and error approximations. -! ------------------------------------------------ -! - nint = npts+1; - a1 = pts(1); - resabs = 0.0d+00 - do i = 1,nint - b1 = pts(i+1) - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,defabs,resa) - !call dqk15(f,a1,b1,area1,error1,defabs,resa) - else - call dqkl9(f,a1,b1,area1,error1,defabs,resa) - endif - abserr = abserr + error1 - result = result + area1 - ndin(i) = 0 - if(error1.eq.resa.and.error1.ne.0.0d+00) ndin(i) = 1 - resabs = resabs + defabs - level(i) = 0 - elist(i) = error1 - alist(i) = a1 - blist(i) = b1 - rlist(i) = area1 - iord(i) = i - a1 = b1 - enddo !50 continue - errsum = 0.0d+00 - do i = 1,nint - if(ndin(i).eq.1) elist(i) = abserr - errsum = errsum+elist(i) - enddo !55 continue -! -! test on accuracy. -! - last = nint - neval = 21*nint - dres = dabs(result) - errbnd = dmax1(epsabs,epsrel*dres) - if(abserr.le.0.1d+03*epmach*resabs.and.abserr.gt.errbnd) ier = 2 - if(nint.eq.1) go to 80 - do 70 i = 1,npts - jlow = i+1 - ind1 = iord(i) - do 60 j = jlow,nint - ind2 = iord(j) - if(elist(ind1).gt.elist(ind2)) go to 60 - ind1 = ind2 - k = j - 60 continue - if(ind1.eq.iord(i)) go to 70 - iord(k) = iord(i) - iord(i) = ind1 - 70 continue - if(limit.lt.npts2) ier = 1 - 80 if(ier.ne.0.or.abserr.le.errbnd) go to 210 - -! -! initialization -! -------------- -! - rlist2(1) = result - maxerr = iord(1) - errmax = elist(maxerr) - area = result - nrmax = 1 - nres = 0 - numrl2 = 1 - ktmin = 0 - extrap = .false. - noext = .false. - erlarg = errsum - ertest = errbnd - levmax = 1 - iroff1 = 0 - iroff2 = 0 - iroff3 = 0 - ierro = 0 - abserr = oflow - ksgn = -1 - if(dres.ge.(0.1d+01-0.5d+02*epmach)*resabs) ksgn = 1 -! -! main do-loop -! ------------ -! - do 160 last = npts2,limit -! -! bisect the subinterval with the nrmax-th largest error -! estimate. -! - levcur = level(maxerr)+1 - a1 = alist(maxerr) - b1 = 0.5d+00*(alist(maxerr)+blist(maxerr)) - a2 = b1 - b2 = blist(maxerr) - erlast = errmax - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,resa,defab1) - call dqk21(f,a2,b2,area2,error2,resa,defab2) - !call dqk15(f,a1,b1,area1,error1,resa,defab1) - !call dqk15(f,a2,b2,area2,error2,resa,defab2) - else - - call dqkl9(f,a1,b1,area1,error1,resa,defab1) - call dqkl9(f,a2,b2,area2,error2,resa,defab2) - endif -! -! improve previous approximations to integral -! and error and test for accuracy. -! - neval = neval+42 - area12 = area1+area2 - erro12 = error1+error2 - errsum = errsum+erro12-errmax - area = area+area12-rlist(maxerr) - if(defab1.eq.error1.or.defab2.eq.error2) go to 95 - if(dabs(rlist(maxerr)-area12).gt.0.1d-04*dabs(area12) - * .or.erro12.lt.0.99d+00*errmax) go to 90 - if(extrap) iroff2 = iroff2+1 - if(.not.extrap) iroff1 = iroff1+1 - 90 if(last.gt.10.and.erro12.gt.errmax) iroff3 = iroff3+1 - 95 level(maxerr) = levcur - level(last) = levcur - rlist(maxerr) = area1 - rlist(last) = area2 - errbnd = dmax1(epsabs,epsrel*dabs(area)) -! -! test for roundoff error and eventually set error flag. -! - if(iroff1+iroff2.ge.10.or.iroff3.ge.20) ier = 2 - if(iroff2.ge.5) ierro = 3 -! -! set error flag in the case that the number of -! subintervals equals limit. -! - if(last.eq.limit) ier = 1 -! -! set error flag in the case of bad integrand behaviour -! at a point of the integration range -! - if(dmax1(dabs(a1),dabs(b2)).le.(0.1d+01+0.1d+03*epmach)* - * (dabs(a2)+0.1d+04*uflow)) ier = 4 -! -! append the newly-created intervals to the list. -! - if(error2.gt.error1) go to 100 - alist(last) = a2 - blist(maxerr) = b1 - blist(last) = b2 - elist(maxerr) = error1 - elist(last) = error2 - go to 110 - 100 alist(maxerr) = a2 - alist(last) = a1 - blist(last) = b1 - rlist(maxerr) = area2 - rlist(last) = area1 - elist(maxerr) = error2 - elist(last) = error1 -! -! call subroutine dqpsrt to maintain the descending ordering -! in the list of error estimates and select the subinterval -! with nrmax-th largest error estimate (to be bisected next). -! - 110 call dqpsrt(limit,last,maxerr,errmax,elist,iord,nrmax) -! ***jump out of do-loop - if(errsum.le.errbnd) go to 190 -! ***jump out of do-loop - if(ier.ne.0) go to 170 - if(noext) go to 160 - erlarg = erlarg-erlast - if(levcur+1.le.levmax) erlarg = erlarg+erro12 - if(extrap) go to 120 -! -! test whether the interval to be bisected next is the -! smallest interval. -! - if(level(maxerr)+1.le.levmax) go to 160 - extrap = .true. - nrmax = 2 - 120 if(ierro.eq.3.or.erlarg.le.ertest) go to 140 -! -! the smallest interval has the largest error. -! before bisecting decrease the sum of the errors over -! the larger intervals (erlarg) and perform extrapolation. -! - id = nrmax - jupbnd = last - if(last.gt.(2+limit/2)) jupbnd = limit+3-last - do 130 k = id,jupbnd - maxerr = iord(nrmax) - errmax = elist(maxerr) -! ***jump out of do-loop - if(level(maxerr)+1.le.levmax) go to 160 - nrmax = nrmax+1 - 130 continue -! -! perform extrapolation. -! - 140 numrl2 = numrl2+1 - rlist2(numrl2) = area - if(numrl2.le.2) go to 155 - call dqelg(numrl2,rlist2,reseps,abseps,res3la,nres) - ktmin = ktmin+1 - if(ktmin.gt.5.and.abserr.lt.0.1d-02*errsum) ier = 5 - if(abseps.ge.abserr) go to 150 - ktmin = 0 - abserr = abseps - result = reseps - correc = erlarg - ertest = dmax1(epsabs,epsrel*dabs(reseps)) -! ***jump out of do-loop - if(abserr.lt.ertest) go to 170 -! -! prepare bisection of the smallest interval. -! - 150 if(numrl2.eq.1) noext = .true. - if(ier.ge.5) go to 170 - 155 maxerr = iord(1) - errmax = elist(maxerr) - nrmax = 1 - extrap = .false. - levmax = levmax + 1 - erlarg = errsum - 160 continue -! -! set the final result. -! --------------------- -! -! - 170 if(abserr.eq.oflow) go to 190 - if((ier+ierro).eq.0) go to 180 - if(ierro.eq.3) abserr = abserr+correc - if(ier.eq.0) ier = 3 - if(result.ne.0.0d+00.and.area.ne.0.0d+00)go to 175 - if(abserr.gt.errsum)go to 190 - if(area.eq.0.0d+00) go to 210 - go to 180 - 175 if(abserr/dabs(result).gt.errsum/dabs(area))go to 190 -! -! test on divergence. -! - 180 if(ksgn.eq.(-1).and.dmax1(dabs(result),dabs(area)).le. - * resabs*0.1d-01) go to 210 - if(0.1d-01.gt.(result/area).or.(result/area).gt.0.1d+03.or. - * errsum.gt.dabs(area)) ier = 6 - go to 210 -! -! compute global integral sum. -! - 190 result = 0.0d+00 - do 200 k = 1,last - result = result+rlist(k) - 200 continue - abserr = errsum - 210 if(ier.gt.2) ier = ier-1 - result = result*sign - 999 return - end subroutine dqagpe - subroutine dqk21(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk21 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 21-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk21 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk,reskh,result,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(10),fv2(10),wg(5),wgk(11),xgk(11) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 21-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 10-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 10-point gauss rule -c -c wgk - weights of the 21-point kronrod rule -c -c wg - weights of the 10-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.0666713443 0868813759 3568809893 332 d0 / - data wg ( 2) / 0.1494513491 5058059314 5776339657 697 d0 / - data wg ( 3) / 0.2190863625 1598204399 5534934228 163 d0 / - data wg ( 4) / 0.2692667193 0999635509 1226921569 469 d0 / - data wg ( 5) / 0.2955242247 1475287017 3892994651 338 d0 / -c - data xgk ( 1) / 0.9956571630 2580808073 5527280689 003 d0 / - data xgk ( 2) / 0.9739065285 1717172007 7964012084 452 d0 / - data xgk ( 3) / 0.9301574913 5570822600 1207180059 508 d0 / - data xgk ( 4) / 0.8650633666 8898451073 2096688423 493 d0 / - data xgk ( 5) / 0.7808177265 8641689706 3717578345 042 d0 / - data xgk ( 6) / 0.6794095682 9902440623 4327365114 874 d0 / - data xgk ( 7) / 0.5627571346 6860468333 9000099272 694 d0 / - data xgk ( 8) / 0.4333953941 2924719079 9265943165 784 d0 / - data xgk ( 9) / 0.2943928627 0146019813 1126603103 866 d0 / - data xgk ( 10) / 0.1488743389 8163121088 4826001129 720 d0 / - data xgk ( 11) / 0.0000000000 0000000000 0000000000 000 d0 / -c - data wgk ( 1) / 0.0116946388 6737187427 8064396062 192 d0 / - data wgk ( 2) / 0.0325581623 0796472747 8818972459 390 d0 / - data wgk ( 3) / 0.0547558965 7435199603 1381300244 580 d0 / - data wgk ( 4) / 0.0750396748 1091995276 7043140916 190 d0 / - data wgk ( 5) / 0.0931254545 8369760553 5065465083 366 d0 / - data wgk ( 6) / 0.1093871588 0229764189 9210590325 805 d0 / - data wgk ( 7) / 0.1234919762 6206585107 7958109831 074 d0 / - data wgk ( 8) / 0.1347092173 1147332592 8054001771 707 d0 / - data wgk ( 9) / 0.1427759385 7706008079 7094273138 717 d0 / - data wgk ( 10) / 0.1477391049 0133849137 4841515972 068 d0 / - data wgk ( 11) / 0.1494455540 0291690566 4936468389 821 d0 / -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk21 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 21-point kronrod approximation to -c the integral, and estimate the absolute error. -c - resg = 0.0d+00 - fc = f(centr) - resk = wgk(11)*fc - resabs = dabs(resk) - do 10 j=1,5 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,5 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(11)*dabs(fc-reskh) - do 20 j=1,10 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0d0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk21 - subroutine dqk15(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk,reskh,result,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 7-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point gauss rule -c -c wgk - weights of the 15-point kronrod rule -c -c wg - weights of the 7-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.129484966168869693270611432679082d0 / - data wg ( 2) / 0.279705391489276667901467771423780d0 / - data wg ( 3) / 0.381830050505118944950369775488975d0 / - data wg ( 4) / 0.417959183673469387755102040816327d0 / - - data xgk ( 1) / 0.991455371120812639206854697526329d0 / - data xgk ( 2) / 0.949107912342758524526189684047851d0 / - data xgk ( 3) / 0.864864423359769072789712788640926d0 / - data xgk ( 4) / 0.741531185599394439863864773280788d0 / - data xgk ( 5) / 0.586087235467691130294144838258730d0 / - data xgk ( 6) / 0.405845151377397166906606412076961d0 / - data xgk ( 7) / 0.207784955007898467600689403773245d0 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.022935322010529224963732008058970d0/ - data wgk ( 2) / 0.063092092629978553290700663189204d0 / - data wgk ( 3) / 0.104790010322250183839876322541518d0 / - data wgk ( 4) / 0.140653259715525918745189590510238d0 / - data wgk ( 5) / 0.169004726639267902826583426598550d0 / - data wgk ( 6) / 0.190350578064785409913256402421014d0 / - data wgk ( 7) / 0.204432940075298892414161999234649d0 / - data wgk ( 8) / 0.209482141084727828012999174891714d0 / - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resg = wg(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0D0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk15 - subroutine dqk9(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk0,resk,reskh,result,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -! xgk(4), xgk(8) abscissae of the 3-point gauss rule -c xgk(2), xgk(4),xgk(6), xgk(8) ... abscissae of the 7-point -c kronrod rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point kronrod rule -c -c wgk - weights of the 15-point kronrod rule -! -! wgk0 - weights of the 7-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - data wg ( 1) / 0.5555555555555555D+00/ - data wg ( 2) / 0.8888888888888889D+00/ - - data wgk0 ( 1) / 0.1046562260264673D+00/ - data wgk0 ( 2) / 0.2684880898683335D+00/ - data wgk0 ( 3) / 0.4013974147759622D+00/ - data wgk0 ( 4) / 0.4509165386584741D+00/ - - data xgk ( 1) / 0.9938319632127550D+00/ - data xgk ( 2) / 0.9604912687080203D+00/ - data xgk ( 3) / 0.8884592328722570D+00 / - data xgk ( 4) / 0.7745966692414834D+00/ - data xgk ( 5) / 0.6211029467372264D+00/ - data xgk ( 6) / 0.4342437493468026D+00/ - data xgk ( 7) / 0.2233866864289669D+00 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.1700171962994028D-01/ - data wgk ( 2) / 0.5160328299707982D-01/ - data wgk ( 3) / 0.9292719531512452D-01/ - data wgk ( 4) / 0.1344152552437843D+00/ - data wgk ( 5) / 0.1715119091363914D+00/ - data wgk ( 6) / 0.2006285293769890D+00/ - data wgk ( 7) / 0.2191568584015875D+00/ - data wgk ( 8) / 0.2255104997982067D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resk0 = wgk0(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(4) + fv2(4)) - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result = resk - call dea3(resg,resk0,resk,abserr,result) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0)) - & * 10.0D0, abserr) - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - - end subroutine dqk9 - subroutine dqkl9(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk0,resk,reskh,result,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(3),wgk(5),xgk(5) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 9-point Gauss-kronrod-lobatto rule -! xgk(1), xgk(5) abscissae of the 3-point gauss-lobatto rule -c xgk(1), xgk(3),xgk(5) abscissae of the 5-point -c kronrod rule -c xgk(2), xgk(4), ... abscissae which are optimally -c added to the 5-point kronrod rule -c -c wgk - weights of the 9-point kronrod rule -! -! wgk0 - weights of the 5-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - - data wg ( 1) / 0.33333333333333333333333333333333333D+00/ - data wg ( 2) / 0.13333333333333333333333333333333333D+01/ - - data wgk0 ( 1) / 0.1000000000000000D+00/ - data wgk0 ( 2) / 0.5444444444444445D+00/ - data wgk0 ( 3) / 0.7111111111111111D+00/ - - data xgk ( 1) / 0.1000000000000000D+01/ - data xgk ( 2) / 0.8904055275126688D+00/ - data xgk ( 3) / 0.6546536707079772D+00/ - data xgk ( 4) / 0.3409822659109930D+00/ - data xgk ( 5) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.3064373897707232D-01/ - data wgk ( 2) / 0.1792626995532074D+00/ - data wgk ( 3) / 0.2839787780481211D+00/ - data wgk ( 4) / 0.3342337398164177D+00/ - data wgk ( 5) / 0.3437620872103631D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(5)*fc - resk0 = wgk0(3)*fc - resabs = dabs(resk) - do 10 j=1,2 - jtw = 2*j - 1 - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(1) + fv2(1)) - do 15 j = 1,2 - jtwm1 = 2*j - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(5)*dabs(fc-reskh) - do 20 j=1,4 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result = resk - call dea3(resg,resk0,resk,abserr,result) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0))* 10.0D0,abserr) - - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqkl9 - subroutine dqpsrt(limit,last,maxerr,ermax,elist,iord,nrmax) - implicit none -c***begin prologue dqpsrt -c***refer to dqage,dqagie,dqagpe,dqawse -c***routines called (none) -c***revision date 810101 (yymmdd) -c***keywords sequential sorting -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose this routine maintains the descending ordering in the -c list of the local error estimated resulting from the -c interval subdivision process. at each call two error -c estimates are inserted using the sequential search -c method, top-down for the largest error estimate and -c bottom-up for the smallest error estimate. -c***description -c -c ordering routine -c standard fortran subroutine -c double precision version -c -c parameters (meaning at output) -c limit - integer -c maximum number of error estimates the list -c can contain -c -c last - integer -c number of error estimates currently in the list -c -c maxerr - integer -c maxerr points to the nrmax-th largest error -c estimate currently in the list -c -c ermax - double precision -c nrmax-th largest error estimate -c ermax = elist(maxerr) -c -c elist - double precision -c vector of dimension last containing -c the error estimates -c -c iord - integer -c vector of dimension last, the first k elements -c of which contain pointers to the error -c estimates, such that -c elist(iord(1)),..., elist(iord(k)) -c form a decreasing sequence, with -c k = last if last.le.(limit/2+2), and -c k = limit+1-last otherwise -c -c nrmax - integer -c maxerr = iord(nrmax) -c -c***end prologue dqpsrt -c - double precision elist,ermax,errmax,errmin - integer i,ibeg,ido,iord,isucc,j,jbnd,jupbn,k,last,limit,maxerr, - * nrmax - dimension elist(last),iord(last) -c -c check whether the list contains more than -c two error estimates. -c -c***first executable statement dqpsrt - if(last.gt.2) go to 10 - iord(1) = 1 - iord(2) = 2 - go to 90 -c -c this part of the routine is only executed if, due to a -c difficult integrand, subdivision increased the error -c estimate. in the normal case the insert procedure should -c start after the nrmax-th largest error estimate. -c - 10 errmax = elist(maxerr) - if(nrmax.eq.1) go to 30 - ido = nrmax-1 - do 20 i = 1,ido - isucc = iord(nrmax-1) -c ***jump out of do-loop - if(errmax.le.elist(isucc)) go to 30 - iord(nrmax) = isucc - nrmax = nrmax-1 - 20 continue -c -c compute the number of elements in the list to be maintained -c in descending order. this number depends on the number of -c subdivisions still allowed. -c - 30 jupbn = last - if(last.gt.(limit/2+2)) jupbn = limit+3-last - errmin = elist(last) -c -c insert errmax by traversing the list top-down, -c starting comparison from the element elist(iord(nrmax+1)). -c - jbnd = jupbn-1 - ibeg = nrmax+1 - if(ibeg.gt.jbnd) go to 50 - do 40 i=ibeg,jbnd - isucc = iord(i) -c ***jump out of do-loop - if(errmax.ge.elist(isucc)) go to 60 - iord(i-1) = isucc - 40 continue - 50 iord(jbnd) = maxerr - iord(jupbn) = last - go to 90 -c -c insert errmin by traversing the list bottom-up. -c - 60 iord(i-1) = maxerr - k = jbnd - do 70 j=i,jbnd - isucc = iord(k) -c ***jump out of do-loop - if(errmin.lt.elist(isucc)) go to 80 - iord(k+1) = isucc - k = k-1 - 70 continue - iord(i) = last - go to 90 - 80 iord(k+1) = last -c -c set maxerr and ermax. -c - 90 maxerr = iord(nrmax) - ermax = elist(maxerr) - return - end subroutine dqpsrt - subroutine dqelg(n,epstab,result,abserr,res3la,nres) - implicit none -c***begin prologue dqelg -c***refer to dqagie,dqagoe,dqagpe,dqagse -c***routines called d1mach -c***revision date 830518 (yymmdd) -c***keywords epsilon algorithm, convergence acceleration, -c extrapolation -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math & progr. div. - k.u.leuven -c***purpose the routine determines the limit of a given sequence of -c approximations, by means of the epsilon algorithm of -c p.wynn. an estimate of the absolute error is also given. -c the condensed epsilon table is computed. only those -c elements needed for the computation of the next diagonal -c are preserved. -c***description -c -c epsilon algorithm -c standard fortran subroutine -c double precision version -c -c parameters -c n - integer -c epstab(n) contains the new element in the -c first column of the epsilon table. -c -c epstab - double precision -c vector of dimension 52 containing the elements -c of the two lower diagonals of the triangular -c epsilon table. the elements are numbered -c starting at the right-hand corner of the -c triangle. -c -c result - double precision -c resulting approximation to the integral -c -c abserr - double precision -c estimate of the absolute error computed from -c result and the 3 previous results -c -c res3la - double precision -c vector of dimension 3 containing the last 3 -c results -c -c nres - integer -c number of calls to the routine -c (should be zero at first call) -c -c***end prologue dqelg -c - double precision abserr,dabs,delta1,delta2,delta3,dmax1, - * epmach,epsinf,epstab,error,err1,err2,err3,e0,e1,e1abs,e2,e3, - * oflow,res,result,res3la,ss,tol1,tol2,tol3 - integer i,ib,ib2,ie,indx,k1,k2,k3,limexp,n,newelm,nres,num - dimension epstab(52),res3la(3) -c -c list of major variables -c ----------------------- -c -c e0 - the 4 elements on which the computation of a new -c e1 element in the epsilon table is based -c e2 -c e3 e0 -c e3 e1 new -c e2 -c newelm - number of elements to be computed in the new -c diagonal -c error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2) -c result - the element in the new diagonal with least value -c of error -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c oflow is the largest positive magnitude. -c limexp is the maximum number of elements the epsilon -c table can contain. if this number is reached, the upper -c diagonal of the epsilon table is deleted. -c -c***first executable statement dqelg - epmach = d1mach(4) - oflow = d1mach(2) - nres = nres+1 - abserr = oflow - result = epstab(n) - if(n.lt.3) go to 100 - limexp = 50 - epstab(n+2) = epstab(n) - newelm = (n-1)/2 - epstab(n) = oflow - num = n - k1 = n - do 40 i = 1,newelm - k2 = k1-1 - k3 = k1-2 - res = epstab(k1+2) - e0 = epstab(k3) - e1 = epstab(k2) - e2 = res - e1abs = dabs(e1) - delta2 = e2-e1 - err2 = dabs(delta2) - tol2 = dmax1(dabs(e2),e1abs)*epmach - delta3 = e1-e0 - err3 = dabs(delta3) - tol3 = dmax1(e1abs,dabs(e0))*epmach - if(err2.gt.tol2.or.err3.gt.tol3) go to 10 -c -c if e0, e1 and e2 are equal to within machine -c accuracy, convergence is assumed. -c result = e2 -c abserr = abs(e1-e0)+abs(e2-e1) -c - result = res - abserr = err2+err3 -c ***jump out of do-loop - go to 100 - 10 e3 = epstab(k1) - epstab(k1) = e1 - delta1 = e1-e3 - err1 = dabs(delta1) - tol1 = dmax1(e1abs,dabs(e3))*epmach -c -c if two elements are very close to each other, omit -c a part of the table by adjusting the value of n -c - if(err1.le.tol1.or.err2.le.tol2.or.err3.le.tol3) go to 20 - ss = 0.1d+01/delta1+0.1d+01/delta2-0.1d+01/delta3 - epsinf = dabs(ss*e1) -c -c test to detect irregular behaviour in the table, and -c eventually omit a part of the table adjusting the value -c of n. -c - if(epsinf.gt.0.1d-03) go to 30 - 20 n = i+i-1 -c ***jump out of do-loop - go to 50 -c -c compute a new element and eventually adjust -c the value of result. -c - 30 res = e1+0.1d+01/ss - epstab(k1) = res - k1 = k1-2 - error = err2+dabs(res-e2)+err3 - if(error.gt.abserr) go to 40 - abserr = error - result = res - 40 continue -c -c shift the table. -c - 50 if(n.eq.limexp) n = 2*(limexp/2)-1 - ib = 1 - if((num/2)*2.eq.num) ib = 2 - ie = newelm+1 - do 60 i=1,ie - ib2 = ib+2 - epstab(ib) = epstab(ib2) - ib = ib2 - 60 continue - if(num.eq.n) go to 80 - indx = num-n+1 - do 70 i = 1,n - epstab(i)= epstab(indx) - indx = indx+1 - 70 continue - 80 if(nres.ge.4) go to 90 - res3la(nres) = result - abserr = oflow - go to 100 -c -c compute error estimate -c - 90 abserr = dabs(result-res3la(3))+dabs(result-res3la(2)) - * +dabs(result-res3la(1)) - res3la(1) = res3la(2) - res3la(2) = res3la(3) - res3la(3) = result - 100 abserr = dmax1(abserr,0.5d+01*epmach*dabs(result)) - return - end subroutine dqelg - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - end module AdaptiveGaussKronrod - - module Integration1DModule - implicit none - interface AdaptiveSimpson - module procedure AdaptiveSimpson2, AdaptiveSimpsonWithBreaks - end interface - -! interface AdaptiveSimpson1 -! module procedure AdaptiveSimpson1 -! end interface - - interface AdaptiveTrapz - module procedure AdaptiveTrapz1, AdaptiveTrapzWithBreaks - end interface - - interface Romberg - module procedure Romberg1, RombergWithBreaks - end interface - - INTERFACE DEA - MODULE PROCEDURE DEA - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - contains - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - subroutine dea3(E0,E1,E2,abserr,result) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result = E2 - abserr = err1 + err2 + E2*small*ten - else - result = E1 + one/ss - abserr = err1 + err2 + abs(result-E2) - endif - endif - end subroutine dea3 - SUBROUTINE DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -C***BEGIN PROLOGUE DEA -C***DATE WRITTEN 800101 (YYMMDD) -C***REVISION DATE 871208 (YYMMDD) -C***CATEGORY NO. E5 -C***KEYWORDS CONVERGENCE ACCELERATION,EPSILON ALGORITHM,EXTRAPOLATION -C***AUTHOR PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. - -C K. U. LEUVEN -C DE DONCKER-KAPENGA, ELISE,WESTERN MICHIGAN UNIVERSITY -C KAHANER, DAVID K., NATIONAL BUREAU OF STANDARDS -C STARKENBURG, C. B., NATIONAL BUREAU OF STANDARDS -C***PURPOSE Given a slowly convergent sequence, this routine attempts -C to extrapolate nonlinearly to a better estimate of the -C sequence's limiting value, thus improving the rate of -C convergence. Routine is based on the epsilon algorithm -C of P. Wynn. An estimate of the absolute error is also -C given. -C***DESCRIPTION -C -C Epsilon algorithm. Standard fortran subroutine. -C Double precision version. -C -C A R G U M E N T S I N T H E C A L L S E Q U E N C E -C -C NEWFLG - LOGICAL (INPUT and OUTPUT) -C On the first call to DEA set NEWFLG to .TRUE. -C (indicating a new sequence). DEA will set NEWFLG -C to .FALSE. -C -C SVALUE - DOUBLE PRECISION (INPUT) -C On the first call to DEA set SVALUE to the first -C term in the sequence. On subsequent calls set -C SVALUE to the subsequent sequence value. -C -C LIMEXP - INTEGER (INPUT) -C An integer equal to or greater than the total -C number of sequence terms to be evaluated. Do not -C change the value of LIMEXP until a new sequence -C is evaluated (NEWFLG=.TRUE.). LIMEXP .GE. 3 -C -C RESULT - DOUBLE PRECISION (OUTPUT) -C Best approximation to the sequence's limit. -C -C ABSERR - DOUBLE PRECISION (OUTPUT) -C Estimate of the absolute error. -C -C EPSTAB - DOUBLE PRECISION (OUTPUT) -C Workvector of DIMENSION at least (LIMEXP+7). -C -C IERR - INTEGER (OUTPUT) -C IERR=0 Normal termination of the routine. -C IERR=1 The input is invalid because LIMEXP.LT.3. -C -C T Y P I C A L P R O B L E M S E T U P -C -C This sample problem uses the trapezoidal rule to evaluate the -C integral of the sin function from 0.0 to 0.5*PI (value = 1.0). The -C program implements the trapezoidal rule 8 times creating an -C increasingly accurate sequence of approximations to the integral. -C Each time the trapezoidal rule is used, it uses twice as many -C panels as the time before. DEA is called to obtain even more -C accurate estimates. -C -C PROGRAM SAMPLE -C IMPLICIT DOUBLE PRECISION (A-H,O-Z) -C DOUBLE PRECISION EPSTAB(57) -CC [57 = LIMEXP + 7] -C LOGICAL NEWFLG -C EXTERNAL F -C DATA LIMEXP/50/ -C WRITE(*,*) ' NO. PANELS TRAP. APPROX' -C * ,' APPROX W/EA ABSERR' -C WRITE(*,*) -C HALFPI = DASIN(1.0D+00) -CC [UPPER INTEGRATION LIMIT = PI/2] -C NEWFLG = .TRUE. -CC [SET FLAG - 1ST DEA CALL] -C DO 10 I = 0,7 -C NPARTS = 2 ** I -C WIDTH = HALFPI/NPARTS -C APPROX = 0.5D+00 * WIDTH * (F(0.0D+00) + F(HALFPI)) -C DO 11 J = 1,NPARTS-1 -C APPROX = APPROX + F(J * WIDTH) * WIDTH -C 11 CONTINUE -CC [END TRAPEZOIDAL RULE APPROX] -C SVALUE = APPROX -CC [SVALUE = NEW SEQUENCE VALUE] -C CALL DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -CC [CALL DEA FOR BETTER ESTIMATE] -C WRITE(*,12) NPARTS,APPROX,RESULT,ABSERR -C 12 FORMAT(' ',I4,T20,F16.13,T40,F16.13,T60,D11.4) -C 10 CONTINUE -C STOP -C END -C -C DOUBLE PRECISION FUNCTION F(X) -C DOUBLE PRECISION X -C F = DSIN(X) -CC [INTEGRAND] -C RETURN -C END -C -C Output from the above program will be: -C -C NO. PANELS TRAP. APPROX APPROX W/EA ABSERR -C -C 1 .7853981633974 .7853981633974 .7854D+00 -C 2 .9480594489685 .9480594489685 .9760D+00 -C 4 .9871158009728 .9994567212570 .2141D+00 -C 8 .9967851718862 .9999667417647 .3060D-02 -C 16 .9991966804851 .9999998781041 .6094D-03 -C 32 .9997991943200 .9999999981026 .5767D-03 -C 64 .9999498000921 .9999999999982 .3338D-04 -C 128 .9999874501175 1.0000000000000 .1238D-06 -C -C----------------------------------------------------------------------- -C***REFERENCES "Acceleration de la convergence en analyse numerique", -C C. Brezinski, "Lecture Notes in Math.", vol. 584, -C Springer-Verlag, New York, 1977. -C***ROUTINES CALLED D1MACH,XERROR -C***END PROLOGUE DEA - double precision, dimension(*), intent(inout) :: EPSTAB - double precision, intent(out) :: RESULT !, ABSERR - double precision, intent(inout) :: ABSERR - double precision, intent(in) :: SVALUE - INTEGER, INTENT(IN) :: LIMEXP - INTEGER, INTENT(OUT) :: IERR - LOGICAL, intent(INOUT) :: NEWFLG - DOUBLE PRECISION :: DELTA1,DELTA2,DELTA3,DRELPR,DEPRN, - 1 ERROR,ERR1,ERR2,ERR3,E0,E1,E2,E3,RES, - 2 SS,TOL1,TOL2,TOL3 - double precision, dimension(3) :: RES3LA - INTEGER I,IB,IB2,IE,IN,K1,K2,K3,N,NEWELM,NUM,NRES -C -C -C LIMEXP is the maximum number of elements the -C epsilon table data can contain. The epsilon table -C is stored in the first (LIMEXP+2) entries of EPSTAB. -C -C -C LIST OF MAJOR VARIABLES -C ----------------------- -C E0,E1,E2,E3 - DOUBLE PRECISION -C The 4 elements on which the computation of -C a new element in the epsilon table is based. -C NRES - INTEGER -C Number of extrapolation results actually -C generated by the epsilon algorithm in prior -C calls to the routine. -C NEWELM - INTEGER -C Number of elements to be computed in the -C new diagonal of the epsilon table. The -C condensed epsilon table is computed. Only -C those elements needed for the computation of -C the next diagonal are preserved. -C RES - DOUBLE PRECISION -C New element in the new diagonal of the -C epsilon table. -C ERROR - DOUBLE PRECISION -C An estimate of the absolute error of RES. -C Routine decides whether RESULT=RES or -C RESULT=SVALUE by comparing ERROR with -C ABSERR from the previous call. -C RES3LA - DOUBLE PRECISION -C Vector of DIMENSION 3 containing at most -C the last 3 results. -C -C -C MACHINE DEPENDENT CONSTANTS -C --------------------------- -C DRELPR is the largest relative spacing. -C -C***FIRST EXECUTABLE STATEMENT DEA - IF(LIMEXP.LT.3) THEN - IERR = 1 -! CALL XERROR('LIMEXP IS LESS THAN 3',21,1,1) - GO TO 110 - ENDIF - IERR = 0 - RES3LA(1)=EPSTAB(LIMEXP+5) - RES3LA(2)=EPSTAB(LIMEXP+6) - RES3LA(3)=EPSTAB(LIMEXP+7) - RESULT=SVALUE - IF(NEWFLG) THEN - N=1 - NRES=0 - NEWFLG=.FALSE. - EPSTAB(N)=SVALUE - ABSERR=ABS(RESULT) - GO TO 100 - ELSE - N=INT(EPSTAB(LIMEXP+3)) - NRES=INT(EPSTAB(LIMEXP+4)) - IF(N.EQ.2) THEN - EPSTAB(N)=SVALUE - ABSERR=.6D+01*ABS(RESULT-EPSTAB(1)) - GO TO 100 - ENDIF - ENDIF - EPSTAB(N)=SVALUE - DRELPR=D1MACH(4) - DEPRN=1.0D+01*DRELPR - EPSTAB(N+2)=EPSTAB(N) - NEWELM=(N-1)/2 - NUM=N - K1=N - DO 40 I=1,NEWELM - K2=K1-1 - K3=K1-2 - RES=EPSTAB(K1+2) - E0=EPSTAB(K3) - E1=EPSTAB(K2) - E2=RES - DELTA2=E2-E1 - ERR2=ABS(DELTA2) - TOL2=MAX(ABS(E2),ABS(E1))*DRELPR - DELTA3=E1-E0 - ERR3=ABS(DELTA3) - TOL3=MAX(ABS(E1),ABS(E0))*DRELPR - IF(ERR2.GT.TOL2.OR.ERR3.GT.TOL3) GO TO 10 -C -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. -C RESULT=E2 -C ABSERR=ABS(E1-E0)+ABS(E2-E1) -C - RESULT=RES - ABSERR=ERR2+ERR3 - GO TO 50 - 10 IF(I.NE.1) THEN - E3=EPSTAB(K1) - EPSTAB(K1)=E1 - DELTA1=E1-E3 - ERR1=ABS(DELTA1) - TOL1=MAX(ABS(E1),ABS(E3))*DRELPR -C -C IF TWO ELEMENTS ARE VERY CLOSE TO EACH OTHER, OMIT -C A PART OF THE TABLE BY ADJUSTING THE VALUE OF N -C - IF(ERR1.LE.TOL1.OR.ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA1+0.1D+01/DELTA2-0.1D+01/DELTA3 - ELSE - EPSTAB(K1)=E1 - IF(ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA2-0.1D+01/DELTA3 - ENDIF -C -C TEST TO DETECT IRREGULAR BEHAVIOUR IN THE TABLE, AND -C EVENTUALLY OMIT A PART OF THE TABLE ADJUSTING THE VALUE -C OF N -C - IF(ABS(SS*E1).GT.0.1D-03) GO TO 30 - 20 N=I+I-1 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ERR3 - RESULT=RES - ELSE IF(NRES.EQ.1) THEN - RESULT=RES3LA(1) - ELSE IF(NRES.EQ.2) THEN - RESULT=RES3LA(2) - ELSE - RESULT=RES3LA(3) - ENDIF - GO TO 50 -C -C COMPUTE A NEW ELEMENT AND EVENTUALLY ADJUST -C THE VALUE OF RESULT -C - 30 RES=E1+0.1D+01/SS - EPSTAB(K1)=RES - K1=K1-2 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ABS(RES-E2)+ERR3 - RESULT=RES - GO TO 40 - ELSE IF(NRES.EQ.1) THEN - ERROR=.6D+01*(ABS(RES-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ERROR=.2D+01*(ABS(RES-RES3LA(2))+ABS(RES-RES3LA(1))) - ELSE - ERROR=ABS(RES-RES3LA(3))+ABS(RES-RES3LA(2)) - 1 +ABS(RES-RES3LA(1)) - ENDIF - IF(ERROR.GT.1.0D+01*ABSERR) GO TO 40 - ABSERR=ERROR - RESULT=RES - 40 CONTINUE -C -C COMPUTE ERROR ESTIMATE -C - IF(NRES.EQ.1) THEN - ABSERR=.6D+01*(ABS(RESULT-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ABSERR=.2D+01*ABS(RESULT-RES3LA(2))+ABS(RESULT-RES3LA(1)) - ELSE IF(NRES.GT.2) THEN - ABSERR=ABS(RESULT-RES3LA(3))+ABS(RESULT-RES3LA(2)) - 1 +ABS(RESULT-RES3LA(1)) - ENDIF -C -C SHIFT THE TABLE -C - 50 IF(N.EQ.LIMEXP) N=2*(LIMEXP/2)-1 - IB=1 - IF((NUM/2)*2.EQ.NUM) IB=2 - IE=NEWELM+1 - DO 60 I=1,IE - IB2=IB+2 - EPSTAB(IB)=EPSTAB(IB2) - IB=IB2 - 60 CONTINUE - IF(NUM.EQ.N) GO TO 80 - IN=NUM-N+1 - DO 70 I=1,N - EPSTAB(I)=EPSTAB(IN) - IN=IN+1 - 70 CONTINUE -C -C UPDATE RES3LA -C - 80 IF(NRES.EQ.0) THEN - RES3LA(1)=RESULT - ELSE IF(NRES.EQ.1) THEN - RES3LA(2)=RESULT - ELSE IF(NRES.EQ.2) THEN - RES3LA(3)=RESULT - ELSE - RES3LA(1)=RES3LA(2) - RES3LA(2)=RES3LA(3) - RES3LA(3)=RESULT - ENDIF - 90 ABSERR=MAX(ABSERR,DEPRN*ABS(RESULT)) - NRES=NRES+1 - 100 N=N+1 - EPSTAB(LIMEXP+3)=DBLE(N) - EPSTAB(LIMEXP+4)=DBLE(NRES) - EPSTAB(LIMEXP+5)=RES3LA(1) - EPSTAB(LIMEXP+6)=RES3LA(2) - EPSTAB(LIMEXP+7)=RES3LA(3) - 110 RETURN - END subroutine DEA - - subroutine AdaptiveIntWithBreaks(f,a,b,N,brks,epsi,iflg - $ ,abserr, val) - use AdaptiveGaussKronrod - implicit none - double precision :: f - integer, intent(in) :: N - double precision, intent(in) :: a,b,epsi - double precision, dimension(:), intent(in) :: brks - double precision, intent(out) :: abserr, val - integer, intent(out) :: iflg - external f -! Locals - double precision, dimension(N+2) :: pts - double precision :: LTol,tol, error, valk, excess, errorEstimate - double precision :: delta, deltaK - integer :: kflg, k, limit,neval - limit = 30 - pts(1) = a - pts(N+2) = b - delta = b - a - do k = 2,N+1 - pts(k) = minval(brks(k-1:N)) !add user supplied break points - enddo - LTol = epsi / delta - abserr = 0.0d0 - val = 0.0D0 - iflg = 0 - do k = 1, N + 1 - deltaK = pts(k+1) - pts(k) - tol = LTol * deltaK - if (deltaK < 0.5D0) then - call AdaptiveSimpson(f,pts(k),pts(k+1),tol, kflg,error,valk) -! call romberg(f,pts(k),pts(k+1),20,tol,kflg,error, valk) - else -! call AdaptiveSimpson3(f,pts(k),pts(k+1),tol,kflg,error,valk) - call dqagp(f,pts(k),pts(k+1),0,pts,tol,0.0D0,limit,valk, - * error,neval,kflg) - - endif - abserr = abserr + abs(error) - - errorEstimate = abserr + (b - pts(k+1)) * LTol - excess = epsi - errorEstimate - if (excess < 0.0D0 ) then - LTol = 0.1D0*LTol - elseif ( epsi < 2.0D0 * excess ) then - LTol = (epsi + excess*0.5D0) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0.0d0 .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif ( Lepsi < 5D0 * excess ) then - LTol = (Lepsi + excess) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn12e = ( Sn1e - Sn2e ) - - Sn24e = (Sn2e - Sn4) -! Sn1e = Sn2e - Sn12e * zpz66666 -! Sn12e = (Sn1e - Sn2e) - - Sn124 = (Sn12e - Sn24) - if ((abs(Sn124)<= hmin) .or. - & .false..and.(Sn24*Sn12e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn24 * zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24 * Sn24 / Sn124 - endif - Sn4e = Sn4 + correction - -! NEWFLG = .TRUE. -! CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn1e,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4e,LIMEXP,val0,localError,EPSTAB,IERR) -! localError is made conservative in order to avoid premature -! termination - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) - !if (h>dhMin) then - !localError = max(localError,abs(correction)) - !else - !val0 = Sn4e - !localError = abs(correction)*two - !endif - else - CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - endif - acceptError = ( localError <= Ltol * h * eight - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(6,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.true..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,fx3,fx4,fx5,x1,h,S,SL,SR] - kp1 = k + 1; -! Process right interval - v(1,kp1) = v(3,k); !fx1R - v(2,kp1) = fx(3); !fx2R - v(3,kp1) = v(4,k); !fx3R - v(4,kp1) = fx(4); !fx4R - v(5,kp1) = v(5,k); !fx5R - v(6,kp1) = v(6,k) + four * h; ! x1R - v(7,kp1) = h; - v(8,kp1) = v(10,k); ! S - v(9:10,kp1) = Sn(3:4); ! SL, SR -! Process left interval - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) unchanged fx1L -! v(6,k) unchanged x1L - v(7,k) = h; - v(8,k) = v(9,k); ! S - v(9:10,k) = Sn(1:2); ! SL, SR - k = kp1; - endif - enddo ! while - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - Sn48 = (Sn4 - Sn8) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn4e = Sn8 - Sn48 * zpz588 - Sn12e = (Sn1e - Sn2e) - Sn24e = (Sn2e - Sn4e) - - Sn124 = (Sn12e - Sn24e) - if ((abs(Sn124)<= hmin) .or. - & (Sn12e*Sn24e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn48*zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24e * Sn24e / Sn124 - !Sn4e = Sn4e + correction - endif - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) -! localError is made conservative in order to avoid premature -! termination -! localError = max(localError,abs(correction)*three) -! localError = abs(correction)*three - else - !CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - NEWFLG = .TRUE. - CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn8,LIMEXP,val0,localError,EPSTAB,IERR) - endif - acceptError = ( localError <= Ltol * h * sixteen - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(Nrule+1,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.TRUE..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,..,fx8,fx9,x1,h,S,SL,SR,SL1,SL2 SR1,SR2] - kp1 = k + 1; -! Process right interval - - v(1,kp1) = v(5,k); !fx1R - v(2,kp1) = fx(5); !fx2R - v(3,kp1) = v(6,k); !fx3R - v(4,kp1) = fx(6); !fx4R - v(5,kp1) = v(7,k); !fx5R - v(6,kp1) = fx(7); !fx6R - v(7,kp1) = v(8,k); !fx7R - v(8,kp1) = fx(8); !fx8R - v(9,kp1) = v(9,k); !fx9R - - v(Nrule+1,kp1) = v(Nrule+1,k) + eight * h ! x1R - v(Nrule+2,kp1) = h; - v(Nrule+3,kp1) = v(Nrule+5,k); ! S - v(Nrule+4,kp1) = v(Nrule+8,k); ! SL - v(Nrule+5,kp1) = v(Nrule+9,k); ! SR - v(Nrule+6:Nrule+9,kp1) = Sn(5:8); ! SL1,SL2,SR1, SR2 -! Process left interval - v(9,k) = v(5,k); ! fx9L - v(8,k) = fx(4); ! fx8L - v(7,k) = v(4,k); ! fx7L - v(6,k) = fx(3); ! fx6L - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) = v(1,k); ! fx1L -! v(Nrule+1,k) unchanged x1L - v(Nrule+2,k) = h; - v(Nrule+3,k) = v(Nrule + 4,k); ! S - v(Nrule+4,k) = v(Nrule+6,k); ! SL - v(Nrule+5,k) = v(Nrule+7,k); ! SR - v(Nrule+6:Nrule+9,k) = Sn(1:4); ! SL1,SL2,SR1, SR2 - k = kp1; - endif - enddo ! while - if (epsi0) iflg = IOR(iflg, kflg) - end do - if (epsi0) iflg = ior(iflg,kflg) - end do - if (epsistepSize) then - Nk = floor((xup-xlo)/stepSize) + 1 - dx = (xup-xlo)/dble(Nk) - do j=1, Nk -1 - Npts = Npts + 1 - breakPoints(Npts) = xlo + dx * dble( j ) - enddo - endif - else - ! Compute candidates for the breakpoints - brkPts(1:2*n) = xup - forall(k=1:n,rho(k) .ne. zero) - indices(2*k-1) = k - indices(2*k ) = k - brkPts(2*k-1) = a(k)/rho(k) - brkPts(2*k ) = b(k)/rho(k) - end forall - ! Sort the candidates - call sortre(brkPts,indices) - ! Make unique list of breakpoints - - do k = 1,2*n - brk = brkPts(k) - if (xlo < brk) then - if ( xup <= brk ) exit ! terminate do loop - -! if (Npts>0) then -! xLow = max(xlo, breakPoints(Npts)) -! else -! xLow = xlo -! endif -! if (brk-xLow>stepSize) then -! Nk = floor((brk-xLow)/stepSize) -! dx = (brk-xLow)/dble(Nk) -! do j=1, Nk -1 -! Npts = Npts + 1 -! breakPoints(Npts) = brk + dx * dble( j ) -! enddo -! endif - - kU = indices(k) - - !if ( xlo + distance < brk .and. brk + distance < xup ) - !then - if ( den(kU) < 0.2) then - distance = max(brkSplit*den(kU),hMin) - z1 = brk + distance - z2 = brk - distance - if (Npts <= 0) then - if (xlo + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - kL = kU - elseif (breakPoints(Npts)+ max(distance - & ,brkSplit*den(kL)) < z1) then - if (breakPoints(Npts) + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - kL = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - kL = kU - endif - else - val1 = 0.0d0 - val2 = 0.0d0 - brkPts(Npts+1) = integrand(z1) - brkPts(Npts+2) = integrand(z2) - if ((xlo+ distance < z1) .and. (z1 + distance < xup)) - & val2 = brkPts(Npts +1) - if ((xlo+ distance < z2) .and. (z2 + distance < xup)) - & val2 = max(val2,brkPts(Npts +2)) - val1 = breakPoints(Npts) - Nprev = 1 - if (Npts>1) then - if (indices2(Npts-1)==kL) then - Nprev = 2 - val1 = max(val1,breakPoints(Npts-1)) - endif - endif - if (val1 < val2) then - !overwrite previous candidate - Npts = Npts - Nprev - if (Npts>0) then - val1 = breakPoints(Npts)+ distance - else - val1 = xlo+ distance - endif - if (val1 < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = brkPtsVal(Npts+Nprev) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - - if ((val1< z2) .and. (z2 + distance < xup)) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - if (Npts>0) kL = indices2(Npts) - endif - endif - endif - endif - enddo - endif - end subroutine GetBreakPoints - subroutine NarrowLimits(zMin,zMax,As,Bs,zCutOff,n,a,b,rho,den) - implicit none - double precision, intent(inout) :: zMin, zMax, As, Bs - double precision,dimension(*),intent(in) :: rho,a,b,den - double precision, intent(in) :: zCutOff - integer, intent(in) :: n -! Locals - double precision, parameter :: zero = 0.0D0, one = 1.0D0 - integer :: k - -! Uses the regression equation to limit the -! integration limits zMin and zMax - - do k = 1,n - if (ZERO < rho(k)) then - zMax = max(zMin, min(zMax,(b(k)+den(k)*zCutOff)/rho(k))) - zMin = min(zMax, max(zMin,(a(k)-den(k)*zCutOff)/rho(k))) - if ( one <= rho(k) ) then - if ( b(k) < Bs ) Bs = b(k) - if ( As < a(k) ) As = a(k) - endif - elseif (rho(k)< ZERO) then - zMax = max(zMin,min(zMax,(a(k)-den(k)*zCutOff)/rho(k))) - zMin = min(zMax,max(zMin,(b(k)+den(k)*zCutOff)/rho(k))) - if ( rho(k) <= -one ) then - if ( -a(k) < Bs ) Bs = -a(k) - if ( As < -b(k) ) As = -b(k) - endif - endif - enddo - As = min(As,Bs) - end subroutine NarrowLimits - - function integrand(z) result (val) - implicit none - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - double precision, parameter :: sqtwopi1 = 0.39894228040143D0 - double precision, parameter :: half = 0.5D0 - val = sqtwopi1 * exp(-half * z * z) * integrand1(z) - return - end function integrand - - function integrand1(z) result (val) - implicit none - double precision, intent(in) :: z - double precision :: val - double precision :: xUp,xLo,zRho - double precision, parameter :: one = 1.0D0, zero = 0.0D0 - integer :: I - val = one - do I = 1, mNdim - zRho = z * mRho(I) - ! Uncomment / mDen below if mRho, mA, mB is not scaled - xUp = ( mB(I) - zRho ) !/ mDen(I) - xLo = ( mA(I) - zRho ) !/ mDen(I) - if (zero0.1 -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION, INTENT(in) :: P - DOUBLE PRECISION :: VAL -!local variables - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, ONE, ZERO, HALF, - & A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - & C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - & E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - & Q, R - PARAMETER ( SPLIT1 = 0.425D0, SPLIT2 = 5.D0, - & CONST1 = 0.180625D0, CONST2 = 1.6D0, - & ONE = 1.D0, ZERO = 0.D0, HALF = 0.5D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( P - HALF) - IF ( ABS(Q) .LE. SPLIT1 ) THEN ! Central range. - R = CONST1 - Q*Q - VAL = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + ONE) - ELSE ! near the endpoints - R = MIN( P, ONE - P ) - IF (R .GT.ZERO) THEN ! ( 2.d0*R .GT. CFxCutOff) THEN ! R .GT.0.d0 - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - VAL = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + ONE ) - ELSE - R = R - SPLIT2 - VAL = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + ONE ) - END IF - ELSE - VAL = 37.D0 !XMAX 9.d0 - END IF - IF ( Q < ZERO ) VAL = - VAL - END IF - RETURN - END FUNCTION FIINV - FUNCTION FI2( Z ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -* -* Normal distribution probabilities accurate to 1.e-15. -* relative error less than 1e-8; -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION :: P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7,XMAX, - * P, EXPNTL, CUTOFF, ROOTPI, ZABS, Z2 - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = 0.70038 30644 43688 1D0, - * P6 = 0.035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = 0.088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) - PARAMETER( XMAX = 8.25D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( Z .GT. XMAX .OR. ZABS .GT. 37) THEN - P = 0.d0 - ELSE -* -* |Z| <= 37 -* - Z2 = ZABS * ZABS - EXPNTL = EXP( -Z2 * 0.5D0 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS < CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1.d0/( ZABS + 2.d0/( ZABS + 3.d0/( ZABS - * + 4.d0/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0.d0 ) P = 1.d0 - P - VALUE = P - RETURN - END FUNCTION FI2 - - FUNCTION FI( Z ) RESULT (VALUE) - USE ERFCOREMOD - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -! Local variables - DOUBLE PRECISION, PARAMETER:: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER:: HALF = 0.5D0 - VALUE = DERFC(-Z*SQ2M1)*HALF - RETURN - END FUNCTION FI - end module mvnProdCorrPrbMod - diff --git a/wafo/source/mvnprd/mvnprodcorrprb_interface.f b/wafo/source/mvnprd/mvnprodcorrprb_interface.f deleted file mode 100644 index 5e27dfd..0000000 --- a/wafo/source/mvnprd/mvnprodcorrprb_interface.f +++ /dev/null @@ -1,33 +0,0 @@ - -C gfortran -fPIC -c mvnprodcorrprb.f -C f2py -m mvnprdmod -c mvnprodcorrprb.o mvnprodcorrprb_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - -C module mvnprdmod -C contains - subroutine prbnormndpc(prb,abserr,IFT,rho,a,b,N,abseps,releps, - & useBreakPoints, useSimpson) - use mvnProdCorrPrbMod, ONLY : mvnprodcorrprb - integer :: N - double precision,dimension(N),intent(in) :: rho,a,b - double precision,intent(in) :: abseps - double precision,intent(in) :: releps - logical, intent(in) :: useBreakPoints - logical, intent(in) :: useSimpson - double precision,intent(out) :: abserr,prb - integer, intent(out) :: IFT - -Cf2py integer, intent(hide), depend(rho) :: N = len(rho) -Cf2py depend(N) a -Cf2py depend(N) b -Cf2py double precision, optional :: abseps = 0.001 -Cf2py double precision, optional :: releps = 0.001 -Cf2py logical, optional :: useBreakPoints =1 -Cf2py logical, optional :: useSimpson = 1 - - - - CALL mvnprodcorrprb(rho,a,b,abseps,releps,useBreakPoints, - & useSimpson,abserr,IFT,prb) - - end subroutine prbnormndpc -C end module mvnprdmod \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/build_all.py b/wafo/source/mvnprd/old/mvnprodcorrprb/build_all.py deleted file mode 100644 index 8b96b40..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/build_all.py +++ /dev/null @@ -1,24 +0,0 @@ -""" -f2py c_library.pyf c_functions.c -c -""" -import os - -def compile_all(): - - compile1_txt = 'gfortran -fPIC -c mvnprodcorrprb.f' - compile2_txt = 'f2py -m mvnprdmod -c mvnprodcorrprb.o mvnprodcorrprb_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71' - os.system(compile1_txt) - os.system(compile2_txt) - # Install gfortran and run the following to build the module: - #compile_format = 'f2py %s %s -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71' - - # Install microsoft visual c++ .NET 2003 and run the following to build the module: - #compile_format = 'f2py %s %s -c' - #pyfs = ('c_library.pyf',) - #files =('c_functions.c',) - - #for pyf,file in zip(pyfs,files): - # os.system(compile_format % (pyf,file)) - -if __name__=='__main__': - compile_all() diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb.f b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb.f deleted file mode 100644 index 8850562..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb.f +++ /dev/null @@ -1,4335 +0,0 @@ -C Does not work: f2py -m mvnprdmod -h mvnprdmod.pyf mvnprodcorrprb.f only: mvnprodcorrprb - - -C gfortran -fPIC -c mvnprodcorrprb.f -C f2py -m mvnprdmod -c mvnprodcorrprb.o mvnprodcorrprb_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C f2py -m mvnprdmod -c mvnprodcorrprb.o mvnprodcorrprb_interface.f --build-dir tmp1 --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - - -* This is a MEX-file for MATLAB. -* and contains a mex-interface to, mvnprodcorrprb a subroutine -* for computing multivariate normal probabilities with product -* correlation structure. -* The file should compile without errors on (Fortran90) -* standard Fortran compilers. -* -* The mex-interface and mvnprodcorrprb was written by -* Per Andreas Brodtkorb -* Norwegian Defence Research Establishment -* P.O. Box 115m -* N-3191 Horten -* Norway -* Email: Per.Brodtkorb@ffi.no -* -* -* MVNPRODCORRPRBMEX Computes multivariate normal probability -* with product correlation structure. -* -* CALL [value,error,inform]=mvnprodcorrprbmex(rho,A,B,abseps,releps,useBreakPoints); -* -* RHO REAL, array of coefficients defining the correlation -* coefficient by: -* correlation(I,J) = RHO(I)*RHO(J) for J/=I -* where -* 1 <= RHO(I) <= 1 -* A REAL, array of lower integration limits. -* B REAL, array of upper integration limits. -* NOTE: any values greater the 10, are considered as -* infinite values. -* ABSEPS REAL absolute error tolerance. -* RELEPS REAL relative error tolerance. -* USEBREAKPOINTS = 1 If extra integration points should be used -* around possible singularities -* 0 If no extra -* -* ERROR REAL estimated absolute error, with 99% confidence level. -* VALUE REAL estimated value for the integral -* INFORM INTEGER, termination status parameter: -* if INFORM = 0, normal completion with ERROR < EPS; -* if INFORM = 1, completion with ERROR > EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* -* MVNPRODCORRPRB calculates multivariate normal probability -* with product correlation structure for rectangular regions. -* The accuracy is up to almost double precision, i.e., about 1e-14. -* -* This file was successfully compiled for matlab 5.3 -* using Compaq Visual Fortran 6.1, and Windows 2000. -* The example here uses Fortran77 source. -* First, you will need to modify your mexopts.bat file. -* To find it, issue the command prefdir(1) from the Matlab command line, -* the directory it answers with will contain your mexopts.bat file. -* Open it for editing. The first section will look like: -* -*rem ******************************************************************** -*rem General parameters -*rem ******************************************************************** -*set MATLAB=%MATLAB% -*set DF_ROOT=C:\Program Files\Microsoft Visual Studio -*set VCDir=%DF_ROOT%\VC98 -*set MSDevDir=%DF_ROOT%\Common\msdev98 -*set DFDir=%DF_ROOT%\DF98 -*set PATH=%MSDevDir%\bin;%DFDir%\BIN;%VCDir%\BIN;%PATH% -*set INCLUDE=%DFDir%\INCLUDE;%DFDir%\IMSL\INCLUDE;%INCLUDE% -*set LIB=%DFDir%\LIB;%VCDir%\LIB -* -* then you are ready to compile this file at the matlab prompt using the -* following command: -* mex -O mvnprodcorrprbmex.f - MODULE ERFCOREMOD - IMPLICIT NONE - - INTERFACE CALERF - MODULE PROCEDURE CALERF - END INTERFACE - - INTERFACE DERF - MODULE PROCEDURE DERF - END INTERFACE - - INTERFACE DERFC - MODULE PROCEDURE DERFC - END INTERFACE - - INTERFACE DERFCX - MODULE PROCEDURE DERFCX - END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C Revised pab Dec 2008 -C updated parameter statements in CALERF so that it works when -C compiling with gfortran. -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- -C DOUBLE PRECISION, DIMENSION(5) :: A, Q -C DOUBLE PRECISION, DIMENSION(4) :: B -C DOUBLE PRECISION, DIMENSION(9) :: C -C DOUBLE PRECISION, DIMENSION(8) :: D -C DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER, DIMENSION(5) :: - & A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/) - DOUBLE PRECISION, PARAMETER, DIMENSION(4) :: - & B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - DOUBLE PRECISION, DIMENSION(9) :: - & C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/) - DOUBLE PRECISION, DIMENSION(8) :: - & D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - DOUBLE PRECISION, parameter, - & DIMENSION(6) :: P =(/3.05326634961232344D-1, - & 3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/) - DOUBLE PRECISION, parameter, - & DIMENSION(5) :: Q =(/2.56852019228982242D00, - & 1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/) -C------------------------------------------------------------------ - - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD - module functionInterface - INTERFACE - FUNCTION F(Z) result (VAL) - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - END FUNCTION F - END INTERFACE - end module functionInterface - module AdaptiveGaussKronrod - implicit none - private - public :: dqagpe,dqagp - - INTERFACE dqagpe - MODULE PROCEDURE dqagpe - END INTERFACE - - INTERFACE dqagp - MODULE PROCEDURE dqagp - END INTERFACE - - INTERFACE dqelg - MODULE PROCEDURE dqelg - END INTERFACE - - INTERFACE dqpsrt - MODULE PROCEDURE dqpsrt - END INTERFACE - - INTERFACE dqk21 - MODULE PROCEDURE dqk21 - END INTERFACE - - INTERFACE dqk15 - MODULE PROCEDURE dqk15 - END INTERFACE - - INTERFACE dqk9 - MODULE PROCEDURE dqk9 - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - - contains - subroutine dea3(E0,E1,E2,abserr,result) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result = E2 - abserr = err1 + err2 + E2*small*ten - else - result = E1 + one/ss - abserr = err1 + err2 + abs(result-E2) - endif - endif - end subroutine dea3 - subroutine dqagp(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier) -! use functionInterface - implicit none - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result1,abserr - integer, intent(out) :: neval,ier - double precision :: f -!Locals - double precision,dimension(limit) :: alist, blist, rlist, elist - double precision,dimension(npts+2) :: pts - integer, dimension(limit) :: iord, level - integer, dimension(npts+2) :: ndin - integer ::last - external f - CALL dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin - $ ,last) - end subroutine dqagp - subroutine dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin, - * last) -! use functionInterface - implicit none -c***begin prologue dqagpe -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a2a1 -c***keywords automatic integrator, general-purpose, -! singularities at user specified points, -! extrapolation, globally adaptive. -c***author piessens,robert ,appl. math. & progr. div. - k.u.leuven -! de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose the routine calculates an approximation result to a given -! definite integral i = integral of f over (a,b), hopefully -! satisfying following claim for accuracy abs(i-result).le. -! max(epsabs,epsrel*abs(i)). break points of the integration -! interval, where local difficulties of the integrand may -! occur(e.g. singularities,discontinuities),provided by user. -c***description -! -! computation of a definite integral -! standard fortran subroutine -! double precision version -! -! parameters -! on entry -! f - double precision -! function subprogram defining the integrand -! function f(x). the actual name for f needs to be -! declared e x t e r n a l in the driver program. -! -! a - double precision -! lower limit of integration -! -! b - double precision -! upper limit of integration -! -! npts2 - integer -! number equal to two more than the number of -! user-supplied break points within the integration -! range, npts2.ge.2. -! if npts2.lt.2, the routine will end with ier = 6. -! -! points - double precision -! vector of dimension npts2, the first (npts2-2) -! elements of which are the user provided break -! points. if these points do not constitute an -! ascending sequence there will be an automati! -! sorting. -! -! epsabs - double precision -! absolute accuracy requested -! epsrel - double precision -! relative accuracy requested -! if epsabs.le.0 -! and epsrel.lt.max(50*rel.mach.acc.,0.5d-28), -! the routine will end with ier = 6. -! -! limit - integer -! gives an upper bound on the number of subintervals -! in the partition of (a,b), limit.ge.npts2 -! if limit.lt.npts2, the routine will end with -! ier = 6. -! -! on return -! result - double precision -! approximation to the integral -! -! abserr - double precision -! estimate of the modulus of the absolute error, -! which should equal or exceed abs(i-result) -! -! neval - integer -! number of integrand evaluations -! -! ier - integer -! ier = 0 normal and reliable termination of the -! routine. it is assumed that the requested -! accuracy has been achieved. -! ier.gt.0 abnormal termination of the routine. -! the estimates for integral and error are -! less reliable. it is assumed that the -! requested accuracy has not been achieved. -! error messages -! ier = 1 maximum number of subdivisions allowed -! has been achieved. one can allow more -! subdivisions by increasing the value of -! limit (and taking the according dimension -! adjustments into account). however, if -! this yields no improvement it is advised -! to analyze the integrand in order to -! determine the integration difficulties. if -! the position of a local difficulty can be -! determined (i.e. singularity, -! discontinuity within the interval), it -! should be supplied to the routine as an -! element of the vector points. if necessary -! an appropriate special-purpose integrator -! must be used, which is designed for -! handling the type of difficulty involved. -! = 2 the occurrence of roundoff error is -! detected, which prevents the requested -! tolerance from being achieved. -! the error may be under-estimated. -! = 3 extremely bad integrand behaviour occurs -! at some points of the integration -! interval. -! = 4 the algorithm does not converge. -! roundoff error is detected in the -! extrapolation table. it is presumed that -! the requested tolerance cannot be -! achieved, and that the returned result is -! the best which can be obtained. -! = 5 the integral is probably divergent, or -! slowly convergent. it must be noted that -! divergence can occur with any other value -! of ier.gt.0. -! = 6 the input is invalid because -! npts2.lt.2 or -! break points are specified outside -! the integration range or -! (epsabs.le.0 and -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) -! or limit.lt.npts2. -! result, abserr, neval, last, rlist(1), -! and elist(1) are set to zero. alist(1) and -! blist(1) are set to a and b respectively. -! -! alist - double precision -! vector of dimension at least limit, the first -! last elements of which are the left end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! blist - double precision -! vector of dimension at least limit, the first -! last elements of which are the right end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! rlist - double precision -! vector of dimension at least limit, the first -! last elements of which are the integral -! approximations on the subintervals -! -! elist - double precision -! vector of dimension at least limit, the first -! last elements of which are the moduli of the -! absolute error estimates on the subintervals -! -! pts - double precision -! vector of dimension at least npts2, containing the -! integration limits and the break points of the -! interval in ascending sequence. -! -! level - integer -! vector of dimension at least limit, containing the -! subdivision levels of the subinterval, i.e. if -! (aa,bb) is a subinterval of (p1,p2) where p1 as -! well as p2 is a user-provided break point or -! integration limit, then (aa,bb) has level l if -! abs(bb-aa) = abs(p2-p1)*2**(-l). -! -! ndin - integer -! vector of dimension at least npts2, after first -! integration over the intervals (pts(i)),pts(i+1), -! i = 0,1, ..., npts2-2, the error estimates over -! some of the intervals may have been increased -! artificially, in order to put their subdivision -! forward. if this happens for the subinterval -! numbered k, ndin(k) is put to 1, otherwise -! ndin(k) = 0. -! -! iord - integer -! vector of dimension at least limit, the first k -! elements of which are pointers to the -! error estimates over the subintervals, -! such that elist(iord(1)), ..., elist(iord(k)) -! form a decreasing sequence, with k = last -! if last.le.(limit/2+2), and k = limit+1-last -! otherwise -! -! last - integer -! number of subintervals actually produced in the -! subdivisions process -! -c***references (none) -c***routines called d1mach,dqelg,dqk21,dqpsrt -c***end prologue dqagpe - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result,abserr - integer, intent(out) :: neval,ier - double precision,dimension(limit), intent(out) :: alist, blist - double precision,dimension(limit), intent(out) :: rlist, elist - double precision,dimension(npts+2),intent(out) :: pts - integer, dimension(limit), intent(out) :: iord, level - integer, dimension(npts+2), intent(out) :: ndin - integer ::last - double precision :: f -! locals - double precision :: area,area1,area12,area2,a1, - * a2,b1,b2,correc,abseps,defabs,defab1,defab2, - * dres,epmach,erlarg,erlast,errbnd, - * errmax,error1,erro12,error2,errsum,ertest,oflow, - * resa,resabs,reseps,sign,temp,uflow, hSplit - double precision, dimension(3) :: res3la(3) - double precision, dimension(52) :: rlist2(52) - integer :: i,id,ierro,ind1,ind2,ip1,iroff1,iroff2,iroff3,j, - * jlow,jupbnd,k,ksgn,ktmin,levcur,levmax,maxerr, - * nint,nintp1,npts2,nres,nrmax,numrl2 - logical :: extrap,noext - external f -! -! - -! -! -! the dimension of rlist2 is determined by the value of -! limexp in subroutine epsalg (rlist2 should be of dimension -! (limexp+2) at least). -! -! -! list of major variables -! ----------------------- -! -! alist - list of left end points of all subintervals -! considered up to now -! blist - list of right end points of all subintervals -! considered up to now -! rlist(i) - approximation to the integral over -! (alist(i),blist(i)) -! rlist2 - array of dimension at least limexp+2 -! containing the part of the epsilon table which -! is still needed for further computations -! elist(i) - error estimate applying to rlist(i) -! maxerr - pointer to the interval with largest error -! estimate -! errmax - elist(maxerr) -! erlast - error on the interval currently subdivided -! (before that subdivision has taken place) -! area - sum of the integrals over the subintervals -! errsum - sum of the errors over the subintervals -! errbnd - requested accuracy max(epsabs,epsrel* -! abs(result)) -! *****1 - variable for the left subinterval -! *****2 - variable for the right subinterval -! last - index for subdivision -! nres - number of calls to the extrapolation routine -! numrl2 - number of elements in rlist2. if an appropriate -! approximation to the compounded integral has -! been obtained, it is put in rlist2(numrl2) after -! numrl2 has been increased by one. -! erlarg - sum of the errors over the intervals larger -! than the smallest interval considered up to now -! extrap - logical variable denoting that the routine -! is attempting to perform extrapolation. i.e. -! before subdividing the smallest interval we -! try to decrease the value of erlarg. -! noext - logical variable denoting that extrapolation is -! no longer allowed (true-value) -! -! machine dependent constants -! --------------------------- -! -! epmach is the largest relative spacing. -! uflow is the smallest positive magnitude. -! oflow is the largest positive magnitude. -! -c***first executable statement dqagpe - epmach = d1mach(4) - uflow = d1mach(1) - oflow = d1mach(2) -! -! test on validity of parameters -! ----------------------------- -! - hSplit = 0.2D0 - ier = 0 - neval = 0 - last = 0 - result = 0.0d+00 - abserr = 0.0d+00 - alist(1) = a - blist(1) = b - rlist(1) = 0.0d+00 - elist(1) = 0.0d+00 - iord(1) = 0 - level(1) = 0 - npts2 = npts+2 - if((npts2.lt.2).or.(limit.le.npts).or. - & ((epsabs.le.0.0d+00).and. - & (epsrel.lt.dmax1(0.5d+02*epmach,0.5d-28)))) then - ier = 6 - go to 999 - endif - - sign = 1.0d+00 - if(a.gt.b) then - go to 999 - endif - if (npts>0) then - if(any(points(1:npts)<=a).or.any(b<=points(1:npts))) then - ier = 6 - go to 999 - endif - endif -! -! if any break points are provided, sort them into an -! ascending sequence. -! - pts(1) = a - pts(npts+2) = b - do i = 1,npts - pts(i+1) = minval(points(i:npts)) - enddo -! -! compute first integral and error approximations. -! ------------------------------------------------ -! - nint = npts+1; - a1 = pts(1); - resabs = 0.0d+00 - do i = 1,nint - b1 = pts(i+1) - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,defabs,resa) - !call dqk15(f,a1,b1,area1,error1,defabs,resa) - else - call dqkl9(f,a1,b1,area1,error1,defabs,resa) - endif - abserr = abserr + error1 - result = result + area1 - ndin(i) = 0 - if(error1.eq.resa.and.error1.ne.0.0d+00) ndin(i) = 1 - resabs = resabs + defabs - level(i) = 0 - elist(i) = error1 - alist(i) = a1 - blist(i) = b1 - rlist(i) = area1 - iord(i) = i - a1 = b1 - enddo !50 continue - errsum = 0.0d+00 - do i = 1,nint - if(ndin(i).eq.1) elist(i) = abserr - errsum = errsum+elist(i) - enddo !55 continue -! -! test on accuracy. -! - last = nint - neval = 21*nint - dres = dabs(result) - errbnd = dmax1(epsabs,epsrel*dres) - if(abserr.le.0.1d+03*epmach*resabs.and.abserr.gt.errbnd) ier = 2 - if(nint.eq.1) go to 80 - do 70 i = 1,npts - jlow = i+1 - ind1 = iord(i) - do 60 j = jlow,nint - ind2 = iord(j) - if(elist(ind1).gt.elist(ind2)) go to 60 - ind1 = ind2 - k = j - 60 continue - if(ind1.eq.iord(i)) go to 70 - iord(k) = iord(i) - iord(i) = ind1 - 70 continue - if(limit.lt.npts2) ier = 1 - 80 if(ier.ne.0.or.abserr.le.errbnd) go to 210 - -! -! initialization -! -------------- -! - rlist2(1) = result - maxerr = iord(1) - errmax = elist(maxerr) - area = result - nrmax = 1 - nres = 0 - numrl2 = 1 - ktmin = 0 - extrap = .false. - noext = .false. - erlarg = errsum - ertest = errbnd - levmax = 1 - iroff1 = 0 - iroff2 = 0 - iroff3 = 0 - ierro = 0 - abserr = oflow - ksgn = -1 - if(dres.ge.(0.1d+01-0.5d+02*epmach)*resabs) ksgn = 1 -! -! main do-loop -! ------------ -! - do 160 last = npts2,limit -! -! bisect the subinterval with the nrmax-th largest error -! estimate. -! - levcur = level(maxerr)+1 - a1 = alist(maxerr) - b1 = 0.5d+00*(alist(maxerr)+blist(maxerr)) - a2 = b1 - b2 = blist(maxerr) - erlast = errmax - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,resa,defab1) - call dqk21(f,a2,b2,area2,error2,resa,defab2) - !call dqk15(f,a1,b1,area1,error1,resa,defab1) - !call dqk15(f,a2,b2,area2,error2,resa,defab2) - else - - call dqkl9(f,a1,b1,area1,error1,resa,defab1) - call dqkl9(f,a2,b2,area2,error2,resa,defab2) - endif -! -! improve previous approximations to integral -! and error and test for accuracy. -! - neval = neval+42 - area12 = area1+area2 - erro12 = error1+error2 - errsum = errsum+erro12-errmax - area = area+area12-rlist(maxerr) - if(defab1.eq.error1.or.defab2.eq.error2) go to 95 - if(dabs(rlist(maxerr)-area12).gt.0.1d-04*dabs(area12) - * .or.erro12.lt.0.99d+00*errmax) go to 90 - if(extrap) iroff2 = iroff2+1 - if(.not.extrap) iroff1 = iroff1+1 - 90 if(last.gt.10.and.erro12.gt.errmax) iroff3 = iroff3+1 - 95 level(maxerr) = levcur - level(last) = levcur - rlist(maxerr) = area1 - rlist(last) = area2 - errbnd = dmax1(epsabs,epsrel*dabs(area)) -! -! test for roundoff error and eventually set error flag. -! - if(iroff1+iroff2.ge.10.or.iroff3.ge.20) ier = 2 - if(iroff2.ge.5) ierro = 3 -! -! set error flag in the case that the number of -! subintervals equals limit. -! - if(last.eq.limit) ier = 1 -! -! set error flag in the case of bad integrand behaviour -! at a point of the integration range -! - if(dmax1(dabs(a1),dabs(b2)).le.(0.1d+01+0.1d+03*epmach)* - * (dabs(a2)+0.1d+04*uflow)) ier = 4 -! -! append the newly-created intervals to the list. -! - if(error2.gt.error1) go to 100 - alist(last) = a2 - blist(maxerr) = b1 - blist(last) = b2 - elist(maxerr) = error1 - elist(last) = error2 - go to 110 - 100 alist(maxerr) = a2 - alist(last) = a1 - blist(last) = b1 - rlist(maxerr) = area2 - rlist(last) = area1 - elist(maxerr) = error2 - elist(last) = error1 -! -! call subroutine dqpsrt to maintain the descending ordering -! in the list of error estimates and select the subinterval -! with nrmax-th largest error estimate (to be bisected next). -! - 110 call dqpsrt(limit,last,maxerr,errmax,elist,iord,nrmax) -! ***jump out of do-loop - if(errsum.le.errbnd) go to 190 -! ***jump out of do-loop - if(ier.ne.0) go to 170 - if(noext) go to 160 - erlarg = erlarg-erlast - if(levcur+1.le.levmax) erlarg = erlarg+erro12 - if(extrap) go to 120 -! -! test whether the interval to be bisected next is the -! smallest interval. -! - if(level(maxerr)+1.le.levmax) go to 160 - extrap = .true. - nrmax = 2 - 120 if(ierro.eq.3.or.erlarg.le.ertest) go to 140 -! -! the smallest interval has the largest error. -! before bisecting decrease the sum of the errors over -! the larger intervals (erlarg) and perform extrapolation. -! - id = nrmax - jupbnd = last - if(last.gt.(2+limit/2)) jupbnd = limit+3-last - do 130 k = id,jupbnd - maxerr = iord(nrmax) - errmax = elist(maxerr) -! ***jump out of do-loop - if(level(maxerr)+1.le.levmax) go to 160 - nrmax = nrmax+1 - 130 continue -! -! perform extrapolation. -! - 140 numrl2 = numrl2+1 - rlist2(numrl2) = area - if(numrl2.le.2) go to 155 - call dqelg(numrl2,rlist2,reseps,abseps,res3la,nres) - ktmin = ktmin+1 - if(ktmin.gt.5.and.abserr.lt.0.1d-02*errsum) ier = 5 - if(abseps.ge.abserr) go to 150 - ktmin = 0 - abserr = abseps - result = reseps - correc = erlarg - ertest = dmax1(epsabs,epsrel*dabs(reseps)) -! ***jump out of do-loop - if(abserr.lt.ertest) go to 170 -! -! prepare bisection of the smallest interval. -! - 150 if(numrl2.eq.1) noext = .true. - if(ier.ge.5) go to 170 - 155 maxerr = iord(1) - errmax = elist(maxerr) - nrmax = 1 - extrap = .false. - levmax = levmax + 1 - erlarg = errsum - 160 continue -! -! set the final result. -! --------------------- -! -! - 170 if(abserr.eq.oflow) go to 190 - if((ier+ierro).eq.0) go to 180 - if(ierro.eq.3) abserr = abserr+correc - if(ier.eq.0) ier = 3 - if(result.ne.0.0d+00.and.area.ne.0.0d+00)go to 175 - if(abserr.gt.errsum)go to 190 - if(area.eq.0.0d+00) go to 210 - go to 180 - 175 if(abserr/dabs(result).gt.errsum/dabs(area))go to 190 -! -! test on divergence. -! - 180 if(ksgn.eq.(-1).and.dmax1(dabs(result),dabs(area)).le. - * resabs*0.1d-01) go to 210 - if(0.1d-01.gt.(result/area).or.(result/area).gt.0.1d+03.or. - * errsum.gt.dabs(area)) ier = 6 - go to 210 -! -! compute global integral sum. -! - 190 result = 0.0d+00 - do 200 k = 1,last - result = result+rlist(k) - 200 continue - abserr = errsum - 210 if(ier.gt.2) ier = ier-1 - result = result*sign - 999 return - end subroutine dqagpe - subroutine dqk21(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk21 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 21-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk21 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk,reskh,result,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(10),fv2(10),wg(5),wgk(11),xgk(11) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 21-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 10-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 10-point gauss rule -c -c wgk - weights of the 21-point kronrod rule -c -c wg - weights of the 10-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.0666713443 0868813759 3568809893 332 d0 / - data wg ( 2) / 0.1494513491 5058059314 5776339657 697 d0 / - data wg ( 3) / 0.2190863625 1598204399 5534934228 163 d0 / - data wg ( 4) / 0.2692667193 0999635509 1226921569 469 d0 / - data wg ( 5) / 0.2955242247 1475287017 3892994651 338 d0 / -c - data xgk ( 1) / 0.9956571630 2580808073 5527280689 003 d0 / - data xgk ( 2) / 0.9739065285 1717172007 7964012084 452 d0 / - data xgk ( 3) / 0.9301574913 5570822600 1207180059 508 d0 / - data xgk ( 4) / 0.8650633666 8898451073 2096688423 493 d0 / - data xgk ( 5) / 0.7808177265 8641689706 3717578345 042 d0 / - data xgk ( 6) / 0.6794095682 9902440623 4327365114 874 d0 / - data xgk ( 7) / 0.5627571346 6860468333 9000099272 694 d0 / - data xgk ( 8) / 0.4333953941 2924719079 9265943165 784 d0 / - data xgk ( 9) / 0.2943928627 0146019813 1126603103 866 d0 / - data xgk ( 10) / 0.1488743389 8163121088 4826001129 720 d0 / - data xgk ( 11) / 0.0000000000 0000000000 0000000000 000 d0 / -c - data wgk ( 1) / 0.0116946388 6737187427 8064396062 192 d0 / - data wgk ( 2) / 0.0325581623 0796472747 8818972459 390 d0 / - data wgk ( 3) / 0.0547558965 7435199603 1381300244 580 d0 / - data wgk ( 4) / 0.0750396748 1091995276 7043140916 190 d0 / - data wgk ( 5) / 0.0931254545 8369760553 5065465083 366 d0 / - data wgk ( 6) / 0.1093871588 0229764189 9210590325 805 d0 / - data wgk ( 7) / 0.1234919762 6206585107 7958109831 074 d0 / - data wgk ( 8) / 0.1347092173 1147332592 8054001771 707 d0 / - data wgk ( 9) / 0.1427759385 7706008079 7094273138 717 d0 / - data wgk ( 10) / 0.1477391049 0133849137 4841515972 068 d0 / - data wgk ( 11) / 0.1494455540 0291690566 4936468389 821 d0 / -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk21 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 21-point kronrod approximation to -c the integral, and estimate the absolute error. -c - resg = 0.0d+00 - fc = f(centr) - resk = wgk(11)*fc - resabs = dabs(resk) - do 10 j=1,5 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,5 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(11)*dabs(fc-reskh) - do 20 j=1,10 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0d0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk21 - subroutine dqk15(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk,reskh,result,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 7-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point gauss rule -c -c wgk - weights of the 15-point kronrod rule -c -c wg - weights of the 7-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.129484966168869693270611432679082d0 / - data wg ( 2) / 0.279705391489276667901467771423780d0 / - data wg ( 3) / 0.381830050505118944950369775488975d0 / - data wg ( 4) / 0.417959183673469387755102040816327d0 / - - data xgk ( 1) / 0.991455371120812639206854697526329d0 / - data xgk ( 2) / 0.949107912342758524526189684047851d0 / - data xgk ( 3) / 0.864864423359769072789712788640926d0 / - data xgk ( 4) / 0.741531185599394439863864773280788d0 / - data xgk ( 5) / 0.586087235467691130294144838258730d0 / - data xgk ( 6) / 0.405845151377397166906606412076961d0 / - data xgk ( 7) / 0.207784955007898467600689403773245d0 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.022935322010529224963732008058970d0/ - data wgk ( 2) / 0.063092092629978553290700663189204d0 / - data wgk ( 3) / 0.104790010322250183839876322541518d0 / - data wgk ( 4) / 0.140653259715525918745189590510238d0 / - data wgk ( 5) / 0.169004726639267902826583426598550d0 / - data wgk ( 6) / 0.190350578064785409913256402421014d0 / - data wgk ( 7) / 0.204432940075298892414161999234649d0 / - data wgk ( 8) / 0.209482141084727828012999174891714d0 / - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resg = wg(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0D0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk15 - subroutine dqk9(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk0,resk,reskh,result,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -! xgk(4), xgk(8) abscissae of the 3-point gauss rule -c xgk(2), xgk(4),xgk(6), xgk(8) ... abscissae of the 7-point -c kronrod rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point kronrod rule -c -c wgk - weights of the 15-point kronrod rule -! -! wgk0 - weights of the 7-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - data wg ( 1) / 0.5555555555555555D+00/ - data wg ( 2) / 0.8888888888888889D+00/ - - data wgk0 ( 1) / 0.1046562260264673D+00/ - data wgk0 ( 2) / 0.2684880898683335D+00/ - data wgk0 ( 3) / 0.4013974147759622D+00/ - data wgk0 ( 4) / 0.4509165386584741D+00/ - - data xgk ( 1) / 0.9938319632127550D+00/ - data xgk ( 2) / 0.9604912687080203D+00/ - data xgk ( 3) / 0.8884592328722570D+00 / - data xgk ( 4) / 0.7745966692414834D+00/ - data xgk ( 5) / 0.6211029467372264D+00/ - data xgk ( 6) / 0.4342437493468026D+00/ - data xgk ( 7) / 0.2233866864289669D+00 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.1700171962994028D-01/ - data wgk ( 2) / 0.5160328299707982D-01/ - data wgk ( 3) / 0.9292719531512452D-01/ - data wgk ( 4) / 0.1344152552437843D+00/ - data wgk ( 5) / 0.1715119091363914D+00/ - data wgk ( 6) / 0.2006285293769890D+00/ - data wgk ( 7) / 0.2191568584015875D+00/ - data wgk ( 8) / 0.2255104997982067D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resk0 = wgk0(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(4) + fv2(4)) - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result = resk - call dea3(resg,resk0,resk,abserr,result) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0)) - & * 10.0D0, abserr) - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - - end subroutine dqk9 - subroutine dqkl9(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk0,resk,reskh,result,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(3),wgk(5),xgk(5) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 9-point Gauss-kronrod-lobatto rule -! xgk(1), xgk(5) abscissae of the 3-point gauss-lobatto rule -c xgk(1), xgk(3),xgk(5) abscissae of the 5-point -c kronrod rule -c xgk(2), xgk(4), ... abscissae which are optimally -c added to the 5-point kronrod rule -c -c wgk - weights of the 9-point kronrod rule -! -! wgk0 - weights of the 5-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - - data wg ( 1) / 0.33333333333333333333333333333333333D+00/ - data wg ( 2) / 0.13333333333333333333333333333333333D+01/ - - data wgk0 ( 1) / 0.1000000000000000D+00/ - data wgk0 ( 2) / 0.5444444444444445D+00/ - data wgk0 ( 3) / 0.7111111111111111D+00/ - - data xgk ( 1) / 0.1000000000000000D+01/ - data xgk ( 2) / 0.8904055275126688D+00/ - data xgk ( 3) / 0.6546536707079772D+00/ - data xgk ( 4) / 0.3409822659109930D+00/ - data xgk ( 5) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.3064373897707232D-01/ - data wgk ( 2) / 0.1792626995532074D+00/ - data wgk ( 3) / 0.2839787780481211D+00/ - data wgk ( 4) / 0.3342337398164177D+00/ - data wgk ( 5) / 0.3437620872103631D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(5)*fc - resk0 = wgk0(3)*fc - resabs = dabs(resk) - do 10 j=1,2 - jtw = 2*j - 1 - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(1) + fv2(1)) - do 15 j = 1,2 - jtwm1 = 2*j - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(5)*dabs(fc-reskh) - do 20 j=1,4 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result = resk - call dea3(resg,resk0,resk,abserr,result) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0))* 10.0D0,abserr) - - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqkl9 - subroutine dqpsrt(limit,last,maxerr,ermax,elist,iord,nrmax) - implicit none -c***begin prologue dqpsrt -c***refer to dqage,dqagie,dqagpe,dqawse -c***routines called (none) -c***revision date 810101 (yymmdd) -c***keywords sequential sorting -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose this routine maintains the descending ordering in the -c list of the local error estimated resulting from the -c interval subdivision process. at each call two error -c estimates are inserted using the sequential search -c method, top-down for the largest error estimate and -c bottom-up for the smallest error estimate. -c***description -c -c ordering routine -c standard fortran subroutine -c double precision version -c -c parameters (meaning at output) -c limit - integer -c maximum number of error estimates the list -c can contain -c -c last - integer -c number of error estimates currently in the list -c -c maxerr - integer -c maxerr points to the nrmax-th largest error -c estimate currently in the list -c -c ermax - double precision -c nrmax-th largest error estimate -c ermax = elist(maxerr) -c -c elist - double precision -c vector of dimension last containing -c the error estimates -c -c iord - integer -c vector of dimension last, the first k elements -c of which contain pointers to the error -c estimates, such that -c elist(iord(1)),..., elist(iord(k)) -c form a decreasing sequence, with -c k = last if last.le.(limit/2+2), and -c k = limit+1-last otherwise -c -c nrmax - integer -c maxerr = iord(nrmax) -c -c***end prologue dqpsrt -c - double precision elist,ermax,errmax,errmin - integer i,ibeg,ido,iord,isucc,j,jbnd,jupbn,k,last,limit,maxerr, - * nrmax - dimension elist(last),iord(last) -c -c check whether the list contains more than -c two error estimates. -c -c***first executable statement dqpsrt - if(last.gt.2) go to 10 - iord(1) = 1 - iord(2) = 2 - go to 90 -c -c this part of the routine is only executed if, due to a -c difficult integrand, subdivision increased the error -c estimate. in the normal case the insert procedure should -c start after the nrmax-th largest error estimate. -c - 10 errmax = elist(maxerr) - if(nrmax.eq.1) go to 30 - ido = nrmax-1 - do 20 i = 1,ido - isucc = iord(nrmax-1) -c ***jump out of do-loop - if(errmax.le.elist(isucc)) go to 30 - iord(nrmax) = isucc - nrmax = nrmax-1 - 20 continue -c -c compute the number of elements in the list to be maintained -c in descending order. this number depends on the number of -c subdivisions still allowed. -c - 30 jupbn = last - if(last.gt.(limit/2+2)) jupbn = limit+3-last - errmin = elist(last) -c -c insert errmax by traversing the list top-down, -c starting comparison from the element elist(iord(nrmax+1)). -c - jbnd = jupbn-1 - ibeg = nrmax+1 - if(ibeg.gt.jbnd) go to 50 - do 40 i=ibeg,jbnd - isucc = iord(i) -c ***jump out of do-loop - if(errmax.ge.elist(isucc)) go to 60 - iord(i-1) = isucc - 40 continue - 50 iord(jbnd) = maxerr - iord(jupbn) = last - go to 90 -c -c insert errmin by traversing the list bottom-up. -c - 60 iord(i-1) = maxerr - k = jbnd - do 70 j=i,jbnd - isucc = iord(k) -c ***jump out of do-loop - if(errmin.lt.elist(isucc)) go to 80 - iord(k+1) = isucc - k = k-1 - 70 continue - iord(i) = last - go to 90 - 80 iord(k+1) = last -c -c set maxerr and ermax. -c - 90 maxerr = iord(nrmax) - ermax = elist(maxerr) - return - end subroutine dqpsrt - subroutine dqelg(n,epstab,result,abserr,res3la,nres) - implicit none -c***begin prologue dqelg -c***refer to dqagie,dqagoe,dqagpe,dqagse -c***routines called d1mach -c***revision date 830518 (yymmdd) -c***keywords epsilon algorithm, convergence acceleration, -c extrapolation -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math & progr. div. - k.u.leuven -c***purpose the routine determines the limit of a given sequence of -c approximations, by means of the epsilon algorithm of -c p.wynn. an estimate of the absolute error is also given. -c the condensed epsilon table is computed. only those -c elements needed for the computation of the next diagonal -c are preserved. -c***description -c -c epsilon algorithm -c standard fortran subroutine -c double precision version -c -c parameters -c n - integer -c epstab(n) contains the new element in the -c first column of the epsilon table. -c -c epstab - double precision -c vector of dimension 52 containing the elements -c of the two lower diagonals of the triangular -c epsilon table. the elements are numbered -c starting at the right-hand corner of the -c triangle. -c -c result - double precision -c resulting approximation to the integral -c -c abserr - double precision -c estimate of the absolute error computed from -c result and the 3 previous results -c -c res3la - double precision -c vector of dimension 3 containing the last 3 -c results -c -c nres - integer -c number of calls to the routine -c (should be zero at first call) -c -c***end prologue dqelg -c - double precision abserr,dabs,delta1,delta2,delta3,dmax1, - * epmach,epsinf,epstab,error,err1,err2,err3,e0,e1,e1abs,e2,e3, - * oflow,res,result,res3la,ss,tol1,tol2,tol3 - integer i,ib,ib2,ie,indx,k1,k2,k3,limexp,n,newelm,nres,num - dimension epstab(52),res3la(3) -c -c list of major variables -c ----------------------- -c -c e0 - the 4 elements on which the computation of a new -c e1 element in the epsilon table is based -c e2 -c e3 e0 -c e3 e1 new -c e2 -c newelm - number of elements to be computed in the new -c diagonal -c error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2) -c result - the element in the new diagonal with least value -c of error -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c oflow is the largest positive magnitude. -c limexp is the maximum number of elements the epsilon -c table can contain. if this number is reached, the upper -c diagonal of the epsilon table is deleted. -c -c***first executable statement dqelg - epmach = d1mach(4) - oflow = d1mach(2) - nres = nres+1 - abserr = oflow - result = epstab(n) - if(n.lt.3) go to 100 - limexp = 50 - epstab(n+2) = epstab(n) - newelm = (n-1)/2 - epstab(n) = oflow - num = n - k1 = n - do 40 i = 1,newelm - k2 = k1-1 - k3 = k1-2 - res = epstab(k1+2) - e0 = epstab(k3) - e1 = epstab(k2) - e2 = res - e1abs = dabs(e1) - delta2 = e2-e1 - err2 = dabs(delta2) - tol2 = dmax1(dabs(e2),e1abs)*epmach - delta3 = e1-e0 - err3 = dabs(delta3) - tol3 = dmax1(e1abs,dabs(e0))*epmach - if(err2.gt.tol2.or.err3.gt.tol3) go to 10 -c -c if e0, e1 and e2 are equal to within machine -c accuracy, convergence is assumed. -c result = e2 -c abserr = abs(e1-e0)+abs(e2-e1) -c - result = res - abserr = err2+err3 -c ***jump out of do-loop - go to 100 - 10 e3 = epstab(k1) - epstab(k1) = e1 - delta1 = e1-e3 - err1 = dabs(delta1) - tol1 = dmax1(e1abs,dabs(e3))*epmach -c -c if two elements are very close to each other, omit -c a part of the table by adjusting the value of n -c - if(err1.le.tol1.or.err2.le.tol2.or.err3.le.tol3) go to 20 - ss = 0.1d+01/delta1+0.1d+01/delta2-0.1d+01/delta3 - epsinf = dabs(ss*e1) -c -c test to detect irregular behaviour in the table, and -c eventually omit a part of the table adjusting the value -c of n. -c - if(epsinf.gt.0.1d-03) go to 30 - 20 n = i+i-1 -c ***jump out of do-loop - go to 50 -c -c compute a new element and eventually adjust -c the value of result. -c - 30 res = e1+0.1d+01/ss - epstab(k1) = res - k1 = k1-2 - error = err2+dabs(res-e2)+err3 - if(error.gt.abserr) go to 40 - abserr = error - result = res - 40 continue -c -c shift the table. -c - 50 if(n.eq.limexp) n = 2*(limexp/2)-1 - ib = 1 - if((num/2)*2.eq.num) ib = 2 - ie = newelm+1 - do 60 i=1,ie - ib2 = ib+2 - epstab(ib) = epstab(ib2) - ib = ib2 - 60 continue - if(num.eq.n) go to 80 - indx = num-n+1 - do 70 i = 1,n - epstab(i)= epstab(indx) - indx = indx+1 - 70 continue - 80 if(nres.ge.4) go to 90 - res3la(nres) = result - abserr = oflow - go to 100 -c -c compute error estimate -c - 90 abserr = dabs(result-res3la(3))+dabs(result-res3la(2)) - * +dabs(result-res3la(1)) - res3la(1) = res3la(2) - res3la(2) = res3la(3) - res3la(3) = result - 100 abserr = dmax1(abserr,0.5d+01*epmach*dabs(result)) - return - end subroutine dqelg - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - end module AdaptiveGaussKronrod - - module Integration1DModule - implicit none - interface AdaptiveSimpson - module procedure AdaptiveSimpson2, AdaptiveSimpsonWithBreaks - end interface - -! interface AdaptiveSimpson1 -! module procedure AdaptiveSimpson1 -! end interface - - interface AdaptiveTrapz - module procedure AdaptiveTrapz1, AdaptiveTrapzWithBreaks - end interface - - interface Romberg - module procedure Romberg1, RombergWithBreaks - end interface - - INTERFACE DEA - MODULE PROCEDURE DEA - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - contains - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - subroutine dea3(E0,E1,E2,abserr,result) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result = E2 - abserr = err1 + err2 + E2*small*ten - else - result = E1 + one/ss - abserr = err1 + err2 + abs(result-E2) - endif - endif - end subroutine dea3 - SUBROUTINE DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -C***BEGIN PROLOGUE DEA -C***DATE WRITTEN 800101 (YYMMDD) -C***REVISION DATE 871208 (YYMMDD) -C***CATEGORY NO. E5 -C***KEYWORDS CONVERGENCE ACCELERATION,EPSILON ALGORITHM,EXTRAPOLATION -C***AUTHOR PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. - -C K. U. LEUVEN -C DE DONCKER-KAPENGA, ELISE,WESTERN MICHIGAN UNIVERSITY -C KAHANER, DAVID K., NATIONAL BUREAU OF STANDARDS -C STARKENBURG, C. B., NATIONAL BUREAU OF STANDARDS -C***PURPOSE Given a slowly convergent sequence, this routine attempts -C to extrapolate nonlinearly to a better estimate of the -C sequence's limiting value, thus improving the rate of -C convergence. Routine is based on the epsilon algorithm -C of P. Wynn. An estimate of the absolute error is also -C given. -C***DESCRIPTION -C -C Epsilon algorithm. Standard fortran subroutine. -C Double precision version. -C -C A R G U M E N T S I N T H E C A L L S E Q U E N C E -C -C NEWFLG - LOGICAL (INPUT and OUTPUT) -C On the first call to DEA set NEWFLG to .TRUE. -C (indicating a new sequence). DEA will set NEWFLG -C to .FALSE. -C -C SVALUE - DOUBLE PRECISION (INPUT) -C On the first call to DEA set SVALUE to the first -C term in the sequence. On subsequent calls set -C SVALUE to the subsequent sequence value. -C -C LIMEXP - INTEGER (INPUT) -C An integer equal to or greater than the total -C number of sequence terms to be evaluated. Do not -C change the value of LIMEXP until a new sequence -C is evaluated (NEWFLG=.TRUE.). LIMEXP .GE. 3 -C -C RESULT - DOUBLE PRECISION (OUTPUT) -C Best approximation to the sequence's limit. -C -C ABSERR - DOUBLE PRECISION (OUTPUT) -C Estimate of the absolute error. -C -C EPSTAB - DOUBLE PRECISION (OUTPUT) -C Workvector of DIMENSION at least (LIMEXP+7). -C -C IERR - INTEGER (OUTPUT) -C IERR=0 Normal termination of the routine. -C IERR=1 The input is invalid because LIMEXP.LT.3. -C -C T Y P I C A L P R O B L E M S E T U P -C -C This sample problem uses the trapezoidal rule to evaluate the -C integral of the sin function from 0.0 to 0.5*PI (value = 1.0). The -C program implements the trapezoidal rule 8 times creating an -C increasingly accurate sequence of approximations to the integral. -C Each time the trapezoidal rule is used, it uses twice as many -C panels as the time before. DEA is called to obtain even more -C accurate estimates. -C -C PROGRAM SAMPLE -C IMPLICIT DOUBLE PRECISION (A-H,O-Z) -C DOUBLE PRECISION EPSTAB(57) -CC [57 = LIMEXP + 7] -C LOGICAL NEWFLG -C EXTERNAL F -C DATA LIMEXP/50/ -C WRITE(*,*) ' NO. PANELS TRAP. APPROX' -C * ,' APPROX W/EA ABSERR' -C WRITE(*,*) -C HALFPI = DASIN(1.0D+00) -CC [UPPER INTEGRATION LIMIT = PI/2] -C NEWFLG = .TRUE. -CC [SET FLAG - 1ST DEA CALL] -C DO 10 I = 0,7 -C NPARTS = 2 ** I -C WIDTH = HALFPI/NPARTS -C APPROX = 0.5D+00 * WIDTH * (F(0.0D+00) + F(HALFPI)) -C DO 11 J = 1,NPARTS-1 -C APPROX = APPROX + F(J * WIDTH) * WIDTH -C 11 CONTINUE -CC [END TRAPEZOIDAL RULE APPROX] -C SVALUE = APPROX -CC [SVALUE = NEW SEQUENCE VALUE] -C CALL DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -CC [CALL DEA FOR BETTER ESTIMATE] -C WRITE(*,12) NPARTS,APPROX,RESULT,ABSERR -C 12 FORMAT(' ',I4,T20,F16.13,T40,F16.13,T60,D11.4) -C 10 CONTINUE -C STOP -C END -C -C DOUBLE PRECISION FUNCTION F(X) -C DOUBLE PRECISION X -C F = DSIN(X) -CC [INTEGRAND] -C RETURN -C END -C -C Output from the above program will be: -C -C NO. PANELS TRAP. APPROX APPROX W/EA ABSERR -C -C 1 .7853981633974 .7853981633974 .7854D+00 -C 2 .9480594489685 .9480594489685 .9760D+00 -C 4 .9871158009728 .9994567212570 .2141D+00 -C 8 .9967851718862 .9999667417647 .3060D-02 -C 16 .9991966804851 .9999998781041 .6094D-03 -C 32 .9997991943200 .9999999981026 .5767D-03 -C 64 .9999498000921 .9999999999982 .3338D-04 -C 128 .9999874501175 1.0000000000000 .1238D-06 -C -C----------------------------------------------------------------------- -C***REFERENCES "Acceleration de la convergence en analyse numerique", -C C. Brezinski, "Lecture Notes in Math.", vol. 584, -C Springer-Verlag, New York, 1977. -C***ROUTINES CALLED D1MACH,XERROR -C***END PROLOGUE DEA - double precision, dimension(*), intent(inout) :: EPSTAB - double precision, intent(out) :: RESULT !, ABSERR - double precision, intent(inout) :: ABSERR - double precision, intent(in) :: SVALUE - INTEGER, INTENT(IN) :: LIMEXP - INTEGER, INTENT(OUT) :: IERR - LOGICAL, intent(INOUT) :: NEWFLG - DOUBLE PRECISION :: DELTA1,DELTA2,DELTA3,DRELPR,DEPRN, - 1 ERROR,ERR1,ERR2,ERR3,E0,E1,E2,E3,RES, - 2 SS,TOL1,TOL2,TOL3 - double precision, dimension(3) :: RES3LA - INTEGER I,IB,IB2,IE,IN,K1,K2,K3,N,NEWELM,NUM,NRES -C -C -C LIMEXP is the maximum number of elements the -C epsilon table data can contain. The epsilon table -C is stored in the first (LIMEXP+2) entries of EPSTAB. -C -C -C LIST OF MAJOR VARIABLES -C ----------------------- -C E0,E1,E2,E3 - DOUBLE PRECISION -C The 4 elements on which the computation of -C a new element in the epsilon table is based. -C NRES - INTEGER -C Number of extrapolation results actually -C generated by the epsilon algorithm in prior -C calls to the routine. -C NEWELM - INTEGER -C Number of elements to be computed in the -C new diagonal of the epsilon table. The -C condensed epsilon table is computed. Only -C those elements needed for the computation of -C the next diagonal are preserved. -C RES - DOUBLE PRECISION -C New element in the new diagonal of the -C epsilon table. -C ERROR - DOUBLE PRECISION -C An estimate of the absolute error of RES. -C Routine decides whether RESULT=RES or -C RESULT=SVALUE by comparing ERROR with -C ABSERR from the previous call. -C RES3LA - DOUBLE PRECISION -C Vector of DIMENSION 3 containing at most -C the last 3 results. -C -C -C MACHINE DEPENDENT CONSTANTS -C --------------------------- -C DRELPR is the largest relative spacing. -C -C***FIRST EXECUTABLE STATEMENT DEA - IF(LIMEXP.LT.3) THEN - IERR = 1 -! CALL XERROR('LIMEXP IS LESS THAN 3',21,1,1) - GO TO 110 - ENDIF - IERR = 0 - RES3LA(1)=EPSTAB(LIMEXP+5) - RES3LA(2)=EPSTAB(LIMEXP+6) - RES3LA(3)=EPSTAB(LIMEXP+7) - RESULT=SVALUE - IF(NEWFLG) THEN - N=1 - NRES=0 - NEWFLG=.FALSE. - EPSTAB(N)=SVALUE - ABSERR=ABS(RESULT) - GO TO 100 - ELSE - N=INT(EPSTAB(LIMEXP+3)) - NRES=INT(EPSTAB(LIMEXP+4)) - IF(N.EQ.2) THEN - EPSTAB(N)=SVALUE - ABSERR=.6D+01*ABS(RESULT-EPSTAB(1)) - GO TO 100 - ENDIF - ENDIF - EPSTAB(N)=SVALUE - DRELPR=D1MACH(4) - DEPRN=1.0D+01*DRELPR - EPSTAB(N+2)=EPSTAB(N) - NEWELM=(N-1)/2 - NUM=N - K1=N - DO 40 I=1,NEWELM - K2=K1-1 - K3=K1-2 - RES=EPSTAB(K1+2) - E0=EPSTAB(K3) - E1=EPSTAB(K2) - E2=RES - DELTA2=E2-E1 - ERR2=ABS(DELTA2) - TOL2=MAX(ABS(E2),ABS(E1))*DRELPR - DELTA3=E1-E0 - ERR3=ABS(DELTA3) - TOL3=MAX(ABS(E1),ABS(E0))*DRELPR - IF(ERR2.GT.TOL2.OR.ERR3.GT.TOL3) GO TO 10 -C -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. -C RESULT=E2 -C ABSERR=ABS(E1-E0)+ABS(E2-E1) -C - RESULT=RES - ABSERR=ERR2+ERR3 - GO TO 50 - 10 IF(I.NE.1) THEN - E3=EPSTAB(K1) - EPSTAB(K1)=E1 - DELTA1=E1-E3 - ERR1=ABS(DELTA1) - TOL1=MAX(ABS(E1),ABS(E3))*DRELPR -C -C IF TWO ELEMENTS ARE VERY CLOSE TO EACH OTHER, OMIT -C A PART OF THE TABLE BY ADJUSTING THE VALUE OF N -C - IF(ERR1.LE.TOL1.OR.ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA1+0.1D+01/DELTA2-0.1D+01/DELTA3 - ELSE - EPSTAB(K1)=E1 - IF(ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA2-0.1D+01/DELTA3 - ENDIF -C -C TEST TO DETECT IRREGULAR BEHAVIOUR IN THE TABLE, AND -C EVENTUALLY OMIT A PART OF THE TABLE ADJUSTING THE VALUE -C OF N -C - IF(ABS(SS*E1).GT.0.1D-03) GO TO 30 - 20 N=I+I-1 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ERR3 - RESULT=RES - ELSE IF(NRES.EQ.1) THEN - RESULT=RES3LA(1) - ELSE IF(NRES.EQ.2) THEN - RESULT=RES3LA(2) - ELSE - RESULT=RES3LA(3) - ENDIF - GO TO 50 -C -C COMPUTE A NEW ELEMENT AND EVENTUALLY ADJUST -C THE VALUE OF RESULT -C - 30 RES=E1+0.1D+01/SS - EPSTAB(K1)=RES - K1=K1-2 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ABS(RES-E2)+ERR3 - RESULT=RES - GO TO 40 - ELSE IF(NRES.EQ.1) THEN - ERROR=.6D+01*(ABS(RES-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ERROR=.2D+01*(ABS(RES-RES3LA(2))+ABS(RES-RES3LA(1))) - ELSE - ERROR=ABS(RES-RES3LA(3))+ABS(RES-RES3LA(2)) - 1 +ABS(RES-RES3LA(1)) - ENDIF - IF(ERROR.GT.1.0D+01*ABSERR) GO TO 40 - ABSERR=ERROR - RESULT=RES - 40 CONTINUE -C -C COMPUTE ERROR ESTIMATE -C - IF(NRES.EQ.1) THEN - ABSERR=.6D+01*(ABS(RESULT-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ABSERR=.2D+01*ABS(RESULT-RES3LA(2))+ABS(RESULT-RES3LA(1)) - ELSE IF(NRES.GT.2) THEN - ABSERR=ABS(RESULT-RES3LA(3))+ABS(RESULT-RES3LA(2)) - 1 +ABS(RESULT-RES3LA(1)) - ENDIF -C -C SHIFT THE TABLE -C - 50 IF(N.EQ.LIMEXP) N=2*(LIMEXP/2)-1 - IB=1 - IF((NUM/2)*2.EQ.NUM) IB=2 - IE=NEWELM+1 - DO 60 I=1,IE - IB2=IB+2 - EPSTAB(IB)=EPSTAB(IB2) - IB=IB2 - 60 CONTINUE - IF(NUM.EQ.N) GO TO 80 - IN=NUM-N+1 - DO 70 I=1,N - EPSTAB(I)=EPSTAB(IN) - IN=IN+1 - 70 CONTINUE -C -C UPDATE RES3LA -C - 80 IF(NRES.EQ.0) THEN - RES3LA(1)=RESULT - ELSE IF(NRES.EQ.1) THEN - RES3LA(2)=RESULT - ELSE IF(NRES.EQ.2) THEN - RES3LA(3)=RESULT - ELSE - RES3LA(1)=RES3LA(2) - RES3LA(2)=RES3LA(3) - RES3LA(3)=RESULT - ENDIF - 90 ABSERR=MAX(ABSERR,DEPRN*ABS(RESULT)) - NRES=NRES+1 - 100 N=N+1 - EPSTAB(LIMEXP+3)=DBLE(N) - EPSTAB(LIMEXP+4)=DBLE(NRES) - EPSTAB(LIMEXP+5)=RES3LA(1) - EPSTAB(LIMEXP+6)=RES3LA(2) - EPSTAB(LIMEXP+7)=RES3LA(3) - 110 RETURN - END subroutine DEA - - subroutine AdaptiveIntWithBreaks(f,a,b,N,brks,epsi,iflg - $ ,abserr, val) - use AdaptiveGaussKronrod - implicit none - double precision :: f - integer, intent(in) :: N - double precision, intent(in) :: a,b,epsi - double precision, dimension(:), intent(in) :: brks - double precision, intent(out) :: abserr, val - integer, intent(out) :: iflg - external f -! Locals - double precision, dimension(N+2) :: pts - double precision :: LTol,tol, error, valk, excess, errorEstimate - double precision :: delta, deltaK - integer :: kflg, k, limit,neval - limit = 30 - pts(1) = a - pts(N+2) = b - delta = b - a - do k = 2,N+1 - pts(k) = minval(brks(k-1:N)) !add user supplied break points - enddo - LTol = epsi / delta - abserr = 0.0d0 - val = 0.0D0 - iflg = 0 - do k = 1, N + 1 - deltaK = pts(k+1) - pts(k) - tol = LTol * deltaK - if (deltaK < 0.5D0) then - call AdaptiveSimpson(f,pts(k),pts(k+1),tol, kflg,error,valk) -! call romberg(f,pts(k),pts(k+1),20,tol,kflg,error, valk) - else -! call AdaptiveSimpson3(f,pts(k),pts(k+1),tol,kflg,error,valk) - call dqagp(f,pts(k),pts(k+1),0,pts,tol,0.0D0,limit,valk, - * error,neval,kflg) - - endif - abserr = abserr + abs(error) - - errorEstimate = abserr + (b - pts(k+1)) * LTol - excess = epsi - errorEstimate - if (excess < 0.0D0 ) then - LTol = 0.1D0*LTol - elseif ( epsi < 2.0D0 * excess ) then - LTol = (epsi + excess*0.5D0) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0.0d0 .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif ( Lepsi < 5D0 * excess ) then - LTol = (Lepsi + excess) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn12e = ( Sn1e - Sn2e ) - - Sn24e = (Sn2e - Sn4) -! Sn1e = Sn2e - Sn12e * zpz66666 -! Sn12e = (Sn1e - Sn2e) - - Sn124 = (Sn12e - Sn24) - if ((abs(Sn124)<= hmin) .or. - & .false..and.(Sn24*Sn12e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn24 * zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24 * Sn24 / Sn124 - endif - Sn4e = Sn4 + correction - -! NEWFLG = .TRUE. -! CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn1e,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4e,LIMEXP,val0,localError,EPSTAB,IERR) -! localError is made conservative in order to avoid premature -! termination - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) - !if (h>dhMin) then - !localError = max(localError,abs(correction)) - !else - !val0 = Sn4e - !localError = abs(correction)*two - !endif - else - CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - endif - acceptError = ( localError <= Ltol * h * eight - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(6,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.true..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,fx3,fx4,fx5,x1,h,S,SL,SR] - kp1 = k + 1; -! Process right interval - v(1,kp1) = v(3,k); !fx1R - v(2,kp1) = fx(3); !fx2R - v(3,kp1) = v(4,k); !fx3R - v(4,kp1) = fx(4); !fx4R - v(5,kp1) = v(5,k); !fx5R - v(6,kp1) = v(6,k) + four * h; ! x1R - v(7,kp1) = h; - v(8,kp1) = v(10,k); ! S - v(9:10,kp1) = Sn(3:4); ! SL, SR -! Process left interval - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) unchanged fx1L -! v(6,k) unchanged x1L - v(7,k) = h; - v(8,k) = v(9,k); ! S - v(9:10,k) = Sn(1:2); ! SL, SR - k = kp1; - endif - enddo ! while - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - Sn48 = (Sn4 - Sn8) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn4e = Sn8 - Sn48 * zpz588 - Sn12e = (Sn1e - Sn2e) - Sn24e = (Sn2e - Sn4e) - - Sn124 = (Sn12e - Sn24e) - if ((abs(Sn124)<= hmin) .or. - & (Sn12e*Sn24e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn48*zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24e * Sn24e / Sn124 - !Sn4e = Sn4e + correction - endif - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) -! localError is made conservative in order to avoid premature -! termination -! localError = max(localError,abs(correction)*three) -! localError = abs(correction)*three - else - !CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - NEWFLG = .TRUE. - CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn8,LIMEXP,val0,localError,EPSTAB,IERR) - endif - acceptError = ( localError <= Ltol * h * sixteen - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(Nrule+1,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.TRUE..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,..,fx8,fx9,x1,h,S,SL,SR,SL1,SL2 SR1,SR2] - kp1 = k + 1; -! Process right interval - - v(1,kp1) = v(5,k); !fx1R - v(2,kp1) = fx(5); !fx2R - v(3,kp1) = v(6,k); !fx3R - v(4,kp1) = fx(6); !fx4R - v(5,kp1) = v(7,k); !fx5R - v(6,kp1) = fx(7); !fx6R - v(7,kp1) = v(8,k); !fx7R - v(8,kp1) = fx(8); !fx8R - v(9,kp1) = v(9,k); !fx9R - - v(Nrule+1,kp1) = v(Nrule+1,k) + eight * h ! x1R - v(Nrule+2,kp1) = h; - v(Nrule+3,kp1) = v(Nrule+5,k); ! S - v(Nrule+4,kp1) = v(Nrule+8,k); ! SL - v(Nrule+5,kp1) = v(Nrule+9,k); ! SR - v(Nrule+6:Nrule+9,kp1) = Sn(5:8); ! SL1,SL2,SR1, SR2 -! Process left interval - v(9,k) = v(5,k); ! fx9L - v(8,k) = fx(4); ! fx8L - v(7,k) = v(4,k); ! fx7L - v(6,k) = fx(3); ! fx6L - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) = v(1,k); ! fx1L -! v(Nrule+1,k) unchanged x1L - v(Nrule+2,k) = h; - v(Nrule+3,k) = v(Nrule + 4,k); ! S - v(Nrule+4,k) = v(Nrule+6,k); ! SL - v(Nrule+5,k) = v(Nrule+7,k); ! SR - v(Nrule+6:Nrule+9,k) = Sn(1:4); ! SL1,SL2,SR1, SR2 - k = kp1; - endif - enddo ! while - if (epsi0) iflg = IOR(iflg, kflg) - end do - if (epsi0) iflg = ior(iflg,kflg) - end do - if (epsistepSize) then - Nk = floor((xup-xlo)/stepSize) + 1 - dx = (xup-xlo)/dble(Nk) - do j=1, Nk -1 - Npts = Npts + 1 - breakPoints(Npts) = xlo + dx * dble( j ) - enddo - endif - else - ! Compute candidates for the breakpoints - brkPts(1:2*n) = xup - forall(k=1:n,rho(k) .ne. zero) - indices(2*k-1) = k - indices(2*k ) = k - brkPts(2*k-1) = a(k)/rho(k) - brkPts(2*k ) = b(k)/rho(k) - end forall - ! Sort the candidates - call sortre(brkPts,indices) - ! Make unique list of breakpoints - - do k = 1,2*n - brk = brkPts(k) - if (xlo < brk) then - if ( xup <= brk ) exit ! terminate do loop - -! if (Npts>0) then -! xLow = max(xlo, breakPoints(Npts)) -! else -! xLow = xlo -! endif -! if (brk-xLow>stepSize) then -! Nk = floor((brk-xLow)/stepSize) -! dx = (brk-xLow)/dble(Nk) -! do j=1, Nk -1 -! Npts = Npts + 1 -! breakPoints(Npts) = brk + dx * dble( j ) -! enddo -! endif - - kU = indices(k) - - !if ( xlo + distance < brk .and. brk + distance < xup ) - !then - if ( den(kU) < 0.2) then - distance = max(brkSplit*den(kU),hMin) - z1 = brk + distance - z2 = brk - distance - if (Npts <= 0) then - if (xlo + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - kL = kU - elseif (breakPoints(Npts)+ max(distance - & ,brkSplit*den(kL)) < z1) then - if (breakPoints(Npts) + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - kL = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - kL = kU - endif - else - val1 = 0.0d0 - val2 = 0.0d0 - brkPts(Npts+1) = integrand(z1) - brkPts(Npts+2) = integrand(z2) - if ((xlo+ distance < z1) .and. (z1 + distance < xup)) - & val2 = brkPts(Npts +1) - if ((xlo+ distance < z2) .and. (z2 + distance < xup)) - & val2 = max(val2,brkPts(Npts +2)) - val1 = breakPoints(Npts) - Nprev = 1 - if (Npts>1) then - if (indices2(Npts-1)==kL) then - Nprev = 2 - val1 = max(val1,breakPoints(Npts-1)) - endif - endif - if (val1 < val2) then - !overwrite previous candidate - Npts = Npts - Nprev - if (Npts>0) then - val1 = breakPoints(Npts)+ distance - else - val1 = xlo+ distance - endif - if (val1 < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = brkPtsVal(Npts+Nprev) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - - if ((val1< z2) .and. (z2 + distance < xup)) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - if (Npts>0) kL = indices2(Npts) - endif - endif - endif - endif - enddo - endif - end subroutine GetBreakPoints - subroutine NarrowLimits(zMin,zMax,As,Bs,zCutOff,n,a,b,rho,den) - implicit none - double precision, intent(inout) :: zMin, zMax, As, Bs - double precision,dimension(*),intent(in) :: rho,a,b,den - double precision, intent(in) :: zCutOff - integer, intent(in) :: n -! Locals - double precision, parameter :: zero = 0.0D0, one = 1.0D0 - integer :: k - -! Uses the regression equation to limit the -! integration limits zMin and zMax - - do k = 1,n - if (ZERO < rho(k)) then - zMax = max(zMin, min(zMax,(b(k)+den(k)*zCutOff)/rho(k))) - zMin = min(zMax, max(zMin,(a(k)-den(k)*zCutOff)/rho(k))) - if ( one <= rho(k) ) then - if ( b(k) < Bs ) Bs = b(k) - if ( As < a(k) ) As = a(k) - endif - elseif (rho(k)< ZERO) then - zMax = max(zMin,min(zMax,(a(k)-den(k)*zCutOff)/rho(k))) - zMin = min(zMax,max(zMin,(b(k)+den(k)*zCutOff)/rho(k))) - if ( rho(k) <= -one ) then - if ( -a(k) < Bs ) Bs = -a(k) - if ( As < -b(k) ) As = -b(k) - endif - endif - enddo - As = min(As,Bs) - end subroutine NarrowLimits - - function integrand(z) result (val) - implicit none - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - double precision, parameter :: sqtwopi1 = 0.39894228040143D0 - double precision, parameter :: half = 0.5D0 - val = sqtwopi1 * exp(-half * z * z) * integrand1(z) - return - end function integrand - - function integrand1(z) result (val) - implicit none - double precision, intent(in) :: z - double precision :: val - double precision :: xUp,xLo,zRho - double precision, parameter :: one = 1.0D0, zero = 0.0D0 - integer :: I - val = one - do I = 1, mNdim - zRho = z * mRho(I) - ! Uncomment / mDen below if mRho, mA, mB is not scaled - xUp = ( mB(I) - zRho ) !/ mDen(I) - xLo = ( mA(I) - zRho ) !/ mDen(I) - if (zero0.1 -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION, INTENT(in) :: P - DOUBLE PRECISION :: VAL -!local variables - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, ONE, ZERO, HALF, - & A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - & C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - & E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - & Q, R - PARAMETER ( SPLIT1 = 0.425D0, SPLIT2 = 5.D0, - & CONST1 = 0.180625D0, CONST2 = 1.6D0, - & ONE = 1.D0, ZERO = 0.D0, HALF = 0.5D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( P - HALF) - IF ( ABS(Q) .LE. SPLIT1 ) THEN ! Central range. - R = CONST1 - Q*Q - VAL = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + ONE) - ELSE ! near the endpoints - R = MIN( P, ONE - P ) - IF (R .GT.ZERO) THEN ! ( 2.d0*R .GT. CFxCutOff) THEN ! R .GT.0.d0 - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - VAL = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + ONE ) - ELSE - R = R - SPLIT2 - VAL = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + ONE ) - END IF - ELSE - VAL = 37.D0 !XMAX 9.d0 - END IF - IF ( Q < ZERO ) VAL = - VAL - END IF - RETURN - END FUNCTION FIINV - FUNCTION FI2( Z ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -* -* Normal distribution probabilities accurate to 1.e-15. -* relative error less than 1e-8; -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION :: P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7,XMAX, - * P, EXPNTL, CUTOFF, ROOTPI, ZABS, Z2 - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = 0.70038 30644 43688 1D0, - * P6 = 0.035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = 0.088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) - PARAMETER( XMAX = 8.25D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( Z .GT. XMAX .OR. ZABS .GT. 37) THEN - P = 0.d0 - ELSE -* -* |Z| <= 37 -* - Z2 = ZABS * ZABS - EXPNTL = EXP( -Z2 * 0.5D0 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS < CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1.d0/( ZABS + 2.d0/( ZABS + 3.d0/( ZABS - * + 4.d0/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0.d0 ) P = 1.d0 - P - VALUE = P - RETURN - END FUNCTION FI2 - - FUNCTION FI( Z ) RESULT (VALUE) - USE ERFCOREMOD - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -! Local variables - DOUBLE PRECISION, PARAMETER:: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER:: HALF = 0.5D0 - VALUE = DERFC(-Z*SQ2M1)*HALF - RETURN - END FUNCTION FI - end module mvnProdCorrPrbMod - - \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb_interface.f b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb_interface.f deleted file mode 100644 index 190f081..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb_interface.f +++ /dev/null @@ -1,33 +0,0 @@ - -C gfortran -fPIC -c mvnprodcorrprb.f -C f2py -m mvnprdmod -c mvnprodcorrprb.o mvnprodcorrprb_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - -C module mvnprdmod -C contains - subroutine prbnormndpc(prb,abserr,IFT,rho,a,b,N,abseps,releps, - & useBreakPoints, useSimpson) - use mvnProdCorrPrbMod, ONLY : mvnprodcorrprb - integer :: N - double precision,dimension(N),intent(in) :: rho,a,b - double precision,intent(in) :: abseps - double precision,intent(in) :: releps - logical, intent(in) :: useBreakPoints - logical, intent(in) :: useSimpson - double precision,intent(out) :: abserr,prb - integer, intent(out) :: IFT - -Cf2py integer, intent(hide), depend(rho) :: N = len(rho) -Cf2py depend(N) a -Cf2py depend(N) b -Cf2py double precision, optional :: abseps = 0.001 -Cf2py double precision, optional :: releps = 0.001 -Cf2py logical, optional :: useBreakPoints =1 -Cf2py logical, optional :: useSimpson = 1 - - - - CALL mvnprodcorrprb(rho,a,b,abseps,releps,useBreakPoints, - & useSimpson,abserr,IFT,prb) - - end subroutine prbnormndpc -C end module mvnprdmod \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/AdaptiveGaussKronrod.f90 b/wafo/source/mvnprd/old/mvnprodcorrprb/old/AdaptiveGaussKronrod.f90 deleted file mode 100644 index 4c65537..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/AdaptiveGaussKronrod.f90 +++ /dev/null @@ -1,1802 +0,0 @@ -! f2py -m adaptivegausskronrod -h adaptivegausskronrod.pyf AdaptiveGaussKronrod.f -! f2py adaptivegausskronrod.pyf AdaptiveGaussKronrod.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -! f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m adaptivegausskronrod -c AdaptiveGaussKronrod.f - module functionInterface - INTERFACE - FUNCTION F(Z) result (VAL) - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - END FUNCTION F - END INTERFACE - end module functionInterface - - module AdaptiveGaussKronrod - implicit none - private - public :: dqagpe,dqagp - - INTERFACE dqagpe - MODULE PROCEDURE dqagpe - END INTERFACE - - INTERFACE dqagp - MODULE PROCEDURE dqagp - END INTERFACE - - INTERFACE dqelg - MODULE PROCEDURE dqelg - END INTERFACE - - INTERFACE dqpsrt - MODULE PROCEDURE dqpsrt - END INTERFACE - - INTERFACE dqk21 - MODULE PROCEDURE dqk21 - END INTERFACE - - INTERFACE dqk15 - MODULE PROCEDURE dqk15 - END INTERFACE - - INTERFACE dqk9 - MODULE PROCEDURE dqk9 - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - - contains - subroutine dea3(E0,E1,E2,abserr,result1) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result1 - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result1 = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result1 = E2 - abserr = err1 + err2 + E2*small*ten - else - result1 = E1 + one/ss - abserr = err1 + err2 + abs(result1-E2) - endif - endif - end subroutine dea3 - subroutine dqagp(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier) -! use functionInterface - implicit none - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result1,abserr - integer, intent(out) :: neval,ier - double precision :: f -!Locals - double precision,dimension(limit) :: alist, blist, rlist, elist - double precision,dimension(npts+2) :: pts - integer, dimension(limit) :: iord, level - integer, dimension(npts+2) :: ndin - integer ::last - external f - CALL dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin - $ ,last) - end subroutine dqagp - subroutine dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin, - * last) -! use functionInterface - implicit none -c***begin prologue dqagpe -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a2a1 -c***keywords automatic integrator, general-purpose, -! singularities at user specified points, -! extrapolation, globally adaptive. -c***author piessens,robert ,appl. math. & progr. div. - k.u.leuven -! de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose the routine calculates an approximation result to a given -! definite integral i = integral of f over (a,b), hopefully -! satisfying following claim for accuracy abs(i-result).le. -! max(epsabs,epsrel*abs(i)). break points of the integration -! interval, where local difficulties of the integrand may -! occur(e.g. singularities,discontinuities),provided by user. -c***description -! -! computation of a definite integral -! standard fortran subroutine -! double precision version -! -! parameters -! on entry -! f - double precision -! function subprogram defining the integrand -! function f(x). the actual name for f needs to be -! declared e x t e r n a l in the driver program. -! -! a - double precision -! lower limit of integration -! -! b - double precision -! upper limit of integration -! -! npts2 - integer -! number equal to two more than the number of -! user-supplied break points within the integration -! range, npts2.ge.2. -! if npts2.lt.2, the routine will end with ier = 6. -! -! points - double precision -! vector of dimension npts2, the first (npts2-2) -! elements of which are the user provided break -! points. if these points do not constitute an -! ascending sequence there will be an automati! -! sorting. -! -! epsabs - double precision -! absolute accuracy requested -! epsrel - double precision -! relative accuracy requested -! if epsabs.le.0 -! and epsrel.lt.max(50*rel.mach.acc.,0.5d-28), -! the routine will end with ier = 6. -! -! limit - integer -! gives an upper bound on the number of subintervals -! in the partition of (a,b), limit.ge.npts2 -! if limit.lt.npts2, the routine will end with -! ier = 6. -! -! on return -! result - double precision -! approximation to the integral -! -! abserr - double precision -! estimate of the modulus of the absolute error, -! which should equal or exceed abs(i-result) -! -! neval - integer -! number of integrand evaluations -! -! ier - integer -! ier = 0 normal and reliable termination of the -! routine. it is assumed that the requested -! accuracy has been achieved. -! ier.gt.0 abnormal termination of the routine. -! the estimates for integral and error are -! less reliable. it is assumed that the -! requested accuracy has not been achieved. -! error messages -! ier = 1 maximum number of subdivisions allowed -! has been achieved. one can allow more -! subdivisions by increasing the value of -! limit (and taking the according dimension -! adjustments into account). however, if -! this yields no improvement it is advised -! to analyze the integrand in order to -! determine the integration difficulties. if -! the position of a local difficulty can be -! determined (i.e. singularity, -! discontinuity within the interval), it -! should be supplied to the routine as an -! element of the vector points. if necessary -! an appropriate special-purpose integrator -! must be used, which is designed for -! handling the type of difficulty involved. -! = 2 the occurrence of roundoff error is -! detected, which prevents the requested -! tolerance from being achieved. -! the error may be under-estimated. -! = 3 extremely bad integrand behaviour occurs -! at some points of the integration -! interval. -! = 4 the algorithm does not converge. -! roundoff error is detected in the -! extrapolation table. it is presumed that -! the requested tolerance cannot be -! achieved, and that the returned result is -! the best which can be obtained. -! = 5 the integral is probably divergent, or -! slowly convergent. it must be noted that -! divergence can occur with any other value -! of ier.gt.0. -! = 6 the input is invalid because -! npts2.lt.2 or -! break points are specified outside -! the integration range or -! (epsabs.le.0 and -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) -! or limit.lt.npts2. -! result, abserr, neval, last, rlist(1), -! and elist(1) are set to zero. alist(1) and -! blist(1) are set to a and b respectively. -! -! alist - double precision -! vector of dimension at least limit, the first -! last elements of which are the left end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! blist - double precision -! vector of dimension at least limit, the first -! last elements of which are the right end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! rlist - double precision -! vector of dimension at least limit, the first -! last elements of which are the integral -! approximations on the subintervals -! -! elist - double precision -! vector of dimension at least limit, the first -! last elements of which are the moduli of the -! absolute error estimates on the subintervals -! -! pts - double precision -! vector of dimension at least npts2, containing the -! integration limits and the break points of the -! interval in ascending sequence. -! -! level - integer -! vector of dimension at least limit, containing the -! subdivision levels of the subinterval, i.e. if -! (aa,bb) is a subinterval of (p1,p2) where p1 as -! well as p2 is a user-provided break point or -! integration limit, then (aa,bb) has level l if -! abs(bb-aa) = abs(p2-p1)*2**(-l). -! -! ndin - integer -! vector of dimension at least npts2, after first -! integration over the intervals (pts(i)),pts(i+1), -! i = 0,1, ..., npts2-2, the error estimates over -! some of the intervals may have been increased -! artificially, in order to put their subdivision -! forward. if this happens for the subinterval -! numbered k, ndin(k) is put to 1, otherwise -! ndin(k) = 0. -! -! iord - integer -! vector of dimension at least limit, the first k -! elements of which are pointers to the -! error estimates over the subintervals, -! such that elist(iord(1)), ..., elist(iord(k)) -! form a decreasing sequence, with k = last -! if last.le.(limit/2+2), and k = limit+1-last -! otherwise -! -! last - integer -! number of subintervals actually produced in the -! subdivisions process -! -c***references (none) -c***routines called d1mach,dqelg,dqk21,dqpsrt -c***end prologue dqagpe - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result1,abserr - integer, intent(out) :: neval,ier - double precision,dimension(limit), intent(out) :: alist, blist - double precision,dimension(limit), intent(out) :: rlist, elist - double precision,dimension(npts+2),intent(out) :: pts - integer, dimension(limit), intent(out) :: iord, level - integer, dimension(npts+2), intent(out) :: ndin - integer ::last - double precision :: f -! locals - double precision :: area,area1,area12,area2,a1, - * a2,b1,b2,correc,abseps,defabs,defab1,defab2, - * dres,epmach,erlarg,erlast,errbnd, - * errmax,error1,erro12,error2,errsum,ertest,oflow, - * resa,resabs,reseps,sign,temp,uflow, hSplit - double precision, dimension(3) :: res3la(3) - double precision, dimension(52) :: rlist2(52) - integer :: i,id,ierro,ind1,ind2,ip1,iroff1,iroff2,iroff3,j, - * jlow,jupbnd,k,ksgn,ktmin,levcur,levmax,maxerr, - * nint,nintp1,npts2,nres,nrmax,numrl2 - logical :: extrap,noext - external f -! -! - -! -! -! the dimension of rlist2 is determined by the value of -! limexp in subroutine epsalg (rlist2 should be of dimension -! (limexp+2) at least). -! -! -! list of major variables -! ----------------------- -! -! alist - list of left end points of all subintervals -! considered up to now -! blist - list of right end points of all subintervals -! considered up to now -! rlist(i) - approximation to the integral over -! (alist(i),blist(i)) -! rlist2 - array of dimension at least limexp+2 -! containing the part of the epsilon table which -! is still needed for further computations -! elist(i) - error estimate applying to rlist(i) -! maxerr - pointer to the interval with largest error -! estimate -! errmax - elist(maxerr) -! erlast - error on the interval currently subdivided -! (before that subdivision has taken place) -! area - sum of the integrals over the subintervals -! errsum - sum of the errors over the subintervals -! errbnd - requested accuracy max(epsabs,epsrel* -! abs(result)) -! *****1 - variable for the left subinterval -! *****2 - variable for the right subinterval -! last - index for subdivision -! nres - number of calls to the extrapolation routine -! numrl2 - number of elements in rlist2. if an appropriate -! approximation to the compounded integral has -! been obtained, it is put in rlist2(numrl2) after -! numrl2 has been increased by one. -! erlarg - sum of the errors over the intervals larger -! than the smallest interval considered up to now -! extrap - logical variable denoting that the routine -! is attempting to perform extrapolation. i.e. -! before subdividing the smallest interval we -! try to decrease the value of erlarg. -! noext - logical variable denoting that extrapolation is -! no longer allowed (true-value) -! -! machine dependent constants -! --------------------------- -! -! epmach is the largest relative spacing. -! uflow is the smallest positive magnitude. -! oflow is the largest positive magnitude. -! -c***first executable statement dqagpe - epmach = d1mach(4) - uflow = d1mach(1) - oflow = d1mach(2) -! -! test on validity of parameters -! ----------------------------- -! - hSplit = 0.2D0 - ier = 0 - neval = 0 - last = 0 - result1 = 0.0d+00 - abserr = 0.0d+00 - alist(1) = a - blist(1) = b - rlist(1) = 0.0d+00 - elist(1) = 0.0d+00 - iord(1) = 0 - level(1) = 0 - npts2 = npts+2 - if((npts2.lt.2).or.(limit.le.npts).or. - & ((epsabs.le.0.0d+00).and. - & (epsrel.lt.dmax1(0.5d+02*epmach,0.5d-28)))) then - ier = 6 - go to 999 - endif - - sign = 1.0d+00 - if(a.gt.b) then - go to 999 - endif - if (npts>0) then - if(any(points(1:npts)<=a).or.any(b<=points(1:npts))) then - ier = 6 - go to 999 - endif - endif -! -! if any break points are provided, sort them into an -! ascending sequence. -! - pts(1) = a - pts(npts+2) = b - do i = 1,npts - pts(i+1) = minval(points(i:npts)) - enddo -! -! compute first integral and error approximations. -! ------------------------------------------------ -! - nint = npts+1; - a1 = pts(1); - resabs = 0.0d+00 - do i = 1,nint - b1 = pts(i+1) - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,defabs,resa) - !call dqk15(f,a1,b1,area1,error1,defabs,resa) - else - call dqkl9(f,a1,b1,area1,error1,defabs,resa) - endif - abserr = abserr + error1 - result1 = result1 + area1 - ndin(i) = 0 - if(error1.eq.resa.and.error1.ne.0.0d+00) ndin(i) = 1 - resabs = resabs + defabs - level(i) = 0 - elist(i) = error1 - alist(i) = a1 - blist(i) = b1 - rlist(i) = area1 - iord(i) = i - a1 = b1 - enddo !50 continue - errsum = 0.0d+00 - do i = 1,nint - if(ndin(i).eq.1) elist(i) = abserr - errsum = errsum+elist(i) - enddo !55 continue -! -! test on accuracy. -! - last = nint - neval = 21*nint - dres = dabs(result1) - errbnd = dmax1(epsabs,epsrel*dres) - if(abserr.le.0.1d+03*epmach*resabs.and.abserr.gt.errbnd) ier = 2 - if(nint.eq.1) go to 80 - do 70 i = 1,npts - jlow = i+1 - ind1 = iord(i) - do 60 j = jlow,nint - ind2 = iord(j) - if(elist(ind1).gt.elist(ind2)) go to 60 - ind1 = ind2 - k = j - 60 continue - if(ind1.eq.iord(i)) go to 70 - iord(k) = iord(i) - iord(i) = ind1 - 70 continue - if(limit.lt.npts2) ier = 1 - 80 if(ier.ne.0.or.abserr.le.errbnd) go to 210 - -! -! initialization -! -------------- -! - rlist2(1) = result1 - maxerr = iord(1) - errmax = elist(maxerr) - area = result1 - nrmax = 1 - nres = 0 - numrl2 = 1 - ktmin = 0 - extrap = .false. - noext = .false. - erlarg = errsum - ertest = errbnd - levmax = 1 - iroff1 = 0 - iroff2 = 0 - iroff3 = 0 - ierro = 0 - abserr = oflow - ksgn = -1 - if(dres.ge.(0.1d+01-0.5d+02*epmach)*resabs) ksgn = 1 -! -! main do-loop -! ------------ -! - do 160 last = npts2,limit -! -! bisect the subinterval with the nrmax-th largest error -! estimate. -! - levcur = level(maxerr)+1 - a1 = alist(maxerr) - b1 = 0.5d+00*(alist(maxerr)+blist(maxerr)) - a2 = b1 - b2 = blist(maxerr) - erlast = errmax - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,resa,defab1) - call dqk21(f,a2,b2,area2,error2,resa,defab2) - !call dqk15(f,a1,b1,area1,error1,resa,defab1) - !call dqk15(f,a2,b2,area2,error2,resa,defab2) - else - - call dqkl9(f,a1,b1,area1,error1,resa,defab1) - call dqkl9(f,a2,b2,area2,error2,resa,defab2) - endif -! -! improve previous approximations to integral -! and error and test for accuracy. -! - neval = neval+42 - area12 = area1+area2 - erro12 = error1+error2 - errsum = errsum+erro12-errmax - area = area+area12-rlist(maxerr) - if(defab1.eq.error1.or.defab2.eq.error2) go to 95 - if(dabs(rlist(maxerr)-area12).gt.0.1d-04*dabs(area12) - * .or.erro12.lt.0.99d+00*errmax) go to 90 - if(extrap) iroff2 = iroff2+1 - if(.not.extrap) iroff1 = iroff1+1 - 90 if(last.gt.10.and.erro12.gt.errmax) iroff3 = iroff3+1 - 95 level(maxerr) = levcur - level(last) = levcur - rlist(maxerr) = area1 - rlist(last) = area2 - errbnd = dmax1(epsabs,epsrel*dabs(area)) -! -! test for roundoff error and eventually set error flag. -! - if(iroff1+iroff2.ge.10.or.iroff3.ge.20) ier = 2 - if(iroff2.ge.5) ierro = 3 -! -! set error flag in the case that the number of -! subintervals equals limit. -! - if(last.eq.limit) ier = 1 -! -! set error flag in the case of bad integrand behaviour -! at a point of the integration range -! - if(dmax1(dabs(a1),dabs(b2)).le.(0.1d+01+0.1d+03*epmach)* - * (dabs(a2)+0.1d+04*uflow)) ier = 4 -! -! append the newly-created intervals to the list. -! - if(error2.gt.error1) go to 100 - alist(last) = a2 - blist(maxerr) = b1 - blist(last) = b2 - elist(maxerr) = error1 - elist(last) = error2 - go to 110 - 100 alist(maxerr) = a2 - alist(last) = a1 - blist(last) = b1 - rlist(maxerr) = area2 - rlist(last) = area1 - elist(maxerr) = error2 - elist(last) = error1 -! -! call subroutine dqpsrt to maintain the descending ordering -! in the list of error estimates and select the subinterval -! with nrmax-th largest error estimate (to be bisected next). -! - 110 call dqpsrt(limit,last,maxerr,errmax,elist,iord,nrmax) -! ***jump out of do-loop - if(errsum.le.errbnd) go to 190 -! ***jump out of do-loop - if(ier.ne.0) go to 170 - if(noext) go to 160 - erlarg = erlarg-erlast - if(levcur+1.le.levmax) erlarg = erlarg+erro12 - if(extrap) go to 120 -! -! test whether the interval to be bisected next is the -! smallest interval. -! - if(level(maxerr)+1.le.levmax) go to 160 - extrap = .true. - nrmax = 2 - 120 if(ierro.eq.3.or.erlarg.le.ertest) go to 140 -! -! the smallest interval has the largest error. -! before bisecting decrease the sum of the errors over -! the larger intervals (erlarg) and perform extrapolation. -! - id = nrmax - jupbnd = last - if(last.gt.(2+limit/2)) jupbnd = limit+3-last - do 130 k = id,jupbnd - maxerr = iord(nrmax) - errmax = elist(maxerr) -! ***jump out of do-loop - if(level(maxerr)+1.le.levmax) go to 160 - nrmax = nrmax+1 - 130 continue -! -! perform extrapolation. -! - 140 numrl2 = numrl2+1 - rlist2(numrl2) = area - if(numrl2.le.2) go to 155 - call dqelg(numrl2,rlist2,reseps,abseps,res3la,nres) - ktmin = ktmin+1 - if(ktmin.gt.5.and.abserr.lt.0.1d-02*errsum) ier = 5 - if(abseps.ge.abserr) go to 150 - ktmin = 0 - abserr = abseps - result1 = reseps - correc = erlarg - ertest = dmax1(epsabs,epsrel*dabs(reseps)) -! ***jump out of do-loop - if(abserr.lt.ertest) go to 170 -! -! prepare bisection of the smallest interval. -! - 150 if(numrl2.eq.1) noext = .true. - if(ier.ge.5) go to 170 - 155 maxerr = iord(1) - errmax = elist(maxerr) - nrmax = 1 - extrap = .false. - levmax = levmax + 1 - erlarg = errsum - 160 continue -! -! set the final result. -! --------------------- -! -! - 170 if(abserr.eq.oflow) go to 190 - if((ier+ierro).eq.0) go to 180 - if(ierro.eq.3) abserr = abserr+correc - if(ier.eq.0) ier = 3 - if(result1.ne.0.0d+00.and.area.ne.0.0d+00)go to 175 - if(abserr.gt.errsum)go to 190 - if(area.eq.0.0d+00) go to 210 - go to 180 - 175 if(abserr/dabs(result1).gt.errsum/dabs(area))go to 190 -! -! test on divergence. -! - 180 if(ksgn.eq.(-1).and.dmax1(dabs(result1),dabs(area)).le. - * resabs*0.1d-01) go to 210 - if(0.1d-01.gt.(result1/area).or.(result1/area).gt.0.1d+03.or. - * errsum.gt.dabs(area)) ier = 6 - go to 210 -! -! compute global integral sum. -! - 190 result1 = 0.0d+00 - do 200 k = 1,last - result1 = result1+rlist(k) - 200 continue - abserr = errsum - 210 if(ier.gt.2) ier = ier-1 - result1 = result1*sign - 999 return - end subroutine dqagpe - subroutine dqk21(f,a,b,result1,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk21 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 21-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk21 -c - double precision,intent(in) :: a,b - double precision, intent(out) :: abserr, result1,resabs,resasc - double precision :: f,absc,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth, - * resg,resk,reskh,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(10),fv2(10),wg(5),wgk(11),xgk(11) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 21-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 10-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 10-point gauss rule -c -c wgk - weights of the 21-point kronrod rule -c -c wg - weights of the 10-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.0666713443 0868813759 3568809893 332 d0 / - data wg ( 2) / 0.1494513491 5058059314 5776339657 697 d0 / - data wg ( 3) / 0.2190863625 1598204399 5534934228 163 d0 / - data wg ( 4) / 0.2692667193 0999635509 1226921569 469 d0 / - data wg ( 5) / 0.2955242247 1475287017 3892994651 338 d0 / -c - data xgk ( 1) / 0.9956571630 2580808073 5527280689 003 d0 / - data xgk ( 2) / 0.9739065285 1717172007 7964012084 452 d0 / - data xgk ( 3) / 0.9301574913 5570822600 1207180059 508 d0 / - data xgk ( 4) / 0.8650633666 8898451073 2096688423 493 d0 / - data xgk ( 5) / 0.7808177265 8641689706 3717578345 042 d0 / - data xgk ( 6) / 0.6794095682 9902440623 4327365114 874 d0 / - data xgk ( 7) / 0.5627571346 6860468333 9000099272 694 d0 / - data xgk ( 8) / 0.4333953941 2924719079 9265943165 784 d0 / - data xgk ( 9) / 0.2943928627 0146019813 1126603103 866 d0 / - data xgk ( 10) / 0.1488743389 8163121088 4826001129 720 d0 / - data xgk ( 11) / 0.0000000000 0000000000 0000000000 000 d0 / -c - data wgk ( 1) / 0.0116946388 6737187427 8064396062 192 d0 / - data wgk ( 2) / 0.0325581623 0796472747 8818972459 390 d0 / - data wgk ( 3) / 0.0547558965 7435199603 1381300244 580 d0 / - data wgk ( 4) / 0.0750396748 1091995276 7043140916 190 d0 / - data wgk ( 5) / 0.0931254545 8369760553 5065465083 366 d0 / - data wgk ( 6) / 0.1093871588 0229764189 9210590325 805 d0 / - data wgk ( 7) / 0.1234919762 6206585107 7958109831 074 d0 / - data wgk ( 8) / 0.1347092173 1147332592 8054001771 707 d0 / - data wgk ( 9) / 0.1427759385 7706008079 7094273138 717 d0 / - data wgk ( 10) / 0.1477391049 0133849137 4841515972 068 d0 / - data wgk ( 11) / 0.1494455540 0291690566 4936468389 821 d0 / -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk21 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 21-point kronrod approximation to -c the integral, and estimate the absolute error. -c - resg = 0.0d+00 - fc = f(centr) - resk = wgk(11)*fc - resabs = dabs(resk) - do 10 j=1,5 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,5 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(11)*dabs(fc-reskh) - do 20 j=1,10 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result1 = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0d0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk21 - subroutine dqk15(f,a,b,result1,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision,intent(in) :: a,b - double precision, intent(out) :: abserr, result1,resabs,resasc - double precision :: f, absc,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth, - * resg,resk,reskh,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 7-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point gauss rule -c -c wgk - weights of the 15-point kronrod rule -c -c wg - weights of the 7-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.129484966168869693270611432679082d0 / - data wg ( 2) / 0.279705391489276667901467771423780d0 / - data wg ( 3) / 0.381830050505118944950369775488975d0 / - data wg ( 4) / 0.417959183673469387755102040816327d0 / - - data xgk ( 1) / 0.991455371120812639206854697526329d0 / - data xgk ( 2) / 0.949107912342758524526189684047851d0 / - data xgk ( 3) / 0.864864423359769072789712788640926d0 / - data xgk ( 4) / 0.741531185599394439863864773280788d0 / - data xgk ( 5) / 0.586087235467691130294144838258730d0 / - data xgk ( 6) / 0.405845151377397166906606412076961d0 / - data xgk ( 7) / 0.207784955007898467600689403773245d0 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.022935322010529224963732008058970d0/ - data wgk ( 2) / 0.063092092629978553290700663189204d0 / - data wgk ( 3) / 0.104790010322250183839876322541518d0 / - data wgk ( 4) / 0.140653259715525918745189590510238d0 / - data wgk ( 5) / 0.169004726639267902826583426598550d0 / - data wgk ( 6) / 0.190350578064785409913256402421014d0 / - data wgk ( 7) / 0.204432940075298892414161999234649d0 / - data wgk ( 8) / 0.209482141084727828012999174891714d0 / - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resg = wg(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result1 = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0D0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk15 - subroutine dqk9(f,a,b,result1,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision,intent(in) :: a,b - double precision, intent(out) :: abserr, result1,resabs,resasc - double precision :: f,absc,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth, - * resg,resk0,resk,reskh,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -! xgk(4), xgk(8) abscissae of the 3-point gauss rule -c xgk(2), xgk(4),xgk(6), xgk(8) ... abscissae of the 7-point -c kronrod rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point kronrod rule -c -c wgk - weights of the 15-point kronrod rule -! -! wgk0 - weights of the 7-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - data wg ( 1) / 0.5555555555555555D+00/ - data wg ( 2) / 0.8888888888888889D+00/ - - data wgk0 ( 1) / 0.1046562260264673D+00/ - data wgk0 ( 2) / 0.2684880898683335D+00/ - data wgk0 ( 3) / 0.4013974147759622D+00/ - data wgk0 ( 4) / 0.4509165386584741D+00/ - - data xgk ( 1) / 0.9938319632127550D+00/ - data xgk ( 2) / 0.9604912687080203D+00/ - data xgk ( 3) / 0.8884592328722570D+00 / - data xgk ( 4) / 0.7745966692414834D+00/ - data xgk ( 5) / 0.6211029467372264D+00/ - data xgk ( 6) / 0.4342437493468026D+00/ - data xgk ( 7) / 0.2233866864289669D+00 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.1700171962994028D-01/ - data wgk ( 2) / 0.5160328299707982D-01/ - data wgk ( 3) / 0.9292719531512452D-01/ - data wgk ( 4) / 0.1344152552437843D+00/ - data wgk ( 5) / 0.1715119091363914D+00/ - data wgk ( 6) / 0.2006285293769890D+00/ - data wgk ( 7) / 0.2191568584015875D+00/ - data wgk ( 8) / 0.2255104997982067D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resk0 = wgk0(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(4) + fv2(4)) - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result1 = resk - call dea3(resg,resk0,resk,abserr,result1) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0)) - & * 10.0D0, abserr) - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - - end subroutine dqk9 - subroutine dqkl9(f,a,b,result1,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision,intent(in) :: a,b - double precision, intent(out) :: abserr, result1,resabs,resasc - double precision :: f,absc,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth, - * resg,resk0,resk,reskh,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(3),wgk(5),xgk(5) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 9-point Gauss-kronrod-lobatto rule -! xgk(1), xgk(5) abscissae of the 3-point gauss-lobatto rule -c xgk(1), xgk(3),xgk(5) abscissae of the 5-point -c kronrod rule -c xgk(2), xgk(4), ... abscissae which are optimally -c added to the 5-point kronrod rule -c -c wgk - weights of the 9-point kronrod rule -! -! wgk0 - weights of the 5-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - - data wg ( 1) / 0.33333333333333333333333333333333333D+00/ - data wg ( 2) / 0.13333333333333333333333333333333333D+01/ - - data wgk0 ( 1) / 0.1000000000000000D+00/ - data wgk0 ( 2) / 0.5444444444444445D+00/ - data wgk0 ( 3) / 0.7111111111111111D+00/ - - data xgk ( 1) / 0.1000000000000000D+01/ - data xgk ( 2) / 0.8904055275126688D+00/ - data xgk ( 3) / 0.6546536707079772D+00/ - data xgk ( 4) / 0.3409822659109930D+00/ - data xgk ( 5) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.3064373897707232D-01/ - data wgk ( 2) / 0.1792626995532074D+00/ - data wgk ( 3) / 0.2839787780481211D+00/ - data wgk ( 4) / 0.3342337398164177D+00/ - data wgk ( 5) / 0.3437620872103631D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(5)*fc - resk0 = wgk0(3)*fc - resabs = dabs(resk) - do 10 j=1,2 - jtw = 2*j - 1 - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(1) + fv2(1)) - do 15 j = 1,2 - jtwm1 = 2*j - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(5)*dabs(fc-reskh) - do 20 j=1,4 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result1 = resk - call dea3(resg,resk0,resk,abserr,result1) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0))* 10.0D0,abserr) - - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqkl9 - subroutine dqpsrt(limit,last,maxerr,ermax,elist,iord,nrmax) - implicit none -c***begin prologue dqpsrt -c***refer to dqage,dqagie,dqagpe,dqawse -c***routines called (none) -c***revision date 810101 (yymmdd) -c***keywords sequential sorting -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose this routine maintains the descending ordering in the -c list of the local error estimated resulting from the -c interval subdivision process. at each call two error -c estimates are inserted using the sequential search -c method, top-down for the largest error estimate and -c bottom-up for the smallest error estimate. -c***description -c -c ordering routine -c standard fortran subroutine -c double precision version -c -c parameters (meaning at output) -c limit - integer -c maximum number of error estimates the list -c can contain -c -c last - integer -c number of error estimates currently in the list -c -c maxerr - integer -c maxerr points to the nrmax-th largest error -c estimate currently in the list -c -c ermax - double precision -c nrmax-th largest error estimate -c ermax = elist(maxerr) -c -c elist - double precision -c vector of dimension last containing -c the error estimates -c -c iord - integer -c vector of dimension last, the first k elements -c of which contain pointers to the error -c estimates, such that -c elist(iord(1)),..., elist(iord(k)) -c form a decreasing sequence, with -c k = last if last.le.(limit/2+2), and -c k = limit+1-last otherwise -c -c nrmax - integer -c maxerr = iord(nrmax) -c -c***end prologue dqpsrt -c - double precision elist,ermax,errmax,errmin - integer i,ibeg,ido,iord,isucc,j,jbnd,jupbn,k,last,limit,maxerr, - * nrmax - dimension elist(last),iord(last) -c -c check whether the list contains more than -c two error estimates. -c -c***first executable statement dqpsrt - if(last.gt.2) go to 10 - iord(1) = 1 - iord(2) = 2 - go to 90 -c -c this part of the routine is only executed if, due to a -c difficult integrand, subdivision increased the error -c estimate. in the normal case the insert procedure should -c start after the nrmax-th largest error estimate. -c - 10 errmax = elist(maxerr) - if(nrmax.eq.1) go to 30 - ido = nrmax-1 - do 20 i = 1,ido - isucc = iord(nrmax-1) -c ***jump out of do-loop - if(errmax.le.elist(isucc)) go to 30 - iord(nrmax) = isucc - nrmax = nrmax-1 - 20 continue -c -c compute the number of elements in the list to be maintained -c in descending order. this number depends on the number of -c subdivisions still allowed. -c - 30 jupbn = last - if(last.gt.(limit/2+2)) jupbn = limit+3-last - errmin = elist(last) -c -c insert errmax by traversing the list top-down, -c starting comparison from the element elist(iord(nrmax+1)). -c - jbnd = jupbn-1 - ibeg = nrmax+1 - if(ibeg.gt.jbnd) go to 50 - do 40 i=ibeg,jbnd - isucc = iord(i) -c ***jump out of do-loop - if(errmax.ge.elist(isucc)) go to 60 - iord(i-1) = isucc - 40 continue - 50 iord(jbnd) = maxerr - iord(jupbn) = last - go to 90 -c -c insert errmin by traversing the list bottom-up. -c - 60 iord(i-1) = maxerr - k = jbnd - do 70 j=i,jbnd - isucc = iord(k) -c ***jump out of do-loop - if(errmin.lt.elist(isucc)) go to 80 - iord(k+1) = isucc - k = k-1 - 70 continue - iord(i) = last - go to 90 - 80 iord(k+1) = last -c -c set maxerr and ermax. -c - 90 maxerr = iord(nrmax) - ermax = elist(maxerr) - return - end subroutine dqpsrt - subroutine dqelg(n,epstab,result1,abserr,res3la,nres) - implicit none -c***begin prologue dqelg -c***refer to dqagie,dqagoe,dqagpe,dqagse -c***routines called d1mach -c***revision date 830518 (yymmdd) -c***keywords epsilon algorithm, convergence acceleration, -c extrapolation -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math & progr. div. - k.u.leuven -c***purpose the routine determines the limit of a given sequence of -c approximations, by means of the epsilon algorithm of -c p.wynn. an estimate of the absolute error is also given. -c the condensed epsilon table is computed. only those -c elements needed for the computation of the next diagonal -c are preserved. -c***description -c -c epsilon algorithm -c standard fortran subroutine -c double precision version -c -c parameters -c n - integer -c epstab(n) contains the new element in the -c first column of the epsilon table. -c -c epstab - double precision -c vector of dimension 52 containing the elements -c of the two lower diagonals of the triangular -c epsilon table. the elements are numbered -c starting at the right-hand corner of the -c triangle. -c -c result - double precision -c resulting approximation to the integral -c -c abserr - double precision -c estimate of the absolute error computed from -c result and the 3 previous results -c -c res3la - double precision -c vector of dimension 3 containing the last 3 -c results -c -c nres - integer -c number of calls to the routine -c (should be zero at first call) -c -c***end prologue dqelg -c - double precision abserr,dabs,delta1,delta2,delta3,dmax1, - * epmach,epsinf,epstab,error,err1,err2,err3,e0,e1,e1abs,e2,e3, - * oflow,res,result1,res3la,ss,tol1,tol2,tol3 - integer i,ib,ib2,ie,indx,k1,k2,k3,limexp,n,newelm,nres,num - dimension epstab(52),res3la(3) -c -c list of major variables -c ----------------------- -c -c e0 - the 4 elements on which the computation of a new -c e1 element in the epsilon table is based -c e2 -c e3 e0 -c e3 e1 new -c e2 -c newelm - number of elements to be computed in the new -c diagonal -c error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2) -c result - the element in the new diagonal with least value -c of error -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c oflow is the largest positive magnitude. -c limexp is the maximum number of elements the epsilon -c table can contain. if this number is reached, the upper -c diagonal of the epsilon table is deleted. -c -c***first executable statement dqelg - epmach = d1mach(4) - oflow = d1mach(2) - nres = nres+1 - abserr = oflow - result1 = epstab(n) - if(n.lt.3) go to 100 - limexp = 50 - epstab(n+2) = epstab(n) - newelm = (n-1)/2 - epstab(n) = oflow - num = n - k1 = n - do 40 i = 1,newelm - k2 = k1-1 - k3 = k1-2 - res = epstab(k1+2) - e0 = epstab(k3) - e1 = epstab(k2) - e2 = res - e1abs = dabs(e1) - delta2 = e2-e1 - err2 = dabs(delta2) - tol2 = dmax1(dabs(e2),e1abs)*epmach - delta3 = e1-e0 - err3 = dabs(delta3) - tol3 = dmax1(e1abs,dabs(e0))*epmach - if(err2.gt.tol2.or.err3.gt.tol3) go to 10 -c -c if e0, e1 and e2 are equal to within machine -c accuracy, convergence is assumed. -c result1 = e2 -c abserr = abs(e1-e0)+abs(e2-e1) -c - result1 = res - abserr = err2+err3 -c ***jump out of do-loop - go to 100 - 10 e3 = epstab(k1) - epstab(k1) = e1 - delta1 = e1-e3 - err1 = dabs(delta1) - tol1 = dmax1(e1abs,dabs(e3))*epmach -c -c if two elements are very close to each other, omit -c a part of the table by adjusting the value of n -c - if(err1.le.tol1.or.err2.le.tol2.or.err3.le.tol3) go to 20 - ss = 0.1d+01/delta1+0.1d+01/delta2-0.1d+01/delta3 - epsinf = dabs(ss*e1) -c -c test to detect irregular behaviour in the table, and -c eventually omit a part of the table adjusting the value -c of n. -c - if(epsinf.gt.0.1d-03) go to 30 - 20 n = i+i-1 -c ***jump out of do-loop - go to 50 -c -c compute a new element and eventually adjust -c the value of result. -c - 30 res = e1+0.1d+01/ss - epstab(k1) = res - k1 = k1-2 - error = err2+dabs(res-e2)+err3 - if(error.gt.abserr) go to 40 - abserr = error - result1 = res - 40 continue -c -c shift the table. -c - 50 if(n.eq.limexp) n = 2*(limexp/2)-1 - ib = 1 - if((num/2)*2.eq.num) ib = 2 - ie = newelm+1 - do 60 i=1,ie - ib2 = ib+2 - epstab(ib) = epstab(ib2) - ib = ib2 - 60 continue - if(num.eq.n) go to 80 - indx = num-n+1 - do 70 i = 1,n - epstab(i)= epstab(indx) - indx = indx+1 - 70 continue - 80 if(nres.ge.4) go to 90 - res3la(nres) = result1 - abserr = oflow - go to 100 -c -c compute error estimate -c - 90 abserr = dabs(result1-res3la(3))+dabs(result1-res3la(2)) - * +dabs(result1-res3la(1)) - res3la(1) = res3la(2) - res3la(2) = res3la(3) - res3la(3) = result1 - 100 abserr = dmax1(abserr,0.5d+01*epmach*dabs(result1)) - return - end subroutine dqelg - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - end module AdaptiveGaussKronrod \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyf b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyf deleted file mode 100644 index 03410ec..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyf +++ /dev/null @@ -1,157 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - -python module dqk21__user__routines - interface dqk21_user_interface - function f(centr) result (fc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod:dqk21:unknown_interface - double precision :: centr - double precision :: fc - end function f - end interface dqk21_user_interface -end python module dqk21__user__routines -python module dqk15__user__routines - interface dqk15_user_interface - function f(centr) result (fc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod:dqk15:unknown_interface - double precision :: centr - double precision :: fc - end function f - end interface dqk15_user_interface -end python module dqk15__user__routines -python module dqk9__user__routines - interface dqk9_user_interface - function f(centr) result (fc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod:dqk9:unknown_interface - double precision :: centr - double precision :: fc - end function f - end interface dqk9_user_interface -end python module dqk9__user__routines -python module dqkl9__user__routines - interface dqkl9_user_interface - function f(centr) result (fc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod:dqkl9:unknown_interface - double precision :: centr - double precision :: fc - end function f - end interface dqkl9_user_interface -end python module dqkl9__user__routines -python module adaptivegausskronrod ! in - interface ! in :adaptivegausskronrod - module functioninterface ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90 - interface ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:functioninterface - function f(z) result (val) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:functioninterface:unknown_interface - double precision intent(in) :: z - double precision :: val - end function f - end interface - end module functioninterface - module adaptivegausskronrod ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90 - subroutine dea3(e0,e1,e2,abserr,result1) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - double precision intent(in) :: e0 - double precision intent(in) :: e1 - double precision intent(in) :: e2 - double precision intent(out) :: abserr - double precision intent(out) :: result1 - end subroutine dea3 - subroutine dqagp(f,a,b,npts,points,epsabs,epsrel,limit,result1,abserr,neval,ier) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - external f - double precision intent(in) :: a - double precision intent(in) :: b - integer optional,intent(in),check(len(points)>=npts),depend(points) :: npts=len(points) - double precision dimension(npts),intent(in) :: points - double precision intent(in) :: epsabs - double precision intent(in) :: epsrel - integer intent(in) :: limit - double precision intent(out) :: result1 - double precision intent(out) :: abserr - integer intent(out) :: neval - integer intent(out) :: ier - end subroutine dqagp - subroutine dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result1,abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin,last) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - external f - double precision intent(in) :: a - double precision intent(in) :: b - integer optional,intent(in),check(len(points)>=npts),depend(points) :: npts=len(points) - double precision dimension(npts),intent(in) :: points - double precision intent(in) :: epsabs - double precision intent(in) :: epsrel - integer intent(in) :: limit - double precision intent(out) :: result1 - double precision intent(out) :: abserr - integer intent(out) :: neval - integer intent(out) :: ier - double precision dimension(limit),intent(out),depend(limit) :: alist - double precision dimension(limit),intent(out),depend(limit) :: blist - double precision dimension(limit),intent(out),depend(limit) :: rlist - double precision dimension(limit),intent(out),depend(limit) :: elist - double precision dimension(npts + 2),intent(out),depend(npts) :: pts - integer dimension(limit),intent(out),depend(limit) :: iord - integer dimension(limit),intent(out),depend(limit) :: level - integer dimension(npts + 2),intent(out),depend(npts) :: ndin - integer :: last - end subroutine dqagpe - subroutine dqk21(f,a,b,result1,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - use dqk21__user__routines - external f - double precision intent(in) :: a - double precision intent(in) :: b - double precision intent(out) :: result1 - double precision intent(out) :: abserr - double precision intent(out) :: resabs - double precision intent(out) :: resasc - end subroutine dqk21 - subroutine dqk15(f,a,b,result1,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - use dqk15__user__routines - external f - double precision intent(in) :: a - double precision intent(in) :: b - double precision intent(out) :: result1 - double precision intent(out) :: abserr - double precision intent(out) :: resabs - double precision intent(out) :: resasc - end subroutine dqk15 - subroutine dqk9(f,a,b,result1,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - use dqk9__user__routines - external f - double precision intent(in) :: a - double precision intent(in) :: b - double precision intent(out) :: result1 - double precision intent(out) :: abserr - double precision intent(out) :: resabs - double precision intent(out) :: resasc - end subroutine dqk9 - subroutine dqkl9(f,a,b,result1,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - use dqkl9__user__routines - external f - double precision intent(in) :: a - double precision intent(in) :: b - double precision intent(out) :: result1 - double precision intent(out) :: abserr - double precision intent(out) :: resabs - double precision intent(out) :: resasc - end subroutine dqkl9 - subroutine dqpsrt(limit,last,maxerr,ermax,elist,iord,nrmax) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - integer :: limit - integer optional,check(len(elist)>=last),depend(elist) :: last=len(elist) - integer :: maxerr - double precision :: ermax - double precision dimension(last) :: elist - integer dimension(last),depend(last) :: iord - integer :: nrmax - end subroutine dqpsrt - subroutine dqelg(n,epstab,result1,abserr,res3la,nres) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - integer :: n - double precision dimension(52) :: epstab - double precision :: result1 - double precision :: abserr - double precision dimension(3) :: res3la - integer :: nres - end subroutine dqelg - function d1mach(i) ! in :adaptivegausskronrod:AdaptiveGaussKronrod.f90:adaptivegausskronrod - integer intent(in) :: i - double precision :: d1mach - end function d1mach - end module adaptivegausskronrod - end interface -end python module adaptivegausskronrod - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/dea.f b/wafo/source/mvnprd/old/mvnprodcorrprb/old/dea.f deleted file mode 100644 index be04810..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/dea.f +++ /dev/null @@ -1,390 +0,0 @@ -C f2py -m -h deamod.pyf dea.f -C f2py integrationmod.pyf integration1Dmodule.f90 .f90 -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -! f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m integrationmod -c integration1Dmodule.f90 - - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - SUBROUTINE DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -C***BEGIN PROLOGUE DEA -C***DATE WRITTEN 800101 (YYMMDD) -C***REVISION DATE 871208 (YYMMDD) -C***CATEGORY NO. E5 -C***KEYWORDS CONVERGENCE ACCELERATION,EPSILON ALGORITHM,EXTRAPOLATION -C***AUTHOR PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. - -C K. U. LEUVEN -C DE DONCKER-KAPENGA, ELISE,WESTERN MICHIGAN UNIVERSITY -C KAHANER, DAVID K., NATIONAL BUREAU OF STANDARDS -C STARKENBURG, C. B., NATIONAL BUREAU OF STANDARDS -C***PURPOSE Given a slowly convergent sequence, this routine attempts -C to extrapolate nonlinearly to a better estimate of the -C sequence's limiting value, thus improving the rate of -C convergence. Routine is based on the epsilon algorithm -C of P. Wynn. An estimate of the absolute error is also -C given. -C***DESCRIPTION -C -C Epsilon algorithm. Standard fortran subroutine. -C Double precision version. -C -C A R G U M E N T S I N T H E C A L L S E Q U E N C E -C -C NEWFLG - LOGICAL (INPUT and OUTPUT) -C On the first call to DEA set NEWFLG to .TRUE. -C (indicating a new sequence). DEA will set NEWFLG -C to .FALSE. -C -C SVALUE - DOUBLE PRECISION (INPUT) -C On the first call to DEA set SVALUE to the first -C term in the sequence. On subsequent calls set -C SVALUE to the subsequent sequence value. -C -C LIMEXP - INTEGER (INPUT) -C An integer equal to or greater than the total -C number of sequence terms to be evaluated. Do not -C change the value of LIMEXP until a new sequence -C is evaluated (NEWFLG=.TRUE.). LIMEXP .GE. 3 -C -C RESULT - DOUBLE PRECISION (OUTPUT) -C Best approximation to the sequence's limit. -C -C ABSERR - DOUBLE PRECISION (OUTPUT) -C Estimate of the absolute error. -C -C EPSTAB - DOUBLE PRECISION (OUTPUT) -C Workvector of DIMENSION at least (LIMEXP+7). -C -C IERR - INTEGER (OUTPUT) -C IERR=0 Normal termination of the routine. -C IERR=1 The input is invalid because LIMEXP.LT.3. -C -C T Y P I C A L P R O B L E M S E T U P -C -C This sample problem uses the trapezoidal rule to evaluate the -C integral of the sin function from 0.0 to 0.5*PI (value = 1.0). The -C program implements the trapezoidal rule 8 times creating an -C increasingly accurate sequence of approximations to the integral. -C Each time the trapezoidal rule is used, it uses twice as many -C panels as the time before. DEA is called to obtain even more -C accurate estimates. -C -C PROGRAM SAMPLE -C IMPLICIT DOUBLE PRECISION (A-H,O-Z) -C DOUBLE PRECISION EPSTAB(57) -CC [57 = LIMEXP + 7] -C LOGICAL NEWFLG -C EXTERNAL F -C DATA LIMEXP/50/ -C WRITE(*,*) ' NO. PANELS TRAP. APPROX' -C * ,' APPROX W/EA ABSERR' -C WRITE(*,*) -C HALFPI = DASIN(1.0D+00) -CC [UPPER INTEGRATION LIMIT = PI/2] -C NEWFLG = .TRUE. -CC [SET FLAG - 1ST DEA CALL] -C DO 10 I = 0,7 -C NPARTS = 2 ** I -C WIDTH = HALFPI/NPARTS -C APPROX = 0.5D+00 * WIDTH * (F(0.0D+00) + F(HALFPI)) -C DO 11 J = 1,NPARTS-1 -C APPROX = APPROX + F(J * WIDTH) * WIDTH -C 11 CONTINUE -CC [END TRAPEZOIDAL RULE APPROX] -C SVALUE = APPROX -CC [SVALUE = NEW SEQUENCE VALUE] -C CALL DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -CC [CALL DEA FOR BETTER ESTIMATE] -C WRITE(*,12) NPARTS,APPROX,RESULT,ABSERR -C 12 FORMAT(' ',I4,T20,F16.13,T40,F16.13,T60,D11.4) -C 10 CONTINUE -C STOP -C END -C -C DOUBLE PRECISION FUNCTION F(X) -C DOUBLE PRECISION X -C F = DSIN(X) -CC [INTEGRAND] -C RETURN -C END -C -C Output from the above program will be: -C -C NO. PANELS TRAP. APPROX APPROX W/EA ABSERR -C -C 1 .7853981633974 .7853981633974 .7854D+00 -C 2 .9480594489685 .9480594489685 .9760D+00 -C 4 .9871158009728 .9994567212570 .2141D+00 -C 8 .9967851718862 .9999667417647 .3060D-02 -C 16 .9991966804851 .9999998781041 .6094D-03 -C 32 .9997991943200 .9999999981026 .5767D-03 -C 64 .9999498000921 .9999999999982 .3338D-04 -C 128 .9999874501175 1.0000000000000 .1238D-06 -C -C----------------------------------------------------------------------- -C***REFERENCES "Acceleration de la convergence en analyse numerique", -C C. Brezinski, "Lecture Notes in Math.", vol. 584, -C Springer-Verlag, New York, 1977. -C***ROUTINES CALLED D1MACH,XERROR -C***END PROLOGUE DEA - double precision, dimension(LIMEXP+7), intent(inout) :: EPSTAB - double precision, intent(out) :: RESULT !, ABSERR - double precision, intent(inout) :: ABSERR - double precision, intent(in) :: SVALUE - INTEGER, INTENT(IN) :: LIMEXP - INTEGER, INTENT(OUT) :: IERR - LOGICAL, intent(INOUT) :: NEWFLG - DOUBLE PRECISION :: DELTA1,DELTA2,DELTA3,DRELPR,DEPRN, - 1 ERROR,ERR1,ERR2,ERR3,E0,E1,E2,E3,RES, - 2 SS,TOL1,TOL2,TOL3 - double precision, dimension(3) :: RES3LA - INTEGER I,IB,IB2,IE,IN,K1,K2,K3,N,NEWELM,NUM,NRES -C -C -C LIMEXP is the maximum number of elements the -C epsilon table data can contain. The epsilon table -C is stored in the first (LIMEXP+2) entries of EPSTAB. -C -C -C LIST OF MAJOR VARIABLES -C ----------------------- -C E0,E1,E2,E3 - DOUBLE PRECISION -C The 4 elements on which the computation of -C a new element in the epsilon table is based. -C NRES - INTEGER -C Number of extrapolation results actually -C generated by the epsilon algorithm in prior -C calls to the routine. -C NEWELM - INTEGER -C Number of elements to be computed in the -C new diagonal of the epsilon table. The -C condensed epsilon table is computed. Only -C those elements needed for the computation of -C the next diagonal are preserved. -C RES - DOUBLE PRECISION -C New element in the new diagonal of the -C epsilon table. -C ERROR - DOUBLE PRECISION -C An estimate of the absolute error of RES. -C Routine decides whether RESULT=RES or -C RESULT=SVALUE by comparing ERROR with -C ABSERR from the previous call. -C RES3LA - DOUBLE PRECISION -C Vector of DIMENSION 3 containing at most -C the last 3 results. -C -C -C MACHINE DEPENDENT CONSTANTS -C --------------------------- -C DRELPR is the largest relative spacing. -C -C***FIRST EXECUTABLE STATEMENT DEA - IF(LIMEXP.LT.3) THEN - IERR = 1 -! CALL XERROR('LIMEXP IS LESS THAN 3',21,1,1) - GO TO 110 - ENDIF - IERR = 0 - RES3LA(1)=EPSTAB(LIMEXP+5) - RES3LA(2)=EPSTAB(LIMEXP+6) - RES3LA(3)=EPSTAB(LIMEXP+7) - RESULT=SVALUE - IF(NEWFLG) THEN - N=1 - NRES=0 - NEWFLG=.FALSE. - EPSTAB(N)=SVALUE - ABSERR=ABS(RESULT) - GO TO 100 - ELSE - N=INT(EPSTAB(LIMEXP+3)) - NRES=INT(EPSTAB(LIMEXP+4)) - IF(N.EQ.2) THEN - EPSTAB(N)=SVALUE - ABSERR=.6D+01*ABS(RESULT-EPSTAB(1)) - GO TO 100 - ENDIF - ENDIF - EPSTAB(N)=SVALUE - DRELPR=D1MACH(4) - DEPRN=1.0D+01*DRELPR - EPSTAB(N+2)=EPSTAB(N) - NEWELM=(N-1)/2 - NUM=N - K1=N - DO 40 I=1,NEWELM - K2=K1-1 - K3=K1-2 - RES=EPSTAB(K1+2) - E0=EPSTAB(K3) - E1=EPSTAB(K2) - E2=RES - DELTA2=E2-E1 - ERR2=ABS(DELTA2) - TOL2=MAX(ABS(E2),ABS(E1))*DRELPR - DELTA3=E1-E0 - ERR3=ABS(DELTA3) - TOL3=MAX(ABS(E1),ABS(E0))*DRELPR - IF(ERR2.GT.TOL2.OR.ERR3.GT.TOL3) GO TO 10 -C -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. -C RESULT=E2 -C ABSERR=ABS(E1-E0)+ABS(E2-E1) -C - RESULT=RES - ABSERR=ERR2+ERR3 - GO TO 50 - 10 IF(I.NE.1) THEN - E3=EPSTAB(K1) - EPSTAB(K1)=E1 - DELTA1=E1-E3 - ERR1=ABS(DELTA1) - TOL1=MAX(ABS(E1),ABS(E3))*DRELPR -C -C IF TWO ELEMENTS ARE VERY CLOSE TO EACH OTHER, OMIT -C A PART OF THE TABLE BY ADJUSTING THE VALUE OF N -C - IF(ERR1.LE.TOL1.OR.ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA1+0.1D+01/DELTA2-0.1D+01/DELTA3 - ELSE - EPSTAB(K1)=E1 - IF(ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA2-0.1D+01/DELTA3 - ENDIF -C -C TEST TO DETECT IRREGULAR BEHAVIOUR IN THE TABLE, AND -C EVENTUALLY OMIT A PART OF THE TABLE ADJUSTING THE VALUE -C OF N -C - IF(ABS(SS*E1).GT.0.1D-03) GO TO 30 - 20 N=I+I-1 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ERR3 - RESULT=RES - ELSE IF(NRES.EQ.1) THEN - RESULT=RES3LA(1) - ELSE IF(NRES.EQ.2) THEN - RESULT=RES3LA(2) - ELSE - RESULT=RES3LA(3) - ENDIF - GO TO 50 -C -C COMPUTE A NEW ELEMENT AND EVENTUALLY ADJUST -C THE VALUE OF RESULT -C - 30 RES=E1+0.1D+01/SS - EPSTAB(K1)=RES - K1=K1-2 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ABS(RES-E2)+ERR3 - RESULT=RES - GO TO 40 - ELSE IF(NRES.EQ.1) THEN - ERROR=.6D+01*(ABS(RES-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ERROR=.2D+01*(ABS(RES-RES3LA(2))+ABS(RES-RES3LA(1))) - ELSE - ERROR=ABS(RES-RES3LA(3))+ABS(RES-RES3LA(2)) - 1 +ABS(RES-RES3LA(1)) - ENDIF - IF(ERROR.GT.1.0D+01*ABSERR) GO TO 40 - ABSERR=ERROR - RESULT=RES - 40 CONTINUE -C -C COMPUTE ERROR ESTIMATE -C - IF(NRES.EQ.1) THEN - ABSERR=.6D+01*(ABS(RESULT-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ABSERR=.2D+01*ABS(RESULT-RES3LA(2))+ABS(RESULT-RES3LA(1)) - ELSE IF(NRES.GT.2) THEN - ABSERR=ABS(RESULT-RES3LA(3))+ABS(RESULT-RES3LA(2)) - 1 +ABS(RESULT-RES3LA(1)) - ENDIF -C -C SHIFT THE TABLE -C - 50 IF(N.EQ.LIMEXP) N=2*(LIMEXP/2)-1 - IB=1 - IF((NUM/2)*2.EQ.NUM) IB=2 - IE=NEWELM+1 - DO 60 I=1,IE - IB2=IB+2 - EPSTAB(IB)=EPSTAB(IB2) - IB=IB2 - 60 CONTINUE - IF(NUM.EQ.N) GO TO 80 - IN=NUM-N+1 - DO 70 I=1,N - EPSTAB(I)=EPSTAB(IN) - IN=IN+1 - 70 CONTINUE -C -C UPDATE RES3LA -C - 80 IF(NRES.EQ.0) THEN - RES3LA(1)=RESULT - ELSE IF(NRES.EQ.1) THEN - RES3LA(2)=RESULT - ELSE IF(NRES.EQ.2) THEN - RES3LA(3)=RESULT - ELSE - RES3LA(1)=RES3LA(2) - RES3LA(2)=RES3LA(3) - RES3LA(3)=RESULT - ENDIF - 90 ABSERR=MAX(ABSERR,DEPRN*ABS(RESULT)) - NRES=NRES+1 - 100 N=N+1 - EPSTAB(LIMEXP+3)=DBLE(N) - EPSTAB(LIMEXP+4)=DBLE(NRES) - EPSTAB(LIMEXP+5)=RES3LA(1) - EPSTAB(LIMEXP+6)=RES3LA(2) - EPSTAB(LIMEXP+7)=RES3LA(3) - 110 RETURN - END subroutine DEA \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/deamod.pyf b/wafo/source/mvnprd/old/mvnprodcorrprb/old/deamod.pyf deleted file mode 100644 index 83b9ecd..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/deamod.pyf +++ /dev/null @@ -1,6 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcore.f90 b/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcore.f90 deleted file mode 100644 index 138a8db..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcore.f90 +++ /dev/null @@ -1,344 +0,0 @@ -C f2py -m erfcore -h erfcore.pyf erfcore.f90 -C f2py erfcore.pyf erfcore.f90 -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m erfcore -c erfcore.f90 -C - - MODULE ERFCOREMOD - IMPLICIT NONE - - INTERFACE CALERF - MODULE PROCEDURE CALERF - END INTERFACE - - INTERFACE DERF - MODULE PROCEDURE DERF - END INTERFACE - - INTERFACE DERFC - MODULE PROCEDURE DERFC - END INTERFACE - - INTERFACE DERFCX - MODULE PROCEDURE DERFCX - END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/integration1Dmodule.f b/wafo/source/mvnprd/old/mvnprodcorrprb/old/integration1Dmodule.f deleted file mode 100644 index c98497e..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/integration1Dmodule.f +++ /dev/null @@ -1,1460 +0,0 @@ -C f2py -m integrationmod -h integrationmod.pyf integration1Dmodule.f -C f2py integrationmod.pyf integration1Dmodule.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -! f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m integrationmod -c integration1Dmodule.f - -! module Integration1DModule -! implicit none -! interface AdaptiveSimpson -! module procedure AdaptiveSimpson2, AdaptiveSimpsonWithBreaks -! end interface - -! interface AdaptiveSimpson1 -! module procedure AdaptiveSimpson1 -! end interface - -! interface AdaptiveTrapz -! module procedure AdaptiveTrapz1, AdaptiveTrapzWithBreaks -! end interface - -! interface Romberg -! module procedure Romberg1, RombergWithBreaks -! end interface - -! INTERFACE DEA -! MODULE PROCEDURE DEA -! END INTERFACE -! INTERFACE d1mach -! MODULE PROCEDURE d1mach -! END INTERFACE -! contains - - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - subroutine dea3(E0,E1,E2,abserr,result1) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result1 - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result1 = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result1 = E2 - abserr = err1 + err2 + E2*small*ten - else - result1 = E1 + one/ss - abserr = err1 + err2 + abs(result1-E2) - endif - endif - end subroutine dea3 - SUBROUTINE DEA(NEWFLG,SVALUE,LIMEXP,result1,ABSERR,EPSTAB,IERR) -C***BEGIN PROLOGUE DEA -C***DATE WRITTEN 800101 (YYMMDD) -C***REVISION DATE 871208 (YYMMDD) -C***CATEGORY NO. E5 -C***KEYWORDS CONVERGENCE ACCELERATION,EPSILON ALGORITHM,EXTRAPOLATION -C***AUTHOR PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. - -C K. U. LEUVEN -C DE DONCKER-KAPENGA, ELISE,WESTERN MICHIGAN UNIVERSITY -C KAHANER, DAVID K., NATIONAL BUREAU OF STANDARDS -C STARKENBURG, C. B., NATIONAL BUREAU OF STANDARDS -C***PURPOSE Given a slowly convergent sequence, this routine attempts -C to extrapolate nonlinearly to a better estimate of the -C sequence's limiting value, thus improving the rate of -C convergence. Routine is based on the epsilon algorithm -C of P. Wynn. An estimate of the absolute error is also -C given. -C***DESCRIPTION -C -C Epsilon algorithm. Standard fortran subroutine. -C Double precision version. -C -C A R G U M E N T S I N T H E C A L L S E Q U E N C E -C -C NEWFLG - LOGICAL (INPUT and OUTPUT) -C On the first call to DEA set NEWFLG to .TRUE. -C (indicating a new sequence). DEA will set NEWFLG -C to .FALSE. -C -C SVALUE - DOUBLE PRECISION (INPUT) -C On the first call to DEA set SVALUE to the first -C term in the sequence. On subsequent calls set -C SVALUE to the subsequent sequence value. -C -C LIMEXP - INTEGER (INPUT) -C An integer equal to or greater than the total -C number of sequence terms to be evaluated. Do not -C change the value of LIMEXP until a new sequence -C is evaluated (NEWFLG=.TRUE.). LIMEXP .GE. 3 -C -C result1 - DOUBLE PRECISION (OUTPUT) -C Best approximation to the sequence's limit. -C -C ABSERR - DOUBLE PRECISION (OUTPUT) -C Estimate of the absolute error. -C -C EPSTAB - DOUBLE PRECISION (OUTPUT) -C Workvector of DIMENSION at least (LIMEXP+7). -C -C IERR - INTEGER (OUTPUT) -C IERR=0 Normal termination of the routine. -C IERR=1 The input is invalid because LIMEXP.LT.3. -C -C T Y P I C A L P R O B L E M S E T U P -C -C This sample problem uses the trapezoidal rule to evaluate the -C integral of the sin function from 0.0 to 0.5*PI (value = 1.0). The -C program implements the trapezoidal rule 8 times creating an -C increasingly accurate sequence of approximations to the integral. -C Each time the trapezoidal rule is used, it uses twice as many -C panels as the time before. DEA is called to obtain even more -C accurate estimates. -C -C PROGRAM SAMPLE -C IMPLICIT DOUBLE PRECISION (A-H,O-Z) -C DOUBLE PRECISION EPSTAB(57) -CC [57 = LIMEXP + 7] -C LOGICAL NEWFLG -C EXTERNAL F -C DATA LIMEXP/50/ -C WRITE(*,*) ' NO. PANELS TRAP. APPROX' -C * ,' APPROX W/EA ABSERR' -C WRITE(*,*) -C HALFPI = DASIN(1.0D+00) -CC [UPPER INTEGRATION LIMIT = PI/2] -C NEWFLG = .TRUE. -CC [SET FLAG - 1ST DEA CALL] -C DO 10 I = 0,7 -C NPARTS = 2 ** I -C WIDTH = HALFPI/NPARTS -C APPROX = 0.5D+00 * WIDTH * (F(0.0D+00) + F(HALFPI)) -C DO 11 J = 1,NPARTS-1 -C APPROX = APPROX + F(J * WIDTH) * WIDTH -C 11 CONTINUE -CC [END TRAPEZOIDAL RULE APPROX] -C SVALUE = APPROX -CC [SVALUE = NEW SEQUENCE VALUE] -C CALL DEA(NEWFLG,SVALUE,LIMEXP,result1,ABSERR,EPSTAB,IERR) -CC [CALL DEA FOR BETTER ESTIMATE] -C WRITE(*,12) NPARTS,APPROX,result1,ABSERR -C 12 FORMAT(' ',I4,T20,F16.13,T40,F16.13,T60,D11.4) -C 10 CONTINUE -C STOP -C END -C -C DOUBLE PRECISION FUNCTION F(X) -C DOUBLE PRECISION X -C F = DSIN(X) -CC [INTEGRAND] -C RETURN -C END -C -C Output from the above program will be: -C -C NO. PANELS TRAP. APPROX APPROX W/EA ABSERR -C -C 1 .7853981633974 .7853981633974 .7854D+00 -C 2 .9480594489685 .9480594489685 .9760D+00 -C 4 .9871158009728 .9994567212570 .2141D+00 -C 8 .9967851718862 .9999667417647 .3060D-02 -C 16 .9991966804851 .9999998781041 .6094D-03 -C 32 .9997991943200 .9999999981026 .5767D-03 -C 64 .9999498000921 .9999999999982 .3338D-04 -C 128 .9999874501175 1.0000000000000 .1238D-06 -C -C----------------------------------------------------------------------- -C***REFERENCES "Acceleration de la convergence en analyse numerique", -C C. Brezinski, "Lecture Notes in Math.", vol. 584, -C Springer-Verlag, New York, 1977. -C***ROUTINES CALLED D1MACH,XERROR -C***END PROLOGUE DEA - double precision, dimension(*), intent(inout) :: EPSTAB - double precision, intent(out) :: result1 - double precision, intent(inout) :: ABSERR - double precision, intent(in) :: SVALUE - INTEGER, INTENT(IN) :: LIMEXP - INTEGER, INTENT(OUT) :: IERR - LOGICAL, intent(INOUT) :: NEWFLG - DOUBLE PRECISION :: DELTA1,DELTA2,DELTA3,DRELPR,DEPRN, - 1 ERROR,ERR1,ERR2,ERR3,E0,E1,E2,E3,RES, - 2 SS,TOL1,TOL2,TOL3 - double precision, dimension(3) :: RES3LA - INTEGER I,IB,IB2,IE,IN,K1,K2,K3,N,NEWELM,NUM,NRES -C -C -C LIMEXP is the maximum number of elements the -C epsilon table data can contain. The epsilon table -C is stored in the first (LIMEXP+2) entries of EPSTAB. -C -C -C LIST OF MAJOR VARIABLES -C ----------------------- -C E0,E1,E2,E3 - DOUBLE PRECISION -C The 4 elements on which the computation of -C a new element in the epsilon table is based. -C NRES - INTEGER -C Number of extrapolation results actually -C generated by the epsilon algorithm in prior -C calls to the routine. -C NEWELM - INTEGER -C Number of elements to be computed in the -C new diagonal of the epsilon table. The -C condensed epsilon table is computed. Only -C those elements needed for the computation of -C the next diagonal are preserved. -C RES - DOUBLE PRECISION -C New element in the new diagonal of the -C epsilon table. -C ERROR - DOUBLE PRECISION -C An estimate of the absolute error of RES. -C Routine decides whether RESULT=RES or -C RESULT=SVALUE by comparing ERROR with -C ABSERR from the previous call. -C RES3LA - DOUBLE PRECISION -C Vector of DIMENSION 3 containing at most -C the last 3 results. -C -C -C MACHINE DEPENDENT CONSTANTS -C --------------------------- -C DRELPR is the largest relative spacing. -C -C***FIRST EXECUTABLE STATEMENT DEA - IF(LIMEXP.LT.3) THEN - IERR = 1 -! CALL XERROR('LIMEXP IS LESS THAN 3',21,1,1) - GO TO 110 - ENDIF - IERR = 0 - RES3LA(1)=EPSTAB(LIMEXP+5) - RES3LA(2)=EPSTAB(LIMEXP+6) - RES3LA(3)=EPSTAB(LIMEXP+7) - result1=SVALUE - IF(NEWFLG) THEN - N=1 - NRES=0 - NEWFLG=.FALSE. - EPSTAB(N)=SVALUE - ABSERR=ABS(result1) - GO TO 100 - ELSE - N=INT(EPSTAB(LIMEXP+3)) - NRES=INT(EPSTAB(LIMEXP+4)) - IF(N.EQ.2) THEN - EPSTAB(N)=SVALUE - ABSERR=.6D+01*ABS(result1-EPSTAB(1)) - GO TO 100 - ENDIF - ENDIF - EPSTAB(N)=SVALUE - DRELPR=D1MACH(4) - DEPRN=1.0D+01*DRELPR - EPSTAB(N+2)=EPSTAB(N) - NEWELM=(N-1)/2 - NUM=N - K1=N - DO 40 I=1,NEWELM - K2=K1-1 - K3=K1-2 - RES=EPSTAB(K1+2) - E0=EPSTAB(K3) - E1=EPSTAB(K2) - E2=RES - DELTA2=E2-E1 - ERR2=ABS(DELTA2) - TOL2=MAX(ABS(E2),ABS(E1))*DRELPR - DELTA3=E1-E0 - ERR3=ABS(DELTA3) - TOL3=MAX(ABS(E1),ABS(E0))*DRELPR - IF(ERR2.GT.TOL2.OR.ERR3.GT.TOL3) GO TO 10 -C -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. -C result1=E2 -C ABSERR=ABS(E1-E0)+ABS(E2-E1) -C - result1=RES - ABSERR=ERR2+ERR3 - GO TO 50 - 10 IF(I.NE.1) THEN - E3=EPSTAB(K1) - EPSTAB(K1)=E1 - DELTA1=E1-E3 - ERR1=ABS(DELTA1) - TOL1=MAX(ABS(E1),ABS(E3))*DRELPR -C -C IF TWO ELEMENTS ARE VERY CLOSE TO EACH OTHER, OMIT -C A PART OF THE TABLE BY ADJUSTING THE VALUE OF N -C - IF(ERR1.LE.TOL1.OR.ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA1+0.1D+01/DELTA2-0.1D+01/DELTA3 - ELSE - EPSTAB(K1)=E1 - IF(ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA2-0.1D+01/DELTA3 - ENDIF -C -C TEST TO DETECT IRREGULAR BEHAVIOUR IN THE TABLE, AND -C EVENTUALLY OMIT A PART OF THE TABLE ADJUSTING THE VALUE -C OF N -C - IF(ABS(SS*E1).GT.0.1D-03) GO TO 30 - 20 N=I+I-1 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ERR3 - result1=RES - ELSE IF(NRES.EQ.1) THEN - result1=RES3LA(1) - ELSE IF(NRES.EQ.2) THEN - result1=RES3LA(2) - ELSE - result1=RES3LA(3) - ENDIF - GO TO 50 -C -C COMPUTE A NEW ELEMENT AND EVENTUALLY ADJUST -C THE VALUE OF result1 -C - 30 RES=E1+0.1D+01/SS - EPSTAB(K1)=RES - K1=K1-2 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ABS(RES-E2)+ERR3 - result1=RES - GO TO 40 - ELSE IF(NRES.EQ.1) THEN - ERROR=.6D+01*(ABS(RES-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ERROR=.2D+01*(ABS(RES-RES3LA(2))+ABS(RES-RES3LA(1))) - ELSE - ERROR=ABS(RES-RES3LA(3))+ABS(RES-RES3LA(2)) - 1 +ABS(RES-RES3LA(1)) - ENDIF - IF(ERROR.GT.1.0D+01*ABSERR) GO TO 40 - ABSERR=ERROR - result1=RES - 40 CONTINUE -C -C COMPUTE ERROR ESTIMATE -C - IF(NRES.EQ.1) THEN - ABSERR=.6D+01*(ABS(result1-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ABSERR=.2D+01*ABS(result1-RES3LA(2))+ABS(result1-RES3LA(1)) - ELSE IF(NRES.GT.2) THEN - ABSERR=ABS(result1-RES3LA(3))+ABS(result1-RES3LA(2)) - 1 +ABS(result1-RES3LA(1)) - ENDIF -C -C SHIFT THE TABLE -C - 50 IF(N.EQ.LIMEXP) N=2*(LIMEXP/2)-1 - IB=1 - IF((NUM/2)*2.EQ.NUM) IB=2 - IE=NEWELM+1 - DO 60 I=1,IE - IB2=IB+2 - EPSTAB(IB)=EPSTAB(IB2) - IB=IB2 - 60 CONTINUE - IF(NUM.EQ.N) GO TO 80 - IN=NUM-N+1 - DO 70 I=1,N - EPSTAB(I)=EPSTAB(IN) - IN=IN+1 - 70 CONTINUE -C -C UPDATE RES3LA -C - 80 IF(NRES.EQ.0) THEN - RES3LA(1)=result1 - ELSE IF(NRES.EQ.1) THEN - RES3LA(2)=result1 - ELSE IF(NRES.EQ.2) THEN - RES3LA(3)=result1 - ELSE - RES3LA(1)=RES3LA(2) - RES3LA(2)=RES3LA(3) - RES3LA(3)=result1 - ENDIF - 90 ABSERR=MAX(ABSERR,DEPRN*ABS(result1)) - NRES=NRES+1 - 100 N=N+1 - EPSTAB(LIMEXP+3)=DBLE(N) - EPSTAB(LIMEXP+4)=DBLE(NRES) - EPSTAB(LIMEXP+5)=RES3LA(1) - EPSTAB(LIMEXP+6)=RES3LA(2) - EPSTAB(LIMEXP+7)=RES3LA(3) - 110 RETURN - END subroutine DEA - - subroutine AdaptiveIntWithBreaks(f,a,b,N,brks,epsi,iflg - $ ,abserr, val) - !use AdaptiveGaussKronrod - implicit none - double precision :: f - integer, intent(in) :: N - double precision, intent(in) :: a,b,epsi - double precision, dimension(:), intent(in) :: brks - double precision, intent(out) :: abserr, val - integer, intent(out) :: iflg - external f -! Locals - double precision, dimension(N+2) :: pts - double precision :: LTol,tol, error, valk, excess, errorEstimate - double precision :: delta, deltaK - integer :: kflg, k, limit,neval - limit = 30 - pts(1) = a - pts(N+2) = b - delta = b - a - do k = 2,N+1 - pts(k) = minval(brks(k-1:N)) !add user supplied break points - enddo - LTol = epsi / delta - abserr = 0.0d0 - val = 0.0D0 - iflg = 0 - do k = 1, N + 1 - deltaK = pts(k+1) - pts(k) - tol = LTol * deltaK - if (deltaK < 0.5D0) then - call AdaptiveSimpson(f,pts(k),pts(k+1),tol, kflg,error,valk) -! call romberg(f,pts(k),pts(k+1),20,tol,kflg,error, valk) - else - call AdaptiveSimpson3(f,pts(k),pts(k+1),tol,kflg,error,valk) -! call dqagp(f,pts(k),pts(k+1),0,pts,tol,0.0D0,limit,valk, -! * error,neval,kflg) - - endif - abserr = abserr + abs(error) - - errorEstimate = abserr + (b - pts(k+1)) * LTol - excess = epsi - errorEstimate - if (excess < 0.0D0 ) then - LTol = 0.1D0*LTol - elseif ( epsi < 2.0D0 * excess ) then - LTol = (epsi + excess*0.5D0) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0.0d0 .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif ( Lepsi < 5D0 * excess ) then - LTol = (Lepsi + excess) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn12e = ( Sn1e - Sn2e ) - - Sn24e = (Sn2e - Sn4) -! Sn1e = Sn2e - Sn12e * zpz66666 -! Sn12e = (Sn1e - Sn2e) - - Sn124 = (Sn12e - Sn24) - if ((abs(Sn124)<= hmin) .or. - & .false..and.(Sn24*Sn12e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn24 * zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24 * Sn24 / Sn124 - endif - Sn4e = Sn4 + correction - -! NEWFLG = .TRUE. -! CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn1e,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4e,LIMEXP,val0,localError,EPSTAB,IERR) -! localError is made conservative in order to avoid premature -! termination - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) - !if (h>dhMin) then - !localError = max(localError,abs(correction)) - !else - !val0 = Sn4e - !localError = abs(correction)*two - !endif - else - CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - endif - acceptError = ( localError <= Ltol * h * eight - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(6,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.true..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,fx3,fx4,fx5,x1,h,S,SL,SR] - kp1 = k + 1; -! Process right interval - v(1,kp1) = v(3,k); !fx1R - v(2,kp1) = fx(3); !fx2R - v(3,kp1) = v(4,k); !fx3R - v(4,kp1) = fx(4); !fx4R - v(5,kp1) = v(5,k); !fx5R - v(6,kp1) = v(6,k) + four * h; ! x1R - v(7,kp1) = h; - v(8,kp1) = v(10,k); ! S - v(9:10,kp1) = Sn(3:4); ! SL, SR -! Process left interval - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) unchanged fx1L -! v(6,k) unchanged x1L - v(7,k) = h; - v(8,k) = v(9,k); ! S - v(9:10,k) = Sn(1:2); ! SL, SR - k = kp1; - endif - enddo ! while - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - Sn48 = (Sn4 - Sn8) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn4e = Sn8 - Sn48 * zpz588 - Sn12e = (Sn1e - Sn2e) - Sn24e = (Sn2e - Sn4e) - - Sn124 = (Sn12e - Sn24e) - if ((abs(Sn124)<= hmin) .or. - & (Sn12e*Sn24e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn48*zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24e * Sn24e / Sn124 - !Sn4e = Sn4e + correction - endif - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) -! localError is made conservative in order to avoid premature -! termination -! localError = max(localError,abs(correction)*three) -! localError = abs(correction)*three - else - !CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - NEWFLG = .TRUE. - CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn8,LIMEXP,val0,localError,EPSTAB,IERR) - endif - acceptError = ( localError <= Ltol * h * sixteen - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(Nrule+1,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.TRUE..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,..,fx8,fx9,x1,h,S,SL,SR,SL1,SL2 SR1,SR2] - kp1 = k + 1; -! Process right interval - - v(1,kp1) = v(5,k); !fx1R - v(2,kp1) = fx(5); !fx2R - v(3,kp1) = v(6,k); !fx3R - v(4,kp1) = fx(6); !fx4R - v(5,kp1) = v(7,k); !fx5R - v(6,kp1) = fx(7); !fx6R - v(7,kp1) = v(8,k); !fx7R - v(8,kp1) = fx(8); !fx8R - v(9,kp1) = v(9,k); !fx9R - - v(Nrule+1,kp1) = v(Nrule+1,k) + eight * h ! x1R - v(Nrule+2,kp1) = h; - v(Nrule+3,kp1) = v(Nrule+5,k); ! S - v(Nrule+4,kp1) = v(Nrule+8,k); ! SL - v(Nrule+5,kp1) = v(Nrule+9,k); ! SR - v(Nrule+6:Nrule+9,kp1) = Sn(5:8); ! SL1,SL2,SR1, SR2 -! Process left interval - v(9,k) = v(5,k); ! fx9L - v(8,k) = fx(4); ! fx8L - v(7,k) = v(4,k); ! fx7L - v(6,k) = fx(3); ! fx6L - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) = v(1,k); ! fx1L -! v(Nrule+1,k) unchanged x1L - v(Nrule+2,k) = h; - v(Nrule+3,k) = v(Nrule + 4,k); ! S - v(Nrule+4,k) = v(Nrule+6,k); ! SL - v(Nrule+5,k) = v(Nrule+7,k); ! SR - v(Nrule+6:Nrule+9,k) = Sn(1:4); ! SL1,SL2,SR1, SR2 - k = kp1; - endif - enddo ! while - if (epsi0) iflg = IOR(iflg, kflg) - end do - if (epsi0) iflg = ior(iflg,kflg) - end do - if (epsi0) iflg = IOR(iflg, kflg) - end do - if (epsi0.0d0 .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif ( Lepsi < 5D0 * excess ) then - LTol = (Lepsi + excess) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn12e = ( Sn1e - Sn2e ) - - Sn24e = (Sn2e - Sn4) -! Sn1e = Sn2e - Sn12e * zpz66666 -! Sn12e = (Sn1e - Sn2e) - - Sn124 = (Sn12e - Sn24) - if ((abs(Sn124)<= hmin) .or. - & .false..and.(Sn24*Sn12e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn24 * zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24 * Sn24 / Sn124 - endif - Sn4e = Sn4 + correction - -! NEWFLG = .TRUE. -! CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn1e,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4e,LIMEXP,val0,localError,EPSTAB,IERR) -! localError is made conservative in order to avoid premature -! termination - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) - !if (h>dhMin) then - !localError = max(localError,abs(correction)) - !else - !val0 = Sn4e - !localError = abs(correction)*two - !endif - else - CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - endif - acceptError = ( localError <= Ltol * h * eight - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(6,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.true..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,fx3,fx4,fx5,x1,h,S,SL,SR] - kp1 = k + 1; -! Process right interval - v(1,kp1) = v(3,k); !fx1R - v(2,kp1) = fx(3); !fx2R - v(3,kp1) = v(4,k); !fx3R - v(4,kp1) = fx(4); !fx4R - v(5,kp1) = v(5,k); !fx5R - v(6,kp1) = v(6,k) + four * h; ! x1R - v(7,kp1) = h; - v(8,kp1) = v(10,k); ! S - v(9:10,kp1) = Sn(3:4); ! SL, SR -! Process left interval - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) unchanged fx1L -! v(6,k) unchanged x1L - v(7,k) = h; - v(8,k) = v(9,k); ! S - v(9:10,k) = Sn(1:2); ! SL, SR - k = kp1; - endif - enddo ! while - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - Sn48 = (Sn4 - Sn8) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn4e = Sn8 - Sn48 * zpz588 - Sn12e = (Sn1e - Sn2e) - Sn24e = (Sn2e - Sn4e) - - Sn124 = (Sn12e - Sn24e) - if ((abs(Sn124)<= hmin) .or. - & (Sn12e*Sn24e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn48*zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24e * Sn24e / Sn124 - !Sn4e = Sn4e + correction - endif - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) -! localError is made conservative in order to avoid premature -! termination -! localError = max(localError,abs(correction)*three) -! localError = abs(correction)*three - else - !CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - NEWFLG = .TRUE. - CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn8,LIMEXP,val0,localError,EPSTAB,IERR) - endif - acceptError = ( localError <= Ltol * h * sixteen - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(Nrule+1,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.TRUE..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,..,fx8,fx9,x1,h,S,SL,SR,SL1,SL2 SR1,SR2] - kp1 = k + 1; -! Process right interval - - v(1,kp1) = v(5,k); !fx1R - v(2,kp1) = fx(5); !fx2R - v(3,kp1) = v(6,k); !fx3R - v(4,kp1) = fx(6); !fx4R - v(5,kp1) = v(7,k); !fx5R - v(6,kp1) = fx(7); !fx6R - v(7,kp1) = v(8,k); !fx7R - v(8,kp1) = fx(8); !fx8R - v(9,kp1) = v(9,k); !fx9R - - v(Nrule+1,kp1) = v(Nrule+1,k) + eight * h ! x1R - v(Nrule+2,kp1) = h; - v(Nrule+3,kp1) = v(Nrule+5,k); ! S - v(Nrule+4,kp1) = v(Nrule+8,k); ! SL - v(Nrule+5,kp1) = v(Nrule+9,k); ! SR - v(Nrule+6:Nrule+9,kp1) = Sn(5:8); ! SL1,SL2,SR1, SR2 -! Process left interval - v(9,k) = v(5,k); ! fx9L - v(8,k) = fx(4); ! fx8L - v(7,k) = v(4,k); ! fx7L - v(6,k) = fx(3); ! fx6L - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) = v(1,k); ! fx1L -! v(Nrule+1,k) unchanged x1L - v(Nrule+2,k) = h; - v(Nrule+3,k) = v(Nrule + 4,k); ! S - v(Nrule+4,k) = v(Nrule+6,k); ! SL - v(Nrule+5,k) = v(Nrule+7,k); ! SR - v(Nrule+6:Nrule+9,k) = Sn(1:4); ! SL1,SL2,SR1, SR2 - k = kp1; - endif - enddo ! while - if (epsi0) iflg = IOR(iflg, kflg) - end do - if (epsi0) iflg = ior(iflg,kflg) - end do - if (epsi EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* -* MVNPRODCORRPRB calculates multivariate normal probability -* with product correlation structure for rectangular regions. -* The accuracy is up to almost double precision, i.e., about 1e-14. -* -* This file was successfully compiled for matlab 5.3 -* using Compaq Visual Fortran 6.1, and Windows 2000. -* The example here uses Fortran77 source. -* First, you will need to modify your mexopts.bat file. -* To find it, issue the command prefdir(1) from the Matlab command line, -* the directory it answers with will contain your mexopts.bat file. -* Open it for editing. The first section will look like: -* -*rem ******************************************************************** -*rem General parameters -*rem ******************************************************************** -*set MATLAB=%MATLAB% -*set DF_ROOT=C:\Program Files\Microsoft Visual Studio -*set VCDir=%DF_ROOT%\VC98 -*set MSDevDir=%DF_ROOT%\Common\msdev98 -*set DFDir=%DF_ROOT%\DF98 -*set PATH=%MSDevDir%\bin;%DFDir%\BIN;%VCDir%\BIN;%PATH% -*set INCLUDE=%DFDir%\INCLUDE;%DFDir%\IMSL\INCLUDE;%INCLUDE% -*set LIB=%DFDir%\LIB;%VCDir%\LIB -* -* then you are ready to compile this file at the matlab prompt using the -* following command: -* mex -O mvnprodcorrprbmex.f - MODULE ERFCOREMOD - IMPLICIT NONE - - INTERFACE CALERF - MODULE PROCEDURE CALERF - END INTERFACE - - INTERFACE DERF - MODULE PROCEDURE DERF - END INTERFACE - - INTERFACE DERFC - MODULE PROCEDURE DERFC - END INTERFACE - - INTERFACE DERFCX - MODULE PROCEDURE DERFCX - END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD - module functionInterface - INTERFACE - FUNCTION F(Z) result (VAL) - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - END FUNCTION F - END INTERFACE - end module functionInterface - module AdaptiveGaussKronrod - implicit none - private - public :: dqagpe,dqagp - - INTERFACE dqagpe - MODULE PROCEDURE dqagpe - END INTERFACE - - INTERFACE dqagp - MODULE PROCEDURE dqagp - END INTERFACE - - INTERFACE dqelg - MODULE PROCEDURE dqelg - END INTERFACE - - INTERFACE dqpsrt - MODULE PROCEDURE dqpsrt - END INTERFACE - - INTERFACE dqk21 - MODULE PROCEDURE dqk21 - END INTERFACE - - INTERFACE dqk15 - MODULE PROCEDURE dqk15 - END INTERFACE - - INTERFACE dqk9 - MODULE PROCEDURE dqk9 - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - - contains - subroutine dea3(E0,E1,E2,abserr,result) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result = E2 - abserr = err1 + err2 + E2*small*ten - else - result = E1 + one/ss - abserr = err1 + err2 + abs(result-E2) - endif - endif - end subroutine dea3 - subroutine dqagp(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier) -! use functionInterface - implicit none - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result1,abserr - integer, intent(out) :: neval,ier - double precision :: f -!Locals - double precision,dimension(limit) :: alist, blist, rlist, elist - double precision,dimension(npts+2) :: pts - integer, dimension(limit) :: iord, level - integer, dimension(npts+2) :: ndin - integer ::last - external f - CALL dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result1, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin - $ ,last) - end subroutine dqagp - subroutine dqagpe(f,a,b,npts,points,epsabs,epsrel,limit,result, - * abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin, - * last) -! use functionInterface - implicit none -c***begin prologue dqagpe -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a2a1 -c***keywords automatic integrator, general-purpose, -! singularities at user specified points, -! extrapolation, globally adaptive. -c***author piessens,robert ,appl. math. & progr. div. - k.u.leuven -! de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose the routine calculates an approximation result to a given -! definite integral i = integral of f over (a,b), hopefully -! satisfying following claim for accuracy abs(i-result).le. -! max(epsabs,epsrel*abs(i)). break points of the integration -! interval, where local difficulties of the integrand may -! occur(e.g. singularities,discontinuities),provided by user. -c***description -! -! computation of a definite integral -! standard fortran subroutine -! double precision version -! -! parameters -! on entry -! f - double precision -! function subprogram defining the integrand -! function f(x). the actual name for f needs to be -! declared e x t e r n a l in the driver program. -! -! a - double precision -! lower limit of integration -! -! b - double precision -! upper limit of integration -! -! npts2 - integer -! number equal to two more than the number of -! user-supplied break points within the integration -! range, npts2.ge.2. -! if npts2.lt.2, the routine will end with ier = 6. -! -! points - double precision -! vector of dimension npts2, the first (npts2-2) -! elements of which are the user provided break -! points. if these points do not constitute an -! ascending sequence there will be an automati! -! sorting. -! -! epsabs - double precision -! absolute accuracy requested -! epsrel - double precision -! relative accuracy requested -! if epsabs.le.0 -! and epsrel.lt.max(50*rel.mach.acc.,0.5d-28), -! the routine will end with ier = 6. -! -! limit - integer -! gives an upper bound on the number of subintervals -! in the partition of (a,b), limit.ge.npts2 -! if limit.lt.npts2, the routine will end with -! ier = 6. -! -! on return -! result - double precision -! approximation to the integral -! -! abserr - double precision -! estimate of the modulus of the absolute error, -! which should equal or exceed abs(i-result) -! -! neval - integer -! number of integrand evaluations -! -! ier - integer -! ier = 0 normal and reliable termination of the -! routine. it is assumed that the requested -! accuracy has been achieved. -! ier.gt.0 abnormal termination of the routine. -! the estimates for integral and error are -! less reliable. it is assumed that the -! requested accuracy has not been achieved. -! error messages -! ier = 1 maximum number of subdivisions allowed -! has been achieved. one can allow more -! subdivisions by increasing the value of -! limit (and taking the according dimension -! adjustments into account). however, if -! this yields no improvement it is advised -! to analyze the integrand in order to -! determine the integration difficulties. if -! the position of a local difficulty can be -! determined (i.e. singularity, -! discontinuity within the interval), it -! should be supplied to the routine as an -! element of the vector points. if necessary -! an appropriate special-purpose integrator -! must be used, which is designed for -! handling the type of difficulty involved. -! = 2 the occurrence of roundoff error is -! detected, which prevents the requested -! tolerance from being achieved. -! the error may be under-estimated. -! = 3 extremely bad integrand behaviour occurs -! at some points of the integration -! interval. -! = 4 the algorithm does not converge. -! roundoff error is detected in the -! extrapolation table. it is presumed that -! the requested tolerance cannot be -! achieved, and that the returned result is -! the best which can be obtained. -! = 5 the integral is probably divergent, or -! slowly convergent. it must be noted that -! divergence can occur with any other value -! of ier.gt.0. -! = 6 the input is invalid because -! npts2.lt.2 or -! break points are specified outside -! the integration range or -! (epsabs.le.0 and -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) -! or limit.lt.npts2. -! result, abserr, neval, last, rlist(1), -! and elist(1) are set to zero. alist(1) and -! blist(1) are set to a and b respectively. -! -! alist - double precision -! vector of dimension at least limit, the first -! last elements of which are the left end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! blist - double precision -! vector of dimension at least limit, the first -! last elements of which are the right end points -! of the subintervals in the partition of the given -! integration range (a,b) -! -! rlist - double precision -! vector of dimension at least limit, the first -! last elements of which are the integral -! approximations on the subintervals -! -! elist - double precision -! vector of dimension at least limit, the first -! last elements of which are the moduli of the -! absolute error estimates on the subintervals -! -! pts - double precision -! vector of dimension at least npts2, containing the -! integration limits and the break points of the -! interval in ascending sequence. -! -! level - integer -! vector of dimension at least limit, containing the -! subdivision levels of the subinterval, i.e. if -! (aa,bb) is a subinterval of (p1,p2) where p1 as -! well as p2 is a user-provided break point or -! integration limit, then (aa,bb) has level l if -! abs(bb-aa) = abs(p2-p1)*2**(-l). -! -! ndin - integer -! vector of dimension at least npts2, after first -! integration over the intervals (pts(i)),pts(i+1), -! i = 0,1, ..., npts2-2, the error estimates over -! some of the intervals may have been increased -! artificially, in order to put their subdivision -! forward. if this happens for the subinterval -! numbered k, ndin(k) is put to 1, otherwise -! ndin(k) = 0. -! -! iord - integer -! vector of dimension at least limit, the first k -! elements of which are pointers to the -! error estimates over the subintervals, -! such that elist(iord(1)), ..., elist(iord(k)) -! form a decreasing sequence, with k = last -! if last.le.(limit/2+2), and k = limit+1-last -! otherwise -! -! last - integer -! number of subintervals actually produced in the -! subdivisions process -! -c***references (none) -c***routines called d1mach,dqelg,dqk21,dqpsrt -c***end prologue dqagpe - integer, intent(in) :: npts,limit - double precision,dimension(npts), intent(in) :: points - double precision, intent(in) :: a, b, epsabs,epsrel - double precision, intent(out) :: result,abserr - integer, intent(out) :: neval,ier - double precision,dimension(limit), intent(out) :: alist, blist - double precision,dimension(limit), intent(out) :: rlist, elist - double precision,dimension(npts+2),intent(out) :: pts - integer, dimension(limit), intent(out) :: iord, level - integer, dimension(npts+2), intent(out) :: ndin - integer ::last - double precision :: f -! locals - double precision :: area,area1,area12,area2,a1, - * a2,b1,b2,correc,abseps,defabs,defab1,defab2, - * dres,epmach,erlarg,erlast,errbnd, - * errmax,error1,erro12,error2,errsum,ertest,oflow, - * resa,resabs,reseps,sign,temp,uflow, hSplit - double precision, dimension(3) :: res3la(3) - double precision, dimension(52) :: rlist2(52) - integer :: i,id,ierro,ind1,ind2,ip1,iroff1,iroff2,iroff3,j, - * jlow,jupbnd,k,ksgn,ktmin,levcur,levmax,maxerr, - * nint,nintp1,npts2,nres,nrmax,numrl2 - logical :: extrap,noext - external f -! -! - -! -! -! the dimension of rlist2 is determined by the value of -! limexp in subroutine epsalg (rlist2 should be of dimension -! (limexp+2) at least). -! -! -! list of major variables -! ----------------------- -! -! alist - list of left end points of all subintervals -! considered up to now -! blist - list of right end points of all subintervals -! considered up to now -! rlist(i) - approximation to the integral over -! (alist(i),blist(i)) -! rlist2 - array of dimension at least limexp+2 -! containing the part of the epsilon table which -! is still needed for further computations -! elist(i) - error estimate applying to rlist(i) -! maxerr - pointer to the interval with largest error -! estimate -! errmax - elist(maxerr) -! erlast - error on the interval currently subdivided -! (before that subdivision has taken place) -! area - sum of the integrals over the subintervals -! errsum - sum of the errors over the subintervals -! errbnd - requested accuracy max(epsabs,epsrel* -! abs(result)) -! *****1 - variable for the left subinterval -! *****2 - variable for the right subinterval -! last - index for subdivision -! nres - number of calls to the extrapolation routine -! numrl2 - number of elements in rlist2. if an appropriate -! approximation to the compounded integral has -! been obtained, it is put in rlist2(numrl2) after -! numrl2 has been increased by one. -! erlarg - sum of the errors over the intervals larger -! than the smallest interval considered up to now -! extrap - logical variable denoting that the routine -! is attempting to perform extrapolation. i.e. -! before subdividing the smallest interval we -! try to decrease the value of erlarg. -! noext - logical variable denoting that extrapolation is -! no longer allowed (true-value) -! -! machine dependent constants -! --------------------------- -! -! epmach is the largest relative spacing. -! uflow is the smallest positive magnitude. -! oflow is the largest positive magnitude. -! -c***first executable statement dqagpe - epmach = d1mach(4) - uflow = d1mach(1) - oflow = d1mach(2) -! -! test on validity of parameters -! ----------------------------- -! - hSplit = 0.2D0 - ier = 0 - neval = 0 - last = 0 - result = 0.0d+00 - abserr = 0.0d+00 - alist(1) = a - blist(1) = b - rlist(1) = 0.0d+00 - elist(1) = 0.0d+00 - iord(1) = 0 - level(1) = 0 - npts2 = npts+2 - if((npts2.lt.2).or.(limit.le.npts).or. - & ((epsabs.le.0.0d+00).and. - & (epsrel.lt.dmax1(0.5d+02*epmach,0.5d-28)))) then - ier = 6 - go to 999 - endif - - sign = 1.0d+00 - if(a.gt.b) then - go to 999 - endif - if (npts>0) then - if(any(points(1:npts)<=a).or.any(b<=points(1:npts))) then - ier = 6 - go to 999 - endif - endif -! -! if any break points are provided, sort them into an -! ascending sequence. -! - pts(1) = a - pts(npts+2) = b - do i = 1,npts - pts(i+1) = minval(points(i:npts)) - enddo -! -! compute first integral and error approximations. -! ------------------------------------------------ -! - nint = npts+1; - a1 = pts(1); - resabs = 0.0d+00 - do i = 1,nint - b1 = pts(i+1) - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,defabs,resa) - !call dqk15(f,a1,b1,area1,error1,defabs,resa) - else - call dqkl9(f,a1,b1,area1,error1,defabs,resa) - endif - abserr = abserr + error1 - result = result + area1 - ndin(i) = 0 - if(error1.eq.resa.and.error1.ne.0.0d+00) ndin(i) = 1 - resabs = resabs + defabs - level(i) = 0 - elist(i) = error1 - alist(i) = a1 - blist(i) = b1 - rlist(i) = area1 - iord(i) = i - a1 = b1 - enddo !50 continue - errsum = 0.0d+00 - do i = 1,nint - if(ndin(i).eq.1) elist(i) = abserr - errsum = errsum+elist(i) - enddo !55 continue -! -! test on accuracy. -! - last = nint - neval = 21*nint - dres = dabs(result) - errbnd = dmax1(epsabs,epsrel*dres) - if(abserr.le.0.1d+03*epmach*resabs.and.abserr.gt.errbnd) ier = 2 - if(nint.eq.1) go to 80 - do 70 i = 1,npts - jlow = i+1 - ind1 = iord(i) - do 60 j = jlow,nint - ind2 = iord(j) - if(elist(ind1).gt.elist(ind2)) go to 60 - ind1 = ind2 - k = j - 60 continue - if(ind1.eq.iord(i)) go to 70 - iord(k) = iord(i) - iord(i) = ind1 - 70 continue - if(limit.lt.npts2) ier = 1 - 80 if(ier.ne.0.or.abserr.le.errbnd) go to 210 - -! -! initialization -! -------------- -! - rlist2(1) = result - maxerr = iord(1) - errmax = elist(maxerr) - area = result - nrmax = 1 - nres = 0 - numrl2 = 1 - ktmin = 0 - extrap = .false. - noext = .false. - erlarg = errsum - ertest = errbnd - levmax = 1 - iroff1 = 0 - iroff2 = 0 - iroff3 = 0 - ierro = 0 - abserr = oflow - ksgn = -1 - if(dres.ge.(0.1d+01-0.5d+02*epmach)*resabs) ksgn = 1 -! -! main do-loop -! ------------ -! - do 160 last = npts2,limit -! -! bisect the subinterval with the nrmax-th largest error -! estimate. -! - levcur = level(maxerr)+1 - a1 = alist(maxerr) - b1 = 0.5d+00*(alist(maxerr)+blist(maxerr)) - a2 = b1 - b2 = blist(maxerr) - erlast = errmax - if (b1-a1 > hSplit) then - call dqk21(f,a1,b1,area1,error1,resa,defab1) - call dqk21(f,a2,b2,area2,error2,resa,defab2) - !call dqk15(f,a1,b1,area1,error1,resa,defab1) - !call dqk15(f,a2,b2,area2,error2,resa,defab2) - else - - call dqkl9(f,a1,b1,area1,error1,resa,defab1) - call dqkl9(f,a2,b2,area2,error2,resa,defab2) - endif -! -! improve previous approximations to integral -! and error and test for accuracy. -! - neval = neval+42 - area12 = area1+area2 - erro12 = error1+error2 - errsum = errsum+erro12-errmax - area = area+area12-rlist(maxerr) - if(defab1.eq.error1.or.defab2.eq.error2) go to 95 - if(dabs(rlist(maxerr)-area12).gt.0.1d-04*dabs(area12) - * .or.erro12.lt.0.99d+00*errmax) go to 90 - if(extrap) iroff2 = iroff2+1 - if(.not.extrap) iroff1 = iroff1+1 - 90 if(last.gt.10.and.erro12.gt.errmax) iroff3 = iroff3+1 - 95 level(maxerr) = levcur - level(last) = levcur - rlist(maxerr) = area1 - rlist(last) = area2 - errbnd = dmax1(epsabs,epsrel*dabs(area)) -! -! test for roundoff error and eventually set error flag. -! - if(iroff1+iroff2.ge.10.or.iroff3.ge.20) ier = 2 - if(iroff2.ge.5) ierro = 3 -! -! set error flag in the case that the number of -! subintervals equals limit. -! - if(last.eq.limit) ier = 1 -! -! set error flag in the case of bad integrand behaviour -! at a point of the integration range -! - if(dmax1(dabs(a1),dabs(b2)).le.(0.1d+01+0.1d+03*epmach)* - * (dabs(a2)+0.1d+04*uflow)) ier = 4 -! -! append the newly-created intervals to the list. -! - if(error2.gt.error1) go to 100 - alist(last) = a2 - blist(maxerr) = b1 - blist(last) = b2 - elist(maxerr) = error1 - elist(last) = error2 - go to 110 - 100 alist(maxerr) = a2 - alist(last) = a1 - blist(last) = b1 - rlist(maxerr) = area2 - rlist(last) = area1 - elist(maxerr) = error2 - elist(last) = error1 -! -! call subroutine dqpsrt to maintain the descending ordering -! in the list of error estimates and select the subinterval -! with nrmax-th largest error estimate (to be bisected next). -! - 110 call dqpsrt(limit,last,maxerr,errmax,elist,iord,nrmax) -! ***jump out of do-loop - if(errsum.le.errbnd) go to 190 -! ***jump out of do-loop - if(ier.ne.0) go to 170 - if(noext) go to 160 - erlarg = erlarg-erlast - if(levcur+1.le.levmax) erlarg = erlarg+erro12 - if(extrap) go to 120 -! -! test whether the interval to be bisected next is the -! smallest interval. -! - if(level(maxerr)+1.le.levmax) go to 160 - extrap = .true. - nrmax = 2 - 120 if(ierro.eq.3.or.erlarg.le.ertest) go to 140 -! -! the smallest interval has the largest error. -! before bisecting decrease the sum of the errors over -! the larger intervals (erlarg) and perform extrapolation. -! - id = nrmax - jupbnd = last - if(last.gt.(2+limit/2)) jupbnd = limit+3-last - do 130 k = id,jupbnd - maxerr = iord(nrmax) - errmax = elist(maxerr) -! ***jump out of do-loop - if(level(maxerr)+1.le.levmax) go to 160 - nrmax = nrmax+1 - 130 continue -! -! perform extrapolation. -! - 140 numrl2 = numrl2+1 - rlist2(numrl2) = area - if(numrl2.le.2) go to 155 - call dqelg(numrl2,rlist2,reseps,abseps,res3la,nres) - ktmin = ktmin+1 - if(ktmin.gt.5.and.abserr.lt.0.1d-02*errsum) ier = 5 - if(abseps.ge.abserr) go to 150 - ktmin = 0 - abserr = abseps - result = reseps - correc = erlarg - ertest = dmax1(epsabs,epsrel*dabs(reseps)) -! ***jump out of do-loop - if(abserr.lt.ertest) go to 170 -! -! prepare bisection of the smallest interval. -! - 150 if(numrl2.eq.1) noext = .true. - if(ier.ge.5) go to 170 - 155 maxerr = iord(1) - errmax = elist(maxerr) - nrmax = 1 - extrap = .false. - levmax = levmax + 1 - erlarg = errsum - 160 continue -! -! set the final result. -! --------------------- -! -! - 170 if(abserr.eq.oflow) go to 190 - if((ier+ierro).eq.0) go to 180 - if(ierro.eq.3) abserr = abserr+correc - if(ier.eq.0) ier = 3 - if(result.ne.0.0d+00.and.area.ne.0.0d+00)go to 175 - if(abserr.gt.errsum)go to 190 - if(area.eq.0.0d+00) go to 210 - go to 180 - 175 if(abserr/dabs(result).gt.errsum/dabs(area))go to 190 -! -! test on divergence. -! - 180 if(ksgn.eq.(-1).and.dmax1(dabs(result),dabs(area)).le. - * resabs*0.1d-01) go to 210 - if(0.1d-01.gt.(result/area).or.(result/area).gt.0.1d+03.or. - * errsum.gt.dabs(area)) ier = 6 - go to 210 -! -! compute global integral sum. -! - 190 result = 0.0d+00 - do 200 k = 1,last - result = result+rlist(k) - 200 continue - abserr = errsum - 210 if(ier.gt.2) ier = ier-1 - result = result*sign - 999 return - end subroutine dqagpe - subroutine dqk21(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk21 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 21-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk21 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk,reskh,result,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(10),fv2(10),wg(5),wgk(11),xgk(11) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 21-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 10-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 10-point gauss rule -c -c wgk - weights of the 21-point kronrod rule -c -c wg - weights of the 10-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.0666713443 0868813759 3568809893 332 d0 / - data wg ( 2) / 0.1494513491 5058059314 5776339657 697 d0 / - data wg ( 3) / 0.2190863625 1598204399 5534934228 163 d0 / - data wg ( 4) / 0.2692667193 0999635509 1226921569 469 d0 / - data wg ( 5) / 0.2955242247 1475287017 3892994651 338 d0 / -c - data xgk ( 1) / 0.9956571630 2580808073 5527280689 003 d0 / - data xgk ( 2) / 0.9739065285 1717172007 7964012084 452 d0 / - data xgk ( 3) / 0.9301574913 5570822600 1207180059 508 d0 / - data xgk ( 4) / 0.8650633666 8898451073 2096688423 493 d0 / - data xgk ( 5) / 0.7808177265 8641689706 3717578345 042 d0 / - data xgk ( 6) / 0.6794095682 9902440623 4327365114 874 d0 / - data xgk ( 7) / 0.5627571346 6860468333 9000099272 694 d0 / - data xgk ( 8) / 0.4333953941 2924719079 9265943165 784 d0 / - data xgk ( 9) / 0.2943928627 0146019813 1126603103 866 d0 / - data xgk ( 10) / 0.1488743389 8163121088 4826001129 720 d0 / - data xgk ( 11) / 0.0000000000 0000000000 0000000000 000 d0 / -c - data wgk ( 1) / 0.0116946388 6737187427 8064396062 192 d0 / - data wgk ( 2) / 0.0325581623 0796472747 8818972459 390 d0 / - data wgk ( 3) / 0.0547558965 7435199603 1381300244 580 d0 / - data wgk ( 4) / 0.0750396748 1091995276 7043140916 190 d0 / - data wgk ( 5) / 0.0931254545 8369760553 5065465083 366 d0 / - data wgk ( 6) / 0.1093871588 0229764189 9210590325 805 d0 / - data wgk ( 7) / 0.1234919762 6206585107 7958109831 074 d0 / - data wgk ( 8) / 0.1347092173 1147332592 8054001771 707 d0 / - data wgk ( 9) / 0.1427759385 7706008079 7094273138 717 d0 / - data wgk ( 10) / 0.1477391049 0133849137 4841515972 068 d0 / - data wgk ( 11) / 0.1494455540 0291690566 4936468389 821 d0 / -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk21 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 21-point kronrod approximation to -c the integral, and estimate the absolute error. -c - resg = 0.0d+00 - fc = f(centr) - resk = wgk(11)*fc - resabs = dabs(resk) - do 10 j=1,5 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,5 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(11)*dabs(fc-reskh) - do 20 j=1,10 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0d0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk21 - subroutine dqk15(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk,reskh,result,uflow,wg,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -c xgk(2), xgk(4), ... abscissae of the 7-point -c gauss rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point gauss rule -c -c wgk - weights of the 15-point kronrod rule -c -c wg - weights of the 7-point gauss rule -c -c -c gauss quadrature weights and kronron quadrature abscissae and weights -c as evaluated with 80 decimal digit arithmetic by l. w. fullerton, -c bell labs, nov. 1981. -c - data wg ( 1) / 0.129484966168869693270611432679082d0 / - data wg ( 2) / 0.279705391489276667901467771423780d0 / - data wg ( 3) / 0.381830050505118944950369775488975d0 / - data wg ( 4) / 0.417959183673469387755102040816327d0 / - - data xgk ( 1) / 0.991455371120812639206854697526329d0 / - data xgk ( 2) / 0.949107912342758524526189684047851d0 / - data xgk ( 3) / 0.864864423359769072789712788640926d0 / - data xgk ( 4) / 0.741531185599394439863864773280788d0 / - data xgk ( 5) / 0.586087235467691130294144838258730d0 / - data xgk ( 6) / 0.405845151377397166906606412076961d0 / - data xgk ( 7) / 0.207784955007898467600689403773245d0 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.022935322010529224963732008058970d0/ - data wgk ( 2) / 0.063092092629978553290700663189204d0 / - data wgk ( 3) / 0.104790010322250183839876322541518d0 / - data wgk ( 4) / 0.140653259715525918745189590510238d0 / - data wgk ( 5) / 0.169004726639267902826583426598550d0 / - data wgk ( 6) / 0.190350578064785409913256402421014d0 / - data wgk ( 7) / 0.204432940075298892414161999234649d0 / - data wgk ( 8) / 0.209482141084727828012999174891714d0 / - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resg = wg(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth*xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1+fval2 - resg = resg+wg(j)*fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth*xgk(jtwm1) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1+fval2 - resk = resk+wgk(jtwm1)*fsum - resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2)) - 15 continue - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - result = resk*hlgth - resabs = resabs*dhlgth - resasc = resasc*dhlgth - abserr = dabs((resk-resg)*hlgth)*10.0D0 - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc*dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqk15 - subroutine dqk9(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk0,resk,reskh,result,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(4),wgk(8),xgk(8) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 15-point kronrod rule -! xgk(4), xgk(8) abscissae of the 3-point gauss rule -c xgk(2), xgk(4),xgk(6), xgk(8) ... abscissae of the 7-point -c kronrod rule -c xgk(1), xgk(3), ... abscissae which are optimally -c added to the 7-point kronrod rule -c -c wgk - weights of the 15-point kronrod rule -! -! wgk0 - weights of the 7-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - data wg ( 1) / 0.5555555555555555D+00/ - data wg ( 2) / 0.8888888888888889D+00/ - - data wgk0 ( 1) / 0.1046562260264673D+00/ - data wgk0 ( 2) / 0.2684880898683335D+00/ - data wgk0 ( 3) / 0.4013974147759622D+00/ - data wgk0 ( 4) / 0.4509165386584741D+00/ - - data xgk ( 1) / 0.9938319632127550D+00/ - data xgk ( 2) / 0.9604912687080203D+00/ - data xgk ( 3) / 0.8884592328722570D+00 / - data xgk ( 4) / 0.7745966692414834D+00/ - data xgk ( 5) / 0.6211029467372264D+00/ - data xgk ( 6) / 0.4342437493468026D+00/ - data xgk ( 7) / 0.2233866864289669D+00 / - data xgk ( 8) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.1700171962994028D-01/ - data wgk ( 2) / 0.5160328299707982D-01/ - data wgk ( 3) / 0.9292719531512452D-01/ - data wgk ( 4) / 0.1344152552437843D+00/ - data wgk ( 5) / 0.1715119091363914D+00/ - data wgk ( 6) / 0.2006285293769890D+00/ - data wgk ( 7) / 0.2191568584015875D+00/ - data wgk ( 8) / 0.2255104997982067D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(8)*fc - resk0 = wgk0(4)*fc - resabs = dabs(resk) - do 10 j=1,3 - jtw = 2*j - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(4) + fv2(4)) - do 15 j = 1,4 - jtwm1 = 2*j-1 - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(8)*dabs(fc-reskh) - do 20 j=1,7 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result = resk - call dea3(resg,resk0,resk,abserr,result) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0)) - & * 10.0D0, abserr) - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - - end subroutine dqk9 - subroutine dqkl9(f,a,b,result,abserr,resabs,resasc) -! use functionInterface - implicit none -c***begin prologue dqk15 -c***date written 800101 (yymmdd) -c***revision date 830518 (yymmdd) -c***category no. h2a1a2 -c***keywords 15-point gauss-kronrod rules extended from a 3 point gaus rule -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose to compute i = integral of f over (a,b), with error -c estimate -c j = integral of abs(f) over (a,b) -c***description -c -c integration rules -c standard fortran subroutine -c double precision version -c -c parameters -c on entry -c f - double precision -c function subprogram defining the integrand -c function f(x). the actual name for f needs to be -c declared e x t e r n a l in the driver program. -c -c a - double precision -c lower limit of integration -c -c b - double precision -c upper limit of integration -c -c on return -c result - double precision -c approximation to the integral i -c result is computed by applying the 21-point -c kronrod rule (resk) obtained by optimal addition -c of abscissae to the 10-point gauss rule (resg). -c -c abserr - double precision -c estimate of the modulus of the absolute error, -c which should not exceed abs(i-result) -c -c resabs - double precision -c approximation to the integral j -c -c resasc - double precision -c approximation to the integral of abs(f-i/(b-a)) -c over (a,b) -c -c***references (none) -c***routines called d1mach -c***end prologue dqk15 -c - double precision :: f, a,absc,abserr,b,centr,dhlgth, - * epmach,fc,fsum,fval1,fval2,fv1,fv2,hlgth,resabs,resasc, - * resg,resk0,resk,reskh,result,uflow,wg,wgk0,wgk,xgk - integer j,jtw,jtwm1 - external f -c - dimension fv1(7),fv2(7),wg(2),wgk0(3),wgk(5),xgk(5) -c -c the abscissae and weights are given for the interval (-1,1). -c because of symmetry only the positive abscissae and their -c corresponding weights are given. -c -c xgk - abscissae of the 9-point Gauss-kronrod-lobatto rule -! xgk(1), xgk(5) abscissae of the 3-point gauss-lobatto rule -c xgk(1), xgk(3),xgk(5) abscissae of the 5-point -c kronrod rule -c xgk(2), xgk(4), ... abscissae which are optimally -c added to the 5-point kronrod rule -c -c wgk - weights of the 9-point kronrod rule -! -! wgk0 - weights of the 5-point kronrod rule -c -c wg - weights of the 3-point gauss rule -c -c -c gauss quadrature weights and kronrod quadrature abscissae and weights -c as evaluated in quadruple precision by Patterson -c - - data wg ( 1) / 0.33333333333333333333333333333333333D+00/ - data wg ( 2) / 0.13333333333333333333333333333333333D+01/ - - data wgk0 ( 1) / 0.1000000000000000D+00/ - data wgk0 ( 2) / 0.5444444444444445D+00/ - data wgk0 ( 3) / 0.7111111111111111D+00/ - - data xgk ( 1) / 0.1000000000000000D+01/ - data xgk ( 2) / 0.8904055275126688D+00/ - data xgk ( 3) / 0.6546536707079772D+00/ - data xgk ( 4) / 0.3409822659109930D+00/ - data xgk ( 5) / 0.000000000000000000000000000000000d0 / - - data wgk ( 1) / 0.3064373897707232D-01/ - data wgk ( 2) / 0.1792626995532074D+00/ - data wgk ( 3) / 0.2839787780481211D+00/ - data wgk ( 4) / 0.3342337398164177D+00/ - data wgk ( 5) / 0.3437620872103631D+00/ - -c -c -c list of major variables -c ----------------------- -c -c centr - mid point of the interval -c hlgth - half-length of the interval -c absc - abscissa -c fval* - function value -c resg - result of the 10-point gauss formula -c resk - result of the 21-point kronrod formula -c reskh - approximation to the mean value of f over (a,b), -c i.e. to i/(b-a) -c -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c uflow is the smallest positive magnitude. -c -c***first executable statement dqk15 - epmach = d1mach(4) - uflow = d1mach(1) -c - centr = 0.5d+00*(a+b) - hlgth = 0.5d+00*(b-a) - dhlgth = dabs(hlgth) -c -c compute the 15-point kronrod approximation to -c the integral, and estimate the absolute error. -c - fc = f(centr) - resk = wgk(5)*fc - resk0 = wgk0(3)*fc - resabs = dabs(resk) - do 10 j=1,2 - jtw = 2*j - 1 - absc = hlgth * xgk(jtw) - fval1 = f(centr-absc) - fval2 = f(centr+absc) - fv1(jtw) = fval1 - fv2(jtw) = fval2 - fsum = fval1 + fval2 - resk0 = resk0 + wgk0(j) * fsum - resk = resk+wgk(jtw)*fsum - resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2)) - 10 continue - resg = wg(2)*fc + wg(1)*(fv1(1) + fv2(1)) - do 15 j = 1,2 - jtwm1 = 2*j - absc = hlgth * xgk(jtwm1) - fval1 = f( centr - absc ) - fval2 = f( centr + absc ) - fv1(jtwm1) = fval1 - fv2(jtwm1) = fval2 - fsum = fval1 + fval2 - resk = resk + wgk(jtwm1) * fsum - resabs = resabs + wgk(jtwm1) * (dabs(fval1) + dabs(fval2)) - 15 continue - - reskh = resk*0.5d+00 - resasc = wgk(5)*dabs(fc-reskh) - do 20 j=1,4 - resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh)) - 20 continue - resg = resg * hlgth - resk0 = resk0 * hlgth - resk = resk * hlgth - resabs = resabs * dhlgth - resasc = resasc * dhlgth - result = resk - call dea3(resg,resk0,resk,abserr,result) - abserr = max((dabs(resk-resk0) + dabs(resg-resk0))* 10.0D0,abserr) - - if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00) then - abserr = resasc * dmin1(0.1d+01, - & (0.2d+03*abserr/resasc)**1.5d+00) - endif - if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1 - * ((epmach*0.5d+02)*resabs,abserr) - return - end subroutine dqkl9 - subroutine dqpsrt(limit,last,maxerr,ermax,elist,iord,nrmax) - implicit none -c***begin prologue dqpsrt -c***refer to dqage,dqagie,dqagpe,dqawse -c***routines called (none) -c***revision date 810101 (yymmdd) -c***keywords sequential sorting -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math. & progr. div. - k.u.leuven -c***purpose this routine maintains the descending ordering in the -c list of the local error estimated resulting from the -c interval subdivision process. at each call two error -c estimates are inserted using the sequential search -c method, top-down for the largest error estimate and -c bottom-up for the smallest error estimate. -c***description -c -c ordering routine -c standard fortran subroutine -c double precision version -c -c parameters (meaning at output) -c limit - integer -c maximum number of error estimates the list -c can contain -c -c last - integer -c number of error estimates currently in the list -c -c maxerr - integer -c maxerr points to the nrmax-th largest error -c estimate currently in the list -c -c ermax - double precision -c nrmax-th largest error estimate -c ermax = elist(maxerr) -c -c elist - double precision -c vector of dimension last containing -c the error estimates -c -c iord - integer -c vector of dimension last, the first k elements -c of which contain pointers to the error -c estimates, such that -c elist(iord(1)),..., elist(iord(k)) -c form a decreasing sequence, with -c k = last if last.le.(limit/2+2), and -c k = limit+1-last otherwise -c -c nrmax - integer -c maxerr = iord(nrmax) -c -c***end prologue dqpsrt -c - double precision elist,ermax,errmax,errmin - integer i,ibeg,ido,iord,isucc,j,jbnd,jupbn,k,last,limit,maxerr, - * nrmax - dimension elist(last),iord(last) -c -c check whether the list contains more than -c two error estimates. -c -c***first executable statement dqpsrt - if(last.gt.2) go to 10 - iord(1) = 1 - iord(2) = 2 - go to 90 -c -c this part of the routine is only executed if, due to a -c difficult integrand, subdivision increased the error -c estimate. in the normal case the insert procedure should -c start after the nrmax-th largest error estimate. -c - 10 errmax = elist(maxerr) - if(nrmax.eq.1) go to 30 - ido = nrmax-1 - do 20 i = 1,ido - isucc = iord(nrmax-1) -c ***jump out of do-loop - if(errmax.le.elist(isucc)) go to 30 - iord(nrmax) = isucc - nrmax = nrmax-1 - 20 continue -c -c compute the number of elements in the list to be maintained -c in descending order. this number depends on the number of -c subdivisions still allowed. -c - 30 jupbn = last - if(last.gt.(limit/2+2)) jupbn = limit+3-last - errmin = elist(last) -c -c insert errmax by traversing the list top-down, -c starting comparison from the element elist(iord(nrmax+1)). -c - jbnd = jupbn-1 - ibeg = nrmax+1 - if(ibeg.gt.jbnd) go to 50 - do 40 i=ibeg,jbnd - isucc = iord(i) -c ***jump out of do-loop - if(errmax.ge.elist(isucc)) go to 60 - iord(i-1) = isucc - 40 continue - 50 iord(jbnd) = maxerr - iord(jupbn) = last - go to 90 -c -c insert errmin by traversing the list bottom-up. -c - 60 iord(i-1) = maxerr - k = jbnd - do 70 j=i,jbnd - isucc = iord(k) -c ***jump out of do-loop - if(errmin.lt.elist(isucc)) go to 80 - iord(k+1) = isucc - k = k-1 - 70 continue - iord(i) = last - go to 90 - 80 iord(k+1) = last -c -c set maxerr and ermax. -c - 90 maxerr = iord(nrmax) - ermax = elist(maxerr) - return - end subroutine dqpsrt - subroutine dqelg(n,epstab,result,abserr,res3la,nres) - implicit none -c***begin prologue dqelg -c***refer to dqagie,dqagoe,dqagpe,dqagse -c***routines called d1mach -c***revision date 830518 (yymmdd) -c***keywords epsilon algorithm, convergence acceleration, -c extrapolation -c***author piessens,robert,appl. math. & progr. div. - k.u.leuven -c de doncker,elise,appl. math & progr. div. - k.u.leuven -c***purpose the routine determines the limit of a given sequence of -c approximations, by means of the epsilon algorithm of -c p.wynn. an estimate of the absolute error is also given. -c the condensed epsilon table is computed. only those -c elements needed for the computation of the next diagonal -c are preserved. -c***description -c -c epsilon algorithm -c standard fortran subroutine -c double precision version -c -c parameters -c n - integer -c epstab(n) contains the new element in the -c first column of the epsilon table. -c -c epstab - double precision -c vector of dimension 52 containing the elements -c of the two lower diagonals of the triangular -c epsilon table. the elements are numbered -c starting at the right-hand corner of the -c triangle. -c -c result - double precision -c resulting approximation to the integral -c -c abserr - double precision -c estimate of the absolute error computed from -c result and the 3 previous results -c -c res3la - double precision -c vector of dimension 3 containing the last 3 -c results -c -c nres - integer -c number of calls to the routine -c (should be zero at first call) -c -c***end prologue dqelg -c - double precision abserr,dabs,delta1,delta2,delta3,dmax1, - * epmach,epsinf,epstab,error,err1,err2,err3,e0,e1,e1abs,e2,e3, - * oflow,res,result,res3la,ss,tol1,tol2,tol3 - integer i,ib,ib2,ie,indx,k1,k2,k3,limexp,n,newelm,nres,num - dimension epstab(52),res3la(3) -c -c list of major variables -c ----------------------- -c -c e0 - the 4 elements on which the computation of a new -c e1 element in the epsilon table is based -c e2 -c e3 e0 -c e3 e1 new -c e2 -c newelm - number of elements to be computed in the new -c diagonal -c error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2) -c result - the element in the new diagonal with least value -c of error -c -c machine dependent constants -c --------------------------- -c -c epmach is the largest relative spacing. -c oflow is the largest positive magnitude. -c limexp is the maximum number of elements the epsilon -c table can contain. if this number is reached, the upper -c diagonal of the epsilon table is deleted. -c -c***first executable statement dqelg - epmach = d1mach(4) - oflow = d1mach(2) - nres = nres+1 - abserr = oflow - result = epstab(n) - if(n.lt.3) go to 100 - limexp = 50 - epstab(n+2) = epstab(n) - newelm = (n-1)/2 - epstab(n) = oflow - num = n - k1 = n - do 40 i = 1,newelm - k2 = k1-1 - k3 = k1-2 - res = epstab(k1+2) - e0 = epstab(k3) - e1 = epstab(k2) - e2 = res - e1abs = dabs(e1) - delta2 = e2-e1 - err2 = dabs(delta2) - tol2 = dmax1(dabs(e2),e1abs)*epmach - delta3 = e1-e0 - err3 = dabs(delta3) - tol3 = dmax1(e1abs,dabs(e0))*epmach - if(err2.gt.tol2.or.err3.gt.tol3) go to 10 -c -c if e0, e1 and e2 are equal to within machine -c accuracy, convergence is assumed. -c result = e2 -c abserr = abs(e1-e0)+abs(e2-e1) -c - result = res - abserr = err2+err3 -c ***jump out of do-loop - go to 100 - 10 e3 = epstab(k1) - epstab(k1) = e1 - delta1 = e1-e3 - err1 = dabs(delta1) - tol1 = dmax1(e1abs,dabs(e3))*epmach -c -c if two elements are very close to each other, omit -c a part of the table by adjusting the value of n -c - if(err1.le.tol1.or.err2.le.tol2.or.err3.le.tol3) go to 20 - ss = 0.1d+01/delta1+0.1d+01/delta2-0.1d+01/delta3 - epsinf = dabs(ss*e1) -c -c test to detect irregular behaviour in the table, and -c eventually omit a part of the table adjusting the value -c of n. -c - if(epsinf.gt.0.1d-03) go to 30 - 20 n = i+i-1 -c ***jump out of do-loop - go to 50 -c -c compute a new element and eventually adjust -c the value of result. -c - 30 res = e1+0.1d+01/ss - epstab(k1) = res - k1 = k1-2 - error = err2+dabs(res-e2)+err3 - if(error.gt.abserr) go to 40 - abserr = error - result = res - 40 continue -c -c shift the table. -c - 50 if(n.eq.limexp) n = 2*(limexp/2)-1 - ib = 1 - if((num/2)*2.eq.num) ib = 2 - ie = newelm+1 - do 60 i=1,ie - ib2 = ib+2 - epstab(ib) = epstab(ib2) - ib = ib2 - 60 continue - if(num.eq.n) go to 80 - indx = num-n+1 - do 70 i = 1,n - epstab(i)= epstab(indx) - indx = indx+1 - 70 continue - 80 if(nres.ge.4) go to 90 - res3la(nres) = result - abserr = oflow - go to 100 -c -c compute error estimate -c - 90 abserr = dabs(result-res3la(3))+dabs(result-res3la(2)) - * +dabs(result-res3la(1)) - res3la(1) = res3la(2) - res3la(2) = res3la(3) - res3la(3) = result - 100 abserr = dmax1(abserr,0.5d+01*epmach*dabs(result)) - return - end subroutine dqelg - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - end module AdaptiveGaussKronrod - - module Integration1DModule - implicit none - interface AdaptiveSimpson - module procedure AdaptiveSimpson2, AdaptiveSimpsonWithBreaks - end interface - -! interface AdaptiveSimpson1 -! module procedure AdaptiveSimpson1 -! end interface - - interface AdaptiveTrapz - module procedure AdaptiveTrapz1, AdaptiveTrapzWithBreaks - end interface - - interface Romberg - module procedure Romberg1, RombergWithBreaks - end interface - - INTERFACE DEA - MODULE PROCEDURE DEA - END INTERFACE - - INTERFACE d1mach - MODULE PROCEDURE d1mach - END INTERFACE - contains - DOUBLE PRECISION FUNCTION D1MACH(I) - implicit none -C -C Double-precision machine constants. -C -C D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude. -C D1MACH( 3) = B**(-T), the smallest relative spacing. -C D1MACH( 4) = B**(1-T), the largest relative spacing. -C D1MACH( 5) = LOG10(B) -C -C Two more added much later: -C -C D1MACH( 6) = Infinity. -C D1MACH( 7) = Not-a-Number. -C -C Reference: Fox P.A., Hall A.D., Schryer N.L.,"Framework for a -C Portable Library", ACM Transactions on Mathematical -C Software, Vol. 4, no. 2, June 1978, PP. 177-188. -C - INTEGER , INTENT(IN) :: I - DOUBLE PRECISION, SAVE :: DMACH(7) - DOUBLE PRECISION :: B, EPS - DOUBLE PRECISION :: ONE = 1.0D0 - DOUBLE PRECISION :: ZERO = 0.0D0 - INTEGER :: EMAX,EMIN,T - DATA DMACH /7*0.0D0/ -! First time through, get values from F90 INTRINSICS: - IF (DMACH(1) .EQ. 0.0D0) THEN - T = DIGITS(ONE) - B = DBLE(RADIX(ONE)) ! base number - EPS = SPACING(ONE) - EMIN = MINEXPONENT(ONE) - EMAX = MAXEXPONENT(ONE) - DMACH(1) = B**(EMIN-1) !TINY(ONE) - DMACH(2) = (B**(EMAX-1)) * (B-B*EPS) !HUGE(ONE) - DMACH(3) = EPS/B ! EPS/B - DMACH(4) = EPS - DMACH(5) = LOG10(B) - DMACH(6) = B**(EMAX+5) !infinity - DMACH(7) = ZERO/ZERO !nan - ENDIF -C - D1MACH = DMACH(I) - RETURN - END FUNCTION D1MACH - subroutine dea3(E0,E1,E2,abserr,result) -!***PURPOSE Given a slowly convergent sequence, this routine attempts -! to extrapolate nonlinearly to a better estimate of the -! sequence's limiting value, thus improving the rate of -! convergence. Routine is based on the epsilon algorithm -! of P. Wynn. An estimate of the absolute error is also -! given. - double precision, intent(in) :: E0,E1,E2 - double precision, intent(out) :: abserr, result - !locals - double precision, parameter :: ten = 10.0d0 - double precision, parameter :: one = 1.0d0 - double precision :: small, delta2, delta1 - double precision :: tol2, tol1, err2, err1,ss - small = spacing(one) - delta2 = E2 - E1 - delta1 = E1 - E0 - err2 = abs(delta2) - err1 = abs(delta1) - tol2 = max(abs(E2),abs(E1)) * small - tol1 = max(abs(E1),abs(E0)) * small - if ( ( err1 <= tol1 ) .or. err2 <= tol2) then -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. - result = E2 - abserr = err1 + err2 + E2*small*ten - else - ss = one/delta2 - one/delta1 - if (abs(ss*E1) <= 1.0d-3) then - result = E2 - abserr = err1 + err2 + E2*small*ten - else - result = E1 + one/ss - abserr = err1 + err2 + abs(result-E2) - endif - endif - end subroutine dea3 - SUBROUTINE DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -C***BEGIN PROLOGUE DEA -C***DATE WRITTEN 800101 (YYMMDD) -C***REVISION DATE 871208 (YYMMDD) -C***CATEGORY NO. E5 -C***KEYWORDS CONVERGENCE ACCELERATION,EPSILON ALGORITHM,EXTRAPOLATION -C***AUTHOR PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. - -C K. U. LEUVEN -C DE DONCKER-KAPENGA, ELISE,WESTERN MICHIGAN UNIVERSITY -C KAHANER, DAVID K., NATIONAL BUREAU OF STANDARDS -C STARKENBURG, C. B., NATIONAL BUREAU OF STANDARDS -C***PURPOSE Given a slowly convergent sequence, this routine attempts -C to extrapolate nonlinearly to a better estimate of the -C sequence's limiting value, thus improving the rate of -C convergence. Routine is based on the epsilon algorithm -C of P. Wynn. An estimate of the absolute error is also -C given. -C***DESCRIPTION -C -C Epsilon algorithm. Standard fortran subroutine. -C Double precision version. -C -C A R G U M E N T S I N T H E C A L L S E Q U E N C E -C -C NEWFLG - LOGICAL (INPUT and OUTPUT) -C On the first call to DEA set NEWFLG to .TRUE. -C (indicating a new sequence). DEA will set NEWFLG -C to .FALSE. -C -C SVALUE - DOUBLE PRECISION (INPUT) -C On the first call to DEA set SVALUE to the first -C term in the sequence. On subsequent calls set -C SVALUE to the subsequent sequence value. -C -C LIMEXP - INTEGER (INPUT) -C An integer equal to or greater than the total -C number of sequence terms to be evaluated. Do not -C change the value of LIMEXP until a new sequence -C is evaluated (NEWFLG=.TRUE.). LIMEXP .GE. 3 -C -C RESULT - DOUBLE PRECISION (OUTPUT) -C Best approximation to the sequence's limit. -C -C ABSERR - DOUBLE PRECISION (OUTPUT) -C Estimate of the absolute error. -C -C EPSTAB - DOUBLE PRECISION (OUTPUT) -C Workvector of DIMENSION at least (LIMEXP+7). -C -C IERR - INTEGER (OUTPUT) -C IERR=0 Normal termination of the routine. -C IERR=1 The input is invalid because LIMEXP.LT.3. -C -C T Y P I C A L P R O B L E M S E T U P -C -C This sample problem uses the trapezoidal rule to evaluate the -C integral of the sin function from 0.0 to 0.5*PI (value = 1.0). The -C program implements the trapezoidal rule 8 times creating an -C increasingly accurate sequence of approximations to the integral. -C Each time the trapezoidal rule is used, it uses twice as many -C panels as the time before. DEA is called to obtain even more -C accurate estimates. -C -C PROGRAM SAMPLE -C IMPLICIT DOUBLE PRECISION (A-H,O-Z) -C DOUBLE PRECISION EPSTAB(57) -CC [57 = LIMEXP + 7] -C LOGICAL NEWFLG -C EXTERNAL F -C DATA LIMEXP/50/ -C WRITE(*,*) ' NO. PANELS TRAP. APPROX' -C * ,' APPROX W/EA ABSERR' -C WRITE(*,*) -C HALFPI = DASIN(1.0D+00) -CC [UPPER INTEGRATION LIMIT = PI/2] -C NEWFLG = .TRUE. -CC [SET FLAG - 1ST DEA CALL] -C DO 10 I = 0,7 -C NPARTS = 2 ** I -C WIDTH = HALFPI/NPARTS -C APPROX = 0.5D+00 * WIDTH * (F(0.0D+00) + F(HALFPI)) -C DO 11 J = 1,NPARTS-1 -C APPROX = APPROX + F(J * WIDTH) * WIDTH -C 11 CONTINUE -CC [END TRAPEZOIDAL RULE APPROX] -C SVALUE = APPROX -CC [SVALUE = NEW SEQUENCE VALUE] -C CALL DEA(NEWFLG,SVALUE,LIMEXP,RESULT,ABSERR,EPSTAB,IERR) -CC [CALL DEA FOR BETTER ESTIMATE] -C WRITE(*,12) NPARTS,APPROX,RESULT,ABSERR -C 12 FORMAT(' ',I4,T20,F16.13,T40,F16.13,T60,D11.4) -C 10 CONTINUE -C STOP -C END -C -C DOUBLE PRECISION FUNCTION F(X) -C DOUBLE PRECISION X -C F = DSIN(X) -CC [INTEGRAND] -C RETURN -C END -C -C Output from the above program will be: -C -C NO. PANELS TRAP. APPROX APPROX W/EA ABSERR -C -C 1 .7853981633974 .7853981633974 .7854D+00 -C 2 .9480594489685 .9480594489685 .9760D+00 -C 4 .9871158009728 .9994567212570 .2141D+00 -C 8 .9967851718862 .9999667417647 .3060D-02 -C 16 .9991966804851 .9999998781041 .6094D-03 -C 32 .9997991943200 .9999999981026 .5767D-03 -C 64 .9999498000921 .9999999999982 .3338D-04 -C 128 .9999874501175 1.0000000000000 .1238D-06 -C -C----------------------------------------------------------------------- -C***REFERENCES "Acceleration de la convergence en analyse numerique", -C C. Brezinski, "Lecture Notes in Math.", vol. 584, -C Springer-Verlag, New York, 1977. -C***ROUTINES CALLED D1MACH,XERROR -C***END PROLOGUE DEA - double precision, dimension(*), intent(inout) :: EPSTAB - double precision, intent(out) :: RESULT !, ABSERR - double precision, intent(inout) :: ABSERR - double precision, intent(in) :: SVALUE - INTEGER, INTENT(IN) :: LIMEXP - INTEGER, INTENT(OUT) :: IERR - LOGICAL, intent(INOUT) :: NEWFLG - DOUBLE PRECISION :: DELTA1,DELTA2,DELTA3,DRELPR,DEPRN, - 1 ERROR,ERR1,ERR2,ERR3,E0,E1,E2,E3,RES, - 2 SS,TOL1,TOL2,TOL3 - double precision, dimension(3) :: RES3LA - INTEGER I,IB,IB2,IE,IN,K1,K2,K3,N,NEWELM,NUM,NRES -C -C -C LIMEXP is the maximum number of elements the -C epsilon table data can contain. The epsilon table -C is stored in the first (LIMEXP+2) entries of EPSTAB. -C -C -C LIST OF MAJOR VARIABLES -C ----------------------- -C E0,E1,E2,E3 - DOUBLE PRECISION -C The 4 elements on which the computation of -C a new element in the epsilon table is based. -C NRES - INTEGER -C Number of extrapolation results actually -C generated by the epsilon algorithm in prior -C calls to the routine. -C NEWELM - INTEGER -C Number of elements to be computed in the -C new diagonal of the epsilon table. The -C condensed epsilon table is computed. Only -C those elements needed for the computation of -C the next diagonal are preserved. -C RES - DOUBLE PRECISION -C New element in the new diagonal of the -C epsilon table. -C ERROR - DOUBLE PRECISION -C An estimate of the absolute error of RES. -C Routine decides whether RESULT=RES or -C RESULT=SVALUE by comparing ERROR with -C ABSERR from the previous call. -C RES3LA - DOUBLE PRECISION -C Vector of DIMENSION 3 containing at most -C the last 3 results. -C -C -C MACHINE DEPENDENT CONSTANTS -C --------------------------- -C DRELPR is the largest relative spacing. -C -C***FIRST EXECUTABLE STATEMENT DEA - IF(LIMEXP.LT.3) THEN - IERR = 1 -! CALL XERROR('LIMEXP IS LESS THAN 3',21,1,1) - GO TO 110 - ENDIF - IERR = 0 - RES3LA(1)=EPSTAB(LIMEXP+5) - RES3LA(2)=EPSTAB(LIMEXP+6) - RES3LA(3)=EPSTAB(LIMEXP+7) - RESULT=SVALUE - IF(NEWFLG) THEN - N=1 - NRES=0 - NEWFLG=.FALSE. - EPSTAB(N)=SVALUE - ABSERR=ABS(RESULT) - GO TO 100 - ELSE - N=INT(EPSTAB(LIMEXP+3)) - NRES=INT(EPSTAB(LIMEXP+4)) - IF(N.EQ.2) THEN - EPSTAB(N)=SVALUE - ABSERR=.6D+01*ABS(RESULT-EPSTAB(1)) - GO TO 100 - ENDIF - ENDIF - EPSTAB(N)=SVALUE - DRELPR=D1MACH(4) - DEPRN=1.0D+01*DRELPR - EPSTAB(N+2)=EPSTAB(N) - NEWELM=(N-1)/2 - NUM=N - K1=N - DO 40 I=1,NEWELM - K2=K1-1 - K3=K1-2 - RES=EPSTAB(K1+2) - E0=EPSTAB(K3) - E1=EPSTAB(K2) - E2=RES - DELTA2=E2-E1 - ERR2=ABS(DELTA2) - TOL2=MAX(ABS(E2),ABS(E1))*DRELPR - DELTA3=E1-E0 - ERR3=ABS(DELTA3) - TOL3=MAX(ABS(E1),ABS(E0))*DRELPR - IF(ERR2.GT.TOL2.OR.ERR3.GT.TOL3) GO TO 10 -C -C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE -C ACCURACY, CONVERGENCE IS ASSUMED. -C RESULT=E2 -C ABSERR=ABS(E1-E0)+ABS(E2-E1) -C - RESULT=RES - ABSERR=ERR2+ERR3 - GO TO 50 - 10 IF(I.NE.1) THEN - E3=EPSTAB(K1) - EPSTAB(K1)=E1 - DELTA1=E1-E3 - ERR1=ABS(DELTA1) - TOL1=MAX(ABS(E1),ABS(E3))*DRELPR -C -C IF TWO ELEMENTS ARE VERY CLOSE TO EACH OTHER, OMIT -C A PART OF THE TABLE BY ADJUSTING THE VALUE OF N -C - IF(ERR1.LE.TOL1.OR.ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA1+0.1D+01/DELTA2-0.1D+01/DELTA3 - ELSE - EPSTAB(K1)=E1 - IF(ERR2.LE.TOL2.OR.ERR3.LE.TOL3) GO TO 20 - SS=0.1D+01/DELTA2-0.1D+01/DELTA3 - ENDIF -C -C TEST TO DETECT IRREGULAR BEHAVIOUR IN THE TABLE, AND -C EVENTUALLY OMIT A PART OF THE TABLE ADJUSTING THE VALUE -C OF N -C - IF(ABS(SS*E1).GT.0.1D-03) GO TO 30 - 20 N=I+I-1 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ERR3 - RESULT=RES - ELSE IF(NRES.EQ.1) THEN - RESULT=RES3LA(1) - ELSE IF(NRES.EQ.2) THEN - RESULT=RES3LA(2) - ELSE - RESULT=RES3LA(3) - ENDIF - GO TO 50 -C -C COMPUTE A NEW ELEMENT AND EVENTUALLY ADJUST -C THE VALUE OF RESULT -C - 30 RES=E1+0.1D+01/SS - EPSTAB(K1)=RES - K1=K1-2 - IF(NRES.EQ.0) THEN - ABSERR=ERR2+ABS(RES-E2)+ERR3 - RESULT=RES - GO TO 40 - ELSE IF(NRES.EQ.1) THEN - ERROR=.6D+01*(ABS(RES-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ERROR=.2D+01*(ABS(RES-RES3LA(2))+ABS(RES-RES3LA(1))) - ELSE - ERROR=ABS(RES-RES3LA(3))+ABS(RES-RES3LA(2)) - 1 +ABS(RES-RES3LA(1)) - ENDIF - IF(ERROR.GT.1.0D+01*ABSERR) GO TO 40 - ABSERR=ERROR - RESULT=RES - 40 CONTINUE -C -C COMPUTE ERROR ESTIMATE -C - IF(NRES.EQ.1) THEN - ABSERR=.6D+01*(ABS(RESULT-RES3LA(1))) - ELSE IF(NRES.EQ.2) THEN - ABSERR=.2D+01*ABS(RESULT-RES3LA(2))+ABS(RESULT-RES3LA(1)) - ELSE IF(NRES.GT.2) THEN - ABSERR=ABS(RESULT-RES3LA(3))+ABS(RESULT-RES3LA(2)) - 1 +ABS(RESULT-RES3LA(1)) - ENDIF -C -C SHIFT THE TABLE -C - 50 IF(N.EQ.LIMEXP) N=2*(LIMEXP/2)-1 - IB=1 - IF((NUM/2)*2.EQ.NUM) IB=2 - IE=NEWELM+1 - DO 60 I=1,IE - IB2=IB+2 - EPSTAB(IB)=EPSTAB(IB2) - IB=IB2 - 60 CONTINUE - IF(NUM.EQ.N) GO TO 80 - IN=NUM-N+1 - DO 70 I=1,N - EPSTAB(I)=EPSTAB(IN) - IN=IN+1 - 70 CONTINUE -C -C UPDATE RES3LA -C - 80 IF(NRES.EQ.0) THEN - RES3LA(1)=RESULT - ELSE IF(NRES.EQ.1) THEN - RES3LA(2)=RESULT - ELSE IF(NRES.EQ.2) THEN - RES3LA(3)=RESULT - ELSE - RES3LA(1)=RES3LA(2) - RES3LA(2)=RES3LA(3) - RES3LA(3)=RESULT - ENDIF - 90 ABSERR=MAX(ABSERR,DEPRN*ABS(RESULT)) - NRES=NRES+1 - 100 N=N+1 - EPSTAB(LIMEXP+3)=DBLE(N) - EPSTAB(LIMEXP+4)=DBLE(NRES) - EPSTAB(LIMEXP+5)=RES3LA(1) - EPSTAB(LIMEXP+6)=RES3LA(2) - EPSTAB(LIMEXP+7)=RES3LA(3) - 110 RETURN - END subroutine DEA - - subroutine AdaptiveIntWithBreaks(f,a,b,N,brks,epsi,iflg - $ ,abserr, val) - use AdaptiveGaussKronrod - implicit none - double precision :: f - integer, intent(in) :: N - double precision, intent(in) :: a,b,epsi - double precision, dimension(:), intent(in) :: brks - double precision, intent(out) :: abserr, val - integer, intent(out) :: iflg - external f -! Locals - double precision, dimension(N+2) :: pts - double precision :: LTol,tol, error, valk, excess, errorEstimate - double precision :: delta, deltaK - integer :: kflg, k, limit,neval - limit = 30 - pts(1) = a - pts(N+2) = b - delta = b - a - do k = 2,N+1 - pts(k) = minval(brks(k-1:N)) !add user supplied break points - enddo - LTol = epsi / delta - abserr = 0.0d0 - val = 0.0D0 - iflg = 0 - do k = 1, N + 1 - deltaK = pts(k+1) - pts(k) - tol = LTol * deltaK - if (deltaK < 0.5D0) then - call AdaptiveSimpson(f,pts(k),pts(k+1),tol, kflg,error,valk) -! call romberg(f,pts(k),pts(k+1),20,tol,kflg,error, valk) - else -! call AdaptiveSimpson3(f,pts(k),pts(k+1),tol,kflg,error,valk) - call dqagp(f,pts(k),pts(k+1),0,pts,tol,0.0D0,limit,valk, - * error,neval,kflg) - - endif - abserr = abserr + abs(error) - - errorEstimate = abserr + (b - pts(k+1)) * LTol - excess = epsi - errorEstimate - if (excess < 0.0D0 ) then - LTol = 0.1D0*LTol - elseif ( epsi < 2.0D0 * excess ) then - LTol = (epsi + excess*0.5D0) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0.0d0 .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif ( Lepsi < 5D0 * excess ) then - LTol = (Lepsi + excess) / delta - endif - val = val + valk - if (kflg>0) iflg = IOR(iflg, kflg) - end do - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn12e = ( Sn1e - Sn2e ) - - Sn24e = (Sn2e - Sn4) -! Sn1e = Sn2e - Sn12e * zpz66666 -! Sn12e = (Sn1e - Sn2e) - - Sn124 = (Sn12e - Sn24) - if ((abs(Sn124)<= hmin) .or. - & .false..and.(Sn24*Sn12e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn24 * zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24 * Sn24 / Sn124 - endif - Sn4e = Sn4 + correction - -! NEWFLG = .TRUE. -! CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn1e,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) -! CALL DEA(NEWFLG,Sn4e,LIMEXP,val0,localError,EPSTAB,IERR) -! localError is made conservative in order to avoid premature -! termination - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) - !if (h>dhMin) then - !localError = max(localError,abs(correction)) - !else - !val0 = Sn4e - !localError = abs(correction)*two - !endif - else - CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - endif - acceptError = ( localError <= Ltol * h * eight - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(6,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.true..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,fx3,fx4,fx5,x1,h,S,SL,SR] - kp1 = k + 1; -! Process right interval - v(1,kp1) = v(3,k); !fx1R - v(2,kp1) = fx(3); !fx2R - v(3,kp1) = v(4,k); !fx3R - v(4,kp1) = fx(4); !fx4R - v(5,kp1) = v(5,k); !fx5R - v(6,kp1) = v(6,k) + four * h; ! x1R - v(7,kp1) = h; - v(8,kp1) = v(10,k); ! S - v(9:10,kp1) = Sn(3:4); ! SL, SR -! Process left interval - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) unchanged fx1L -! v(6,k) unchanged x1L - v(7,k) = h; - v(8,k) = v(9,k); ! S - v(9:10,k) = Sn(1:2); ! SL, SR - k = kp1; - endif - enddo ! while - if (epsi0) then - Sn12 = (Sn1 - Sn2) - Sn24 = (Sn2 - Sn4) - Sn48 = (Sn4 - Sn8) - ! Extrapolate Sn1 and Sn2: - Sn1e = Sn2 - Sn12 * zpz66666 - Sn2e = Sn4 - Sn24 * zpz66666 - Sn4e = Sn8 - Sn48 * zpz588 - Sn12e = (Sn1e - Sn2e) - Sn24e = (Sn2e - Sn4e) - - Sn124 = (Sn12e - Sn24e) - if ((abs(Sn124)<= hmin) .or. - & (Sn12e*Sn24e < zero)) then -! Correction based on the assumption of slowly varying fourth derivative - correction = -Sn48*zpz588 ! - else -! Correction based on assumption that the termination error -! is of the form: C*h^q - correction = -Sn24e * Sn24e / Sn124 - !Sn4e = Sn4e + correction - endif - CALL DEA3(Sn1e,Sn2e,Sn4e,localError,val0) -! localError is made conservative in order to avoid premature -! termination -! localError = max(localError,abs(correction)*three) -! localError = abs(correction)*three - else - !CALL DEA3(Sn1,Sn2,Sn4,localError,val0) - NEWFLG = .TRUE. - CALL DEA(NEWFLG,Sn1,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn2,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn4,LIMEXP,val0,localError,EPSTAB,IERR) - CALL DEA(NEWFLG,Sn8,LIMEXP,val0,localError,EPSTAB,IERR) - endif - acceptError = ( localError <= Ltol * h * sixteen - & .or. localError < small) - else - acceptError = .FALSE. - endif - - stepSizeTooSmall = ( h < hMin) - if (lastInStack .or. - & ( stepSizeOK .and. acceptError ) .or. - & stepSizeTooSmall) then -! Stop subdividing interval when -! 1) accuracy is sufficient, or -! 2) interval too narrow, or -! 3) subdivided too often. (stack limit reached) - -! Add partial integral and take a new vector from the bottom of the stack. - - abserr = abserr + max(localError, ten*small*val0) - val = val + val0 - k = k - 1 - if (.not.acceptError) then - if (lastInStack) iflg = IOR(iflg,1) !stack limit reached - if (stepSizeTooSmall) iflg = IOR(iflg,2) !stepSize limit reached - endif - if (k <= 0) then - exit ! while loop - endif - deltaK = (v(Nrule+1,k+1)-a) - errorEstimate = abserr + deltaK * Ltol - excess = Lepsi - errorEstimate - if (excess < zero ) then - if (deltaK > zero .and. Lepsi > abserr) then - LTol = (Lepsi - abserr) / deltaK - else - LTol = 0.1D0 * LTol - endif - elseif (.TRUE..or. Lepsi < four * excess ) then - LTol = (Lepsi + 0.9D0 * excess) / delta - endif - else -! Subdivide the interval and create two new vectors in the stack, -! one of which overwrites the vector just processed. -! -! v(:,k) = [fx1,fx2,..,fx8,fx9,x1,h,S,SL,SR,SL1,SL2 SR1,SR2] - kp1 = k + 1; -! Process right interval - - v(1,kp1) = v(5,k); !fx1R - v(2,kp1) = fx(5); !fx2R - v(3,kp1) = v(6,k); !fx3R - v(4,kp1) = fx(6); !fx4R - v(5,kp1) = v(7,k); !fx5R - v(6,kp1) = fx(7); !fx6R - v(7,kp1) = v(8,k); !fx7R - v(8,kp1) = fx(8); !fx8R - v(9,kp1) = v(9,k); !fx9R - - v(Nrule+1,kp1) = v(Nrule+1,k) + eight * h ! x1R - v(Nrule+2,kp1) = h; - v(Nrule+3,kp1) = v(Nrule+5,k); ! S - v(Nrule+4,kp1) = v(Nrule+8,k); ! SL - v(Nrule+5,kp1) = v(Nrule+9,k); ! SR - v(Nrule+6:Nrule+9,kp1) = Sn(5:8); ! SL1,SL2,SR1, SR2 -! Process left interval - v(9,k) = v(5,k); ! fx9L - v(8,k) = fx(4); ! fx8L - v(7,k) = v(4,k); ! fx7L - v(6,k) = fx(3); ! fx6L - v(5,k) = v(3,k); ! fx5L - v(4,k) = fx(2); ! fx4L - v(3,k) = v(2,k); ! fx3L - v(2,k) = fx(1); ! fx2L -! v(1,k) = v(1,k); ! fx1L -! v(Nrule+1,k) unchanged x1L - v(Nrule+2,k) = h; - v(Nrule+3,k) = v(Nrule + 4,k); ! S - v(Nrule+4,k) = v(Nrule+6,k); ! SL - v(Nrule+5,k) = v(Nrule+7,k); ! SR - v(Nrule+6:Nrule+9,k) = Sn(1:4); ! SL1,SL2,SR1, SR2 - k = kp1; - endif - enddo ! while - if (epsi0) iflg = IOR(iflg, kflg) - end do - if (epsi0) iflg = ior(iflg,kflg) - end do - if (epsistepSize) then - Nk = floor((xup-xlo)/stepSize) + 1 - dx = (xup-xlo)/dble(Nk) - do j=1, Nk -1 - Npts = Npts + 1 - breakPoints(Npts) = xlo + dx * dble( j ) - enddo - endif - else - ! Compute candidates for the breakpoints - brkPts(1:2*n) = xup - forall(k=1:n,rho(k) .ne. zero) - indices(2*k-1) = k - indices(2*k ) = k - brkPts(2*k-1) = a(k)/rho(k) - brkPts(2*k ) = b(k)/rho(k) - end forall - ! Sort the candidates - call sortre(brkPts,indices) - ! Make unique list of breakpoints - - do k = 1,2*n - brk = brkPts(k) - if (xlo < brk) then - if ( xup <= brk ) exit ! terminate do loop - -! if (Npts>0) then -! xLow = max(xlo, breakPoints(Npts)) -! else -! xLow = xlo -! endif -! if (brk-xLow>stepSize) then -! Nk = floor((brk-xLow)/stepSize) -! dx = (brk-xLow)/dble(Nk) -! do j=1, Nk -1 -! Npts = Npts + 1 -! breakPoints(Npts) = brk + dx * dble( j ) -! enddo -! endif - - kU = indices(k) - - !if ( xlo + distance < brk .and. brk + distance < xup ) - !then - if ( den(kU) < 0.2) then - distance = max(brkSplit*den(kU),hMin) - z1 = brk + distance - z2 = brk - distance - if (Npts <= 0) then - if (xlo + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - kL = kU - elseif (breakPoints(Npts)+ max(distance - & ,brkSplit*den(kL)) < z1) then - if (breakPoints(Npts) + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - kL = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - kL = kU - endif - else - val1 = 0.0d0 - val2 = 0.0d0 - brkPts(Npts+1) = integrand(z1) - brkPts(Npts+2) = integrand(z2) - if ((xlo+ distance < z1) .and. (z1 + distance < xup)) - & val2 = brkPts(Npts +1) - if ((xlo+ distance < z2) .and. (z2 + distance < xup)) - & val2 = max(val2,brkPts(Npts +2)) - val1 = breakPoints(Npts) - Nprev = 1 - if (Npts>1) then - if (indices2(Npts-1)==kL) then - Nprev = 2 - val1 = max(val1,breakPoints(Npts-1)) - endif - endif - if (val1 < val2) then - !overwrite previous candidate - Npts = Npts - Nprev - if (Npts>0) then - val1 = breakPoints(Npts)+ distance - else - val1 = xlo+ distance - endif - if (val1 < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = brkPtsVal(Npts+Nprev) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - - if ((val1< z2) .and. (z2 + distance < xup)) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - if (Npts>0) kL = indices2(Npts) - endif - endif - endif - endif - enddo - endif - end subroutine GetBreakPoints - subroutine NarrowLimits(zMin,zMax,As,Bs,zCutOff,n,a,b,rho,den) - implicit none - double precision, intent(inout) :: zMin, zMax, As, Bs - double precision,dimension(*),intent(in) :: rho,a,b,den - double precision, intent(in) :: zCutOff - integer, intent(in) :: n -! Locals - double precision, parameter :: zero = 0.0D0, one = 1.0D0 - integer :: k - -! Uses the regression equation to limit the -! integration limits zMin and zMax - - do k = 1,n - if (ZERO < rho(k)) then - zMax = max(zMin, min(zMax,(b(k)+den(k)*zCutOff)/rho(k))) - zMin = min(zMax, max(zMin,(a(k)-den(k)*zCutOff)/rho(k))) - if ( one <= rho(k) ) then - if ( b(k) < Bs ) Bs = b(k) - if ( As < a(k) ) As = a(k) - endif - elseif (rho(k)< ZERO) then - zMax = max(zMin,min(zMax,(a(k)-den(k)*zCutOff)/rho(k))) - zMin = min(zMax,max(zMin,(b(k)+den(k)*zCutOff)/rho(k))) - if ( rho(k) <= -one ) then - if ( -a(k) < Bs ) Bs = -a(k) - if ( As < -b(k) ) As = -b(k) - endif - endif - enddo - As = min(As,Bs) - end subroutine NarrowLimits - - function integrand(z) result (val) - implicit none - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - double precision, parameter :: sqtwopi1 = 0.39894228040143D0 - double precision, parameter :: half = 0.5D0 - val = sqtwopi1 * exp(-half * z * z) * integrand1(z) - return - end function integrand - - function integrand1(z) result (val) - implicit none - double precision, intent(in) :: z - double precision :: val - double precision :: xUp,xLo,zRho - double precision, parameter :: one = 1.0D0, zero = 0.0D0 - integer :: I - val = one - do I = 1, mNdim - zRho = z * mRho(I) - ! Uncomment / mDen below if mRho, mA, mB is not scaled - xUp = ( mB(I) - zRho ) !/ mDen(I) - xLo = ( mA(I) - zRho ) !/ mDen(I) - if (zero0.1 -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION, INTENT(in) :: P - DOUBLE PRECISION :: VAL -!local variables - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, ONE, ZERO, HALF, - & A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - & C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - & E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - & Q, R - PARAMETER ( SPLIT1 = 0.425D0, SPLIT2 = 5.D0, - & CONST1 = 0.180625D0, CONST2 = 1.6D0, - & ONE = 1.D0, ZERO = 0.D0, HALF = 0.5D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( P - HALF) - IF ( ABS(Q) .LE. SPLIT1 ) THEN ! Central range. - R = CONST1 - Q*Q - VAL = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + ONE) - ELSE ! near the endpoints - R = MIN( P, ONE - P ) - IF (R .GT.ZERO) THEN ! ( 2.d0*R .GT. CFxCutOff) THEN ! R .GT.0.d0 - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - VAL = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + ONE ) - ELSE - R = R - SPLIT2 - VAL = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + ONE ) - END IF - ELSE - VAL = 37.D0 !XMAX 9.d0 - END IF - IF ( Q < ZERO ) VAL = - VAL - END IF - RETURN - END FUNCTION FIINV - FUNCTION FI2( Z ) RESULT (VALUE) -! USE GLOBALDATA, ONLY : XMAX - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -* -* Normal distribution probabilities accurate to 1.e-15. -* relative error less than 1e-8; -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION :: P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7,XMAX, - * P, EXPNTL, CUTOFF, ROOTPI, ZABS, Z2 - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = 0.70038 30644 43688 1D0, - * P6 = 0.035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = 0.088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) - PARAMETER( XMAX = 8.25D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( ZABS .GT. XMAX ) THEN - P = 0.d0 - ELSE -* -* |Z| <= 37 -* - Z2 = ZABS * ZABS - EXPNTL = EXP( -Z2 * 0.5D0 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS < CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1.d0/( ZABS + 2.d0/( ZABS + 3.d0/( ZABS - * + 4.d0/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0.d0 ) P = 1.d0 - P - VALUE = P - RETURN - END FUNCTION FI2 - - FUNCTION FI( Z ) RESULT (VALUE) - USE ERFCOREMOD - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -! Local variables - DOUBLE PRECISION, PARAMETER:: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER:: HALF = 0.5D0 - VALUE = DERFC(-Z*SQ2M1)*HALF - RETURN - END FUNCTION FI - end module mvnProdCorrPrbMod - - \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprb.pyf b/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprb.pyf deleted file mode 100644 index fa380b9..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprb.pyf +++ /dev/null @@ -1,24 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - -python module mvnprdcrprb ! in - interface ! in :mvnprdcrprb - subroutine pymvnprdcrprb(rho,a,b,n,abseps,releps,usebreakpoints,usesimpson,prb,abserr,ift) ! in :mvnprdcrprb:mvnprodcorrprb_interface.f - use mvnprodcorrprbmod,,only: mvnprodcorrprb - double precision dimension(n),intent(in),depend(n) :: rho - double precision dimension(n),intent(in),depend(n) :: a - double precision dimension(n),intent(in),depend(n) :: b - integer intent(in) :: n - double precision intent(in) :: abseps - double precision intent(in) :: releps - logical intent(in) :: usebreakpoints - logical intent(in) :: usesimpson - double precision intent(out) :: prb - double precision intent(out) :: abserr - integer intent(out) :: ift - end subroutine pymvnprdcrprb - end interface -end python module mvnprdcrprb - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprbmod.f90 b/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprbmod.f90 deleted file mode 100644 index 7c6a8b2..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprbmod.f90 +++ /dev/null @@ -1,666 +0,0 @@ - module mvnProdCorrPrbMod - implicit none - private - public :: mvnprodcorrprb - double precision, parameter :: mINFINITY = 8.25D0 ! - ! Inputs to integrand - integer mNdim ! # of mRho/=0 and mRho/=+/-1 and -infstepSize) then - Nk = floor((xup-xlo)/stepSize) + 1 - dx = (xup-xlo)/dble(Nk) - do j=1, Nk -1 - Npts = Npts + 1 - breakPoints(Npts) = xlo + dx * dble( j ) - enddo - endif - else - ! Compute candidates for the breakpoints - brkPts(1:2*n) = xup - forall(k=1:n,rho(k) .ne. zero) - indices(2*k-1) = k - indices(2*k ) = k - brkPts(2*k-1) = a(k)/rho(k) - brkPts(2*k ) = b(k)/rho(k) - end forall - ! Sort the candidates - call sortre(brkPts,indices) - ! Make unique list of breakpoints - - do k = 1,2*n - brk = brkPts(k) - if (xlo < brk) then - if ( xup <= brk ) exit ! terminate do loop - -! if (Npts>0) then -! xLow = max(xlo, breakPoints(Npts)) -! else -! xLow = xlo -! endif -! if (brk-xLow>stepSize) then -! Nk = floor((brk-xLow)/stepSize) -! dx = (brk-xLow)/dble(Nk) -! do j=1, Nk -1 -! Npts = Npts + 1 -! breakPoints(Npts) = brk + dx * dble( j ) -! enddo -! endif - - kU = indices(k) - - !if ( xlo + distance < brk .and. brk + distance < xup ) - !then - if ( den(kU) < 0.2) then - distance = max(brkSplit*den(kU),hMin) - z1 = brk + distance - z2 = brk - distance - if (Npts <= 0) then - if (xlo + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - kL = kU - elseif (breakPoints(Npts)+ max(distance - & ,brkSplit*den(kL)) < z1) then - if (breakPoints(Npts) + distance < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = integrand(z1) - indices2(Npts) = kU - kL = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - if ( z2 + distance < xup) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - kL = kU - endif - else - val1 = 0.0d0 - val2 = 0.0d0 - brkPts(Npts+1) = integrand(z1) - brkPts(Npts+2) = integrand(z2) - if ((xlo+ distance < z1) .and. (z1 + distance < xup)) - & val2 = brkPts(Npts +1) - if ((xlo+ distance < z2) .and. (z2 + distance < xup)) - & val2 = max(val2,brkPts(Npts +2)) - val1 = breakPoints(Npts) - Nprev = 1 - if (Npts>1) then - if (indices2(Npts-1)==kL) then - Nprev = 2 - val1 = max(val1,breakPoints(Npts-1)) - endif - endif - if (val1 < val2) then - !overwrite previous candidate - Npts = Npts - Nprev - if (Npts>0) then - val1 = breakPoints(Npts)+ distance - else - val1 = xlo+ distance - endif - if (val1 < z1) then - Npts = Npts + 1 - breakPoints(Npts) = z1 - brkPtsVal(Npts) = brkPtsVal(Npts+Nprev) - indices2(Npts) = kU - endif -! Nprev = Nprev + 1 -! breakPoints(Npts + Nprev) = brk - - if ((val1< z2) .and. (z2 + distance < xup)) then - Npts = Npts + 1 - breakPoints(Npts) = z2 - brkPtsVal(Npts) = integrand(z2) - indices2(Npts) = kU - endif - if (Npts>0) kL = indices2(Npts) - endif - endif - endif - endif - enddo - endif - end subroutine GetBreakPoints - subroutine NarrowLimits(zMin,zMax,As,Bs,zCutOff,n,a,b,rho,den) - implicit none - double precision, intent(inout) :: zMin, zMax, As, Bs - double precision,dimension(*),intent(in) :: rho,a,b,den - double precision, intent(in) :: zCutOff - integer, intent(in) :: n -! Locals - double precision, parameter :: zero = 0.0D0, one = 1.0D0 - integer :: k - -! Uses the regression equation to limit the -! integration limits zMin and zMax - - do k = 1,n - if (ZERO < rho(k)) then - zMax = max(zMin, min(zMax,(b(k)+den(k)*zCutOff)/rho(k))) - zMin = min(zMax, max(zMin,(a(k)-den(k)*zCutOff)/rho(k))) - if ( one <= rho(k) ) then - if ( b(k) < Bs ) Bs = b(k) - if ( As < a(k) ) As = a(k) - endif - elseif (rho(k)< ZERO) then - zMax = max(zMin,min(zMax,(a(k)-den(k)*zCutOff)/rho(k))) - zMin = min(zMax,max(zMin,(b(k)+den(k)*zCutOff)/rho(k))) - if ( rho(k) <= -one ) then - if ( -a(k) < Bs ) Bs = -a(k) - if ( As < -b(k) ) As = -b(k) - endif - endif - enddo - As = min(As,Bs) - end subroutine NarrowLimits - - function integrand(z) result (val) - implicit none - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION :: VAL - double precision, parameter :: sqtwopi1 = 0.39894228040143D0 - double precision, parameter :: half = 0.5D0 - val = sqtwopi1 * exp(-half * z * z) * integrand1(z) - return - end function integrand - - function integrand1(z) result (val) - implicit none - double precision, intent(in) :: z - double precision :: val - double precision :: xUp,xLo,zRho - double precision, parameter :: one = 1.0D0, zero = 0.0D0 - integer :: I - val = one - do I = 1, mNdim - zRho = z * mRho(I) - ! Uncomment / mDen below if mRho, mA, mB is not scaled - xUp = ( mB(I) - zRho ) !/ mDen(I) - xLo = ( mA(I) - zRho ) !/ mDen(I) - if (zero0.1 -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION, INTENT(in) :: P - DOUBLE PRECISION :: VAL -!local variables - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, ONE, ZERO, HALF, - & A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - & C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - & E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - & Q, R - PARAMETER ( SPLIT1 = 0.425D0, SPLIT2 = 5.D0, - & CONST1 = 0.180625D0, CONST2 = 1.6D0, - & ONE = 1.D0, ZERO = 0.D0, HALF = 0.5D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( P - HALF) - IF ( ABS(Q) .LE. SPLIT1 ) THEN ! Central range. - R = CONST1 - Q*Q - VAL = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + ONE) - ELSE ! near the endpoints - R = MIN( P, ONE - P ) - IF (R .GT.ZERO) THEN ! ( 2.d0*R .GT. CFxCutOff) THEN ! R .GT.0.d0 - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - VAL = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + ONE ) - ELSE - R = R - SPLIT2 - VAL = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + ONE ) - END IF - ELSE - VAL = 37.D0 !XMAX 9.d0 - END IF - IF ( Q < ZERO ) VAL = - VAL - END IF - RETURN - END FUNCTION FIINV - FUNCTION FI2( Z ) RESULT (VALUE) -! USE GLOBALDATA, ONLY : XMAX - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -* -* Normal distribution probabilities accurate to 1.e-15. -* relative error less than 1e-8; -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION :: P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7,XMAX, - * P, EXPNTL, CUTOFF, ROOTPI, ZABS, Z2 - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = 0.70038 30644 43688 1D0, - * P6 = 0.035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = 0.088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) - PARAMETER( XMAX = 8.25D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( ZABS .GT. XMAX ) THEN - P = 0.d0 - ELSE -* -* |Z| <= 37 -* - Z2 = ZABS * ZABS - EXPNTL = EXP( -Z2 * 0.5D0 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS < CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1.d0/( ZABS + 2.d0/( ZABS + 3.d0/( ZABS - * + 4.d0/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0.d0 ) P = 1.d0 - P - VALUE = P - RETURN - END FUNCTION FI2 - - FUNCTION FI( Z ) RESULT (VALUE) - USE ERFCOREMOD - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -! Local variables - DOUBLE PRECISION, PARAMETER:: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER:: HALF = 0.5D0 - VALUE = DERFC(-Z*SQ2M1)*HALF - RETURN - END FUNCTION FI - end module mvnProdCorrPrbMod \ No newline at end of file diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsp b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsp deleted file mode 100644 index 9c291cc..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsp +++ /dev/null @@ -1,97 +0,0 @@ -# Microsoft Developer Studio Project File - Name="test_mvnprodcorrprb" - Package Owner=<4> -# Microsoft Developer Studio Generated Build File, Format Version 6.00 -# ** DO NOT EDIT ** - -# TARGTYPE "Win32 (x86) Console Application" 0x0103 - -CFG=test_mvnprodcorrprb - Win32 Debug -!MESSAGE This is not a valid makefile. To build this project using NMAKE, -!MESSAGE use the Export Makefile command and run -!MESSAGE -!MESSAGE NMAKE /f "test_mvnprodcorrprb.mak". -!MESSAGE -!MESSAGE You can specify a configuration when running NMAKE -!MESSAGE by defining the macro CFG on the command line. For example: -!MESSAGE -!MESSAGE NMAKE /f "test_mvnprodcorrprb.mak" CFG="test_mvnprodcorrprb - Win32 Debug" -!MESSAGE -!MESSAGE Possible choices for configuration are: -!MESSAGE -!MESSAGE "test_mvnprodcorrprb - Win32 Release" (based on "Win32 (x86) Console Application") -!MESSAGE "test_mvnprodcorrprb - Win32 Debug" (based on "Win32 (x86) Console Application") -!MESSAGE - -# Begin Project -# PROP AllowPerConfigDependencies 0 -# PROP Scc_ProjName "" -# PROP Scc_LocalPath "" -CPP=cl.exe -F90=df.exe -RSC=rc.exe - -!IF "$(CFG)" == "test_mvnprodcorrprb - Win32 Release" - -# PROP BASE Use_MFC 0 -# PROP BASE Use_Debug_Libraries 0 -# PROP BASE Output_Dir "Release" -# PROP BASE Intermediate_Dir "Release" -# PROP BASE Target_Dir "" -# PROP Use_MFC 0 -# PROP Use_Debug_Libraries 0 -# PROP Output_Dir "Release" -# PROP Intermediate_Dir "Release" -# PROP Target_Dir "" -# ADD BASE F90 /compile_only /nologo /warn:nofileopt -# ADD F90 /compile_only /nologo /warn:nofileopt -# ADD BASE CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c -# ADD CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c -# ADD BASE RSC /l 0x414 /d "NDEBUG" -# ADD RSC /l 0x414 /d "NDEBUG" -BSC32=bscmake.exe -# ADD BASE BSC32 /nologo -# ADD BSC32 /nologo -LINK32=link.exe -# ADD BASE LINK32 kernel32.lib /nologo /subsystem:console /machine:I386 -# ADD LINK32 kernel32.lib /nologo /subsystem:console /machine:I386 - -!ELSEIF "$(CFG)" == "test_mvnprodcorrprb - Win32 Debug" - -# PROP BASE Use_MFC 0 -# PROP BASE Use_Debug_Libraries 1 -# PROP BASE Output_Dir "Debug" -# PROP BASE Intermediate_Dir "Debug" -# PROP BASE Target_Dir "" -# PROP Use_MFC 0 -# PROP Use_Debug_Libraries 1 -# PROP Output_Dir "Debug" -# PROP Intermediate_Dir "Debug" -# PROP Target_Dir "" -# ADD BASE F90 /check:bounds /compile_only /debug:full /nologo /traceback /warn:argument_checking /warn:nofileopt -# ADD F90 /check:bounds /compile_only /debug:full /nologo /traceback /warn:argument_checking /warn:nofileopt -# ADD BASE CPP /nologo /W3 /Gm /GX /ZI /Od /D "WIN32" /D "_DEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /GZ /c -# ADD CPP /nologo /W3 /Gm /GX /ZI /Od /D "WIN32" /D "_DEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /GZ /c -# ADD BASE RSC /l 0x414 /d "_DEBUG" -# ADD RSC /l 0x414 /d "_DEBUG" -BSC32=bscmake.exe -# ADD BASE BSC32 /nologo -# ADD BSC32 /nologo -LINK32=link.exe -# ADD BASE LINK32 kernel32.lib /nologo /subsystem:console /debug /machine:I386 /pdbtype:sept -# ADD LINK32 kernel32.lib /nologo /subsystem:console /debug /machine:I386 /pdbtype:sept - -!ENDIF - -# Begin Target - -# Name "test_mvnprodcorrprb - Win32 Release" -# Name "test_mvnprodcorrprb - Win32 Debug" -# Begin Source File - -SOURCE=.\mvnprodcorrprb.f -# End Source File -# Begin Source File - -SOURCE=.\test_mvnprodcorrprb.f -# End Source File -# End Target -# End Project diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsw b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsw deleted file mode 100644 index 95d7427..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsw +++ /dev/null @@ -1,29 +0,0 @@ -Microsoft Developer Studio Workspace File, Format Version 6.00 -# WARNING: DO NOT EDIT OR DELETE THIS WORKSPACE FILE! - -############################################################################### - -Project: "test_mvnprodcorrprb"=.\test_mvnprodcorrprb.dsp - Package Owner=<4> - -Package=<5> -{{{ -}}} - -Package=<4> -{{{ -}}} - -############################################################################### - -Global: - -Package=<5> -{{{ -}}} - -Package=<3> -{{{ -}}} - -############################################################################### - diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.f b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.f deleted file mode 100644 index 018dc3a..0000000 --- a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.f +++ /dev/null @@ -1,39 +0,0 @@ - program mvn -C gfortran -fPIC -c mvnprodcorrprb.f -C f2py -m mvnprdmod -c mvnprodcorrprb.o mvnprodcorrprb_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - -C module mvnprdmod -C contains - - use mvnProdCorrPrbMod, ONLY : mvnprodcorrprb - integer, parameter :: N = 2 - double precision,dimension(N) :: rho,a,b - double precision :: abseps,releps - logical :: useBreakPoints,useSimpson - double precision :: abserr,prb - integer :: IFT - -Cf2py depend(rho) N -Cf2py intent(hide) :: N = len(rho) -Cf2py depend(N) a -Cf2py depend(N) b - abseps = 1.0e-3 - releps = 1.0e-3 - useBreakPoints = 1 - useSimpson = 1 - rho(:)=1.0/100000000 - a(:) = 0.0 - b(:) = 5.0 - - CALL mvnprodcorrprb(rho,a,b,abseps,releps,useBreakPoints, - & useSimpson,abserr,IFT,prb) - - print *, 'prb =', prb - print *, 'rho =', rho - print *, 'a =', a - print *, 'b =', b - - print *, 'abseps =', abseps - print *, 'releps =', releps - print *, 'abserr =', abserr - end program \ No newline at end of file diff --git a/wafo/source/mvnprd/setup.py b/wafo/source/mvnprd/setup.py deleted file mode 100644 index cbf6e05..0000000 --- a/wafo/source/mvnprd/setup.py +++ /dev/null @@ -1,32 +0,0 @@ -''' -python setup.py build_src build_ext --inplace - -See also http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW -''' - -# File setup.py - - -def compile_all(): - import os - files = ['mvnprd', 'mvnprodcorrprb'] - compile1_format = 'gfortran -fPIC -c %s.f' - for file_ in files: - os.system(compile1_format % file_) - file_objects = ['%s.o' % file_ for file_ in files] - return file_objects - - -def configuration(parent_package='', top_path=None): - from numpy.distutils.misc_util import Configuration - libs = compile_all() - config = Configuration('', parent_package, top_path) - - config.add_extension('mvnprdmod', - libraries=libs, - sources=['mvnprd_interface.f']) - return config -if __name__ == "__main__": - - from numpy.distutils.core import setup - setup(**configuration(top_path='').todict()) diff --git a/wafo/source/old/dunnettprb.f b/wafo/source/old/dunnettprb.f deleted file mode 100644 index 296b54e..0000000 --- a/wafo/source/old/dunnettprb.f +++ /dev/null @@ -1,1209 +0,0 @@ - - MODULE ERFCOREMOD - IMPLICIT NONE - - INTERFACE CALERF - MODULE PROCEDURE CALERF - END INTERFACE - - INTERFACE DERF - MODULE PROCEDURE DERF - END INTERFACE - - INTERFACE DERFC - MODULE PROCEDURE DERFC - END INTERFACE - - INTERFACE DERFCX - MODULE PROCEDURE DERFCX - END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD - - MODULE DUNNETMOD - - SUBROUTINE MVNPRD(A, B, BPD, EPS, N, INF, IERC, HINC, PROB, - & BOUND,IFAULT) -C -C ALGORITHM AS 251.1 APPL.STATIST. (1989), VOL.38, NO.3 -C -C FOR A MULTIVARIATE NORMAL VECTOR WITH CORRELATION STRUCTURE -C DEFINED BY RHO(I,J) = BPD(I) * BPD(J), COMPUTES THE PROBABILITY -C THAT THE VECTOR FALLS IN A RECTANGLE IN N-SPACE WITH ERROR -C LESS THAN EPS. -C - INTEGER NN - PARAMETER (NN = 50) - REAL A(*), B(*), BPD(*), ESTT(22), FV(5), FD(5), F1T(22), - * F2T(22), F3T(22), G1T(22), G3T(22), PSUM(22), H(NN), HL(NN), - * BB(NN) - INTEGER INF(*), INFT(NN), LDIR(22) - REAL ZERO, HALF, ONE, TWO, FOUR, SIX, PT1, PT24, ONEP5, - * X2880, SMALL, DXMIN, SQRT2, PROB, ERRL, BI, START, - * Z, HINC, ADDN, EPS2, EPS1, EPS, ZU, Z2, Z3, Z4, Z5, ZZ, - * ERFAC, EL, EL1, BOUND, PART0, PART2, PART3, FUNC0, FUNC2, - * FUNCN, WT, CONTRB, DLG, DX, DA, ESTL, ESTR, SUM, EXCESS, ERROR, - * PROB1, SAFE - INTEGER N, IERC, IFAULT, I, NTM, NMAX, LVL, NR, NDIM - REAL ALNORM, PPND7 - EXTERNAL ALNORM, PPND7 - DATA ZERO, HALF, ONE, TWO, FOUR, SIX /0.0, 0.5, 1.0, 2.0, - * 4.0, 6.0/ - DATA PT1, PT24, ONEP5, X2880 /0.1, 0.24, 1.5, 2880.0/ - DATA SMALL, DXMIN, SQRT2 /1.0E-10, 0.0000001, 1.41421356237310/ -C -C CHECK FOR INPUT VALUES OUT OF RANGE. -C - PROB = ZERO - BOUND = ZERO - IFAULT = 1 - IF (N .LT. 1 .OR. N .GT. NN) RETURN - DO 10 I = 1, N - BI = ABS(BPD(I)) - IFAULT = 2 - IF (BI .GE. ONE) RETURN - IFAULT = 3 - IF (INF(I) .LT. 0 .OR. INF(I) .GT. 2) RETURN - IFAULT = 4 - IF (INF(I) .EQ. 2 .AND. A(I) .LE. B(I)) RETURN - 10 CONTINUE - IFAULT = 0 - PROB = ONE -C -C CHECK WHETHER ANY BPD(I) = 0. -C - NDIM = 0 - DO 20 I = 1, N - IF (BPD(I) .NE. ZERO) THEN - NDIM = NDIM + 1 - H(NDIM) = A(I) - HL(NDIM) = B(I) - BB(NDIM) = BPD(I) - INFT(NDIM) = INF(I) - ELSE -C -C IF ANY BPD(I) = 0, THE CONTRIBUTION TO PROB FOR THAT -C VARIABLE IS COMPUTED FROM A UNIVARIATE NORMAL. -C - IF (INF(I) .LT. 1) THEN - PROB = PROB * (ONE - ALNORM(B(I), .FALSE.)) - ELSE IF (INF(I) .EQ. 1) THEN - PROB = PROB * ALNORM(A(I), .FALSE.) - ELSE - PROB = PROB * (ALNORM(A(I), .FALSE.) - - * ALNORM(B(I), .FALSE.)) - END IF - IF (PROB .LE. SMALL) PROB = ZERO - END IF - 20 CONTINUE - IF (NDIM .EQ. 0 .OR. PROB .EQ. ZERO) RETURN -C -C IF NOT ALL BPD(I) = 0, PROB IS COMPUTED BY SIMPSON'S RULE. -C BUT FIRST, INITIALIZE THE VARIABLES. -C - Z = ZERO - IF (HINC .LE. ZERO) HINC = PT24 - ADDN = -ONE - DO 30 I = 1, NDIM - IF (INFT(I) .EQ. 2 .OR. - * (INFT(I) .NE. INFT(1) .AND. BB(I) * BB(1) .GT. ZERO) .OR. - * (INFT(I) .EQ. INFT(1) .AND. BB(I) * BB(1) .LT. ZERO)) - * ADDN = ZERO - 30 CONTINUE -C -C THE VALUE OF ADDN IS TO BE ADDED TO THE PRODUCT EXPRESSIONS IN -C THE INTEGRAND TO INSURE THAT THE LIMITING VALUE IS ZERO. -C - PROB1 = ZERO - NTM = 0 - NMAX = 400 - IF (IERC .EQ. 0) NMAX = NMAX * 2 - CALL PFUNC (Z, H, HL, BB, NDIM, INFT, ADDN, SAFE, FUNC0, NTM, - * IERC, PART0) - EPS2 = EPS * PT1 * HALF -C -C SET UPPER BOUND ON Z AND APPORTION EPS. -C - ZU = -PPND7(EPS2, IFAULT) / SQRT2 - IF (IFAULT .NE. 0) THEN - IFAULT = 6 - RETURN - END IF - NR = IFIX(ZU / HINC) + 1 - ERFAC = ONE - IF (IERC .NE. 0) ERFAC = X2880 / HINC ** 5 - EL = (EPS - EPS2) / FLOAT(NR) * ERFAC - EL1 = EL -C -C START COMPUTATIONS FOR THE INTERVAL (Z, Z + HINC). -C - 40 ERROR = ZERO - LVL = 0 - FV(1) = PART0 - FD(1) = SAFE - START = Z - DA = HINC - Z3 = START + HALF * DA - CALL PFUNC(Z3, H, HL, BB, NDIM, INFT, ADDN, FD(3), FUNCN, NTM, - * IERC, FV(3)) - Z5 = START + DA - CALL PFUNC(Z5, H, HL, BB, NDIM, INFT, ADDN, FD(5), FUNC2, NTM, - * IERC, FV(5)) - PART2 = FV(5) - SAFE = FD(5) - WT = DA / SIX - CONTRB = WT * (FV(1) + FOUR * FV(3) + FV(5)) - DLG = ZERO - IF (IERC .NE. 0) THEN - CALL WMAX(FD(1), FD(3), FD(5), DLG) - IF (DLG .LE. EL) GO TO 90 - DX = DA - GO TO 60 - END IF - LVL = 1 - LDIR(LVL) = 2 - PSUM(LVL) = ZERO -C -C BISECT INTERVAL. IF IERC = 1, COMPUTE ESTIMATE ON LEFT -C HALF; IF IERC = 0, ON BOTH HALVES. -C - 50 DX = HALF * DA - WT = DX / SIX - Z2 = START + HALF * DX - CALL PFUNC(Z2, H, HL, BB, NDIM, INFT, ADDN, FD(2), FUNCN, NTM, - * IERC,FV(2)) - ESTL = WT * (FV(1) + FOUR * FV(2) + FV(3)) - IF (IERC .EQ. 0) THEN - Z4 = START + ONEP5 * DX - CALL PFUNC(Z4, H, HL, BB, NDIM, INFT, ADDN, FD(4), FUNCN, - * NTM, IERC, FV(4)) - ESTR = WT * (FV(3) + FOUR * FV(4) + FV(5)) - SUM = ESTL + ESTR - DLG = ABS(CONTRB - SUM) - EPS1 = EL / TWO ** (LVL - 1) - ERRL = DLG - ELSE - FV(3) = FV(2) - FD(3) = FD(2) - CALL WMAX(FD(1), FD(3), FD(5), DLG) - ERRL = DLG / TWO ** (5 * LVL) - SUM = ESTL - EPS1 = EL * (TWO ** LVL) ** 4 - END IF -C -C STOP SUBDIVIDING INTERVAL WHEN ACCURACY IS SUFFICIENT, -C OR IF INTERVAL TOO NARROW OR SUBDIVIDED TOO OFTEN. -C - IF (DLG .LE. EPS1 .OR. DLG .LT. SMALL) GO TO 70 - IF (IFAULT .EQ. 0 .AND. NTM .GE. NMAX) IFAULT = 5 - IF (ABS(DX) .LE. DXMIN .OR. LVL .GT. 21) IFAULT = 7 - IF (IFAULT .NE. 0) GO TO 70 -C -C RAISE LEVEL. STORE INFORMATION FOR RIGHT HALF AND APPLY -C SIMPSON'S RULE TO LEFT HALF. -C - 60 LVL = LVL + 1 - LDIR(LVL) = 1 - F1T(LVL) = FV(3) - F3T(LVL) = FV(5) - DA = DX - FV(5) = FV(3) - IF (IERC .EQ. 0) THEN - F2T(LVL) = FV(4) - ESTT(LVL) = ESTR - CONTRB = ESTL - FV(3) = FV(2) - ELSE - G1T(LVL) = FD(3) - G3T(LVL) = FD(5) - FD(5) = FD(3) - END IF - GO TO 50 -C -C ACCEPT APPROXIMATE VALUE FOR INTERVAL. -C RESTORE SAVED INFORMATION TO PROCESS -C RIGHT HALF INTERVAL. -C - 70 ERROR = ERROR + ERRL - 80 IF (LDIR(LVL) .EQ. 1) THEN - PSUM(LVL) = SUM - LDIR(LVL) = 2 - IF (IERC .EQ. 0) DX = DX * TWO - START = START + DX - DA = HINC / TWO ** (LVL - 1) - FV(1) = F1T(LVL) - IF (IERC .EQ. 0) THEN - FV(3) = F2T(LVL) - CONTRB = ESTT(LVL) - ELSE - FV(3) = F3T(LVL) - FD(1) = G1T(LVL) - FD(5) = G3T(LVL) - END IF - FV(5) = F3T(LVL) - GO TO 50 - END IF - SUM = SUM + PSUM(LVL) - LVL = LVL - 1 - IF (LVL .GT. 0) GO TO 80 - CONTRB = SUM - LVL = 1 - DLG = ERROR - 90 PROB1 = PROB1 + CONTRB - BOUND = BOUND + DLG - EXCESS = EL - DLG - EL = EL1 - IF (EXCESS .GT. ZERO) EL = EL1 + EXCESS - IF ((FUNC0 .GT. ZERO .AND. FUNC2 .LE. FUNC0) .OR. - * (FUNC0 .LT. ZERO .AND. FUNC2 .GE. FUNC0)) THEN - ZZ = -SQRT2 * Z5 - PART3 = ABS(FUNC2) * ALNORM(ZZ, .FALSE.) + BOUND / ERFAC - IF (PART3 .LE. EPS .OR. NTM .GE. NMAX .OR. Z5 .GE. ZU) GOTO 100 - END IF - Z = Z5 - PART0 = PART2 - FUNC0 = FUNC2 - IF (Z .LT. ZU .AND. NTM .LT. NMAX) GO TO 40 - 100 PROB = (PROB1 - ADDN * HALF) * PROB - BOUND = PART3 - IF (NTM .GE. NMAX .AND. IFAULT .EQ. 0) IFAULT = 5 - IF (BOUND .GT. EPS .AND. IFAULT .EQ. 0) IFAULT = 8 - RETURN - END - SUBROUTINE PFUNC(Z, A, B, BPD, N, INF, ADDN, DERIV, FUNCN, NTM, - * IERC, RESULT) -C -C ALGORITHM AS 251.2 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C COMPUTE FUNCTION IN INTEGRAND AND ITS 4TH DERIVATIVE. -C - INTEGER NN - PARAMETER (NN = 50) - REAL A(*), B(*), BPD(*), FOU(NN), FOU1(4, NN), TMP(4), GOU(NN), - * GOU1(4, NN), FF(4), GF(4), TERM(4), GERM(4) - INTEGER INF(*) - REAL ZERO, ONE, TWO, THREE, FOUR, SIX, EIGHT, TWELVE, SIXTN, - * SMALL, Z, U, U1, U2, BI, HI, HLI, BP, ADDN, DERIV, FUNCN, - * RESULT, RSLT1, RSLT2, DEN, SQRT2, SQRTPI, PHI, PHI1, PHI2, - * PHI3, PHI4, FRM, GRM - INTEGER N, NTM, IERC, INFI, I, J, K, M, L, IK - REAL ALNORM - EXTERNAL ALNORM - DATA ZERO, ONE, TWO, THREE, FOUR, SIX, EIGHT, TWELVE, SIXTN, - * SMALL /0.0, 1.0, 2.0, 3.0, 4.0, 6.0, 8.0, 12.0, 16.0, 0.1E-12/ - DATA SQRT2, SQRTPI /1.41421356237310, 1.77245385090552/ - DERIV = ZERO - NTM = NTM + 1 - RSLT1 = ONE - RSLT2 = ONE - BI = ONE - HI = A(1) + ONE - HLI = B(1) + ONE - INFI = -1 - DO 60 I = 1, N - IF (BPD(I) .EQ. BI .AND. A(I) .EQ. HI .AND. B(I) .EQ. HLI .AND. - * INF(I) .EQ. INFI) THEN - FOU(I) = FOU(I - 1) - GOU(I) = GOU(I - 1) - DO 10 IK = 1, 4 - FOU1(IK, I) = FOU1(IK, I - 1) - GOU1(IK, I) = GOU1(IK, I - 1) - 10 CONTINUE - ELSE - BI = BPD(I) - HI = A(I) - HLI = B(I) - INFI = INF(I) - IF (BI .EQ. ZERO) THEN - IF (INFI .LT. 1) THEN - FOU(I) = ONE - ALNORM(HLI, .FALSE.) - ELSE IF (INFI .EQ. 1) THEN - FOU(I) = ALNORM(HI, .FALSE.) - ELSE - FOU(I) = ALNORM(HI, .FALSE.) - ALNORM(HLI, .FALSE.) - END IF - GOU(I) = FOU(I) - DO 20 IK = 1, 4 - FOU1(IK, I) = ZERO - GOU1(IK, I) = ZERO - 20 CONTINUE - ELSE - DEN = SQRT(ONE - BI * BI) - BP = BI * SQRT2 / DEN - IF (INFI .LT. 1) THEN - U = -HLI / DEN + Z * BP - FOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, FOU1(1, I)) - BP = -BP - U = -HLI / DEN + Z * BP - GOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, GOU1(1, I)) - ELSE IF (INFI .EQ. 1) THEN - U = HI / DEN + Z * BP - GOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, GOU1(1, I)) - BP = -BP - U = HI / DEN + Z * BP - FOU(I) = ALNORM(U, .FALSE.) - CALL ASSIGN (U, BP, FOU1(1, I)) - ELSE - U2 = -HLI / DEN + Z * BP - CALL ASSIGN (U2, BP, FOU1(1, I)) - BP = -BP - U1 = HI / DEN + Z * BP - CALL ASSIGN (U1, BP, TMP(1)) - FOU(I) = ALNORM(U1, .FALSE.) + ALNORM(U2, .FALSE.) - ONE - DO 30 IK = 1, 4 - FOU1(IK, I) = FOU1(IK, I) + TMP(IK) - 30 CONTINUE - IF (-HLI .EQ. HI) THEN - GOU(I) = FOU(I) - DO 40 IK = 1, 4 - GOU1(IK, I) = FOU1(IK, I) - 40 CONTINUE - ELSE - U2 = -HLI / DEN + Z * BP - CALL ASSIGN (U2, BP, GOU1(1, I)) - BP = -BP - U1 = HI / DEN + Z * BP - GOU(I) = ALNORM(U1, .FALSE.) + ALNORM(U2, .FALSE.)-ONE - CALL ASSIGN (U1, BP, TMP(1)) - DO 50 IK = 1, 4 - GOU1(IK, I) = GOU1(IK, I) + TMP(IK) - 50 CONTINUE - END IF - END IF - END IF - END IF - RSLT1 = RSLT1 * FOU(I) - RSLT2 = RSLT2 * GOU(I) - IF (RSLT1 .LE. SMALL) RSLT1 = ZERO - IF (RSLT2 .LE. SMALL) RSLT2 = ZERO - 60 CONTINUE - FUNCN = RSLT1 + RSLT2 + ADDN - RESULT = FUNCN * EXP(-Z * Z) / SQRTPI -C -C IF 4TH DERIVATIVE IS NOT WANTED, STOP HERE. -C OTHERWISE, PROCEED TO COMPUTE 4TH DERIVATIVE. -C - IF (IERC .EQ. 0) RETURN - DO 70 IK = 1, 4 - FF(IK) = ZERO - GF(IK) = ZERO - 70 CONTINUE - DO 100 I = 1, N - FRM = ONE - GRM = ONE - DO 80 J = 1, N - IF (J .EQ. 1) GO TO 80 - FRM = FRM * FOU(J) - GRM = GRM * GOU(J) - IF (FRM .LE. SMALL) FRM = ZERO - IF (GRM .LE. SMALL) GRM = ZERO - 80 CONTINUE - DO 90 IK = 1, 4 - FF(IK) = FF(IK) + FRM * FOU1(IK, I) - GF(IK) = GF(IK) + GRM * GOU1(IK, I) - 90 CONTINUE - 100 CONTINUE - IF (N .LE. 2) GO TO 230 - DO 130 I = 1, N - DO 120 J = I + 1, N - TERM(2) = FOU1(1, I) * FOU1(1, J) - GERM(2) = GOU1(1, I) * GOU1(1, J) - TERM(3) = FOU1(2, I) * FOU1(1, J) - GERM(3) = GOU1(2, I) * GOU1(1, J) - TERM(4) = FOU1(3, I) * FOU1(1, J) - GERM(4) = GOU1(3, I) * GOU1(1, J) - TERM(1) = FOU1(2, I) * FOU1(2, J) - GERM(1) = GOU1(2, I) * GOU1(2, J) - DO 110 K = 1, N - IF (K .EQ. I .OR. K .EQ. J) GO TO 110 - CALL TOOSML (1, TERM, FOU(K)) - CALL TOOSML (1, GERM, GOU(K)) - 110 CONTINUE - FF(2) = FF(2) + TWO * TERM(2) - FF(3) = FF(3) + TWO * TERM(3) * THREE - FF(4) = FF(4) + TWO * (TERM(4) * FOUR + TERM(1) * THREE) - GF(2) = GF(2) + TWO * GERM(2) - GF(3) = GF(3) + TWO * GERM(3) * THREE - GF(4) = GF(4) + TWO * (GERM(4) * FOUR + GERM(1) * THREE) - 120 CONTINUE - 130 CONTINUE - DO 170 I = 1, N - DO 160 J = I + 1, N - DO 150 K = J + 1, N - TERM(3) = FOU1(1, I) * FOU1(1, J) * FOU1(1, K) - TERM(4) = FOU1(2, I) * FOU1(1, J) * FOU1(1, K) - GERM(3) = GOU1(1, I) * GOU1(1, J) * GOU1(1, K) - GERM(4) = GOU1(2, I) * GOU1(1, J) * GOU1(1, K) - IF (N .GT. 3) THEN - DO 140 M = 1, N - IF (M .EQ. I .OR. M .EQ. J .OR. M .EQ. K) GO TO 140 - CALL TOOSML (3, TERM, FOU(M)) - CALL TOOSML (3, GERM, GOU(M)) - 140 CONTINUE - END IF - FF(3) = FF(3) + SIX * TERM(3) - FF(4) = FF(4) + SIX * TERM(4) * SIX - GF(3) = GF(3) + SIX * GERM(3) - GF(4) = GF(4) + SIX * GERM(4) * SIX - 150 CONTINUE - 160 CONTINUE - 170 CONTINUE - IF (N .LE. 3) GO TO 230 - DO 220 I = 1, N - DO 210 J = I + 1, N - DO 200 K = J + 1, N - DO 190 M = K + 1, N - TERM(4) = FOU1(1, I) * FOU1(1, J) * FOU1(1, K) * FOU1(1, M) - GERM(4) = GOU1(1, I) * GOU1(1, J) * GOU1(1, K) * GOU1(1, M) - IF (N .GT. 4) THEN - DO 180 L = 1, N - IF (L .EQ. I .OR. L .EQ. J .OR. L .EQ. K .OR. L .EQ. M)GOTO 180 - CALL TOOSML (4, TERM, FOU(L)) - CALL TOOSML (4, GERM, GOU(L)) - 180 CONTINUE - END IF - FF(4) = FF(4) + FOUR * SIX * TERM(4) - GF(4) = GF(4) + FOUR * SIX * GERM(4) - 190 CONTINUE - 200 CONTINUE - 210 CONTINUE - 220 CONTINUE -C - 230 CONTINUE - PHI = EXP(-Z * Z) / SQRTPI - PHI1 = -TWO * Z * PHI - PHI2 = (FOUR * Z ** 2 - TWO) * PHI - PHI3 = (-EIGHT * Z ** 3 + TWELVE * Z) * PHI - PHI4 = (SIXTN * Z ** 2 * (Z ** 2 - THREE) + TWELVE) * PHI - DERIV = PHI * (FF(4) + GF(4)) + FOUR * PHI1 * (FF(3) + GF(3)) - * + SIX * PHI2 * (FF(2) + GF(2)) + FOUR * PHI3 * (FF(1) + GF(1)) - * + PHI4 * FUNCN - RETURN - END - SUBROUTINE ASSIGN (U, BP, FF) -C -C ALGORITHM AS 251.3 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C COMPUTE DERIVATIVES OF NORMAL CDF'S. -C - REAL FF(4) - REAL U, U2, BP, HALF, ONE, THREE, SQ2PI, T1, T2, T3 - INTEGER I - DATA HALF, ONE, THREE, SQ2PI /0.5, 1.0, 3.0, 2.50662827463100/ - DATA ZERO, UMAX, SMALL /0.0, 8.0, 0.1E-07/ - IF (ABS(U) .GT. UMAX) THEN - DO 10 I = 1, 4 - FF(I) = ZERO - 10 CONTINUE - ELSE - U2 = U * U - T1 = BP * EXP(-HALF * U2) / SQ2PI - T2 = BP * T1 - T3 = BP * T2 - FF(1) = T1 - FF(2) = -U * T2 - FF(3) = (U2 - ONE) * T3 - FF(4) = (THREE - U2) * U * BP * T3 - DO 20 I = 1, 4 - IF(ABS(FF(I)) .LT. SMALL) FF(I) = ZERO - 20 CONTINUE - END IF - RETURN - END - SUBROUTINE WMAX(W1, W2, W3, DLG) -C -C ALGORITHM AS 251.4 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C LARGEST ABSOLUTE VALUE OF QUADRATIC FUNCTION FITTED -C TO THREE POINTS. -C - REAL W1, W2, W3, DLG, QUAD, QLIM, QMIN, ONE, TWO, B2C - DATA ONE, TWO, QMIN /1.0, 2.0, 0.00001/ - DLG = MAX( ABS(W1), ABS(W3) ) - QUAD = W1 - W2 * TWO + W3 - QLIM = MAX( ABS(W1 - W3) / TWO , QMIN) - IF (ABS(QUAD) .LE. QLIM) RETURN - B2C = (W1 - W3) / QUAD / TWO - IF (ABS(B2C) .GE. ONE) RETURN - DLG = MAX( DLG, ABS(W2 - B2C * QUAD * B2C / TWO) ) - RETURN - END - SUBROUTINE TOOSML (N, FF, F) -C -C ALGORITHM AS 251.5 APPL.STATIST. (1989), VOL.38, NO.3 -C -C -C MULTIPLY FF(I) BY F FOR I = N TO 4. SET TO ZERO IF TOO SMALL. -C - REAL FF(4), F, ZERO, SMALL - INTEGER N, I - DATA ZERO, SMALL /0.0, 0.1E-12/ - DO 10 I = N, 4 - FF(I) = FF(I) * F - IF (ABS(FF(I)) .LE. SMALL) FF(I) = ZERO - 10 CONTINUE - RETURN - END - REAL FUNCTION ALNORM(X, UPPER) -C -C ALGORITHM AS 66 APPL. STATIST. (1973) VOL.22, P.424 -C -C EVALUATES THE TAIL AREA OF THE STANDARDIZED NORMAL CURVE -C FROM X TO INFINITY IF UPPER IS .TRUE. OR -C FROM MINUS INFINITY TO X IF UPPER IS .FALSE. -C - REAL LTONE, UTZERO, ZERO, HALF, ONE, CON, A1, A2, A3, - $ A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, B8, B9, - $ B10, B11, B12, X, Y, Z, ZEXP - LOGICAL UPPER, UP -C -C LTONE AND UTZERO MUST BE SET TO SUIT THE PARTICULAR COMPUTER -C (SEE INTRODUCTORY TEXT) -C - DATA LTONE, UTZERO /7.0, 18.66/ - DATA ZERO, HALF, ONE, CON /0.0, 0.5, 1.0, 1.28/ - DATA A1, A2, A3, - $ A4, A5, A6, - $ A7 - $ /0.398942280444, 0.399903438504, 5.75885480458, - $ 29.8213557808, 2.62433121679, 48.6959930692, - $ 5.92885724438/ - DATA B1, B2, B3, - $ B4, B5, B6, - $ B7, B8, B9, - $ B10, B11, B12 - $ /0.398942280385, 3.8052E-8, 1.00000615302, - $ 3.98064794E-4, 1.98615381364, 0.151679116635, - $ 5.29330324926, 4.8385912808, 15.1508972451, - $ 0.742380924027, 30.789933034, 3.99019417011/ -C - ZEXP(Z) = EXP(Z) -C - UP = UPPER - Z = X - IF (Z .GE. ZERO) GOTO 10 - UP = .NOT. UP - Z = -Z - 10 IF (Z .LE. LTONE .OR. UP .AND. Z .LE. UTZERO) GOTO 20 - ALNORM = ZERO - GOTO 40 - 20 Y = HALF * Z * Z - IF (Z .GT. CON) GOTO 30 -C - ALNORM = HALF - Z * (A1 - A2 * Y / (Y + A3 - A4 / (Y + A5 + - $ A6 / (Y + A7)))) - GOTO 40 -C - 30 ALNORM = B1 * ZEXP(-Y) / (Z - B2 + B3 / (Z + B4 + B5 / (Z - - $ B6 + B7 / (Z + B8 - B9 / (Z + B10 + B11 / (Z + B12)))))) -C - 40 IF (.NOT. UP) ALNORM = ONE - ALNORM - RETURN - END - REAL FUNCTION PPND7 (P, IFAULT) -C -C ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3 -C -C PRODUCES THE NORMAL DEVIATE Z CORRESPONDING TO A GIVEN LOWER -C TAIL AREA OF P; Z IS ACCURATE TO ABOUT 1 PART IN 10**7. -C -C THE HASH SUMS BELOW ARE THE SUMS OF THE MANTISSAS OF THE -C COEFFICIENTS. THEY ARE INCLUDED FOR USE IN CHECKING -C TRANSCRIPTION. -C - INTEGER IFAULT - REAL ZERO, ONE, HALF, SPLIT1, SPLIT2, CONST1, CONST2, - * A0, A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, D1, D2, - * E0, E1, E2, E3, F1, F2, P, Q, R - PARAMETER (ZERO = 0.0E0, ONE = 1.0E0, HALF = 0.5E0, - * SPLIT1 = 0.425E0, SPLIT2 = 5.0E0, - * CONST1 = 0.180625E0, CONST2 = 1.6E0) -C -C COEFFICIENTS FOR P CLOSE TO 1/2 - PARAMETER (A0 = 3.38713 27179E0, - * A1 = 5.04342 71938E1, - * A2 = 1.59291 13202E2, - * A3 = 5.91093 74720E1, - * B1 = 1.78951 69469E1, - * B2 = 7.87577 57664E1, - * B3 = 6.71875 63600E1) -C HASH SUM AB 32.31845 77772 -C -C COEFFICIENTS FOR P NEITHER CLOSE TO 1/2 NOR 0 OR 1 - PARAMETER (C0 = 1.42343 72777E0, - * C1 = 2.75681 53900E0, - * C2 = 1.30672 84816E0, - * C3 = 1.70238 21103E-1, - * D1 = 7.37001 64250E-1, - * D2 = 1.20211 32975E-1) -C HASH SUM CD 15.76149 29821 -C -C COEFFICIENTS FOR P NEAR 0 OR 1 - PARAMETER (E0 = 6.65790 51150E0, - * E1 = 3.08122 63860E0, - * E2 = 4.28682 94337E-1, - * E3 = 1.73372 03997E-2, - * F1 = 2.41978 94225E-1, - * F2 = 1.22582 02635E-2) -C HASH SUM EF 19.40529 10204 -C - IFAULT = 0 - Q = P - HALF - IF (ABS(Q) .LE. SPLIT1) THEN - R = CONST1 - Q * Q - PPND7 = Q * (((A3 * R + A2) * R + A1) * R + A0) / - * (((B3 * R + B2) * R + B1) * R + ONE) - RETURN - ELSE - IF (Q .LT. 0) THEN - R = P - ELSE - R = ONE - P - ENDIF - IF (R .LE. ZERO) THEN - IFAULT = 1 - PPND7 = ZERO - RETURN - ENDIF - R = SQRT(-LOG(R)) - IF (R .LE. SPLIT2) THEN - R = R - CONST2 - PPND7 = (((C3 * R + C2) * R + C1) * R + C0) / - * ((D2 * R + D1) * R + ONE) - ELSE - R = R - SPLIT2 - PPND7 = (((E3 * R + E2) * R + E1) * R + E0) / - * ((F2 * R + F1) * R + ONE) - ENDIF - IF (Q .LT. 0) PPND7 = -PPND7 - RETURN - ENDIF - END - - SUBROUTINE SIMPSN (NDF,A,B,BPD,ERRB,N,INF,D,IERC,HNC,PROB, - * BND,IFLT) -C -C STUDENTIZES A MULTIVARIATE INTEGRAL USING SIMPSON'S RULE. -C - DIMENSION A(*),B(*),BPD(*),INF(*),D(*), - * FV(5),F1T(30),F2T(30),F3T(30), - * LDIR(30),PSUM(30),ESTT(30),ERRR(30),GV(5),G1T(30),G2T(30), - * G3T(30),GSUM(30) - DATA ZERO,HALF,ONE,ONEP5,TWO,FOUR,SIX,DXMIN /0.0,0.5,1.0,1.5, - * 2.0,4.0,6.0,0.000004/ - PROB = ZERO - BOUNDA = ZERO - BOUNDG = ZERO - IFLAG = 0 - IER = 0 - START = -ONE - DAX = ONE - ERB2 = ERRB * HALF - EPS1 = ERB2 * HALF - CALL FUN (ZERO,NDF,A,B,BPD,ERB2,N,INF,D,F0,G0,IERC,HNC,IER) - 10 FV(1) = ZERO - GV(1) = ZERO - ERROR = ZERO - DA = DAX - LVL = 1 - Z3 = START + HALF*DA - CALL FUN(Z3,NDF,A,B,BPD,ERB2,N,INF,D,FV(3),GV(3),IERC,HNC,IER) - FV(5) = F0 - GV(5) = G0 - WT = ABS(DA) / SIX - CONTRB = WT * (FV(1) + FOUR * FV(3) + FV(5)) - CONTRG = WT * (GV(1) + FOUR * GV(3) + GV(5)) - LDIR(LVL) = 2 - PSUM(LVL) = ZERO - GSUM(LVL) = ZERO -C -C BISECT INTERVAL; COMPUTE ESTIMATES FOR EACH HALF. -C - 20 DX = HALF * DA - WT = ABS(DX) / SIX - Z2 = START + HALF * DX - CALL FUN(Z2,NDF,A,B,BPD,ERB2,N,INF,D,FV(2),GV(2),IERC,HNC,IER) - Z4 = START + ONEP5 * DX - CALL FUN(Z4,NDF,A,B,BPD,ERB2,N,INF,D,FV(4),GV(4),IERC,HNC,IER) - ESTL = WT * (FV(1) + FOUR * FV(2) + FV(3)) - ESTR = WT * (FV(3) + FOUR * FV(4) + FV(5)) - ESTGL = WT * (GV(1) + FOUR * GV(2) + GV(3)) - ESTGR = WT * (GV(3) + FOUR * GV(4) + GV(5)) - SUM = ESTL + ESTR - SUMG = ESTGL + ESTGR - DLG = ABS(CONTRB - SUM) - ERRL = DLG -C -C STOP BISECTING WHEN ACCURACY SUFFICIENT, OR IF -C INTERVAL TOO NARROW OR BISECTED TOO OFTEN. -C - 30 IF (DLG .LE. EPS1) GO TO 50 - IF (ABS(DX) .LE. DXMIN .OR. LVL .GE. 30) GO TO 40 -C -C RAISE LEVEL. STORE INFORMATION FOR RIGHT HALF -C AND APPLY SIMPSON'S RULE TO LEFT HALF. -C - LVL = LVL + 1 - LDIR(LVL) = 1 - F1T(LVL) = FV(3) - F2T(LVL) = FV(4) - F3T(LVL) = FV(5) - G1T(LVL) = GV(3) - G2T(LVL) = GV(4) - G3T(LVL) = GV(5) - DA = DX - FV(5) = FV(3) - FV(3) = FV(2) - GV(5) = GV(3) - GV(3) = GV(2) - ESTT(LVL) = ESTR - CONTRB = ESTL - CONTRG = ESTGL - EPS1 = EPS1 * HALF - ERRR(LVL) = EPS1 - GO TO 20 -C -C ACCEPT APPROXIMATE VALUE FOR INTERVAL. -C - 40 IFLAG = 11 - 50 ERROR = ERROR + ERRL - 60 IF (LDIR(LVL) .EQ. 1) GO TO 70 - SUM = SUM + PSUM(LVL) - SUMG = SUMG + GSUM(LVL) - LVL = LVL - 1 - IF (LVL .GT. 0) GO TO 60 - CONTRB = SUM - CONTRG = SUMG - LVL = 1 - DLG = ERROR - GO TO 80 -C -C RESTORE SAVED INFORMATION TO PROCESS RIGHT HALF. -C - 70 PSUM(LVL) = SUM - GSUM(LVL) = SUMG - LDIR(LVL) = 2 - DA = DAX / TWO**(LVL-1) - START = START + DX * TWO - FV(1) = F1T(LVL) - FV(3) = F2T(LVL) - FV(5) = F3T(LVL) - GV(1) = G1T(LVL) - GV(3) = G2T(LVL) - GV(5) = G3T(LVL) - CONTRB = ESTT(LVL) - EXCESS = EPS1 - DLG - EPS1 = ERRR(LVL) - IF (EXCESS .GT. ZERO) EPS1 = EPS1 + EXCESS - GO TO 20 - 80 PROB = PROB + CONTRB - BOUNDG = BOUNDG + CONTRG - BOUNDA = BOUNDA + DLG - IF (Z4 .LE. ZERO) GO TO 90 - IF (IFLT .EQ. 0) IFLT = IER - IF (IFLT .EQ. 0) IFLT = IFLAG - BOUNDA = BOUNDA + BOUNDG - IF (BND .LT. BOUNDA) BND = BOUNDA - RETURN - 90 EPS1 = ERB2 * HALF - EXCESS = EPS1 - BND - IF (EXCESS .GT. ZERO) EPS1 = EPS1 + EXCESS - START = ONE - DAX = -ONE - GO TO 10 - END - FUNCTION SDIST(Y,N) -C -C COMPUTE Y**(N/2 - 1) EXP(-Y) / GAMMA(N/2) -C -C (Revised: 1994-01-19) -C - DATA ZERO, HALF, ONE, X23 / 0.0, 0.5, 1.0, -23.0 / - DATA SQRTPI / 1.77245385090552 / - SDIST = ZERO - IF (Y .LE. ZERO) RETURN - JJ = N/2 - 1 - JK = 2 * JJ - N + 2 - JKP = JJ - JK - SDIST = ONE - IF (JK .LT. 0) SDIST = SDIST / SQRT(Y) / SQRTPI - IF (JKP .EQ. 0) GO TO 20 - XN = FLOAT(N) * HALF - TEST = ALOG(Y) - Y / FLOAT(JKP) - IF ( TEST .LT. X23 ) THEN - SDIST = ZERO - RETURN - ENDIF - SDIST = ALOG ( SDIST ) - DO 10 J = 1, JKP - XN = XN - ONE - SDIST = SDIST + TEST - ALOG(XN) - 10 CONTINUE - IF ( SDIST .LT. X23 ) THEN - SDIST = ZERO - ELSE - SDIST = EXP( SDIST ) - ENDIF - RETURN - 20 SDIST = SDIST * EXP(-Y) - RETURN - END - SUBROUTINE FUN (Z,NDF,H,HL,BPD,ERB2,N,INF,D,F0,G0,IERC - * ,HNC,IER) - INTEGER NN - PARAMETER (NN=50) - DIMENSION A(NN),B(NN),H(*),HL(*),BPD(*),INF(*),D(*) - DATA ZERO, ONE, TWO, SMALL / 0.0, 1.0, 2.0, 1.0E-08 / - F0 = ZERO - G0 = ZERO - IF (Z .LE. -ONE .OR. Z .GE. ONE) RETURN - DF = FLOAT(NDF) - ARG = (ONE + Z) / (ONE - Z) - TERM = ARG * DF * TWO / (ONE-Z)**2 * SDIST(DF/TWO*ARG*ARG,NDF) - IF (TERM .LE. SMALL) RETURN - DO 10 I = 1, N - A(I) = ARG * H(I) - D(I) - B(I) = ARG * HL(I) - D(I) - 10 CONTINUE - CALL MVNPRD (A,B,BPD,ERB2,N,INF,IERC,HNC,PROB,BND,IFLT) - IF (IER .EQ. 0) IER = IFLT - G0 = TERM * BND - F0 = TERM * PROB - RETURN - END - -C * * * * * * * * * * * * * * * * * * * * * * * * * * * * -C Charles Dunnett -C Dept. of Mathematics and Statistics -C McMaster University -C Hamilton, Ontario L8S 4K1 -C Canada -C E-mail: dunnett@mcmaster.ca -C Tel.: (905) 525-9140 (Ext. 27104) -C * * * * * * * * * * * * * * * * * * * * * * * * * * * * - END MODULE DUNNETMOD diff --git a/wafo/source/old/erfcore.f b/wafo/source/old/erfcore.f deleted file mode 100644 index 79c705c..0000000 --- a/wafo/source/old/erfcore.f +++ /dev/null @@ -1,524 +0,0 @@ -C $ f2py -m erfcore -h erfcore.pyf erfcore.f -C f2py erfcore.pyf erfcore.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C $ f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m erfcore -c erfcore.f -C -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - FUNCTION FIINV(P) RESULT (VAL) - IMPLICIT NONE -* -* ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3 -* -* Produces the normal deviate Z corresponding to a given lower -* tail area of P. -* Absolute error less than 1e-13 -* Relative error less than 1e-15 for abs(VAL)>0.1 -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION, INTENT(in) :: P - DOUBLE PRECISION :: VAL -!local variables - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, ONE, ZERO, HALF, - & A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - & C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - & E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - & Q, R - PARAMETER ( SPLIT1 = 0.425D0, SPLIT2 = 5.D0, - & CONST1 = 0.180625D0, CONST2 = 1.6D0, - & ONE = 1.D0, ZERO = 0.D0, HALF = 0.5D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( P - HALF) - IF ( ABS(Q) .LE. SPLIT1 ) THEN ! Central range. - R = CONST1 - Q*Q - VAL = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + ONE) - ELSE ! near the endpoints - R = MIN( P, ONE - P ) - IF (R .GT.ZERO) THEN ! ( 2.d0*R .GT. CFxCutOff) THEN ! R .GT.0.d0 - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - VAL = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + ONE ) - ELSE - R = R - SPLIT2 - VAL = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + ONE ) - END IF - ELSE - VAL = 37.D0 !XMAX 9.d0 - END IF - IF ( Q < ZERO ) VAL = - VAL - END IF - RETURN - END FUNCTION FIINV - FUNCTION FI2( Z ) RESULT (VALUE) -! USE GLOBALDATA, ONLY : XMAX - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -* -* Normal distribution probabilities accurate to 1.e-15. -* relative error less than 1e-8; -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION :: P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7,XMAX, - * P, EXPNTL, CUTOFF, ROOTPI, ZABS, Z2 - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = 0.70038 30644 43688 1D0, - * P6 = 0.035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = 0.088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) - PARAMETER( XMAX = 8.25D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( ZABS .GT. XMAX ) THEN - P = 0.d0 - ELSE -* -* |Z| <= 37 -* - Z2 = ZABS * ZABS - EXPNTL = EXP( -Z2 * 0.5D0 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS < CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1.d0/( ZABS + 2.d0/( ZABS + 3.d0/( ZABS - * + 4.d0/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0.d0 ) P = 1.d0 - P - VALUE = P - RETURN - END FUNCTION FI2 - - FUNCTION FI( Z ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -! Local variables - DOUBLE PRECISION, PARAMETER:: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER:: HALF = 0.5D0 - VALUE = DERFC(-Z*SQ2M1)*HALF - RETURN - END FUNCTION FI \ No newline at end of file diff --git a/wafo/source/old/erfcore.pyf b/wafo/source/old/erfcore.pyf deleted file mode 100644 index e84f3cd..0000000 --- a/wafo/source/old/erfcore.pyf +++ /dev/null @@ -1,39 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - -python module erfcore ! in - interface ! in :erfcore - function derf(x) result (value) ! in :erfcore:erfcore.f - double precision intent(in) :: x - double precision :: value - end function derf - function derfc(x) result (value) ! in :erfcore:erfcore.f - double precision intent(in) :: x - double precision :: value - end function derfc - function derfcx(x) result (value) ! in :erfcore:erfcore.f - double precision intent(in) :: x - double precision :: value - end function derfcx - subroutine calerf(arg,result,jint) ! in :erfcore:erfcore.f - double precision intent(in) :: arg - double precision intent(inout) :: result - integer intent(in) :: jint - end subroutine calerf - function fiinv(p) result (val) ! in :erfcore:erfcore.f - double precision intent(in) :: p - double precision :: val - end function fiinv - function fi2(z) result (value) ! in :erfcore:erfcore.f - double precision intent(in) :: z - double precision :: value - end function fi2 - function fi(z) result (value) ! in :erfcore:erfcore.f - double precision intent(in) :: z - double precision :: value - end function fi - end interface -end python module erfcore - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/old/erfcoremod.f b/wafo/source/old/erfcoremod.f deleted file mode 100644 index 583be61..0000000 --- a/wafo/source/old/erfcoremod.f +++ /dev/null @@ -1,346 +0,0 @@ -C $ f2py -m erfcoremod -h erfcoremod.pyf erfcoremod.f -C f2py erfcoremod.pyf erfcoremod.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C $ f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m erfcoremod -c erfcoremod.f - -C gfortran -fPIC -c erfcoremod.f -C f2py -m erfcoremod -c erfcoremod.o erfcoremod_interface.f - - MODULE ERFCOREMOD -C IMPLICIT NONE - -C INTERFACE CALERF -C MODULE PROCEDURE CALERF -C END INTERFACE - -C INTERFACE DERF -C MODULE PROCEDURE DERF -C END INTERFACE - -C INTERFACE DERFC -C MODULE PROCEDURE DERFC -C END INTERFACE - -C INTERFACE DERFCX -C MODULE PROCEDURE DERFCX -c END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD diff --git a/wafo/source/old/erfcoremod.f90 b/wafo/source/old/erfcoremod.f90 deleted file mode 100644 index 3ecb6d4..0000000 --- a/wafo/source/old/erfcoremod.f90 +++ /dev/null @@ -1,346 +0,0 @@ -!C $ f2py -m erf!Coremod -h erf!Coremod.pyf erf!Coremod.f -!C f2py erf!Coremod.pyf erf!Coremod.f -!C --f!Compiler=gnu95 --!Compiler=mingw32 -lmsv!Cr71 -!C $ f2py --f!Compiler=gnu95 --!Compiler=mingw32 -lmsv!Cr71 -m erf!Coremod -!C erf!Coremod.f - -!C gfortran -fPI!C -!C erf!Coremod.f -!C f2py -m erf!Coremod -DUPPER!CASE_FORTRAN -!C erf!Coremod.o erf!Coremod_interfa!Ce.f - - MODULE ERFCOREMOD -!C IMPLI!CIT NONE - -!C INTERFA!CE !CALERF -!C MODULE PRO!CEDURE !CALERF -!C END INTERFA!CE - -!C INTERFA!CE DERF -!C MODULE PRO!CEDURE DERF -!C END INTERFA!CE - -!C INTERFA!CE DERF!C -!C MODULE PRO!CEDURE DERF!C -!C END INTERFA!CE - -!C INTERFA!CE DERF!CX -!C MODULE PRO!CEDURE DERF!CX -!C END INTERFA!CE - CONTAINS -!C-------------------------------------------------------------------- -!C -!C DERF subprogram !Computes approximate values for erf(x). -!C (see !Comments heading !CALERF). -!C -!C Author/date: W. J. !Cody, January 8, 1985 -!C -!C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -!C-------------------------------------------------------------------- -!C -!C DERF!C subprogram !Computes approximate values for erf!C(x). -!C (see !Comments heading !CALERF). -!C -!C Author/date: W. J. !Cody, January 8, 1985 -!C -!C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -!C------------------------------------------------------------------ -!C -!C DERFCX subprogram Computes approximate values for exp(x*x) * erfC(x). -!C (see !Comments heading !CALERF). -!C -!C Author/date: W. J. !Cody, Mar!Ch 30, 1987 -!C -!C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -!C------------------------------------------------------------------ -!C -!C !CALERF pa!Cket evaluates erf(x), erf!C(x), and exp(x*x)*erf!C(x) -!C for a real argument x. It !Contains three FUN!CTION type -!C subprograms: ERF, ERF!C, and ERF!CX (or DERF, DERF!C, and DERF!CX), -!C and one SUBROUTINE type subprogram, !CALERF. The !Calling -!C statements for the primary entries are: -!C -!C Y=ERF(X) (or Y=DERF(X)), -!C -!C Y=ERF!C(X) (or Y=DERF!C(X)), -!C and -!C Y=ERF!CX(X) (or Y=DERF!CX(X)). -!C -!C The routine !CALERF is intended for internal pa!Cket use only, -!C all !Computations within the pa!Cket being !Con!Centrated in this -!C routine. The fun!Ction subprograms invoke !CALERF with the -!C statement -!C -!C !CALL !CALERF(ARG,RESULT,JINT) -!C -!C where the parameter usage is as follows -!C -!C Fun!Ction Parameters for !CALERF -!C !Call ARG Result JINT -!C -!C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -!C ERF!C(ARG) ABS(ARG) .LT. XBIG ERF!C(ARG) 1 -!C ERF!CX(ARG) XNEG .LT. ARG .LT. XMAX ERF!CX(ARG) 2 -!C -!C The main !Computation evaluates near-minimax approximations -!C from "Rational !Chebyshev approximations for the error fun!Ction" -!C by W. J. !Cody, Math. !Comp., 1969, PP. 631-638. This -!C transportable program uses rational fun!Ctions that theoreti!Cally -!C approximate erf(x) and erf!C(x) to at least 18 signifi!Cant -!C de!Cimal digits. The a!C!Cura!Cy a!Chieved depends on the arithmeti!C -!C system, the !Compiler, the intrinsi!C fun!Ctions, and proper -!C sele!Ction of the ma!Chine-dependent !Constants. -!C -!C******************************************************************* -!C******************************************************************* -!C -!C Explanation of ma!Chine-dependent !Constants -!C -!C XMIN = the smallest positive floating-point number. -!C XINF = the largest positive finite floating-point number. -!C XNEG = the largest negative argument a!C!Ceptable to ERF!CX; -!C the negative of the solution to the equation -!C 2*exp(x*x) = XINF. -!C XSMALL = argument below whi!Ch erf(x) may be represented by -!C 2*x/sqrt(pi) and above whi!Ch x*x will not underflow. -!C A !Conservative value is the largest ma!Chine number X -!C su!Ch that 1.0 + X = 1.0 to ma!Chine pre!Cision. -!C XBIG = largest argument a!C!Ceptable to ERF!C; solution to -!C the equation: W(x) * (1-0.5/x**2) = XMIN, where -!C W(x) = exp(-x*x)/[x*sqrt(pi)]. -!C XHUGE = argument above whi!Ch 1.0 - 1/(2*x*x) = 1.0 to -!C ma!Chine pre!Cision. A !Conservative value is -!C 1/[2*sqrt(XSMALL)] -!C XMAX = largest a!C!Ceptable argument to ERF!CX; the minimum -!C of XINF and 1/[sqrt(pi)*XMIN]. -!C -!C Approximate values for some important ma!Chines are: -!C -!C XMIN XINF XNEG XSMALL -!C -!C !C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -!C !CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -!C IEEE (IBM/XT, -!C SUN, et!C.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -!C IEEE (IBM/XT, -!C SUN, et!C.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -!C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -!C UNIVA!C 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -!C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -!C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -!C -!C -!C XBIG XHUGE XMAX -!C -!C !C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -!C !CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -!C IEEE (IBM/XT, -!C SUN, et!C.) (S.P.) 9.194 2.90E+3 4.79E+37 -!C IEEE (IBM/XT, -!C SUN, et!C.) (D.P.) 26.543 6.71D+7 2.53D+307 -!C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -!C UNIVA!C 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -!C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -!C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -!C -!C******************************************************************* -!C******************************************************************* -!C -!C Error returns -!C -!C The program returns ERF!C = 0 for ARG .GE. XBIG; -!C -!C ERF!CX = XINF for ARG .LT. XNEG; -!C and -!C ERF!CX = 0 for ARG .GE. XMAX. -!C -!C -!C Intrinsi!C funCtions required are: -!C -!C ABS, AINT, EXP -!C -!C -!C Author: W. J. Cody -!C MathematiCs and Computer SCienCe Division -!C Argonne National Laboratory -!C Argonne, IL 60439 -!C -!C Latest modifiCation: MarCh 19, 1990 -!C Updated to F90 by pab 23.03.2003 -!C -!C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Lo!Cal variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -!C------------------------------------------------------------------ -!C MathematiCal Constants -!C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -!C------------------------------------------------------------------ -!C MaChine-dependent Constants -!C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! !Coeffi!Cents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -!C------------------------------------------------------------------ -!C !Coeffi!Cients for approximation to erf in first interval -!C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -!C------------------------------------------------------------------ -!C CoeffiCients for approximation to erfC in seCond interval -!C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -!C------------------------------------------------------------------ -!C !Coeffi!Cients for approximation to erf!C in third interval -!C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -!C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -!C------------------------------------------------------------------ -!C Evaluate erf for |X| <= 0.46875 -!C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -!C------------------------------------------------------------------ -!C Evaluate erf!C for 0.46875 <= |X| <= 4.0 -!C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -!C------------------------------------------------------------------ -!C Evaluate erfC for |X| > 4.0 -!C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -!C------------------------------------------------------------------ -!C Fix up for negative argument, erf, etC. -!C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD diff --git a/wafo/source/old/erfcoremod.pyf b/wafo/source/old/erfcoremod.pyf deleted file mode 100644 index 07869ab..0000000 --- a/wafo/source/old/erfcoremod.pyf +++ /dev/null @@ -1,29 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - -python module erfcoremod ! in - interface ! in :erfcoremod - module erfcoremod ! in :erfcoremod:erfcoremod.f90 - function derf(x) result (value) ! in :erfcoremod:erfcoremod.f90:erfcoremod - double precision intent(in) :: x - double precision :: value - end function derf - function derfc(x) result (value) ! in :erfcoremod:erfcoremod.f90:erfcoremod - double precision intent(in) :: x - double precision :: value - end function derfc - function derfcx(x) result (value) ! in :erfcoremod:erfcoremod.f90:erfcoremod - double precision intent(in) :: x - double precision :: value - end function derfcx - subroutine calerf(arg,result,jint) ! in :erfcoremod:erfcoremod.f90:erfcoremod - double precision intent(in) :: arg - double precision intent(inout) :: result - integer intent(in) :: jint - end subroutine calerf - end module erfcoremod - end interface -end python module erfcoremod - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/old/erfcoremod0.f90 b/wafo/source/old/erfcoremod0.f90 deleted file mode 100644 index 583be61..0000000 --- a/wafo/source/old/erfcoremod0.f90 +++ /dev/null @@ -1,346 +0,0 @@ -C $ f2py -m erfcoremod -h erfcoremod.pyf erfcoremod.f -C f2py erfcoremod.pyf erfcoremod.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -C $ f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m erfcoremod -c erfcoremod.f - -C gfortran -fPIC -c erfcoremod.f -C f2py -m erfcoremod -c erfcoremod.o erfcoremod_interface.f - - MODULE ERFCOREMOD -C IMPLICIT NONE - -C INTERFACE CALERF -C MODULE PROCEDURE CALERF -C END INTERFACE - -C INTERFACE DERF -C MODULE PROCEDURE DERF -C END INTERFACE - -C INTERFACE DERFC -C MODULE PROCEDURE DERFC -C END INTERFACE - -C INTERFACE DERFCX -C MODULE PROCEDURE DERFCX -c END INTERFACE - CONTAINS -C-------------------------------------------------------------------- -C -C DERF subprogram computes approximate values for erf(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -C-------------------------------------------------------------------- -C -C DERFC subprogram computes approximate values for erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, January 8, 1985 -C -C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -C------------------------------------------------------------------ -C -C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -C (see comments heading CALERF). -C -C Author/date: W. J. Cody, March 30, 1987 -C -C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -C------------------------------------------------------------------ -C -C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -C for a real argument x. It contains three FUNCTION type -C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -C and one SUBROUTINE type subprogram, CALERF. The calling -C statements for the primary entries are: -C -C Y=ERF(X) (or Y=DERF(X)), -C -C Y=ERFC(X) (or Y=DERFC(X)), -C and -C Y=ERFCX(X) (or Y=DERFCX(X)). -C -C The routine CALERF is intended for internal packet use only, -C all computations within the packet being concentrated in this -C routine. The function subprograms invoke CALERF with the -C statement -C -C CALL CALERF(ARG,RESULT,JINT) -C -C where the parameter usage is as follows -C -C Function Parameters for CALERF -C call ARG Result JINT -C -C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -C -C The main computation evaluates near-minimax approximations -C from "Rational Chebyshev approximations for the error function" -C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -C transportable program uses rational functions that theoretically -C approximate erf(x) and erfc(x) to at least 18 significant -C decimal digits. The accuracy achieved depends on the arithmetic -C system, the compiler, the intrinsic functions, and proper -C selection of the machine-dependent constants. -C -C******************************************************************* -C******************************************************************* -C -C Explanation of machine-dependent constants -C -C XMIN = the smallest positive floating-point number. -C XINF = the largest positive finite floating-point number. -C XNEG = the largest negative argument acceptable to ERFCX; -C the negative of the solution to the equation -C 2*exp(x*x) = XINF. -C XSMALL = argument below which erf(x) may be represented by -C 2*x/sqrt(pi) and above which x*x will not underflow. -C A conservative value is the largest machine number X -C such that 1.0 + X = 1.0 to machine precision. -C XBIG = largest argument acceptable to ERFC; solution to -C the equation: W(x) * (1-0.5/x**2) = XMIN, where -C W(x) = exp(-x*x)/[x*sqrt(pi)]. -C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -C machine precision. A conservative value is -C 1/[2*sqrt(XSMALL)] -C XMAX = largest acceptable argument to ERFCX; the minimum -C of XINF and 1/[sqrt(pi)*XMIN]. -C -C Approximate values for some important machines are: -C -C XMIN XINF XNEG XSMALL -C -C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -C -C -C XBIG XHUGE XMAX -C -C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -C IEEE (IBM/XT, -C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -C IEEE (IBM/XT, -C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -C -C******************************************************************* -C******************************************************************* -C -C Error returns -C -C The program returns ERFC = 0 for ARG .GE. XBIG; -C -C ERFCX = XINF for ARG .LT. XNEG; -C and -C ERFCX = 0 for ARG .GE. XMAX. -C -C -C Intrinsic functions required are: -C -C ABS, AINT, EXP -C -C -C Author: W. J. Cody -C Mathematics and Computer Science Division -C Argonne National Laboratory -C Argonne, IL 60439 -C -C Latest modification: March 19, 1990 -C Updated to F90 by pab 23.03.2003 -C -C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -C------------------------------------------------------------------ -C Mathematical constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -C------------------------------------------------------------------ -C Machine-dependent constants -C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -C------------------------------------------------------------------ -C Coefficients for approximation to erf in first interval -C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in second interval -C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -C------------------------------------------------------------------ -C Coefficients for approximation to erfc in third interval -C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -C------------------------------------------------------------------ -C Evaluate erf for |X| <= 0.46875 -C------------------------------------------------------------------ - !YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -C------------------------------------------------------------------ -C Evaluate erfc for 0.46875 <= |X| <= 4.0 -C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -C------------------------------------------------------------------ -C Evaluate erfc for |X| > 4.0 -C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -C------------------------------------------------------------------ -C Fix up for negative argument, erf, etc. -C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD diff --git a/wafo/source/old/erfcoremod1.pyf b/wafo/source/old/erfcoremod1.pyf deleted file mode 100644 index 02b4929..0000000 --- a/wafo/source/old/erfcoremod1.pyf +++ /dev/null @@ -1,27 +0,0 @@ -! -*- f90 -*- -! Note: the context of this file is case sensitive. - -python module erfcoremod ! in - interface ! in :erfcoremod - function derf(x) result (value) ! in :erfcoremod:erfcoremod.f - double precision intent(in) :: x - double precision :: value - end function derf - function derfc(x) result (value) ! in :erfcoremod:erfcoremod.f - double precision intent(in) :: x - double precision :: value - end function derfc - function derfcx(x) result (value) ! in :erfcoremod:erfcoremod.f - double precision intent(in) :: x - double precision :: value - end function derfcx - subroutine calerf(arg,result,jint) ! in :erfcoremod:erfcoremod.f - double precision intent(in) :: arg - double precision intent(inout) :: result - integer intent(in) :: jint - end subroutine calerf - end interface -end python module erfcoremod - -! This file was auto-generated with f2py (version:2_5972). -! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/source/old/erfcoremod_interface.f90 b/wafo/source/old/erfcoremod_interface.f90 deleted file mode 100644 index 6c62758..0000000 --- a/wafo/source/old/erfcoremod_interface.f90 +++ /dev/null @@ -1,11 +0,0 @@ - - module bindings - use erfcoremod - contains - function pyderf(x) result (value) ! in :erfcore:erfcore.f - double precision intent(in) :: x - double precision :: value - value = derf(x) - return - end function pyderf - end module bindings \ No newline at end of file diff --git a/wafo/source/rind2007/.cproject b/wafo/source/rind2007/.cproject deleted file mode 100644 index 5bb1192..0000000 --- a/wafo/source/rind2007/.cproject +++ /dev/null @@ -1,608 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -make - - -true -true -true - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -make - - -true -true -true - - - - - - - - - diff --git a/wafo/source/rind2007/.project b/wafo/source/rind2007/.project deleted file mode 100644 index 269ed5c..0000000 --- a/wafo/source/rind2007/.project +++ /dev/null @@ -1,81 +0,0 @@ - - - test_rind - - - - - - org.eclipse.cdt.managedbuilder.core.genmakebuilder - clean,full,incremental, - - - ?name? - - - - org.eclipse.cdt.make.core.append_environment - true - - - org.eclipse.cdt.make.core.autoBuildTarget - all - - - org.eclipse.cdt.make.core.buildArguments - - - - org.eclipse.cdt.make.core.buildCommand - make - - - org.eclipse.cdt.make.core.buildLocation - ${workspace_loc:/test_rind/Debug} - - - org.eclipse.cdt.make.core.cleanBuildTarget - clean - - - org.eclipse.cdt.make.core.contents - org.eclipse.cdt.make.core.activeConfigSettings - - - org.eclipse.cdt.make.core.enableAutoBuild - false - - - org.eclipse.cdt.make.core.enableCleanBuild - true - - - org.eclipse.cdt.make.core.enableFullBuild - true - - - org.eclipse.cdt.make.core.fullBuildTarget - all - - - org.eclipse.cdt.make.core.stopOnError - true - - - org.eclipse.cdt.make.core.useDefaultBuildCmd - true - - - - - org.eclipse.cdt.managedbuilder.core.ScannerConfigBuilder - - - - - - org.eclipse.cdt.managedbuilder.core.ScannerConfigNature - org.eclipse.cdt.managedbuilder.core.managedBuildNature - org.eclipse.cdt.core.cnature - - diff --git a/wafo/source/rind2007/Debug/makefile b/wafo/source/rind2007/Debug/makefile deleted file mode 100644 index b6ca9fc..0000000 --- a/wafo/source/rind2007/Debug/makefile +++ /dev/null @@ -1,43 +0,0 @@ -################################################################################ -# Automatically-generated file. Do not edit! -################################################################################ - --include ../makefile.init - -RM := rm -rf - -# All of the sources participating in the build are defined here --include sources.mk --include subdir.mk --include objects.mk - -ifneq ($(MAKECMDGOALS),clean) -ifneq ($(strip $(C_DEPS)),) --include $(C_DEPS) -endif -endif - --include ../makefile.defs - -# Add inputs and outputs from these tool invocations to the build variables - -# All Target -all: test_rind - -# Tool invocations -test_rind: $(OBJS) $(USER_OBJS) - @echo 'Building target: $@' - @echo 'Invoking: GNU Fortran Linker' - gfortran -o"test_rind" $(OBJS) $(USER_OBJS) $(LIBS) - @echo 'Finished building target: $@' - @echo ' ' - -# Other Targets -clean: - -$(RM) $(OBJS)$(C_DEPS)$(EXECUTABLES) test_rind - -@echo ' ' - -.PHONY: all clean dependents -.SECONDARY: - --include ../makefile.targets diff --git a/wafo/source/rind2007/Debug/objects.mk b/wafo/source/rind2007/Debug/objects.mk deleted file mode 100644 index dc028f6..0000000 --- a/wafo/source/rind2007/Debug/objects.mk +++ /dev/null @@ -1,7 +0,0 @@ -################################################################################ -# Automatically-generated file. Do not edit! -################################################################################ - -USER_OBJS := - -LIBS := diff --git a/wafo/source/rind2007/Debug/sources.mk b/wafo/source/rind2007/Debug/sources.mk deleted file mode 100644 index 32db9ff..0000000 --- a/wafo/source/rind2007/Debug/sources.mk +++ /dev/null @@ -1,21 +0,0 @@ -################################################################################ -# Automatically-generated file. Do not edit! -################################################################################ - -O_SRCS := -F03_SRCS := -C_SRCS := -S_SRCS := -F_SRCS := -OBJ_SRCS := -ASM_SRCS := -F90_SRCS := -F95_SRCS := -OBJS := -C_DEPS := -EXECUTABLES := - -# Every subdirectory with source files must be described here -SUBDIRS := \ -. \ - diff --git a/wafo/source/rind2007/Debug/subdir.mk b/wafo/source/rind2007/Debug/subdir.mk deleted file mode 100644 index bd0fcfc..0000000 --- a/wafo/source/rind2007/Debug/subdir.mk +++ /dev/null @@ -1,47 +0,0 @@ -################################################################################ -# Automatically-generated file. Do not edit! -################################################################################ - -# Add inputs and outputs from these tool invocations to the build variables -F_SRCS += \ -../fimod.f \ -../intmodule.f \ -../jacobmod.f \ -../rindmod2007.f \ -../swapmod.f \ -../test_fimod.f \ -../test_rindmod2007.f - -OBJS += \ -./fimod.o \ -./intmodule.o \ -./jacobmod.o \ -./rindmod2007.o \ -./swapmod.o \ -./test_fimod.o \ -./test_rindmod2007.o - - -# Each subdirectory must supply rules for building sources it contributes -%.o: ../%.f - @echo 'Building file: $<' - @echo 'Invoking: GNU Fortran Compiler' - gfortran -funderscoring -O0 -g -Wall -c -fmessage-length=0 -o"$@" "$<" - @echo 'Finished building: $<' - @echo ' ' - -fimod.o: ../fimod.f - -intmodule.o: ../intmodule.f - -jacobmod.o: ../jacobmod.f - -rindmod2007.o: ../rindmod2007.f FIMOD.o RCRUDEMOD.o JACOBMOD.o SWAPMOD.o - -swapmod.o: ../swapmod.f - -test_fimod.o: ../test_fimod.f FIMOD.o - -test_rindmod2007.o: ../test_rindmod2007.f FIMOD.o - - diff --git a/wafo/source/rind2007/build_all.py b/wafo/source/rind2007/build_all.py deleted file mode 100644 index f143f99..0000000 --- a/wafo/source/rind2007/build_all.py +++ /dev/null @@ -1,31 +0,0 @@ -""" -Builds rindmod.pyd - -See also -http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW - -""" -import os -import sys -from wafo.f2py_tools import f2py_call_str - - -def compile_all(): - f2py_call = f2py_call_str() - print '=' * 75 - print 'compiling rind2007' - print '=' * 75 - - files = ['intmodule', 'jacobmod', 'swapmod', - 'fimod', 'rindmod', 'rind71mod'] - compile1_format = 'gfortran -fPIC -c %s.f' - format1 = '%s.o ' * len(files) - for file_ in files: - os.system(compile1_format % file_) - file_objects = format1 % tuple(files) - - os.system(f2py_call + ' -m rindmod -c %s rind_interface.f ' % - file_objects) - -if __name__ == '__main__': - compile_all() diff --git a/wafo/source/rind2007/erfcoremod.f b/wafo/source/rind2007/erfcoremod.f deleted file mode 100644 index 47ca438..0000000 --- a/wafo/source/rind2007/erfcoremod.f +++ /dev/null @@ -1,339 +0,0 @@ - MODULE ERFCOREMOD - IMPLICIT NONE - - INTERFACE CALERF - MODULE PROCEDURE CALERF - END INTERFACE - - INTERFACE DERF - MODULE PROCEDURE DERF - END INTERFACE - - INTERFACE DERFC - MODULE PROCEDURE DERFC - END INTERFACE - - INTERFACE DERFCX - MODULE PROCEDURE DERFCX - END INTERFACE - CONTAINS -!C-------------------------------------------------------------------- -!C -!C DERF subprogram computes approximate values for erf(x). -!C (see comments heading CALERF). -!C -!C Author/date: W. J. Cody, January 8, 1985 -!C -!C-------------------------------------------------------------------- - FUNCTION DERF( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 0 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERF -!C-------------------------------------------------------------------- -!C -!C DERFC subprogram computes approximate values for erfc(x). -!C (see comments heading CALERF). -!C -!C Author/date: W. J. Cody, January 8, 1985 -!C -!C-------------------------------------------------------------------- - FUNCTION DERFC( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 1 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFC -!C------------------------------------------------------------------ -!C -!C DERFCX subprogram computes approximate values for exp(x*x) * erfc(x). -!C (see comments heading CALERF). -!C -!C Author/date: W. J. Cody, March 30, 1987 -!C -!C------------------------------------------------------------------ - FUNCTION DERFCX( X ) RESULT (VALUE) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: X - DOUBLE PRECISION :: VALUE - INTEGER, PARAMETER :: JINT = 2 - CALL CALERF(X,VALUE,JINT) - RETURN - END FUNCTION DERFCX - - SUBROUTINE CALERF(ARG,RESULT,JINT) - IMPLICIT NONE -!C------------------------------------------------------------------ -!C -!C CALERF packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) -!C for a real argument x. It contains three FUNCTION type -!C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), -!C and one SUBROUTINE type subprogram, CALERF. The calling -!C statements for the primary entries are: -!C -!C Y=ERF(X) (or Y=DERF(X)), -!C -!C Y=ERFC(X) (or Y=DERFC(X)), -!C and -!C Y=ERFCX(X) (or Y=DERFCX(X)). -!C -!C The routine CALERF is intended for internal packet use only, -!C all computations within the packet being concentrated in this -!C routine. The function subprograms invoke CALERF with the -!C statement -!C -!C CALL CALERF(ARG,RESULT,JINT) -!C -!C where the parameter usage is as follows -!C -!C Function Parameters for CALERF -!C call ARG Result JINT -!C -!C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 -!C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 -!C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 -!C -!C The main computation evaluates near-minimax approximations -!C from "Rational Chebyshev approximations for the error function" -!C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This -!C transportable program uses rational functions that theoretically -!C approximate erf(x) and erfc(x) to at least 18 significant -!C decimal digits. The accuracy achieved depends on the arithmetic -!C system, the compiler, the intrinsic functions, and proper -!C selection of the machine-dependent constants. -!C -!C******************************************************************* -!C******************************************************************* -!C -!C Explanation of machine-dependent constants -!C -!C XMIN = the smallest positive floating-point number. -!C XINF = the largest positive finite floating-point number. -!C XNEG = the largest negative argument acceptable to ERFCX; -!C the negative of the solution to the equation -!C 2*exp(x*x) = XINF. -!C XSMALL = argument below which erf(x) may be represented by -!C 2*x/sqrt(pi) and above which x*x will not underflow. -!C A conservative value is the largest machine number X -!C such that 1.0 + X = 1.0 to machine precision. -!C XBIG = largest argument acceptable to ERFC; solution to -!C the equation: W(x) * (1-0.5/x**2) = XMIN, where -!C W(x) = exp(-x*x)/[x*sqrt(pi)]. -!C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to -!C machine precision. A conservative value is -!C 1/[2*sqrt(XSMALL)] -!C XMAX = largest acceptable argument to ERFCX; the minimum -!C of XINF and 1/[sqrt(pi)*XMIN]. -!C -!C Approximate values for some important machines are: -!C -!C XMIN XINF XNEG XSMALL -!C -!C C 7600 (S.P.) 3.13E-294 1.26E+322 -27.220 7.11E-15 -!C CRAY-1 (S.P.) 4.58E-2467 5.45E+2465 -75.345 7.11E-15 -!C IEEE (IBM/XT, -!C SUN, etc.) (S.P.) 1.18E-38 3.40E+38 -9.382 5.96E-8 -!C IEEE (IBM/XT, -!C SUN, etc.) (D.P.) 2.23D-308 1.79D+308 -26.628 1.11D-16 -!C IBM 195 (D.P.) 5.40D-79 7.23E+75 -13.190 1.39D-17 -!C UNIVAC 1108 (D.P.) 2.78D-309 8.98D+307 -26.615 1.73D-18 -!C VAX D-Format (D.P.) 2.94D-39 1.70D+38 -9.345 1.39D-17 -!C VAX G-Format (D.P.) 5.56D-309 8.98D+307 -26.615 1.11D-16 -!C -!C -!C XBIG XHUGE XMAX -!C -!C C 7600 (S.P.) 25.922 8.39E+6 1.80X+293 -!C CRAY-1 (S.P.) 75.326 8.39E+6 5.45E+2465 -!C IEEE (IBM/XT, -!C SUN, etc.) (S.P.) 9.194 2.90E+3 4.79E+37 -!C IEEE (IBM/XT, -!C SUN, etc.) (D.P.) 26.543 6.71D+7 2.53D+307 -!C IBM 195 (D.P.) 13.306 1.90D+8 7.23E+75 -!C UNIVAC 1108 (D.P.) 26.582 5.37D+8 8.98D+307 -!C VAX D-Format (D.P.) 9.269 1.90D+8 1.70D+38 -!C VAX G-Format (D.P.) 26.569 6.71D+7 8.98D+307 -!C -!C******************************************************************* -!C******************************************************************* -!C -!C Error returns -!C -!C The program returns ERFC = 0 for ARG .GE. XBIG; -!C -!C ERFCX = XINF for ARG .LT. XNEG; -!C and -!C ERFCX = 0 for ARG .GE. XMAX. -!C -!C -!C Intrinsic functions required are: -!C -!C ABS, AINT, EXP -!C -!C -!C Author: W. J. Cody -!C Mathematics and Computer Science Division -!C Argonne National Laboratory -!C Argonne, IL 60439 -!C -!C Latest modification: March 19, 1990 -!C Updated to F90 by pab 23.03.2003 -!C -!C------------------------------------------------------------------ - DOUBLE PRECISION, INTENT(IN) :: ARG - INTEGER, INTENT(IN) :: JINT - DOUBLE PRECISION, INTENT(INOUT):: RESULT -! Local variables - INTEGER :: I - DOUBLE PRECISION :: DEL,X,XDEN,XNUM,Y,YSQ -!C------------------------------------------------------------------ -!C Mathematical constants -!C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: HALF = 0.05D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: TWO = 2.0D0 - DOUBLE PRECISION, PARAMETER :: FOUR = 4.0D0 - DOUBLE PRECISION, PARAMETER :: SIXTEN = 16.0D0 - DOUBLE PRECISION, PARAMETER :: SQRPI = 5.6418958354775628695D-1 - DOUBLE PRECISION, PARAMETER :: THRESH = 0.46875D0 -!C------------------------------------------------------------------ -!C Machine-dependent constants -!C------------------------------------------------------------------ - DOUBLE PRECISION, PARAMETER :: XNEG = -26.628D0 - DOUBLE PRECISION, PARAMETER :: XSMALL = 1.11D-16 - DOUBLE PRECISION, PARAMETER :: XBIG = 26.543D0 - DOUBLE PRECISION, PARAMETER :: XHUGE = 6.71D7 - DOUBLE PRECISION, PARAMETER :: XMAX = 2.53D307 - DOUBLE PRECISION, PARAMETER :: XINF = 1.79D308 -!--------------------------------------------------------------- -! Coefficents to the rational polynomials -!-------------------------------------------------------------- - DOUBLE PRECISION, DIMENSION(5) :: A, Q - DOUBLE PRECISION, DIMENSION(4) :: B - DOUBLE PRECISION, DIMENSION(9) :: C - DOUBLE PRECISION, DIMENSION(8) :: D - DOUBLE PRECISION, DIMENSION(6) :: P -!C------------------------------------------------------------------ -!C Coefficients for approximation to erf in first interval -!C------------------------------------------------------------------ - PARAMETER (A = (/ 3.16112374387056560D00, - & 1.13864154151050156D02,3.77485237685302021D02, - & 3.20937758913846947D03, 1.85777706184603153D-1/)) - PARAMETER ( B = (/2.36012909523441209D01,2.44024637934444173D02, - & 1.28261652607737228D03,2.84423683343917062D03/)) -!C------------------------------------------------------------------ -!C Coefficients for approximation to erfc in second interval -!C------------------------------------------------------------------ - PARAMETER ( C=(/5.64188496988670089D-1,8.88314979438837594D0, - 1 6.61191906371416295D01,2.98635138197400131D02, - 2 8.81952221241769090D02,1.71204761263407058D03, - 3 2.05107837782607147D03,1.23033935479799725D03, - 4 2.15311535474403846D-8/)) - PARAMETER ( D =(/1.57449261107098347D01,1.17693950891312499D02, - 1 5.37181101862009858D02,1.62138957456669019D03, - 2 3.29079923573345963D03,4.36261909014324716D03, - 3 3.43936767414372164D03,1.23033935480374942D03/)) -!C------------------------------------------------------------------ -!C Coefficients for approximation to erfc in third interval -!C------------------------------------------------------------------ - PARAMETER ( P =(/3.05326634961232344D-1,3.60344899949804439D-1, - 1 1.25781726111229246D-1,1.60837851487422766D-2, - 2 6.58749161529837803D-4,1.63153871373020978D-2/)) - PARAMETER (Q =(/2.56852019228982242D00,1.87295284992346047D00, - 1 5.27905102951428412D-1,6.05183413124413191D-2, - 2 2.33520497626869185D-3/)) -!C------------------------------------------------------------------ - X = ARG - Y = ABS(X) - IF (Y .LE. THRESH) THEN -!C------------------------------------------------------------------ -!C Evaluate erf for |X| <= 0.46875 -!C------------------------------------------------------------------ - YSQ = ZERO - IF (Y .GT. XSMALL) THEN - YSQ = Y * Y - XNUM = A(5)*YSQ - XDEN = YSQ - DO I = 1, 3 - XNUM = (XNUM + A(I)) * YSQ - XDEN = (XDEN + B(I)) * YSQ - END DO - RESULT = X * (XNUM + A(4)) / (XDEN + B(4)) - ELSE - RESULT = X * A(4) / B(4) - ENDIF - IF (JINT .NE. 0) RESULT = ONE - RESULT - IF (JINT .EQ. 2) RESULT = EXP(YSQ) * RESULT - GO TO 800 -!C------------------------------------------------------------------ -!C Evaluate erfc for 0.46875 <= |X| <= 4.0 -!C------------------------------------------------------------------ - ELSE IF (Y .LE. FOUR) THEN - XNUM = C(9)*Y - XDEN = Y - DO I = 1, 7 - XNUM = (XNUM + C(I)) * Y - XDEN = (XDEN + D(I)) * Y - END DO - RESULT = (XNUM + C(8)) / (XDEN + D(8)) - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF -!C------------------------------------------------------------------ -!C Evaluate erfc for |X| > 4.0 -!C------------------------------------------------------------------ - ELSE - RESULT = ZERO - IF (Y .GE. XBIG) THEN - IF ((JINT .NE. 2) .OR. (Y .GE. XMAX)) GO TO 300 - IF (Y .GE. XHUGE) THEN - RESULT = SQRPI / Y - GO TO 300 - END IF - END IF - YSQ = ONE / (Y * Y) - XNUM = P(6)*YSQ - XDEN = YSQ - DO I = 1, 4 - XNUM = (XNUM + P(I)) * YSQ - XDEN = (XDEN + Q(I)) * YSQ - ENDDO - RESULT = YSQ *(XNUM + P(5)) / (XDEN + Q(5)) - RESULT = (SQRPI - RESULT) / Y - IF (JINT .NE. 2) THEN - YSQ = AINT(Y*SIXTEN)/SIXTEN - DEL = (Y-YSQ)*(Y+YSQ) - RESULT = EXP(-YSQ*YSQ) * EXP(-DEL) * RESULT - END IF - END IF -!C------------------------------------------------------------------ -!C Fix up for negative argument, erf, etc. -!C------------------------------------------------------------------ - 300 IF (JINT .EQ. 0) THEN - RESULT = (HALF - RESULT) + HALF - IF (X .LT. ZERO) RESULT = -RESULT - ELSE IF (JINT .EQ. 1) THEN - IF (X .LT. ZERO) RESULT = TWO - RESULT - ELSE - IF (X .LT. ZERO) THEN - IF (X .LT. XNEG) THEN - RESULT = XINF - ELSE - YSQ = AINT(X*SIXTEN)/SIXTEN - DEL = (X-YSQ)*(X+YSQ) - Y = EXP(YSQ*YSQ) * EXP(DEL) - RESULT = (Y+Y) - RESULT - END IF - END IF - END IF - 800 RETURN - END SUBROUTINE CALERF - END MODULE ERFCOREMOD \ No newline at end of file diff --git a/wafo/source/rind2007/fimod.f b/wafo/source/rind2007/fimod.f deleted file mode 100644 index 83f2ebb..0000000 --- a/wafo/source/rind2007/fimod.f +++ /dev/null @@ -1,1595 +0,0 @@ - MODULE TRIVARIATEVAR -! Global variables used in calculation of TRIVARIATE -! normal and TRIVARIATE student T probabilties - INTEGER :: NU - DOUBLE PRECISION :: H1, H2, H3, R23, RUA, RUB, AR, RUC - END MODULE TRIVARIATEVAR -! -! FIMOD contains functions for calculating 1D, 2D and 3D Normal and student T probabilites -! and 1D expectations - MODULE FIMOD -! USE ERFCOREMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: NORMPRB, FI, FIINV, MVNLIMITS, MVNLMS, BVU,BVNMVN - PUBLIC :: GAUSINT, GAUSINT2, EXLMS, EXINV - PUBLIC :: STUDNT, BVTL, TVTL, TVNMVN - - INTERFACE NORMPRB - MODULE PROCEDURE NORMPRB - END INTERFACE - - INTERFACE FI - MODULE PROCEDURE FI - END INTERFACE - - INTERFACE FI2 - MODULE PROCEDURE FI2 - END INTERFACE - - INTERFACE FIINV - MODULE PROCEDURE FIINV - END INTERFACE - - INTERFACE MVNLIMITS - MODULE PROCEDURE MVNLIMITS - END INTERFACE - - INTERFACE MVNLMS - MODULE PROCEDURE MVNLMS - END INTERFACE - - INTERFACE BVU - MODULE PROCEDURE BVU - END INTERFACE - - INTERFACE BVNMVN - MODULE PROCEDURE BVNMVN - END INTERFACE - - INTERFACE STUDNT - MODULE PROCEDURE STUDNT - END INTERFACE - - INTERFACE BVTL - MODULE PROCEDURE BVTL - END INTERFACE - - INTERFACE TVTL - MODULE PROCEDURE TVTL - END INTERFACE - - INTERFACE GAUSINT - MODULE PROCEDURE GAUSINT - END INTERFACE - - INTERFACE GAUSINT2 - MODULE PROCEDURE GAUSINT2 - END INTERFACE - - INTERFACE EXLMS - MODULE PROCEDURE EXLMS - END INTERFACE - - INTERFACE EXINV - MODULE PROCEDURE EXINV - END INTERFACE - - CONTAINS - FUNCTION FIINV(P) RESULT (VAL) - IMPLICIT NONE -* -* ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3 -* -* Produces the normal deviate Z corresponding to a given lower -* tail area of P. -* Absolute error less than 1e-13 -* Relative error less than 1e-15 for abs(VAL)>0.1 -* -* The hash sums below are the sums of the mantissas of the -* coefficients. They are included for use in checking -* transcription. -* - DOUBLE PRECISION, INTENT(in) :: P - DOUBLE PRECISION :: VAL -!local variables - DOUBLE PRECISION SPLIT1, SPLIT2, CONST1, CONST2, ONE, ZERO, HALF, - & A0, A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, - & C0, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, - & E0, E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, - & Q, R - PARAMETER ( SPLIT1 = 0.425D0, SPLIT2 = 5.D0, - & CONST1 = 0.180625D0, CONST2 = 1.6D0, - & ONE = 1.D0, ZERO = 0.D0, HALF = 0.5D0 ) -* -* Coefficients for P close to 0.5 -* - PARAMETER ( - * A0 = 3.38713 28727 96366 6080D0, - * A1 = 1.33141 66789 17843 7745D+2, - * A2 = 1.97159 09503 06551 4427D+3, - * A3 = 1.37316 93765 50946 1125D+4, - * A4 = 4.59219 53931 54987 1457D+4, - * A5 = 6.72657 70927 00870 0853D+4, - * A6 = 3.34305 75583 58812 8105D+4, - * A7 = 2.50908 09287 30122 6727D+3, - * B1 = 4.23133 30701 60091 1252D+1, - * B2 = 6.87187 00749 20579 0830D+2, - * B3 = 5.39419 60214 24751 1077D+3, - * B4 = 2.12137 94301 58659 5867D+4, - * B5 = 3.93078 95800 09271 0610D+4, - * B6 = 2.87290 85735 72194 2674D+4, - * B7 = 5.22649 52788 52854 5610D+3 ) -* HASH SUM AB 55.88319 28806 14901 4439 -* -* Coefficients for P not close to 0, 0.5 or 1. -* - PARAMETER ( - * C0 = 1.42343 71107 49683 57734D0, - * C1 = 4.63033 78461 56545 29590D0, - * C2 = 5.76949 72214 60691 40550D0, - * C3 = 3.64784 83247 63204 60504D0, - * C4 = 1.27045 82524 52368 38258D0, - * C5 = 2.41780 72517 74506 11770D-1, - * C6 = 2.27238 44989 26918 45833D-2, - * C7 = 7.74545 01427 83414 07640D-4, - * D1 = 2.05319 16266 37758 82187D0, - * D2 = 1.67638 48301 83803 84940D0, - * D3 = 6.89767 33498 51000 04550D-1, - * D4 = 1.48103 97642 74800 74590D-1, - * D5 = 1.51986 66563 61645 71966D-2, - * D6 = 5.47593 80849 95344 94600D-4, - * D7 = 1.05075 00716 44416 84324D-9 ) -* HASH SUM CD 49.33206 50330 16102 89036 -* -* Coefficients for P near 0 or 1. -* - PARAMETER ( - * E0 = 6.65790 46435 01103 77720D0, - * E1 = 5.46378 49111 64114 36990D0, - * E2 = 1.78482 65399 17291 33580D0, - * E3 = 2.96560 57182 85048 91230D-1, - * E4 = 2.65321 89526 57612 30930D-2, - * E5 = 1.24266 09473 88078 43860D-3, - * E6 = 2.71155 55687 43487 57815D-5, - * E7 = 2.01033 43992 92288 13265D-7, - * F1 = 5.99832 20655 58879 37690D-1, - * F2 = 1.36929 88092 27358 05310D-1, - * F3 = 1.48753 61290 85061 48525D-2, - * F4 = 7.86869 13114 56132 59100D-4, - * F5 = 1.84631 83175 10054 68180D-5, - * F6 = 1.42151 17583 16445 88870D-7, - * F7 = 2.04426 31033 89939 78564D-15 ) -* HASH SUM EF 47.52583 31754 92896 71629 -* - Q = ( P - HALF) - IF ( ABS(Q) .LE. SPLIT1 ) THEN ! Central range. - R = CONST1 - Q*Q - VAL = Q*( ( ( ((((A7*R + A6)*R + A5)*R + A4)*R + A3) - * *R + A2 )*R + A1 )*R + A0 ) - * /( ( ( ((((B7*R + B6)*R + B5)*R + B4)*R + B3) - * *R + B2 )*R + B1 )*R + ONE) - ELSE ! near the endpoints - R = MIN( P, ONE - P ) - IF (R .GT.ZERO) THEN ! ( 2.d0*R .GT. CFxCutOff) THEN ! R .GT.0.d0 - R = SQRT( -LOG(R) ) - IF ( R .LE. SPLIT2 ) THEN - R = R - CONST2 - VAL = ( ( ( ((((C7*R + C6)*R + C5)*R + C4)*R + C3) - * *R + C2 )*R + C1 )*R + C0 ) - * /( ( ( ((((D7*R + D6)*R + D5)*R + D4)*R + D3) - * *R + D2 )*R + D1 )*R + ONE ) - ELSE - R = R - SPLIT2 - VAL = ( ( ( ((((E7*R + E6)*R + E5)*R + E4)*R + E3) - * *R + E2 )*R + E1 )*R + E0 ) - * /( ( ( ((((F7*R + F6)*R + F5)*R + F4)*R + F3) - * *R + F2 )*R + F1 )*R + ONE ) - END IF - ELSE - VAL = 37.0d0 !9.D0 !XMAX 9.d0 - END IF - IF ( Q < ZERO ) VAL = - VAL - END IF - RETURN - END FUNCTION FIINV - ! ********************************* - SUBROUTINE NORMPRB(Z, P, Q) -! USE ERFCOREMOD -! USE GLOBALDATA, ONLY : XMAX -! Normal distribution probabilities accurate to 18 digits between -! -XMAX and XMAX -! -! Z = no. of standard deviations from the mean. -! P, Q = probabilities to the left & right of Z. P + Q = 1. -! -! by pab 23.03.2003 -! - IMPLICIT NONE - DOUBLE PRECISION, INTENT(IN) :: Z - DOUBLE PRECISION, INTENT(OUT) :: P - DOUBLE PRECISION, INTENT(OUT), OPTIONAL :: Q -!Local variables - DOUBLE PRECISION :: PP, ZABS - DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0 - DOUBLE PRECISION, PARAMETER :: ONE = 1.0D0 - DOUBLE PRECISION, PARAMETER :: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER :: HALF = 0.5D0 - DOUBLE PRECISION, PARAMETER :: XMAX = 37D0 - ZABS = ABS(Z) -! -! |Z| > 37 (or XMAX) -! - IF ( ZABS .GT. XMAX ) THEN - IF (Z > ZERO) THEN - P = ONE - IF (PRESENT(Q)) Q = ZERO - ELSE - P = ZERO - IF (PRESENT(Q)) Q = ONE - END IF - ELSE -! -! |Z| <= 37 -! - PP = DERFC(ZABS*SQ2M1)*HALF - - IF (Z < ZERO) THEN - P = PP - IF (PRESENT(Q)) Q = ONE - PP - ELSE - P = ONE - PP - IF (PRESENT(Q)) Q = PP - END IF - END IF - - RETURN - END SUBROUTINE NORMPRB - FUNCTION FI( Z ) RESULT (VALUE) -! USE ERFCOREMOD -! USE GLOBALDATA, ONLY : XMAX - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -! Local variables - DOUBLE PRECISION :: ZABS - DOUBLE PRECISION, PARAMETER:: SQ2M1 = 0.70710678118655D0 ! 1/SQRT(2) - DOUBLE PRECISION, PARAMETER:: HALF = 0.5D0 - DOUBLE PRECISION, PARAMETER:: XMAX = 37.D0 - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( ZABS .GT. XMAX ) THEN - IF (Z < 0.0D0) THEN - VALUE = 0.0D0 - ELSE - VALUE = 1.0D0 - ENDIF - ELSE - VALUE = DERFC(-Z*SQ2M1)*HALF - ENDIF - RETURN - END FUNCTION FI - - FUNCTION FI2( Z ) RESULT (VALUE) -! USE GLOBALDATA, ONLY : XMAX - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE -* -* Normal distribution probabilities accurate to 1.e-15. -* relative error less than 1e-8; -* Z = no. of standard deviations from the mean. -* -* Based upon algorithm 5666 for the error function, from: -* Hart, J.F. et al, 'Computer Approximations', Wiley 1968 -* -* Programmer: Alan Miller -* -* Latest revision - 30 March 1986 -* - DOUBLE PRECISION :: P0, P1, P2, P3, P4, P5, P6, - * Q0, Q1, Q2, Q3, Q4, Q5, Q6, Q7,XMAX, - * P, EXPNTL, CUTOFF, ROOTPI, ZABS, Z2 - PARAMETER( - * P0 = 220.20 68679 12376 1D0, - * P1 = 221.21 35961 69931 1D0, - * P2 = 112.07 92914 97870 9D0, - * P3 = 33.912 86607 83830 0D0, - * P4 = 6.3739 62203 53165 0D0, - * P5 = 0.70038 30644 43688 1D0, - * P6 = 0.035262 49659 98910 9D0 ) - PARAMETER( - * Q0 = 440.41 37358 24752 2D0, - * Q1 = 793.82 65125 19948 4D0, - * Q2 = 637.33 36333 78831 1D0, - * Q3 = 296.56 42487 79673 7D0, - * Q4 = 86.780 73220 29460 8D0, - * Q5 = 16.064 17757 92069 5D0, - * Q6 = 1.7556 67163 18264 2D0, - * Q7 = 0.088388 34764 83184 4D0 ) - PARAMETER( ROOTPI = 2.5066 28274 63100 1D0 ) - PARAMETER( CUTOFF = 7.0710 67811 86547 5D0 ) - PARAMETER( XMAX = 37.D0 ) -* - ZABS = ABS(Z) -* -* |Z| > 37 (or XMAX) -* - IF ( ZABS .GT. XMAX ) THEN - P = 0.d0 - ELSE -* -* |Z| <= 37 -* - Z2 = ZABS * ZABS - EXPNTL = EXP( -Z2 * 0.5D0 ) -* -* |Z| < CUTOFF = 10/SQRT(2) -* - IF ( ZABS < CUTOFF ) THEN - P = EXPNTL*( (((((P6*ZABS + P5)*ZABS + P4)*ZABS + P3)*ZABS - * + P2)*ZABS + P1)*ZABS + P0)/(((((((Q7*ZABS + Q6)*ZABS - * + Q5)*ZABS + Q4)*ZABS + Q3)*ZABS + Q2)*ZABS + Q1)*ZABS - * + Q0 ) -* -* |Z| >= CUTOFF. -* - ELSE - P = EXPNTL/( ZABS + 1.d0/( ZABS + 2.d0/( ZABS + 3.d0/( ZABS - * + 4.d0/( ZABS + 0.65D0 ) ) ) ) )/ROOTPI - END IF - END IF - IF ( Z .GT. 0.d0 ) P = 1.d0 - P - VALUE = P - RETURN - END FUNCTION FI2 - - SUBROUTINE MVNLIMITS( A, B, INFIN, AP, PRB, AQ) -! RETURN probabilities for being between A and B -! WHERE -! AP = FI(A), AQ = 1 - FI(A) -! BP = FI(B), BQ = 1 - FI(B) -! PRB = BP-AP IF BP+AP<1 -! = AQ-BQ OTHERWISE -! - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: A, B - DOUBLE PRECISION, INTENT(out) :: AP - DOUBLE PRECISION, INTENT(out),OPTIONAL :: PRB,AQ - INTEGER,INTENT(in) :: INFIN -! LOCAL VARIABLES - DOUBLE PRECISION :: BP,AQQ, BQQ - DOUBLE PRECISION, PARAMETER :: ONE=1.D0, ZERO = 0.D0 - - SELECT CASE (infin) - CASE (:-1) - AP = ZERO -! BP = ONE - IF (PRESENT(PRB)) PRB = ONE - IF (PRESENT(AQ)) AQ = ONE -! IF (PRESENT(BQ)) BQ = ZERO - CASE (0) - AP = ZERO - CALL NORMPRB(B,BP) !,BQQ) - IF (PRESENT(PRB)) PRB = BP - IF (PRESENT(AQ)) AQ = ONE -! IF (PRESENT(BQ)) BQ = BQQ - CASE (1) -! BP = ONE - CALL NORMPRB(A,AP,AQQ) - IF (PRESENT(PRB)) PRB = AQQ - IF (PRESENT(AQ)) AQ = AQQ -! IF (PRESENT(BQ)) BQ = ZERO - CASE (2:) - CALL NORMPRB(A,AP,AQQ) - CALL NORMPRB(B,BP,BQQ) - IF (PRESENT(PRB)) THEN - IF (AP+BP < ONE) THEN - PRB = BP - AP - ELSE - PRB = AQQ - BQQ - END IF - ENDIF - IF (PRESENT(AQ)) AQ = AQQ -! IF (PRESENT(BQ)) BQ = BQQ - END SELECT - RETURN - END SUBROUTINE MVNLIMITS - - - SUBROUTINE MVNLMS( A, B, INFIN, LOWER, UPPER ) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(in) :: A, B - DOUBLE PRECISION, INTENT(out) :: LOWER, UPPER - INTEGER,INTENT(in) :: INFIN - - LOWER = 0.0D0 - UPPER = 1.0D0 - IF ( INFIN < 0 ) RETURN - IF ( INFIN .NE. 0 ) LOWER = FI(A) - IF ( INFIN .NE. 1 ) UPPER = FI(B) - RETURN - END SUBROUTINE MVNLMS - - FUNCTION TVNMVN(A, B, INFIN, R, EPSI ) RESULT (VAL) - IMPLICIT NONE -* -* A function for computing trivariate normal probabilities. -* -* Parameters -* -* A REAL, array of lower integration limits. -* B REAL, array of upper integration limits. -! R REAL, array of correlation coefficents -! R = [r12 r13 r23] -! EPSI = REAL tolerance -* INFIN INTEGER, array of integration limits flags: -* if INFIN(I) = 0, Ith limits are (-infinity, B(I)]; -* if INFIN(I) = 1, Ith limits are [A(I), infinity); -* if INFIN(I) = 2, Ith limits are [A(I), B(I)]. - DOUBLE PRECISION, DIMENSION(:), INTENT (IN) :: A, B , R - DOUBLE PRECISION, INTENT (IN) :: EPSI - INTEGER, DIMENSION(:), INTENT (IN) :: INFIN - DOUBLE PRECISION :: VAL - - IF ( INFIN(1) .EQ. 2 ) THEN - IF ( INFIN(2) .EQ. 2 ) THEN - IF (INFIN(3) .EQ. 2 ) THEN !OK - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( A(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( B(1), A(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( B(1), B(2), A(3),R(1),R(2),R(3),EPSI ) - & + TVNL( A(1), A(2), B(3),R(1),R(2),R(3),EPSI ) - & + TVNL( A(1), B(2), A(3),R(1),R(2),R(3),EPSI ) - $ + TVNL( B(1), A(2), A(3),R(1),R(2),R(3),EPSI ) - & - TVNL( A(1), A(2), A(3),R(1),R(2),R(3),EPSI ) - ELSE IF (INFIN(3) .EQ. 1 ) THEN ! B(3) = inf ok - VAL = TVNL( B(1), B(2), -A(3),R(1),-R(2),-R(3),EPSI ) - & - TVNL( A(1), B(2), -A(3),R(1),-R(2),-R(3),EPSI ) - & - TVNL( B(1), A(2), -A(3),R(1),-R(2),-R(3),EPSI ) - & + TVNL( A(1), A(2), -A(3),R(1),-R(2),-R(3),EPSI ) - ELSE IF (INFIN(3) .EQ. 0 ) THEN !OK A(3) = -inf - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( A(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( B(1), A(2), B(3),R(1),R(2),R(3),EPSI ) - & + TVNL( A(1), A(2), B(3),R(1),R(2),R(3),EPSI ) - ELSE ! INFIN(1:2)=2 - VAL = BVNMVN( A ,B, INFIN, R(1) ) - ENDIF - ELSE IF (INFIN(2) .EQ. 1 ) THEN ! B(2) = inf - IF (INFIN(3) .EQ. 2 ) THEN - VAL = TVNL( B(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI ) - & - TVNL( A(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI ) - & - TVNL( B(1), -A(2), A(3),-R(1),R(2),-R(3),EPSI ) - & + TVNL( A(1), -A(2), A(3),-R(1),R(2),-R(3),EPSI ) - ELSE IF (INFIN(3) .EQ. 1 ) THEN - VAL = TVNL( B(1), -A(2), -A(3),-R(1),-R(2),R(3),EPSI ) - $ - TVNL( A(1), -A(2), -A(3),-R(1),-R(2),R(3),EPSI ) - ELSE IF (INFIN(3) .EQ. 0 ) THEN - VAL = TVNL( B(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI) - $ - TVNL( A(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI) - ELSE - VAL = BVNMVN( A ,B, INFIN, R(1) ) - ENDIF - ELSE IF (INFIN(2) .EQ. 0 ) THEN - SELECT CASE (INFIN(3)) - CASE (2:) ! % % A(2)=-INF - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - $ - TVNL( A(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - $ - TVNL( B(1), B(2), A(3),R(1),R(2),R(3),EPSI ) - $ + TVNL( A(1), B(2), A(3),R(1),R(2),R(3),EPSI ) - CASE (1) !% % A(2)=-INF B(3) = INF - VAL = TVNL( B(1), B(2), -A(3),R(1),-R(2),-R(3),EPSI) - $ - TVNL(A(1), B(2), -A(3),R(1),-R(2),-R(3),EPSI) - CASE (0) ! % % A(2)=-INF A(3) = -INF - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - $ - TVNL( A(1), B(2), B(3),R(1),R(2),R(3),EPSI) - CASE DEFAULT - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - ELSE - VAL = BVNMVN(A(1:3:2),B(1:3:2),INFIN(1:3:2),R(2)) - ENDIF - ELSE IF ( INFIN(1) .EQ. 1 ) THEN - SELECT CASE (INFIN(2)) - CASE (2) - SELECT CASE (INFIN(3)) - CASE (2) !% B(1) = INF %OK - VAL = TVNL(-A(1), B(2), B(3),-R(1),-R(2),R(3),EPSI ) - $ - TVNL(-A(1), B(2), A(3),-R(1),-R(2),R(3),EPSI ) - $ - TVNL(-A(1), A(2), B(3),-R(1),-R(2),R(3),EPSI ) - $ + TVNL(-A(1), A(2), A(3),-R(1),-R(2),R(3),EPSI ) - CASE (1) ! % B(1) = INF B(3) = INF %OK - VAL = TVNL(-A(1), B(2), -A(3),-R(1),R(2),-R(3),EPSI ) - $ - TVNL(-A(1), A(2), -A(3),-R(1),R(2),-R(3),EPSI) - CASE (0) ! % B(1) = INF A(3) = -INF %OK - VAL = TVNL(-A(1), B(2), B(3),-R(1),-R(2),R(3),EPSI ) - $ - TVNL(-A(1), A(2), B(3),-R(1),-R(2),R(3),EPSI) - CASE (-1) - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - CASE (1) !%B(2) = INF - SELECT CASE (INFIN(3)) - CASE (2) ! % B(1) = INF B(2) = INF % OK - VAL = TVNL( -A(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI ) - & - TVNL( -A(1), -A(2),A(3),-R(1),R(2),-R(3),EPSI ) - CASE (1) ! % B(1:3) = INF %OK - VAL = TVNL( -A(1), -A(2), -A(3),R(1),R(2),R(3),EPSI) - CASE (0) ! % B(1:2) = INF A(3) = -INF %OK - VAL = TVNL( -A(1), -A(2), B(3),R(1),-R(2),-R(3),EPSI ) - CASE (:-1) - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - CASE (0) ! A(2) = -INF - SELECT CASE ( INFIN(3)) - CASE (2) ! B(1) = INF , A(2) = -INF %OK - VAL = TVNL( -A(1), B(2), B(3),-R(1),R(2),-R(3),EPSI ) - & - TVNL( -A(1), B(2),A(3),-R(1),R(2),-R(3),EPSI ) - CASE (1) ! B(1) = INF , A(2) = -INF B(3) = INF % OK - VAL = TVNL( -A(1), B(2), -A(3),-R(1),-R(2),R(3),EPSI) - CASE (0) !% B(1) = INF , A(2:3) = -INF - VAL = TVNL( -A(1), B(2), B(3),-R(1),-R(2),R(3),EPSI ) - CASE (:-1) - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - CASE DEFAULT - VAL = BVNMVN(A(1:3:2),B(1:3:2),INFIN(1:3:2),R(2)) - END SELECT - ELSE IF ( INFIN(1) .EQ. 0 ) THEN - SELECT CASE (INFIN(2)) - CASE (2) - SELECT CASE (INFIN(3)) - CASE (2:) ! A(1) = -INF %OK - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( B(1), B(2), A(3),R(1),R(2),R(3),EPSI) - & - TVNL( B(1), A(2), B(3),R(1),R(2),R(3),EPSI ) - & + TVNL( B(1), A(2), A(3),R(1),R(2),R(3),EPSI ) - CASE (1) ! % A(1) = -INF , B(3) = INF %OK - VAL = TVNL( B(1), B(2), -A(3),R(1),-R(2),-R(3),EPSI ) - $ - TVNL( B(1), A(2), -A(3),R(1),-R(2),-R(3),EPSI ) - CASE (0) ! A(1) = -INF , A(3) = -INF %OK - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - & - TVNL( B(1), A(2), B(3),R(1),R(2),R(3),EPSI ) - CASE DEFAULT - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - CASE (1) ! B(2) = INF - SELECT CASE (INFIN(3)) - CASE (2:) ! A(1) = -INF B(2) = INF %OK - VAL = TVNL( B(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI) - $ - TVNL( B(1), -A(2), A(3),-R(1),R(2),-R(3),EPSI) - CASE (1) ! A(1) = -INF B(2) = INF B(3) = INF %OK - VAL = TVNL( B(1), -A(2), -A(3),-R(1),-R(2),R(3),EPSI) - CASE (0) ! % A(1) = -INF B(2) = INF A(3) = -INF %OK - VAL = TVNL(B(1), -A(2), B(3),-R(1),R(2),-R(3),EPSI) - CASE DEFAULT - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - CASE (0) ! A(2) = -INF - SELECT CASE (INFIN(3)) - CASE (2:) ! % A(1:2) = -INF - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI) - $ - TVNL( B(1), B(2), A(3),R(1),R(2),R(3),EPSI) - CASE (1) ! A(1:2) = -INF B(3) = INF - VAL = TVNL( B(1), B(2), -A(3),R(1),-R(2),-R(3),EPSI) - CASE (0) ! % A(1:3) = -INF - VAL = TVNL( B(1), B(2), B(3),R(1),R(2),R(3),EPSI ) - CASE DEFAULT - VAL = BVNMVN(A,B,INFIN,R(1)) - END SELECT - CASE DEFAULT - VAL = BVNMVN(A(1:3:2),B(1:3:2),INFIN(1:3:2),R(2)) - END SELECT - ELSE - VAL = BVNMVN(A(2:3),B(2:3),INFIN(2:3),R(3)) - END IF - CONTAINS - DOUBLE PRECISION FUNCTION TVNL(H1,H2,H3, R12,R13,R23, EPSI ) - !Returns Trivariate Normal CDF - DOUBLE PRECISION, INTENT(IN) :: R12,R13,R23 - DOUBLE PRECISION, INTENT(IN) :: H1,H2,H3, EPSI -! Locals - INTEGER, PARAMETER :: NU = 0 - DOUBLE PRECISION,DIMENSION(3) :: H,R - H(:) = (/ H1, H2, H3 /) - R(:) = (/ R12, R13, R23 /) - TVNL = TVTL(NU,H,R,EPSI) - END FUNCTION TVNL - END FUNCTION TVNMVN - FUNCTION BVNMVN( LOWER, UPPER, INFIN, CORREL ) RESULT (VAL) - IMPLICIT NONE -* -* A function for computing bivariate normal probabilities. -* -* Parameters -* -* LOWER REAL, array of lower integration limits. -* UPPER REAL, array of upper integration limits. -* INFIN INTEGER, array of integration limits flags: -* if INFIN(I) = 0, Ith limits are (-infinity, UPPER(I)]; -* if INFIN(I) = 1, Ith limits are [LOWER(I), infinity); -* if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)]. -* CORREL REAL, correlation coefficient. -* - - DOUBLE PRECISION, DIMENSION(:), INTENT (IN) :: LOWER, UPPER - DOUBLE PRECISION, INTENT (IN) :: CORREL - INTEGER, DIMENSION(:), INTENT (IN) :: INFIN - DOUBLE PRECISION :: VAL - DOUBLE PRECISION :: E - SELECT CASE (INFIN(1)) - CASE (2:) - SELECT CASE ( INFIN(2) ) - CASE (2:) - VAL = BVU ( LOWER(1), LOWER(2), CORREL ) - & - BVU ( UPPER(1), LOWER(2), CORREL ) - & - BVU ( LOWER(1), UPPER(2), CORREL ) - & + BVU ( UPPER(1), UPPER(2), CORREL ) - - CASE (1) - VAL = BVU ( LOWER(1), LOWER(2), CORREL ) - & - BVU ( UPPER(1), LOWER(2), CORREL ) - CASE (0) - VAL = BVU ( -UPPER(1), -UPPER(2), CORREL ) - & - BVU ( -LOWER(1), -UPPER(2), CORREL ) - CASE DEFAULT - CALL MVNLIMITS(LOWER(1),UPPER(1),INFIN(1),E,VAL) - END SELECT - CASE (1) - SELECT CASE ( INFIN(2)) - CASE ( 2: ) - VAL = BVU ( LOWER(1), LOWER(2), CORREL ) - & - BVU ( LOWER(1), UPPER(2), CORREL ) - CASE (1) - VAL = BVU ( LOWER(1), LOWER(2), CORREL ) - CASE (0) - VAL = BVU ( LOWER(1), -UPPER(2), -CORREL ) - CASE DEFAULT - CALL MVNLIMITS(LOWER(2),UPPER(2),INFIN(2),E,VAL) - END SELECT - CASE (0) - SELECT CASE ( INFIN(2)) - CASE ( 2: ) - VAL = BVU ( -UPPER(1), -UPPER(2), CORREL ) - & - BVU ( -UPPER(1), -LOWER(2), CORREL ) - CASE ( 1 ) - VAL = BVU ( -UPPER(1), LOWER(2), -CORREL ) - CASE (0) - VAL = BVU ( -UPPER(1), -UPPER(2), CORREL ) - CASE DEFAULT - CALL MVNLIMITS(LOWER(1),UPPER(1),INFIN(1),E,VAL) - END SELECT - CASE DEFAULT !ELSE !INFIN(1)<0 - CALL MVNLIMITS(LOWER(2),UPPER(2),INFIN(2),E,VAL) - END SELECT - END FUNCTION BVNMVN - FUNCTION BVU( SH, SK, R ) RESULT (VAL) -! USE GLOBALDATA, ONLY: XMAX - IMPLICIT NONE -* -! A function for computing bivariate normal probabilities. -! -! Yihong Ge -! Department of Computer Science and Electrical Engineering -! Washington State University -! Pullman, WA 99164-2752 -! and -! Alan Genz -! Department of Mathematics -! Washington State University -! Pullman, WA 99164-3113 -! Email : alangenz@wsu.edu -! -! This function is based on the method described by -! Drezner, Z and G.O. Wesolowsky, (1989), -! On the computation of the bivariate normal integral, -! Journal of Statist. Comput. Simul. 35, pp. 101-107, -! with major modifications for double precision, and for |R| close to 1. -! -! BVU - calculate the probability that X > SH and Y > SK. -! (to accuracy of 1e-16?) -! -! Parameters -! -! SH REAL, lower integration limit -! SK REAL, lower integration limit -! R REAL, correlation coefficient -! -! LG INTEGER, number of Gauss Rule Points and Weights -! -! Revised pab added check on XMAX - DOUBLE PRECISION, INTENT(IN) :: SH, SK, R - DOUBLE PRECISION :: VAL -! Local variables - DOUBLE PRECISION :: ZERO,ONE,FOUR - DOUBLE PRECISION :: SQTWOPI ,TWOPI1,FOURPI1 - DOUBLE PRECISION :: HALF,ONETHIRD,ONEEIGHT,ONESIXTEEN - DOUBLE PRECISION :: TWELVE, EXPMIN, XMAX - INTEGER :: I, LG, NG - PARAMETER ( ZERO = 0.D0,ONE=1.0D0,HALF=0.5D0) - PARAMETER (FOUR = 4.0D0, TWELVE = 12.0D0) - PARAMETER (EXPMIN = -100.0D0) - PARAMETER (ONESIXTEEN = 0.0625D0) !1/16 - PARAMETER (ONEEIGHT = 0.125D0 ) !1/8 - PARAMETER (ONETHIRD = 0.3333333333333333333333D0) -! PARAMETER (TWOPI = 6.283185307179586D0 ) - PARAMETER (TWOPI1 = 0.15915494309190D0 ) !1/(2*pi) - PARAMETER (FOURPI1 = 0.0795774715459476D0 ) !/1/(4*pi) - PARAMETER (SQTWOPI = 2.50662827463100D0) ! SQRT(2*pi) - PARAMETER (XMAX = 8.3D0) - DOUBLE PRECISION, DIMENSION(10,3) :: X, W - DOUBLE PRECISION :: AS, A, B, C, D, RS, XS - DOUBLE PRECISION :: SN, ASR, H, K, BS, HS, HK -! Gauss Legendre Points and Weights, N = 6 - DATA ( W(I,1), X(I,1), I = 1,3) / - * 0.1713244923791705D+00,-0.9324695142031522D+00, - * 0.3607615730481384D+00,-0.6612093864662647D+00, - * 0.4679139345726904D+00,-0.2386191860831970D+00/ -! Gauss Legendre Points and Weights, N = 12 - DATA ( W(I,2), X(I,2), I = 1,6) / - * 0.4717533638651177D-01,-0.9815606342467191D+00, - * 0.1069393259953183D+00,-0.9041172563704750D+00, - * 0.1600783285433464D+00,-0.7699026741943050D+00, - * 0.2031674267230659D+00,-0.5873179542866171D+00, - * 0.2334925365383547D+00,-0.3678314989981802D+00, - * 0.2491470458134029D+00,-0.1252334085114692D+00/ -! Gauss Legendre Points and Weights, N = 20 - DATA ( W(I,3), X(I,3), I = 1,10) / - * 0.1761400713915212D-01,-0.9931285991850949D+00, - * 0.4060142980038694D-01,-0.9639719272779138D+00, - * 0.6267204833410906D-01,-0.9122344282513259D+00, - * 0.8327674157670475D-01,-0.8391169718222188D+00, - * 0.1019301198172404D+00,-0.7463319064601508D+00, - * 0.1181945319615184D+00,-0.6360536807265150D+00, - * 0.1316886384491766D+00,-0.5108670019508271D+00, - * 0.1420961093183821D+00,-0.3737060887154196D+00, - * 0.1491729864726037D+00,-0.2277858511416451D+00, - * 0.1527533871307259D+00,-0.7652652113349733D-01/ - SAVE W, X - VAL = ZERO - HK = MIN(SH,SK) - IF ( HK < -XMAX) THEN ! pab 24.05.2003 - VAL = FI(-MAX(SH,SK)) - RETURN - ELSE IF ( XMAX < MAX(SH,SK)) THEN - RETURN - ENDIF - IF ( ABS(R) < 0.3D0 ) THEN - NG = 1 - LG = 3 - ELSE IF ( ABS(R) < 0.75D0 ) THEN - NG = 2 - LG = 6 - ELSE - NG = 3 - LG = 10 - ENDIF - H = SH - K = SK - HK = H*K - - IF ( ABS(R) < 0.925D0 ) THEN - IF (ABS(R) .GT. ZERO ) THEN - HS = ( H*H + K*K )*HALF - ASR = ASIN(R) - DO I = 1, LG - SN = SIN(ASR*(ONE + X(I,NG))*HALF) - VAL = VAL + W(I,NG)*EXP( ( SN*HK - HS )/( ONE - SN*SN ) ) - SN = SIN(ASR*(ONE - X(I,NG))*HALF) - VAL = VAL + W(I,NG)*EXP( ( SN*HK - HS )/( ONE - SN*SN ) ) - END DO - VAL = VAL*ASR*FOURPI1 - ENDIF - VAL = VAL + FI(-H)*FI(-K) - ELSE - IF ( R < ZERO ) THEN - K = -K - HK = -HK - ENDIF - IF ( ABS(R) < ONE ) THEN - AS = ( ONE - R )*( ONE + R ) - A = SQRT(AS) - B = ABS( H - K ) !**2 - BS = B * B - C = ( FOUR - HK ) * ONEEIGHT !/8D0 - D = ( TWELVE - HK ) * ONESIXTEEN !/16D0 - ASR = -(BS/AS + HK)*HALF - IF (ASR.GT.EXPMIN) THEN - VAL = A*EXP( ASR ) * - & ( ONE - C*(BS - AS)*(ONE - D*BS*0.2D0)*ONETHIRD + - & C*D*AS*AS*0.2D0 ) - ENDIF - IF ( HK .GT. EXPMIN ) THEN - VAL = VAL - EXP(-HK*HALF)*SQTWOPI*FI(-B/A)*B - + *( ONE - C*BS*( ONE - D*BS*0.2D0 )*ONETHIRD ) - ENDIF - A = A * HALF - DO I = 1, LG - XS = ( A * (ONE + X(I,NG)) ) !**2 - XS = XS * XS - RS = SQRT( ONE - XS ) - ASR = -(BS / XS + HK) * HALF - IF (ASR.GT.EXPMIN) THEN - VAL = VAL + A*W(I,NG)*EXP( ASR ) - & * ( EXP( - HALF*HK*( ONE - RS )/( ONE + RS ) )/RS - $ -( ONE + C*XS*( ONE + D*XS ) ) ) - ENDIF - XS = ( A * (ONE - X(I,NG)) ) !**2 - XS = XS * XS - RS = SQRT( ONE - XS ) - ASR = -(BS / XS + HK) * HALF - IF (ASR.GT.EXPMIN) THEN - VAL = VAL + A*W(I,NG)*EXP( ASR ) - & *( EXP( - HALF*HK*( ONE - RS )/( ONE + RS ) )/RS- - $ ( ONE + C*XS*( ONE + D*XS ) ) ) - ENDIF - END DO - VAL = -VAL*TWOPI1 - ENDIF - IF ( R .GT. ZERO ) THEN - VAL = VAL + FI( -MAX( H, K ) ) - ELSE - VAL = -VAL - IF ( H < K ) VAL = VAL + FI(K)-FI(H) - ENDIF - ENDIF - RETURN - END FUNCTION BVU - DOUBLE PRECISION FUNCTION STUDNT( NU, T ) - IMPLICIT NONE -! -! Student t Distribution Function -! -! T -! STUDNT = C I ( 1 + y*y/NU )**( -(NU+1)/2 ) dy -! NU -INF -! - INTEGER, INTENT(IN) :: NU - DOUBLE PRECISION, INTENT(IN) :: T -! Locals - INTEGER :: J - DOUBLE PRECISION :: ZRO, ONE - PARAMETER ( ZRO = 0.0D0, ONE = 1.0D0 ) - DOUBLE PRECISION, PARAMETER :: PI = 3.14159265358979D0 - DOUBLE PRECISION :: CSSTHE, SNTHE, POLYN, TT, TS, RN - - IF ( NU < 1 ) THEN - STUDNT = FI( T ) - ELSE IF ( NU .EQ. 1 ) THEN - STUDNT = ( ONE + 2.0D0*ATAN(T)/PI )*0.5D0 - ELSE IF ( NU .EQ. 2 ) THEN - STUDNT = ( ONE + T/SQRT( 2.0D0 + T*T ))*0.5D0 - ELSE - RN = NU ! convert to double - TT = T * T - CSSTHE = ONE/( ONE + TT/RN ) - POLYN = 1 - DO J = NU-2, 2, -2 - POLYN = ONE + ( J - 1 )*CSSTHE*POLYN/J - END DO - - IF ( MOD( NU, 2 ) .EQ. 1 ) THEN - TS = T/SQRT(RN) - STUDNT = ( ONE + 2.0D0*( ATAN(TS) + - & TS*CSSTHE*POLYN )/PI )*0.5D0 - ELSE - SNTHE = T/SQRT( RN + TT ) - STUDNT = ( ONE + SNTHE*POLYN )*0.5D0 - END IF - STUDNT = MAX( ZRO, MIN( STUDNT, ONE ) ) - ENDIF - END FUNCTION STUDNT - DOUBLE PRECISION FUNCTION BVTL( NU, DH, DK, R ) - IMPLICIT NONE -!* -!* A function for computing bivariate t probabilities. -!* -!* Alan Genz -!* Department of Mathematics -!* Washington State University -!* Pullman, WA 99164-3113 -!* Email : alangenz@wsu.edu -!* -!* This function is based on the method described by -!* Dunnett, C.W. and M. Sobel, (1954), -!* A bivariate generalization of Student's t-distribution -!* with tables for certain special cases, -!* Biometrika 41, pp. 153-169. -!* -!* BVTL - calculate the probability that X < DH and Y < DK. -!* -!* parameters -!* -!* NU number of degrees of freedom (NOTE: NU = 0 gives bivariate normal prb) -!* DH 1st lower integration limit -!* DK 2nd lower integration limit -!* R correlation coefficient -!* - INTEGER, INTENT(IN) ::NU - DOUBLE PRECISION, INTENT(IN) :: DH, DK, R -! Locals - INTEGER :: J, HS, KS - DOUBLE PRECISION :: ORS, HRK, KRH, BVT - DOUBLE PRECISION :: DH2, DK2, SNU ,DNU, DHDK -!, BVND, STUDNT - DOUBLE PRECISION :: GMPH, GMPK, XNKH, XNHK, QHRK, HKN, HPK, HKRN - DOUBLE PRECISION :: BTNCKH, BTNCHK, BTPDKH, BTPDHK - DOUBLE PRECISION :: ZERO, ONE, EPS, PI,TPI - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, EPS = 1.0D-15 ) - PARAMETER (PI = 3.14159265358979D0, TPI = 6.28318530717959D0) - IF ( NU < 1 ) THEN - BVTL = BVU( -DH, -DK, R ) - ELSE IF ( ONE - R .LE. EPS .OR. 1.0D+161' - -! The inverse cdf of 0 is -inf, and the inverse cdf of 1 is inf. - if (P.LE.EPSL.OR.P+EPSL.GE.1.D0) THEN - VAL = SIGN(xmax,P-0.5D0) - return - endif - Ak = ABS(A) - if (EPSL < Ak .AND. Ak < amax) THEN - IF (ABS(p-Pa).LE.EPSL) THEN - VAL = SIGN(MIN(Ak,xmax),-A) - RETURN - ENDIF - IF (Ak < 1D-2) THEN ! starting guess always less than 0.2 from the true value - IF (P.GE.0.5D0) THEN - xk = SQRT(-2D0*log(2D0*(1D0-P))) - ELSE - xk = -SQRT(-2D0*log(2D0*P)) - ENDIF - ELSE - xk = FIINV(P) ! starting guess always less than 0.8 from the true value - ! Modify starting guess if possible in order to speed up Newtons method - IF (1D-3.LE.P.AND. P.LE.0.99D0.AND. - & 3.5.LE.Ak.AND.Ak.LE.1D3 ) THEN - SGN = SIGN(1.d0,-A) - Zk = xk*SGN - xk = SGN*(Zk+((1D0/(64.9495D0*Ak-178.3191D0)-0.02D0/Ak)* - & Zk+1D0/(-0.99679234298211D0*Ak-0.07195350071872D0))/ - & (Zk/(-1.48430620263825D0*Ak-0.33340759016175D0)+1D0)) - ELSEIF ((P < 1D-3.AND.A.LE.-3.5D0).OR. - & (3.5D0.LE.A.AND.P.GT.0.99D0)) THEN - SGN = SIGN(1.d0,-A) - Zk = xk*SGN - P1 = -2.00126182192701D0*Ak-2.57306603933111D0 - xk = SGN*Zk*(1D0+ - & P1/((-0.99179258785909D0*Ak-0.21359746002397D0)* - & (Zk+P1))) - ENDIF - ENDIF - ! Check if the starting guess is on the correct side of the inflection point - IF (xk.LE.-A .AND. P.GT.Pa) xk = 1.D-2-A - IF (xk.GE.-A .AND. P < Pa) xk = -1.D-2-A - - - IF (P < Pa) THEN - VAL = funca(xk,A,P*Ca) - ELSE ! exploit the symmetry of the CDF - VAL = -funca(-xk,-A,(1.D0-P)*Ca) - ENDIF - - ELSEIF (ABS(A).LE.EPSL) THEN - IF (P>=0.5D0) THEN - VAL = SQRT(-2D0*log(2D0*(1.D0-P))) - ELSE - VAL = -SQRT(-2D0*log(2D0*P)) - ENDIF - ELSE ! ABS(A) > AMAX - VAL = FIINV(P) - ENDIF - !CALL EXLMS(A,0.d0,VAL,0,ak,P1,zk,sgn) - !If (ABS(p-P1).GT.0.0001) PRINT *,'excdf(x,a)-p',p-P1 - RETURN - - CONTAINS - - function funca(xk0,ak,CaP) RESULT (xk) - double precision, intent(in) :: xk0,ak,CaP ! =Ca*P - DOUBLE PRECISION :: xk -!Local variables - INTEGER, PARAMETER :: ixmax = 25 - double precision, parameter :: crit = 7.1D-08 ! = sqrt(1e-15) - double precision, parameter :: SQTWOPI1 = 0.39894228040143D0 !=1/SQRT(2*pi) - double precision, parameter :: SQTWOPI = 2.50662827463100D0 !=SQRT(2*pi) - INTEGER :: IX - DOUBLE PRECISION :: H,H1,tmp0,tmp1,XNEW - ! Newton's Method or Fixed point iteration to find the inverse of the EXCDF. - ! Assumption: xk0 < -ak and xk < -ak - ! Permit no more than IXMAX iterations. - IX = 0 - H = 1.D0 - xk = xk0 ! starting guess for the iteration - - -! Break out of the iteration loop for the following: -! 1) The last update is very small (compared to x). -! 2) The last update is very small (compared to sqrt(eps)=crit). -! 3) There are more than 15 iterations. This should NEVER happen. - IF (.TRUE..OR.ABS(ak) < 1.D-2) THEN - ! Newton's method - !~~~~~~~~~~~~~~~~~ - DO WHILE( ABS(H).GT.MIN(crit*ABS(xk),crit).AND.IX < IXMAX) - - IX = IX+1 - !print *,'Iteration ',IX - - tmp0 = FI(xk) - tmp1 = EXP(-xk*xk*0.5D0)*SQTWOPI1 ! =normpdf(x) - H1 = (tmp1-ak*tmp0-CaP)/(ABS(xk+ak)*tmp1) - H = DSIGN(MIN(ABS(H1),0.7D0/DBLE(IX)),H1) ! Only allow smaller and smaller steps - - xnew = xk - H - ! Make sure that the current guess is less than -a. - ! When Newton's Method suggests steps that lead to -a guesses - ! take a step 9/10ths of the way to -a: - IF (xnew.GT.-ak-crit) THEN - xnew = (xk - 9.D0*ak)*1D-1 - H = xnew - xk - ENDIF - xk = xnew - END DO - ELSE ! FIXED POINT iteration - !~~~~~~~~~~~~~~~~~~~~~~~ - DO WHILE (ABS(H).GT.MIN(crit*ABS(xk),crit).AND.IX < IXMAX) - IX = IX+1 - tmp0 = SQTWOPI1*EXP(-xk*xk*0.5D0)/FI(xk) - tmp1 = -2.D0*LOG(SQTWOPI*CaP*tmp0/(tmp0-ak)) - SGN = sign(1.D0,tmp1) - xnew = -SQRT(SGN*tmp1)*SGN - ! Make sure that the current guess is less than -a. - ! When this method suggests steps that lead to -a guesses - ! take a step 9/10ths of the way to -a: - IF (xnew.GT.-ak-crit) xnew = (xk - 9.D0*ak)*1.D-1 - - H = xnew - xk - xk = xnew - END DO - ENDIF - - !print *,'EXINV total number of iterations ',IX - if (IX.GE.IXMAX) THEN -! print *, 'Warning: EXINV did not converge. Cap=',Cap -! print *, 'The last step was: ', h, ' value=,',xk,' ak=',ak - endif - return - END FUNCTION FUNCA - END FUNCTION EXINV - END MODULE FIMOD diff --git a/wafo/source/rind2007/intmodule.f b/wafo/source/rind2007/intmodule.f deleted file mode 100644 index b7e9e95..0000000 --- a/wafo/source/rind2007/intmodule.f +++ /dev/null @@ -1,3856 +0,0 @@ -! INTMODULE contains the modules: -! - ADAPTMOD -! - RCRUDEMOD -! - KROBOVMOD -! - KRBVRCMOD -! - DKBVRCMOD -! -! which contains several different Multidimensional Integration Subroutines -! -! See descriptions below -! -* ADAPTMOD is a module containing a: -* -* Adaptive Multidimensional Integration Subroutine -* -* Author: Alan Genz -* Department of Mathematics -* Washington State University -* Pullman, WA 99164-3113 USA -* -* Revised pab 21.11.2000 -* A bug found by Igor in dksmrc: VK was not correctly randomized -* is now fixed -* Revised pab 07.10.2000, -* 1) Removed LENWRK and WORK from input in ADAPT. -* 2) Defined LENWRK internally and Put a save statement before WORK instead -* 3) Bug fix in ADBASE: DIVAXN was undetermined when MINCLS<0. Solution: -* put a save statement on DIVAXN in order to save/keep its last value. -* 4) MAXDIM is now a global variable defining the maximum number of dimensions -* it is possible to integrate. -* -* revised pab 07.09.2000 -* - solaris compiler complained on the DATA statements -* for the P and C matrices in the krbvrc and krobov routine -* => made separate DATA statements for P and C and moved them -* to right after the variable definitions. -* revised pab 10.03.2000 -* - updated to f90 (i.e. changed to assumed shape arrays + changing integers to DBLE) -* - put it into a module -* -* This subroutine computes an approximation to the integral -* -* 1 1 1 -* I I ... I FUNCTN(NDIM,X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -*************** Parameters for SADAPT ******************************** -* -********Input Parameters -* -* N INTEGER, the number of variables. -* MAXPTS INTEGER, maximum number of function values allowed. This -* parameter can be used to limit the time taken. A -* sensible strategy is to start with MAXPTS = 1000*N, and then -* increase MAXPTS if ERROR is too large. -* FUNCTN Externally declared real user defined integrand. Its -* parameters must be (N, Z), where Z is a real array of -* length N. -* ABSEPS REAL absolute error tolerance. -* RELEPS REAL relative error tolerance. -* -*******Output Parameters -* -* ERROR REAL estimated absolute error, with 99% confidence level. -* VALUE REAL estimated value for the integral -* INFORM INTEGER, termination status parameter: -* if INFORM = 0, normal completion with ERROR < EPS; -* if INFORM = 1, completion with ERROR > EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* if INFORM = 2, N > 20 or N < 1. -* -*************** Parameters for ADAPT ******************************** -* -****** Input Parameters -* -* NDIM Integer number of integration variables. -* MINCLS Integer minimum number of FUNCTN calls to be allowed; MINCLS -* must not exceed MAXCLS. If MINCLS < 0, then ADAPT assumes -* that a previous call of ADAPT has been made with the same -* integrand and continues that calculation. -* MAXCLS Integer maximum number of FUNCTN calls to be used; MAXCLS -* must be >= RULCLS, the number of function calls required for -* one application of the basic integration rule. -* IF ( NDIM .EQ. 1 ) THEN -* RULCLS = 11 -* ELSE IF ( NDIM .LT. 15 ) THEN -* RULCLS = 2**NDIM + 2*NDIM*(NDIM+3) + 1 -* ELSE -* RULCLS = 1 + NDIM*(24-NDIM*(6-NDIM*4))/3 -* ENDIF -* FUNCTN Externally declared real user defined integrand. Its -* parameters must be (NDIM, Z), where Z is a real array of -* length NDIM. -* ABSREQ Real required absolute accuracy. -* RELREQ Real required relative accuracy. -* -****** Output Parameters -* -* MINCLS Actual number of FUNCTN calls used by ADAPT. -* ABSEST Real estimated absolute accuracy. -* FINEST Real estimated value of integral. -* INFORM INFORM = 0 for normal exit, when ABSEST <= ABSREQ or -* ABSEST <= |FINEST|*RELREQ with MINCLS <= MAXCLS. -* INFORM = 1 if MAXCLS was too small for ADAPT to obtain the -* result FINEST to within the requested accuracy. -* INFORM = 2 if MINCLS > MAXCLS, LENWRK < 16*NDIM + 27 or -* RULCLS > MAXCLS. -* -* -* -* ADAPT revised by pab 07.10.2000, -* 1) Removed LENWRK and WORK from input. -* 2) Defined LENWRK internally and Put a save statement before WORK instead -* -* WORK Real array (length LENWRK) of working storage. This contains -* information that is needed for additional calls of ADAPT -* using the same integrand (input MINCLS < 0). -* LENWRK Integer length of real array WORK (working storage); ADAPT -* needs LENWRK >= 16*NDIM + 27. For maximum efficiency LENWRK -* should be about 2*NDIM*MAXCLS/RULCLS if MAXCLS FUNCTN -* calls are needed. If LENWRK is significantly less than this, -* ADAPT may be less efficient. - MODULE ADAPTMOD - IMPLICIT NONE - INTEGER,PRIVATE, PARAMETER :: MAXDIM=20 - PRIVATE - PUBLIC :: ADAPT, SADAPT - - INTERFACE SADAPT - MODULE PROCEDURE SADAPT - END INTERFACE - - INTERFACE ADAPT - MODULE PROCEDURE ADAPT - END INTERFACE - - INTERFACE ADBASE - MODULE PROCEDURE ADBASE - END INTERFACE - - INTERFACE BSINIT - MODULE PROCEDURE BSINIT - END INTERFACE - - INTERFACE RULNRM - MODULE PROCEDURE RULNRM - END INTERFACE - - INTERFACE DIFFER - MODULE PROCEDURE DIFFER - END INTERFACE - - INTERFACE BASRUL - MODULE PROCEDURE BASRUL - END INTERFACE - - INTERFACE FULSUM - MODULE PROCEDURE FULSUM - END INTERFACE - - INTERFACE TRESTR - MODULE PROCEDURE TRESTR - END INTERFACE - !-------------------------------- - CONTAINS - -!*********************************************************** -! MAIN INTEGRATION ROUTINE SADAPT -!*********************************************************** - - SUBROUTINE SADAPT(N,MAXPTS,FUNCTN,ABSEPS, - & RELEPS,ERROR,VALUE,INFORM) - IMPLICIT NONE -* -* A subroutine for computing multivariate integrals -* This subroutine uses an algorithm given in the paper -* "Numerical Computation of Multivariate Normal Probabilities", in -* J. of Computational and Graphical Stat., 1(1992), pp. 141-149, by -* Alan Genz -* Department of Mathematics -* Washington State University -* Pullman, WA 99164-3113 -* Email : alangenz@wsu.edu -* -* revised pab 15.03.2000 -* - changed name from SADMVN to SADAPT -* - Made it general for any integral not just the multivariate normal integral -* -********Input Parameters -* -* N INTEGER, the number of variables. -* MAXPTS INTEGER, maximum number of function values allowed. This -* parameter can be used to limit the time taken. A -* sensible strategy is to start with MAXPTS = 1000*N, and then -* increase MAXPTS if ERROR is too large. -* FUNCTN Externally declared real user defined integrand. Its -* parameters must be (N, Z), where Z is a real array of -* length N. -* ABSEPS REAL absolute error tolerance. -* RELEPS REAL relative error tolerance. -* -*******Output Parameters -* -* ERROR REAL estimated absolute error, with 99% confidence level. -* VALUE REAL estimated value for the integral -* INFORM INTEGER, termination status parameter: -* if INFORM = 0, normal completion with ERROR < EPS; -* if INFORM = 1, completion with ERROR > EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* if INFORM = 2, N > 20 or N < 1. -* - INTEGER, INTENT(IN) :: N, MAXPTS - INTEGER, INTENT(OUT) :: INFORM - !INTEGER :: NL, LENWRK, - INTEGER :: RULCLS, TOTCLS, NEWCLS, MAXCLS - DOUBLE PRECISION, INTENT(IN) :: ABSEPS, RELEPS - DOUBLE PRECISION, INTENT(OUT) :: ERROR, VALUE - DOUBLE PRECISION :: OLDVAL - !PARAMETER ( NL = 20 ) - !PARAMETER ( LENWRK = 20*NL**2 ) - !DOUBLE PRECISION, DIMENSION(LENWRK) :: WORK - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - IF ( N .GT. MAXDIM .OR. N .LT. 1 ) THEN - INFORM = 2 - VALUE = 0.d0 - ERROR = 1.d0 - RETURN - ENDIF - INFORM = 1 -* -* Call the subregion adaptive integration subroutine -* - RULCLS = 1 - CALL ADAPT( N, RULCLS, 0, FUNCTN, ABSEPS, RELEPS, - & ERROR, VALUE, INFORM ) - MAXCLS = MIN( 10*RULCLS, MAXPTS ) - TOTCLS = 0 - CALL ADAPT(N, TOTCLS, MAXCLS, FUNCTN, ABSEPS, RELEPS, - & ERROR, VALUE, INFORM) - IF ( ERROR .GT. MAX( ABSEPS, RELEPS*ABS(VALUE) ) ) THEN - 10 OLDVAL = VALUE - MAXCLS = MAX( 2*RULCLS,MIN(INT(3*MAXCLS/2),MAXPTS-TOTCLS)) - NEWCLS = -1 - CALL ADAPT(N, NEWCLS, MAXCLS, FUNCTN, ABSEPS, RELEPS, - & ERROR, VALUE, INFORM) - TOTCLS = TOTCLS + NEWCLS - ERROR = ABS(VALUE-OLDVAL) + - & SQRT(DBLE(RULCLS)*ERROR**2/DBLE(TOTCLS)) - IF ( ERROR .GT. MAX( ABSEPS, RELEPS*ABS(VALUE) ) ) THEN - IF ( MAXPTS - TOTCLS .GT. 2*RULCLS ) GO TO 10 - ELSE - INFORM = 0 - END IF - ENDIF - - END SUBROUTINE SADAPT - - - -!*********************************************************** -! MAIN INTEGRATION ROUTINE ADAPT -!*********************************************************** - - - SUBROUTINE ADAPT(NDIM, MINCLS, MAXCLS, FUNCTN, - & ABSREQ, RELREQ, ABSEST, FINEST, INFORM) - IMPLICIT NONE -* -* Adaptive Multidimensional Integration Subroutine -* -* Author: Alan Genz -* Department of Mathematics -* Washington State University -* Pullman, WA 99164-3113 USA -* -* This subroutine computes an approximation to the integral -* -* 1 1 1 -* I I ... I FUNCTN(NDIM,X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -*************** Parameters for ADAPT ******************************** -* -****** Input Parameters -* -* NDIM Integer number of integration variables. -* MINCLS Integer minimum number of FUNCTN calls to be allowed; MINCLS -* must not exceed MAXCLS. If MINCLS < 0, then ADAPT assumes -* that a previous call of ADAPT has been made with the same -* integrand and continues that calculation. -* MAXCLS Integer maximum number of FUNCTN calls to be used; MAXCLS -* must be >= RULCLS, the number of function calls required for -* one application of the basic integration rule. -* IF ( NDIM .EQ. 1 ) THEN -* RULCLS = 11 -* ELSE IF ( NDIM .LT. 15 ) THEN -* RULCLS = 2**NDIM + 2*NDIM*(NDIM+3) + 1 -* ELSE -* RULCLS = 1 + NDIM*(24-NDIM*(6-NDIM*4))/3 -* ENDIF -* FUNCTN Externally declared real user defined integrand. Its -* parameters must be (NDIM, Z), where Z is a real array of -* length NDIM. -* ABSREQ Real required absolute accuracy. -* RELREQ Real required relative accuracy. -* -****** Output Parameters -* -* MINCLS Actual number of FUNCTN calls used by ADAPT. -* ABSEST Real estimated absolute accuracy. -* FINEST Real estimated value of integral. -* INFORM INFORM = 0 for normal exit, when ABSEST <= ABSREQ or -* ABSEST <= |FINEST|*RELREQ with MINCLS <= MAXCLS. -* INFORM = 1 if MAXCLS was too small for ADAPT to obtain the -* result FINEST to within the requested accuracy. -* INFORM = 2 if MINCLS > MAXCLS, LENWRK < 16*NDIM + 27 or -* RULCLS > MAXCLS. -* -************************************************************************ -* -* Begin driver routine. This routine partitions the working storage -* array and then calls the main subroutine ADBASE. -* -* Revised pab 07.10.2000, -* 1) Removed LENWRK and WORK from input. -* 2) Defined LENWRK internally and Put a save statement before WORK instead -* -* LENWRK Integer length of real array WORK (working storage); ADAPT -* needs LENWRK >= 16*NDIM + 27. For maximum efficiency LENWRK -* should be about 2*NDIM*MAXCLS/RULCLS if MAXCLS FUNCTN -* calls are needed. If LENWRK is significantly less than this, -* ADAPT may be less efficient. -* -* WORK Real array (length LENWRK) of working storage. This contains -* information that is needed for additional calls of ADAPT -* using the same integrand (input MINCLS < 0). -* - INTEGER, INTENT(IN) :: NDIM, MAXCLS - INTEGER, INTENT(INOUT) :: MINCLS - INTEGER, INTENT(OUT) :: INFORM - DOUBLE PRECISION, INTENT(IN) :: ABSREQ, RELREQ - DOUBLE PRECISION, INTENT(OUT) :: ABSEST, FINEST -* Local variables - INTEGER, PARAMETER :: LENWRK=20*MAXDIM*MAXDIM - DOUBLE PRECISION, DIMENSION(LENWRK) :: WORK ! length lenwrk - DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: POINTS,WEGHTS,LUM - INTEGER :: SBRGNS, MXRGNS, RULCLS, LENRUL, - & INERRS, INVALS, INPTRS, INLWRS, INUPRS, INMSHS, INPNTS, INWGTS, - & INLOWR, INUPPR, INWDTH, INMESH, INWORK - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - SAVE WORK -! print *,'adapt, ndim', ndim - IF ( NDIM .EQ. 1 ) THEN - LENRUL = 5 - RULCLS = 9 - ELSE IF ( NDIM .LT. 12 ) THEN - LENRUL = 6 - RULCLS = 2**NDIM + 2*NDIM*(NDIM+2) + 1 - ELSE - LENRUL = 6 -! RULCLS = 1 + 2*NDIM*(1+2*NDIM) ! old call pab 15.03.2003 - RULCLS = 1851 + 2*NDIM*(1+2*NDIM) - ENDIF - IF ( LENWRK .GE. LENRUL*(NDIM+4) + 10*NDIM + 3 .AND. - & RULCLS. LE. MAXCLS .AND. MINCLS .LE. MAXCLS ) THEN - MXRGNS = ( LENWRK - LENRUL*(NDIM+4) - 7*NDIM )/( 3*NDIM + 3 ) - INERRS = 1 - INVALS = INERRS + MXRGNS - INPTRS = INVALS + MXRGNS - INLWRS = INPTRS + MXRGNS - INUPRS = INLWRS + MXRGNS*NDIM - INMSHS = INUPRS + MXRGNS*NDIM - INWGTS = INMSHS + MXRGNS*NDIM - INPNTS = INWGTS + LENRUL*4 - INLOWR = INPNTS + LENRUL*NDIM - INUPPR = INLOWR + NDIM - INWDTH = INUPPR + NDIM - INMESH = INWDTH + NDIM - INWORK = INMESH + NDIM - - ALLOCATE(POINTS(NDIM,LENRUL)) - ALLOCATE(WEGHTS(LENRUL,4)) - ALLOCATE(LUM(NDIM,MXRGNS*3)) - - IF (MINCLS .LT. 0 ) THEN - SBRGNS = WORK(LENWRK) - LUM = reshape(WORK(INLWRS:INWGTS-1),(/ NDIM,MXRGNS*3/)) - WEGHTS = reshape(WORK(INWGTS:INPNTS-1),(/ LENRUL , 4 /)) - POINTS = reshape(WORK(INPNTS:INLOWR-1),(/ NDIM, LENRUL/)) - !ELSE - ! WORK=0.D0;LUM=0.D0;WEGHTS=0.D0;POINTS=0.D0 - ENDIF - CALL ADBASE(NDIM, MINCLS, MAXCLS, FUNCTN, ABSREQ, RELREQ, - & ABSEST, FINEST, SBRGNS, MXRGNS, RULCLS, LENRUL, - & WORK(INERRS:INVALS-1), WORK(INVALS:INPTRS-1), - & WORK(INPTRS:INLWRS-1), LUM(:,1:MXRGNS), - & LUM(:,MXRGNS+1:2*MXRGNS),LUM(:,2*MXRGNS+1:3*MXRGNS), - & WEGHTS,POINTS,WORK(INLOWR:INUPPR-1),WORK(INUPPR:INWDTH-1), - & WORK(INWDTH:INMESH-1), WORK(INMESH:INWORK-1), - & WORK(INWORK:INWORK+2*NDIM-1), INFORM) - WORK(LENWRK) = SBRGNS -! LUM = LOWERS UPPERS MESHES - WORK(INLWRS:INWGTS-1) = reshape(LUM ,(/ NDIM*MXRGNS*3/)) - WORK(INWGTS:INPNTS-1) = reshape(WEGHTS,(/ LENRUL*4 /)) - WORK(INPNTS:INLOWR-1) = reshape(POINTS,(/ NDIM*LENRUL/)) - DEALLOCATE(POINTS) - DEALLOCATE(WEGHTS) - DEALLOCATE(LUM) - ELSE - INFORM = 2 - MINCLS = RULCLS - ENDIF - RETURN - END SUBROUTINE ADAPT - SUBROUTINE BSINIT(NDIM, W, LENRUL, G) - IMPLICIT NONE -* -* For initializing basic rule weights and symmetric sum parameters. -* - INTEGER, INTENT(IN) :: NDIM, LENRUL - DOUBLE PRECISION , DIMENSION(:,:), INTENT(OUT) :: W, G -* DOUBLE PRECISION W(LENRUL,4), G(NDIM,LENRUL) -* Local variables - INTEGER :: I, J - INTEGER, PARAMETER :: NUMNUL=4, SDIM=12 - INTEGER, DIMENSION(6) :: RULPTS - DOUBLE PRECISION LAM1, LAM2, LAM3, LAM4, LAMP, RULCON -* -* The following code determines rule parameters and weights for a -* degree 7 rule (W(1,1),...,W(5,1)), two degree 5 comparison rules -* (W(1,2),...,W(5,2) and W(1,3),...,W(5,3)) and a degree 3 -* comparison rule (W(1,4),...W(5,4)). -* -* If NDIM = 1, then LENRUL = 5 and total points = 9. -* If NDIM < SDIM, then LENRUL = 6 and -* total points = 1+2*NDIM*(NDIM+2)+2**NDIM. -* If NDIM > = SDIM, then LENRUL = 6 and -* total points = 1+2*NDIM*(1+2*NDIM). -* -! print *,'BSINIT, ndim', ndim -! DO I = 1,LENRUL -! DO J = 1,NDIM -! G(J,I) = 0.d0 -! END DO -! DO J = 1,NUMNUL -! W(I,J) = 0.d0 -! END DO -! END DO - G = 0.D0 - W = 0.D0 - I = 2*NDIM - RULPTS(5) = I*(NDIM-1) - RULPTS(4) = I - RULPTS(3) = I - RULPTS(2) = I - RULPTS(1) = 1 - LAMP = 0.85d0 - LAM3 = 0.4707d0 - LAM2 = 4d0/(15.d0 - 5.d0/LAM3) - LAM4 = 1.D0/(27.D0*LAM3*LAM3*LAM3) - W(5,1) = ( 3.d0 - 5.d0*LAM3 )/( 180.d0*(LAM2-LAM3)*LAM2*LAM2) - IF ( NDIM .LT. SDIM ) THEN - RULPTS(LENRUL) = 2**NDIM - LAM1 = 8.d0*LAM3*(31.d0*LAM3-15.d0)/ - & ( (3.d0*LAM3-1.d0)*(5.d0*LAM3-3.d0)*35.d0 ) - W(LENRUL,1) = LAM4/DBLE(RULPTS(LENRUL)) - ELSE - LAM1 = ( LAM3*(15.d0 - 21.d0*LAM2) + - & 35.d0*DBLE(NDIM-1)*(LAM2-LAM3)/9.d0 ) - & / ( LAM3*(21.d0 - 35.d0*LAM2) + - & 35.d0*DBLE(NDIM-1)*(LAM2/LAM3-1.d0)/9.d0 ) - W(6,1) = LAM4*0.25D0 - RULPTS(6) = 2*NDIM*(NDIM-1) - ENDIF - W(3,1) = ( 15.d0 - 21.d0*(LAM3+LAM1) + 35.d0*LAM3*LAM1 ) - & /(210.d0*LAM2*(LAM2-LAM3)*(LAM2-LAM1))-DBLE(2*(NDIM-1))*W(5,1) - W(2,1) = ( 15.d0 - 21.d0*(LAM3+LAM2) + 35.d0*LAM3*LAM2 ) - & /( 210.d0*LAM1*(LAM1-LAM3)*(LAM1-LAM2) ) - LAM3 = SQRT(LAM3) - IF ( NDIM .LT. SDIM ) THEN - G(1:NDIM,LENRUL) = LAM3 - ELSE - G(1,6) = LAM3 - G(2,6) = LAM3 - ENDIF - IF ( NDIM .GT. 1 ) THEN - W(5,2) = 1.d0/(6.d0*LAM2)**2 - W(5,3) = W(5,2) - ENDIF - W(3,2) = ( 3.d0 - 5.d0*LAM1 )/( 30.d0*LAM2*(LAM2-LAM1) ) - & - DBLE(2*(NDIM-1))*W(5,2) - W(2,2) = ( 3.d0 - 5.d0*LAM2 )/( 30.d0*LAM1*(LAM1-LAM2) ) - W(4,3) = ( 3.d0 - 5.d0*LAM2 )/( 30.d0*LAMP*(LAMP-LAM2) ) - W(3,3) = ( 3.d0 - 5.d0*LAMP )/( 30.d0*LAM2*(LAM2-LAMP) ) - & - DBLE(2*(NDIM-1))*W(5,3) - W(2,4) = 1.d0/(6.d0*LAM1) - LAMP = SQRT(LAMP) - LAM2 = SQRT(LAM2) - LAM1 = SQRT(LAM1) - G(1,2) = LAM1 - G(1,3) = LAM2 - G(1,4) = LAMP - IF ( NDIM .GT. 1 ) THEN - G(1,5) = LAM2 - G(2,5) = LAM2 - ENDIF - DO J = 1, NUMNUL - W(1,J) = 1.d0 - DO I = 2,LENRUL - W(1,J) = W(1,J) - DBLE(RULPTS(I))*W(I,J) - END DO - END DO - RULCON = 0.5d0 - CALL RULNRM( LENRUL, NUMNUL, RULPTS, W, RULCON ) - END SUBROUTINE BSINIT -! -! - SUBROUTINE RULNRM( LENRUL, NUMNUL, RULPTS, W, RULCON ) - IMPLICIT NONE - INTEGER, INTENT(IN) :: LENRUL, NUMNUL - INTEGER, DIMENSION(:), INTENT(IN) :: RULPTS - DOUBLE PRECISION, DIMENSION(:,:), INTENT(INOUT) :: W !(LENRUL, *), - DOUBLE PRECISION, INTENT(IN) :: RULCON -* Local variables - INTEGER :: I, J, K - DOUBLE PRECISION :: ALPHA, NORMCF, NORMNL - -* -* Compute orthonormalized null rules. -* -! print *,'RULNRM, lenrul, numnul', lenrul,NUMNUL - NORMCF = 0.d0 - DO I = 1,LENRUL - NORMCF = NORMCF + DBLE(RULPTS(I))*W(I,1)*W(I,1) - END DO - DO K = 2,NUMNUL - DO I = 1,LENRUL - W(I,K) = W(I,K) - W(I,1) - END DO - DO J = 2,K-1 - ALPHA = 0.d0 - DO I = 1,LENRUL - ALPHA = ALPHA + DBLE(RULPTS(I))*W(I,J)*W(I,K) - END DO - ALPHA = -ALPHA/NORMCF - DO I = 1,LENRUL - W(I,K) = W(I,K) + ALPHA*W(I,J) - END DO - END DO - NORMNL = 0.d0 - DO I = 1,LENRUL - NORMNL = NORMNL + DBLE(RULPTS(I))*W(I,K)*W(I,K) - END DO - ALPHA = SQRT(NORMCF/NORMNL) - DO I = 1,LENRUL - W(I,K) = ALPHA*W(I,K) - END DO - END DO - DO J = 2, NUMNUL - DO I = 1,LENRUL - W(I,J) = W(I,J)*RULCON - END DO - END DO - RETURN - END SUBROUTINE RULNRM -! -! - SUBROUTINE ADBASE(NDIM, MINCLS, MAXCLS, FUNCTN, ABSREQ, RELREQ, - & ABSEST, FINEST, SBRGNS, MXRGNS, RULCLS, LENRUL, - & ERRORS, VALUES, PONTRS, LOWERS, - & UPPERS, MESHES, WEGHTS, POINTS, - & LOWER, UPPER, WIDTH, MESH, WORK, INFORM) - IMPLICIT NONE -* -* Main adaptive integration subroutine -* - INTEGER,INTENT(IN) :: NDIM, MAXCLS, MXRGNS,LENRUL, RULCLS - INTEGER, INTENT(INOUT) :: MINCLS, SBRGNS - INTEGER, INTENT(OUT) :: INFORM - DOUBLE PRECISION, INTENT(IN) :: ABSREQ, RELREQ - DOUBLE PRECISION, INTENT(OUT) :: ABSEST, FINEST - DOUBLE PRECISION, DIMENSION(:), INTENT(INOUT) :: ERRORS, VALUES, - & PONTRS, LOWER, UPPER, WIDTH, MESH, WORK - DOUBLE PRECISION, DIMENSION(:,:), INTENT(INOUT) :: WEGHTS, POINTS - ! shape (LENRUL,4) and (NDIM,LENRUL) - DOUBLE PRECISION, DIMENSION(:,:), INTENT(INOUT) :: LOWERS, UPPERS, - & MESHES !SHAPE (NDIM,MXRGNS), - INTEGER :: I, J,NWRGNS, DIVAXN, TOP, RGNCLS, FUNCLS, DIFCLS - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE -* -* Initialization of subroutine -* -! print *,'ADBASE, ndim', ndim, shape(POINTS) - SAVE DIVAXN ! added pab 07.11.2000 (divaxn may have negative values otherwise) - INFORM = 2 - FUNCLS = 0 - CALL BSINIT(NDIM, WEGHTS, LENRUL, POINTS) - IF ( MINCLS .GE. 0) THEN -* -* When MINCLS >= 0 determine initial subdivision of the -* integration region and apply basic rule to each subregion. -* - SBRGNS = 0 - DO I = 1,NDIM - LOWER(I) = 0.d0 - MESH(I) = 1.d0 - WIDTH(I) = 1.d0/(2.d0*MESH(I)) - UPPER(I) = 1.d0 - END DO - DIVAXN = 0 - RGNCLS = RULCLS - NWRGNS = 1 - 10 CONTINUE - !IF (abs(DIVAXN).GT.NDIM) PRINT *,'adbase DIVAXN1',DIVAXN - CALL DIFFER(NDIM, LOWER, UPPER, WIDTH, WORK(1:NDIM), - & WORK(NDIM+1:2*NDIM), FUNCTN, DIVAXN, DIFCLS) - FUNCLS = FUNCLS + DIFCLS - IF (DBLE(RGNCLS)*(MESH(DIVAXN)+1.d0)/MESH(DIVAXN) - & .LE. DBLE(MINCLS-FUNCLS) ) THEN - RGNCLS = NINT(DBLE(RGNCLS)*(MESH(DIVAXN)+1.d0)/MESH(DIVAXN)) - NWRGNS = NINT(DBLE(NWRGNS)*(MESH(DIVAXN)+1.d0)/MESH(DIVAXN)) - MESH(DIVAXN) = MESH(DIVAXN) + 1.d0 - WIDTH(DIVAXN) = 1.d0/( 2.d0*MESH(DIVAXN) ) - GO TO 10 - ENDIF - IF ( NWRGNS .LE. MXRGNS ) THEN - DO I = 1,NDIM - UPPER(I) = LOWER(I) + 2.d0*WIDTH(I) - MESH(I) = 1.d0 - END DO - ENDIF -* -* Apply basic rule to subregions and store results in heap. -* - 20 SBRGNS = SBRGNS + 1 - CALL BASRUL(NDIM, LOWER, UPPER, WIDTH, FUNCTN, - & WEGHTS, LENRUL, POINTS, WORK(1:NDIM), WORK(NDIM+1:2*NDIM), - & ERRORS(SBRGNS),VALUES(SBRGNS)) - CALL TRESTR(SBRGNS, SBRGNS, PONTRS, ERRORS) - DO I = 1,NDIM - LOWERS(I,SBRGNS) = LOWER(I) - UPPERS(I,SBRGNS) = UPPER(I) - MESHES(I,SBRGNS) = MESH(I) - END DO - DO I = 1,NDIM - LOWER(I) = UPPER(I) - UPPER(I) = LOWER(I) + 2.d0*WIDTH(I) - IF (LOWER(I)+WIDTH(I) .LT. 1.D0) GO TO 20 - LOWER(I) = 0.d0 - UPPER(I) = LOWER(I) + 2.d0*WIDTH(I) - END DO - FUNCLS = FUNCLS + SBRGNS*RULCLS - ENDIF -* -* Check for termination -* - 30 FINEST = 0.d0 - ABSEST = 0.d0 - DO I = 1, SBRGNS - FINEST = FINEST + VALUES(I) - ABSEST = ABSEST + ERRORS(I) - END DO - IF ( ABSEST .GT. MAX( ABSREQ, RELREQ*ABS(FINEST) ) - & .OR. FUNCLS .LT. MINCLS ) THEN -* -* Prepare to apply basic rule in (parts of) subregion with -* largest error. -* - TOP = PONTRS(1) - RGNCLS = RULCLS - DO I = 1,NDIM - LOWER(I) = LOWERS(I,TOP) - UPPER(I) = UPPERS(I,TOP) - MESH(I) = MESHES(I,TOP) - WIDTH(I) = (UPPER(I)-LOWER(I))/(2.D0*MESH(I)) - RGNCLS = NINT(DBLE(RGNCLS)*MESH(I)) - END DO - !IF (abs(DIVAXN).GT.NDIM) PRINT *,'adbase DIVAXN2',DIVAXN - CALL DIFFER(NDIM, LOWER, UPPER, WIDTH, WORK(1:NDIM), - & WORK(NDIM+1:2*NDIM), FUNCTN, DIVAXN, DIFCLS) - FUNCLS = FUNCLS + DIFCLS - RGNCLS = NINT(DBLE(RGNCLS)*(MESH(DIVAXN)+1.D0))/MESH(DIVAXN) - IF ( FUNCLS + RGNCLS .LE. MAXCLS ) THEN - IF ( SBRGNS + 1 .LE. MXRGNS ) THEN -* -* Prepare to subdivide into two pieces. -* - NWRGNS = 1 - WIDTH(DIVAXN) = 0.5d0*WIDTH(DIVAXN) - ELSE - NWRGNS = 0 - WIDTH(DIVAXN) = WIDTH(DIVAXN) - & *MESH(DIVAXN)/( MESH(DIVAXN) + 1.d0 ) - MESHES(DIVAXN,TOP) = MESH(DIVAXN) + 1.d0 - ENDIF - IF ( NWRGNS .GT. 0 ) THEN -* -* Only allow local subdivision when space is available. -* - DO J = SBRGNS+1,SBRGNS+NWRGNS - DO I = 1,NDIM - LOWERS(I,J) = LOWER(I) - UPPERS(I,J) = UPPER(I) - MESHES(I,J) = MESH(I) - END DO - END DO - UPPERS(DIVAXN,TOP) = LOWER(DIVAXN) + 2.d0*WIDTH(DIVAXN) - LOWERS(DIVAXN,SBRGNS+1) = UPPERS(DIVAXN,TOP) - ENDIF - FUNCLS = FUNCLS + RGNCLS - CALL BASRUL(NDIM, LOWERS(:,TOP), UPPERS(:,TOP), WIDTH, - & FUNCTN, WEGHTS, LENRUL, POINTS, WORK(1:NDIM), - & WORK(NDIM+1:2*NDIM),ERRORS(TOP), VALUES(TOP)) - CALL TRESTR(TOP, SBRGNS, PONTRS, ERRORS) - DO I = SBRGNS+1, SBRGNS+NWRGNS -* -* Apply basic rule and store results in heap. -* - CALL BASRUL(NDIM, LOWERS(:,I), UPPERS(:,I), WIDTH, - & FUNCTN, WEGHTS, LENRUL, POINTS, WORK(1:NDIM), - & WORK(NDIM+1:2*NDIM),ERRORS(I), VALUES(I)) - CALL TRESTR(I, I, PONTRS, ERRORS) - END DO - SBRGNS = SBRGNS + NWRGNS - GO TO 30 - ELSE - INFORM = 1 - ENDIF - ELSE - INFORM = 0 - ENDIF - MINCLS = FUNCLS - RETURN - END SUBROUTINE ADBASE - SUBROUTINE BASRUL( NDIM, A, B, WIDTH, FUNCTN, W, LENRUL, G, - & CENTER, Z, RGNERT, BASEST ) - IMPLICIT NONE -* -* For application of basic integration rule -* - INTEGER, INTENT(IN) :: LENRUL, NDIM - DOUBLE PRECISION, DIMENSION(: ), INTENT(IN) :: A, B, WIDTH !(NDIM) - DOUBLE PRECISION, DIMENSION(:,:), INTENT(IN) :: W !(LENRUL,4), - DOUBLE PRECISION, DIMENSION(:,:), INTENT(INOUT) :: G !(NDIM,LENRUL), - DOUBLE PRECISION, DIMENSION(: ), INTENT(INOUT) :: CENTER, Z !(NDIM) - DOUBLE PRECISION, INTENT(OUT) :: RGNERT, BASEST - INTEGER :: I - DOUBLE PRECISION :: FSYMSM, RGNCMP, RGNVAL, - & RGNVOL, RGNCPT, RGNERR - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE -* -* Compute Volume and Center of Subregion -* -! print *,'BASRULE, ndim', ndim - RGNVOL = 1.d0 - DO I = 1,NDIM - RGNVOL = 2.d0*RGNVOL*WIDTH(I) - CENTER(I) = A(I) + WIDTH(I) - END DO - BASEST = 0.d0 - RGNERT = 0.d0 -* -* Compute basic rule and error -* - 10 RGNVAL = 0.d0 - RGNERR = 0.d0 - RGNCMP = 0.d0 - RGNCPT = 0.d0 - DO I = 1,LENRUL - FSYMSM = FULSUM(NDIM, CENTER, WIDTH, Z, G(:,I), FUNCTN) -* Basic Rule - RGNVAL = RGNVAL + W(I,1)*FSYMSM -* First comparison rule - RGNERR = RGNERR + W(I,2)*FSYMSM -* Second comparison rule - RGNCMP = RGNCMP + W(I,3)*FSYMSM -* Third Comparison rule - RGNCPT = RGNCPT + W(I,4)*FSYMSM - END DO -* -* Error estimation -* - RGNERR = SQRT(RGNCMP*RGNCMP + RGNERR*RGNERR) - RGNCMP = SQRT(RGNCPT*RGNCPT + RGNCMP*RGNCMP) - IF ( 4.d0*RGNERR .LT. RGNCMP ) RGNERR = 0.5d0*RGNERR - IF ( 2.d0*RGNERR .GT. RGNCMP ) RGNERR = MAX( RGNERR, RGNCMP ) - RGNERT = RGNERT + RGNVOL*RGNERR - BASEST = BASEST + RGNVOL*RGNVAL -* -* When subregion has more than one piece, determine next piece and -* loop back to apply basic rule. -* - DO I = 1,NDIM - CENTER(I) = CENTER(I) + 2.d0*WIDTH(I) - IF ( CENTER(I) .LT. B(I) ) GO TO 10 - CENTER(I) = A(I) + WIDTH(I) - END DO - RETURN - END SUBROUTINE BASRUL - DOUBLE PRECISION FUNCTION FULSUM(S, CENTER, HWIDTH, X, G, F) - IMPLICIT NONE -* -**** To compute fully symmetric basic rule sum -* - INTEGER, INTENT(IN) :: S - DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: CENTER, HWIDTH - DOUBLE PRECISION, DIMENSION(:), INTENT(INOUT) :: X, G ! shape S - INTEGER :: IXCHNG, LXCHNG, I, L - DOUBLE PRECISION :: INTSUM, GL, GI - INTERFACE - DOUBLE PRECISION FUNCTION F(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION F - END INTERFACE -! print *,'FULSUM, S', S, shape(X) - FULSUM = 0.d0 -* -* Compute centrally symmetric sum for permutation of G -* - 10 INTSUM = 0.d0 - !DO I = 1,S - ! X(I) = CENTER(I) + G(I)*HWIDTH(I) - !END DO - X = CENTER + G*HWIDTH - 20 INTSUM = INTSUM + F(S,X) - DO I = 1,S - G(I) = -G(I) - X(I) = CENTER(I) + G(I)*HWIDTH(I) - IF ( G(I) .LT. 0.d0 ) GO TO 20 - END DO - FULSUM = FULSUM + INTSUM -* -* Find next distinct permuation of G and loop back for next sum -* - DO I = 2,S - IF ( G(I-1) .GT. G(I) ) THEN - GI = G(I) - IXCHNG = I - 1 - DO L = 1,(I-1)/2 - GL = G(L) - G(L) = G(I-L) - G(I-L) = GL - IF ( GL .LE. GI ) IXCHNG = IXCHNG - 1 - IF ( G(L) .GT. GI ) LXCHNG = L - END DO - IF ( G(IXCHNG) .LE. GI ) IXCHNG = LXCHNG - G(I) = G(IXCHNG) - G(IXCHNG) = GI - GO TO 10 - ENDIF - END DO -* -* End loop for permutations of G and associated sums -* -* Restore original order to G's -* - DO I = 1,S/2 - GI = G(I) - G(I) = G(S+1-I) - G(S+1-I) = GI - END DO - RETURN - END FUNCTION FULSUM - SUBROUTINE DIFFER(NDIM, A, B, WIDTH, Z, DIF, FUNCTN, - & DIVAXN, DIFCLS) - IMPLICIT NONE -* -* Compute fourth differences and subdivision axes -* - INTEGER, INTENT(IN) :: NDIM - INTEGER, INTENT(INOUT) :: DIVAXN - INTEGER, INTENT(OUT) :: DIFCLS - DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: A, B, WIDTH ! (NDIM) - DOUBLE PRECISION, DIMENSION(:),INTENT(OUT) :: Z, DIF ! (NDIM) - DOUBLE PRECISION :: FRTHDF, FUNCEN, WIDTHI - INTEGER :: I - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE -! print *,'DIFFER, ndim', ndim, shape(Z) - DIFCLS = 0 -! IF (abs(DIVAXN).GT.NDIM) PRINT *,'DIFFER DIVAXN1',DIVAXN - - DIVAXN = MOD(DIVAXN, NDIM ) + 1 - !print *,'DIFFER, divaxn2', divaxn - IF ( NDIM .GT. 1 ) THEN - !DO I = 1,NDIM - ! DIF(I) = 0.d0 - ! Z(I) = A(I) + WIDTH(I) - !END DO - DIF = 0.D0 - Z(1:NDIM) = A(1:NDIM) + WIDTH(1:NDIM) -! print *,'Z', Z - 10 FUNCEN = FUNCTN(NDIM, Z) - DO I = 1,NDIM - WIDTHI = 0.2d0*WIDTH(I) - FRTHDF = 6.d0*FUNCEN - Z(I) = Z(I) - 4.d0*WIDTHI - FRTHDF = FRTHDF + FUNCTN(NDIM,Z) - Z(I) = Z(I) + 2.d0*WIDTHI - FRTHDF = FRTHDF - 4.d0*FUNCTN(NDIM,Z) - Z(I) = Z(I) + 4.d0*WIDTHI - FRTHDF = FRTHDF - 4.d0*FUNCTN(NDIM,Z) - Z(I) = Z(I) + 2.d0*WIDTHI - FRTHDF = FRTHDF + FUNCTN(NDIM,Z) -* Do not include differences below roundoff -! IF ( FUNCEN + FRTHDF/8.d0 .NE. FUNCEN ) - IF ( FUNCEN + FRTHDF*0.125D0 .NE. FUNCEN ) - & DIF(I) = DIF(I) + ABS(FRTHDF)*WIDTH(I) - Z(I) = Z(I) - 4.d0*WIDTHI - END DO - DIFCLS = DIFCLS + 4*NDIM + 1 - DO I = 1,NDIM - Z(I) = Z(I) + 2.D0*WIDTH(I) - IF ( Z(I) .LT. B(I) ) GO TO 10 - Z(I) = A(I) + WIDTH(I) - END DO - !IF (abs(DIVAXN).GT.NDIM) PRINT *,'DIFFER DIVAXN',DIVAXN,shape(dif),ndim - DO I = 1,NDIM - IF ( DIF(DIVAXN) .LT. DIF(I) ) DIVAXN = I - END DO - ENDIF - RETURN - END SUBROUTINE DIFFER - SUBROUTINE TRESTR(POINTR, SBRGNS, PONTRS, RGNERS) - IMPLICIT NONE -****BEGIN PROLOGUE TRESTR -****PURPOSE TRESTR maintains a heap for subregions. -****DESCRIPTION TRESTR maintains a heap for subregions. -* The subregions are ordered according to the size of the -* greatest error estimates of each subregion (RGNERS). -* -* PARAMETERS -* -* POINTR Integer. -* The index for the subregion to be inserted in the heap. -* SBRGNS Integer. -* Number of subregions in the heap. -* PONTRS Real array of dimension SBRGNS. -* Used to store the indices for the greatest estimated errors -* for each subregion. -* RGNERS Real array of dimension SBRGNS. -* Used to store the greatest estimated errors for each -* subregion. -* -****ROUTINES CALLED NONE -****END PROLOGUE TRESTR -* -* Global variables. -* - INTEGER, INTENT(IN) ::POINTR, SBRGNS - DOUBLE PRECISION, DIMENSION(:), INTENT(INOUT) :: PONTRS - DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: RGNERS -* -* Local variables. -* -* RGNERR Intermediate storage for the greatest error of a subregion. -* SUBRGN Position of child/parent subregion in the heap. -* SUBTMP Position of parent/child subregion in the heap. -* - INTEGER SUBRGN, SUBTMP - DOUBLE PRECISION RGNERR -* -****FIRST PROCESSING STATEMENT TRESTR -* -! print *,'TRESTR' - RGNERR = RGNERS(POINTR) - IF ( POINTR.EQ.NINT(PONTRS(1))) THEN -* -* Move the new subregion inserted at the top of the heap -* to its correct position in the heap. -* - SUBRGN = 1 - 10 SUBTMP = 2*SUBRGN - IF ( SUBTMP .LE. SBRGNS ) THEN - IF ( SUBTMP .NE. SBRGNS ) THEN -* -* Find maximum of left and right child. -* - IF ( RGNERS(NINT(PONTRS(SUBTMP))) .LT. - & RGNERS(NINT(PONTRS(SUBTMP+1))) ) SUBTMP = SUBTMP + 1 - ENDIF -* -* Compare maximum child with parent. -* If parent is maximum, then done. -* - IF ( RGNERR .LT. RGNERS(NINT(PONTRS(SUBTMP))) ) THEN -* -* Move the pointer at position subtmp up the heap. -* - PONTRS(SUBRGN) = PONTRS(SUBTMP) - SUBRGN = SUBTMP - GO TO 10 - ENDIF - ENDIF - ELSE -* -* Insert new subregion in the heap. -* - SUBRGN = SBRGNS - 20 SUBTMP = SUBRGN/2 - IF ( SUBTMP .GE. 1 ) THEN -* -* Compare child with parent. If parent is maximum, then done. -* - IF ( RGNERR .GT. RGNERS(NINT(PONTRS(SUBTMP))) ) THEN -* -* Move the pointer at position subtmp down the heap. -* - PONTRS(SUBRGN) = PONTRS(SUBTMP) - SUBRGN = SUBTMP - GO TO 20 - ENDIF - ENDIF - ENDIF - PONTRS(SUBRGN) = DBLE(POINTR) -* -****END TRESTR -* - RETURN - END SUBROUTINE TRESTR - END MODULE ADAPTMOD - - - -* RCRUDEMOD is a module containing two: -* -* Automatic Multidimensional Integration Subroutines -* -* AUTHOR: Alan Genz -* Department of Mathematics -* Washington State University -* Pulman, WA 99164-3113 -* Email: AlanGenz@wsu.edu -* -* Last Change: 5/15/98 -* revised pab 10.03.2000 -* - updated to f90 (i.e. changed to assumed shape arrays + changing integers to DBLE) -* - put it into a module -* - added ranlhmc -* -* RCRUDEMOD computes an approximation to the integral -* -* 1 1 1 -* I I ... I F(X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -! References: -! Alan Genz (1992) -! 'Numerical Computation of Multivariate Normal Probabilites' -! J. computational Graphical Statistics, Vol.1, pp 141--149 (RANMC) -! -! William H. Press, Saul Teukolsky, -! William T. Wetterling and Brian P. Flannery (1997) -! "Numerical recipes in Fortran 77", Vol. 1, pp 55-63 (SVDCMP,PYTHAG) -! -! Donald E. Knuth (1973) "The art of computer programming,", -! Vol. 3, pp 84- (sorting and searching) (SORTRE) - - -! You may initialize the random generator before you -! call RANLHMC or RANMC by the following lines: -! -! call random_seed(SIZE=seed_size) -! allocate(seed(seed_size)) -! call random_seed(GET=seed(1:seed_size)) ! get current seed -! seed(1)=seed1 ! change seed -! call random_seed(PUT=seed(1:seed_size)) -! deallocate(seed) - - - - MODULE RCRUDEMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: RANMC - INTEGER :: NDIMMAX - - INTERFACE RANMC - MODULE PROCEDURE RANMC - END INTERFACE - - INTERFACE RCRUDE - MODULE PROCEDURE RCRUDE - END INTERFACE - - INTERFACE SVDCMP - MODULE PROCEDURE SVDCMP - END INTERFACE - - INTERFACE PYTHAG - MODULE PROCEDURE PYTHAG - END INTERFACE - - INTERFACE SPEARCORR - MODULE PROCEDURE SPEARCORR - END INTERFACE - - INTERFACE SORTRE - MODULE PROCEDURE SORTRE - END INTERFACE - - INTERFACE BINSORT - MODULE PROCEDURE BINSORT - END INTERFACE - - INTERFACE SWAPRE - MODULE PROCEDURE SWAPRE - END INTERFACE - - INTERFACE SWAPINT - MODULE PROCEDURE SWAPINT - END INTERFACE - - PARAMETER (NDIMMAX=1000) - !-------------------------------- - CONTAINS - SUBROUTINE RANMC( N, MAXPTS, FUNCTN, ABSEPS, - & RELEPS, ERROR, VALUE, INFORM ) - IMPLICIT NONE -* -* A subroutine for computing multivariate integrals. -* This subroutine uses the Monte-Carlo algorithm given in the paper -* "Numerical Computation of Multivariate Normal Probabilities", in -* J. of Computational and Graphical Stat., 1(1992), pp. 141-149, by -* Alan Genz -* Department of Mathematics -* Washington State University -* Pullman, WA 99164-3113 -* Email : alangenz@wsu.edu -* -* This subroutine computes an approximation to the integral -* -* 1 1 1 -* I I ... I FUNCTN(NDIM,X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -*************** Parameters for RANMC ******************************** -* -****** Input Parameters -* -* N INTEGER, the number of variables. -* MAXPTS INTEGER, maximum number of function values allowed. This -* parameter can be used to limit the time taken. A -* sensible strategy is to start with MAXPTS = 1000*N, and then -* increase MAXPTS if ERROR is too large. -* ABSEPS REAL absolute error tolerance. -* RELEPS REAL relative error tolerance. -* -****** Output Parameters -* -* ERROR REAL estimated absolute error, with 99% confidence level. -* VALUE REAL estimated value for the integral -* INFORM INTEGER, termination status parameter: -* if INFORM = 0, normal completion with ERROR < EPS; -* if INFORM = 1, completion with ERROR > EPS and MAXPTS -* function vaules used; increase MAXPTS to -* decrease ERROR; -* if INFORM = 2, N > 100 or N < 1. -* - INTEGER :: N, MAXPTS, MPT, INFORM, IVLS - DOUBLE PRECISION :: ABSEPS, RELEPS, ERROR, VALUE, EPS - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - INFORM=0 - IF ( N .GT. NDIMMAX .OR. N .LT. 1 ) THEN - INFORM = 2 - VALUE = 0.d0 - ERROR = 1.d0 - RETURN - ENDIF -* -* Call then Monte-Carlo integration subroutine -* - MPT = 25 + 10*N - CALL RCRUDE(N, MPT, FUNCTN, ERROR, VALUE, 0) - IVLS = MPT - 10 EPS = MAX( ABSEPS, RELEPS*ABS(VALUE) ) - IF ( ERROR .GT. EPS .AND. IVLS .LT. MAXPTS ) THEN - MPT = MAX( MIN( INT(MPT*(ERROR/(EPS))**2), - & MAXPTS-IVLS ), 10 ) - CALL RCRUDE(N, MPT, FUNCTN, ERROR, VALUE, 1) - IVLS = IVLS + MPT - GO TO 10 - ENDIF - IF ( ERROR. GT. EPS .AND. IVLS .GE. MAXPTS ) INFORM = 1 - !IF (INFORM.EQ.1) print *,'ranmc eps',EPS - END SUBROUTINE RANMC - SUBROUTINE RCRUDE(NDIM, MAXPTS, FUNCTN, ABSEST, FINEST, IR) - IMPLICIT NONE -* -* Crude Monte-Carlo Algorithm with simple antithetic variates -* and weighted results on restart -* - INTEGER :: NDIM, MAXPTS, M, IR, NPTS - DOUBLE PRECISION :: FINEST, ABSEST, FUN, - & VARSQR, VAREST, VARPRD, FINDIF, FINVAL - DOUBLE PRECISION, DIMENSION(NDIMMAX) :: X - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - SAVE VAREST - IF ( IR .LE. 0 ) THEN - VAREST = 0.d0 - FINEST = 0.d0 - ENDIF - FINVAL = 0.d0 - VARSQR = 0.d0 - NPTS = INT(MAXPTS/2) - DO M = 1,NPTS - CALL random_number(X(1:NDIM)) - FUN = FUNCTN(NDIM, X(1:NDIM)) - X(1:NDIM) = 1.d0 - X(1:NDIM) - FUN = (FUNCTN(NDIM, X(1:NDIM)) + FUN )*0.5d0 - FINDIF = ( FUN - FINVAL )/DBLE(M) - VARSQR = DBLE( M - 2 )*VARSQR/DBLE(M) + FINDIF*FINDIF - FINVAL = FINVAL + FINDIF - END DO - VARPRD = VAREST*VARSQR - FINEST = FINEST + ( FINVAL - FINEST )/(1.d0 + VARPRD) - IF ( VARSQR .GT. 0 ) VAREST = (1.d0 + VARPRD)/VARSQR - ABSEST = 3.d0*SQRT( VARSQR/( 1.d0 + VARPRD ) ) - MAXPTS=2*NPTS - END SUBROUTINE RCRUDE - - SUBROUTINE BINSORT(indices,rarray) - IMPLICIT NONE - TYPE ENTRY - DOUBLE PRECISION, POINTER :: VAL - INTEGER :: IX - TYPE( ENTRY), POINTER :: NEXT - END TYPE ENTRY - DOUBLE PRECISION, DIMENSION(:), INTENT(in) :: rarray - INTEGER, DIMENSION(:), INTENT(inout) :: indices - DOUBLE PRECISION, DIMENSION(SIZE(rarray)),TARGET :: A - TYPE(ENTRY), DIMENSION(:), ALLOCATABLE,TARGET :: B - TYPE(ENTRY), POINTER :: FIRST,CURRENT - -! local variables - INTEGER :: i,im,n - DOUBLE PRECISION :: mx, mn -! Bucket sort: -! This subroutine sorts the indices according to rarray. The Assumption is that rarray consists of -! uniformly distributed numbers. If the assumption holds it runs in O(n) time - n=size(indices) - IF (n.EQ.1) RETURN - !indices=(/(i,i=1,n)/) - mx = MAXVAL(rarray) - mn = MINVAL(rarray) - A=(rarray-mn)/(mx-mn) ! make sure the numbers are between 0 and 1 - - !print *,'binsort ind=',indices - !print *,'binsort rar=',rarray - !print *,'binsort rar=',A - ALLOCATE(B(0:n-1)) - !IF (ASSOCIATED(B(0)%VAL)) print *,'binsort B(0)=',B(0)%VAL - DO I=0,n-1 - NULLIFY(B(I)%VAL) - NULLIFY(B(I)%NEXT) - ENDDO - - DO I=1,n - IM=min(ABS(FLOOR(n*A(I))),N-1) - IF (ASSOCIATED(B(IM)%VAL)) THEN ! insert the new item by insertion sorting - ALLOCATE(CURRENT) - IF (A(I).LT.B(IM)%VAL) THEN - CURRENT = B(IM) - B(IM) = ENTRY(A(I),indices(I),CURRENT) - ELSE - FIRST => B(IM) - DO WHILE(ASSOCIATED(FIRST%NEXT).AND. - & FIRST%NEXT%VAL.LT.A(I)) - FIRST=FIRST%NEXT - END DO - - CURRENT = ENTRY(A(I),indices(I),FIRST%NEXT) - FIRST%NEXT => CURRENT - ENDIF - ELSE - B(IM)%VAL => A(I) - B(IM)%IX = indices(I) - ENDIF - END DO - IM=0 - I=0 - DO WHILE (IM.LT.N .AND. I.LT.N) - IF (ASSOCIATED(B(I)%VAL)) THEN - IM=IM+1 - indices(IM)=B(I)%IX - DO WHILE (ASSOCIATED(B(I)%NEXT)) - CURRENT => B(I)%NEXT - B(I)%NEXT => B(I)%NEXT%NEXT - IM=IM+1 - indices(IM)=CURRENT%IX - DEALLOCATE(CURRENT) - END DO - ENDIF - I=I+1 - END DO - DEALLOCATE(B) - !print *,'binsort ind=',indices - RETURN - END SUBROUTINE BINSORT - - SUBROUTINE SORTRE(indices,rarray) - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:), INTENT(inout) :: rarray - INTEGER, DIMENSION(:), INTENT(inout) :: indices -! local variables - INTEGER :: i,im,j,k,m,n - -! diminishing increment sort as described by -! Donald E. Knuth (1973) "The art of computer programming,", -! Vol. 3, pp 84- (sorting and searching) - n=size(indices) - ! if the below is commented out then assume indices are already initialized - !indices=(/(i,i=1,n)/) -!100 continue - if (n.le.1) goto 800 - m=1 -200 continue - m=m+m - if (m.lt.n) goto 200 - m=m-1 -300 continue - m=m/2 - if (m.eq.0) goto 800 - k=n-m - j=1 -400 continue - i=j -500 continue - im=i+m - if (rarray(i).gt.rarray(im)) goto 700 -600 continue - j=j+1 - if (j.gt.k) goto 300 - goto 400 -700 continue - CALL swapre(rarray(i),rarray(im)) - CALL swapint(indices(i),indices(im)) - i=i-m - if (i.lt.1) goto 600 - goto 500 -800 continue - RETURN - END SUBROUTINE SORTRE - - SUBROUTINE swapRe(m,n) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(inout) :: m,n - DOUBLE PRECISION :: tmp - tmp=m - m=n - n=tmp - END SUBROUTINE swapRe - - SUBROUTINE swapint(m,n) - IMPLICIT NONE - INTEGER, INTENT(inout) :: m,n - INTEGER :: tmp - tmp=m - m=n - n=tmp - END SUBROUTINE swapint -!______________________________________________________ - - SUBROUTINE spearcorr(C,D) - IMPLICIT NONE - DOUBLE PRECISION, dimension(:,:), INTENT(out) :: C - integer, dimension(:,:),intent(in) :: D ! rank matrix - double precision, dimension(:,:),allocatable :: DD !,DDT - double precision, dimension(:),allocatable :: tmp - INTEGER :: N,M,ix,iy - DOUBLE PRECISION :: dN -! this procedure calculates spearmans correlation coefficient -! between the columns of D - - N=size(D,dim=1);M=SIZE(D,dim=2) - dN=dble(N) - allocate(DD(1:N,1:M)) - DD=dble(D) -! if (.false.) then ! old call -! allocate(DDt(1:M,1:N)) -! DDT=transpose(DD) -! C = matmul(DDt,DD)*12.d0/(dn*(dn*dn-1.d0)) -! C=(C-3.d0*(dn+1.d0)/(dn-1.d0)) -! deallocate(DDT) -! else - allocate(tmp(1:N)) - do ix=1, m-1 - do iy=ix+1,m - tmp= DD(1:N,ix)-DD(1:N,iy) - C(ix,iy)=1.d0-6.d0*SUM(tmp*tmp)/dn/(dn*dn-1.d0) - C(iy,ix)=C(ix,iy) - enddo - C(ix,ix) = 1.d0 - enddo - C(m,m)=1.d0 - deallocate(tmp) -! endif - deallocate(DD) - return - END SUBROUTINE spearcorr - - SUBROUTINE SVDCMP(A,W,V) - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(: ), INTENT(out) :: W - DOUBLE PRECISION, DIMENSION(:,:), INTENT(inout) :: A - DOUBLE PRECISION, DIMENSION(:,:), INTENT(OUT) :: V -!LOCAL VARIABLES - DOUBLE PRECISION, DIMENSION(:), allocatable :: RV1 - DOUBLE PRECISION :: G,S,SCALE,ANORM,F,H,C,X,Y,Z - INTEGER M,N,NM,I,J,K,L,ITS - - !PARAMETER (NMAX=100) -C Maximum anticipated values of N - -C DIMENSION A(MP,NP),W(NP),V(NP,NP),RV1(NMAX) -C Given a matrix A, with logical dimensions M by N and physical -C dimensions MP by NP, this routine computes its singular value -C decomposition, A=U.W.V^T, see Numerical Recipes, by Press W.,H. -C Flannery, B. P., Teukolsky S.A. and Vetterling W., T. Cambrige -C University Press 1986, Chapter 2.9. The matrix U replaces A on -C output. The diagonal matrix of singular values W is output as a vector -C W. The matrix V (not the transpose V^T) is output as V. M must be -C greater or equal to N; if it is smaller, then A should be filled up -C to square with zero rows. -C - - M=size(A,dim=1);N=size(A,dim=2) - !Mp=M;Np=N - allocate(RV1(1:N)) - IF (M.LT.N) then -! Print *,'SVDCMP: You must augment A with extra zero rows.' - endif -C Householder reduction to bidiagonal form - G=0.d0 - SCALE=0.d0 - ANORM=0.d0 - DO 25 I=1,N - L=I+1 - RV1(I)=SCALE*G - G=0.D0 - S=0.D0 - SCALE=0.D0 - IF (I.LE.M) THEN - DO K=I,M - SCALE=SCALE+ABS(A(K,I)) - enddo - IF (SCALE.NE.0.D0) THEN - DO K=I,M - A(K,I)=A(K,I)/SCALE - S=S+A(K,I)*A(K,I) - enddo - F=A(I,I) - G=-SIGN(SQRT(S),F) - H=F*G-S - A(I,I)=F-G - IF (I.NE.N) THEN - DO J=L,N - S=0.D0 - DO K=I,M - S=S+A(K,I)*A(K,J) - enddo - F=S/H - DO K=I,M - A(K,J)=A(K,J)+F*A(K,I) - enddo - enddo - ENDIF - DO K=I,M - A(K,I)=SCALE*A(K,I) - enddo - ENDIF - ENDIF - W(I)=SCALE*G - G=0.d0 - S=0.d0 - SCALE=0.d0 - IF ((I.LE.M).AND.(I.NE.N)) THEN - DO K=L,N - SCALE=SCALE+ABS(A(I,K)) - enddo - IF (SCALE.NE.0.0) THEN - DO K=L,N - A(I,K)=A(I,K)/SCALE - S=S+A(I,K)*A(I,K) - enddo - F=A(I,L) - G=-SIGN(SQRT(S),F) - H=F*G-S - A(I,L)=F-G - DO K=L,N - RV1(K)=A(I,K)/H - enddo - IF (I.NE.M) THEN - DO J=L,M - S=0.D0 - DO K=L,N - S=S+A(J,K)*A(I,K) - enddo - DO K=L,N - A(J,K)=A(J,K)+S*RV1(K) - enddo - enddo - ENDIF - DO K=L,N - A(I,K)=SCALE*A(I,K) - enddo - ENDIF - ENDIF - ANORM=MAX(ANORM,(ABS(W(I))+ABS(RV1(I)))) -25 CONTINUE -c print *,'25' -C Accumulation of right-hand transformations. - DO I=N,1,-1 - IF (I.LT.N) THEN - IF (G.NE.0.d0) THEN - DO J=L,N - V(J,I)=(A(I,J)/A(I,L))/G -C Double division to avoid possible underflow. - enddo - DO J=L,N - S=0.d0 - DO K=L,N - S=S+A(I,K)*V(K,J) - enddo - DO K=L,N - V(K,J)=V(K,J)+S*V(K,I) - enddo - enddo - ENDIF - DO J=L,N - V(I,J)=0.d0 - V(J,I)=0.d0 - enddo - ENDIF - V(I,I)=1.d0 - G=RV1(I) - L=I - enddo -c print *,'32' - -C Accumulation of the left-hang transformation - DO 39 I=N,1,-1 - L=I+1 - G=W(I) - IF (I.LT.N) THEN - DO J=L,N - A(I,J)=0.d0 - enddo - ENDIF - IF (G.NE.0.d0) THEN - G=1.d0/G - IF (I.NE.N) THEN - DO J=L,N - S=0.d0 - DO K=L,M - S=S+A(K,I)*A(K,J) - enddo - F=(S/A(I,I))*G - DO K=I,M - A(K,J)=A(K,J)+F*A(K,I) - enddo - enddo - ENDIF - DO J=I,M - A(J,I)=A(J,I)*G - enddo - ELSE - DO J=I,M - A(J,I)=0.d0 - enddo - ENDIF - A(I,I)=A(I,I)+1.d0 -39 CONTINUE -c print *,'39' - -C Diagonalization of the bidiagonal form -C Loop over singular values - DO 49 K=N,1,-1 -C Loop allowed iterations - DO 48 ITS=1,30 -C Test for spliting - DO L=K,1,-1 - NM=L-1 -C Note that RV1(1) is always zero -! old call which may cause inconsistent results -! IF((ABS(RV1(L))+ANORM).EQ.ANORM) GO TO 2 -! IF((ABS(W(NM))+ANORM).EQ.ANORM) GO TO 1 -! NEW CALL - IF (((ABS(RV1(L))+ANORM).GE.NEAREST(ANORM,-1.d0)).AND. - & ((ABS(RV1(L))+ANORM).LE.NEAREST(ANORM,1.d0)) ) GO TO 2 - IF (((ABS(W(NM))+ANORM).GE.NEAREST(ANORM,-1.d0)).AND. - & ((ABS(W(NM))+ANORM).LE.NEAREST(ANORM,1.d0)) ) GO TO 1 - - enddo -c print *,'41' -1 C=0.d0 - S=1.d0 - DO I=L,K - F=S*RV1(I) -! old call which may cause inconsistent results - - IF (((ABS(F)+ANORM).LT.ANORM).OR. - & ((ABS(F)+ANORM).GT.ANORM)) THEN - G=W(I) - H=SQRT(F*F+G*G) - W(I)=H - H=1.D0/H - C= (G*H) - S=-(F*H) - DO J=1,M - Y=A(J,NM) - Z=A(J,I) - A(J,NM)=(Y*C)+(Z*S) - A(J,I)=-(Y*S)+(Z*C) - enddo - ENDIF - enddo -c print *,'43' -2 Z=W(K) - IF (L.EQ.K) THEN -C Convergence - IF (Z.LT.0.d0) THEN -C Singular values are made nonnegative - W(K)=-Z - DO J=1,N - V(J,K)=-V(J,K) - enddo - ENDIF - GO TO 3 - ENDIF - IF (ITS.EQ.30) then -! print *,'SVDCMP: No convergence in 30 iterations' - endif - X=W(L) - NM=K-1 - Y=W(NM) - G=RV1(NM) - H=RV1(K) - F=((Y-Z)*(Y+Z)+(G-H)*(G+H))/(2.d0*H*Y) - G=SQRT(F*F+1.D0) - F=((X-Z)*(X+Z)+H*((Y/(F+SIGN(G,F)))-H))/X -C Next QR transformation - C=1.d0 - S=1.d0 - DO 47 J=L,NM - I=J+1 - G=RV1(I) - Y=W(I) - H=S*G - G=C*G - Z=SQRT(F*F+H*H) - RV1(J)=Z - C=F/Z - S=H/Z - F= (X*C)+(G*S) - G=-(X*S)+(G*C) - H=Y*S - Y=Y*C - DO NM=1,N - X=V(NM,J) - Z=V(NM,I) - V(NM,J)= (X*C)+(Z*S) - V(NM,I)=-(X*S)+(Z*C) - enddo -c print *,'45',F,H - Z=pythag(F,H) - W(J)=Z -C Rotation can be arbitrary if Z=0. - IF (Z.NE.0.d0) THEN -c print *,1/Z - Z=1.d0/Z -c print *,'*' - C=F*Z - S=H*Z - ENDIF - F= (C*G)+(S*Y) - X=-(S*G)+(C*Y) - DO NM=1,M - Y=A(NM,J) - Z=A(NM,I) - A(NM,J)= (Y*C)+(Z*S) - A(NM,I)=-(Y*S)+(Z*C) - enddo -c print *,'46' - -47 CONTINUE -c print *,'47' - RV1(L)=0.D0 - RV1(K)=F - W(K)=X -48 CONTINUE -3 CONTINUE -49 CONTINUE -c print *,'49' - deallocate(RV1) - RETURN - END SUBROUTINE SVDCMP - - FUNCTION pythag(a,b) RESULT (VALUE) - DOUBLE PRECISION, INTENT(IN) :: a,b - DOUBLE PRECISION :: VALUE - DOUBLE PRECISION :: absa,absb - absa=abs(a) - absb=abs(b) - IF (absa.GT.absb) THEN - VALUE=absa*SQRT(1.d0+(absb/absa)**2) - ELSE - IF (absb.EQ.0) THEN - VALUE=0.D0 - ELSE - VALUE=absb*SQRT(1.d0+(absa/absb)**2) - ENDIF - ENDIF - RETURN - END FUNCTION PYTHAG - END MODULE RCRUDEMOD - - - - - - - - -* KRBVRCMOD is a module containing a: -* -* Automatic Multidimensional Integration Subroutine -* -* AUTHOR: Alan Genz -* Department of Mathematics -* Washington State University -* Pulman, WA 99164-3113 -* Email: AlanGenz@wsu.edu -* -* Last Change: 5/15/98 -* revised pab 10.03.2000 -* - updated to f90 (i.e. changed to assumed shape arrays + changing integers to DBLE) -* - put it into a module -* -* KRBVRC computes an approximation to the integral -* -* 1 1 1 -* I I ... I F(X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -* -* KRBVRC uses randomized Korobov rules for the first 20 variables. -* The primary references are -* "Randomization of Number Theoretic Methods for Multiple Integration" -* R. Cranley and T.N.L. Patterson, SIAM J Numer Anal, 13, pp. 904-14, -* and -* "Optimal Parameters for Multidimensional Integration", -* P. Keast, SIAM J Numer Anal, 10, pp.831-838. -* If there are more than 20 variables, the remaining variables are -* integrated using Richtmeyer rules. A reference is -* "Methods of Numerical Integration", P.J. Davis and P. Rabinowitz, -* Academic Press, 1984, pp. 482-483. -* -*************** Parameters for KRBVRC ******************************************** -****** Input parameters -* NDIM Number of variables, must exceed 1, but not exceed 100 -* MINVLS Integer minimum number of function evaluations allowed. -* MINVLS must not exceed MAXVLS. If MINVLS < 0 then the -* routine assumes a previous call has been made with -* the same integrand and continues that calculation. -* MAXVLS Integer maximum number of function evaluations allowed. -* FUNCTN EXTERNALly declared user defined function to be integrated. -* It must have parameters (NDIM,Z), where Z is a real array -* of dimension NDIM. -* -* ABSEPS Required absolute accuracy. -* RELEPS Required relative accuracy. -* -****** Output parameters -* -* MINVLS Actual number of function evaluations used. -* ABSERR Estimated absolute accuracy of FINEST. -* FINEST Estimated value of integral. -* INFORM INFORM = 0 for normal exit, when -* ABSERR <= MAX(ABSEPS, RELEPS*ABS(FINEST)) -* and -* INTVLS <= MAXCLS. -* INFORM = 1 If MAXVLS was too small to obtain the required -* accuracy. In this case a value FINEST is returned with -* estimated absolute accuracy ABSERR. -************************************************************************ -! William H. Press, Saul Teukolsky, -! William T. Wetterling and Brian P. Flannery (1997) -! "Numerical recipes in Fortran 77", Vol. 1, pp 299--305 (SOBSEQ) - -! You may initialize the random generator before you -! call KRBVRC by the following lines: -! -! call random_seed(SIZE=seed_size) -! allocate(seed(seed_size)) -! call random_seed(GET=seed(1:seed_size)) ! get current seed -! seed(1)=seed1 ! change seed -! call random_seed(PUT=seed(1:seed_size)) -! deallocate(seed) -! - MODULE KRBVRCMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: KRBVRC -! - INTERFACE KRBVRC - MODULE PROCEDURE KRBVRC - END INTERFACE -! - INTERFACE DKSMRC - MODULE PROCEDURE DKSMRC - END INTERFACE -! - INTERFACE DKRCHT - MODULE PROCEDURE DKRCHT - END INTERFACE - - INTERFACE SOBSEQ - MODULE PROCEDURE SOBSEQ - END INTERFACE -! - CONTAINS - -!*********************************************************** -! MAIN INTEGRATION ROUTINE KRBVRC -!*********************************************************** - - SUBROUTINE KRBVRC( NDIM, MINVLS, MAXVLS, FUNCTN, ABSEPS, RELEPS, - & ABSERR, FINEST, INFORM ) -* -* Automatic Multidimensional Integration Subroutine -* -* AUTHOR: Alan Genz -* Department of Mathematics -* Washington State University -* Pulman, WA 99164-3113 -* Email: AlanGenz@wsu.edu -* -* Last Change: 5/15/98 -* -* KRBVRC computes an approximation to the integral -* -* 1 1 1 -* I I ... I F(X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -* -* KRBVRC uses randomized Korobov rules for the first 20 variables. -* The primary references are -* "Randomization of Number Theoretic Methods for Multiple Integration" -* R. Cranley and T.N.L. Patterson, SIAM J Numer Anal, 13, pp. 904-14, -* and -* "Optimal Parameters for Multidimensional Integration", -* P. Keast, SIAM J Numer Anal, 10, pp.831-838. -* If there are more than 20 variables, the remaining variables are -* integrated using Richtmeyer rules. A reference is -* "Methods of Numerical Integration", P.J. Davis and P. Rabinowitz, -* Academic Press, 1984, pp. 482-483. -* -*************** Parameters ******************************************** -****** Input parameters -* NDIM Number of variables, must exceed 1, but not exceed 100 -* MINVLS Integer minimum number of function evaluations allowed. -* MINVLS must not exceed MAXVLS. If MINVLS < 0 then the -* routine assumes a previous call has been made with -* the same integrand and continues that calculation. -* MAXVLS Integer maximum number of function evaluations allowed. -* FUNCTN EXTERNALly declared user defined function to be integrated. -* It must have parameters (NDIM,Z), where Z is a real array -* of dimension NDIM. -* -* ABSEPS Required absolute accuracy. -* RELEPS Required relative accuracy. -****** Output parameters -* MINVLS Actual number of function evaluations used. -* ABSERR Estimated absolute accuracy of FINEST. -* FINEST Estimated value of integral. -* INFORM INFORM = 0 for normal exit, when -* ABSERR <= MAX(ABSEPS, RELEPS*ABS(FINEST)) -* and -* INTVLS <= MAXCLS. -* INFORM = 1 If MAXVLS was too small to obtain the required -* accuracy. In this case a value FINEST is returned with -* estimated absolute accuracy ABSERR. -* INFORM = 2 If NDIM>100 or NDIM<1 -************************************************************************ - INTEGER, INTENT(IN) :: NDIM, MAXVLS - INTEGER, INTENT(INOUT) :: MINVLS - INTEGER, INTENT(OUT) :: INFORM - DOUBLE PRECISION, INTENT(IN) :: ABSEPS, RELEPS - DOUBLE PRECISION, INTENT(OUT) :: FINEST, ABSERR - INTEGER :: NP,PLIM,NLIM,KLIM,KLIMI,SAMPLS,I,INTVLS,MINSMP,NK - PARAMETER ( PLIM = 25, NLIM = 100, KLIM = 20, MINSMP = 8 ) - INTEGER , DIMENSION(PLIM) :: P - INTEGER , DIMENSION(PLIM,KLIM-1) :: C - DOUBLE PRECISION :: DIFINT,FINVAL,VARSQR,VAREST,VARPRD,VALUE - DOUBLE PRECISION, PARAMETER :: ONE = 1.D0 , ZERO = 0.D0 - DOUBLE PRECISION, DIMENSION(2*NLIM) :: X = 0.d0 - DOUBLE PRECISION, DIMENSION(KLIM ) :: VK = 0.d0 - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - DATA P / 31, 47, 73, 113, 173, 263, 397, 593, 907, 1361, - & 2053, 3079, 4621, 6947, 10427, 15641, 23473, 35221, - & 52837, 79259, 118891, 178349, 267523, 401287, 601943/ - DATA (C( 1,I), I = 1, 19)/ 12, 9, 9, - & 13, 12, 12, 12, 12, 12, 12, 12, - & 12, 3, 3, 3, 12, 7, 7, 12/ - DATA (C( 2,I), I = 1, 19)/ 13, 11, 17, - & 10, 15, 15, 15, 15, 15, 15, 22, - & 15, 15, 6, 6, 6, 15, 15, 9/ - DATA (C( 3,I), I = 1, 19)/ 27, 28, 10, - & 11, 11, 20, 11, 11, 28, 13, 13, - & 28, 13, 13, 13, 14, 14, 14, 14/ - DATA (C( 4,I), I = 1, 19)/ 35, 27, 27, - & 36, 22, 29, 29, 20, 45, 5, 5, - & 5, 21, 21, 21, 21, 21, 21, 21/ - DATA (C( 5,I), I = 1, 19)/ 64, 66, 28, - & 28, 44, 44, 55, 67, 10, 10, 10, - & 10, 10, 10, 38, 38, 10, 10, 10/ - DATA (C( 6,I), I = 1, 19)/ 111, 42, 54, - & 118, 20, 31, 31, 72, 17, 94, 14, - & 14, 11, 14, 14, 14, 94, 10, 10/ - DATA (C( 7,I), I = 1, 19)/ 163, 154, 83, - & 43, 82, 92, 150, 59, 76, 76, 47, - & 11, 11, 100, 131, 116, 116, 116, 116/ - DATA (C( 8,I), I = 1, 19)/ 246, 189, 242, - & 102, 250, 250, 102, 250, 280, 118, 196, - & 118, 191, 215, 121, 121, 49, 49, 49/ - DATA (C( 9,I), I = 1, 19)/ 347, 402, 322, - & 418, 215, 220, 339, 339, 339, 337, 218, - & 315, 315, 315, 315, 167, 167, 167, 167/ - DATA (C(10,I), I = 1, 19)/ 505, 220, 601, - & 644, 612, 160, 206, 206, 206, 422, 134, - & 518, 134, 134, 518, 652, 382, 206, 158/ - DATA (C(11,I), I = 1, 19)/ 794, 325, 960, - & 528, 247, 247, 338, 366, 847, 753, 753, - & 236, 334, 334, 461, 711, 652, 381, 381/ - DATA (C(12,I), I = 1, 19)/ 1189, 888, 259, - & 1082, 725, 811, 636, 965, 497, 497, 1490, - & 1490, 392, 1291, 508, 508, 1291, 1291, 508/ - DATA (C(13,I), I = 1, 19)/ 1763, 1018, 1500, - & 432, 1332, 2203, 126, 2240, 1719, 1284, 878, - & 1983, 266, 266, 266, 266, 747, 747, 127/ - DATA (C(14,I), I = 1, 19)/ 2872, 3233, 1534, - & 2941, 2910, 393, 1796, 919, 446, 919, 919, - & 1117, 103, 103, 103, 103, 103, 103, 103/ - DATA (C(15,I), I = 1, 19)/ 4309, 3758, 4034, - & 1963, 730, 642, 1502, 2246, 3834, 1511, 1102, - & 1102, 1522, 1522, 3427, 3427, 3928, 915, 915/ - DATA (C(16,I), I = 1, 19)/ 6610, 6977, 1686, - & 3819, 2314, 5647, 3953, 3614, 5115, 423, 423, - & 5408, 7426, 423, 423, 487, 6227, 2660, 6227/ - DATA (C(17,I), I = 1, 19)/ 9861, 3647, 4073, - & 2535, 3430, 9865, 2830, 9328, 4320, 5913, 10365, - & 8272, 3706, 6186, 7806, 7806, 7806, 8610, 2563/ - DATA (C(18,I), I = 1, 19)/ 10327, 7582, 7124, - & 8214, 9600, 10271, 10193, 10800, 9086, 2365, 4409, - & 13812, 5661, 9344, 9344, 10362, 9344, 9344, 8585/ - DATA (C(19,I), I = 1, 19)/ 19540, 19926, 11582, - & 11113, 24585, 8726, 17218, 419, 4918, 4918, 4918, - & 15701, 17710, 4037, 4037, 15808, 11401, 19398, 25950/ - DATA (C(20,I), I = 1, 19)/ 34566, 9579, 12654, - & 26856, 37873, 38806, 29501, 17271, 3663, 10763, 18955, - & 1298, 26560, 17132, 17132, 4753, 4753, 8713, 18624/ - DATA (C(21,I), I = 1, 19)/ 31929, 49367, 10982, - & 3527, 27066, 13226, 56010, 18911, 40574, 20767, 20767, - & 9686, 47603, 47603, 11736, 11736, 41601, 12888, 32948/ - DATA (C(22,I), I = 1, 19)/ 40701, 69087, 77576, - & 64590, 39397, 33179, 10858, 38935, 43129, 35468, 35468, - & 2196, 61518, 61518, 27945, 70975, 70975, 86478, 86478/ - DATA (C(23,I), I = 1, 19)/ 103650, 125480, 59978, - & 46875, 77172, 83021, 126904, 14541, 56299, 43636, 11655, - & 52680, 88549, 29804, 101894, 113675, 48040, 113675, 34987/ - DATA (C(24,I), I = 1, 19)/ 165843, 90647, 59925, - & 189541, 67647, 74795, 68365, 167485, 143918, 74912, 167289, - & 75517, 8148, 172106, 126159, 35867, 35867, 35867, 121694/ - DATA (C(25,I), I = 1, 19)/ 130365, 236711, 110235, - & 125699, 56483, 93735, 234469, 60549, 1291, 93937, 245291, - & 196061, 258647, 162489, 176631, 204895, 73353, 172319, 28881/ -* - SAVE P, C, SAMPLS, NP, VAREST - IF ( NDIM .GT. NLIM .OR. NDIM .LT. 1 ) THEN - INFORM = 2 - FINEST = ZERO - ABSERR = ONE - RETURN - ENDIF - INFORM = 1 - INTVLS = 0 - KLIMI = KLIM - IF ( MINVLS .GE. 0 ) THEN - FINEST = ZERO - VAREST = ZERO - SAMPLS = MINSMP - DO I = 1, PLIM - NP = I - IF ( MINVLS .LT. 2*SAMPLS*P(I) ) GO TO 10 - END DO - SAMPLS = MAX( MINSMP, MINVLS/( 2*P(NP) ) ) - ENDIF - 10 VK(1) = ONE/DBLE(P(NP)) - NK = MIN( NDIM, KLIM ) - DO I = 2, NK - VK(I) = MOD(DBLE(C(NP,NK-1))*VK(I-1), ONE ) - END DO - FINVAL = ZERO - VARSQR = ZERO - DO I = 1, SAMPLS - CALL DKSMRC( NDIM, KLIMI, VALUE, P(NP), VK, FUNCTN, X ) - DIFINT = ( VALUE - FINVAL )/DBLE(I) - FINVAL = FINVAL + DIFINT - VARSQR = DBLE( I - 2 )*VARSQR/DBLE(I) + DIFINT*DIFINT - END DO - INTVLS = INTVLS + 2*SAMPLS*P(NP) - VARPRD = VAREST*VARSQR - FINEST = FINEST + ( FINVAL - FINEST )/( ONE + VARPRD ) - IF ( VARSQR .GT. ZERO ) VAREST = ( ONE + VARPRD )/VARSQR - ABSERR = 3.d0*SQRT( VARSQR/( ONE + VARPRD ) ) - IF ( ABSERR .GT. MAX( ABSEPS, ABS(FINEST)*RELEPS ) ) THEN - IF ( NP .LT. PLIM ) THEN - NP = NP + 1 - ELSE - SAMPLS = MIN( 3*SAMPLS/2, ( MAXVLS - INTVLS )/( 2*P(NP) ) ) - SAMPLS = MAX( MINSMP, SAMPLS ) - ENDIF - IF ( INTVLS + 2*SAMPLS*P(NP) .LE. MAXVLS ) GO TO 10 - ELSE - INFORM = 0 - ENDIF - MINVLS = INTVLS -* - END SUBROUTINE KRBVRC -* - SUBROUTINE DKSMRC( NDIM, KLIM, SUMKRO, PRIME, VK, FUNCTN, X ) - INTEGER, INTENT(IN):: NDIM, KLIM, PRIME - DOUBLE PRECISION, INTENT(OUT) :: SUMKRO - DOUBLE PRECISION, DIMENSION(:), INTENT(INOUT) :: VK,X - INTEGER :: K, J, JP, NK - DOUBLE PRECISION :: ONE, XT, MVNUNI - PARAMETER ( ONE = 1.d0 ) - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - SUMKRO = 0.d0 -* -* Randomize Variable Order -* - NK = MIN( NDIM, KLIM ) - DO J = 1, NK-1 - CALL random_number(MVNUNI) -! JP = J + NINT(MVNUNI*DBLE( NK + 1 - J )) - JP = J + NINT(MVNUNI*DBLE( NK - J )) ! pab 21.11.2000 - XT = VK(J) - VK(J) = VK(JP) - VK(JP) = XT - END DO -* -* Determine Random Shifts for each Variable -* - CALL random_number(X(NDIM+1:2*NDIM)) -* -* Compute periodized and symmetrized lattice rule sum -* - DO K = 1, PRIME - X(1:NK) = MOD( DBLE(K)*VK(1:NK), ONE ) - IF ( NDIM. GT. KLIM ) CALL DKRCHT(KLIM, NDIM-KLIM, X) !X(KLIM+1:NDIM) ) - DO J = 1, NDIM - XT = X(J) + X(NDIM+J) - IF ( XT .GT. ONE ) XT = XT - 1.d0 - X(J) = ABS( 2.d0*XT - 1.d0 ) - END DO - SUMKRO = SUMKRO+(FUNCTN(NDIM,X)-SUMKRO)/DBLE(2*K-1) - X(1:NDIM) = 1.d0 - X(1:NDIM) - SUMKRO = SUMKRO+(FUNCTN(NDIM,X)-SUMKRO)/DBLE(2*K) - END DO - END SUBROUTINE DKSMRC -* - SUBROUTINE DKRCHT(KLIM, S, QUASI ) -* -* This subroutine generates a new quasi-random Richtmeyer vector. -* A reference is -* "Methods of Numerical Integration", P.J. Davis and P. Rabinowitz, -* Academic Press, 1984, pp. 482-483. -* -* INPUTS: -* KLIM - Lower start value -* S - the number of dimensions; -* DKRCHT is initialized for each new S or S < 1. -* -* OUTPUTS: -* QUASI - a new quasi-random S-vector -* -* revised pab 28.05.2003 -* - added klim in order to avoid copying of arrays in and out -* revised pab 01.11.1999 -* updated to fortran 90 - INTEGER, INTENT(IN) :: S,KLIM - DOUBLE PRECISION , DIMENSION(:) :: QUASI - INTEGER :: MXDIM, MXHSUM, B - PARAMETER ( MXDIM = 80, MXHSUM = 48, B = 2 ) - INTEGER :: HISUM, I, OLDS - DOUBLE PRECISION , DIMENSION(MXDIM) :: PSQT - INTEGER, DIMENSION(MXDIM ) :: PRIME - INTEGER, DIMENSION(0:MXHSUM) :: N - - - DOUBLE PRECISION :: ONE, RN - PARAMETER ( ONE = 1.D0 ) - PARAMETER ( PRIME = (/ - & 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, - & 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, - & 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, - & 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, - & 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, - & 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, - & 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, - & 353, 359, 367, 373, 379, 383, 389, 397, 401, 409/)) -* Primes to continue -* 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 -* 503 509 521 523 541 547 557 563 569 571 577 587 593 599 - SAVE OLDS, PSQT, HISUM, N - DATA OLDS / 0 / - IF ( S .NE. OLDS .OR. S .LT. 1 ) THEN - OLDS = ABS(S) ! pab 14.03.2000 - N(0) = 0 - HISUM = 0 - DO I = 1, OLDS - RN = DBLE(PRIME(I)) - PSQT(I) = SQRT( RN ) - END DO - END IF - DO I = 0, HISUM - N(I) = N(I) + 1 - IF ( N(I) .LT. B ) GO TO 10 - N(I) = 0 - END DO - HISUM = HISUM + 1 - IF ( HISUM .GT. MXHSUM ) HISUM = 0 - N(HISUM) = 1 - 10 RN = 0.d0 - DO I = HISUM, 0, -1 - RN = DBLE(N(I)) + DBLE(B)*RN - END DO - DO I = 1, OLDS - QUASI(KLIM+I) = MOD( RN*PSQT(I), ONE ) - END DO - END SUBROUTINE DKRCHT -! -! SOBSEQ is not taken in to use: -! - SUBROUTINE SOBSEQ(N,X) - IMPLICIT NONE - DOUBLE PRECISION,DIMENSION(:), INTENT(OUT):: X - INTEGER, INTENT(IN) :: N - INTEGER,PARAMETER ::MAXBIT=30,MAXDIM=6 - INTEGER :: I,IM, IN,IPP,J,K,L, OLDN - INTEGER, DIMENSION(MAXDIM) :: IP,MDEG,IX - INTEGER, DIMENSION(MAXDIM,MAXBIT) ::IU - INTEGER, DIMENSION(MAXDIM*MAXBIT) ::IV - DOUBLE PRECISION :: FAC - SAVE IP,MDEG,IX,IV,IN,FAC, OLDN - DATA OLDN / 0 / - DATA IP /0,1,1,2,1,4 /, MDEG /1,2,3,3,4,4 / - DATA IX /0,0,0,0,0,0 / - DATA IV /1,1,1,1,1,1,3,1,3,3,1,1,5, - & 7,7,3,3,5,15,11,5,15,13,9,156*0/ - !(MAXDIM*MAXBIT-24) - EQUIVALENCE (IV,IU) ! to allow both 1D and 2D addressing -! returns sobols sequence of quasi-random numbers between 0 1 -! When n is new or is negative, internally initializes a set of MAXBIT -! direction numbers for each of MAXDIM different sobol -! sequences. When n is positive (but < MAXDIM) -! returns as the vector x(1:n) the next values from n of these sequences -! (n must not be changed between initializations) -! -! This routine is initialised for maximum of n=6 dimensions -! and a word length of 30 bits. These parameter may be increased by -!changing MAXBIT and MAXDIM and add more initializing data to -! ip (primitive polynomials), mdeg (their degrees) and iv -! (the starting value for the recurrence relation) - -!reference -! William H. Press, Saul Teukolsky, William T. Wetterling and Brian P. Flannery (1997) -! "Numerical recipes in Fortran 77", Vol. 1, pp 299--305 - - - IF (N.LT.0 .OR. OLDN.NE.N ) THEN ! INITIALIZE, DO NOT RETURN VECTOR - OLDN = ABS(N) - IX=0 - IN=0 ! RANDOM STARTPOINT: CALL RANDOM_NUMBER(P); IN=P*2^MAXBIT - ! AND REMOVE WARNING MESSAGE BELOW - !IF (IV(1).NE.1) RETURN - - IF (IV(1).EQ.1) THEN - FAC=1.D0/2.D0**MAXBIT - DO K=1,MAXDIM - DO J=1,MDEG(K) ! STORED VALUES NEED NORMALIZATION - IU(K,J)=IU(K,J)*2**(MAXBIT-J) - ENDDO - DO J=1,MDEG(K)+1,MAXBIT ! USE RECCURENCE TO GET OTHER VALUES - IPP=IP(K) - I=IU(K,J-MDEG(K)) - I=IEOR(I,I/2**MDEG(K)) - DO L=MDEG(K)-1,1,-1 - IF (IAND(IPP,1).NE.0) I=IEOR(I,IU(K,J-L)) - IPP=IPP/2 - ENDDO - IU(K,J)=I - ENDDO - ENDDO - ENDIF - ENDIF ! CALCULATE THE NEXT VECTOR IN THE SEQUENCE - IM=IN - DO J=1,MAXBIT ! FIND THE RIGHTMOST ZERO BIT - IF (IAND(IM,1).EQ.0) GOTO 1 - IM=IM/2 - ENDDO -! PRINT *,'MAXBIT TOO SMALL IN SOBSEQ' - 1 IM=(J-1)*MAXDIM - DO K=1,MIN(OLDN,MAXDIM) !XOR THE - IX(K)=IEOR(IX(K),IV(IM+K)) - X(K)=IX(K)*FAC - ENDDO - IN=IN+1 ! INCREMENT COUNTER - - RETURN - END SUBROUTINE SOBSEQ - END MODULE KRBVRCMOD - - MODULE DKBVRCMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: DKBVRC -! - INTERFACE DKBVRC - MODULE PROCEDURE DKBVRC - END INTERFACE -! - INTERFACE DKSMRC - MODULE PROCEDURE DKSMRC - END INTERFACE -! - CONTAINS - SUBROUTINE DKBVRC( NDIM, MINVLS, MAXVLS, FUNCTN, ABSEPS, RELEPS, - & ABSERR, FINEST, INFORM ) -* -* Automatic Multidimensional Integration Subroutine -* -* AUTHOR: Alan Genz -* Department of Mathematics -* Washington State University -* Pulman, WA 99164-3113 -* Email: AlanGenz@wsu.edu -* -* Last Change: 1/15/03 -* -! revised pab June 2004 -! updated to F90 -* -* DKBVRC computes an approximation to the integral -* -* 1 1 1 -* I I ... I F(X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -* -* DKBVRC uses randomized Korobov rules for the first 100 variables. -* The primary references are -* "Randomization of Number Theoretic Methods for Multiple Integration" -* R. Cranley and T.N.L. Patterson, SIAM J Numer Anal, 13, pp. 904-14, -* and -* "Optimal Parameters for Multidimensional Integration", -* P. Keast, SIAM J Numer Anal, 10, pp.831-838. -* If there are more than 100 variables, the remaining variables are -* integrated using the rules described in the reference -* "On a Number-Theoretical Integration Method" -* H. Niederreiter, Aequationes Mathematicae, 8(1972), pp. 304-11. -* -*************** Parameters ******************************************** -****** Input parameters -* NDIM Number of variables, must exceed 1, but not exceed 1000 -* MINVLS Integer minimum number of function evaluations allowed. -* MINVLS must not exceed MAXVLS. If MINVLS < 0 then the -* routine assumes a previous call has been made with -* the same integrand and continues that calculation. -* MAXVLS Integer maximum number of function evaluations allowed. -* FUNCTN EXTERNALly declared user defined function to be integrated. -* It must have parameters (NDIM,Z), where Z is a real array -* of dimension NDIM. -* -* ABSEPS Required absolute accuracy. -* RELEPS Required relative accuracy. -****** Output parameters -* MINVLS Actual number of function evaluations used. -* ABSERR Estimated absolute accuracy of FINEST. -* FINEST Estimated value of integral. -* INFORM INFORM = 0 for normal exit, when -* ABSERR <= MAX(ABSEPS, RELEPS*ABS(FINEST)) -* and -* INTVLS <= MAXCLS. -* INFORM = 1 If MAXVLS was too small to obtain the required -* accuracy. In this case a value FINEST is returned with -* estimated absolute accuracy ABSERR. -* INFORM = 2 If NDIM>1000 or NDIM<1 -************************************************************************ - INTEGER, INTENT(IN) :: NDIM, MAXVLS - INTEGER, INTENT(INOUT) :: MINVLS - INTEGER, INTENT(OUT) :: INFORM - DOUBLE PRECISION, INTENT(IN) :: ABSEPS, RELEPS - DOUBLE PRECISION, INTENT(OUT) :: FINEST, ABSERR - INTEGER :: NP,PLIM,NLIM,KLIM,KLIMI,SAMPLS,I,INTVLS,MINSMP - PARAMETER ( PLIM = 28, NLIM = 1000, KLIM = 100, MINSMP = 8 ) - INTEGER P(PLIM), C(PLIM,KLIM-1) - DOUBLE PRECISION :: DIFINT, FINVAL, VARSQR, VAREST, VARPRD, VALUE - DOUBLE PRECISION, PARAMETER :: ONE= 1.D0,ZERO = 0.D0 - DOUBLE PRECISION X(2*NLIM), VK(NLIM) - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - SAVE P, C, SAMPLS, NP, VAREST - IF ( NDIM .GT. NLIM .OR. NDIM .LT. 1 ) THEN - INFORM = 2 - FINEST = ZERO - ABSERR = ONE - RETURN - ENDIF - INFORM = 1 - INTVLS = 0 - KLIMI = KLIM - IF ( MINVLS .GE. 0 ) THEN - FINEST = ZERO - VAREST = ZERO - SAMPLS = MINSMP - DO I = 1, PLIM - NP = I - IF ( MINVLS .LT. 2*SAMPLS*P(I) ) GO TO 10 - END DO - SAMPLS = MAX( MINSMP, MINVLS/( 2*P(NP) ) ) - ENDIF - 10 VK(1) = ONE/P(NP) - DO I = 2, NDIM - IF ( I .LE. KLIM ) THEN - VK(I) = MOD( C(NP, MIN(NDIM-1,KLIM-1))*VK(I-1), ONE ) - ELSE - VK(I) = INT( P(NP)*2**(DBLE(I-KLIM)/(NDIM-KLIM+1)) ) - VK(I) = MOD( VK(I)/P(NP), ONE ) - END IF - END DO - FINVAL = ZERO - VARSQR = ZERO - DO I = 1, SAMPLS - CALL DKSMRC( NDIM, KLIMI, VALUE, P(NP), VK, FUNCTN, X ) - DIFINT = ( VALUE - FINVAL )/DBLE(I) - FINVAL = FINVAL + DIFINT - VARSQR = DBLE( I - 2 )*VARSQR/DBLE(I) + DIFINT**2 - END DO - INTVLS = INTVLS + 2*SAMPLS*P(NP) - VARPRD = VAREST*VARSQR - FINEST = FINEST + ( FINVAL - FINEST )/( ONE + VARPRD ) - IF ( VARSQR .GT. ZERO ) VAREST = ( ONE + VARPRD )/VARSQR - ABSERR = 3.0D0*SQRT( VARSQR/( ONE + VARPRD ) ) - IF ( ABSERR .GT. MAX( ABSEPS, ABS(FINEST)*RELEPS ) ) THEN - IF ( NP .LT. PLIM ) THEN - NP = NP + 1 - ELSE - SAMPLS = MIN( 3*SAMPLS/2, ( MAXVLS - INTVLS )/( 2*P(NP) ) ) - SAMPLS = MAX( MINSMP, SAMPLS ) - ENDIF - IF ( INTVLS + 2*SAMPLS*P(NP) .LE. MAXVLS ) GO TO 10 - ELSE - INFORM = 0 - ENDIF - MINVLS = INTVLS -* -* Optimal Parameters for Lattice Rules -* - DATA P( 1),(C( 1,I),I = 1,99)/ 31, 12, 2*9, 13, 8*12, 3*3, 12, - & 2*7, 9*12, 3*3, 12, 2*7, 9*12, 3*3, 12, 2*7, 9*12, 3*3, 12, 2*7, - & 8*12, 7, 3*3, 3*7, 21*3/ - DATA P( 2),(C( 2,I),I = 1,99)/ 47, 13, 11, 17, 10, 6*15, - & 22, 2*15, 3*6, 2*15, 9, 13, 3*2, 13, 2*11, 10, 9*15, 3*6, 2*15, - & 9, 13, 3*2, 13, 2*11, 10, 9*15, 3*6, 2*15, 9, 13, 3*2, 13, 2*11, - & 2*10, 8*15, 6, 2, 3, 2, 3, 12*2/ - DATA P( 3),(C( 3,I),I = 1,99)/ 73, 27, 28, 10, 2*11, 20, - & 2*11, 28, 2*13, 28, 3*13, 16*14, 2*31, 3*5, 31, 13, 6*11, 7*13, - & 16*14, 2*31, 3*5, 11, 13, 7*11, 2*13, 11, 13, 4*5, 14, 13, 8*5/ - DATA P( 4),(C( 4,I),I = 1,99)/ 113, 35, 2*27, 36, 22, 2*29, - & 20, 45, 3*5, 16*21, 29, 10*17, 12*23, 21, 27, 3*3, 24, 2*27, - & 17, 3*29, 17, 4*5, 16*21, 3*17, 6, 2*17, 6, 3, 2*6, 5*3/ - DATA P( 5),(C( 5,I),I = 1,99)/ 173, 64, 66, 2*28, 2*44, 55, - & 67, 6*10, 2*38, 5*10, 12*49, 2*38, 31, 2*4, 31, 64, 3*4, 64, - & 6*45, 19*66, 11, 9*66, 45, 11, 7, 3, 3*2, 27, 5, 2*3, 2*5, 7*2/ - DATA P( 6),(C( 6,I),I = 1,99)/ 263, 111, 42, 54, 118, 20, - & 2*31, 72, 17, 94, 2*14, 11, 3*14, 94, 4*10, 7*14, 3*11, 7*8, - & 5*18, 113, 2*62, 2*45, 17*113, 2*63, 53, 63, 15*67, 5*51, 12, - & 51, 12, 51, 5, 2*3, 2*2, 5/ - DATA P( 7),(C( 7,I),I = 1,99)/ 397, 163, 154, 83, 43, 82, - & 92, 150, 59, 2*76, 47, 2*11, 100, 131, 6*116, 9*138, 21*101, - & 6*116, 5*100, 5*138, 19*101, 8*38, 5*3/ - DATA P( 8),(C( 8,I),I = 1,99)/ 593, 246, 189, 242, 102, - & 2*250, 102, 250, 280, 118, 196, 118, 191, 215, 2*121, - & 12*49, 34*171, 8*161, 17*14, 6*10, 103, 4*10, 5/ - DATA P( 9),(C( 9,I),I = 1,99)/ 907, 347, 402, 322, 418, - & 215, 220, 3*339, 337, 218, 4*315, 4*167, 361, 201, 11*124, - & 2*231, 14*90, 4*48, 23*90, 10*243, 9*283, 16, 283, 16, 2*283/ - DATA P(10),(C(10,I),I = 1,99)/ 1361, 505, 220, 601, 644, - & 612, 160, 3*206, 422, 134, 518, 2*134, 518, 652, 382, - & 206, 158, 441, 179, 441, 56, 2*559, 14*56, 2*101, 56, - & 8*101, 7*193, 21*101, 17*122, 4*101/ - DATA P(11),(C(11,I),I = 1,99)/ 2053, 794, 325, 960, 528, - & 2*247, 338, 366, 847, 2*753, 236, 2*334, 461, 711, 652, - & 3*381, 652, 7*381, 226, 7*326, 126, 10*326, 2*195, 19*55, - & 7*195, 11*132, 13*387/ - DATA P(12),(C(12,I),I = 1,99)/ 3079, 1189, 888, 259, 1082, 725, - & 811, 636, 965, 2*497, 2*1490, 392, 1291, 2*508, 2*1291, 508, - & 1291, 2*508, 4*867, 934, 7*867, 9*1284, 4*563, 3*1010, 208, - & 838, 3*563, 2*759, 564, 2*759, 4*801, 5*759, 8*563, 22*226/ - DATA P(13),(C(13,I),I = 1,99)/ 4621, 1763, 1018, 1500, 432, - & 1332, 2203, 126, 2240, 1719, 1284, 878, 1983, 4*266, - & 2*747, 2*127, 2074, 127, 2074, 1400, 10*1383, 1400, 7*1383, - & 507, 4*1073, 5*1990, 9*507, 17*1073, 6*22, 1073, 6*452, 318, - & 4*301, 2*86, 15/ - DATA P(14),(C(14,I),I = 1,99)/ 6947, 2872, 3233, 1534, 2941, - & 2910, 393, 1796, 919, 446, 2*919, 1117, 7*103, 2311, 3117, 1101, - & 2*3117, 5*1101, 8*2503, 7*429, 3*1702, 5*184, 34*105, 13*784/ - DATA P(15),(C(15,I),I = 1,99)/ 10427, 4309, 3758, 4034, 1963, - & 730, 642, 1502, 2246, 3834, 1511, 2*1102, 2*1522, 2*3427, - & 3928, 2*915, 4*3818, 3*4782, 3818, 4782, 2*3818, 7*1327, 9*1387, - & 13*2339, 18*3148, 3*1776, 3*3354, 925, 2*3354, 5*925, 8*2133/ - DATA P(16),(C(16,I),I = 1,99)/ 15641, 6610, 6977, 1686, 3819, - & 2314, 5647, 3953, 3614, 5115, 2*423, 5408, 7426, 2*423, - & 487, 6227, 2660, 6227, 1221, 3811, 197, 4367, 351, - & 1281, 1221, 3*351, 7245, 1984, 6*2999, 3995, 4*2063, 1644, - & 2063, 2077, 3*2512, 4*2077, 19*754, 2*1097, 4*754, 248, 754, - & 4*1097, 4*222, 754,11*1982/ - DATA P(17),(C(17,I),I = 1,99)/ 23473, 9861, 3647, 4073, 2535, - & 3430, 9865, 2830, 9328, 4320, 5913, 10365, 8272, 3706, 6186, - & 3*7806, 8610, 2563, 2*11558, 9421, 1181, 9421, 3*1181, 9421, - & 2*1181, 2*10574, 5*3534, 3*2898, 3450, 7*2141, 15*7055, 2831, - & 24*8204, 3*4688, 8*2831/ - DATA P(18),(C(18,I),I = 1,99)/ 35221, 10327, 7582, 7124, 8214, - & 9600, 10271, 10193, 10800, 9086, 2365, 4409, 13812, - & 5661, 2*9344, 10362, 2*9344, 8585, 11114, 3*13080, 6949, - & 3*3436, 13213, 2*6130, 2*8159, 11595, 8159, 3436, 18*7096, - & 4377, 7096, 5*4377, 2*5410, 32*4377, 2*440, 3*1199/ - DATA P(19),(C(19,I),I = 1,99)/ 52837, 19540, 19926, 11582, - & 11113, 24585, 8726, 17218, 419, 3*4918, 15701, 17710, - & 2*4037, 15808, 11401, 19398, 2*25950, 4454, 24987, 11719, - & 8697, 5*1452, 2*8697, 6436, 21475, 6436, 22913, 6434, 18497, - & 4*11089, 2*3036, 4*14208, 8*12906, 4*7614, 6*5021, 24*10145, - & 6*4544, 4*8394/ - DATA P(20),(C(20,I),I = 1,99)/ 79259, 34566, 9579, 12654, - & 26856, 37873, 38806, 29501, 17271, 3663, 10763, 18955, - & 1298, 26560, 2*17132, 2*4753, 8713, 18624, 13082, 6791, - & 1122, 19363, 34695, 4*18770, 15628, 4*18770, 33766, 6*20837, - & 5*6545, 14*12138, 5*30483, 19*12138, 9305, 13*11107, 2*9305/ - DATA P(21),(C(21,I),I = 1,99)/118891, 31929, 49367, 10982, 3527, - & 27066, 13226, 56010, 18911, 40574, 2*20767, 9686, 2*47603, - & 2*11736, 41601, 12888, 32948, 30801, 44243, 2*53351, 16016, - & 2*35086, 32581, 2*2464, 49554, 2*2464, 2*49554, 2464, 81, 27260, - & 10681, 7*2185, 5*18086, 2*17631, 3*18086, 37335, 3*37774, - & 13*26401, 12982, 6*40398, 3*3518, 9*37799, 4*4721, 4*7067/ - DATA P(22),(C(22,I),I = 1,99)/178349, 40701, 69087, 77576, 64590, - & 39397, 33179, 10858, 38935, 43129, 2*35468, 5279, 2*61518, 27945, - & 2*70975, 2*86478, 2*20514, 2*73178, 2*43098, 4701, - & 2*59979, 58556, 69916, 2*15170, 2*4832, 43064, 71685, 4832, - & 3*15170, 3*27679, 2*60826, 2*6187, 5*4264, 45567, 4*32269, - & 9*62060, 13*1803, 12*51108, 2*55315, 5*54140, 13134/ - DATA P(23),(C(23,I),I = 1,99)/267523, 103650, 125480, 59978, - & 46875, 77172, 83021, 126904, 14541, 56299, 43636, 11655, - & 52680, 88549, 29804, 101894, 113675, 48040, 113675, - & 34987, 48308, 97926, 5475, 49449, 6850, 2*62545, 9440, - & 33242, 9440, 33242, 9440, 33242, 9440, 62850, 3*9440, - & 3*90308, 9*47904, 7*41143, 5*36114, 24997, 14*65162, 7*47650, - & 7*40586, 4*38725, 5*88329/ - DATA P(24),(C(24,I),I = 1,99)/401287, 165843, 90647, 59925, - & 189541, 67647, 74795, 68365, 167485, 143918, 74912, - & 167289, 75517, 8148, 172106, 126159,3*35867, 121694, - & 52171, 95354, 2*113969, 76304, 2*123709, 144615, 123709, - & 2*64958, 32377, 2*193002, 25023, 40017, 141605, 2*189165, - & 141605, 2*189165, 3*141605, 189165, 20*127047, 10*127785, - & 6*80822, 16*131661, 7114, 131661/ - DATA P(25),(C(25,I),I = 1,99)/601943, 130365, 236711, 110235, - & 125699, 56483, 93735, 234469, 60549, 1291, 93937, - & 245291, 196061, 258647, 162489, 176631, 204895, 73353, - & 172319, 28881, 136787,2*122081, 275993, 64673, 3*211587, - & 2*282859, 211587, 242821, 3*256865, 122203, 291915, 122203, - & 2*291915, 122203, 2*25639, 291803, 245397, 284047, - & 7*245397, 94241, 2*66575, 19*217673, 10*210249, 15*94453/ - DATA P(26),(C(26,I),I = 1,99)/902933, 333459, 375354, 102417, - & 383544, 292630, 41147, 374614, 48032, 435453, 281493, 358168, - & 114121, 346892, 238990, 317313, 164158, 35497, 2*70530, 434839, - & 3*24754, 393656, 2*118711, 148227, 271087, 355831, 91034, - & 2*417029, 2*91034, 417029, 91034, 2*299843, 2*413548, 308300, - & 3*413548, 3*308300, 413548, 5*308300, 4*15311, 2*176255, 6*23613, - & 172210, 4* 204328, 5*121626, 5*200187, 2*121551, 12*248492, - & 5*13942/ - DATA P(27), (C(27,I), I = 1,99)/ 1354471, 500884, 566009, 399251, - & 652979, 355008, 430235, 328722, 670680, 2*405585, 424646, - & 2*670180, 641587, 215580, 59048, 633320, 81010, 20789, 2*389250, - & 2*638764, 2*389250, 398094, 80846, 2*147776, 296177, 2*398094, - & 2*147776, 396313, 3*578233, 19482, 620706, 187095, 620706, - & 187095, 126467, 12*241663, 321632, 2*23210, 3*394484, 3*78101, - & 19*542095, 3*277743, 12*457259/ - DATA P(28), (C(28,I), I = 1, 99)/ 2031713, 858339, 918142, 501970, - & 234813, 460565, 31996, 753018, 256150, 199809, 993599, 245149, - & 794183, 121349, 150619, 376952, 2*809123, 804319, 67352, 969594, - & 434796, 969594, 804319, 391368, 761041, 754049, 466264, 2*754049, - & 466264, 2*754049, 282852, 429907, 390017, 276645, 994856, 250142, - & 144595, 907454, 689648, 4*687580, 978368, 687580, 552742, 105195, - & 942843, 768249, 4*307142, 7*880619, 11*117185, 11*60731, - & 4*178309, 8*74373, 3*214965/ -* - END SUBROUTINE DKBVRC -* - SUBROUTINE DKSMRC( NDIM, KLIM, SUMKRO, PRIME, VK, FUNCTN, X ) - INTEGER, INTENT(IN):: NDIM, KLIM, PRIME - DOUBLE PRECISION, INTENT(OUT) :: SUMKRO - DOUBLE PRECISION, DIMENSION(:), INTENT(INOUT) :: VK,X - INTEGER :: K, J, JP, NK - DOUBLE PRECISION :: ONE, XT, MVNUNI - PARAMETER ( ONE = 1.d0 ) - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - SUMKRO = 0.D0 -* -* Randomize Variable Order -* - NK = MIN( NDIM, KLIM ) - DO J = 1, NK - 1 - CALL random_number(MVNUNI) -! JP = J + MVNUNI()*( NK + 1 - J ) - JP = J + NINT(MVNUNI*DBLE( NK - J )) ! pab 12 May 2004 - - XT = VK(J) - VK(J) = VK(JP) - VK(JP) = XT - END DO -* -* Determine Random Shifts for each Variable -* - CALL random_number(X(NDIM+1:2*NDIM)) - DO K = 1, PRIME - X(1:NDIM) = ABS( 2.d0*MOD( DBLE(K)*VK(1:NDIM) + - & X(NDIM+1:2*NDIM), ONE ) - ONE ) -! DO J = 1, NDIM -! X(J) = ABS( 2*MOD( K*VK(J) + X(NDIM+J), ONE ) - ONE ) -! END DO - SUMKRO = SUMKRO + ( FUNCTN(NDIM,X) - SUMKRO )/DBLE( 2*K - 1 ) - X(1:NDIM) = ONE - X(1:NDIM) - SUMKRO = SUMKRO + ( FUNCTN(NDIM,X) - SUMKRO )/DBLE( 2*K ) - END DO - END SUBROUTINE DKSMRC - END MODULE DKBVRCMOD - - MODULE PRECISIONMOD - IMPLICIT NONE - PUBLIC -! Note double precision is the fastest choice for x86 machines -! double (15,307) single (6,37) precision constants - INTEGER, PARAMETER :: gP = SELECTED_REAL_KIND(15,307) - END MODULE PRECISIONMOD - - MODULE SSOBOLMOD - USE PRECISIONMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: initSobol, sobolSeq, sobnied - -! BLOCK DATA BDSOBL -! -! INITIALIZES LABELLED COMMON /SOBDAT/ -! FOR "INSOBL". -! -! THE ARRAY POLY GIVES SUCCESSIVE PRIMITIVE -! POLYNOMIALS CODED IN BINARY, E.G. -! 45 = 100101 -! HAS BITS 5, 2, AND 0 SET (COUNTING FROM THE -! RIGHT) AND THEREFORE REPRESENTS -! X**5 + X**2 + X**0 -! -! THESE POLYNOMIALS ARE IN THE ORDER USED BY -! SOBOL IN USSR COMPUT. MATHS. MATH. PHYS. 16 (1977), -! 236-242. A MORE COMPLETE TABLE IS GIVEN IN SOBOL AND -! LEVITAN, THE PRODUCTION OF POINTS UNIFORMLY -! DISTRIBUTED IN A MULTIDIMENSIONAL CUBE (IN RUSSIAN), -! PREPRINT IPM AKAD. NAUK SSSR, NO. 40, MOSCOW 1976. -! -! THE INITIALIZATION OF THE ARRAY mVINIT IS FROM THE -! LATTER PAPER. FOR A POLYNOMIAL OF DEGREE M, M INITIAL -! VALUES ARE NEEDED : THESE ARE THE VALUES GIVEN HERE. -! SUBSEQUENT VALUES ARE CALCULATED IN "INSOBL". -! -! ASSUME WE ARE WORKING ON A COMPUTER WITH -! WORD LENGTH AT LEAST mMaxBit BITS EXCLUDING SIGN. - integer :: mI - integer, parameter :: mMaxBit = 31 - integer, parameter :: mMaxDim = 40 - integer, parameter :: mMaxAtMost = 2**(mMaxBit-1) -!COMMON SOBOL -! mSV TABLE OF DIRECTION NUMBERS -! mS DIMENSION -! mMAXCOL LAST COLUMN OF V TO BE USED -! mCOUNT SEQUENCE NUMBER OF THIS CALL -! mLASTQ NUMERATORS FOR LAST VECTOR GENERATED -! mRECIPD (1/DENOMINATOR) FOR THESE NUMERATORS - INTEGER, dimension(mMaxDim,mMaxBit), SAVE :: mSV - INTEGER, dimension(mMaxDim), SAVE :: mLASTQ - INTEGER, SAVE :: mS,mMAXCOL,mCOUNT,mATMOST - REAL(KIND=gP), save :: mRECIPD -! COMMON SOBDAT - INTEGER, save, dimension(2:mMaxDim) :: mPOLY - integer, save, dimension(2:mMaxDim,8) :: mVINIT - - DATA mPOLY /3,7,11,13,19,25,37,59,47, - & 61,55,41,67,97,91,109,103,115,131, - & 193,137,145,143,241,157,185,167,229,171, - & 213,191,253,203,211,239,247,285,369,299/ -! - DATA (mVINIT(mI,1),mI=2,40) /39*1/ - DATA (mVINIT(mI,2),mI=3,40) /1,3,1,3,1,3,3,1, - & 3,1,3,1,3,1,1,3,1,3, - & 1,3,1,3,3,1,3,1,3,1, - & 3,1,1,3,1,3,1,3,1,3/ - DATA (mVINIT(mI,3),mI=4,40) /7,5,1,3,3,7,5, - & 5,7,7,1,3,3,7,5,1,1, - & 5,3,3,1,7,5,1,3,3,7, - & 5,1,1,5,7,7,5,1,3,3/ - DATA (mVINIT(mI,4),mI=6,40) /1,7,9,13,11, - & 1,3,7,9,5,13,13,11,3,15, - & 5,3,15,7,9,13,9,1,11,7, - & 5,15,1,15,11,5,3,1,7,9/ - DATA (mVINIT(mI,5),mI=8,40) /9,3,27, - & 15,29,21,23,19,11,25,7,13,17, - & 1,25,29,3,31,11,5,23,27,19, - & 21,5,1,17,13,7,15,9,31,9/ - DATA (mVINIT(mI,6),mI=14,40) /37,33,7,5,11,39,63, - & 27,17,15,23,29,3,21,13,31,25, - & 9,49,33,19,29,11,19,27,15,25/ - DATA (mVINIT(mI,7),mI=20,40) /13, - & 33,115,41,79,17,29,119,75,73,105, - & 7,59,65,21,3,113,61,89,45,107/ - DATA (mVINIT(mI,8),mI=38,40) /7,23,39/ - - INTERFACE getMSBP - MODULE PROCEDURE getMSBP - END INTERFACE - - INTERFACE initSobol - MODULE PROCEDURE initSobol - END INTERFACE - - INTERFACE GENSCRML - MODULE PROCEDURE GENSCRML - END INTERFACE - - INTERFACE GENSCRMU - MODULE PROCEDURE GENSCRMU - END INTERFACE - - INTERFACE sobolSeq - MODULE PROCEDURE sobolSeq - END INTERFACE - - INTERFACE sobnied - MODULE PROCEDURE sobnied - END INTERFACE - - INTERFACE dksmrc - MODULE PROCEDURE dksmrc - END INTERFACE - - INTERFACE uni - MODULE PROCEDURE uni - END INTERFACE - - CONTAINS - - FUNCTION getMSBP(J) result (nb) -!getMSBP Returns the Most Significant Bit position -! -! CALL ix = getMSBP(x); -! -! ix = Most Significant Bit position -! x = number -! -! getMSBP calculates the most significant bit position in X that contains a -! one, i.e., -! MSB(X) = max(i|2^i<=x) for X~=0 -! - integer, intent(in) :: J - integer :: nb - integer :: I - nb = 0 - I = J/2 - DO WHILE (I>0) - nb = nb + 1 - I = I / 2 - ENDDO - end function getMSBP - - SUBROUTINE initSobol(INFORM,TAUS,NDIM, ATMOST, - * NUMDS,IFLAG) -! InitSobol Initializes the sobol sequence -! Inputs: -! NDIM : Number of dimensions -! ATMOST : Maximum sequence length, i.e., upper bound on the number -! of calls the user intends to make on "ssobseq" -! NUMDS : Number of Digits to Scramble if IFLAG==1 or IFLAG==3 -! IFLAG : integer defining scrambling of sequences: -! 0 : No Scrambling -! 1 : Owen type Scrambling -! 2 : Faure-Tezuka type Scrambling -! 3 : Owen + Faure-Tezuka type Scrambling -! Uses the member variables: mPOLY and mVINIT -! Outputs: -! INFORM = 0 If no error occurred otherwise -! 2 If NDIM < 1 .OR. mMaxDim < NDIM -! 3 If ATMOST < 1 .OR. mMaxAtMost <= ATMOST -! 4 If ((IFLAG==1 OR IFLAG==3) AND (mMaxBit < NUMDS)) -! TAUS = Defines "FAVORABLE" values as -! discussed in BRATLEY/FOX. These have the form -! N = 2**K WHERE K .GE. (TAUS+NDIM-1) for integration -! and k .gt. taus for global optimization. -! If NDIM>12 then TAUS = -1 -! Initializes the member variables: -! mSV, mS, mMAXCOL, mCOUNT, mLASTQ, mRECIPD, mATMOST -! Used in SOBOLSEQ -! -! InitSobol initializes member variables for scrambled sobol sequence -! -! -! THIS IS MODIFIED ROUTINE OF "INSOBL". -! -! NEXT CHECK "ATMOST", AN UPPER BOUND ON THE NUMBER -! OF CALLS THE USER INTENDS TO MAKE ON "GOSOBL". IF -! THIS IS POSITIVE AND LESS THAN mMaxAtMost = 2**(mMaxBit-1), -! THEN FLAG(2) = .TRUE. -! (WE ASSUME WE ARE WORKING ON A COMPUTER WITH -! WORD LENGTH AT LEAST mMaxBit BITS EXCLUDING SIGN.) -! THE NUMBER OF COLUMNS OF THE ARRAY V WHICH -! ARE INITIALIZED IS -! mMAXCOL = NUMBER OF BITS IN ATMOST. -! IN "GOSOBL" WE CHECK THAT THIS IS NOT EXCEEDED. -! -! THE LEADING ELEMENTS OF EACH ROW OF V ARE -! INITIALIZED USING "mVINIT" FROM "BDSOBL". -! EACH ROW CORRESPONDS TO A PRIMITIVE POLYNOMIAL -! (AGAIN, SEE "BDSOBL"). IF THE POLYNOMIAL HAS -! DEGREE M, ELEMENTS AFTER THE FIRST M ARE CALCULATED. -! -! THE NUMBERS IN V ARE ACTUALLY BINARY FRACTIONS. -! LSM ARE LOWER TRIAUGULAR SCRAMBLING MATRICES. -! USM ARE UPPER TRIAUGULAR SCRMABLING MATRIX. -! mSV ARE SCAMBLING GENERATING MATRICES AND THE NUMBERS -! ARE BINARY FRACTIONS. -! "mRECIPD" HOLDS 1/(THE COMMON DENOMINATOR OF ALL -! OF THEM). -! -! -! "INSSOBL" IMPLICITLY COMPUTES THE FIRST SHIFTED -! VECTOR "mLASTQ", AND RETURN IT TO THE CALLING -! PROGRAM. SUBSEQUENT VECTORS COME FROM "GOSSOBL". -! "mLASTQ" HOLDS NUMERATORS OF THE LAST VECTOR GENERATED. -! -! - integer, intent(in) :: NDIM,ATMOST,NUMDS,IFLAG - INTEGER, INTENT(OUT) :: INFORM,TAUS -! REAL(kind=gP), dimension(:), intent(out) :: QUASI - INTEGER, dimension(mMaxDim,mMaxBit) :: V, LSM - integer, dimension(mMaxBit,mMaxBit) :: USM - integer, dimension(mMaxDim,mMaxBit,mMaxBit) :: TV - integer, dimension(mMaxDim) :: SHIFT - integer, dimension(mMaxBit) :: USHIFT - INTEGER, dimension(13),save :: TAU - INTEGER I,J,K,P,M,NEWV,L,PP - INTEGER TEMP1,TEMP2,TEMP3,TEMP4,MAXX - REAL(KIND=gP) :: LL - LOGICAL, dimension(8) :: INCLUD -! EXTERNAL IEOR -! COMMON /SOBDAT/ mPOLY,mVINIT -! COMMON /SOBOL/ mS,mMAXCOL,mSV,mCOUNT,mLASTQ,mRECIPD -! SAVE /SOBDAT/,/SOBOL/ - DATA TAU /0,0,1,3,5,8,11,15,19,23,27,31,35/ - inform = 0 - mMAXCOL = 0 - mS = NDIM - mATMOST = ATMOST - IF (mS < 1 .OR. mMaxDim < mS) THEN - INFORM = 2 - RETURN - ENDIF - IF ( mATMOST < 1 .OR. mMaxAtMost <= mATMOST) THEN - INFORM = 3 - RETURN - ENDIF - if ((IFLAG.EQ.1 .or. IFLAG.EQ.3) .AND. (mMaxBit < NUMDS)) then - INFORM = 4 - return - endif - IF (mS .LE. 13) THEN - TAUS = TAU(mS) - ELSE - TAUS = -1 -! RETURN A DUMMY VALUE TO THE CALLING PROGRAM - ENDIF - -! FIND NUMBER OF BITS IN ATMOST - mMAXCOL = getMSBP(mATMOST)+1 - - -! INITIALIZE V - V(1,1:mMAXCOL) = 1 - DO I = 2, mS ! 100 -! FIND DEGREE OF POLYNOMIAL I FROM BINARY ENCODING - - J = mPOLY(I) - M = getMSBP(J) - -! WE EXPAND THIS BIT PATTERN TO SEPARATE COMPONENTS -! OF THE LOGICAL ARRAY INCLUD. - - DO K = M, 1, -1 - INCLUD(K) = (MOD(J,2) .EQ. 1) - J = J / 2 - enddo ! K - -! THE LEADING ELEMENTS OF ROW I COME FROM mVINIT - V(I,1:M) = mVINIT(I, 1:M) -! -! CALCULATE REMAINING ELEMENTS OF ROW I AS EXPLAINED -! IN BRATLEY AND FOX, SECTION 2 - DO J = M+1, mMAXCOL - NEWV = V(I, J-M) - L = 1 - DO K = 1, M - L = 2 * L - IF (INCLUD(K)) NEWV = IEOR(NEWV, L * V(I, J-K)) - enddo ! K - V(I,J) = NEWV - enddo ! J - enddo ! I -! -! MULTIPLY COLUMNS OF V BY APPROPRIATE POWER OF 2 -! - L = 1 - DO J = mMAXCOL-1, 1, -1 - L = 2 * L - V(1:mS,J) = V(1:mS,J) * L - enddo ! J -! -! COMPUTING GENERATOR MATRICES OF USER CHOICE -! - IF (IFLAG .EQ. 0) THEN - FORALL (I = 1:mS, J = 1:mMAXCOL) mSV(I,J) = V(I,J) - SHIFT(1:mS) = 0 - LL = DBLE(2**(mMAXCOL)) - ELSE - IF ((IFLAG .EQ. 1) .OR. (IFLAG .EQ. 3)) THEN - CALL GENSCRML(NUMDS,LSM,SHIFT) - DO I = 1,mS - DO J = 1,mMAXCOL - L = 1 - TEMP2 = 0 - DO P = NUMDS,1,-1 - TEMP1 = 0 - DO K = 1,mMAXCOL - TEMP1 = TEMP1+ - & (IBITS(LSM(I,P),K-1,1)*IBITS(V(I,J),K-1,1)) - enddo ! K - TEMP1 = MOD(TEMP1,2) - TEMP2 = TEMP2+TEMP1*L - L = 2 * L - enddo ! P - mSV(I,J) = TEMP2 - enddo ! J - enddo ! I - LL= DBLE(2**(NUMDS)) - ENDIF - IF ((IFLAG .EQ. 2) .OR. (IFLAG .EQ. 3)) THEN - CALL GENSCRMU(USM,USHIFT) - IF (IFLAG .EQ. 2) THEN - MAXX = mMAXCOL - ELSE - MAXX = NUMDS - ENDIF - DO I = 1,mS - DO J = 1,mMAXCOL - P = MAXX - DO K = 1,MAXX - IF (IFLAG .EQ. 2) THEN - TV(I,P,J) = IBITS(V(I,J),K-1,1) - ELSE - TV(I,P,J) = IBITS(mSV(I,J),K-1,1) - ENDIF - P = P-1 - enddo ! K - enddo ! J - DO PP = 1,mMAXCOL - TEMP2 = 0 - TEMP4 = 0 - L = 1 - DO J = MAXX,1,-1 - TEMP1 = 0 - TEMP3 = 0 - DO P = 1,mMAXCOL - TEMP1 = TEMP1 + TV(I,J,P)*USM(P,PP) - IF (PP .EQ. 1) THEN - TEMP3 = TEMP3 + TV(I,J,P)*USHIFT(P) - ENDIF - enddo ! P - TEMP1 = MOD(TEMP1,2) - TEMP2 = TEMP2 + TEMP1*L - IF (PP .EQ. 1) THEN - TEMP3 = MOD(TEMP3,2) - TEMP4 = TEMP4 + TEMP3*L - ENDIF - L = 2*L - enddo ! J - mSV(I,PP) = TEMP2 - IF (PP .EQ. 1) THEN - IF (IFLAG .EQ. 3) THEN - SHIFT(I) = IEOR(TEMP4, SHIFT(I)) - ELSE - SHIFT(I) = TEMP4 - ENDIF - ENDIF - enddo ! PP - enddo ! I - LL = DBLE(2**(MAXX)) - ENDIF - ENDIF -! -! mRECIPD IS 1/(COMMON DENOMINATOR OF THE ELEMENTS IN V) -! - mRECIPD = 1.0_gP / LL - -! SET UP FIRST VECTOR AND VALUES FOR "SOBOLSEQ" - mCOUNT = 0 - mLASTQ(1:mS) = SHIFT(1:mS) -! QUASI(1:mS) = DBLE(mLASTQ(1:mS))*mRECIPD - RETURN - END subroutine initSobol - FUNCTION UNI() result (val) -* -* Random number generator, adapted from F. James -* "A Review of Random Number Generators" -* Comp. Phys. Comm. 60(1990), pp. 329-344. -* - real(kind=gP) SEEDS(24), TWOM24, CARRY,val - PARAMETER ( TWOM24 = 1.0_gP/16777216.0_gP ) - INTEGER I, J - SAVE I, J, CARRY, SEEDS - DATA I, J, CARRY / 24, 10, 0.0 / - DATA SEEDS / - & 0.8804418, 0.2694365, 0.0367681, 0.4068699, 0.4554052, 0.2880635, - & 0.1463408, 0.2390333, 0.6407298, 0.1755283, 0.7132940, 0.4913043, - & 0.2979918, 0.1396858, 0.3589528, 0.5254809, 0.9857749, 0.4612127, - & 0.2196441, 0.7848351, 0.4096100, 0.9807353, 0.2689915, 0.5140357/ -! & 0.8804418_gP, 0.2694365_gP, 0.0367681_gP, 0.4068699_gP, -! & 0.4554052_gP, 0.2880635_gP, -! & 0.1463408_gP, 0.2390333_gP, 0.6407298_gP, 0.1755283_gP, -! & 0.7132940_gP, 0.4913043_gP, -! & 0.2979918_gP, 0.1396858_gP, 0.3589528_gP, 0.5254809_gP, -! & 0.9857749_gP, 0.4612127_gP, -! & 0.2196441_gP, 0.7848351_gP, 0.4096100_gP, 0.9807353_gP, -! & 0.2689915_gP, 0.5140357_gP/ - - CALL random_number(val) - return - val = SEEDS(I) - SEEDS(J) - CARRY - IF ( val .LT. 0.0_gP ) THEN - val = val + 1.0_gP - CARRY = TWOM24 - ELSE - CARRY = 0.0_gP - ENDIF - SEEDS(I) = val - I = 24 - MOD( 25-I, 24 ) - J = 24 - MOD( 25-J, 24 ) - RETURN - END function uni - SUBROUTINE GENSCRML(NUMDS,LSM,SHIFT) -! GENERATING LOWER TRIANGULAR SCRMABLING MATRICES AND SHIFT VECTORS. -! INPUTS : -! FROM INSSOBL : NUMDS -! FROM BLOCK DATA "SOBOL" : mS, mMAXCOL, -! -! OUTPUTS : -! TO initSobol : LSM, SHIFT - integer,intent(in) :: NUMDS - integer, dimension(mMaxDim,mMaxBit), intent(inout) :: LSM - integer, dimension(mMaxDim), intent(inout) :: SHIFT - INTEGER :: P,I,J,TEMP,STEMP,L,LL -! REAL(KIND=gP) :: UNI -! COMMON /SOBOL/ mS,mMAXCOL -! SAVE /SOBOL/ - - DO 10 P = 1,mS - SHIFT(P) = 0 - L = 1 - DO 20 I = NUMDS,1,-1 - LSM(P,I) = 0 -! CALL random_number(UNI) - STEMP = MOD((int(UNI()*1000.0_gP)),2) - SHIFT(P) = SHIFT(P)+STEMP*L - L = 2 * L - LL = 1 - DO 30 J = mMAXCOL,1,-1 - IF (J .EQ. I) THEN - TEMP = 1 - ELSE IF (J .LT. I) THEN -! CALL random_number(UNI) - TEMP = MOD((int(UNI()*1000.0_gP)),2) - ELSE - TEMP = 0 - ENDIF - LSM(P,I) = LSM(P,I) + TEMP*LL - LL = 2 * LL - 30 CONTINUE - 20 CONTINUE - 10 CONTINUE - RETURN - END SUBROUTINE GENSCRML - - SUBROUTINE GENSCRMU(USM,USHIFT) - -! GENERATING UPPER TRIANGULAR SCRMABLING MATRICES AND -! SHIFT VECTORS. -! INPUTS : -! FROM BLOCK DATA "SOBOL" : mS, mMAXCOL, -! -! OUTPUTS : -! TO INSSOBL : USM, USHIFT - integer, dimension(mMaxBit,mMaxBit), intent(inout) :: USM - integer, dimension(mMaxBit), intent(inout) :: USHIFT - INTEGER I,J,TEMP -! REAL(KIND=gP) :: UNI -! COMMON /SOBOL/ mS,mMAXCOL -! SAVE /SOBOL/ - - DO 20 I = 1,mMAXCOL -! CALL random_number(UNI) - USHIFT(I) = MOD((int(UNI()*1000.0_gP)),2) - DO 30 J = 1,mMAXCOL - IF (J .EQ. I) THEN - TEMP = 1 - ELSE IF (J .GT. I) THEN -! CALL random_number(UNI) - TEMP = MOD((int(UNI()*1000.0_gP)),2) - ELSE - TEMP = 0 - ENDIF - USM(I,J) = TEMP - 30 CONTINUE - 20 CONTINUE - RETURN - END SUBROUTINE GENSCRMU - - SUBROUTINE sobolSeq(QUASI,INFORM) -!SOBOLSEQ GENERATES A NEW QUASIRANDOM VECTOR WITH EACH CALL -! -! IT ADAPTS THE IDEAS OF ANTONOV AND SALEEV, -! USSR COMPUT. MATHS. MATH. PHYS. 19 (1980), -! 252 - 256 -! -! The user must call "initSobol" before calling -! "sobolSeq". After calling "initsobol", test -! if inform == 0. if inform>0 then -! do not call "sobolSeq". -! "sobolSeq" checks that the user does not make more calls -! than he said he would : see the comments -! to "initSobol". -! -! INPUTS: -! FROM USER'S CALLING PROGRAM: -! NONE -! -! FROM LABELLED COMMON /SOBOL/: -! mSV TABLE OF DIRECTION NUMBERS -! mS DIMENSION -! mMAXCOL LAST COLUMN OF mSV TO BE USED -! mCOUNT SEQUENCE NUMBER OF THIS CALL -! mLASTQ NUMERATORS FOR LAST VECTOR GENERATED -! mRECIPD (1/DENOMINATOR) FOR THESE NUMERATORS -! - REAL(KIND=gP), dimension(:), intent(out) :: QUASI - integer, intent(inout) :: inform - INTEGER :: I,L -! INTEGER mSV(40,31),mS,mMAXCOL,mCOUNT,mLASTQ(40) -! COMMON /SOBOL/ S,mMAXCOL,mSV,mCOUNT,mLASTQ,mRECIPD -! SAVE /SOBOL/ -! - -! FORALL ( I = 1:mS) -! QUASI(I) = DBLE(mLASTQ(I)) * mRECIPD -! END FORALL - QUASI(1:mS) = DBLE(mLASTQ(1:mS))*mRECIPD -! FIND POSITION OF RIGHTMOST ZERO BIT IN mCOUNT - L = 1 - I = mCOUNT - do while (MOD(I,2) .EQ. 1) - I = I / 2 - L = L + 1 - ENDDO -! CHECK THAT THE USER IS NOT CHEATING - IF (L > mMAXCOL) THEN - INFORM = 4 -! WARNING: Reached the end of the sobol sequence -! Next call will wrap around and return the same numbers -! as for mCOUNT = 0 -! Call initSobol to increase mATMOST before calling sobolseq again. - else - INFORM = 0 -! Calculate the new components of quasi, -! first the numerators - FORALL ( I = 1:mS) - mLASTQ(I) = IEOR(mLASTQ(I), mSV(I,L)) - END FORALL - mCOUNT = mCOUNT + 1 - ENDIF - RETURN - END SUBROUTINE sobolSeq - - -!*********************************************************** -! MAIN INTEGRATION ROUTINE SOBNIED -!*********************************************************** - - SUBROUTINE SOBNIED( NDIM, MINVLS, MAXVLS, FUNCTN, ABSEPS, RELEPS, - & ABSERR, FINEST, INFORM ) - use precisionmod - implicit none -* -* Automatic Multidimensional Integration Subroutine -* -* AUTHOR: Per A. Brodtkorb -! Norwegian Defence Research Establishment -! P.O. Box 115 -! N-3191 Horten -! Norway -! Email: Per.Brodtkorb@ffi.no -! -* Last Change: 6/19/2004 -* -* SOBNIED computes an approximation to the integral -* -* 1 1 1 -* I I ... I F(X) dx(NDIM)...dx(2)dx(1) -* 0 0 0 -* -* -* SOBNIED uses scrambled SOBOL sequences for the first 40 variables. -* The primary reference is - -* If there are more than 40 variables, the remaining variables are -* integrated using the rule described in the reference -* "On a Number-Theoretical Integration Method" -* H. Niederreiter, Aequationes Mathematicae, 8(1972), pp. 304-11. -* -*************** Parameters ******************************************** -****** Input parameters -* NDIM Number of variables, must exceed 1, but not exceed 100 -* MINVLS Integer minimum number of function evaluations allowed. -* MINVLS must not exceed MAXVLS. If MINVLS < 0 then the -* routine assumes a previous call has been made with -* the same integrand and continues that calculation. -* MAXVLS Integer maximum number of function evaluations allowed. -* FUNCTN EXTERNALly declared user defined function to be integrated. -* It must have parameters (NDIM,Z), where Z is a real array -* of dimension NDIM. -* -* ABSEPS Required absolute accuracy. -* RELEPS Required relative accuracy. -****** Output parameters -* MINVLS Actual number of function evaluations used. -* ABSERR Estimated absolute accuracy of FINEST. -* FINEST Estimated value of integral. -* INFORM INFORM = 0 for normal exit, when -* ABSERR <= MAX(ABSEPS, RELEPS*ABS(FINEST)) -* and -* INTVLS <= MAXCLS. -* INFORM = 1 If MAXVLS was too small to obtain the required -* accuracy. In this case a value FINEST is returned with -* estimated absolute accuracy ABSERR. -* INFORM = 2 If NDIM>1040 or NDIM<1 -************************************************************************ - INTEGER, INTENT(IN) :: NDIM, MAXVLS - INTEGER, INTENT(INOUT) :: MINVLS - INTEGER, INTENT(OUT) :: INFORM - REAL(KIND=gP), INTENT(IN) :: ABSEPS, RELEPS - REAL(KIND=gP), INTENT(OUT) :: FINEST, ABSERR - INTEGER :: NP,PLIM,NLIM,KLIM,KLIMI,SAMPLS,I,INTVLS,MINSMP,NK - integer :: numRep, J, TAUS - INTEGER, parameter :: NUMDS=30,IFLAG=1 - PARAMETER ( PLIM = 28, NLIM = 1040, KLIM = mMaxDim, MINSMP = 8 ) - INTEGER , DIMENSION(PLIM) :: P - REAL(KIND=gP) :: DIFINT,FINVAL,VARSQR,VAREST,VARPRD,VALUE - REAL(KIND=gP), PARAMETER :: ONE = 1.D0 , ZERO = 0.D0 - REAL(KIND=gP), DIMENSION(2*NLIM) :: X = 0.d0 - REAL(KIND=gP), DIMENSION(NLIM) :: VK = 0.d0 - logical :: NPtooSmall,errorTooLarge,numSamplesOk - INTERFACE - REAL(KIND=gP) FUNCTION FUNCTN(N,Z) - use precisionmod - REAL(KIND=gP),DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - DATA P / 31, 47, 73, 113, 173, 263, 397, 593, 907, 1361, - & 2053, 3079, 4621, 6947, 10427, 15641, 23473, 35221, - & 52837, 79259, 118891, 178349, 267523, 401287, 601943, - & 902933,1354471,2031713/ - SAVE P, SAMPLS, NP, VAREST - IF ( NDIM .GT. NLIM .OR. NDIM .LT. 1 ) THEN - INFORM = 2 - FINEST = ZERO - ABSERR = ONE - RETURN - ENDIF - NK = MIN( NDIM, KLIM ) - - - IF ( MINVLS >= 0 ) THEN - FINEST = ZERO - VAREST = ZERO - SAMPLS = MINSMP - NP = 1 - NPtooSmall = ( MINVLS >= 2*SAMPLS*P(NP) ) - do while(NPtooSmall .AND. NP= 2*SAMPLS*P(NP) ) - enddo - if (NPtooSmall) then - SAMPLS = MAX( MINSMP, MINVLS/( 2*P(NP) ) ) - endif - ENDIF - numRep = 1 !max(1,nint(MAXVLS/mMaxAtMost)) - - INFORM = 1 - INTVLS = 0 - KLIMI = KLIM - errorTooLarge = .TRUE. - do J = 1,numRep - CALL initSobol(inform,TAUS,NK,MAXVLS/numRep,NUMDS,IFLAG) - if (inform.ne.0) then - FINEST = ZERO - ABSERR = ONE - RETURN - endif - INFORM = 1 - numSamplesOk = ( INTVLS + 2*SAMPLS*P(NP) <= MAXVLS ) - do while (errorTooLarge .and. numSamplesOk) - DO I = 1, NDIM-NK - VK(I) = INT( P(NP)*2**(DBLE(I)/(NDIM-KLIM+1)) ) - VK(I) = MOD( VK(I)/P(NP), ONE ) - END DO - FINVAL = ZERO - VARSQR = ZERO - DO I = 1, SAMPLS - CALL DKSMRC( NDIM, KLIMI, VALUE, P(NP),VK, FUNCTN, X ) - DIFINT = ( VALUE - FINVAL )/DBLE(I) - FINVAL = FINVAL + DIFINT - VARSQR = DBLE( I - 2 )*VARSQR/DBLE(I) + DIFINT*DIFINT - END DO - INTVLS = INTVLS + 2*SAMPLS*P(NP) - VARPRD = VAREST*VARSQR - FINEST = FINEST + ( FINVAL - FINEST )/( ONE + VARPRD ) - IF ( VARSQR > ZERO ) VAREST = ( ONE + VARPRD )/VARSQR - ABSERR = 3.0_gP*SQRT( VARSQR/( ONE + VARPRD ) ) - errorTooLarge = (ABSERR > MAX(ABSEPS, ABS(FINEST)*RELEPS)) - IF ( errorTooLarge ) THEN - IF ( NP < PLIM ) THEN - NP = NP + 1 - ELSE - SAMPLS = MIN(3*SAMPLS/2, (MAXVLS - INTVLS)/(2*P(NP))) - SAMPLS = MAX( MINSMP, SAMPLS ) - ENDIF - numSamplesOk = ( INTVLS + 2*SAMPLS*P(NP) <= MAXVLS ) - ELSE - INFORM = 0 - ENDIF - enddo - enddo - MINVLS = INTVLS - END SUBROUTINE SOBNIED - SUBROUTINE DKSMRC( NDIM, KLIM, SUMKRO, PRIME, VK,FUNCTN, X ) - use precisionmod - implicit none - INTEGER, INTENT(IN):: NDIM, KLIM, PRIME - REAL(KIND=gP), INTENT(OUT) :: SUMKRO - REAL(KIND=gP), DIMENSION(:), INTENT(INOUT) :: VK,X - INTEGER :: K, NK, inform - REAL(KIND=gP) :: ONE, XT, MVNUNI - PARAMETER ( ONE = 1.0_gP ) - INTERFACE - REAL(KIND=gP) FUNCTION FUNCTN(N,Z) - use precisionmod - REAL(KIND=gP),DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - SUMKRO = 0.0_gP - NK = MIN( NDIM, KLIM ) -* Determine Random Shifts for each Variable - if (NK100 or NDIM<1 -************************************************************************ - IMPLICIT NONE - INTEGER, INTENT(IN) :: NDIM, MAXVLS - INTEGER, INTENT(INOUT) ::MINVLS - INTEGER, INTENT(OUT) ::INFORM - DOUBLE PRECISION, INTENT(IN) :: ABSEPS, RELEPS - DOUBLE PRECISION, INTENT(OUT) :: FINEST, ABSERR -! Local variables: - INTEGER :: NP, PLIM, NLIM, SAMPLS, I, INTVLS, MINSMP - PARAMETER ( PLIM = 20, NLIM = 100, MINSMP = 6 ) - INTEGER, DIMENSION(PLIM,NLIM) :: C - INTEGER, DIMENSION(PLIM) :: P - DOUBLE PRECISION :: DIFINT, FINVAL, VARSQR, VAREST, VARPRD, VALUE - DOUBLE PRECISION, DIMENSION(NLIM) :: ALPHA, X, VK - DOUBLE PRECISION :: ONE - PARAMETER ( ONE = 1.d0 ) - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - DATA P /113, 173, 263,397,593,907,1361,2053,3079,4621,6947, - & 10427, 15641,23473, 35221, 52837, 79259, - & 118891, 178349, 267523 / - DATA ( C( 1,I), I = 1, 99 ) / - & 42, 54, 55, 32, 13, 26, 26, 13, 26, - & 14, 13, 26, 35, 2, 2, 2, 2, 56, - & 28, 7, 7, 28, 4, 49, 4, 40, 48, - & 5, 35, 27, 16, 16, 2, 2, 7, 28, - & 4, 49, 4, 56, 8, 2, 2, 56, 7, - & 16, 28, 7, 7, 28, 4, 49, 4, 37, - & 55, 21, 33, 40, 16, 16, 28, 7, 16, - & 28, 4, 49, 4, 56, 35, 2, 2, 2, - & 16, 16, 28, 4, 16, 28, 4, 49, 4, - & 40, 40, 5, 42, 27, 16, 16, 28, 4, - & 16, 28, 4, 49, 4, 8, 8, 2, 2/ - DATA ( C( 2,I), I = 1, 99 ) / - & 64, 34, 57, 9, 72, 86, 16, 75, 75, - & 70, 42, 2, 86, 62, 62, 30, 30, 5, - & 42, 70, 70, 70, 53, 70, 70, 53, 42, - & 62, 53, 53, 53, 69, 75, 5, 53, 86, - & 2, 5, 30, 75, 59, 2, 69, 5, 5, - & 63, 62, 5, 69, 30, 44, 30, 86, 86, - & 2, 69, 5, 5, 2, 2, 61, 69, 17, - & 2, 2, 2, 53, 69, 2, 2, 86, 69, - & 13, 2, 2, 37, 43, 65, 2, 2, 30, - & 86, 45, 16, 32, 18, 86, 86, 86, 9, - & 63, 63, 11, 76, 76, 76, 63, 60, 70/ - DATA ( C( 3,I), I = 1, 99 ) / - & 111, 67, 98, 36, 48, 110, 2, 131, 2, - & 2, 124, 124, 48, 2, 2, 124, 124, 70, - & 70, 48, 126, 48, 126, 56, 65, 48, 48, - & 70, 2, 92, 124, 92, 126, 131, 124, 70, - & 70, 70, 20, 105, 70, 2, 2, 27, 108, - & 27, 39, 2, 131, 131, 92, 92, 48, 2, - & 126, 20, 126, 2, 2, 131, 38, 117, 2, - & 131, 68, 58, 38, 90, 38, 108, 38, 2, - & 131, 131, 131, 68, 14, 94, 131, 131, 131, - & 108, 18, 131, 56, 85, 117, 117, 9, 131, - & 131, 55, 92, 92, 92, 131, 131, 48, 48/ - DATA ( C( 4,I), I = 1, 99 ) / - & 151, 168, 46, 197, 69, 64, 2, 198, 191, - & 134, 134, 167, 124, 16, 124, 124, 124, 124, - & 141, 134, 128, 2, 2, 32, 32, 32, 31, - & 31, 64, 64, 99, 4, 4, 167, 124, 124, - & 124, 124, 124, 124, 107, 85, 79, 85, 111, - & 85, 128, 31, 31, 31, 31, 64, 167, 4, - & 107, 167, 124, 124, 124, 124, 124, 124, 107, - & 183, 2, 2, 2, 62, 32, 31, 31, 31, - & 31, 31, 167, 4, 107, 167, 124, 124, 124, - & 124, 124, 124, 107, 142, 184, 184, 65, 65, - & 183, 31, 31, 31, 31, 31, 167, 4, 107/ - DATA ( C( 5,I), I = 1, 99 ) / - & 229, 40, 268, 42, 153, 294, 71, 2, 130, - & 199, 199, 199, 149, 199, 149, 153, 130, 149, - & 149, 15, 119, 294, 31, 82, 260, 122, 209, - & 209, 122, 296, 130, 130, 260, 260, 30, 206, - & 94, 209, 94, 122, 209, 209, 122, 122, 209, - & 130, 2, 130, 130, 38, 38, 79, 82, 94, - & 82, 122, 122, 209, 209, 122, 122, 168, 220, - & 62, 60, 168, 282, 282, 82, 209, 122, 94, - & 209, 122, 122, 122, 122, 258, 148, 286, 256, - & 256, 62, 62, 82, 122, 82, 82, 122, 122, - & 122, 209, 122, 15, 79, 79, 79, 79, 168/ - DATA ( C( 6,I), I = 1, 99 ) / - & 264, 402, 406, 147, 452, 153, 224, 2, 2, - & 224, 224, 449, 101, 182, 449, 101, 451, 181, - & 181, 101, 101, 377, 85, 453, 453, 453, 85, - & 197, 451, 2, 2, 101, 449, 449, 449, 173, - & 173, 2, 453, 453, 2, 426, 66, 367, 426, - & 101, 453, 2, 32, 32, 32, 101, 2, 2, - & 453, 223, 147, 449, 290, 2, 453, 2, 83, - & 223, 101, 453, 2, 83, 83, 147, 2, 453, - & 147, 147, 147, 147, 147, 147, 147, 453, 153, - & 153, 147, 2, 224, 290, 320, 453, 147, 431, - & 383, 290, 290, 2, 162, 162, 147, 2, 162/ - DATA ( C( 7,I), I = 1, 99 ) / - & 505, 220, 195, 410, 199, 248, 460, 471, 2, - & 331, 662, 547, 209, 547, 547, 209, 2, 680, - & 680, 629, 370, 574, 63, 63, 259, 268, 259, - & 547, 209, 209, 209, 547, 547, 209, 209, 547, - & 547, 108, 63, 63, 108, 63, 63, 108, 259, - & 268, 268, 547, 209, 209, 209, 209, 547, 209, - & 209, 209, 547, 108, 63, 63, 63, 405, 285, - & 234, 259, 259, 259, 259, 209, 209, 209, 209, - & 209, 209, 209, 209, 547, 289, 289, 234, 285, - & 316, 2, 410, 259, 259, 259, 268, 209, 209, - & 209, 209, 547, 547, 209, 209, 209, 285, 316/ - DATA ( C( 8,I), I = 1, 99 ) / - & 468, 635, 849, 687, 948, 37, 1014, 513, 2, - & 2, 2, 2, 2, 1026, 2, 2, 1026, 201, - & 201, 2, 1026, 413, 1026, 1026, 2, 2, 703, - & 703, 2, 2, 393, 393, 678, 413, 1026, 2, - & 2, 1026, 1026, 2, 405, 953, 2, 1026, 123, - & 123, 953, 953, 123, 405, 794, 123, 647, 613, - & 1026, 647, 768, 953, 405, 953, 405, 918, 918, - & 123, 953, 953, 918, 953, 536, 405, 70, 124, - & 1005, 529, 207, 405, 405, 953, 953, 123, 918, - & 918, 953, 405, 918, 953, 468, 405, 794, 794, - & 647, 613, 548, 405, 953, 405, 953, 123, 918/ - DATA ( C( 9,I), I = 1, 99 ) / - & 1189, 1423, 287, 186, 341, 77, 733, 733, 1116, - & 2, 1539, 2, 2, 2, 2, 2, 1116, 847, - & 1174, 2, 827, 713, 910, 944, 139, 1174, 1174, - & 1539, 1397, 1397, 1174, 370, 33, 1210, 2, 370, - & 1423, 370, 370, 1423, 1423, 1423, 434, 1423, 901, - & 139, 1174, 427, 427, 200, 1247, 114, 114, 1441, - & 139, 728, 1116, 1174, 139, 113, 113, 113, 1406, - & 1247, 200, 200, 200, 200, 1247, 1247, 27, 427, - & 427, 1122, 1122, 696, 696, 427, 1539, 435, 1122, - & 758, 1247, 1247, 1247, 200, 200, 200, 1247, 114, - & 27, 118, 118, 113, 118, 453, 453, 1084, 1406/ - DATA ( C(10,I), I = 1, 99 ) / - & 1764, 1349, 1859, 693, 78, 438, 531, 68, 2234, - & 2310, 2310, 2310, 2, 2310, 2310, 2102, 2102, 178, - & 314, 921, 1074, 1074, 1074, 2147, 314, 1869, 178, - & 178, 1324, 1324, 510, 2309, 1541, 1541, 1541, 1541, - & 342, 1324, 1324, 1324, 1324, 510, 570, 570, 2197, - & 173, 1202, 998, 1324, 1324, 178, 1324, 1324, 1541, - & 1541, 1541, 342, 1541, 886, 178, 1324, 1324, 1324, - & 510, 784, 784, 501, 652, 1541, 1541, 1324, 178, - & 1324, 178, 1324, 1541, 342, 1541, 2144, 784, 2132, - & 1324, 1324, 1324, 1324, 510, 652, 1804, 1541, 1541, - & 1541, 2132, 1324, 1324, 1324, 178, 510, 1541, 652/ - DATA ( C(11,I), I = 1, 99 ) / - & 2872, 1238, 387, 2135, 235, 1565, 221, 1515, 2950, - & 486, 3473, 2, 2950, 982, 2950, 3122, 2950, 3172, - & 2091, 2091, 9, 3449, 3122, 2846, 3122, 3122, 1947, - & 2846, 3122, 772, 1387, 2895, 1387, 3, 3, 3, - & 1320, 1320, 2963, 2963, 1320, 1320, 2380, 108, 1284, - & 702, 1429, 907, 3220, 3125, 1320, 2963, 1320, 1320, - & 2963, 1320, 1639, 3168, 1660, 2895, 2895, 2895, 2895, - & 1639, 1297, 1639, 404, 3168, 2963, 2943, 2943, 550, - & 1387, 1387, 2895, 2895, 2895, 1387, 2895, 1387, 2895, - & 1320, 1320, 2963, 1320, 1320, 1320, 2963, 1320, 2, - & 3473, 2, 3473, 772, 2550, 9, 1320, 2963, 1320/ - DATA ( C(12,I), I = 1, 99 ) / - & 4309, 2339, 4154, 4480, 4967, 630, 5212, 2592, 4715, - & 1808, 1808, 5213, 2, 216, 4014, 3499, 3499, 4204, - & 2701, 2701, 5213, 4157, 1209, 4157, 4460, 335, 4460, - & 1533, 4575, 4013, 4460, 1881, 2701, 4030, 4030, 1881, - & 4030, 1738, 249, 335, 57, 2561, 2561, 2561, 1533, - & 1533, 1533, 4013, 4013, 4013, 4013, 4013, 1533, 856, - & 856, 468, 468, 468, 2561, 468, 2022, 2022, 2434, - & 138, 4605, 1100, 2561, 2561, 57, 57, 3249, 468, - & 468, 468, 57, 468, 1738, 313, 856, 6, 3877, - & 468, 557, 468, 57, 468, 4605, 2022, 2, 4605, - & 138, 1100, 57, 2561, 57, 57, 2022, 5213, 3249/ - DATA ( C(13,I), I = 1, 99 ) / - & 6610, 1658, 3022, 2603, 5211, 265, 4985, 3, 4971, - & 2127, 1877, 1877, 2, 2925, 3175, 3878, 1940, 1940, - & 1940, 5117, 5117, 5771, 5117, 5117, 5117, 5117, 5117, - & 5771, 5771, 5117, 3658, 3658, 3658, 3658, 3658, 3658, - & 5255, 2925, 2619, 1714, 4100, 6718, 6718, 4100, 2322, - & 842, 4100, 6718, 5119, 4728, 5255, 5771, 5771, 5771, - & 5117, 5771, 5117, 5117, 5117, 5117, 5117, 5117, 5771, - & 5771, 1868, 4483, 4728, 3658, 5255, 3658, 5255, 3658, - & 3658, 5255, 5255, 3658, 6718, 6718, 842, 2322, 6718, - & 4100, 6718, 4100, 4100, 5117, 5771, 5771, 5117, 5771, - & 5771, 5771, 5771, 5117, 5117, 5117, 5771, 5771, 1868/ - DATA ( C(14,I), I = 1, 99 ) / - & 9861, 7101, 6257, 7878, 11170, 11638, 7542, 2592, 2591, - & 6074, 1428, 8925, 11736, 8925, 5623, 5623, 1535, 6759, - & 9953, 9953, 11459, 9953, 7615, 7615, 11377, 11377, 2762, - & 11734, 11459, 6892, 1535, 6759, 4695, 1535, 6892, 2, - & 2, 6892, 6892, 4177, 4177, 6339, 6950, 1226, 1226, - & 1226, 4177, 6892, 6890, 3640, 3640, 1226, 10590, 10590, - & 6950, 6950, 6950, 1226, 6950, 6950, 7586, 7586, 7565, - & 7565, 3640, 3640, 6950, 7565, 6950, 3599, 3599, 3599, - & 2441, 4885, 4885, 4885, 7565, 7565, 1226, 1226, 1226, - & 6950, 7586, 1346, 2441, 6339, 3640, 6950, 10590, 6339, - & 6950, 6950, 6950, 1226, 1226, 6950, 836, 6891, 7565/ - DATA ( C(15,I), I = 1, 99 ) / - & 13482, 5629, 6068, 11974, 4732, 14946, 12097, 17609, 11740, - & 15170, 10478, 10478, 17610, 2, 2, 7064, 7064, 7064, - & 5665, 1771, 2947, 4453, 12323, 17610, 14809, 14809, 5665, - & 5665, 2947, 2947, 2947, 2947, 12323, 12323, 4453, 4453, - & 2026, 11772, 2026, 11665, 12323, 12323, 3582, 2940, 2940, - & 6654, 4449, 9254, 11470, 304, 304, 11470, 304, 11470, - & 6156, 9254, 11772, 6654, 11772, 6156, 11470, 11470, 11772, - & 11772, 11772, 11470, 11470, 304, 11470, 11470, 304, 11470, - & 304, 11470, 304, 304, 304, 6654, 11508, 304, 304, - & 6156, 3582, 11470, 11470, 11470, 17274, 6654, 6654, 6744, - & 6711, 6654, 6156, 3370, 6654, 12134, 3370, 6654, 3582/ - DATA ( C(16,I), I = 1, 99 ) / - & 13482, 5629, 6068, 11974, 4732, 14946, 12097, 17609, 11740, - & 15170, 10478, 10478, 17610, 2, 2, 7064, 7064, 7064, - & 5665, 1771, 2947, 4453, 12323, 17610, 14809, 14809, 5665, - & 5665, 2947, 2947, 2947, 2947, 12323, 12323, 4453, 4453, - & 2026, 11772, 2026, 11665, 12323, 12323, 3582, 2940, 2940, - & 6654, 4449, 9254, 11470, 304, 304, 11470, 304, 11470, - & 6156, 9254, 11772, 6654, 11772, 6156, 11470, 11470, 11772, - & 11772, 11772, 11470, 11470, 304, 11470, 11470, 304, 11470, - & 304, 11470, 304, 304, 304, 6654, 11508, 304, 304, - & 6156, 3582, 11470, 11470, 11470, 17274, 6654, 6654, 6744, - & 6711, 6654, 6156, 3370, 6654, 12134, 3370, 6654, 3582/ - DATA ( C(17,I), I = 1, 99 ) / - & 34566, 38838, 23965, 17279, 35325, 33471, 330, 36050, 26419, - & 3012, 38428, 36430, 36430, 36755, 39629, 5749, 5749, 36755, - & 5749, 14353, 14353, 14353, 32395, 32395, 32395, 32395, 32396, - & 32396, 32396, 32396, 27739, 14353, 36430, 36430, 36430, 15727, - & 38428, 28987, 28987, 27739, 38428, 27739, 18786, 14353, 15727, - & 28987, 19151, 19757, 19757, 19757, 14353, 22876, 19151, 24737, - & 24737, 4412, 30567, 30537, 19757, 30537, 19757, 30537, 30537, - & 4412, 24737, 28987, 19757, 19757, 19757, 30537, 30537, 33186, - & 4010, 4010, 4010, 17307, 15217, 32789, 37709, 4010, 4010, - & 4010, 33186, 33186, 4010, 11057, 39388, 33186, 1122, 15089, - & 39629, 2, 2, 23899, 16466, 16466, 17038, 9477, 9260/ - DATA ( C(18,I), I = 1, 99 ) / - & 31929, 40295, 2610, 5177, 17271, 23770, 9140, 952, 39631, - & 3, 11424, 49719, 38267, 25172, 2, 2, 59445, 2, - & 59445, 38267, 44358, 14673, 53892, 14674, 14673, 14674, 41368, - & 17875, 17875, 30190, 20444, 55869, 15644, 25499, 15644, 20983, - & 44358, 15644, 15644, 485, 41428, 485, 485, 485, 41428, - & 53798, 50230, 53798, 50253, 50253, 35677, 35677, 17474, 7592, - & 4098, 17474, 485, 41428, 485, 41428, 485, 41428, 485, - & 41428, 41428, 41428, 41428, 41428, 9020, 22816, 4098, 4098, - & 4098, 7592, 42517, 485, 50006, 50006, 22816, 22816, 9020, - & 485, 41428, 41428, 41428, 41428, 50006, 485, 41428, 41428, - & 41428, 41428, 22816, 41428, 41428, 485, 485, 485, 9020/ - DATA ( C(19,I), I = 1, 99 ) / - & 73726, 16352, 16297, 74268, 60788, 8555, 1077, 25486, 86595, - & 59450, 19958, 62205, 62205, 4825, 4825, 89174, 89174, 62205, - & 19958, 62205, 19958, 27626, 63080, 62205, 62205, 62205, 19958, - & 8914, 83856, 30760, 47774, 47774, 19958, 62205, 39865, 39865, - & 74988, 75715, 75715, 74988, 34522, 74988, 74988, 25101, 44621, - & 44621, 44621, 25101, 25101, 25101, 44621, 47768, 41547, 44621, - & 10273, 74988, 74988, 74988, 74988, 74988, 74988, 34522, 34522, - & 67796, 67796, 30208, 2, 67062, 18500, 29251, 29251, 2, - & 67796, 67062, 38649, 59302, 6225, 67062, 6475, 6225, 46772, - & 38649, 67062, 46772, 46772, 67062, 46772, 25372, 67062, 6475, - & 25372, 67062, 67062, 67062, 6225, 67062, 67062, 68247, 80676/ - DATA ( C(20,I), I = 1, 99 )/ - & 103650, 50089, 70223, 41805, 74847,112775, 40889, 64866, 44053, - & 1754,129471, 13630, 53467, 53467, 61378,133761, 2,133761, - & 2,133761,133761, 65531, 65531, 65531, 38080,133761,133761, - & 131061, 5431, 65531, 78250, 11397, 38841, 38841,107233,107233, - & 111286, 19065, 38841, 19065, 19065, 16099,127638, 82411, 96659, - & 96659, 82411, 96659, 82411, 51986,101677, 39264, 39264,101677, - & 39264, 39264, 47996, 96659, 82411, 47996, 10971, 10004, 82411, - & 96659, 82411, 82411, 82411, 96659, 96659, 96659, 82411, 96659, - & 51986,110913, 51986, 51986,110913, 82411, 54713, 54713, 22360, - & 117652, 22360, 78250, 78250, 91996, 22360, 91996, 97781, 91996, - & 97781, 91996, 97781, 97781, 91996, 97781, 97781, 36249, 39779/ - SAVE P, C, SAMPLS, NP, VAREST - IF ( NDIM .GT. NLIM .OR. NDIM .LT. 1 ) THEN - INFORM = 2 - FINEST = 0.d0 - ABSERR = 1.d0 - RETURN - ENDIF - INFORM = 1 - INTVLS = 0 - IF ( MINVLS .GE. 0 ) THEN - FINEST = 0.d0 - VAREST = 0.d0 - SAMPLS = MINSMP - DO I = 1, PLIM - NP = I - IF ( MINVLS .LT. 2*SAMPLS*P(I) ) GO TO 10 - END DO - SAMPLS = MAX( MINSMP, INT(MINVLS/( 2*P(NP)) ) ) - ENDIF - 10 VK(1) = ONE/DBLE(P(NP)) - DO I = 2, NDIM - VK(I) = MOD( DBLE(C(NP,NDIM-1))*VK(I-1), ONE ) - END DO - FINVAL = 0.d0 - VARSQR = 0.d0 -* -* Compute mean and standard error for SAMPLS randomized lattice rules -* - DO I = 1, SAMPLS - CALL KROSUM( NDIM, VALUE, P(NP), VK, FUNCTN, ALPHA, X ) - DIFINT = ( VALUE - FINVAL )/DBLE(I) - FINVAL = FINVAL + DIFINT - VARSQR = DBLE(I - 2)*VARSQR/DBLE(I) + DIFINT*DIFINT - END DO - INTVLS = INTVLS + 2*SAMPLS*P(NP) - VARPRD = VAREST*VARSQR - FINEST = FINEST + ( FINVAL - FINEST )/( 1.d0 + VARPRD ) - IF ( VARSQR .GT. 0.d0 ) VAREST = ( 1.d0 + VARPRD )/VARSQR - ABSERR = 3.d0*SQRT( VARSQR/( 1.d0 + VARPRD ) ) - IF ( ABSERR .GT. MAX( ABSEPS, ABS(FINEST)*RELEPS ) ) THEN - IF ( NP .LT. PLIM ) THEN - NP = NP + 1 - ELSE - SAMPLS = MIN( 3*SAMPLS/2, ( MAXVLS - INTVLS )/( 2*P(NP) ) ) - SAMPLS = MAX( MINSMP, SAMPLS ) - ENDIF - IF ( INTVLS + 2*SAMPLS*P(NP) .LE. MAXVLS ) GO TO 10 - ELSE - INFORM = 0 - ENDIF - MINVLS = INTVLS - END SUBROUTINE KROBOV -* - SUBROUTINE KROSUM( NDIM, SUMKRO, PRIME, VK, FUNCTN, ALPHA, X ) - INTEGER, INTENT(IN):: NDIM, PRIME - DOUBLE PRECISION, INTENT(OUT) :: SUMKRO - DOUBLE PRECISION, DIMENSION(:), INTENT(INOUT) :: ALPHA,X ! size NDIM - INTEGER :: K !, J - DOUBLE PRECISION :: ONE - DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: VK - INTERFACE - DOUBLE PRECISION FUNCTION FUNCTN(N,Z) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - END FUNCTION FUNCTN - END INTERFACE - PARAMETER ( ONE = 1.d0 ) - SUMKRO = 0.d0 - CALL random_number(ALPHA(1:NDIM)) - DO K = 1, PRIME - X(1:NDIM) = MOD( DBLE(K)*VK(1:NDIM) + ALPHA(1:NDIM), ONE ) - X(1:NDIM) = ABS( 2.d0*X(1:NDIM) - ONE ) -! PRINT *,'KROSUM W=',X(1:NDIM) - SUMKRO = SUMKRO+(FUNCTN(NDIM,X)-SUMKRO)/DBLE(2*K-1) - X(1:NDIM) = ONE - X(1:NDIM) - SUMKRO = SUMKRO+(FUNCTN(NDIM,X)-SUMKRO)/DBLE(2*K) - END DO - END SUBROUTINE KROSUM - END MODULE KROBOVMOD - diff --git a/wafo/source/rind2007/jacobmod.f b/wafo/source/rind2007/jacobmod.f deleted file mode 100644 index 7f4a193..0000000 --- a/wafo/source/rind2007/jacobmod.f +++ /dev/null @@ -1,20 +0,0 @@ - MODULE JACOBMOD - IMPLICIT NONE - PRIVATE - PUBLIC :: JACOB - INTERFACE JACOB - MODULE PROCEDURE JACOB - END INTERFACE - CONTAINS - FUNCTION JACOB ( xd,xc) RESULT (value1) - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:),INTENT(in) :: xd ,xc - DOUBLE PRECISION :: value1 - ! default - value1 = ABS(PRODUCT(xd)) - ! Other possibilities given below: - ! value1 = 1.d0 - ! value1 = ABS(PRODUCT(xd)*PRODUCT(xc)) - RETURN - END FUNCTION JACOB - END MODULE JACOBMOD \ No newline at end of file diff --git a/wafo/source/rind2007/rind71mod.f b/wafo/source/rind2007/rind71mod.f deleted file mode 100644 index 16ec81f..0000000 --- a/wafo/source/rind2007/rind71mod.f +++ /dev/null @@ -1,4157 +0,0 @@ -!**************************************************************************** -! if compilation complains about too many continuation lines extend it. -! -! -! modules: GLOBALDATA, QUAD, RIND71MOD Version 1.0 -! -! Programs available in module RIND71MOD : -! (NB! the GLOBALDATA and QUAD module is also used to transport the inputs) -! -! -! SETDATA initializes global constants explicitly: -! -! CALL SETDATA(EPSS,REPS,EPS2,NIT,xCutOff,NINT,XSPLT) -! -! GLOBALDATA module : -! EPSS,CEPSS = 1.d0 - EPSS , controlling the accuracy of indicator function -! EPS2 = if conditional variance is less it is considered as zero -! i.e., the variable is considered deterministic -! xCutOff = 5 (standard deviations by default) -! -! QUAD module: -! Nint1(i) = quadrature formulae used in integration of Xd(i) -! implicitly determining # nodes -! -! INITDATA initializes global constants implicitly: -! -! CALL INITDATA (speed) -! -! speed = 1,2,...,9 (1=slowest and most accurate,9=fastest, -! but less accurate) -! -! see the GLOBALDATA and QUAD module for other constants and default values -! -! -!RIND71 computes E[Jacobian*Indicator|Condition]*f_{Xc}(xc(:,ix)) -! -! where -! "Indicator" = I{ H_lo(i) < X(i) < H_up(i), i=1:Nt+Nd } -! "Jacobian" = J(X(Nt+1),...,X(Nt+Nd+Nc)), special case is -! "Jacobian" = |X(Nt+1)*...*X(Nt+Nd)|=|Xd(1)*Xd(2)..Xd(Nd)| -! "condition" = Xc=xc(:,ix), ix=1,...,Nx. -! X = [Xt; Xd ;Xc], a stochastic vector of Multivariate Gaussian -! variables where Xt,Xd and Xc have the length Nt, Nd and Nc, -! respectively. -! (Recommended limitations Nx, Nt<101, Nd<7 and NIT,Nc<11) -! (RIND = Random Integration N Dimensions) -! -!CALL RIND71(E,S,m,xc,indI,Blo,Bup,xcScale); -! -! E = expectation/density as explained above size 1 x Nx (out) -! S = Covariance matrix of X=[Xt;Xd;Xc] size N x N (N=Nt+Nd+Nc) (inout) -! NB!: out=conditional sorted Covariance matrix -! m = the expectation of X=[Xt;Xd;Xc] size N x 1 (in) -! xc = values to condition on size Nc x Nx (in) -! indI = vector of indices to the different barriers in the (in) -! indicator function, length NI, where NI = Nb+1 -! (NB! restriction indI(1)=0, indI(NI)=Nt+Nd ) -!Blo,Bup = Lower and upper barrier coefficients used to compute the (in) -! integration limits Hlo and Hup, respectively. -! size Mb x Nb. If Mb 0 then you must initialize the random generator before you -! call rindd by the following lines: -! -! call random_seed(SIZE=seed_size) -! allocate(seed(seed_size)) -! call random_seed(GET=seed(1:seed_size)) ! get current seed -! seed(1)=seed1 ! change seed -! call random_seed(PUT=seed(1:seed_size)) -! deallocate(seed) -! -! For further description see the modules -! -! -! References -! Podgorski et. al. (1999) -! "Exact distributions for apparent waves in irregular seas" -! Ocean Engineering (RINDXXX) -! -! R. Ambartzumian, A. Der Kiureghian, V. Ohanian and H. -! Sukiasian (1998) -! "Multinormal probabilities by sequential conditioned -! importance sampling: theory and application" (RINDSCIS, MNORMPRB,MVNFUN,MVNFUN2) -! Probabilistic Engineering Mechanics, Vol. 13, No 4. pp 299-308 -! -! Alan Genz (1992) -! 'Numerical Computation of Multivariate Normal Probabilites' -! J. computational Graphical Statistics, Vol.1, pp 141--149 -! -! William H. Press, Saul Teukolsky, -! William T. Wetterling and Brian P. Flannery (1997) -! "Numerical recipes in Fortran 77", Vol. 1, pp 55-63, 299--305 (SVDCMP,SOBSEQ) -! -! Igor Rychlik and Georg Lindgren (1993) -! "Crossreg - A technique for first passage and wave density analysis" (RINDXXX) -! Probability in the Engineering and informational Sciences, -! Vol 7, pp 125--148 -! -! Igor Rychlik (1992) -! "Confidence bands for linear regressions" (RIND2,RINDNIT) -! Commun. Statist. -simula., Vol 21,No 2, pp 333--352 -! -! -! Donald E. Knuth (1973) "The art of computer programming,", -! Vol. 3, pp 84- (sorting and searching) (SORTRE) - -! Tested on: DIGITAL UNIX Fortran90 compiler -! PC pentium II with Lahey Fortran90 compiler -! Solaris with SunSoft F90 compiler Version 1.0.1.0 (21229283) -! History: -! revised pab aug 2009 -! -moved c1c2 to c1c2mod -! -removed rateLHD, useMIDP, FxCutOff, CFxCutOff from globaldata module -! revised pab July 2007 -! -reordered integration methods (SCIS) -! revised pab 9 may 2004 -! removed xcutoff2 -! introduced XcScale to rindd -! revised pab 17.02.2003 -! -new name rind71 -! commented out all print statements -! revised pab 08.02.2001 -! - New name rind70.f -! - moved the jacob function to a separate module. -! - jacobdef in module GLOBALDATA is now obsolete. -! revised pab 19.01.2001 -! - added a NEW BVU function -! revised pab 06.11.2000 -! - added checks in condsort2, condsort3, condsort4 telling if the matrix is -! negative definit -! - changed the order of SCIS integration again. -! revised pab 07.09.2000 -! - To many continuation lines in QUAD module => -! broke them up and changed PARAMETER statements into DATA -! statements instead. -! revised pab 22.05.2000 -! - changed order of SCIS integration: moved the less important SCIS -! revised pab 19.04.2000 -! - found a bug in THL when L<-1, now fixed -! revised pab 18.04.2000 -! new name rind60 -! New assumption of BIG for the conditional sorted variables: -! BIG(I,I)=sqrt(Var(X(I)|X(I+1)...X(N))=SQI -! BIG(1:I-1,I)=COV(X(1:I-1),X(I)|X(I+1)...X(N))/SQI -! Otherwise -! BIG(I,I) = Var(X(I)|X(I+1)...X(N) -! BIG(1:I-1,I)=COV(X(1:I-1),X(I)|X(I+1)...X(N)) -! This also affects C1C2: SQ0=sqrt(Var(X(I)|X(I+1)...X(N)) is removed from input -! => A lot of wasteful divisions are avoided -! revised pab 23.03.2000 -! - done some optimization in initdata -! - added some things in THL + optimized THL -! - fixed a bug in condsort and condsort0 when Nd+Nj=0 -! revised pab 20.03.2000 -! - new name rind57 -! - added condsort0 and condsort4 which sort the covariance matrix using the shortest -! expected integration interval => integration time is much shorter for all methods. -! condsort and condsort3 sort by decreasing conditional variance -! revised pab 17.03.2000 -! - changed argp0 so that I0 and I1 really are the indices to the minimum and the second minimum -! - changed rindnit so that norm2dprb is called whenever NITL<1 and Nsnew>=2 -! - changed default parameters for initdata for speed=7,8 and 9 to increase accuracy. -! - Changed so that xCutOff varies with speed => program is much faster without loosing any accuracy it seems -! revised pab 15.03.2000 -! - changed rindscis and mnormprb: moved the actual multidimensional integration -! into separate module, rcrudemod.f (as a consequence SVDCMP,PYTHAG and SORTRE -! are also moved into this module) => made the structure of the program simpler -! - added the possibility to use adapt, krbvrc, krobov and ranmc to integrate -! - Set NUGGET to 0 when Nc=0, since it is no longer needed -! - added the module MVNFUNDATA -! revised pab 03.03.2000 -! - BIG are no longer changed when called by RINDD instead it is copied into a new variable -! - new name rind55.f -! - fixed the bug in THL, i.e. THL forgot to return a value in some cases giving floating invalid -!revised by I.R. 27.01.2000, Removed bugs in RINDNIT (There where some returns -! without deallocating some variables. A misco error in THL, leading -! to floating invalid on alpha has been repaired by seting value=zero. -! Probably there is an error somehere making variable "value" to behave badly. -!Revised by IR. 03.01.2000 Bug in C1C2 fixed and deallocation of ind in RINDNIT. -!revised by I.R. 27.12.1999, New name RIND51.f -! I have changed assumption about deterministic variables. Those have now -! variances equal EPS2 not zero and have consequences for C1C2 and on some -! places in RINDND. The effect is that barriers becomes fuzzy (not sharp) -! and prevents for discountinuities due to numerical errors of order 1E-16. -! The program RIND0 is removed making the structure of program simpler. -! We have still a problem when variables in indicator become -! deterministic before conditioning on derivatives in Xd - it needs to be solved. -!revised by Igor Rychlik 01.12.1999 New name RIND49.f -! - changed RINDNIT and ARGP0 in order to exclude -! irrelevant variables (such that probability of beeing -! between barriers is 1.) All computations related to NIT -! are moved to RINDNIT (removing RIND2,RIND3). This caused some changes -! in RIND0,RINDDND. Furthermore RINDD1 is removed and moved -! some parts of it to RINDDND. This made program few seconds slower. The lower -! bound in older ARGP0 programs contained logical error - corrected. -!revised by Per A. Brodtkorb 08.11.1999 -! - fixed a bug in rinddnd -! new line: CmNew(Nst+1:Nsd-1)= Cm(Nst+1:Nsd-1) -!revised by Per A. Brodtkorb 28.10.1999 -! - fixed a bug in rinddnd -! - changed rindscis, mnormprb -! - added MVNFUN, MVNFUN2 -! - replaced CVaccept with RelEps -!revised by Per A. Brodtkorb 27.10.1999 -! - changed NINT to NINT1 due to naming conflict with an intrinsic of the same name -!revised by Per A. Brodtkorb 25.10.1999 -! - added an alternative FIINV for use in rindscis and mnormprb -!revised by Per A. Brodtkorb 13.10.1999 -! - added useMIDP for use in rindscis and mnormprb -! -!revised by Per A. Brodtkorb 22.09.1999 -! - removed all underscore letters due to -! problems with SunSoft F90 compiler -! (i.e. changed GLOBAL_DATA to GLOBALDATA etc.) -!revised by Per A. Brodtkorb 09.09.1999 -! - added sobseq: Sobol sequence (quasi random numbers) -! an alternative to random_number in RINDSCIS and mnormprb -!revised by Per A. Brodtkorb 07.09.1999 -! - added pythag,svdcmp,sortre -! - added RINDSCIS: evaluating multinormal integrals by SCIS -! condsort3: prepares BIG for use with RINDSCIS and mnormprb -!revised by Per A. Brodtkorb 03.09.1999 -! - added mnormprb: evaluating multinormal probabilities by SCIS -! See globaldata for SCIS -! revised by Per A. Brodtkorb 01.09.1999 -! - increased the default NUGGET from 1.d-12 to 1.d-8 -! - also set NUGGET depending on speed in INITDATA -! revised by Per A. Brodtkorb 27.08.1999 -! - changed rindnit,rind2: -! enabled option to do the integration faster/(smarter?). -! See GLOBALDATA for XSPLT -! revised by Per A. Brodtkorb 17.08.1999 -! - added THL, norm2dprb not taken in to use -! due to some mysterious floating invalid -! occuring from time to time in norm2dprb (on DIGITAL unix) -! revised by Per A. Brodtkorb 02.08.1999 -! - updated condsort -! - enabled the use of C1C2 in rinddnd -! revised by Per A. Brodtkorb 14.05.1999 -! - updated to fortran90 -! - enabled recursive calls -! - No limitations on size of the inputs -! - fixed some bugs -! - added some additonal checks -! - added Hermite, Laguerre quadratures for alternative integration -! - rewritten CONDSORT, conditional covariance matrix in upper -! triangular. -! - RINDXXX routines only work on the upper triangular -! of the covariance matrix -! - Added a Nugget effect to the covariance matrix in order -! to ensure the conditioning is not corrupted by numerical errors -! - added the option to condsort Nj variables of Xt, i.e., -! enabling direct integration like the integration of Xd -! by Igor Rychlik 29.10.1998 (PROGRAM RIND11 --- Version 1.0) -! which was a revision of program RIND from 3.9.1993 - the program that -! is used in wave_t and wave_t2 programs. - -!********************************************************************* - - MODULE GLOBALDATA - IMPLICIT NONE - ! Constants determining accuracy of integration - !----------------------------------------------- - !if the conditional variance are less than: - DOUBLE PRECISION :: EPS2=1.d-4 !- EPS2, the variable is - ! considered deterministic - DOUBLE PRECISION :: EPS = 1.d-2 ! SQRT(EPS2) - DOUBLE PRECISION :: XCEPS2=1.d-16 ! if Var(Xc) is less return NaN - DOUBLE PRECISION :: EPSS = 5.d-5 ! accuracy of Indicator - DOUBLE PRECISION :: CEPSS=0.99995 ! accuracy of Indicator - DOUBLE PRECISION :: EPS0 = 5.d-5 ! used in GAUSSLE1 to implicitly - ! determ. # nodes - DOUBLE PRECISION :: xcScale=0.d0 - DOUBLE PRECISION :: fxcEpss=1.d-20 ! if less do not compute E(...|Xc) - DOUBLE PRECISION :: xCutOff=5.d0 ! upper/lower truncation limit of the - ! normal CDF - ! Nugget>0: Adds a small value to diagonal - ! elements of the covariance matrix to ensure - ! that the inversion is not corrupted by - ! round off errors. - ! Good choice might be 1e-8 - DOUBLE PRECISION :: NUGGET=1.d-8 ! Obs NUGGET must be smaller then EPS2 - -!parameters controlling the performance of RINDSCIS and MNORMPRB: - INTEGER :: SCIS=0 !=0 integr. all by quadrature - !=1 Integrate all by SADAPT for Ndim<9 and by KRBVRC otherwise - !=2 Integrate all by SADAPT for Ndim<9 and by KROBOV otherwise - !=3 Integrate all by KRBVRC (Fast and reliable) - !=4 Integrate all by KROBOV (Fast and reliable) - !=5 Integrate all by RCRUDE (Reliable) - !=6 Integrate all by SOBNIED (NDIM<1041) - !=7 Integrate all by DKBVRC (Ndim<1001) - INTEGER :: NSIMmax = 1000 ! maximum number of simulations per stochastic dimension - INTEGER :: NSIMmin = 10 ! minimum number of simulations per stochastic dimension - INTEGER :: Ntscis = 0 ! Ntscis=Nt-Nj-Njj when SCIS>0 otherwise Ntscis=0 - DOUBLE PRECISION :: RelEps = 0.001 ! Relative error, i.e. if - ! 3.0*STD(XIND)/XIND is less we accept the estimate - ! The following may be allocated outside RINDD - ! if one wants the coefficient of variation, i.e. - ! STDEV(XIND)/XIND when SCIS=2. (NB: size Nx) - DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: COV - integer :: COVix ! counting variable for COV - LOGICAL,PARAMETER :: useC1C2=.true. ! use C1C2 in rindscis,mnormprb - LOGICAL,PARAMETER :: C1C2det=.true. ! use C1C2 only on the variables that becomes - ! deterministic after conditioning on X(N) - ! used in rinddnd rindd1 and rindscis mnormprb - -!parameters controlling performance of quadrature integration: - ! if Hup>=xCutOff AND Hlo<-XSPLT OR - ! Hup>=XSPLT AND Hl0<=-xCutOff then - ! do a different integration to increase speed - ! in rind2 and rindnit. This give slightly different - ! results - ! DEFAULT 5 =xCutOff => do the same integration allways - ! However, a resonable value is XSPLT=1.5 - DOUBLE PRECISION :: XSPLT = 5.d0 ! DEFAULT XSPLT= 5 =xCutOff - ! weight between upper&lower limit returned by ARGP0 - DOUBLE PRECISION, PARAMETER :: Plowgth=0.d0 ! 0 => no weight to - ! lower limit - INTEGER :: NIT=2 ! NIT=maximum # of iterations/integrations by - ! quadrature used to calculate the indicator function - - ! size information of the covariance matrix BIG - ! Nt,Nd,....Ntd,Nx must be set before calling - ! RINDD. NsXtmj, NsXdj is set in RINDD - INTEGER :: Nt,Nd,Nc,Ntdc,Ntd,Nx - ! Constants determines how integration is done - INTEGER :: Nj=0,Njj=0 ! Njj is not implemented yet - ! size information of indI, Blo,Bup - ! Blo/Bup size Mb x NI-1 - ! indI vector of length NI - INTEGER :: NI,Mb ! must be set before calling RINDD - - ! The following is allocated in RINDD - DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: SQ - DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: Hlo,Hup - INTEGER, DIMENSION(:), ALLOCATABLE :: index1,xedni,indXtd - INTEGER, DIMENSION(:), ALLOCATABLE :: NsXtmj, NsXdj - - ! global constants - DOUBLE PRECISION, PARAMETER :: SQTWOPI1=3.9894228040143d-1 !=1/sqrt(2*pi) - DOUBLE PRECISION, PARAMETER :: SQPI1=5.6418958354776d-1 !=1/sqrt(pi) - DOUBLE PRECISION, PARAMETER :: SQPI= 1.77245385090552d0 !=sqrt(pi) - DOUBLE PRECISION, PARAMETER :: SQTWO=1.41421356237310d0 !=sqrt(2) - DOUBLE PRECISION, PARAMETER :: SQTWO1=0.70710678118655d0 !=1/sqrt(2) - DOUBLE PRECISION, PARAMETER :: PI1=0.31830988618379d0 !=1/pi - DOUBLE PRECISION, PARAMETER :: PI= 3.14159265358979D0 !=pi - DOUBLE PRECISION, PARAMETER :: TWOPI=6.28318530717958D0 !=2*pi - END MODULE GLOBALDATA - - MODULE C1C2MOD - IMPLICIT NONE - INTERFACE C1C2 - MODULE PROCEDURE C1C2 - END INTERFACE - CONTAINS - SUBROUTINE C1C2(C1, C2, Cm, B1, SQ, ind) -! The regression equation for the conditional distr. of Y given X=x -! is equal to the conditional expectation of Y given X=x, i.e., -! -! E(Y|X=x)=E(Y)+Cov(Y,X)/Var(X)[x-E(X)] -! -! Let x1=(x-E(X))/SQRT(Var(X)) be zero mean, C1Hup(I) or -! -! b) Cm(I)+x1*B1(I)+C*SQ(I)0 - CC1 = (HHlo - CSQ) / BdSQ0 - CC2 = (HHup + CSQ) / BdSQ0 - ENDIF - IF (C1.LT.CC1) THEN - C1 = CC1 !changedLimits=1 - IF (C2.GT.CC2) C2 = CC2 - IF (C1.GE.C2) GO TO 112 - ELSEIF (C2.GT.CC2) THEN - C2 = CC2 !changedLimits=1 - IF (C1.GE.C2) GO TO 112 - END IF - ENDIF - END DO -!IF (changedLimits.EQ.1) THEN -! PRINT *,'C1C2=',C1,C2 -!END IF - RETURN - 112 continue - C1 = -2D0*xCutOff - C2 = -2D0*xCutOff - - RETURN - END SUBROUTINE C1C2 - END MODULE C1C2MOD - -!************************************** - - MODULE FUNCMOD -! FUNCTION module containing constants transfeered to mvnfun and mvnfun2 - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: BIG - DOUBLE PRECISION, DIMENSION(: ), ALLOCATABLE :: Cm,CmN,xd,xc - DOUBLE PRECISION :: Pl1,Pu1 - - INTERFACE MVNFUN - MODULE PROCEDURE MVNFUN - END INTERFACE - - INTERFACE MVNFUN2 - MODULE PROCEDURE MVNFUN2 - END INTERFACE - - CONTAINS - function MVNFUN(Ndim,W) RESULT (XIND) - USE FIMOD - USE C1C2MOD - USE JACOBMOD - USE GLOBALDATA, ONLY : Hlo,Hup,xCutOff,Nt,Nd,Nj,Ntd,SQ, - & NsXtmj, NsXdj,indXtd,index1,useC1C2,C1C2det,EPS2 - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: W - INTEGER, INTENT(in) :: Ndim - DOUBLE PRECISION :: XIND -!local variables - DOUBLE PRECISION :: Pl,Pu - DOUBLE PRECISION :: X,Y,XMI,XMA,SQ0 - INTEGER :: Nst,NstN,NsdN,Nst0,Nsd,Nsd0,K - INTEGER :: Ndleft,Ndjleft,Ntmj - -!MVNFUN Multivariate Normal integrand function -! where the integrand is transformed from an integral -! having integration limits Hl0 and Hup to an -! integral having constant integration limits i.e. -! Hup 1 -! int jacob(xd,xc)*f(xd,xt)dxt dxd = int F2(W) dW -!Hlo 0 -! -! W - new transformed integration variables, valid range 0..1 -! The vector must have the length Ndim=Nst0+Ntd-Nsd0 -! BIG - conditional sorted covariance matrix (IN) -! Cm = conditional mean of Xd and Xt given Xc, E(Xd,Xt|Xc) -! CmN - local conditional mean -! xd - variables to the jacobian variable, need no initialization -! xc - conditional variables (IN) -! Pl1 = FI(XMI) for the first integration variable (IN) -! Pu1 = FI(XMA) ------||------------------------------- -! print *,'MVNFUN, ndim', ndim, shape(W) - CmN(1:Ntd) = Cm(1:Ntd) ! initialize conditional mean - Nst = NsXtmj(Ntd+1) ! index to last stoch variable of Xt before conditioning on X(Ntd) - Ntmj=Nt-Nj - Nsd0=NsXdj(1) - if (Nt.gt.Nj) then - Nst0=NsXtmj(Ntmj) - else - Nst0=0 - endif - Pl=Pl1 - Pu=Pu1 -! IF (NDIM.LT.Nst0+Ntd-Nsd0+1) PRINT *, 'MVNFUN NDIM,',NDIM - Y=Pu-Pl - if (Nd+Nj.EQ.0) then - SQ0=SQ(1,1) - goto 200 - endif - Ndjleft=Nd+Nj - Nsd = NsXdj(Ndjleft+1) ! index to last stoch variable of Xd and Nj of Xt before conditioning on X(Ntd) - Ndleft=Nd - SQ0=SQ(Ntd,Ntd) - !print *,'mvnfun,nst,nsd,nd,nj',nst,nsd,Nd,Nj - !print *,'mvn start K loop' - DO K=Ntd-1,Nsd0,-1 - X=FIINV(Pl+W(Ntd-K)*(Pu-Pl)) - IF (index1(K+1).GT.Nt) THEN ! isXd - xd (Ndleft) = CmN(K+1)+X*SQ0 - Ndleft=Ndleft-1 - END IF - Nst = NsXtmj(K+1) ! # stoch. var. of Xt before conditioning on X(K) - if (Nst.GT.0) CmN(1:Nst) =CmN(1:Nst)+X*BIG(1:Nst,K+1) !/SQ0 - CmN(Nsd:K) =CmN(Nsd:K)+X*BIG(Nsd:K,K+1) !/SQ0 - - Ndjleft = Ndjleft-1 - Nsd = NsXdj(Ndjleft+1) - SQ0 = SQ(K,K) - - XMA = (Hup (K)-CmN(K))/SQ0 - XMI = (Hlo (K)-CmN(K))/SQ0 - - if (useC1C2) then ! see if we can narrow down sampling range - XMI=max(XMI,-xCutOff) - XMA=min(XMA,xCutOff) - if (C1C2det) then - NsdN = NsXdj(Ndjleft) - NstN = NsXtmj(K) - CALL C1C2(XMI,XMA,CmN(Nsd:NsdN-1), - & BIG(Nsd:NsdN-1,K),SQ(Nsd:NsdN-1,K), - & indXtd(Nsd:NsdN-1)) - CALL C1C2(XMI,XMA,CmN(NstN+1:Nst), - & BIG(NstN+1:Nst,K),SQ(NstN+1:Nst,K), - & indXtd(NstN+1:Nst)) - else - CALL C1C2(XMI,XMA,CmN(Nsd:K-1),BIG(Nsd:K-1,K), - & SQ(Nsd:K-1,Ntmj+Ndjleft),indXtd(Nsd:K-1)) - CALL C1C2(XMI,XMA,CmN(1:Nst),BIG(1:Nst,K) - & ,SQ(1:Nst,Ntmj+Ndjleft),indXtd(1:Nst)) - endif - IF (XMA.LE.XMI) goto 260 - endif - Pl = FI(XMI) - Pu = FI(XMA) - Y=Y*(Pu-Pl) - ENDDO ! K LOOP - X = FIINV(Pl+W(Ntd-Nsd0+1)*(Pu-Pl)) - Nst = NsXtmj(Nsd0) ! # stoch. var. of Xt after conditioning on X(Nsd0) - ! and before conditioning on X(1) -! CmN(1:Nst)=CmN(1:Nst)+X*BIG(1:Nst,Nsd0) !/SQ0) - if (Nd.gt.0) then - CmN(Nsd:Nsd0-1) = CmN(Nsd:Nsd0-1)+X*BIG(Nsd:Nsd0-1,Nsd0) !/SQ0 - if (Ndleft.gt.0) then - if (index1(Nsd0).GT.Nt) then - xd (Ndleft) = CmN(Nsd0)+X*SQ0 - Ndleft=Ndleft-1 - endif - K=Nsd0-1 - do while (Ndleft.gt.0) - if ((index1(K).GT.Nt)) THEN ! isXd - xd (Ndleft) = CmN(K) - Ndleft=Ndleft-1 - END IF - K=K-1 - ENDDO - endif ! Ndleft - Y = Y*jacob ( xd,xc) ! jacobian of xd,xc - endif ! Nd>0 - if (Nst0.gt.0) then - CmN(1:Nst)=CmN(1:Nst)+X*BIG(1:Nst,Nsd0) !/SQ0) - SQ0 = SQ(1,1) - XMA = MIN((Hup (1)-CmN(1))/SQ0,xCutOff) - XMI = MAX((Hlo (1)-CmN(1))/SQ0,-xCutOff) - - if (C1C2det) then - NstN = NsXtmj(1) ! # stoch. var. after conditioning - CALL C1C2(XMI,XMA,CmN(NstN+1:Nst), - & BIG(1,NstN+1:Nst),SQ(NstN+1:Nst,1), - & indXtd(NstN+1:Nst)) - else - CALL C1C2(XMI,XMA,CmN(2:Nst),BIG(1,2:Nst), - & SQ(2:Nst,1),indXtd(2:Nst)) - endif - IF (XMA.LE.XMI) GO TO 260 - Pl = FI(XMI) - Pu = FI(XMA) - Y = Y*(Pu-Pl) - endif - !if (COVix.gt.2) then - !print *,' mvnfun start K2 loop' - !endif - 200 do K = 2,Nst0 - X = FIINV(Pl+W(Ntd-Nsd0+K)*(Pu-Pl)) - Nst = NsXtmj(K-1) ! index to last stoch. var. before conditioning on X(K) - CmN(K:Nst)=CmN(K:Nst)+X*BIG(K-1,K:Nst) !/SQ0 - SQ0 = SQ(K,K) - XMA = MIN((Hup (K)-CmN(K))/SQ0,xCutOff) - XMI = MAX((Hlo (K)-CmN(K))/SQ0,-xCutOff) - - if (C1C2det) then - NstN = NsXtmj(K) ! index to last stoch. var. after conditioning X(K) - CALL C1C2(XMI,XMA,CmN(NstN+1:Nst), - & BIG(K,NstN+1:Nst),SQ(NstN+1:Nst,K), - & indXtd(NstN+1:Nst)) - else - CALL C1C2(XMI,XMA,CmN(K+1:Nst),BIG(K,K+1:Nst), - & SQ(K+1:Nst,K),indXtd(K+1:Nst)) - endif - IF (XMA.LE.XMI) GO TO 260 - Pl = FI(XMI) - Pu = FI(XMA) - Y=Y*(Pu-Pl) - enddo ! K loop - XIND = Y - RETURN - 260 XIND = 0.D0 - !if (Y.LT.0.d0) PRINT *,'MVNFUN NEGATIVE INTEGRAND' - !print *,' mvnfun leaving' - return - END FUNCTION MVNFUN - - function MVNFUN2(Ndim,W) RESULT (XIND) - USE FIMOD - USE C1C2MOD - USE GLOBALDATA, ONLY : Hlo,Hup,xCutOff,Njj,Nj,Ntscis,Ntd,SQ, - & NsXtmj, NsXdj,indXtd,index1,useC1C2,C1C2det,Nt,EPS2 - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: W - INTEGER, INTENT(in) :: Ndim - DOUBLE PRECISION :: XIND -!local variables - DOUBLE PRECISION :: Pl,Pu - DOUBLE PRECISION :: X,Y,XMI,XMA,SQ0 - INTEGER :: Nst,NstN,Nst0,K - -!MVNFUN2 Multivariate Normal integrand function -! where the integrand is transformed from an integral -! having integration limits Hl0 and Hup to an -! integral having constant integration limits i.e. -! Hup 1 -! int f(xt)dxt = int F2(W) dW -!Hlo 0 -! -! W - new transformed integration variables, valid range 0..1 -! The vector must have the size Nst0 -! BIG - conditional sorted covariance matrix (IN) -! CmN - Local conditional mean -! Cm = Conditional mean E(Xt,Xd|Xc) -! Pl1 = FI(XMI) for the first integration variable -! Pu1 = FI(XMA) ------||------------------------- - - !print *,'MVNFUN2, ndim', ndim, shape(W) - Nst0 = NsXtmj(Njj+Ntscis) - - if (Njj.GT.0) then - Nst = NsXtmj(Njj) - else - Nst = NsXtmj(Ntscis+1) - endif -! IF (NDIM.LT.Nst0+Njj) PRINT *, 'MVNFUN2 NDIM,',NDIM - ! initialize conditional mean - CmN(1:Nst)=Cm(1:Nst) - - Pl = Pl1 - Pu = Pu1 - - Y = Pu-Pl - SQ0 = SQ(1,1) - - do K = 2,Nst0 - X = FIINV(Pl+W(K-1)*(Pu-Pl)) - Nst = NsXtmj(K-1) ! index to last stoch. var. before conditioning on X(K) - CmN(K:Nst)=CmN(K:Nst)+X*BIG(K-1,K:Nst) !/SQ0 - SQ0 = SQ(K,K) - XMA = MIN((Hup (K)-CmN(K))/SQ0,xCutOff) - XMI = MAX((Hlo (K)-CmN(K))/SQ0,-xCutOff) - - if (C1C2det) then - NstN=NsXtmj(K) ! index to last stoch. var. after conditioning on X(K) - CALL C1C2(XMI,XMA,CmN(NstN+1:Nst), - & BIG(K,NstN+1:Nst),SQ(NstN+1:Nst,K), - & indXtd(NstN+1:Nst)) - else - CALL C1C2(XMI,XMA,CmN(K+1:Nst),BIG(K,K+1:Nst), - & SQ(K+1:Nst,K),indXtd(K+1:Nst)) - endif - IF (XMA.LE.XMI) GO TO 260 - Pl = FI(XMI) - Pu = FI(XMA) - Y = Y*(Pu-Pl) - enddo ! K loop - XIND = Y - RETURN - 260 XIND = 0.d0 - return - END FUNCTION MVNFUN2 - END MODULE FUNCMOD - - MODULE QUAD - IMPLICIT NONE ! Quadratures available: Legendre,Hermite,Laguerre - INTEGER :: I - INTEGER, PARAMETER :: PMAX=24 ! maximum # nodes - INTEGER, PARAMETER :: sizNint=13 ! size of Nint1 - INTEGER :: minQNr=1 ! minimum quadrature number - ! used in GaussLe1, Gaussle2 - INTEGER :: Le2QNr=8 ! quadr. number used in rind2,rindnit - INTEGER, DIMENSION(sizNint) :: Nint1 ! use quadr. No. Nint1(i) in - ! integration of Xd(i) - - ! # different quadratures stored for : - !------------------------------------- - INTEGER,PARAMETER :: NLeW=13 ! Legendre - INTEGER,PARAMETER :: NHeW=13 ! Hermite - INTEGER,PARAMETER :: NLaW=13 ! Laguerre - ! Quadrature Number stored for : - !------------------------------------- - INTEGER, DIMENSION(NLeW) :: LeQNr ! Legendre - INTEGER, DIMENSION(NHeW) :: HeQNr ! Hermite - INTEGER, DIMENSION(NLaW) :: LaQNr ! Laguerre - PARAMETER (LeQNr=(/ 2,3,4,5,6,7, 8, 9, 10, 12, 16, 20, 24 /)) - PARAMETER (HeQNr=(/ 2,3,4,5,6,7, 8, 9, 10, 12, 16, 20, 24 /)) - PARAMETER (LaQNr=(/ 2,3,4,5,6,7, 8, 9, 10, 12, 16, 20, 24 /)) - - - ! The indices to the weights & nodes stored for: - !------------------------------------------------ - INTEGER, DIMENSION(NLeW+1) :: LeIND !Legendre - INTEGER, DIMENSION(NHeW+1) :: HeIND !Hermite - INTEGER, DIMENSION(NLaW+1) :: LaIND !Laguerre - - PARAMETER (LeIND=(/0,2,5,9,14,20,27,35,44,54,66,82,102,126/)) !Legendre - PARAMETER (HeIND=(/0,2,5,9,14,20,27,35,44,54,66,82,102,126/)) !Hermite - PARAMETER (LaIND=(/0,2,5,9,14,20,27,35,44,54,66,82,102,126/)) !Laguerre - - !------------------------------------------------ - DOUBLE PRECISION, DIMENSION(126) :: LeBP,LeWF,HeBP,HeWF - DOUBLE PRECISION, DIMENSION(126) :: LaBP0,LaWF0,LaBP5,LaWF5 - -!The Hermite Quadrature integrates an integral of the form -! inf n -! Int (exp(-x^2) F(x)) dx = Sum wf(j)*F( bp(j) ) -! -Inf j=1 -!The Laguerre Quadrature integrates an integral of the form -! inf n -! Int (x^alpha exp(-x) F(x)) dx = Sum wf(j)*F( bp(j) ) -! 0 j=1 -! weights stored here are for alpha=0 and alpha=-0.5 - - ! initialize Legendre weights, wf, and nodes, bp -!PARAMETER ( LeWF = ( - DATA ( LeWF(I), I = 1, 78 ) - * / 1.d0, 1.d0, 0.555555555555556d0, - * 0.888888888888889d0, 0.555555555555556d0, - * 0.347854845137454d0, 0.652145154862546d0, - * 0.652145154862546d0, 0.347854845137454d0, - * 0.236926885056189d0, 0.478628670499366d0, - * 0.568888888888889d0, 0.478628670499366d0, - * 0.236926885056189d0, 0.171324492379170d0, - * 0.360761573048139d0, 0.467913934572691d0, - * 0.467913934572691d0, 0.360761573048139d0, - * 0.171324492379170d0, 0.129484966168870d0, - * 0.279705391489277d0, 0.381830050505119d0, - * 0.417959183673469d0, 0.381830050505119d0, - * 0.279705391489277d0, 0.129484966168870d0, - * 0.101228536290376d0, 0.222381034453374d0, - * 0.313706645877887d0, 0.362683783378362d0, - * 0.362683783378362d0, 0.313706645877887d0, - * 0.222381034453374d0, 0.101228536290376d0, - * 0.081274388361574d0, 0.180648160694857d0, - * 0.260610696402935d0, 0.312347077040003d0, - * 0.330239355001260d0, 0.312347077040003d0, - * 0.260610696402935d0, 0.180648160694857d0, - * 0.081274388361574d0, 0.066671344308688d0, - * 0.149451349150581d0, 0.219086362515982d0, - * 0.269266719309996d0, 0.295524224714753d0, - * 0.295524224714753d0, 0.269266719309996d0, - * 0.219086362515982d0, 0.149451349150581d0, - * 0.066671344308688d0, 0.047175336386512d0, - * 0.106939325995318d0, 0.160078328543346d0, - * 0.203167426723066d0, 0.233492536538355d0, - * 0.249147048513403d0, 0.249147048513403d0, - * 0.233492536538355d0, - * 0.203167426723066d0, 0.160078328543346d0, - * 0.106939325995318d0, 0.047175336386512d0, - * 0.027152459411754094852d0, 0.062253523938647892863d0, - * 0.095158511682492784810d0, 0.124628971255533872052d0, - * 0.149595988816576732081d0, 0.169156519395002538189d0, - * 0.182603415044923588867d0, 0.189450610455068496285d0, - * 0.189450610455068496285d0, 0.182603415044923588867d0, - * 0.169156519395002538189d0, 0.149595988816576732081d0/ - DATA ( LeWF(I), I = 79, 126 ) - * / 0.124628971255533872052d0, 0.095158511682492784810d0, - * 0.062253523938647892863d0, 0.027152459411754094852d0, - * 0.017614007139152118312d0, 0.040601429800386941331d0, - * 0.062672048334109063570d0, 0.083276741576704748725d0, - * 0.101930119817240435037d0, 0.118194531961518417312d0, - * 0.131688638449176626898d0, 0.142096109318382051329d0, - * 0.149172986472603746788d0, 0.152753387130725850698d0, - * 0.152753387130725850698d0, 0.149172986472603746788d0, - * 0.142096109318382051329d0, 0.131688638449176626898d0, - * 0.118194531961518417312d0, 0.101930119817240435037d0, - * 0.083276741576704748725d0, 0.062672048334109063570d0, - * 0.040601429800386941331d0, 0.017614007139152118312d0, - * 0.012341229799987199547d0, 0.028531388628933663181d0, - * 0.044277438817419806169d0, 0.059298584915436780746d0, - * 0.073346481411080305734d0, 0.086190161531953275917d0, - * 0.097618652104113888270d0, 0.107444270115965634783d0, - * 0.115505668053725601353d0, 0.121670472927803391204d0, - * 0.125837456346828296121d0, 0.127938195346752156974d0, - * 0.127938195346752156974d0, 0.125837456346828296121d0, - * 0.121670472927803391204d0, 0.115505668053725601353d0, - * 0.107444270115965634783d0, 0.097618652104113888270d0, - * 0.086190161531953275917d0, 0.073346481411080305734d0, - * 0.059298584915436780746d0, 0.044277438817419806169d0, - * 0.028531388628933663181d0, 0.012341229799987199547d0 / -! PARAMETER - DATA ( LeBP(I), I=1,77) - * / -0.577350269189626d0,0.577350269189626d0, - * -0.774596669241483d0, 0.d0, - * 0.774596669241483d0, -0.861136311594053d0, - * -0.339981043584856d0, 0.339981043584856d0, - * 0.861136311594053d0, -0.906179845938664d0, - * -0.538469310105683d0, 0.d0, - * 0.538469310105683d0, 0.906179845938664d0, - * -0.932469514203152d0, -0.661209386466265d0, - * -0.238619186083197d0, 0.238619186083197d0, - * 0.661209386466265d0, 0.932469514203152d0, - * -0.949107912342759d0, -0.741531185599394d0, - * -0.405845151377397d0, 0.d0, - * 0.405845151377397d0, 0.741531185599394d0, - * 0.949107912342759d0, -0.960289856497536d0, - * -0.796666477413627d0, -0.525532409916329d0, - * -0.183434642495650d0, 0.183434642495650d0, - * 0.525532409916329d0, 0.796666477413627d0, - * 0.960289856497536d0, -0.968160239507626d0, - * -0.836031107326636d0, -0.613371432700590d0, - * -0.324253423403809d0, 0.d0, - * 0.324253423403809d0, 0.613371432700590d0, - * 0.836031107326636d0, 0.968160239507626d0, - * -0.973906528517172d0, -0.865063366688985d0, - * -0.679409568299024d0, -0.433395394129247d0, - * -0.148874338981631d0, 0.148874338981631d0, - * 0.433395394129247d0, 0.679409568299024d0, - * 0.865063366688985d0, 0.973906528517172d0, - * -0.981560634246719d0, -0.904117256370475d0, - * -0.769902674194305d0, -0.587317954286617d0, - * -0.367831498198180d0, -0.125233408511469d0, - * 0.125233408511469d0, 0.367831498198180d0, - * 0.587317954286617d0, 0.769902674194305d0, - * 0.904117256370475d0, 0.981560634246719d0, - * -0.989400934991649932596d0, - * -0.944575023073232576078d0, -0.865631202387831743880d0, - * -0.755404408355003033895d0, -0.617876244402643748447d0, - * -0.458016777657227386342d0, -0.281603550779258913230d0, - * -0.095012509837637440185d0, 0.095012509837637440185d0, - * 0.281603550779258913230d0, 0.458016777657227386342d0/ - DATA ( LeBP(I), I=78,126) - * / 0.617876244402643748447d0, 0.755404408355003033895d0, - * 0.865631202387831743880d0, 0.944575023073232576078d0, - * 0.989400934991649932596d0, -0.993128599185094924786d0, - * -0.963971927277913791268d0, -0.912234428251325905868d0, - * -0.839116971822218823395d0, -0.746331906460150792614d0, - * -0.636053680726515025453d0, -0.510867001950827098004d0, - * -0.373706088715419560673d0, -0.227785851141645078080d0, - * -0.076526521133497333755d0, 0.076526521133497333755d0, - * 0.227785851141645078080d0, 0.373706088715419560673d0, - * 0.510867001950827098004d0, 0.636053680726515025453d0, - * 0.746331906460150792614d0, 0.839116971822218823395d0, - * 0.912234428251325905868d0, - * 0.963971927277913791268d0, 0.993128599185094924786d0, - * -0.995187219997021360180d0, -0.974728555971309498198d0, - * -0.938274552002732758524d0, -0.886415527004401034213d0, - * -0.820001985973902921954d0, -0.740124191578554364244d0, - * -0.648093651936975569252d0, -0.545421471388839535658d0, - * -0.433793507626045138487d0, -0.315042679696163374387d0, - * -0.191118867473616309159d0, -0.064056892862605626085d0, - * 0.064056892862605626085d0, 0.191118867473616309159d0, - * 0.315042679696163374387d0, 0.433793507626045138487d0, - * 0.545421471388839535658d0, 0.648093651936975569252d0, - * 0.740124191578554364244d0, 0.820001985973902921954d0, - * 0.886415527004401034213d0, 0.938274552002732758524d0, - * 0.974728555971309498198d0, 0.995187219997021360180d0 / - - ! initialize Hermite weights in HeWF and - ! nodes in HeBP - ! NB! the relative error of these numbers - ! are less than 10^-15 -! PARAMETER - DATA (HeWF(I),I=1,78) / 8.8622692545275816d-1, - * 8.8622692545275816d-1, - * 2.9540897515091930d-1, 1.1816359006036770d0, - * 2.9540897515091930d-1, 8.1312835447245310d-2, - * 8.0491409000551251d-1, 8.0491409000551295d-1, - * 8.1312835447245213d-2, 1.9953242059045910d-2, - * 3.9361932315224146d-1, 9.4530872048294134d-1, - * 3.9361932315224102d-1, 1.9953242059045962d-2, - * 4.5300099055088378d-3, 1.5706732032285636d-1, - * 7.2462959522439319d-1, 7.2462959522439241d-1, - * 1.5706732032285681d-1, 4.5300099055088534d-3, - * 9.7178124509952175d-4, 5.4515582819126975d-2, - * 4.2560725261012805d-1, 8.1026461755680768d-1, - * 4.2560725261012783d-1, 5.4515582819126975d-2, - * 9.7178124509951828d-4, 1.9960407221136729d-4, - * 1.7077983007413571d-2, 2.0780232581489183d-1, - * 6.6114701255824082d-1, 6.6114701255824138d-1, - * 2.0780232581489202d-1, 1.7077983007413498d-2, - * 1.9960407221136775d-4, 3.9606977263264446d-5, - * 4.9436242755369411d-3, 8.8474527394376654d-2, - * 4.3265155900255586d-1, 7.2023521560605108d-1, - * 4.3265155900255559d-1, 8.8474527394376543d-2, - * 4.9436242755369350d-3, 3.9606977263264324d-5, - * 7.6404328552326139d-6, 1.3436457467812229d-3, - * 3.3874394455481210d-2, 2.4013861108231502d-1, - * 6.1086263373532623d-1, 6.1086263373532546d-1, - * 2.4013861108231468d-1, 3.3874394455480884d-2, - * 1.3436457467812298d-3, 7.6404328552325919d-6, - * 2.6585516843562997d-7, 8.5736870435879089d-5, - * 3.9053905846291028d-3, 5.1607985615883860d-2, - * 2.6049231026416092d-1, 5.7013523626247820d-1, - * 5.7013523626248030d-1, 2.6049231026416109d-1, - * 5.1607985615883846d-2, 3.9053905846290530d-3, - * 8.5736870435878506d-5, 2.6585516843562880d-7, - * 2.6548074740111735d-10, 2.3209808448651987d-7, - * 2.7118600925379007d-5, 9.3228400862418819d-4, - * 1.2880311535509989d-2, 8.3810041398985652d-2, - * 2.8064745852853318d-1, 5.0792947901661278d-1, - * 5.0792947901661356d-1, 2.8064745852853334d-1, - * 8.3810041398985735d-2, 1.2880311535510015d-2/ - DATA (HeWF(I),I=79,126) / - * 9.3228400862418407d-4, 2.7118600925378956d-5, - * 2.3209808448651966d-7, 2.6548074740111787d-10, - * 2.2293936455342015d-13, 4.3993409922730765d-10, - * 1.0860693707692910d-7, 7.8025564785320463d-6, - * 2.2833863601635403d-4, 3.2437733422378719d-3, - * 2.4810520887463536d-2, 1.0901720602002360d-1, - * 2.8667550536283382d-1, 4.6224366960061047d-1, - * 4.6224366960061070d-1, 2.8667550536283398d-1, - * 1.0901720602002325d-1, 2.4810520887463588d-2, - * 3.2437733422378649d-3, 2.2833863601635316d-4, - * 7.8025564785321005d-6, 1.0860693707692749d-7, - * 4.3993409922731370d-10, 2.2293936455342167d-13, - * 1.6643684964891124d-16, 6.5846202430781508d-13, - * 3.0462542699875022d-10, 4.0189711749413878d-8, - * 2.1582457049023452d-6, 5.6886916364043773d-5, - * 8.2369248268841073d-4, 7.0483558100726748d-3, - * 3.7445470503230736d-2, 1.2773962178455966d-1, - * 2.8617953534644325d-1, 4.2693116386869828d-1, - * 4.2693116386869912d-1, 2.8617953534644286d-1, - * 1.2773962178455908d-1, 3.7445470503230875d-2, - * 7.0483558100726844d-3, 8.2369248268842027d-4, - * 5.6886916364044037d-5, 2.1582457049023460d-6, - * 4.0189711749414963d-8, 3.0462542699876118d-10, - * 6.5846202430782225d-13, 1.6643684964889408d-16 / - - !hermite nodes -! PARAMETER (HeBP = ( - DATA (HeBP(I),I=1,79) / -7.07106781186547572d-1, - * 7.0710678118654752d-1, -1.2247448713915894d0, - * 0.d0, 1.2247448713915894d0, - * -1.6506801238857845d0, -5.2464762327529035d-1, - * 5.2464762327529035d-1, 1.6506801238857845d0, - * -2.0201828704560869d0, -9.5857246461381806d-1, - * 0.d0, 9.5857246461381851d-1, - * 2.0201828704560860d0, -2.3506049736744918d0, - * -1.3358490740136963d0, -4.3607741192761629d-1, - * 4.3607741192761657d-1, 1.3358490740136963d0, - * 2.3506049736744927d0, -2.6519613568352334d0, - * -1.6735516287674728d0, -8.1628788285896470d-1, - * 0.d0, 8.1628788285896470d-1, - * 1.6735516287674705d0, 2.6519613568352325d0, - * -2.9306374202572423d0, -1.9816567566958434d0, - * -1.1571937124467806d0, -3.8118699020732233d-1, - * 3.8118699020732211d-1, 1.1571937124467804d0, - * 1.9816567566958441d0, 2.9306374202572423d0, - * -3.1909932017815290d0, -2.2665805845318436d0, - * -1.4685532892166682d0, -7.2355101875283812d-1, - * 0.d0, 7.2355101875283756d-1, - * 1.4685532892166657d0, 2.2665805845318405d0, - * 3.1909932017815281d0, -3.4361591188377387d0, - * -2.5327316742327906d0, -1.7566836492998805d0, - * -1.0366108297895140d0, -3.4290132722370548d-1, - * 3.4290132722370464d-1, 1.0366108297895136d0, - * 1.7566836492998834d0, 2.5327316742327857d0, - * 3.4361591188377396d0, -3.8897248978697796d0, - * -3.0206370251208856d0, -2.2795070805010567d0, - * -1.5976826351526050d0, -9.4778839124016290d-1, - * -3.1424037625435908d-1, 3.1424037625435935d-1, - * 9.4778839124016356d-1, 1.5976826351526054d0, - * 2.2795070805010602d0, 3.0206370251208905d0, - * 3.8897248978697831d0, -4.6887389393058214d0, - * -3.8694479048601251d0, -3.1769991619799582d0, - * -2.5462021578474765d0, -1.9517879909162541d0, - * -1.3802585391988809d0, -8.2295144914465523d-1, - * -2.7348104613815177d-1, 2.7348104613815244d-1, - * 8.2295144914465579d-1, 1.3802585391988802d0, - * 1.9517879909162534d0, 2.5462021578474801d0/ - DATA (HeBP(I),I=80,126) / - * 3.1769991619799565d0, 3.8694479048601265d0, - * 4.6887389393058196d0, -5.3874808900112274d0, - * -4.6036824495507513d0, -3.9447640401156296d0, - * -3.3478545673832154d0, -2.7888060584281300d0, - * -2.2549740020892721d0, -1.7385377121165839d0, - * -1.2340762153953209d0, -7.3747372854539361d-1, - * -2.4534070830090124d-1, 2.4534070830090149d-1, - * 7.3747372854539439d-1, 1.2340762153953226d0, - * 1.7385377121165866d0, 2.2549740020892770d0, - * 2.7888060584281282d0, 3.3478545673832105d0, - * 3.9447640401156230d0, 4.6036824495507398d0, - * 5.3874808900112274d0, -6.0159255614257390d0, - * -5.2593829276680442d0, -4.6256627564237904d0, - * -4.0536644024481472d0, -3.5200068130345219d0, - * -3.0125461375655647d0, -2.5238810170114276d0, - * -2.0490035736616989d0, -1.5842500109616944d0, - * -1.1267608176112460d0, -6.7417110703721150d-1, - * -2.2441454747251538d-1, 2.2441454747251532d-1, - * 6.7417110703721206d-1, 1.1267608176112454d0, - * 1.5842500109616939d0, 2.0490035736616958d0, - * 2.5238810170114281d0, 3.0125461375655687d0, - * 3.5200068130345232d0, 4.0536644024481499d0, - * 4.6256627564237816d0, 5.2593829276680353d0, - * 6.0159255614257550d0 / - !initialize Laguerre weights and nodes (basepoints) - ! for alpha=0 - ! NB! the relative error of these numbers - ! are less than 10^-15 -! PARAMETER - DATA (LaWF0(I),I=1,75) / 8.5355339059327351d-1, - * 1.4644660940672624d-1, 7.1109300992917313d-1, - * 2.7851773356924092d-1, 1.0389256501586137d-2, - * 6.0315410434163386d-1, - * 3.5741869243779956d-1, 3.8887908515005364d-2, - * 5.3929470556132730d-4, 5.2175561058280850d-1, - * 3.9866681108317570d-1, 7.5942449681707588d-2, - * 3.6117586799220489d-3, 2.3369972385776180d-5, - * 4.5896467394996360d-1, 4.1700083077212080d-1, - * 1.1337338207404497d-1, 1.0399197453149061d-2, - * 2.6101720281493249d-4, 8.9854790642961944d-7, - * 4.0931895170127397d-1, 4.2183127786171964d-1, - * 1.4712634865750537d-1, - * 2.0633514468716974d-2, 1.0740101432807480d-3, - * 1.5865464348564158d-5, 3.1703154789955724d-8, - * 3.6918858934163773d-1, 4.1878678081434328d-1, - * 1.7579498663717152d-1, 3.3343492261215649d-2, - * 2.7945362352256712d-3, 9.0765087733581999d-5, - * 8.4857467162725493d-7, 1.0480011748715038d-9, - * 3.3612642179796304d-1, 4.1121398042398466d-1, - * 1.9928752537088576d0, 4.7460562765651609d-2, - * 5.5996266107945772d-3, 3.0524976709321133d-4, - * 6.5921230260753743d-6, 4.1107693303495271d-8, - * 3.2908740303506941d-11, - * 3.0844111576502009d-1, 4.0111992915527328d-1, - * 2.1806828761180935d-1, 6.2087456098677683d-2, - * 9.5015169751810902d-3, 7.5300838858753855d-4, - * 2.8259233495995652d-5, 4.2493139849626742d-7, - * 1.8395648239796174d-9, 9.9118272196090085d-13, - & 2.6473137105544342d-01, - & 3.7775927587313773d-01, 2.4408201131987739d-01, - & 9.0449222211681030d-02, 2.0102381154634138d-02, - & 2.6639735418653122d-03, 2.0323159266299895d-04, - & 8.3650558568197802d-06, 1.6684938765409045d-07, - & 1.3423910305150080d-09, 3.0616016350350437d-12, - & 8.1480774674261369d-16, 2.0615171495780091d-01, - & 3.3105785495088480d-01, 2.6579577764421392d-01, - & 1.3629693429637740d-01, 4.7328928694125222d-02, - & 1.1299900080339390d-02, 1.8490709435263156d-03, - & 2.0427191530827761d-04, 1.4844586873981184d-05/ - DATA (LaWF0(I),I=76,126) / - & 6.8283193308711422d-07, 1.8810248410796518d-08, - & 2.8623502429738514d-10, 2.1270790332241105d-12, - & 6.2979670025179594d-15, 5.0504737000353956d-18, - & 4.1614623703728548d-22, 1.6874680185111446d-01, - & 2.9125436200606764d-01, 2.6668610286700062d-01, - & 1.6600245326950708d-01, 7.4826064668792408d-02, - & 2.4964417309283247d-02, 6.2025508445722223d-03, - & 1.1449623864769028d-03, 1.5574177302781227d-04, - & 1.5401440865224898d-05, 1.0864863665179799d-06, - & 5.3301209095567054d-08, 1.7579811790505857d-09, - & 3.7255024025122967d-11, 4.7675292515782048d-13, - & 3.3728442433624315d-15, 1.1550143395004071d-17, - & 1.5395221405823110d-20, 5.2864427255691140d-24, - & 1.6564566124989991d-28, 1.4281197333478154d-01, - & 2.5877410751742391d-01, 2.5880670727286992d-01, - & 1.8332268897777793d-01, 9.8166272629918963d-02, - & 4.0732478151408603d-02, 1.3226019405120104d-02, - & 3.3693490584783083d-03, 6.7216256409355021d-04, - & 1.0446121465927488d-04, 1.2544721977993268d-05, - & 1.1513158127372857d-06, 7.9608129591336357d-08, - & 4.0728589875500037d-09, 1.5070082262925912d-10, - & 3.9177365150584634d-12, 6.8941810529581520d-14, - & 7.8198003824593093d-16, 5.3501888130099474d-18, - & 2.0105174645555229d-20, 3.6057658645531092d-23, - & 2.4518188458785009d-26, 4.0883015936805334d-30, - & 5.5753457883284229d-35 / -! PARAMETER (LaBP0=(/ - DATA (LaBP0(I),I=1,78) /5.8578643762690485d-1, - * 3.4142135623730949d+00, 4.1577455678347897d-1, - * 2.2942803602790409d0, 6.2899450829374803d0, - * 3.2254768961939217d-1, 1.7457611011583465d0, - * 4.5366202969211287d0, 9.3950709123011364d0, - * 2.6356031971814076d-1, 1.4134030591065161d0, - * 3.5964257710407206d0, 7.0858100058588356d0, - * 1.2640800844275784d+01, 2.2284660417926061d-1, - * 1.1889321016726229d0, 2.9927363260593141d+00, - * 5.7751435691045128d0, 9.8374674183825839d0, - * 1.5982873980601699d+01, 1.9304367656036231d-1, - * 1.0266648953391919d0, 2.5678767449507460d0, - * 4.9003530845264844d0, 8.1821534445628572d0, - * 1.2734180291797809d+01, 1.9395727862262543d+01, - * 1.7027963230510107d-1, 9.0370177679938035d-1, - * 2.2510866298661316d0, 4.2667001702876597d0, - * 7.0459054023934673d0, 1.0758516010180994d+01, - * 1.5740678641278004d+01, 2.2863131736889272d+01, - * 1.5232222773180798d-1, 8.0722002274225590d-1, - * 2.0051351556193473d0, 3.7834739733312328d0, - * 6.2049567778766175d0, 9.3729852516875773d0, - * 1.3466236911092089d+01, 1.8833597788991703d+01, - * 2.6374071890927389d+01, 1.3779347054049221d-1, - * 7.2945454950317090d-1, 1.8083429017403163d0, - * 3.4014336978548996d0, - * 5.5524961400638029d0, 8.3301527467644991d0, - * 1.1843785837900066d+01, 1.6279257831378107d+01, - * 2.1996585811980765d+01, 2.9920697012273894d+01 , - & 1.1572211735802050d-01, 6.1175748451513112d-01, - & 1.5126102697764183d+00, 2.8337513377435077d+00, - & 4.5992276394183476d+00, 6.8445254531151809d+00, - & 9.6213168424568707d+00, 1.3006054993306348d+01, - & 1.7116855187462260d+01, 2.2151090379397019d+01, - & 2.8487967250983996d+01, 3.7099121044466933d+01, - & 8.7649410478926978d-02, 4.6269632891508106d-01, - & 1.1410577748312269d+00, 2.1292836450983796d+00, - & 3.4370866338932058d+00, 5.0780186145497677d+00, - & 7.0703385350482320d+00, 9.4383143363919331d+00, - & 1.2214223368866158d+01, 1.5441527368781616d+01, - & 1.9180156856753147d+01, 2.3515905693991915d+01/ - DATA (LaBP0(I),I=79,126) / - & 2.8578729742882153d+01, - & 3.4583398702286622d+01, 4.1940452647688396d+01, - & 5.1701160339543350d+01, 7.0539889691989419d-02, - & 3.7212681800161185d-01, 9.1658210248327376d-01, - & 1.7073065310283420d+00, 2.7491992553094309d+00, - & 4.0489253138508827d+00, 5.6151749708616148d+00, - & 7.4590174536710663d+00, 9.5943928695810943d+00, - & 1.2038802546964314d+01, 1.4814293442630738d+01, - & 1.7948895520519383d+01, 2.1478788240285009d+01, - & 2.5451702793186907d+01, 2.9932554631700611d+01, - & 3.5013434240478986d+01, 4.0833057056728535d+01, - & 4.7619994047346523d+01, 5.5810795750063903d+01, - & 6.6524416525615763d+01, 5.9019852181507730d-02, - & 3.1123914619848325d-01, 7.6609690554593646d-01, - & 1.4255975908036129d+00, 2.2925620586321909d+00, - & 3.3707742642089964d+00, 4.6650837034671726d+00, - & 6.1815351187367655d+00, 7.9275392471721489d+00, - & 9.9120980150777047d+00, 1.2146102711729766d+01, - & 1.4642732289596671d+01, 1.7417992646508978d+01, - & 2.0491460082616424d+01, 2.3887329848169724d+01, - & 2.7635937174332710d+01, 3.1776041352374712d+01, - & 3.6358405801651635d+01, 4.1451720484870783d+01, - & 4.7153106445156347d+01, 5.3608574544695017d+01, - & 6.1058531447218698d+01, 6.9962240035105026d+01, - & 8.1498279233948850d+01/ - - !Laguerre nodes for alpha=-0.5 -! PARAMETER (LaBP5 = (/ - DATA (LaBP5(I),I=1,79) /2.7525512860841095e-01, - & 2.7247448713915889e+00, 1.9016350919348812e-01, - & 1.7844927485432514e+00, 5.5253437422632619e+00, - & 1.4530352150331699e-01, 1.3390972881263605e+00, - & 3.9269635013582880e+00, 8.5886356890120332e+00, - & 1.1758132021177792e-01, 1.0745620124369035e+00, - & 3.0859374437175511e+00, 6.4147297336620337e+00, - & 1.1807189489971735e+01, 9.8747014068480951e-02, - & 8.9830283456961701e-01, 2.5525898026681721e+00, - & 5.1961525300544675e+00, 9.1242480375311814e+00, - & 1.5129959781108084e+01, 8.5115442997593743e-02, - & 7.7213792004277715e-01, 2.1805918884504596e+00, - & 4.3897928867310174e+00, 7.5540913261017897e+00, - & 1.1989993039823887e+01, 1.8528277495852500e+01, - & 7.4791882596818141e-02, 6.7724908764928937e-01, - & 1.9051136350314275e+00, 3.8094763614849056e+00, - & 6.4831454286271679e+00, 1.0093323675221344e+01, - & 1.4972627088426393e+01, 2.1984272840962646e+01, - & 6.6702230958194261e-02, 6.0323635708174905e-01, - & 1.6923950797931777e+00, 3.3691762702432655e+00, - & 5.6944233429577471e+00, 8.7697567302685968e+00, - & 1.2771825354869195e+01, 1.8046505467728977e+01, - & 2.5485979166099078e+01, 6.0192063149587700e-02, - & 5.4386750029464592e-01, 1.5229441054044432e+00, - & 3.0225133764515753e+00, 5.0849077500985240e+00, - & 7.7774392315254426e+00, 1.1208130204348663e+01, - & 1.5561163332189356e+01, 2.1193892096301536e+01, - & 2.9024950340236231e+01, 5.0361889117293709e-02, - & 4.5450668156378027e-01, 1.2695899401039612e+00, - & 2.5098480972321284e+00, 4.1984156448784127e+00, - & 6.3699753880306362e+00, 9.0754342309612088e+00, - & 1.2390447963809477e+01, 1.6432195087675318e+01, - & 2.1396755936166095e+01, 2.7661108779846099e+01, - & 3.6191360360615583e+01, 3.7962914575312985e-02, - & 3.4220015601094805e-01, 9.5355315539086472e-01, - & 1.8779315076960728e+00, 3.1246010507021431e+00, - & 4.7067267076675874e+00, 6.6422151797414388e+00, - & 8.9550013377233881e+00, 1.1677033673975952e+01, - & 1.4851431341801243e+01, 1.8537743178606682e+01, - & 2.2821300693525199e+01, 2.7831438211328681e+01/ - DATA (LaBP5(I),I=80,126) / - & 3.3781970488226136e+01, 4.1081666525491165e+01, - & 5.0777223877537075e+01, 3.0463239279482423e-02, - & 2.7444471579285024e-01, 7.6388755844391365e-01, - & 1.5018014976681033e+00, 2.4928301451213657e+00, - & 3.7434180412162927e+00, 5.2620558537883513e+00, - & 7.0596277357415627e+00, 9.1498983120306470e+00, - & 1.1550198286442805e+01, 1.4282403685210406e+01, - & 1.7374366975199074e+01, 2.0862075185437845e+01, - & 2.4793039892463458e+01, 2.9231910157093431e+01, - & 3.4270428925039589e+01, 4.0046815790245596e+01, - & 4.6788846392124952e+01, 5.4931555621020564e+01, - & 6.5589931990639684e+01, 2.5437996585689085e-02, - & 2.2910231649262403e-01, 6.3729027873266897e-01, - & 1.2517406323627462e+00, 2.0751129098523808e+00, - & 3.1110524551477146e+00, 4.3642830769353065e+00, - & 5.8407332713236055e+00, 7.5477046800234531e+00, - & 9.4940953300264859e+00, 1.1690695926056069e+01, - & 1.4150586187285759e+01, 1.6889671928527100e+01, - & 1.9927425875242456e+01, 2.3287932824879903e+01, - & 2.7001406056472355e+01, 3.1106464709046559e+01, - & 3.5653703516328221e+01, 4.0711598185543110e+01, - & 4.6376979557540103e+01, 5.2795432527283602e+01, - & 6.0206666963057259e+01, 6.9068601975304347e+01, - & 8.0556280819950416e+01/ - -! PARAMETER (LaWF5 = (/ - DATA (LaWF5(I),I=1,79) / 1.6098281800110255e+00, - & 1.6262567089449037e-01, 1.4492591904487846e+00, - & 3.1413464064571323e-01, 9.0600198110176913e-03, - & 1.3222940251164819e+00, 4.1560465162978422e-01, - & 3.4155966014826969e-02, 3.9920814442273529e-04, - & 1.2217252674706509e+00, 4.8027722216462992e-01, - & 6.7748788910962143e-02, 2.6872914935624635e-03, - & 1.5280865710465251e-05, 1.1402704725249586e+00, - & 5.2098462052832328e-01, 1.0321597123176789e-01, - & 7.8107811692581406e-03, 1.7147374087175731e-04, - & 5.3171033687126004e-07, 1.0728118194241802e+00, - & 5.4621121812849427e-01, 1.3701106844693015e-01, - & 1.5700109452915889e-02, 7.1018522710384658e-04, - & 9.4329687100378043e-06, 1.7257182336250307e-08, - & 1.0158589580332265e+00, 5.6129491705706813e-01, - & 1.6762008279797133e-01, 2.5760623071019968e-02, - & 1.8645680172483614e-03, 5.4237201850757696e-05, - & 4.6419616897304271e-07, 5.3096149480223697e-10, - & 9.6699138945091101e-01, 5.6961457133995952e-01, - & 1.9460349528263074e-01, 3.7280084775089407e-02, - & 3.7770452605368474e-03, 1.8362253735858719e-04, - & 3.6213089621868382e-06, 2.0934411591584102e-08, - & 1.5656399544231742e-11, 9.2448733920121973e-01, - & 5.7335101072566907e-01, 2.1803441204004675e-01, - & 4.9621041774927162e-02, 6.4875466844757246e-03, - & 4.5667727203270848e-04, 1.5605112957064066e-05, - & 2.1721387415385585e-07, 8.7986819845463701e-10, - & 4.4587872910682818e-13, 8.5386232773739834e-01, - & 5.7235907069288550e-01, 2.5547924356911883e-01, - & 7.4890941006461639e-02, 1.4096711620145414e-02, - & 1.6473849653768340e-03, 1.1377383272808749e-04, - & 4.3164914098046565e-06, 8.0379423498828602e-08, - & 6.0925085399751771e-10, 1.3169240486156312e-12, - & 3.3287369929782692e-16, 7.5047670518560539e-01, - & 5.5491628460505815e-01, 3.0253946815328553e-01, - & 1.2091626191182542e-01, 3.5106857663146820e-02, - & 7.3097806533088429e-03, 1.0725367310559510e-03, - & 1.0833168123639965e-04, 7.3011702591247581e-06, - & 3.1483355850911864e-07, 8.1976643295418016e-09, - & 1.1866582926793190e-10, 8.4300204226528705e-13/ - DATA (LaWF5(I),I=80,126) / - & 2.3946880341857530e-15, 1.8463473073036743e-18, - & 1.4621352854768128e-22, 6.7728655485117817e-01, - & 5.3145650375475362e-01, 3.2675746542654360e-01, - & 1.5694921173080897e-01, 5.8625131072344717e-02, - & 1.6921776016516312e-02, 3.7429936591959084e-03, - & 6.2770718908266166e-04, 7.8738679621849850e-05, - & 7.2631523013860402e-06, 4.8222883273410492e-07, - & 2.2424721664551585e-08, 7.0512415827308280e-10, - & 1.4313056105380569e-11, 1.7611415290432366e-13, - & 1.2016717578981511e-15, 3.9783620242330409e-18, - & 5.1351867308233644e-21, 1.7088113927550770e-24, - & 5.1820874276942667e-29, 6.2200206075592535e-01, - & 5.0792308532951769e-01, 3.3840894389128295e-01, - & 1.8364459415856996e-01, 8.0959353969207851e-02, - & 2.8889923149962169e-02, 8.3060098239550965e-03, - & 1.9127846396388331e-03, 3.5030086360234562e-04, - & 5.0571980554969836e-05, 5.6945173834697106e-06, - & 4.9373179873395243e-07, 3.2450282717915824e-08, - & 1.5860934990330932e-09, 5.6305930756763865e-11, - & 1.4093865163091798e-12, 2.3951797309583852e-14, - & 2.6303192453168292e-16, 1.7460319202373756e-18, - & 6.3767746470103704e-21, 1.1129154937804721e-23, - & 7.3700721603011131e-27, 1.1969225386627985e-30, - & 1.5871102921547987e-35 / - - INTERFACE GAUSSLA0 - MODULE PROCEDURE GAUSSLA0 - END INTERFACE - - INTERFACE GAUSSLE0 - MODULE PROCEDURE GAUSSLE0 - END INTERFACE - - INTERFACE GAUSSHE0 - MODULE PROCEDURE GAUSSHE0 - END INTERFACE - - - INTERFACE GAUSSLE1 - MODULE PROCEDURE GAUSSLE1 - END INTERFACE - - INTERFACE GAUSSLE2 - MODULE PROCEDURE GAUSSLE2 - END INTERFACE - - INTERFACE GAUSSQ - MODULE PROCEDURE GAUSSQ - END INTERFACE - - CONTAINS - SUBROUTINE GAUSSLE1 (N,WFout,BPOUT,XMI,XMA) - USE GLOBALDATA,ONLY : EPS0 - USE FIMOD -! USE QUAD , ONLY: LeBP,LeWF,LeIND,NLeW,minQnr - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:),INTENT(out) :: BPOUT, WFout - DOUBLE PRECISION, INTENT(in) :: XMI,XMA - INTEGER, INTENT(inout) :: N - ! local variables - DOUBLE PRECISION :: Z1,SDOT, SDOT1, DIFF1 - DOUBLE PRECISION,PARAMETER :: SQTWOPI1 = 0.39894228040143D0 !=1/sqrt(2*pi) - INTEGER :: NN,I,J,k - - ! The subroutine picks the lowest Gauss-Legendre - ! quadrature needed to integrate the test function - ! gaussint to the specified accuracy, EPS0. - ! The nodes and weights between the integration - ! limits XMI and XMA (all normalized) are returned. - ! Note that the weights are multiplied with - ! 1/sqrt(2*pi)*exp(.5*bpout^2) - - IF (XMA.LE.XMI) THEN -! PRINT * , 'Warning XMIN>=XMAX in GAUSSLE1 !',XMI,XMA - RETURN - ENDIF - - DO I = minQnr, NLeW - NN = N !initialize - DO J = LeIND(I)+1, LeIND(I+1) - BPOUT (NN+1) = 0.5d0*(LeBP(J)*(XMA-XMI)+XMA+XMI) - Z1 = BPOUT (NN+1) * BPOUT (NN+1) - !IF (Z1.LE.xCutOff2) THEN - NN=NN+1 - WFout (NN) = 0.5d0 * SQTWOPI1 * (XMA - XMI) * - & LeWF(J) *EXP ( - 0.5d0* Z1 ) - !ENDIF - ENDDO - - SDOT = GAUSINT (XMI, XMA, - 2.5d0, 2.d0, 2.5d0, 2.d0) - SDOT1 = 0.d0 - - DO k = N+1, NN - SDOT1 = SDOT1+WFout(k)*(-2.5d0+2.d0*BPOUT(k) )* - & (2.5d0 + 2.d0 * BPOUT (k) ) - ENDDO - DIFF1 = ABS (SDOT - SDOT1) - - IF (EPS0.GT.DIFF1) THEN - N=NN -! PRINT * ,'gaussle1, XMI,XMA,NN',XMI,XMA,NN - RETURN - END IF - END DO - RETURN - END SUBROUTINE GAUSSLE1 - - SUBROUTINE GAUSSLE0 (N, wfout, bpout, XMI, XMA, N0) - USE GLOBALDATA, ONLY : EPSS -! USE QUAD, ONLY : LeBP,LeWF,NLeW,LeIND - IMPLICIT NONE - INTEGER, INTENT(in) :: N0 - INTEGER, INTENT(inout) :: N - DOUBLE PRECISION, DIMENSION(:), INTENT(out) :: wfout,bpout - DOUBLE PRECISION, INTENT(in) :: XMI,XMA -! Local variables - DOUBLE PRECISION,PARAMETER :: SQTWOPI1 = 0.39894228040143D0 !=1/sqrt(2*pi) - DOUBLE PRECISION :: Z1 - INTEGER :: J - ! The subroutine computes Gauss-Legendre - ! nodes and weights between - ! the (normalized) integration limits XMI and XMA - ! Note that the weights are multiplied with - ! 1/sqrt(2*pi)*exp(.5*bpout^2) so that - ! b - ! int f(x)*exp(-x^2/2)/sqrt(2*pi)dx=sum f(bp(j))*wf(j) - ! a j - - IF (XMA.LE.XMI) THEN - !PRINT * , 'Warning XMIN>=XMAX in GAUSSLE0 !',XMI,XMA - RETURN ! no more nodes added - ENDIF - IF ((XMA-XMI).LT.EPSS) THEN - N=N+1 - BPout (N) = 0.5d0 * (XMA + XMI) - Z1 = BPOUT (N) * BPOUT (N) - WFout (N) = SQTWOPI1 * (XMA - XMI) *EXP ( - 0.5d0* Z1 ) - RETURN - ENDIF - IF (N0.GT.NLeW) THEN - !PRINT * , 'error in GAUSSLE0, quadrature not available' - STOP - ENDIF - !print *, 'GAUSSLE0',N0 - - !print *, N - DO J = LeIND(N0)+1, LeIND(N0+1) - - BPout (N+1) = 0.5d0 * (LeBP(J) * (XMA - XMI) + XMA + XMI) - Z1 = BPOUT (N+1) * BPOUT (N+1) - ! IF (Z1.LE.xCutOff2) THEN - N=N+1 ! add a new node and weight - WFout (N) = 0.5d0 * SQTWOPI1 * (XMA - XMI) * - & LeWF(J) *EXP ( - 0.5d0* Z1 ) - ! ENDIF - ENDDO - !print *,BPout - RETURN - END SUBROUTINE GAUSSLE0 - - SUBROUTINE GAUSSLE2 (N, wfout, bpout, XMI, XMA, N0) - USE GLOBALDATA, ONLY : xCutOff,EPSS -! USE QUAD, ONLY : LeBP,LeWF,NLeW,LeIND,minQNr - IMPLICIT NONE - INTEGER, INTENT(in) :: N0 - INTEGER, INTENT(inout) :: N - DOUBLE PRECISION, DIMENSION(:), INTENT(out) :: wfout,bpout - DOUBLE PRECISION, INTENT(in) :: XMI,XMA -! Local variables - DOUBLE PRECISION :: Z1 - INTEGER :: J,N1 - DOUBLE PRECISION,PARAMETER :: SQTWOPI1 = 0.39894228040143D0 !=1/sqrt(2*pi) - ! The subroutine computes Gauss-Legendre - ! nodes and weights between - ! the (normalized) integration limits XMI and XMA - ! This procedure select number of nodes - ! depending on the length of the integration interval. - ! Note that the weights are multiplied with - ! 1/sqrt(2*pi)*exp(.5*bpout^2) so that - ! b - ! int f(x)*exp(-x^2/2)/sqrt(2*pi)dx=sum f(bp(j))*wf(j) - ! a j - - IF (XMA.LE.XMI) THEN - !PRINT * , 'Warning XMIN>=XMAX in GAUSSLE2 !',XMI,XMA - RETURN ! no more nodes added - ENDIF -! IF (XMA.LT.XMI+EPSS) THEN -! N=N+1 -! BPout (N) = 0.65d0 * (XMA + XMI) -! Z1 = BPOUT (N) * BPOUT (N) -! WFout (N) = SQTWOPI1 * (XMA - XMI) *EXP ( - 0.5d0* Z1 ) -! RETURN -! ENDIF - IF (N0.GT.NLeW) THEN - !PRINT * , 'Warning in GAUSSLE2, quadrature not available' - ENDIF - !print *, 'GAUSSLE2',N0 - - !print *, N - N1=CEILING(0.5d0*(XMA-XMI)*DBLE(N0)/xCutOff) !0.65d0 - N1=MAX(MIN(N1,NLew),minQNr) - - DO J = LeIND(N1)+1, LeIND(N1+1) - - BPout (N+1) = 0.5d0 * (LeBP(J) * (XMA - XMI) + XMA + XMI) - Z1 = BPOUT (N+1) * BPOUT (N+1) - ! IF (Z1.LE.xCutOff2) THEN - N=N+1 ! add a new node and weight - WFout (N) = 0.5d0 * SQTWOPI1 * (XMA - XMI) * - & LeWF(J) *EXP ( - 0.5d0* Z1 ) - ! ENDIF - ENDDO - !PRINT * ,'gaussle2, XMI,XMA,N',XMI,XMA,N - !print *,BPout - RETURN - END SUBROUTINE GAUSSLE2 - - SUBROUTINE GAUSSHE0 (N, WFout, BPout, XMI, XMA, N0) -! USE QUAD, ONLY : HeBP,HeWF,HeIND,NHeW - IMPLICIT NONE - INTEGER, INTENT(in) :: N0 - INTEGER, INTENT(inout) :: N - DOUBLE PRECISION, DIMENSION(:), INTENT(out) :: wfout,bpout - DOUBLE PRECISION, INTENT(in) :: XMI,XMA -! Local variables - DOUBLE PRECISION, PARAMETER :: SQPI1= 5.6418958354776D-1 !=1/sqrt(pi) - DOUBLE PRECISION, PARAMETER :: SQTWO= 1.41421356237310D0 !=sqrt(2) - INTEGER :: J - ! The subroutine returns modified Gauss-Hermite - ! nodes and weights between - ! the integration limits XMI and XMA - ! for the chosen number of nodes - ! implicitly assuming that the integrand - ! goes smoothly towards zero as its approach XMI or XMA - ! Note that the nodes and weights are modified - ! according to - ! Inf - ! int f(x)*exp(-x^2/2)/sqrt(2*pi)dx=sum f(bp(j))*wf(j) - ! -Inf j - - IF (XMA.LE.XMI) THEN - !PRINT * , 'Warning XMIN>=XMAX in GAUSSHE0 !',XMI,XMA - RETURN ! no more nodes added - ENDIF - IF (N0.GT.NHeW) THEN - !PRINT * , 'error in GAUSSHE0, quadrature not available' - STOP - ENDIF - - DO J = HeIND(N0)+1, HeIND(N0+1) - BPout (N+1) = HeBP (J) * SQTWO - IF (BPout (N+1).GT.XMA) THEN - RETURN - END IF - IF (BPout (N+1).GE.XMI) THEN - N=N+1 ! add the node - WFout (N) = HeWF (J) * SQPI1 - END IF - ENDDO - RETURN - END SUBROUTINE GAUSSHE0 - - SUBROUTINE GAUSSLA0 (N, WFout, BPout, XMI, XMA, N0) - USE GLOBALDATA, ONLY : SQPI1 -! USE QUAD, ONLY : LaBP5,LaWF5,LaIND,NLaW - IMPLICIT NONE - INTEGER, INTENT(in) :: N0 - INTEGER, INTENT(inout) :: N - DOUBLE PRECISION, DIMENSION(:), INTENT(out) :: wfout,bpout - DOUBLE PRECISION, INTENT(in) :: XMI, XMA - INTEGER :: J - ! The subroutine returns modified Gauss-Laguerre - ! nodes and weights for alpha=-0.5 between - ! the integration limits XMI and XMA - ! for the chosen number of nodes - ! implicitly assuming the integrand - ! goes smoothly towards zero as its approach XMI or XMA - ! Note that the nodes and weights are modified - ! according to - ! Inf - ! int f(x)*exp(-x^2/2)/sqrt(2*pi)dx=sum f(bp(j))*wf(j) - ! 0 j - - IF (XMA.LE.XMI) THEN - !PRINT * , 'Warning XMIN>=XMAX in GAUSSLA0 !',XMI,XMA - RETURN !no more nodes added - ENDIF - IF (N0.GT.NLaW) THEN - !PRINT * , 'error in GAUSSLA0, quadrature not available' - STOP - ENDIF - - DO J = LaIND(N0)+1, LaIND(N0+1) - IF (XMA.LE.0.d0) THEN - BPout (N+1) = -SQRT(2.d0*LaBP5(J)) - ELSE - BPout (N+1) = SQRT(2.d0*LaBP5(J)) - END IF - IF (BPout (N+1).GT.XMA) THEN - RETURN - END IF - IF (BPout (N+1).GE.XMI) THEN - N=N+1 ! add the node - WFout (N) = LaWF5 (J)*0.5d0*SQPI1 - END IF - ENDDO - !PRINT *,'gaussla0, bp',LaBP5(LaIND(N0)+1:LaIND(N0+1)) - !PRINT *,'gaussla0, wf',LaWF5(LaIND(N0)+1:LaIND(N0+1)) - RETURN - END SUBROUTINE GAUSSLA0 - - SUBROUTINE GAUSSQ(N, WF, BP, XMI, XMA, N0) - USE GLOBALDATA, ONLY : xCutOff -! USE QUAD , ONLY : minQNr - IMPLICIT NONE - INTEGER, INTENT(in) :: N0 - INTEGER, INTENT(inout) :: N - DOUBLE PRECISION, DIMENSION(:), INTENT(out) :: wf,bp - DOUBLE PRECISION, INTENT(in) :: XMI,XMA - INTEGER :: N1 - ! The subroutine returns - ! nodes and weights between - ! the integration limits XMI and XMA - ! for the chosen number of nodes - ! Note that the nodes and weights are modified - ! according to - ! Inf - ! int f(x)*exp(-x^2/2)/sqrt(2*pi)dx=sum f(bp(j))*wf(j) - ! 0 j - - !IF (XMA.LE.XMI) THEN - ! PRINT * , 'Warning XMIN>=XMAX in GAUSSQ !',XMI,XMA - ! RETURN !no more nodes added - !ENDIF - CALL GAUSSLE0(N,WF,BP,XMI,XMA,N0) - RETURN - IF ((XMA.GE.xCutOff).AND.(XMI.LE.-xCutOff)) THEN - CALL GAUSSHE0(N,WF,BP,XMI,XMA,N0) - ELSE - CALL GAUSSLE2(N,WF,BP,XMI,XMA,N0) - RETURN - IF (((XMA.LT.xCutOff).AND.(XMI.GT.-xCutOff)).OR.(.TRUE.) - & .OR.(XMI.GT.0.d0).OR.(XMA.LT.0.d0)) THEN - ! Grid by Gauss-LegENDre quadrature - CALL GAUSSLE2(N,WF,BP,XMI,XMA,N0) - ELSE - ! this does not work well - !PRINT *,'N0',N0,N - N1=CEILING(DBLE(N0)/2.d0) - IF (XMA.GE.xCutOff) THEN - IF (XMI.LT.0.d0) THEN - CALL GAUSSLE2 (N, WF, BP,XMI ,0.d0,N0) - ENDIF - CALL GAUSSLA0 (N, WF, BP,0.d0, XMA, N1) - ELSE - IF (XMA.GT.0.d0) THEN - CALL GAUSSLE2 (N, WF,BP,0.d0,XMA,N0) - ENDIF - CALL GAUSSLA0 (N, WF,BP,XMI,0.d0, N1) - END IF - END IF - ENDIF - !PRINT *,'gaussq, wf',wf(1:N) - !PRINT *,'gaussq, bp',bp(1:N) - RETURN - END SUBROUTINE GAUSSQ - END MODULE QUAD - - MODULE RIND71MOD - IMPLICIT NONE - PRIVATE - PUBLIC :: RIND71, INITDATA, SETDATA,ECHO - - INTERFACE - FUNCTION MVNFUN(N,Z) result (VAL) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - DOUBLE PRECISION :: VAL - END FUNCTION MVNFUN - END INTERFACE - - INTERFACE - FUNCTION MVNFUN2(N,Z) result (VAL) - DOUBLE PRECISION,DIMENSION(:), INTENT(IN) :: Z - INTEGER, INTENT(IN) :: N - DOUBLE PRECISION :: VAL - END FUNCTION MVNFUN2 - END INTERFACE - - INTERFACE - FUNCTION FI( Z ) RESULT (VALUE) - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE - END FUNCTION FI - END INTERFACE - - INTERFACE - FUNCTION FIINV( Z ) RESULT (VALUE) - DOUBLE PRECISION, INTENT(in) :: Z - DOUBLE PRECISION :: VALUE - END FUNCTION FIINV - END INTERFACE - - INTERFACE - FUNCTION JACOB(XD,XC) RESULT (VALUE) - DOUBLE PRECISION, DIMENSION(:), INTENT(in) :: XD,XC - DOUBLE PRECISION :: VALUE - END FUNCTION JACOB - END INTERFACE - - INTERFACE RIND71 - MODULE PROCEDURE RIND71 - END INTERFACE - - INTERFACE SETDATA - MODULE PROCEDURE SETDATA - END INTERFACE - - INTERFACE INITDATA - MODULE PROCEDURE INITDATA - END INTERFACE - - INTERFACE ARGP0 - MODULE PROCEDURE ARGP0 - END INTERFACE - - INTERFACE RINDDND - MODULE PROCEDURE RINDDND - END INTERFACE - - INTERFACE RINDSCIS - MODULE PROCEDURE RINDSCIS - END INTERFACE - - INTERFACE RINDNIT - MODULE PROCEDURE RINDNIT - END INTERFACE - - INTERFACE BARRIER - MODULE PROCEDURE BARRIER - END INTERFACE - - INTERFACE echo - MODULE PROCEDURE echo - END INTERFACE - - INTERFACE swapRe - MODULE PROCEDURE swapRe - END INTERFACE - - INTERFACE swapint - MODULE PROCEDURE swapint - END INTERFACE - - INTERFACE getdiag - MODULE PROCEDURE getdiag - END INTERFACE - - INTERFACE CONDSORT0 - MODULE PROCEDURE CONDSORT0 - END INTERFACE - - INTERFACE CONDSORT - MODULE PROCEDURE CONDSORT - END INTERFACE - - - INTERFACE CONDSORT2 - MODULE PROCEDURE CONDSORT2 - END INTERFACE - - INTERFACE CONDSORT3 - MODULE PROCEDURE CONDSORT3 - END INTERFACE - - INTERFACE CONDSORT4 - MODULE PROCEDURE CONDSORT4 - END INTERFACE - - CONTAINS - SUBROUTINE SETDATA(method,scale, dEPSS,dREPS,dEPS2, - & dNIT,dXc, dNINT,dXSPLT) - USE GLOBALDATA - USE FIMOD - USE QUAD, ONLY: sizNint,Nint1,minQnr,Le2Qnr - IMPLICIT NONE - DOUBLE PRECISION , INTENT(in) :: scale, dEPSS,dREPS - DOUBLE PRECISION , INTENT(in) :: dEPS2,dXc, dXSPLT - !INTEGER, DIMENSION(:), INTENT(in) :: dNINT - INTEGER, INTENT(in) :: method,dNINT,dNIT - INTEGER :: N=1 - - !N=SIZE(dNINT) - IF (sizNint.LT.N) THEN - !PRINT *,'Error in setdata, Nint too large' - N=sizNint - ENDIF - NINT1(1:N)=dNINT !(1:N) ! quadrature formulae for the Xd variables - IF (N.LT.sizNint) THEN - NINT1(N:sizNint)=NINT1(N) - END IF - minQnr = 1 - Le2Qnr = NINT1(1) - - SCIS = method - XcScale = scale - RelEps = dREPS - EPSS = dEPSS ! accuracy of integration - CEPSS = 1.d0 - EPSS - EPS2 = dEPS2 ! Constants controlling - EPS = SQRT(EPS2) - xCutOff = dXc - XSPLT = dXSPLT - NIT = dNIT - - IF (Nc.LT.1) NUGGET=0.d0 ! Nugget is not needed when Nc=0 - - IF (EPSS.LE.1e-4) NsimMax=2000 - IF (EPSS.LE.1e-5) NsimMax=4000 - IF (EPSS.LE.1e-6) NsimMax=8000 - RETURN - IF (.FALSE.) THEN - print *,'Requested parameters :' - SELECT CASE (SCIS) - CASE (:0) - PRINT *,'NIT = ',NIT,' integration by quadrature' - CASE (1) - PRINT *,'SCIS = 1 SADAPT if NDIM<9 otherwise by KRBVRC' - CASE (2) - PRINT *,'SCIS = 2 SADAPT if NDIM<20 otherwise by KRBVRC' - CASE (3) - PRINT *,'SCIS = 3 KRBVRC (Ndim<101)' - CASE (4) - PRINT *,'SCIS = 4 KROBOV (Ndim<101)' - CASE (5) - PRINT *,'SCIS = 5 RCRUDE (Ndim<1001)' - CASE (6) - PRINT *,'SCIS = 6 SOBNIED (Ndim<1041)' - CASE (7:) - PRINT *,'SCIS = 7 DKBVRC (Ndim<1001)' - END SELECT - PRINT *,'EPSS = ', EPSS, ' RELEPS = ' ,RELEPS - PRINT *,'EPS2 = ',EPS2, ' xCutOff = ',xCutOff - PRINT *,'NsimMax = ',NsimMax !,FIINV(EPSS) - ENDIF - RETURN - END SUBROUTINE SETDATA - - SUBROUTINE INITDATA (speed) - USE GLOBALDATA - USE FIMOD - USE QUAD, ONLY: sizNint,Nint1,minQnr,Le2Qnr - IMPLICIT NONE - INTEGER , INTENT(in) :: speed - SELECT CASE (speed) - CASE (9:) - NINT1 (1) = 2 - NINT1 (2) = 3 - NINT1 (3) = 4 - CASE (8) - NINT1 (1) = 3 - NINT1 (2) = 4 - NINT1 (3) = 5 - CASE (7) - NINT1 (1) = 4 - NINT1 (2) = 5 - NINT1 (3) = 6 - CASE (6) - NINT1 (1) = 5 - NINT1 (2) = 6 - NINT1 (3) = 7 - CASE (5) - NINT1 (1) = 6 - NINT1 (2) = 7 - NINT1 (3) = 8 - CASE (4) ! quadrature formulae for the Xd variables - NINT1 (1) = 7 ! use quadr. form. No. 6 in integration of Xd(1) - NINT1 (2) = 8 ! use quadr. form. No. 7 in integration of Xd(2) - NINT1 (3) = 9 ! use quadr. form. No. 8 in integration of Xd(3) - CASE (3) - NINT1 (1) = 8 - NINT1 (2) = 9 - NINT1 (3) = 10 - CASE (2) - NINT1 (1) = 9 - NINT1 (2) = 10 - NINT1 (3) = 11 - CASE (:1) - NINT1 (1) = 11 - NINT1 (2) = 12 - NINT1 (3) = 13 - END SELECT - NsimMax=1000*abs(10-min(speed,9)) - NsimMin=0 - SELECT case (speed) - CASE (11:) - EPSS = 1d-1 - CASE (10) - EPSS = 1d-2 - CASE (7:9) - EPSS = 1d-3 - CASE (4:6) - EPSS = 1d-4 - CASE (:3) - EPSS = 1d-5 - END SELECT - - - EPSS=EPSS*1d-1 - RELEPS = MIN(EPSS ,1.d-2) - EPS2=EPSS*1.d1 - !EPS2*1.d+1 - !EPS2=1.d-10 - !xCutOff=MIN(MAX(ABS(FIINV(EPSS)),3.5d0),5.d0) - !xCutOff=ABS(FIINV(EPSS*1.d-1)) ! this is good - xCutOff=ABS(FIINV(EPSS)) - !xCutOff=ABS(FIINV(EPSS*5.d-1)) - if (SCIS.gt.0) then - xCutOff= MIN(MAX(xCutOff+0.5d0,4.d0),5.d0) -! This gives approximately the same accuracy as when using RINDDND and RINDNIT - EPSS=EPSS*1.d+2 - !EPS2=1.d-10 - endif - NINT1(1:sizNint)=NINT1(3) - Le2Qnr=NINT1(1) - minQnr=1 ! minimum quadrature No. used in GaussLe1,Gaussle2 - - NUGGET = EPS2*1.d-1 - IF (Nc.LT.1) NUGGET=0.d0 ! Nugget is not needed when Nc=0 - EPS = SQRT(EPS2) - CEPSS = 1.d0 - EPSS - -! If SCIS=0 then the absolute error is usually less than EPSS*100 -! otherwise absolute error is less than EPSS - - return - IF (.FALSE.) THEN - print *,'Requested parameters :' - SELECT CASE (SCIS) - CASE (:0) - PRINT *,'NIT = ',NIT,' integration by quadrature' - CASE (1) - PRINT *,'SCIS = 1 SADAPT if NDIM<9 otherwise by KRBVRC' - CASE (2) - PRINT *,'SCIS = 2 SADAPT if NDIM<19 otherwise by KRBVRC' - CASE (3) - PRINT *,'SCIS = 3 KRBVRC (Ndim<101)' - CASE (4) - PRINT *,'SCIS = 4 KROBOV (Ndim<101)' - CASE (5) - PRINT *,'SCIS = 5 RCRUDE (Ndim<1001)' - CASE (6) - PRINT *,'SCIS = 6 SOBNIED (Ndim<1041)' - CASE (7:) - PRINT *,'SCIS = 7 DKBVRC (Ndim<1001)' - END SELECT - PRINT *,'EPSS = ', EPSS, ' RELEPS = ' ,RELEPS - PRINT *,'EPS2 = ',EPS2, ' xCutOff = ',xCutOff - PRINT *,'NsimMax = ',NsimMax !,FIINV(EPSS) - ENDIF - RETURN - END SUBROUTINE INITDATA - - SUBROUTINE ECHO(array) - INTEGER ::j - DOUBLE PRECISION,DIMENSION(:,:)::array - DO j=1,size(array,1) - PRINT 111,j,array(j,:) -111 FORMAT (i2,':',10F10.5) - END DO - END SUBROUTINE ECHO - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -!!******************* RIND71 - the main program *********************!! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - SUBROUTINE RIND71(fxind,BIG1,Ex,xc1,Nt1,indI,Blo,Bup) - USE FUNCMOD, ONLY : BIG, Cm,CmN,xd,xc - USE GLOBALDATA, ONLY :Nt,Nj,Njj,Nd,Nc,Nx,Ntd,Ntdc,NsXtmj,NsXdj, - & indXtd,index1,xedni,SQ,Hlo,Hup,fxcepss,EPS2,XCEPS2,NIT, - & SQTWOPI1,xCutOff,SCIS,Ntscis,COVix,EPS, xcScale - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: BIG1 - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: xc1 - DOUBLE PRECISION, DIMENSION(:), INTENT(in) :: Ex - DOUBLE PRECISION, DIMENSION(:), INTENT(out):: fxind - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: Blo, Bup - INTEGER, DIMENSION(:), INTENT(in) :: indI - INTEGER, INTENT(IN) :: Nt1 -! local variables - INTEGER :: J,ix,Ntdcmj,Nst,Nsd,INFORM - DOUBLE PRECISION :: xind,SQ0,xx,fxc,quant -! IF (.NOT.PRESENT(xcScale)) THEN -! xcScale = 0.0d0 -! ENDIF - Nt =Nt1 - !print *,'rindd SCIS',SCIS - Nc = size(xc1,dim=1) - Nx = MAX(size(xc1,dim=2),1) - Ntdc = size(BIG1,dim=1) - IF (Nt+Nc.GT.Ntdc) Nt=Ntdc-Nc ! make sure it does not exceed Ntdc-Nc - Nd = Ntdc - Nt - Nc - Ntd = Nt + Nd - - !Initialization - !Call Initdata(speed) - Nj = MIN(Nj,MAX(Nt,0)) ! make sure Nj<=Nt - Njj = MIN(Njj,MAX(Nt-Nj,0)) ! make sure Njj<=Nt-Nj - ALLOCATE(xc(1:Nc)) - IF (Nd.GT.0) THEN - ALLOCATE(xd(1:Nd)) - xd = 0.d0 - END IF - - If (SCIS.GT.0) then - Ntscis=Nt-Nj-Njj - ALLOCATE(SQ(1:Ntd,1:Ntd)) ! Cond. stdev's - ALLOCATE(NsXtmj(1:Ntd+1)) ! indices to stoch. var. See condsort - else - Ntscis=0 - ALLOCATE(SQ(1:Ntd,1:max(Njj+Nj+Nd,1)) ) ! Cond. stdev's - ALLOCATE(NsXtmj(1:Nd+Nj+Njj+1)) ! indices to stoch. var. See condsort - endif - ALLOCATE(BIG(Ntdc,Ntdc)) - ALLOCATE(Cm(Ntdc),CmN(Ntd)) !Cond. mean which has the same order as local - Cm = 0.d0 !covariance matrices (after sorting) or excluding - !irrelevant variables. - - ALLOCATE(index1(Ntdc)) ! indices to the var. original place in BIG - index1=(/(J,J=1,Ntdc)/) ! (before sort.) - ALLOCATE(xedni(Ntdc)) ! indices to var. new place (after sorting), - xedni=index1 ! eg. the point xedni(1) is the original position - ! of variable with conditional mean CM(1). - ALLOCATE(Hlo(Ntd)) ! lower and upper integration limits are computed - ! in the new order that is the same as CM. - ! This convention is expressed in the vector indXTD. - Hlo = 0.d0 ! However later on some variables will be exluded - ! since those are irrelevant and hence CMnew(1) - ! does not to be conditional mean of the same variable - ! as CM(1) is from the beginning. Consequently - ALLOCATE(Hup(Ntd)) ! the order of Hup, Hlo will be unchanged. So we need - Hup=0.d0 ! to know where the relevant variables bounds are - ! This will be given in the subroutines by a vector indS. - - ALLOCATE(NsXdj(Nd+Nj+1)) ! indices to stoch. var. See condsort - NsXdj=0 - ALLOCATE(indXtd(Ntd)) ! indices to Xt and Xd as they are - indXtd=(/(J,J=1,Ntd)/) ! sorted in Hlo and Hup - - - BIG = BIG1(1:Ntdc,1:Ntdc) !conditional covariance matrix BIG - - IF (.TRUE.) THEN ! sort by shortest expected int. interval - Cm = Ex (1:Ntdc) - !xc = SUM(xc1(1:Nc,1:Nx),DIM=2)/DBLE(Nx) ! average of all xc's - xc = xc1(1:Nc,max(Nx/2,1)) ! Or select the one in the middle - CALL BARRIER(xc,indI,Blo,Bup) ! compute average integrationlimits - - ! print *,'rindd,xcmean:',xc - ! print *,'rindd,Hup:',Hup - ! print *,'rindd,Hlo:',Hlo - - CALL CONDSORT0(BIG,Cm,xc,SQ,index1,xedni,NsXtmj,NsXdj,INFORM) - ELSE ! sort by decreasing cond. variance - CALL CONDSORT (BIG,SQ,index1,xedni,NsXtmj,NsXdj,INFORM) - ENDIF - IF (INFORM.GT.0) GOTO 110 !Degenerated case the density can not computed - -! PRINT *, 'index=', index1 -! PRINT *,(sqrt(BIG(J,J)),J=1,Ntdc) -! PRINT *, 'BIG' -! CALL ECHO(BIG(1:Ntdc,1:MIN(Ntdc,10))) - !PRINT *, 'xedni=', xedni - !print *,'NsXtmj=',NsXtmj - !print *,'NsXdj=',NsXdj - - fxind = 0.d0 ! initialize - ! Now the loop over all different values of - ! variables Xc (the one one is conditioning on) - DO ix = 1, Nx ! is started. The density f_{Xc}(xc(:,ix)) - COVix = ix ! will be computed and denoted by fxc. - xind = 0.d0 - fxc = 1.d0 -! Cm = Ex (1:Ntdc) -! index1=(/(J,J=1,Ntdc)/) -! xedni=index1 -! BIG = BIG1(1:Ntdc,1:Ntdc) -! CALL BARRIER(xc1(1:Nc,ix),indI,Blo,Bup) ! integrationlimits -! CALL CONDSORT0 (BIG,Cm,xc1(:,ix),SQ, index1, -! & xedni, NsXtmj,NsXdj) - - ! Set the original means of the variables - Cm =Ex (index1(1:Ntdc)) ! Cm(1:Ntdc) =Ex (index1(1:Ntdc)) - quant = 0.0d0 - DO J = 1, Nc !Recursive conditioning on the last Nc variables - Ntdcmj=Ntdc-J - SQ0 = BIG(Ntdcmj+1,Ntdcmj+1) ! SQRT(var(X(i)|X(i+1),X(i+2),...,X(Ntdc))) - ! i=Ntdc-J+1 (J=1 var(X(Ntdc)) - - xx = (xc1(index1(Ntdcmj+1)-Ntd,ix)-Cm(Ntdcmj+1))/SQ0 - !Trick to calculate - !fxc = fxc*SQTWPI1*EXP(-0.5*(XX**2))/SQ0 - quant = quant - 0.5d0 * xx * xx + LOG(SQTWOPI1) - LOG(SQ0) - - ! conditional mean (expectation) - ! E(X(1:i-1)|X(i),X(i+1),...,X(Ntdc)) - Cm(1:Ntdcmj) = Cm(1:Ntdcmj)+xx*BIG (1:Ntdcmj,Ntdcmj+1) - ENDDO -! fxc probability density for i=Ntdc-J+1, -! fXc=f(X(i)|X(i+1),X(i+2)...X(Ntdc))* - ! f(X(i+1)|X(i+2)...X(Ntdc))*..*f(X(Ntdc)) - - fxc = EXP(QUANT+XcScale) - !print *,'density',fxc ! J - !PRINT *, 'Rindd, Cm=',Cm(xedni(max(1,Nt-5):Ntdc)) - !PRINT *, 'Rindd, Cm=',Cm(xedni(1:Ntdc)) - - !IF (fxc .LT.fxcEpss) print *,'small, fxc=',fxc - IF (fxc .LT.fxcEpss) GOTO 100 ! Small probability don't bother calculating it - - !set the global integration limits Hlo,Hup - CALL BARRIER(xc1(1:Nc,ix),indI,Blo,Bup) - - - - Nst = NsXtmj(Ntscis+Njj+Nd+Nj+1) - Nsd = NsXdj(Nd+Nj+1) - IF (any((Cm(Nst+1:Nsd-1) .GT.Hup(Nst+1:Nsd-1)+EPS ).OR. - * (Cm (Nst+1:Nsd-1)+EPS .LT.Hlo (Nst+1:Nsd-1)))) GO TO 100 !degenerate case - !mean of deterministic variable(s) is - ! outside the barriers - - !PRINT *,'RINDD SCIS',SCIS - IF (SCIS.GE.1.AND.SCIS.LE.9) then ! integrate all by SCIS - XIND=RINDSCIS(xc1(:,ix)) - GO TO 100 - endif - - SELECT CASE (Nd+Nj) - CASE (:0) - IF (SCIS.NE.0) then ! integrate all by SCIS - XIND=MNORMPRB(Cm(1:Nst)) - ELSE - XIND=RINDNIT(BIG,SQ(1:Nst,1),Cm,indXtd(1:Nst),NIT) - END IF - CASE (1:) - xind=RINDDND(BIG,Cm,xd,xc1(:,ix),Nd,Nj) - END SELECT - 100 fxind(ix)=xind*fxc - !IF (fxc .LT.fxcEpss) print *,'small, fxc, xind',fxc,xind - !PRINT *, 'Rindd, Cm=',Cm(xedni(1:Ntdc)) - ENDDO !ix -! PRINT *, 'Rindd, Cm=',Cm(xedni(1:Ntdc)) - 110 CONTINUE - IF (ALLOCATED(xc)) DEALLOCATE(xc) - IF (ALLOCATED(xd)) DEALLOCATE(xd) - IF (ALLOCATED(SQ)) DEALLOCATE(SQ) - IF (ALLOCATED(NsXtmj)) DEALLOCATE(NsXtmj) - IF (ALLOCATED(Cm)) DEALLOCATE(Cm) - IF (ALLOCATED(CmN)) DEALLOCATE(CmN) - IF (ALLOCATED(BIG)) DEALLOCATE(BIG) - IF (ALLOCATED(index1)) DEALLOCATE(index1) - IF (ALLOCATED(xedni)) DEALLOCATE(xedni) -! print *,'before dealocation',Ntd,size(Hup),size(Hlo) - IF (ALLOCATED(Hlo)) DEALLOCATE(Hlo) - IF (ALLOCATED(Hup)) DEALLOCATE(Hup) - IF (ALLOCATED(NsXdj)) DEALLOCATE(NsXdj) - IF (ALLOCATED(indXtd)) DEALLOCATE(indXtd) - RETURN - END SUBROUTINE RIND71 - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -!!*************************** ARGP0 *********************************!! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - SUBROUTINE ARGP0 (I0,I1,P0,Plo,SQ,Cm,indS,ind,Nind) - USE FIMOD - USE GLOBALDATA, ONLY : Hlo,Hup,xCutOff,EPSS,EPS2,EPS - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:), INTENT(in) :: SQ , Cm !stdev./mean - INTEGER, DIMENSION(:), INTENT(in) :: indS - INTEGER, DIMENSION(:), INTENT(out) :: ind - DOUBLE PRECISION, INTENT(out) :: P0,Plo - INTEGER, INTENT(out) :: I0, I1 - INTEGER, INTENT(out) :: Nind - DOUBLE PRECISION :: P1,Prb - DOUBLE PRECISION :: Xup, Xlo - INTEGER :: I, Nstoc - ! indS contains the indices to the limits - Nstoc = SIZE(indS) ! in Hlo/Hup of variables in the indicator - ! ind contains indices to the relevant - ! variables which are Nind<=Nstoc. - ! We wish to compute P(HloX(i0)>XMI)= - P0 = Prb ! min Prob(Hup(i)> X(i)>Hlo(i)) - IF (P0.LT.EPSS) THEN - Plo=0.d0 - RETURN - ENDIF - ELSEIF (Prb.LT.P1) THEN - I1 = Nind - P1 = Prb - ENDIF - ENDIF - ENDDO - - Plo = MAX(0.d0,1.d0-DBLE(Nind)+Plo) - P0 = MIN(1.d0,P0) -! print *,'ARGP0',Nstoc,Nind,P0,Plo,I0,I1,CM(ind(I0)) - RETURN - END SUBROUTINE ARGP0 - - - -!Ntmj is the number of elements in indicator -!since Nj points of process valeus (Nt) have -!been moved to the jacobian. -!index1 contains the original -!positions of variables in the -!covaraince matrix before condsort -!and that why if index(Ntmj+1)>Nt -!it means the variable to conditon on -!is a derivative isXd=1 - -!= # stochastic variables before -!conditioning on X(Ntmj+1). This -!I still not checked why. - - - -! ******************* RINDDND **************************************** -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - RECURSIVE FUNCTION RINDDND (BIG,Cm,xd,xc,Ndleft,Njleft) - & RESULT (xind) - USE JACOBMOD - USE GLOBALDATA, ONLY :SQPI1, SQTWOPI1,Hup,Hlo,Nt,Nj,Njj,Nd, - & NsXtmj,NsXdj,EPS2,NIT,xCutOff,EPSS,CEPSS,index1, - & indXtd,SQ,SQTWO,SQTWO1,SCIS,Ntscis,C1C2det,EPS - USE FIMOD - USE C1C2MOD - USE QUAD - IMPLICIT NONE - INTEGER,INTENT(in) :: Ndleft,Njleft ! # DIMENSIONs to integrate - DOUBLE PRECISION, DIMENSION(:,:), INTENT(inout) :: BIG - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: Cm ! conditional mean - DOUBLE PRECISION, DIMENSION(: ), INTENT(inout) :: xd ! integr. variables - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: xc ! conditional values -!local variables - DOUBLE PRECISION :: xind - DOUBLE PRECISION :: xind1 - DOUBLE PRECISION, DIMENSION(PMAX) :: WXdi, Xdi !weights/nodes - DOUBLE PRECISION, DIMENSION(: ), ALLOCATABLE :: CmNEW - INTEGER :: Nrr, Nr, J, N,Ndleft1,Ndjleft,Ntmj,isXd - INTEGER :: Nst,Nstn,Nsd,NsdN - DOUBLE PRECISION :: SQ0,fxd,XMA,XMI - - Ntmj=Nt-Nj - Ndjleft= Ndleft+Njleft - N=Ntmj+Ndjleft - - IF (index1(N).GT.Nt) THEN - isXd=1 - ELSE - isXd=0 - END IF - - XIND = 0.d0 - SQ0 = BIG (N, N) -! index to last stoch. variable of Xt before conditioning on X(N) - Nst = NsXtmj(Ntscis+Njj+Ndjleft+1) - -!******************************************************************************** -!** Here Starts the degenerated case the remaining variables are deterministic ** -!******************************************************************************** - - IF (SQ0.LT.EPS2) THEN - !Next is the check for the special situation - !that after conditioning on Xc all derivatives are - !singular and not satisfying the limitations - !(so something is generally wrong) - IF (any((Cm(Nst+1:N).GT.Hup(Nst+1:N)+EPS ).OR. - & (Cm(Nst+1:N)+EPS.LT.Hlo(Nst+1:N)))) THEN - RETURN !the mean of Xd or Xt is too extreme - ENDIF - !Here we are putting in all conditional expectations - !for the values of the "deterministic" derivatives. - IF (Nd.GT.0) THEN - Ndleft1=Ndleft - DO WHILE (Ndleft1.GT.0) - IF (index1(N).GT.Nt) THEN ! isXd - xd (Ndleft1) = Cm (N) - Ndleft1=Ndleft1-1 - END IF - N=N-1 - ENDDO - fxd = jacob (xd,xc) ! jacobian of xd,xc - ELSE - fxd = 1.d0 ! XIND = FxCutOff??? - END IF - - XIND=fxd - IF (Nst.le.0) RETURN - IF (SCIS.ne.0) then - XIND=fxd*MNORMPRB(Cm(1:Nst)) - ELSE - XIND=fxd*RINDNIT(BIG,SQ(:,Ntscis+Njj+1), - & Cm,indXtd(1:Nst),NIT) - END IF - RETURN - ENDIF - -!***** Here Starts the conditioning on the last variable (nondeterministic) * -!**************************************************************************** - - ! SQ0 = SQ(N,Ntscis+Njj+Ndjleft) !SQRT (SS0) - - !print *,'RINDD SQO', SQ0,SQ(N,Ntscis+Njj+Ndjleft) !SQ(1:N,Ndjleft) - - XMA=MIN((Hup (indXtd(N))-Cm (N))/SQ0, xCutOff) - XMI=MAX((Hlo (indXtd(N))-Cm (N))/SQ0,-xCutOff) - - ! See if we can narrow down integration range - ! index to first stoch. variable of Xd before conditioning on X(N) - Nsd = NsXdj(Ndjleft+1) - ! index to last stoch. variable of Xt after cond. on X(N) - NstN = NsXtmj(Ntscis+Njj+Ndjleft) - - !PRINT *,xmi,xma -! print *,Ntscis+Njj+Ndjleft -! print *,'CM=',Cm(1:N-1) -! print *,'SQ=', SQ(1:N-1,Ntscis+Njj+Ndjleft) - if (C1C2det) then ! checking only on the variables that becomes deterministic -! index to first stoch. variable of Xd after conditioning on X(N) - NsdN = NsXdj(Ndjleft) - CALL C1C2(XMI,XMA,Cm(Nsd:NsdN-1),BIG(Nsd:NsdN-1,N), - & SQ(Nsd:NsdN-1,Ntscis+Njj+Ndjleft),indXtd(Nsd:NsdN-1)) - CALL C1C2(XMI,XMA,Cm(NstN+1:Nst),BIG(NstN+1:Nst,N), - & SQ(NstN+1:Nst,Ntscis+Njj+Ndjleft),indXtd(NstN+1:Nst)) - else ! check on all variables - CALL C1C2(XMI,XMA,Cm(Nsd:N-1),BIG(Nsd:N-1,N), - & SQ(Nsd:N-1,Ntscis+Njj+Ndjleft),indXtd(Nsd:N-1)) - CALL C1C2(XMI,XMA,Cm(1:Nst),BIG(1:Nst,N), - & SQ(1:Nst,Ntscis+Njj+Ndjleft),indXtd(1:Nst)) - endif -! CALL C1C2(XMI,XMA,Cm(1:N-1),BIG(1:N-1,N), -! & SQ(1:N-1,Ntscis+Njj+Ndjleft),SQ0,indXtd(1:N-1)) - !PRINT *,xmi,xma -! if (Ndleft<2) stop - IF (XMA.LE.XMI) THEN - XIND=0.d0 - RETURN - ENDIF - Nrr = NINT1 (MIN(Ndjleft,sizNint)) - Nr=0 ! initialize # of nodes - !print *, 'rinddnd Nrr',Nrr - !Grid the interval [XMI,XMA] by GAUSS quadr. - CALL GAUSSLE2(Nr, WXdi, Xdi,XMI,XMA, Nrr) - !print *, 'Xdi',Xdi - ALLOCATE(CmNEW(1:N-1)) - ! The following variables are independent of X(N) - ! because BIG(Nst+1:Nsd-1,N) is set to 0 in condsrort. - ! Thus the mean is not changed for these variables - ! in order to avoid numerical problems - ! The following if test is necessary on Solaris F90 compiler. - if (Nst+1.LT.Nsd) CmNEW(Nst+1:Nsd-1)=Cm(Nst+1:Nsd-1) -! print *,Ndjleft,N,NstN+1,Nsd-1 -! print *,BIG(Nst+1:Nsd-1,N) -! print *,'Cm=',Cm(NstN+1:Nsd-1) - DO J = 1, Nr -! IF (Wxdi(J).GT.(CFxCutOff)) GO TO 100 !THEN ! EPSS??? - IF (isXd.EQ.1) xd (Ndleft) = Xdi (J)*SQ0 + Cm (N) - - ! Here we start with the case when there - ! some derivatives left to integrate. - ! The following if test is necessary on Solaris F90 compiler. - if (1.LE.Nst) CmNEW(1:Nst) = Cm(1:Nst)+Xdi(J)*BIG(1:Nst,N) - if (Nsd.LT.N) CmNEW(Nsd:(N-1)) = Cm(Nsd:(N-1))+ - & Xdi(J)*BIG(Nsd:(N-1),N) - !print *,'CmNew=',N-1,Ndjleft,CmNew(1:N-1) - fxd = Wxdi(J) - IF (Ndjleft.GT.1) THEN - XIND1=RINDDND(BIG,CmNEW,xd,xc,Ndleft-isXd,Njleft-1+isXd) - ELSE ! Here all is conditioned on - ! and we wish to compute the - ! conditional probability that - ! variables in indicator stays between barriers. - XIND1 = 1.d0 - !if there are derivatives we need - !to compute the jacobian, jacob(xd,xc) - IF (Nd.GT.0) fxd = fxd *jacob(xd(1:Nd),xc) - !If there are no derivatives - !then we assume that jacob(xc)=1 - - IF (NstN.LT.1) GOTO 100 !Here there are no points in indicator - !left to integrate and hence XIND1=1. - - !integrate by Monte Carlo - SCIS - IF (SCIS.NE.0) XIND1 = MNORMPRB(CmNEW) - !integrate by quadrature - IF (SCIS.EQ.0) XIND1 = RINDNIT(BIG, - & SQ(:,Ntscis+Njj+1),CmNEW,indXtd(1:NstN),NIT) - !print *,'jacobian',xind,xind1,xind+fxd*xind1 - END IF - 100 CONTINUE - XIND = XIND+XIND1 * fxd !END IF - ENDDO - - DEALLOCATE(CmNEW) - RETURN - END FUNCTION RINDDND - - -! ******************* RINDNIT **************************************** -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - - ! old procedure rind2-6 - RECURSIVE FUNCTION RINDNIT(R,SQ,Cm,indS,NITL) RESULT (xind) - USE GLOBALDATA, ONLY : Hlo,Hup,EPS2, EPSS,CEPSS - & ,xCutOff,Plowgth,XSPLT - USE FIMOD - USE C1C2MOD - USE QUAD - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: R - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: SQ - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: Cm - DOUBLE PRECISION :: xind - INTEGER, DIMENSION(: ), INTENT(in) :: indS - INTEGER, INTENT(in) :: NITL -! local variables - DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: RNEW - DOUBLE PRECISION, DIMENSION(: ), ALLOCATABLE :: B,SQnew - DOUBLE PRECISION, DIMENSION(: ), ALLOCATABLE :: CmNEW - INTEGER, DIMENSION(: ), ALLOCATABLE :: indSNEW,ind - INTEGER :: I0,I1 - - DOUBLE PRECISION, DIMENSION(PMAX) :: H1, XX1 - DOUBLE PRECISION :: XIND1,XIND2,SQ0,SQ1,SS0,SS1,SS - DOUBLE PRECISION, DIMENSION(2) :: XMI, XMA - INTEGER, DIMENSION(2) :: INFIN - DOUBLE PRECISION :: SGN,P0,Plo,rho - INTEGER :: Ns,Nsnew,row,r1,r2,J,N1 - -! Assumption is that there is at least one variable X in the indicator, -! LNIT nonegative integer. -! If LNIT=0 or the number of relevant variables is less then 3, the recursion -! stops. It gives exact value if after removing irrelevant variables there -! are maximum 2 variables left in the indicator. The program is not using -! RIND2 function any more. IR. 28 XI 1999 - Indianapolis. -! -! explanation to variables (above): -! R = cov. matr. -! B = R(I,I0) I=1:Ns -! SQ = SQRT(R(I,I)) I=1:Ns -! Cm = cond. mean -! indS = indices to the stochastic variables as they are stored in -! the global variables Hlo and Hup -! Ns = size of indS =# of variables in indicator before conditioning -! Nsnew = # of relevant variables in indicator before conditioning -! I0,I1 = indicies to minimum prob. and next minimal, respectively -! ..NEW = the var. above after conditioning on X(I0) or used in recursion -! ind = temp. variable storing indices - - Ns=SIZE(indS) !=# stochastic variables before conditioning - XIND=1.d0 - - if (Ns.lt.1) return - - ALLOCATE(ind(1:Ns)) - CALL ARGP0(I0,I1,P0,Plo,SQ,Cm,indS,ind,NSnew) -! print *,'NSnew,P0,Plo=',NSnew,P0,Plo - !The probability of being between barriers is one - !since there are no relevant variables. - -! print *,'NIT',NITl,P0,Plo,Ns,Nsnew - IF (NSnew.lt.1) GOTO 300 - XIND=(P0*DBLE(NSnew)+Plowgth*Plo)/(DBLE(NSnew)+Plowgth) - !Lower bound Plo and upper bound P0 are close - !or all variables are close to be irrelevant, - !e.g. Nsnew=1. - IF ((P0.LT.Plo+EPSS).OR.(P0.GT.CEPSS)) GOTO 300 - -! Now CEPSS>P0>EPSS+Plo and there are more than one relevant variable (NSnew>1) -! Those have indices ind(I0), ind(I1). -! Hence we have nondegenerated case. - - SS0 = R (ind(I0) ,ind(I0)) - SQ0 = SQRT(SS0) - r1=indS(ind(I0)) -! print *,'P0-Plo,SS0,Sq0',P0-Plo,SS0,Sq0 - XMA(1) = MIN((Hup (r1)-Cm (ind(I0)))/SQ0,xCutOff) - XMI(1) = MAX((Hlo (r1)-Cm (ind(I0)))/SQ0,-xCutOff) - -!If NSnew = 2 then we can compute the probability exactly and recursion stops. - IF ((NSnew.EQ.2).OR.(NITL.LT.1)) THEN !.OR.(NITL.LT.1) -! Not necessary any longer: -! I1=2 -! if (I0.eq.2) I1=1 -! if (I0.eq.I1) print *,'rindnit, I1,I0:',I1,I0 - SS1 = R (ind(I1) ,ind(I1)) - SQ1 = SQRT(SS1) - - IF (ind(I0).LT.ind(I1)) THEN - SS=R(ind(I0),ind(I1)) - ELSE - SS=R(ind(I1),ind(I0)) - ENDIF - rho= SS/(SQ0*SQ1) - - r2=indS(ind(I1)) - XMA(2) = MIN((Hup (r2)-Cm (ind(I1)))/SQ1,xCutOff) - XMI(2) = MAX((Hlo (r2)-Cm (ind(I1)))/SQ1,-xCutOff) - IF (ABS(rho).gt.1.d0+EPSS) THEN - !print *,'rindnit, Correlation > 1, rho=',rho - IF (ABS(rho).gt.1.d0+EPSS) GO TO 300 - rho = sign(1.D0,rho) -! print *,'rindnit, P0,Plo',P0,Plo,XIND -! print *,'rindnit I0,I1:',I0,I1 -! print *,'rindnit XMI,XMA,XMI1,XMA1:',XMI(1),XMA(1), -! & XMI(2),XMA(2) -! print *,'rindnit cov(I1,I0):',R(ind(I1),ind(I0)) -! print *,'rindnit cov(I0,I1):',R(ind(I0),ind(I1)) -! print *,'rindnit SS,SS1,SS0:',SS,SS1,SS0 -! print *,'rindnit ind:',ind(1:NSnew) - ENDIF -! print *,XMA1,XMI1,XMA,XMI,rho -! XIND = NORM2DPRB(XMI(1),XMA(1),XMI(2),XMA(2),rho) -! GO TO 300 -* if INFIN(I) = 0, Ith limits are (-infinity, UPPER(I)]; -* if INFIN(I) = 1, Ith limits are [LOWER(I), infinity); -* if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)]. -! INFIN = 2 - IF (XMI(1).LE.-xCutOff) INFIN(1)=0 - IF (XMI(2).LE.-xCutOff) INFIN(2)=0 - IF (XMA(1).GE. xCutOff) INFIN(1)=1 - IF (XMA(2).GE. xCutOff) INFIN(2)=1 - - !print *,'rindnit, xind,xind2=', XIND, BVNMVN(XMI,XMA,INFIN,rho) - XIND = BVNMVN(XMI,XMA,INFIN,rho) -! print *,xind - GOTO 300 - END IF - !If NITL=0 which means computations without conditioning on X(ind(I0)) - IF(NITL.lt.1) GOTO 300 - -!We have NITL>0 and at least 3 variables in the indicator, ie. -!we will condition on X(ind(I0)). -!First we check whether one can use XSPLIT variant of integration. - - if ((XMA(1).GE.xCutOff).AND.(XMI(1).LT.-XSPLT)) THEN ! (.FALSE.).AND. - XMA(1)=XMI(1) - XMI(1)=-xCutOff - SGN=-1.d0 - elseif ((XMA(1).GT.XSPLT).AND.(XMI(1).LE.-xCutOff)) THEN - XMI(1)=XMA(1) - XMA(1)=xCutOff - SGN=-1.d0 - else - SGN=1.d0 - XIND2=0.d0 - endif - - ! Must allocate several variables to recursively - ! transfer them to rindnit: Rnew, SQnew, CMnew, indSnew - ! The variable B is used in computations of conditional mean and cov. - ! The size is NSnew-1 (the relevant variables minus X(ind(I0)). - - ALLOCATE(indSNEW(1:NSnew-1)) - ALLOCATE(RNEW(NSnew-1,NSnew-1)) - ALLOCATE(CMnew(1:NSnew-1)) - ALLOCATE(SQnew(1:NSnew-1)) - ALLOCATE(B(1:NSnew-1)) - !This DO loop is divided in two parts in order - !to only work on the upper triangular of R - DO row=1,I0-1 - r1=ind(row) - Rnew(row,row:I0-1)=R(r1,ind(row:I0-1)) - ! The if test below is required on Solaris F90 compiler - IF (I0.LT.Nsnew) Rnew(row,I0:NSnew-1)=R(r1,ind(I0+1:NSnew)) - B(row)=R(r1,ind(I0))/SQ0 - enddo - DO row=I0+1,NSnew - r1=ind(row) - Rnew(row-1,row-1:NSnew-1) = R(r1,ind(row:NSnew)) - B(row-1)=R(ind(i0),r1)/SQ0 - enddo - DO row=I0+1,NSnew - ind(row-1)=ind(row) - enddo - - - CMnew=CM(ind(1:NSnew-1)) - SQnew=SQ(ind(1:NSnew-1)) - indSnew=indS(ind(1:NSnew-1)) - - !USE the XSPLIT variant - IF (SGN.LT.0.d0) XIND2 = RINDNIT(Rnew,SQnew,CMnew,indSnew,NITL-1) - - ! Perform conditioning on X(I0) - NSnew=NSnew-1 - N1=0 - DO row = 1, NSnew - Rnew(row,row:NSnew) = Rnew(row,row:NSnew) - - & B(row)*B(row:NSnew) !/SS0) - SS = RNEW(row,row) - IF (SS.GE.EPS2) then - SQNEW (row) = SQRT (SS) - ELSE - SQNEW(row) = 0.d0 - N1=N1+1 ! count number of deterministic variables - END IF - ENDDO - - !See if we can Narrow down the limits - CALL C1C2(XMI(1),XMA(1),CmNew,B,SQNEW,indSnew) - XIND = (FI (XMA(1)) - FI (XMI(1))) - ! if Nsnew<=N1 then PRB = XIND almost always - ! if this check is not performed then - ! the numerical integration may currupt the answer due - ! to the limited number of nodes used in the integration - IF (XIND.LT.EPSS.OR.Nsnew.LT.N1+1) GOTO 200 - - ! print *,'rindnit gaussle2' - N1=0 ! computing nodes for num. integration. - CALL GAUSSLE2 (N1, H1, XX1, XMI(1), XMA(1),LE2Qnr) - ! new conditional covariance - - XIND = 0.d0 -! print *,'rindnit for loop',N1 - DO J = 1, N1 - !IF (H1(J).GT.CFxCutOff) THEN - CMnew=Cm(ind(1:NSnew)) + XX1(J)*B !/ SQ0) - XIND1=RINDNIT(Rnew,SQnew,CMnew,indSnew,NITL-1) - XIND = XIND+XIND1 * H1 (J) - !END IF - ENDDO -200 CONTINUE - XIND=XIND2+SGN*XIND -! Print *,'XIND, XIND2',XIND,XIND2 -! Print *,'XMI',XMI -! Print *,'XMA',XMA -! Print *,'xind,nit', xind,nitl,shape(indsnew),shape(ind) - !fix up round off errors and make sure 0=0 the order of Xd and Xt(Nt-Nj+1:Nt) may be mixed. -! The covariances, Cov(X(1:I-1),X(I)|X(I+1:N)), needed for computation of the -! conditional expectation, E(X(1:I-1)|X(I:N), are saved in column I of R -! for I=Nt-Nj+1:Ntdc. -! -! IF any of the variables have variance less than EPS2. They will be -! be treated as deterministic and not stochastic variables by the -! RindXXX subroutines. The deterministic variables are moved to -! middle in the order they became deterministic in order to -! keep track of them. Their variance and covariance with -! the remaining stochastic variables are set to zero in -! order to avoid numerical difficulties. -! -! NsXtmj(I) is the number of variables among the Nt-Nj -! first we treat stochastically after conditioning on X(Nt-Nj+I). -! The covariance matrix is sorted so that all variables with indices -! from 1 to NsXtmj(I) are stochastic after conditioning -! on X(Nt-Nj+I). Thus NsXtmj(I) may also be considered -! as the index to the last stochastic variable after conditioning -! on X(Nt-Nj+I). In other words NsXtmj keeps track of the deterministic -! and stochastic variables among the Nt-Nj first variables in each -! conditioning step. -! -! Similarly NsXdj(I) keeps track of the deterministic and stochastic -! variables among the Nd+Nj following variables in each conditioning step. -! NsXdj(I) is the index to the first stochastic variable -! among the Nd+Nj following variables after conditioning on X(Nt-Nj+I). -! The covariance matrix is sorted so that all variables with indices -! from NsXdj(I+1) to NsXdj(I)-1 are deterministic conditioned on -! X(Nt-Nj+I). -! - -! Var(Xc(1))>Var(Xc(2)|Xc(1))>...>Var(Xc(Nc)|Xc(1),Xc(2),...,Xc(Nc)). -! If Nj=0 then -! Var(Xd(1)|Xc)>Var(Xd(2)|Xd(1),Xc)>...>Var(Xd(Nd)|Xd(1),Xd(2),...,Xd(Nd),Xc). -! -! NB!! Since R is symmetric, only the upper triangular contains the -! sorted conditional covariance. The whole matrix -! is easily obtained by copying elements of the upper triangle to -! the lower or by uncommenting some lines in the end of this subroutine -! -! revised pab 18.04.2000 -! new name rind60 -! New assumption of BIG for the conditional sorted variables: -! BIG(I,I)=sqrt(Var(X(I)|X(I+1)...X(N))=SQI -! BIG(1:I-1,I)=COV(X(1:I-1),X(I)|X(I+1)...X(N))/SQI -! Otherwise -! BIG(I,I) = Var(X(I)|X(I+1)...X(N) -! BIG(1:I-1,I)=COV(X(1:I-1),X(I)|X(I+1)...X(N)) -! This also affects C1C2: SQ0=sqrt(Var(X(I)|X(I+1)...X(N)) is removed from input -! => A lot of wasteful divisions are avoided - - -! Using SQ to temporarily store the diagonal of R -! Adding a nugget effect to ensure the the inversion is -! not corrupted by round off errors -! good choice for nugget might be 1e-8 - !call getdiag(SQ,R) - INFORM = 0 - ALLOCATE(SQ(1:Ntdc)) - ALLOCATE(ind(1:Ntdc)) - IF (Nd+Nj+Njj+Ntscis.GT.0) THEN - ALLOCATE(CSTD2(1:Ntd,1:Nd+Nj+Njj+Ntscis)) - CSTD2=0.d0 ! initialize CSTD - ENDIF - !CALL ECHO(R,Ntdc) - DO ix = 1, Ntdc - R(ix,ix) = R(ix,ix)+Nugget - SQ(ix) = R(ix,ix) - index1 (ix) = ix ! initialize index1 - ENDDO - - Ntmj = Nt-Nj - Njleft = Nj - NstoXd = Ntmj+1 - Nstoc = Ntmj - - - DO ix = 1, Nc ! Condsort Xc - r1=Ntdc-ix - m=r1+2-MAXLOC(SQ(r1+1:Ntd+1:-1)) - IF (SQ(m(1)).LT.XCEPS2) THEN - INFORM = 1 - !PRINT *,'Condsort0, degenerate Xc' - !degenerate=1 - GOTO 200 ! RETURN !degenerate case - ENDIF - m1 = index1(m(1)) - CALL swapint(index1(m(1)),index1(r1+1)) - CALL swapre(Cm(m(1)),Cm(r1+1)) - SQ(r1+1) = SQRT(SQ(m(1))) - R(index1(1:r1+1),m1) = R(index1(1:r1+1),m1)/SQ(r1+1) - R(m1,index1(1:r1)) = R(index1(1:r1),m1) - - ! Calculate the conditional mean - Cm(1:r1)=Cm(1:r1)+(xcmean(index1(r1+1)-Ntd)-Cm(r1+1))* - & R(index1(1:r1),m1) !/SQ(r1+1) - ! sort and calculate conditional covariances - CALL CONDSORT2(R,SQ,index1,Nstoc,NstoXd,Njleft,m1,r1) - ENDDO ! ix - ! index to first stochastic variable of Xd and Nj of Xt - NsXdj(Nd+Nj+1) = NstoXd - ! index to last stochastic variable of Nt-Nj of Xt - NsXtmj(Nd+Nj+Njj+Ntscis+1) = Nstoc - !print *, 'condsort index1', index1 - !print *, 'condsort Xd' - !call echo(R,Ntdc) - - DO ix = 1, Nd+Nj ! Condsort Xd + Nj of Xt - CALL ARGP0(I1,r2,P1,XX,SQRT(SQ(NstoXd:Ntd-ix+1)), - & Cm(NstoXd:Ntd-ix+1),index1(NstoXd:Ntd-ix+1),ind,r1) - IF (r1.NE.0) I1=ind(I1) - m = MIN(NstoXd+I1-1,Ntd-ix+1) - IF (Njleft.GT.0) THEN - - CALL ARGP0(I0,r2,P0,XX,SQRT(SQ(1:Nstoc)), - & Cm(1:Nstoc),index1(1:Nstoc),ind,r1) - IF (r1.NE.0) I0=ind(I0) -! m=Ntd-ix+2-MAXLOC(SQ(Ntd-ix+1:1:-1)) - IF (P0.LT.P1.AND.r1.GT.0) THEN - m = I0 - P1 = P0 - END IF - Ntmp = NstoXd+Njleft-1 - IF (((NstoXd.LE.m(1)).AND.(m(1).LE.Ntmp)) - & .OR.(m(1).LE.Nstoc)) THEN - CALL swapint(index1(m(1)),index1(Ntmp)) - CALL swapRe(SQ(m(1)),SQ(Ntmp)) - CALL swapre(Cm(m(1)),Cm(Ntmp)) - m(1)=Ntmp - Njleft=Njleft-1 - END IF - END IF ! Njleft - IF (SQ(m(1)).LT.EPS2) THEN - !PRINT *,'Condsort, degenerate Xd' - Ntmp = Nd+Nj+1-ix - NsXtmj(Ntscis+Njj+1:Ntmp+Ntscis+Njj+1) = Nstoc - NsXdj(1:Ntmp+1) = NstoXd - IF (ix.EQ.1) THEN - DO iy = 1,Ntd !sqrt(VAR(X(I)|X(Ntd-ix+1:Ntdc)) - r1 = index1(iy) - CSTD2(r1,Ntscis+Njj+1:Ntmp+Ntscis+Njj)=SQRT(SQ(iy)) - ENDDO - ELSE - DO iy=ix,Nd+Nj - CSTD2(:,Nd+Nj+Ntscis+Njj+1-iy)= - & CSTD2(:,Ntmp+Ntscis+Njj+1) - ENDDO - ENDIF - GOTO 200 ! degenerate case - END IF - r1 = Ntd-ix - m1 = index1(m(1)); - CALL swapint(index1(m(1)),index1(r1+1)) - CALL swapre(Cm(m(1)),Cm(r1+1)) - ! CALL swapre(SQ(r1+1),SQ(m(1))) - SQ0 = SQRT(SQ(m(1))) - SQ(r1+1) = SQ0 - CSTD2(m1,Nd+Nj+Ntscis+Njj+1-ix)=SQ0 - - R(index1(1:r1+1),m1) = R(index1(1:r1+1),m1)/SQ0 - R(m1,index1(1:r1)) = R(index1(1:r1),m1) - - XMA = MIN( (Hup (index1(r1+1)) - Cm (r1+1))/ SQ0,xCutOff) - XMA = MAX(XMA,-xCutOff) - XMI = MAX( (Hlo (index1(r1+1)) - Cm (r1+1))/ SQ0,-xCutOff) - XMI = MIN(XMI,xCutOff) - -! There is something wrong with XX - IF (P1.GT. EPSS ) THEN - ! Calculate the normalized expected mean without the jacobian - XX = SQTWOPI1*(EXP(-0.5d0*XMI*XMI)-EXP(-0.5d0*XMA*XMA))/P1 - ELSE - IF ( XMI .LE. -xCutOff ) XX = XMA - IF ( XMA .GE. xCutOff ) XX = XMI - IF (XMI.GT.-xCutOff.AND.XMA.LT.xCutOff) XX=(XMI+XMA)*0.5d0 - END IF - - ! Calculate the conditional expected mean - Cm(1:r1) = Cm(1:r1)+XX*R(index1(1:r1),m1) - - ! Calculating conditional variances - CALL CONDSORT2(R,SQ,index1,Nstoc,NstoXd,Njleft,m1,Ntd-ix) - ! saving indices - NsXtmj(Nd+Nj+Njj+Ntscis+1-ix)=Nstoc - NsXdj(Nd+Nj+1-ix)=NstoXd - - ! Calculating standard deviations non-deterministic variables - DO r2=1,Nstoc - r1=index1(r2) - CSTD2(r1,Nd+Nj+Njj+Ntscis+1-ix)=SQRT(SQ(r2)) !sqrt(VAR(X(I)|X(Ntd-ix+1:Ntdc)) - ENDDO - DO r2=NstoXd,Ntd-ix - r1=index1(r2) - CSTD2(r1,Nd+Nj+Ntscis+Njj+1-ix)=SQRT(SQ(r2)) !sqrt(VAR(X(I)|X(Ntd-ix+1:Ntdc)) - ENDDO - ENDDO ! ix - - - 200 IF ((SCIS.GT.0).OR. (Njj.gt.0)) THEN ! check on Njj instead - ! Calculating conditional variances and sort for Nstoc of Xt - CALL CONDSORT4(R,Cm,CSTD2,SQ,index1,NsXtmj,Nstoc) - !Nst0=Nstoc - ENDIF - IF (Nd+Nj+Njj+Ntscis.GT.0) THEN - DO r2=1,Ntd ! sorting CSTD according to index1 - r1=index1(r2) - CSTD(r2,:)= CSTD2(r1,:) - END DO - DEALLOCATE(CSTD2) - ELSE - IF (Nc.EQ.0) THEN - ix=1; Nstoc=Ntmj - DO WHILE (ix.LE.Nstoc) - IF (SQ(ix).LT.EPS2) THEN - DO WHILE ((SQ(Nstoc).LT.EPS2).AND.(ix.LT.Nstoc)) - SQ(Nstoc)=0.d0 !MAX(0.d0,SQ(Nstoc)) - Nstoc=Nstoc-1 - END DO - CALL swapint(index1(ix),index1(Nstoc)) ! swap indices - !CALL swapre(SQ(ix),SQ(Nstoc)) - SQ(ix)=SQ(Nstoc);SQ(Nstoc)=0.d0 - Nstoc=Nstoc-1 - ENDIF - ix=ix+1 - END DO - ENDIF - CSTD(1:Nt,1)=SQRT(SQ(1:Nt)) - NsXtmj(1)=Nstoc - ENDIF - - changed=0 - DO r2=Ntdc,1,-1 ! sorting the upper triangular of the - r1=index1(r2) ! covariance matrix according to index1 - xedni(r1)=r2 - !PRINT *,'condsort,xedni',xedni - !PRINT *,'condsort,r1,r2',r1,r2 - IF ((r1.NE.r2).OR.(changed.EQ.1)) THEN - changed=1 - R(r2,r2) = SQ(r2) - DO c2=r2+1,Ntdc - c1=index1(c2) - IF (c1.GT.r1) THEN - R(r2,c2)=R(c1,r1) - ELSE - R(r2,c2)=R(r1,c1) - END IF - END DO - END IF - END DO - ! you may sort the lower triangular according - ! to index1 also, but it is not needed - ! since R is symmetric. Uncomment the - ! following if the whole matrix is needed - DO c2=1,Ntdc - DO r2=c2+1,Ntdc - R(r2,c2)=R(c2,r2) ! R symmetric - END DO - END DO -! IF (degenerate.EQ.1) THEN -! PRINT *,'condsort,R=' -! call echo(R,Ntdc) -! PRINT *,'condsort,SQ=' -! call echo(CSTD,Ntd) -! PRINT *,'index=',index1 -! PRINT *,'xedni=',xedni -! ENDIF -! PRINT * , 'big' -!600 FORMAT(4F8.4) -! PRINT 600, R -! PRINT 600, SQ - DEALLOCATE(SQ) - IF (ALLOCATED(ind)) DEALLOCATE(ind) - RETURN - END SUBROUTINE CONDSORT0 - - - - SUBROUTINE CONDSORT4(R,Cm,CSTD2,SQ,index1,NsXtmj,Nstoc) - USE GLOBALDATA, ONLY : EPS2,Njj,Ntscis,SQTWOPI1,Hlo,Hup, - & xCutOff,EPSS - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), INTENT(inout) :: R,CSTD2 - DOUBLE PRECISION, DIMENSION(: ), INTENT(inout) :: Cm - DOUBLE PRECISION, DIMENSION(:), INTENT(inout) :: SQ ! diag. of R - INTEGER, DIMENSION(: ), INTENT(inout) :: index1,NsXtmj - INTEGER, INTENT(inout) :: Nstoc -! local variables - DOUBLE PRECISION :: P0,Plo,XMI,XMA,SQ0,XX - INTEGER :: I0 - INTEGER, DIMENSION(1) :: m - INTEGER, DIMENSION(:), ALLOCATABLE :: ind - INTEGER :: m1 - INTEGER :: Nsold - INTEGER :: r1,c1,row,col,iy,ix -! This function condsort all the Xt variables for use with RINDSCIS and -! MNORMPRB - - !Nsoold=Nstoc - ix=1 - ALLOCATE(ind(1:Nstoc)) - DO WHILE ((ix.LE.Nstoc).and.(ix.LE.(Ntscis+Njj))) - CALL ARGP0(I0,c1,P0,Plo,SQRT(SQ(ix:Nstoc)), - & Cm(ix:Nstoc),index1(ix:Nstoc),ind,r1) - IF (r1.NE.0) I0=ind(I0) - m = ix-1+max(I0-1,1) -! m=ix-1+MAXLOC(SQ(ix:Nstoc)) - - IF (SQ(m(1)).LT.EPS2) THEN - !PRINT *,'Condsort3, error degenerate X' - NsXtmj(1:Njj+Ntscis)=0 - Nstoc=0 !degenerate=1 - RETURN !degenerate case - ENDIF - m1=index1(m(1)); - CALL swapint(index1(m(1)),index1(ix)) - CALL swapre(SQ(ix),SQ(m(1))) - SQ0=SQRT(SQ(ix)) - CSTD2(m1,ix)=SQ0 - - R(index1(ix:Nstoc),m1) = R(index1(ix:Nstoc),m1)/SQ0 - R(m1,index1(ix+1:Nstoc)) = R(index1(ix+1:Nstoc),m1) - CALL swapre(Cm(m(1)),Cm(ix)) - - - XMA = MIN( (Hup (index1(ix)) - Cm (ix))/ SQ0,xCutOff) - XMI = MAX( (Hlo (index1(ix)) - Cm (ix))/ SQ0,-xCutOff) - XMA = MAX(XMA,-xCutOff) - XMI = MIN(XMI,xCutOff) - IF (P0.GT. EPSS ) THEN - ! Calculate the expected mean - XX= SQTWOPI1*(EXP(-0.5d0*XMI*XMI)-EXP(-0.5d0*XMA*XMA))/P0 - ELSE - IF ( XMI .LE. -xCutOff ) XX = XMA - IF ( XMA .GE. xCutOff ) XX = XMI - IF (XMI.GT.-xCutOff.AND.XMA.LT.xCutOff) XX=(XMI+XMA)*0.5d0 - END IF - - ! Calculate the conditional expected mean - Cm(ix+1:Nstoc)=Cm(ix+1:Nstoc)+XX* - & R(m1,index1(ix+1:Nstoc)) - - - ! Calculating conditional variances for the - ! first Nstoc variables. - ! variables with variance less than EPS2 - ! will be treated as deterministic and not - ! stochastic variables and are therefore moved - ! to the end among these variables. - ! Nstoc is the # of variables we treat - ! stochastically - iy=ix+1;Nsold=Nstoc - DO WHILE (iy.LE.Nstoc) - r1=index1(iy) - SQ(iy)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - IF (SQ(iy).LT.EPS2) THEN -! IF (SQ(iy).LT.-EPS2) THEN -! PRINT *,'Cndsrt4,Error Covariance negative definit' -! ENDIF - IF (iy.LT.Nstoc) THEN - r1=index1(Nstoc) - SQ(Nstoc)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - DO WHILE ((SQ(Nstoc).LT.EPS2).AND.(iy.LT.Nstoc)) -! IF (SQ(Nstoc).LT.-EPS2) THEN -! PRINT *,'Cndsrt4,Error Covariance negative definit' -! ENDIF - SQ(Nstoc)=0.d0 !MAX(0.d0,SQ(Nstoc)) - Nstoc=Nstoc-1 - r1=index1(Nstoc) - SQ(Nstoc)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - END DO - CALL swapint(index1(iy),index1(Nstoc)) ! swap indices - !CALL swapre(SQ(iy),SQ(Nstoc)) ! swap values - SQ(iy)=SQ(Nstoc); - ENDIF - SQ(Nstoc)=0.d0 - Nstoc=Nstoc-1 - ENDIF - iy=iy+1 - END DO - NsXtmj(ix)=Nstoc ! saving index to last stoch. var. after conditioning - ! Calculating Covariances for non-deterministic variables - DO row=ix+1,Nstoc - r1=index1(row) - R(r1,r1)=SQ(row) - CSTD2(r1,ix)=SQRT(SQ(row)) ! saving stdev after conditioning on ix - DO col=row+1,Nstoc - c1=index1(col) - R(c1,r1)=R(r1,c1)-R(r1,m1)*R(m1,c1) !/R(m1,m1) - R(r1,c1)=R(c1,r1) - ENDDO - ENDDO - ! similarly for deterministic values - DO row=Nstoc+1,Nsold - r1=index1(row) - SQ(row) = 0.d0 !MAX(0.d0,SQ(row)) - CSTD2(r1,ix)=0.d0 !SQRT(SQ(row)) ! saving stdev after conditioning on ix - R(r1,r1) = SQ(row) - DO col=ix+1,Nsold !row-1 - c1=index1(col) - R(c1,r1)=0.d0 - R(r1,c1)=0.d0 - ENDDO - ENDDO - ix=ix+1 - ENDDO - if (Nstoc.LT.Njj+Ntscis) THEN - ! This test is necessary on Solaris F90 compiler. - NsXtmj(Nstoc+1:Njj+Ntscis) = Nstoc -! else -! PRINT *,'Condsort4' -! PRINT *,'Nstoc,Njj, Ntscis',Nstoc,Njj,Ntscis - endif - IF (ALLOCATED(ind)) DEALLOCATE(ind) - RETURN - END SUBROUTINE CONDSORT4 - - SUBROUTINE CONDSORT (R,CSTD,index1,xedni,NsXtmj,NsXdj,INFORM) - USE GLOBALDATA, ONLY : Nt,Nj,Njj,Nd,Nc,Ntdc,Ntd,EPS2,Nugget, - & XCEPS2,SCIS,Ntscis - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), INTENT(inout) :: R - DOUBLE PRECISION, DIMENSION(:,:), INTENT(out) :: CSTD - INTEGER, DIMENSION(: ), INTENT(out) :: index1 - INTEGER, DIMENSION(: ), INTENT(out) :: xedni - INTEGER, DIMENSION(: ), INTENT(out) :: NsXtmj - INTEGER, DIMENSION(: ), INTENT(out) :: NsXdj - INTEGER, INTENT(out) :: INFORM -! local variables - DOUBLE PRECISION, DIMENSION(: ), allocatable :: SQ - DOUBLE PRECISION, DIMENSION(:,:), allocatable :: CSTD2 - INTEGER, DIMENSION(1 ) :: m - INTEGER :: Nstoc,Ntmp,NstoXd !,degenerate - INTEGER :: changed,m1,r1,c1,row,col,ix,iy,Njleft,Ntmj - -! R = Input: Cov(X) where X=[Xt Xd Xc] is stochastic vector -! Output: sorted Conditional Covar. matrix Shape N X N (N=Nt+Nd+Nc) -! CSTD = SQRT(Var(X(1:I-1)|X(I:N))) -! conditional standard deviation. Shape Ntd X max(Nd+Nj,1) -! index1 = indices to the variables original place. Size Ntdc -! xedni = indices to the variables new place. Size Ntdc -! NsXtmj(I) = indices to the last stochastic variable -! among Nt-Nj first of Xt after conditioning on -! X(Nt-Nj+I). Size Nd+Nj+Njj+Ntscis+1 -! NsXdj(I) = indices to the first stochastic variable -! among Xd+Nj of Xt after conditioning on -! X(Nt-Nj+I). Size Nd+Nj+1 -! -! R=Cov([Xt,Xd,Xc]) is a covariance matrix of the stochastic vector X=[Xt Xd Xc] -! where the variables Xt, Xd and Xc have the size Nt, Nd and Nc, respectively. -! Xc is (are) the conditional variable(s). -! Xd and Xt are the variables to integrate. -! Xd + Nj variables of Xt are integrated directly by the RindDXX -! subroutines in the order of decreasing conditional variance. -! The remaining Nt-Nj variables of Xt are integrated in -! increasing order of the marginal probabilities by the RindXX subroutines. -! CONDSORT prepare and rearrange the covariance matrix -! by decreasing order of conditional variances in a special way -! to accomodate this strategy: -! -! After conditioning and sorting, the first Nt-Nj x Nt-Nj block of R -! will contain the conditional covariance matrix -! of Xt(1:Nt-Nj) given Xt(Nt-Nj+1:Nt) Xd and Xc, i.e., -! Cov(Xt(1:Nt-Nj),Xt(1:Nt-Nj)|Xt(Nt-Nj+1:Nt), Xd,Xc) -! NB! for Nj>0 the order of Xd and Xt(Nt-Nj+1:Nt) may be mixed. -! The covariances, Cov(X(1:I-1),X(I)|X(I+1:N)), needed for computation of the -! conditional expectation, E(X(1:I-1)|X(I:N), are saved in column I of R -! for I=Nt-Nj+1:Ntdc. -! -! IF any of the variables have variance less than EPS2. They will be -! be treated as deterministic and not stochastic variables by the -! RindXXX subroutines. The deterministic variables are moved to -! middle in the order they became deterministic in order to -! keep track of them. Their variance and covariance with -! the remaining stochastic variables are set to zero in -! order to avoid numerical difficulties. -! -! NsXtmj(I) is the number of variables among the Nt-Nj -! first we treat stochastically after conditioning on X(Nt-Nj+I). -! The covariance matrix is sorted so that all variables with indices -! from 1 to NsXtmj(I) are stochastic after conditioning -! on X(Nt-Nj+I). Thus NsXtmj(I) may also be considered -! as the index to the last stochastic variable after conditioning -! on X(Nt-Nj+I). In other words NsXtmj keeps track of the deterministic -! and stochastic variables among the Nt-Nj first variables in each -! conditioning step. -! -! Similarly NsXdj(I) keeps track of the deterministic and stochastic -! variables among the Nd+Nj following variables in each conditioning step. -! NsXdj(I) is the index to the first stochastic variable -! among the Nd+Nj following variables after conditioning on X(Nt-Nj+I). -! The covariance matrix is sorted so that all variables with indices -! from NsXdj(I+1) to NsXdj(I)-1 are deterministic conditioned on -! X(Nt-Nj+I). -! - -! Var(Xc(1))>Var(Xc(2)|Xc(1))>...>Var(Xc(Nc)|Xc(1),Xc(2),...,Xc(Nc)). -! If Nj=0 then -! Var(Xd(1)|Xc)>Var(Xd(2)|Xd(1),Xc)>...>Var(Xd(Nd)|Xd(1),Xd(2),...,Xd(Nd),Xc). -! -! NB!! Since R is symmetric, only the upper triangular contains the -! sorted conditional covariance. The whole matrix -! is easily obtained by copying elements of the upper triangle to -! the lower or by uncommenting some lines in the end of this subroutine - -! revised pab 18.04.2000 -! new name rind60 -! New assumption of BIG for the conditional sorted variables: -! BIG(I,I)=sqrt(Var(X(I)|X(I+1)...X(N))=SQI -! BIG(1:I-1,I)=COV(X(1:I-1),X(I)|X(I+1)...X(N))/SQI -! Otherwise -! BIG(I,I) = Var(X(I)|X(I+1)...X(N) -! BIG(1:I-1,I)=COV(X(1:I-1),X(I)|X(I+1)...X(N)) -! This also affects C1C2: SQ0=sqrt(Var(X(I)|X(I+1)...X(N)) is removed from input -! => A lot of wasteful divisions are avoided - - - -! Using SQ to temporarily store the diagonal of R -! Adding a nugget effect to ensure the the inversion is -! not corrupted by round off errors -! good choice for nugget might be 1e-8 - !call getdiag(SQ,R) - INFORM = 0 - ALLOCATE(SQ(1:Ntdc)) - - IF (Nd+Nj+Njj+Ntscis.GT.0) THEN - ALLOCATE(CSTD2(1:Ntd,1:Nd+Nj+Njj+Ntscis)) - CSTD2=0.d0 ! initialize CSTD - ENDIF - !CALL ECHO(R,Ntdc) - DO ix = 1, Ntdc - R(ix,ix)=R(ix,ix)+Nugget - SQ(ix)=R(ix,ix) - index1 (ix) = ix ! initialize index1 - ENDDO - - Ntmj=Nt-Nj - !NsXtmj(Njj+Nd+Nj+1)=Ntmj ! index to last stochastic variable of Nt-Nj of Xt - !NsXdj(Nd+Nj+1)=Ntmj+1 ! index to first stochastic variable of Xd and Nj of Xt - !degenerate=0 - Njleft=Nj - NstoXd=Ntmj+1;Nstoc=Ntmj - - - DO ix = 1, Nc ! Condsort Xc - r1 = Ntdc-ix - m=r1+2-MAXLOC(SQ(r1+1:Ntd+1:-1)) - IF (SQ(m(1)).LT.XCEPS2) THEN - INFORM = 1 - !PRINT *,'Condsort, degenerate Xc' - IF (SQ(m(1)).LT.-XCEPS2) THEN - !print *, 'Condsort, Not semi-positive definit' - ENDIF - !degenerate=1 - GOTO 200 ! RETURN !degenerate case - ENDIF - m1=index1(m(1)); - CALL swapint(index1(m(1)),index1(Ntdc-ix+1)) - !CALL swapRe(SQ(r1+1),SQ(m(1))) - SQ(r1+1) = SQRT(SQ(m(1))) - R(index1(1:r1+1),m1) = R(index1(1:r1+1),m1)/SQ(r1+1) - R(m1,index1(1:r1)) = R(index1(1:r1),m1) - ! sort and calculate conditional covariances - CALL CONDSORT2(R,SQ,index1,Nstoc,NstoXd,Njleft,m1,Ntdc-ix) - ENDDO ! ix - - NsXdj(Nd+Nj+1) = NstoXd ! index to first stochastic variable of Xd and Nj of Xt - NsXtmj(Nd+Nj+Njj+Ntscis+1) = Nstoc ! index to last stochastic variable of Nt-Nj of Xt - !print *, 'condsort index1', index1 - !print *, 'condsort Xd' - !call echo(R,Ntdc) - - DO ix = 1, Nd+Nj ! Condsort Xd + Nj of Xt - r1 = Ntd-ix - IF (Njleft.GT.0) THEN - m=r1+2-MAXLOC(SQ(r1+1:1:-1)) - Ntmp=NstoXd+Njleft-1 - IF (((NstoXd.LE.m(1)).AND.(m(1).LE.Ntmp)) - & .OR.(m(1).LE.Nstoc)) THEN - CALL swapint(index1(m(1)),index1(Ntmp)) - CALL swapRe(SQ(m(1)),SQ(Ntmp)) - m(1)=Ntmp - Njleft=Njleft-1 - END IF - ELSE - m=r1+2-MAXLOC(SQ(r1+1:Ntmj+1:-1)) - END IF - IF (SQ(m(1)).LT.EPS2) THEN - !PRINT *,'Condsort, degenerate Xd' - !degenerate=1 - Ntmp=Nd+Nj+1-ix - NsXtmj(Ntscis+Njj+1:Ntmp+Ntscis+Njj+1)=Nstoc - NsXdj(1:Ntmp+1)=NstoXd - IF (ix.EQ.1) THEN - DO iy=1,Ntd !sqrt(VAR(X(I)|X(Ntd-ix+1:Ntdc)) - r1=index1(iy) - CSTD2(r1,Ntscis+Njj+1:Ntmp+Ntscis+Njj)=SQRT(SQ(iy)) - ENDDO - ELSE - DO iy=ix,Nd+Nj - CSTD2(:,Nd+Nj+Ntscis+Njj+1-iy)= - & CSTD2(:,Ntmp+Ntscis+Njj+1) - ENDDO - ENDIF - GOTO 200 ! degenerate case - END IF - m1=index1(m(1)); - CALL swapint(index1(m(1)),index1(r1+1)) - !CSTD2(m1,Nd+Nj+Ntscis+Njj+1-ix)=SQRT(SQ(m(1))) - !CALL swapRe(SQ(Ntd-ix+1),SQ(m(1))) - SQ(r1+1) = SQRT(SQ(m(1))) - CSTD2(m1,Nd+Nj+Ntscis+Njj+1-ix) = SQ(r1+1) - - R(index1(1:r1+1),m1) = R(index1(1:r1+1),m1)/SQ(r1+1) - R(m1,index1(1:r1)) = R(index1(1:r1),m1) - - ! Calculating conditional variances - CALL CONDSORT2(R,SQ,index1,Nstoc,NstoXd,Njleft,m1,Ntd-ix) - ! saving indices - NsXtmj(Nd+Nj+Njj+Ntscis+1-ix)=Nstoc - NsXdj(Nd+Nj+1-ix)=NstoXd - - ! Calculating standard deviations non-deterministic variables - DO row=1,NsXtmj(Nd+Nj+Njj+Ntscis+2-ix) !Nstoc - r1=index1(row) - CSTD2(r1,Nd+Nj+Njj+Ntscis+1-ix)=SQRT(SQ(row)) !sqrt(VAR(X(I)|X(Ntd-ix+1:Ntdc)) - ENDDO - DO row=NsXdj(Nd+Nj+2-ix),Ntd-ix !NstoXd,Ntd-ix - r1=index1(row) - CSTD2(r1,Nd+Nj+Ntscis+Njj+1-ix)=SQRT(SQ(row)) !sqrt(VAR(X(I)|X(Ntd-ix+1:Ntdc)) - ENDDO - ENDDO ! ix - - - 200 IF ((SCIS.GT.0).OR. (Njj.gt.0)) THEN ! check on Njj instead - ! Calculating conditional variances and sort for Nstoc of Xt - CALL CONDSORT3(R,CSTD2,SQ,index1,NsXtmj,Nstoc) - !Nst0=Nstoc - ENDIF - IF ((Nd+Nj+Njj+Ntscis.GT.0)) THEN - DO row=1,Ntd ! sorting CSTD according to index1 - r1=index1(row) - CSTD(row,:)= CSTD2(r1,:) - END DO - DEALLOCATE(CSTD2) - ELSE - IF (Nc.EQ.0) THEN - ix=1; Nstoc=Ntmj - DO WHILE (ix.LE.Nstoc) - IF (SQ(ix).LT.EPS2) THEN - DO WHILE ((SQ(Nstoc).LT.EPS2).AND.(ix.LT.Nstoc)) - SQ(Nstoc)=0.d0 !max(0.d0,SQ(Nstoc)) - Nstoc=Nstoc-1 - END DO - CALL swapint(index1(ix),index1(Nstoc)) ! swap indices - !CALL swapRe(SQ(ix),SQ(Nstoc)) - SQ(ix)=SQ(Nstoc);SQ(Nstoc)=0.d0 - Nstoc=Nstoc-1 - ENDIF - ix=ix+1 - END DO - ENDIF - CSTD(1:Nt,1)=SQRT(SQ(1:Nt)) - NsXtmj(1)=Nstoc - ENDIF - - changed=0 - DO row=Ntdc,1,-1 ! sorting the upper triangular of the - r1=index1(row) ! covariance matrix according to index1 - xedni(r1)=row - !PRINT *,'condsort,xedni',xedni - !PRINT *,'condsort,r1,row',r1,row - IF ((r1.NE.row).OR.(changed.EQ.1)) THEN - changed=1 - R(row,row)=SQ(row) - DO col=row+1,Ntdc - c1=index1(col) - IF (c1.GT.r1) THEN - R(row,col)=R(c1,r1) - ELSE - R(row,col)=R(r1,c1) - END IF - END DO - END IF - END DO - ! you may sort the lower triangular according - ! to index1 also, but it is not needed - ! since R is symmetric. Uncomment the - ! following if the whole matrix is needed -! DO col=1,Ntdc -! DO row=col+1,Ntdc -! R(row,col)=R(col,row) ! R symmetric -! END DO -! END DO -! IF (degenerate.EQ.1) THEN -! PRINT *,'condsort,R=' -! call echo(R,Ntdc) -! PRINT *,'condsort,SQ=' -! call echo(CSTD,Ntd) -! PRINT *,'index=',index1 -! PRINT *,'xedni=',xedni -! ENDIF -! PRINT * , 'big' -!600 FORMAT(4F8.4) -! PRINT 600, R -! PRINT 600, SQ - DEALLOCATE(SQ) - - RETURN - END SUBROUTINE CONDSORT - - - SUBROUTINE CONDSORT2(R,SQ,index1,Nstoc,NstoXd,Njleft,m1,N) - USE GLOBALDATA, ONLY : Ntd,EPS2,XCEPS2 - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), INTENT(inout) :: R - DOUBLE PRECISION, DIMENSION(:), INTENT(inout) :: SQ - INTEGER, DIMENSION(: ), INTENT(inout) :: index1 - INTEGER, INTENT(inout) :: Nstoc,NstoXd,Njleft - INTEGER, INTENT(in) :: m1,N -! local variables - INTEGER :: Nsold,Ndold, Ntmp - INTEGER :: r1,c1,row,col,iy - -! save their old values - Nsold=Nstoc;Ndold=NstoXd - - ! Calculating conditional variances for the - ! Xc variables. - DO row=Ntd+1,N - r1 = index1(row) - SQ(row) = R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - IF (SQ(row).LT.XCEPS2) THEN - IF (SQ(row).LT.-XCEPS2) THEN - !print *, 'Condsort2,Error: Covariance negative definit' - ENDIF - R(r1,r1) = 0.d0 - SQ(row) = 0.d0 - !PRINT *,'condsort2, degenerate xc' - RETURN ! degenerate case XIND should return NaN - ELSE - R(r1,r1)=SQ(row) - DO col=row+1,N - c1 = index1(col) - R(c1,r1) = R(r1,c1)-R(r1,m1)*R(m1,c1) !/R(m1,m1) - R(r1,c1) = R(c1,r1) - ENDDO - ENDIF - ENDDO ! Calculating conditional variances for the - ! first Nstoc variables. - ! variables with variance less than EPS2 - ! will be treated as deterministic and not - ! stochastic variables and are therefore moved - ! to the end among these Nt-Nj first variables. - ! Nstoc is the # of variables we treat - ! stochastically - iy=1 - DO WHILE (iy.LE.Nstoc) - r1=index1(iy) - SQ(iy)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - IF (SQ(iy).LT.EPS2) THEN - IF (SQ(iy).LT.-EPS2) THEN - !print *, 'Condsort2,Error: Covariance negative definit' - ENDIF - r1=index1(Nstoc) - SQ(Nstoc)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - - DO WHILE ((SQ(Nstoc).LT.EPS2).AND.(iy.LT.Nstoc)) - IF (SQ(Nstoc).LT.-EPS2) THEN - !print *, 'Condsort2,Error: Covariance negative definit' - ENDIF - SQ(Nstoc)=0.d0 !MAX(0.d0,SQ(Nstoc)) - Nstoc=Nstoc-1 - r1=index1(Nstoc) - SQ(Nstoc)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - END DO - CALL swapint(index1(iy),index1(Nstoc)) ! swap indices - !CALL swapre(SQ(iy),SQ(Nstoc)) ! swap values - SQ(iy)=SQ(Nstoc);SQ(Nstoc)=0.d0 - Nstoc=Nstoc-1 - ENDIF - iy=iy+1 - END DO - - ! Calculating conditional variances for the - ! stochastic variables Xd and Njleft of Xt. - ! Variables with conditional variance less than - ! EPS2 are moved to the beginning among these - ! with only One exception: if it is one of the - ! Xt variables and Nstoc>0 then it switch place - ! with Xt(Nstoc) - - DO iy=Ndold,MIN(Ntd,N) - r1=index1(iy) - SQ(iy)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - IF (SQ(iy).LT.EPS2) THEN - IF (Njleft.GT.0) THEN - Ntmp=NstoXd+Njleft - IF (iy.LT.Ntmp) THEN - IF (Nstoc.GT.0) THEN !switch place with Xt(Nstoc) - CALL swapint(index1(iy),index1(Nstoc)) - !CALL swapre(SQ(iy),SQ(Nstoc)) - SQ(iy)=SQ(Nstoc);SQ(Nstoc)=0.d0 - Nstoc=Nstoc-1 - ELSE - CALL swapint(index1(iy),index1(NstoXd)) - !CALL swapre(SQ(iy),SQ(NstoXd)) - SQ(iy)=SQ(NstoXd);SQ(NstoXd)=0.d0 - Njleft=Njleft-1 - NstoXd=NstoXd+1 - ENDIF - ELSE - CALL swapint(index1(iy),index1(Ntmp)) - CALL swapint(index1(Ntmp),index1(NstoXd)) - !CALL swapre(SQ(iy),SQ(Ntmp)) - !CALL swapre(SQ(Ntmp),SQ(NstoXd)) - SQ(iy)=SQ(Ntmp);SQ(Ntmp)=SQ(NstoXd) - SQ(NstoXd)=0.d0 - NstoXd=NstoXd+1 - ENDIF - ELSE - CALL swapint(index1(iy),index1(NstoXd)) - !CALL swapre(SQ(iy),SQ(NstoXd)) ! - SQ(iy)=SQ(NstoXd);SQ(NstoXd)=0.d0 - NstoXd=NstoXd+1 - ENDIF - ENDIF ! SQ < EPS2 - ENDDO - - - ! Calculating Covariances for non-deterministic variables - DO row=1,Nstoc - r1=index1(row) - R(r1,r1)=SQ(row) - DO col=row+1,Nstoc - c1=index1(col) - R(c1,r1)=R(r1,c1)-R(r1,m1)*R(m1,c1) !/R(m1,m1) - R(r1,c1)=R(c1,r1) - ENDDO - DO col=NstoXd,N - c1=index1(col) - R(c1,r1)=R(r1,c1)-R(r1,m1)*R(m1,c1) !/R(m1,m1) - R(r1,c1)=R(c1,r1) - ENDDO - ENDDO - DO row=NstoXd,MIN(Ntd,N) - r1=index1(row) - R(r1,r1)=SQ(row) - - DO col=row+1,N - c1=index1(col) - R(c1,r1)=R(r1,c1)-R(r1,m1)*R(m1,c1) !/R(m1,m1) - R(r1,c1)=R(c1,r1) - ENDDO - ENDDO - - ! Set covariances for Deterministic variables to zero - ! in order to avoid numerical problems - - DO row=Ndold,NStoXd-1 - r1=index1(row) - SQ(row) = 0.d0 !MAX(SQ(row),0.d0) - R(r1,r1) = SQ(row) - DO col=row+1,N - c1=index1(col) - R(c1,r1)=0.d0 - R(r1,c1)=0.d0 - ENDDO - DO col=1,Nsold - c1=index1(col) - R(c1,r1)=0.d0 - R(r1,c1)=0.d0 - ENDDO - ENDDO - - DO row=Nstoc+1,Nsold - r1=index1(row) - SQ(row) = 0.d0 !MAX(SQ(row),0.d0) - R(r1,r1)=SQ(row) - DO col=1,row-1 - c1=index1(col) - R(c1,r1)=0.d0 - R(r1,c1)=0.d0 - ENDDO - DO col=NstoXd,N - c1=index1(col) - R(c1,r1)=0.d0 - R(r1,c1)=0.d0 - ENDDO - ENDDO - RETURN - END SUBROUTINE CONDSORT2 - - SUBROUTINE CONDSORT3(R,CSTD2,SQ,index1,NsXtmj,Nstoc) - USE GLOBALDATA, ONLY : EPS2,Njj,Ntscis - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(:,:), INTENT(inout) :: R,CSTD2 - DOUBLE PRECISION, DIMENSION(:), INTENT(inout) :: SQ ! diag. of R - INTEGER, DIMENSION(: ), INTENT(inout) :: index1,NsXtmj - INTEGER, DIMENSION(1) :: m - INTEGER, INTENT(inout) :: Nstoc -! local variables - INTEGER :: m1 - INTEGER :: Nsold - INTEGER :: r1,c1,row,col,iy,ix -! This function condsort all the Xt variables for use with RINDSCIS and -! MNORMPRB - - !Nsoold=Nstoc - ix=1 - - DO WHILE ((ix.LE.Nstoc).and.(ix.LE.(Ntscis+Njj))) - m=ix-1+MAXLOC(SQ(ix:Nstoc)) - IF (SQ(m(1)).LT.EPS2) THEN - !PRINT *,'Condsort3, error degenerate X' - NsXtmj(1:Njj+Ntscis)=0 - Nstoc=0 !degenerate=1 - RETURN !degenerate case - ENDIF - m1=index1(m(1)); - CALL swapint(index1(m(1)),index1(ix)) - SQ(ix) = SQRT(SQ(m(1))) - CSTD2(m1,ix) = SQ(ix) - - R(index1(ix:Nstoc),m1) = R(index1(ix:Nstoc),m1)/SQ(ix) - R(m1,index1(ix+1:Nstoc)) = R(index1(ix+1:Nstoc),m1) - ! Calculating conditional variances for the - ! first Nstoc variables. - ! variables with variance less than EPS2 - ! will be treated as deterministic and not - ! stochastic variables and are therefore moved - ! to the end among these variables. - ! Nstoc is the # of variables we treat - ! stochastically - iy=ix+1;Nsold=Nstoc - DO WHILE (iy.LE.Nstoc) - r1=index1(iy) - SQ(iy)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - IF (SQ(iy).LT.EPS2) THEN - IF (SQ(iy).LT.-EPS2) THEN - !print *,'Cndsrt3,Error:Covariance negative definit' - ENDIF - r1=index1(Nstoc) - SQ(Nstoc)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - DO WHILE ((SQ(Nstoc).LT.EPS2).AND.(iy.LT.Nstoc)) - IF (SQ(Nstoc).LT.-EPS2) THEN - !print *,'Cndsrt3,Error:Covariance negative definit' - ENDIF - SQ(Nstoc)=0.d0 !MAX(0.d0,SQ(Nstoc)) - Nstoc=Nstoc-1 - r1=index1(Nstoc) - SQ(Nstoc)=R(r1,r1)-R(r1,m1)*R(m1,r1) !/R(m1,m1) - END DO - CALL swapint(index1(iy),index1(Nstoc)) ! swap indices - !CALL swapre(SQ(iy),SQ(Nstoc)) ! - SQ(iy)=SQ(Nstoc); SQ(Nstoc)=0.d0 ! swap values - Nstoc=Nstoc-1 - ENDIF - iy=iy+1 - END DO - NsXtmj(ix)=Nstoc ! saving index to last stoch. var. after conditioning - ! Calculating Covariances for non-deterministic variables - DO row=ix+1,Nstoc - r1=index1(row) - R(r1,r1)=SQ(row) - CSTD2(r1,ix)=SQRT(SQ(row)) ! saving stdev after conditioning on ix - DO col=row+1,Nstoc - c1=index1(col) - R(c1,r1)=R(r1,c1)-R(r1,m1)*R(m1,c1) !/R(m1,m1) - R(r1,c1)=R(c1,r1) - ENDDO - ENDDO - ! similarly for deterministic values - DO row=Nstoc+1,Nsold - r1=index1(row) - SQ(row)=0.d0 !MAX(SQ(row),0.d0) - R(r1,r1)=SQ(row) - DO col=ix+1,Nsold !row-1 - c1=index1(col) - R(c1,r1)=0.d0 - R(r1,c1)=0.d0 - ENDDO - ENDDO - ix=ix+1 - ENDDO - NsXtmj(Nstoc+1:Njj+Ntscis)=Nstoc - RETURN - END SUBROUTINE CONDSORT3 - - SUBROUTINE swapRe(m,n) - IMPLICIT NONE - DOUBLE PRECISION, INTENT(inout) :: m,n - DOUBLE PRECISION :: tmp - tmp=m - m=n - n=tmp - END SUBROUTINE swapRe - - SUBROUTINE swapint(m,n) - IMPLICIT NONE - INTEGER, INTENT(inout) :: m,n - INTEGER :: tmp - tmp=m - m=n - n=tmp - END SUBROUTINE swapint - - SUBROUTINE getdiag(diag,matrix) - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(: ), INTENT(out) :: diag - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: matrix - DOUBLE PRECISION, DIMENSION(: ), ALLOCATABLE :: vector - - ALLOCATE(vector(SIZE(matrix))) - vector=PACK(matrix,.TRUE.) - diag=vector(1:SIZE(matrix):SIZE(matrix,dim=1)+1) - DEALLOCATE(vector) - END SUBROUTINE getdiag - - END MODULE RIND71MOD - - - - - - - - diff --git a/wafo/source/rind2007/rind_interface.f b/wafo/source/rind2007/rind_interface.f deleted file mode 100644 index 237ec9c..0000000 --- a/wafo/source/rind2007/rind_interface.f +++ /dev/null @@ -1,223 +0,0 @@ -! This is a interface-file for Python -! This file contains a interface to RIND a subroutine -! for computing multivariate normal expectations. -! The file is self contained and should compile without errors on (Fortran90) -! standard Fortran compilers. -! -! The interface was written by -! Per Andreas Brodtkorb -! Norwegian Defence Research Establishment -! P.O. Box 115 -! N-3191 Horten -! Norway -! Email: Per.Brodtkorb@ffi.no -! -! -! RIND Computes multivariate normal expectations -! -! E[Jacobian*Indicator|Condition ]*f_{Xc}(xc(:,ix)) -! where -! "Indicator" = I{ H_lo(i) < X(i) < H_up(i), i=1:N_t+N_d } -! "Jacobian" = J(X(Nt+1),...,X(Nt+Nd+Nc)), special case is -! "Jacobian" = |X(Nt+1)*...*X(Nt+Nd)|=|Xd(1)*Xd(2)..Xd(Nd)| -! "condition" = Xc=xc(:,ix), ix=1,...,Nx. -! X = [Xt; Xd; Xc], a stochastic vector of Multivariate Gaussian -! variables where Xt,Xd and Xc have the length Nt, Nd and Nc, -! respectively. (Recommended limitations Nx,Nt<=100, Nd<=6 and Nc<=10) -! -! CALL: [value,error,terror,inform]=rind(S,m,indI,Blo,Bup,INFIN,xc, -! Nt,SCIS,XcScale,ABSEPS,RELEPS,COVEPS,MAXPTS,MINPTS,seed,NIT,xCutOff,Nc1c2); -! -! -! VALUE = estimated value for the expectation as explained above size 1 x Nx -! ERROR = estimated sampling error, with 99% confidence level. size 1 x Nx -! TERROR = estimated truncation error -! INFORM = INTEGER, termination status parameter: (not implemented yet) -! if INFORM = 0, normal completion with ERROR < EPS; -! if INFORM = 1, completion with ERROR > EPS and MAXPTS -! function vaules used; increase MAXPTS to -! decrease ERROR; -! if INFORM = 2, N > 100 or N < 1. -! -! S = Covariance matrix of X=[Xt;Xd;Xc] size Ntdc x Ntdc (Ntdc=Nt+Nd+Nc) -! m = the expectation of X=[Xt;Xd;Xc] size N x 1 -! indI = vector of indices to the different barriers in the -! indicator function, length NI, where NI = Nb+1 -! (NB! restriction indI(1)=0, indI(NI)=Nt+Nd ) -! B_lo,B_up = Lower and upper barriers used to compute the integration -! limits, Hlo and Hup, respectively. size Mb x Nb -! INFIN = INTEGER, array of integration limits flags: size 1 x Nb (in) -! if INFIN(I) < 0, Ith limits are (-infinity, infinity); -! if INFIN(I) = 0, Ith limits are (-infinity, Hup(I)]; -! if INFIN(I) = 1, Ith limits are [Hlo(I), infinity); -! if INFIN(I) = 2, Ith limits are [Hlo(I), Hup(I)]. -! xc = values to condition on size Nc x Nx -! Nt = size of Xt -! SCIS = Integer defining integration method -! 1 Integrate all by SADAPT for Ndim<9 and by KRBVRC otherwise -! 2 Integrate all by SADAPT by Genz (1992) (Fast) -! 3 Integrate all by KRBVRC by Genz (1993) (Fast) -! 4 Integrate all by KROBOV by Genz (1992) (Fast) -! 5 Integrate all by RCRUDE by Genz (1992) -! XcScale = REAL to scale the conditinal probability density, i.e., -! f_{Xc} = exp(-0.5*Xc*inv(Sxc)*Xc + XcScale) -! ABSEPS = REAL absolute error tolerance. -! RELEPS = REAL relative error tolerance. -! COVEPS = REAL error in cholesky factorization -! MAXPTS = INTEGER, maximum number of function values allowed. This -! parameter can be used to limit the time. A sensible -! strategy is to start with MAXPTS = 1000*N, and then -! increase MAXPTS if ERROR is too large. -! MINPTS = INTEGER, minimum number of function values allowed -! SEED = INTEGER, seed to the random generator used in the integrations -! NIT = INTEGER, maximum number of Xt variables to integrate -! xCutOff = REAL upper/lower truncation limit of the marginal normal CDF -! Nc1c2 = INTEGER number of times to use the regression equation to restrict -! integration area. Nc1c2 = 1,2 is recommended. -! -! -! If Mb=0, -! IF INFIN(j)~=0, Hlo(i)=Blo(1,j)+Blo(2:Mb,j).'*xc(1:Mb-1,ix), -! IF INFIN(j)~=1, Hup(i)=Bup(1,j)+Bup(2:Mb,j).'*xc(1:Mb-1,ix), -! -! where i=indI(j-1)+1:indI(j), j=2:NI, ix=1:Nx -! -! This file was successfully compiled for matlab 5.3 -! using Compaq Visual Fortran 6.1, and Windows 2000 and windows XP. -! The example here uses Fortran90 source. -! First, you will need to modify your mexopts.bat file. -! To find it, issue the command prefdir(1) from the Matlab command line, -! the directory it answers with will contain your mexopts.bat file. -! Open it for editing. The first section will look like: -! -!rem ******************************************************************** -!rem General parameters -!rem ******************************************************************** -!set MATLAB=%MATLAB% -!set DF_ROOT=C:\Program Files\Microsoft Visual Studio -!set VCDir=%DF_ROOT%\VC98 -!set MSDevDir=%DF_ROOT%\Common\msdev98 -!set DFDir=%DF_ROOT%\DF98 -!set PATH=%MSDevDir%\bin;%DFDir%\BIN;%VCDir%\BIN;%PATH% -!set INCLUDE=%DFDir%\INCLUDE;%DFDir%\IMSL\INCLUDE;%INCLUDE% -!set LIB=%DFDir%\LIB;%VCDir%\LIB -! -! then you are ready to compile this file at the matlab prompt using the following command: -! -! mex -O -output mexrind2007 intmodule.f jacobmod.f rind2007.f mexrind2007.f -! - - - subroutine set_constants(method,xcscale,abseps,releps,coveps, - & maxpts,minpts,nit,xcutoff,Nc1c2, NINT1, xsplit) - use rindmod, only : setconstants - use rind71mod, only : setdata - double precision :: xcscale,abseps,releps,coveps,xcutoff,xsplit - integer method, maxpts, minpts, nit, Nc1c2, NINT1 -Cf2py double precision, optional :: xcscale = 0.0e0 -Cf2py double precision, optional :: abseps = 0.01e0 -Cf2py double precision, optional :: releps = 0.01e0 -Cf2py double precision, optional :: coveps = 1.0e-10 -Cf2py double precision, optional :: xcutoff = 5.0e0 -Cf2py double precision, optional :: xsplit = 5.0e0 - -Cf2py integer, optional :: method = 3 -Cf2py integer, optional :: minpts = 0 -Cf2py integer, optional :: maxpts = 40000 -Cf2py integer, optional :: nit = 1000 -Cf2py integer, optional :: Nc1c2 = 2 -Cf2py integer, optional :: nint1 = 2 - -! Method>0 - call setconstants(method,xcscale,abseps,releps,coveps, - & maxpts,minpts,nit,xcutoff,Nc1c2) -! method==0 - call SETDATA(method,xcscale,abseps,releps,coveps, - & nit, xCutOff,NINT1,xsplit) - return - end subroutine set_constants - SUBROUTINE show_constants() - use rindmod - print *, 'method=', mMethod - print *, 'xcscale=', mXcScale - print *, 'abseps=', mAbsEps - print *, 'releps=', mRelEps - print *, 'coveps=', mCovEps - print *, 'maxpts=', mMaxPts - print *, 'minpts=', mMinPts - print *, 'nit=', mNit - print *, 'xcutOff=', mXcutOff - print *, 'Nc1c2=', mNc1c2 - end subroutine show_constants - - SUBROUTINE rind(VALS,ERR,TERR,Big,Ex,Xc,Nt,INDI,Blo,Bup, - & INFIN,seed1,Ntdc,Nc,Nx,Ni,Mb,Nb,Nx1) - USE rindmod - USE rind71mod, only : rind71 - IMPLICIT NONE - INTEGER :: Ntd -C INTEGER :: Nj,K, I - INTEGER :: seed1 - integer :: Nx,Nx1,Nt, Nc,Ntdc,Ni,Nb,Mb - DOUBLE PRECISION, dimension(Ntdc,Ntdc) :: BIG - DOUBLE PRECISION, dimension(Ntdc) :: Ex - DOUBLE PRECISION, dimension(Nc,Nx1) :: Xc - DOUBLE PRECISION, dimension(Mb,Nb) :: Blo,Bup - DOUBLE PRECISION, dimension(Nx) :: VALS, ERR,TERR - INTEGER, dimension(Ni) :: IndI - INTEGER, DIMENSION(Nb) :: INFIN - INTEGER, ALLOCATABLE :: seed(:) - INTEGER :: seed_size -Cf2py integer, intent(hide), depend(Ex) :: Ntdc = len(Ex) -Cf2py integer, intent(hide), depend(Xc) :: Nc = shape(Xc,0) -Cf2py integer, intent(hide), depend(Xc) :: Nx1 = shape(Xc,1) -Cf2py integer, intent(hide), depend(Xc) :: Nx = max(shape(Xc,1),1) -Cf2py integer, intent(hide), depend(Blo) :: Mb = shape(Blo,0), Nb = shape(Blo,1), -Cf2py integer, intent(hide), depend(Indi) :: Ni = len(Indi) -Cf2py depend(Ntdc) Big -Cf2py depend(Nb) INFIN -Cf2py depend(Mb,Nb) Bup -Cf2py double precision, intent(out), depend(Nx) :: VALS -Cf2py double precision, intent(out), depend(Nx) :: ERR -Cf2py double precision, intent(out), depend(Nx) :: TERR - -C print *, 'Ntdc=', Ntdc,' Nt=',Nt,' Nc=',Nc -C print *, 'Nx=', Nx, 'Mb=', Mb, ' Nb=', Nb, ' Ni=',Ni -C Ni = Nb+1 -C Nx = max(Nx1,1) - if (Ni.EQ.Nb+1) then - else - print *, '(ni==nb+1) failed: rind:ni=', Ni, ', nb=',Nb - return - endif - - Ntd = Ntdc - Nc; -! Nd = Ntd - Nt - - IF (Ntd.EQ.INDI(Ni)) THEN -! Call the computational subroutine. - IF (mMethod.gt.0) THEN - CALL random_seed(SIZE=seed_size) - ALLOCATE(seed(seed_size)) - !print *,'rindinterface seed', seed1 - CALL random_seed(GET=seed(1:seed_size)) ! get current state - seed(1:seed_size)=seed1 ! change seed - CALL random_seed(PUT=seed(1:seed_size)) - CALL random_seed(GET=seed(1:seed_size)) ! get current state - !print *,'rindinterface seed', seed - DEALLOCATE(seed) - CALL RINDD(VALS,ERR,TERR,Big,Ex,Xc,Nt,INDI,Blo,Bup,INFIN) - ELSE - CALL RIND71(VALS,Big,Ex,Xc,Nt,INDI,Blo,Bup) - ERR(:) = -1 - TERR(:) = -1 - ENDIF - ELSE - print *,'INDI(Ni) must equal Nt+Nd!' - ENDIF - - RETURN - END SUBROUTINE rind - diff --git a/wafo/source/rind2007/rindmod.f b/wafo/source/rind2007/rindmod.f deleted file mode 100644 index 73c5bf9..0000000 --- a/wafo/source/rind2007/rindmod.f +++ /dev/null @@ -1,2435 +0,0 @@ -! Programs available in module RINDMOD : -! -! 1) setConstants -! 2) RINDD -! -! SETCONSTANTS set member variables controlling the performance of RINDD -! -! CALL setConstants(method,xcscale,abseps,releps,coveps,maxpts,minpts,nit,xcutoff,Nc1c2) -! -! METHOD = INTEGER defining the SCIS integration method -! 1 Integrate by SADAPT for Ndim<9 and by KRBVRC otherwise -! 2 Integrate by SADAPT for Ndim<20 and by KRBVRC otherwise -! 3 Integrate by KRBVRC by Genz (1993) (Fast Ndim<101) (default) -! 4 Integrate by KROBOV by Genz (1992) (Fast Ndim<101) -! 5 Integrate by RCRUDE by Genz (1992) (Slow Ndim<1001) -! 6 Integrate by SOBNIED (Fast Ndim<1041) -! 7 Integrate by DKBVRC by Genz (2003) (Fast Ndim<1001) -! -! XCSCALE = REAL to scale the conditinal probability density, i.e., -! f_{Xc} = exp(-0.5*Xc*inv(Sxc)*Xc + XcScale) (default XcScale =0) -! ABSEPS = REAL absolute error tolerance. (default 0) -! RELEPS = REAL relative error tolerance. (default 1e-3) -! COVEPS = REAL error tolerance in Cholesky factorization (default 1e-13) -! MAXPTS = INTEGER, maximum number of function values allowed. This -! parameter can be used to limit the time. A sensible -! strategy is to start with MAXPTS = 1000*N, and then -! increase MAXPTS if ERROR is too large. -! (Only for METHOD~=0) (default 40000) -! MINPTS = INTEGER, minimum number of function values allowed. -! (Only for METHOD~=0) (default 0) -! NIT = INTEGER, maximum number of Xt variables to integrate -! This parameter can be used to limit the time. -! If NIT is less than the rank of the covariance matrix, -! the returned result is a upper bound for the true value -! of the integral. (default 1000) -! XCUTOFF = REAL cut off value where the marginal normal -! distribution is truncated. (Depends on requested -! accuracy. A value between 4 and 5 is reasonable.) -! NC1C2 = number of times to use the regression equation to restrict -! integration area. Nc1c2 = 1,2 is recommended. (default 2) -! -! -!RIND computes E[Jacobian*Indicator|Condition]*f_{Xc}(xc(:,ix)) -! -! where -! "Indicator" = I{ H_lo(i) < X(i) < H_up(i), i=1:Nt+Nd } -! "Jacobian" = J(X(Nt+1),...,X(Nt+Nd+Nc)), special case is -! "Jacobian" = |X(Nt+1)*...*X(Nt+Nd)|=|Xd(1)*Xd(2)..Xd(Nd)| -! "condition" = Xc=xc(:,ix), ix=1,...,Nx. -! X = [Xt; Xd ;Xc], a stochastic vector of Multivariate Gaussian -! variables where Xt,Xd and Xc have the length Nt, Nd and Nc, -! respectively. -! (Recommended limitations Nx, Nt<101, Nd<7 and NIT,Nc<11) -! (RIND = Random Integration N Dimensions) -! -!CALL RINDD(E,err,terr,S,m,xc,Nt,indI,Blo,Bup,INFIN); -! -! E = expectation/density as explained above size 1 x Nx (out) -! ERR = estimated sampling error size 1 x Nx (out) -! TERR = estimated truncation error size 1 x Nx (out) -! S = Covariance matrix of X=[Xt;Xd;Xc] size N x N (N=Nt+Nd+Nc) (in) -! m = the expectation of X=[Xt;Xd;Xc] size N x 1 (in) -! xc = values to condition on size Nc x Nx (in) -! indI = vector of indices to the different barriers in the (in) -! indicator function, length NI, where NI = Nb+1 -! (NB! restriction indI(1)=0, indI(NI)=Nt+Nd ) -! Blo,Bup = Lower and upper barrier coefficients used to compute the (in) -! integration limits A and B, respectively. -! size Mb x Nb. If Mb=0, -! IF INFIN(j)~=0, A(i)=Blo(1,j)+Blo(2:Mb,j).'*xc(1:Mb-1,ix), -! IF INFIN(j)~=1, B(i)=Bup(1,j)+Bup(2:Mb,j).'*xc(1:Mb-1,ix), -! -! where i=indI(j-1)+1:indI(j), j=1:NI-1, ix=1:Nx -! Thus the integration limits may change with the conditional -! variables. -!Example: -! The indices, indI=[0 3 5 6], and coefficients Blo=[0 0 -1], -! Bup=[0 0 5], INFIN=[0 1 2] -! means that A = [-inf -inf -inf 0 0 -1] B = [0 0 0 inf inf 5] -! -! -! (Recommended limitations Nx,Nt<101, Nd<7 and Nc<11) -! Also note that the size information have to be transferred to RINDD -! through the input arguments E,S,m,Nt,IndI,Blo,Bup and INFIN -! -! For further description see the modules -! -! References -! Podgorski et al. (2000) -! "Exact distributions for apparent waves in irregular seas" -! Ocean Engineering, Vol 27, no 1, pp979-1016. (RINDD) -! -! R. Ambartzumian, A. Der Kiureghian, V. Ohanian and H. -! Sukiasian (1998) -! "Multinormal probabilities by sequential conditioned -! importance sampling: theory and application" (MVNFUN) -! Probabilistic Engineering Mechanics, Vol. 13, No 4. pp 299-308 -! -! Alan Genz (1992) -! 'Numerical Computation of Multivariate Normal Probabilites' (MVNFUN) -! J. computational Graphical Statistics, Vol.1, pp 141--149 -! -! Alan Genz and Koon-Shing Kwong (2000?) -! 'Numerical Evaluation of Singular Multivariate Normal Distributions' (MVNFUN,COVSRT) -! Computational Statistics and Data analysis -! -! -! P. A. Brodtkorb (2004), (RINDD, MVNFUN, COVSRT) -! Numerical evaluation of multinormal expectations -! In Lund university report series -! and in the Dr.Ing thesis: -! The probability of Occurrence of dangerous Wave Situations at Sea. -! Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, -! Trondheim, Norway. - -! Tested on: DIGITAL UNIX Fortran90 compiler -! PC pentium II with Lahey Fortran90 compiler -! Solaris with SunSoft F90 compiler Version 1.0.1.0 (21229283) -! History: -! Revised pab aug. 2009 -! -renamed from rind2007 to rindmod -! Revised pab July 2007 -! - separated the absolute error into ERR and TERR. -! - renamed from alanpab24 -> rind2007 -! revised pab 23may2004 -! RIND module totally rewritten according to the last reference. - - - MODULE GLOBALCONST ! global constants - IMPLICIT NONE - DOUBLE PRECISION, PARAMETER :: gSQTWPI1= 0.39894228040143D0 !=1/sqrt(2*pi) - DOUBLE PRECISION, PARAMETER :: gSQPI1 = 0.56418958354776D0 !=1/sqrt(pi) - DOUBLE PRECISION, PARAMETER :: gSQPI = 1.77245385090552D0 !=sqrt(pi) - DOUBLE PRECISION, PARAMETER :: gSQTW = 1.41421356237310D0 !=sqrt(2) - DOUBLE PRECISION, PARAMETER :: gSQTW1 = 0.70710678118655D0 !=1/sqrt(2) - DOUBLE PRECISION, PARAMETER :: gPI1 = 0.31830988618379D0 !=1/pi - DOUBLE PRECISION, PARAMETER :: gPI = 3.14159265358979D0 !=pi - DOUBLE PRECISION, PARAMETER :: gTWPI = 6.28318530717958D0 !=2*pi - DOUBLE PRECISION, PARAMETER :: gSQTWPI = 2.50662827463100D0 !=sqrt(2*pi) - DOUBLE PRECISION, PARAMETER :: gONE = 1.D0 - DOUBLE PRECISION, PARAMETER :: gTWO = 2.D0 - DOUBLE PRECISION, PARAMETER :: gHALF = 0.5D0 - DOUBLE PRECISION, PARAMETER :: gZERO = 0.D0 - DOUBLE PRECISION, PARAMETER :: gINFINITY = 37.D0 ! SQRT(-gTWO*LOG(1.D+12*TINY(gONE))) -! Set gINFINITY (infinity). -! Such that EXP(-2.x^2) > 10^(12) times TINY -! SAVE gINFINITY - END MODULE GLOBALCONST - - MODULE RINDMOD - USE GLOBALCONST -! USE PRINTMOD ! used for debugging only - IMPLICIT NONE - PRIVATE - PUBLIC :: RINDD, SetConstants - PUBLIC :: mCovEps, mAbsEps,mRelEps, mXcutOff, mXcScale - PUBLIC :: mNc1c2, mNIT, mMaxPts,mMinPts, mMethod, mSmall - private :: preInit - private :: initIntegrand - private :: initfun,mvnfun,cvsrtxc,covsrt1,covsrt,rcscale,rcswap - private :: cleanUp - - INTERFACE RINDD - MODULE PROCEDURE RINDD - END INTERFACE - - INTERFACE SetConstants - MODULE PROCEDURE SetConstants - END INTERFACE - -! mInfinity = what is considered as infinite value in FI -! mFxcEpss = if fxc is less, do not compute E(...|Xc) -! mXcEps2 = if any Var(Xc(j)|Xc(1),...,Xc(j-1)) <= XCEPS2 then return NAN - double precision, parameter :: mInfinity = 8.25d0 ! 37.0d0 - double precision, parameter :: mFxcEpss = 1.0D-20 - double precision, save :: mXcEps2 = 2.3d-16 -! Constants defining accuracy of integration: -! mCovEps = termination criteria for Cholesky decomposition -! mAbsEps = requested absolute tolerance -! mRelEps = requested relative tolerance -! mXcutOff = truncation value to c1c2 -! mXcScale = scale factor in the exponential (in order to avoid overflow) -! mNc1c2 = number of times to use function c1c2, i.e.,regression -! equation to restrict integration area. -! mNIT = maximum number of Xt variables to integrate -! mMethod = integration method: -! 1 Integrate all by SADAPT if NDIM<9 otherwise by KRBVRC (default) -! 2 Integrate all by SADAPT if NDIM<19 otherwise by KRBVRC -! 3 Integrate all by KRBVRC by Genz (1998) (Fast and reliable) -! 4 Integrate all by KROBOV by Genz (1992) (Fast and reliable) -! 5 Integrate all by RCRUDE by Genz (1992) (Reliable) -! 6 Integrate all by SOBNIED by Hong and Hickernell -! 7 Integrate all by DKBVRC by Genz (2003) (Fast Ndim<1001) - double precision, save :: mCovEps = 1.0d-10 - double precision, save :: mAbsEps = 0.01d0 - double precision, save :: mRelEps = 0.01d0 - double precision, save :: mXcutOff = 5.d0 - double precision, save :: mXcScale = 0.0d0 - integer, save :: mNc1c2 = 2 - integer, save :: mNIT = 1000 - integer, save :: mMaxPts = 40000 - integer, save :: mMinPts = 0 - integer, save :: mMethod = 3 - - -! Integrand variables: -! mBIG = Cholesky Factor/Covariance matrix: -! Upper triangular part is the cholesky factor -! Lower triangular part contains the conditional -! standarddeviations -! (mBIG2 is only used if mNx>1) -! mCDI = Cholesky DIagonal elements -! mA,mB = Integration limits -! mINFI = integrationi limit flags -! mCm = conditional mean -! mINFIXt, -! mINFIXd = # redundant variables of Xt and Xd, -! respectively -! mIndex1, -! mIndex2 = indices to the variables original place. Size Ntdc -! xedni = indices to the variables new place. Size Ntdc -! mNt = # Xt variables -! mNd = # Xd variables -! mNc = # Xc variables -! mNtd = mNt + mNd -! mNtdc = mNt + mNd + mNc -! mNx = # different integration limits - - double precision,allocatable, dimension(:,:) :: mBIG,mBIG2 - double precision,allocatable, dimension(:) :: mA,mB,mCDI,mCm - INTEGER, DIMENSION(:),ALLOCATABLE :: mInfi,mIndex1,mIndex2,mXedni - INTEGER,SAVE :: mNt,mNd,mNc,mNtdc, mNtd, mNx ! Size information - INTEGER,SAVE :: mInfiXt,mInfiXd - logical,save :: mInitIntegrandCalled = .FALSE. - - DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: mCDIXd, mCmXd - DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: mXd, mXc, mY - double precision, save :: mSmall = 2.3d-16 - -! variables set in initfun and used in mvnfun: - INTEGER, PRIVATE :: mI0,mNdleftN0 - DOUBLE PRECISION, PRIVATE :: mE1,mD1, mVAL0 - - contains - subroutine setConstants(method,xcscale,abseps,releps,coveps, - & maxpts,minpts,nit,xcutoff,Nc1c2) - double precision, optional, intent(in) :: xcscale,abseps,releps - $ ,coveps, xcutoff - integer, optional,intent(in) :: method,nit,maxpts,minpts,Nc1c2 - double precision, parameter :: one = 1.0d0 - mSmall = spacing(one) - if (present(method)) mMethod = method - if (present(xcscale)) mXcScale = xcscale - if (present(abseps)) mAbsEps = max(abseps,mSmall) - if (present(releps)) mRelEps = max(releps,0.0d0) - if (present(coveps)) mCovEps = max(coveps,1d-12) - if (present(maxpts)) mMaxPts = maxpts - if (present(minpts)) mMinPts = minpts - if (present(nit)) mNit = nit - if (present(xcutOff)) mXcutOff = xCutOff - if (present(Nc1c2)) mNc1c2 = max(Nc1c2,1) -! print *, 'method=', mMethod -! print *, 'xcscale=', mXcScale -! print *, 'abseps=', mAbsEps -! print *, 'releps=', mRelEps -! print *, 'coveps=', mCovEps -! print *, 'maxpts=', mMaxPts -! print *, 'minpts=', mMinPts -! print *, 'nit=', mNit -! print *, 'xcutOff=', mXcutOff -! print *, 'Nc1c2=', mNc1c2 - end subroutine setConstants - - subroutine preInit(BIG,Xc,Nt,inform) - double precision,dimension(:,:), intent(in) :: BIG - double precision,dimension(:,:), intent(in) :: Xc - integer, intent(in) :: Nt - integer, intent(out) :: inform -! Local variables - integer :: I,J - inform = 0 - mInitIntegrandCalled = .FALSE. -! Find the size information -!~~~~~~~~~~~~~~~~~~~~~~~~~~ - mNt = Nt - mNc = SIZE( Xc, dim = 1 ) - mNx = MAX( SIZE( Xc, dim = 2), 1 ) - mNtdc = SIZE( BIG, dim = 1 ) - ! make sure it does not exceed Ntdc-Nc - IF (mNt+mNc.GT.mNtdc) mNt = mNtdc - mNc - mNd = mNtdc-mNt-mNc - mNtd = mNt+mNd - IF (mNd < 0) THEN -! PRINT *,'RIND Nt,Nd,Nc,Ntdc=',Nt,Nd,Nc,Ntdc - ! Size information inconsistent - inform = 3 - return - ENDIF - - ! PRINT *,'Nt Nd Nc Ntd Ntdc,',Nt, Nd, Nc, Ntd, Ntdc - -! ALLOCATION -!~~~~~~~~~~~~ - IF (mNd>0) THEN - ALLOCATE(mXd(mNd),mCmXd(mNd),mCDIXd(mNd)) - mCmXd(:) = gZERO - mCDIXd(:) = gZERO - mxd(:) = gZERO - END IF - ALLOCATE(mBIG(mNtdc,mNtdc),mCm(mNtdc),mY(mNtd)) - ALLOCATE(mIndex1(mNtdc),mA(mNtd),mB(mNtd),mINFI(mNtd),mXc(mNc)) - ALLOCATE(mCDI(mNtd),mXedni(mNtdc),mIndex2(mNtdc)) - -! Initialization -!~~~~~~~~~~~~~~~~~~~~~ -! Copy upper triangular of input matrix, only. - do i = 1,mNtdc - mBIG(1:i,i) = BIG(1:i,i) - end do - - mIndex2 = (/(J,J=1,mNtdc)/) - -! CALL mexprintf('BIG Before CovsrtXc'//CHAR(10)) -! CALL ECHO(BIG) -! sort BIG by decreasing cond. variance for Xc - CALL CVSRTXC(mNt,mNd,mBIG,mIndex2,INFORM) -! CALL mexprintf('BIG after CovsrtXc'//CHAR(10)) -! CALL ECHO(BIG) - - IF (INFORM.GT.0) return ! degenerate case exit VALS=0 for all - ! (should perhaps return NaN instead??) - - - DO I=mNtdc,1,-1 - J = mIndex2(I) ! covariance matrix according to index2 - mXedni(J) = I - END DO - - IF (mNx>1) THEN - ALLOCATE(mBIG2(mNtdc,mNtdc)) - do i = 1,mNtdc - mBIG2(1:i,i) = mBIG(1:i,i) !Copy input matrix - end do - ENDIF - return - end subroutine preInit - subroutine initIntegrand(ix,Xc,Ex,indI,Blo,Bup,INFIN, - & fxc,value,abserr,NDIM,inform) - integer, intent(in) :: ix ! integrand number - double precision, dimension(:),intent(in) :: Ex - double precision, dimension(:,:), intent(in) :: Xc,Blo,Bup - integer, dimension(:), intent(in) :: indI,INFIN - double precision, intent(out) :: fxc,value,abserr - integer, intent(out) :: NDIM, inform -! Locals - DOUBLE PRECISION :: SQ0,xx,quant - integer :: I,J - inform = 0 - NDIM = 0 - VALUE = gZERO - fxc = gONE - abserr = mSmall - - IF (mInitIntegrandCalled) then - do i = 1,mNtdc - mBIG(1:i,i) = mBIG2(1:i,i) !Copy input matrix - end do - else - mInitIntegrandCalled = .TRUE. - endif - - ! Set the original means of the variables - mCm(:) = Ex(mIndex2(1:mNtdc)) ! Cm(1:Ntdc) =Ex (index1(1:Ntdc)) - IF (mNc>0) THEN - mXc(:) = Xc(:,ix) - !mXc(1:Nc) = Xc(1:Nc,ix) - QUANT = DBLE(mNc)*LOG(gSQTWPI1) - I = mNtdc - DO J = 1, mNc -! Iterative conditioning on the last Nc variables - SQ0 = mBIG(I,I) ! SQRT(Var(X(i)|X(i+1),X(i+2),...,X(Ntdc))) - xx = (mXc(mIndex2(I) - mNtd) - mCm(I))/SQ0 - !Trick to calculate - !fxc = fxc*SQTWPI1*EXP(-0.5*(XX**2))/SQ0 - QUANT = QUANT - gHALF*xx*xx - LOG(SQ0) - ! conditional mean (expectation) - ! E(X(1:i-1)|X(i),X(i+1),...,X(Ntdc)) - mCm(1:I-1) = mCm(1:I-1) + xx*mBIG(1:I-1,I) - I = I-1 - ENDDO - ! Calculating the - ! fxc probability density for i=Ntdc-J+1, - ! fXc=f(X(i)|X(i+1),X(i+2)...X(Ntdc))* - ! f(X(i+1)|X(i+2)...X(Ntdc))*..*f(X(Ntdc)) - fxc = EXP(QUANT+mXcScale) - - ! if fxc small: don't bother - ! calculating it, goto end - IF (fxc < mFxcEpss) then - abserr = gONE - inform = 1 - return - endif - END IF -! Set integration limits mA,mB and mINFI -! NOTE: mA and mB are integration limits with mCm subtracted - CALL setIntLimits(mXc,indI,Blo,Bup,INFIN,inform) - if (inform>0) return - mIndex1(:) = mIndex2(:) - CALL COVSRT(.FALSE., mNt,mNd,mBIG,mCm,mA,mB,mINFI, - & mINDEX1,mINFIXt,mINFIXd,NDIM,mY,mCDI) - - CALL INITFUN(VALUE,abserr,INFORM) -! IF INFORM>0 : degenerate case: -! Integral can be calculated excactly, ie. -! mean of deterministic variables outside the barriers, -! or NDIM = 1 - return - end subroutine initIntegrand - subroutine cleanUp -! Deallocate all work arrays and vectors - IF (ALLOCATED(mXc)) DEALLOCATE(mXc) - IF (ALLOCATED(mXd)) DEALLOCATE(mXd) - IF (ALLOCATED(mCm)) DEALLOCATE(mCm) - IF (ALLOCATED(mBIG2)) DEALLOCATE(mBIG2) - IF (ALLOCATED(mBIG)) DEALLOCATE(mBIG) - IF (ALLOCATED(mIndex2)) DEALLOCATE(mIndex2) - IF (ALLOCATED(mIndex1)) DEALLOCATE(mIndex1) - IF (ALLOCATED(mXedni)) DEALLOCATE(mXedni) - IF (ALLOCATED(mA)) DEALLOCATE(mA) - IF (ALLOCATED(mB)) DEALLOCATE(mB) - IF (ALLOCATED(mY)) DEALLOCATE(mY) - IF (ALLOCATED(mCDI)) DEALLOCATE(mCDI) - IF (ALLOCATED(mCDIXd)) DEALLOCATE(mCDIXd) - IF (ALLOCATED(mCmXd)) DEALLOCATE(mCmXd) - IF (ALLOCATED(mINFI)) DEALLOCATE(mINFI) - end subroutine cleanUp - function integrandBound(I0,N,Y,FINY) result (bound1) - use FIMOD - integer, intent(in) :: I0,N,FINY - double precision, intent(in) :: Y - double precision :: bound1 -! locals - integer :: I,IK,FINA, FINB - double precision :: AI,BI,D1,E1 - double precision :: TMP -! Computes the upper bound for the intgrand - bound1 = gzero - if (FINY<1) return - FINA = 0 - FINB = 0 - IK = 2 - DO I = I0, N - ! E(Y(I) | Y(1))/STD(Y(IK)|Y(1)) - TMP = mBIG(IK-1,I)*Y - IF (mINFI(I) > -1) then -! May have infinite int. Limits if Nd>0 - IF ( mINFI(I) .NE. 0 ) THEN - IF ( FINA .EQ. 1 ) THEN - AI = MAX( AI, mA(I) - tmp ) - ELSE - AI = mA(I) - tmp - FINA = 1 - END IF - END IF - IF ( mINFI(I) .NE. 1 ) THEN - IF ( FINB .EQ. 1 ) THEN - BI = MIN( BI, mB(I) - tmp) - ELSE - BI = mB(I) - tmp - FINB = 1 - END IF - END IF - endif - - IF (I.EQ.N.OR.mBIG(IK+1,I+1)>gZERO) THEN - CALL MVNLMS( AI, BI,2*FINA+FINB-1, D1, E1 ) - IF (D1Nt then variable no. I is one of the Xd -! variables otherwise it is one of Xt. - - !PRINT *,'Mvnfun,ndim',Ndim - INFORM = 0 - VALUE = gZERO - abserr = max(mCovEps , 6.0d0*mSmall) - mVAL0 = gONE - - - mNdleftN0 = mNd ! Counter for number of Xd variables left - - mI0 = 0 - FINA = 0 - FINB = 0 - N = mNt + mNd - mINFIXt - mINFIXd-1 - IF (mINFIXt+mINFIXd > 0) THEN -! CHCKLIM Check if the conditional mean Cm = E(Xt,Xd|Xc) for the -! deterministic variables are between the barriers, i.e., -! A=Hlo-Cm< 0 -1) THEN - IF ((mINFI(I).NE.0).AND.(mAbsEps < mA(I))) GOTO 200 - IF ((mINFI(I).NE.1).AND.(mB(I) < -mAbsEps )) GOTO 200 - ENDIF - ENDDO - - IF (mINFIXd>0) THEN - ! Redundant variables of Xd: replace Xd with the mean - I = mNt + mNd !-INFIS - J = mNdleftN0-mINFIXd - - DO WHILE (mNdleftN0>J) - isXd = (mNt < mIndex1(I)) - IF (isXd) THEN - mXd (mNdleftN0) = mCm (I) - mNdleftN0 = mNdleftN0-1 - END IF - I = I-1 - ENDDO - ENDIF - IF (N+1 < 1) THEN -! Degenerate case, No relevant variables left to integrate -! Print *,'rind ndim1',Ndim1 - IF (mNd>0) THEN - VALUE = jacob (mXd,mXc) ! jacobian of xd,xc - ELSE - VALUE = gONE - END IF - GOTO 200 - ENDIF - ENDIF - IF (mNIT<=100) THEN - xCut = mXcutOff - - J = 1 - DO I = 2, N+1 - IF (mBIG(J+1,I)>gZERO) THEN - J = J + 1 - ELSE - ! Add xCut std to deterministic variables to get an upper - ! bound for integral - mA(I) = mA(I) - xCut * mBIG(I,J) - mB(I) = mB(I) + xCut * mBIG(I,J) - ENDIF - END DO - ELSE - xCut = gZERO - ENDIF - - NdleftO = mNdleftN0 - useC1C2 = (1<=mNc1c2) - DO I = 1, N+1 - IF (mINFI(I) > -1) then -! May have infinite int. Limits if Nd>0 - IF ( mINFI(I) .NE. 0 ) THEN - IF ( FINA .EQ. 1 ) THEN - AI = MAX( AI, mA(I) ) - ELSE - AI = mA(I) - FINA = 1 - END IF - END IF - IF ( mINFI(I) .NE. 1 ) THEN - IF ( FINB .EQ. 1 ) THEN - BI = MIN( BI, mB(I) ) - ELSE - BI = mB(I) - FINB = 1 - END IF - END IF - endif - isXd = (mINDEX1(I)>mNt) - IF (isXd) THEN ! Save the mean for Xd - mCmXd(mNdleftN0) = mCm(I) - mCDIXd(mNdleftN0) = mCDI(I) - mNdleftN0 = mNdleftN0-1 - END IF - - IF (I.EQ.N+1.OR.mBIG(2,I+1)>gZERO) THEN - IF (useC1C2.AND.I=E0) GOTO 200 - - CALL C1C2(I+1,N+1,1,mA,mB,mINFI,mY,mBIG,AI,BI,FINA,FINB) - CALL MVNLMS( AI, BI,2*FINA+FINB-1, mD1, mE1 ) - IF (mD1>=mE1) GOTO 200 - maxTruncError = FI(-ABS(mXcutOff))*dble(mNc1c2) - upError = abs(E0-mE1) - loError = abs(D0-mD1) - if (upError>mSmall) then - upError = upError*integrandBound(I+1,N+1,BI,FINB) - endif - if (loError>mSmall) then - loError = loError*integrandBound(I+1,N+1,AI,FINA) - endif - abserr = abserr + min(upError + loError,maxTruncError) - !CALL printvar(log10(loError+upError+msmall),'lo+up-err') - ELSE - CALL MVNLMS( AI, BI,2*FINA+FINB-1, mD1, mE1 ) - IF (mD1>=mE1) GOTO 200 - ENDIF - !CALL MVNLMS( AI, BI,2*FINA+FINB-1, mD1, mE1 ) - !IF (mD1>=mE1) GOTO 200 - IF ( NdleftO<=0) THEN - IF (mNd>0) mVAL0 = JACOB(mXd,mXc) - SELECT CASE (I-N) - CASE (1) !IF (I.EQ.N+1) THEN - VALUE = (mE1-mD1)*mVAL0 - abserr = abserr*mVAL0 - GO TO 200 - CASE (0) !ELSEIF (I.EQ.N) THEN - !D1=1/sqrt(1-rho^2)=1/STD(X(I+1)|X(1)) - mD1 = SQRT( gONE + mBIG(1,I+1)*mBIG(1,I+1) ) - mINFI(2) = mINFI(I+1) - mA(1) = AI - mB(1) = BI - mINFI(1) = 2*FINA+FINB-1 - IF ( mINFI(2) .NE. 0 ) mA(2) = mA(I+1)/mD1 - IF ( mINFI(2) .NE. 1 ) mB(2) = mB(I+1)/mD1 - VALUE = BVNMVN( mA, mB,mINFI,mBIG(1,I+1)/mD1 )*mVAL0 - abserr = (abserr+1.0d-14)*mVAL0 - GO TO 200 - CASE ( -1 ) !ELSEIF (I.EQ.N-1) THEN - IF (.FALSE.) THEN -! TODO :this needs further checking! (it should work though) - !1/D1= sqrt(1-r12^2) = STD(X(I+1)|X(1)) - !1/E1= STD(X(I+2)|X(1)X(I+1)) - !D1 = BIG(I+1,1) - !E1 = BIG(I+2,2) - - mD1 = gONE/SQRT( gONE + mBIG(1,I+1)*mBIG(1,I+1) ) - R12 = mBIG( 1, I+1 ) * mD1 - if (mBIG(3,I+2)>gZERO) then - mE1 = gONE/SQRT( gONE + mBIG(1,I+2)*mBIG(1,I+2) + - & mBIG(2,I+2)*mBIG(2,I+2) ) - R13 = mBIG( 1, I+2 ) * mE1 - R23 = mBIG( 2, I+2 ) * (mE1 * mD1) + R12 * R13 - else - mE1 = mCDI(I+2) - R13 = mBIG( 1, I+2 ) * mE1 - R23 = mE1*mD1 + R12 * R13 - IF ((mE1 < gZERO).AND. mINFI(I+2)>-1) THEN - CALL SWAP(mA(I+2),mB(I+2)) - IF (mINFI(I+2).NE. 2) mINFI(I+2) = 1-mINFI(I+2) - END IF - !R23 = BIG( 2, I+2 ) * (E1 * D1) + R12 * R13 - endif - mINFI(2) = mINFI(I+1) - mINFI(3) = mINFI(I+2) - mA(1) = AI - mB(1) = BI - mINFI(1) = 2*FINA+FINB-1 - IF ( mINFI(2) .NE. 0 ) mA(2) = mA(I+1) * mD1 - IF ( mINFI(2) .NE. 1 ) mB(2) = mB(I+1) * mD1 - IF ( mINFI(3) .NE. 0 ) mA(3) = mA(I+2) * mE1 - IF ( mINFI(3) .NE. 1 ) mB(3) = mB(I+2) * mE1 - if(.false.) then - CALL PRINTVECD((/R12, R13, R23 /),'R12 = ') - CALL PRINTVECD((/mD1, mE1 /),'D1 = ') - CALL PRINTVECD(mBIG(1,1:3),'BIG(1,1:3) = ') - CALL PRINTVECD(mBIG(2,2:3),'BIG(2,2:3) = ') - CALL PRINTVECD(mBIG(1:3,1),'BIG(1:3,1) = ') - CALL PRINTVECD(mBIG(2:3,2),'BIG(2:3,2) = ') - CALL PRINTVECD(mA(1:I+2),'A = ') - CALL PRINTVECD(mB(1:I+2),'B = ') - CALL PRINTVECI(mINFI(1:I+2),'INFI = ') - CALL PRINTVECI(mINDEX1(1:I+2),'index1 = ') - endif - VALUE = TVNMVN( mA, mB,mINFI, - & (/R12, R13, R23 /),1.0d-13) * mVAL0 - ABSERR = (ABSERR + 1.0d-13)*mVAL0 - GOTO 200 - ENDIF - END SELECT !ENDIF - ENDIF - ABSERR = mVAL0*ABSERR - mVAL0 = mVAL0 * (mE1-mD1) - mI0 = I - RETURN - ENDIF - ENDDO - RETURN - 200 INFORM = 1 - RETURN - END SUBROUTINE INITFUN -! -! Integrand subroutine -! - FUNCTION MVNFUN( Ndim, W ) RESULT (VAL) - USE JACOBMOD - USE FIMOD - IMPLICIT NONE - INTEGER, INTENT (IN) :: Ndim - DOUBLE PRECISION, DIMENSION(:), INTENT(in) :: W - DOUBLE PRECISION :: VAL -! local variables: - INTEGER :: N,I, J, FINA, FINB - INTEGER :: NdleftN, NdleftO ,IK - DOUBLE PRECISION :: TMP, AI, BI, DI, EI - LOGICAL :: useC1C2, isXd -!MVNFUN Multivariate Normal integrand function -! where the integrand is transformed from an integral -! having integration limits A and B to an -! integral having constant integration limits i.e. -! B 1 -! int jacob(xd,xc)*f(xd,xt)dxt dxd = int F2(W) dW -! A 0 -! -! W - new transformed integration variables, valid range 0..1 -! The vector must have the length Ndim returned from Covsrt -! mBIG - conditional sorted ChOlesky Factor of the covariance matrix (IN) -! mCDI - Cholesky DIagonal elements used to calculate the mean -! mCm - conditional mean of Xd and Xt given Xc, E(Xd,Xt|Xc) -! mXd - variables to the jacobian variable, need no initialization size Nd -! mXc - conditional variables (IN) -! mINDEX1 - if mINDEX1(I)>Nt then variable No. I is one of the Xd -! variables otherwise it is one of Xt - - !PRINT *,'Mvnfun,ndim',Ndim - -! xCut = gZERO ! xCutOff - - N = mNt+mNd-mINFIXt-mINFIXd-1 - IK = 1 ! Counter for Ndim - FINA = 0 - FINB = 0 - - NdleftN = mNdleftN0 ! Counter for number of Xd variables left - VAL = mVAL0 - NdleftO = mNd - mINFIXd - mY(IK) = FIINV( mD1 + W(IK)*( mE1 - mD1 ) ) - useC1C2 = (IK+1.LE.mNc1c2) - IF (useC1C2) THEN - ! Calculate the conditional mean - ! E(Y(I) | Y(1),...Y(I0))/STD(Y(I)|Y(1),,,,Y(I0)) - mY(mI0+1:N+1) = mBIG(IK, mI0+1:N+1)*mY(IK) - ENDIF - IF (NdleftO.GT.NdleftN ) THEN - mXd(NdleftN+1:NdleftO) = mCmXd(NdleftN+1:NdleftO)+ - & mY(IK) * mCDIXd(NdleftN+1:NdleftO) - ENDIF - NdleftO = NdleftN - IK = 2 !=IK+1 - - - DO I = mI0+1, N+1 - IF (useC1C2) THEN - TMP = mY(I) - ELSE - TMP = 0.d0 - DO J = 1, IK-1 - ! E(Y(I) | Y(1),...Y(IK-1))/STD(Y(IK)|Y(1),,,,Y(IK-1)) - TMP = TMP + mBIG(J,I)*mY(J) - END DO - ENDIF - IF (mINFI(I) < 0) GO TO 100 - ! May have infinite int. Limits if Nd>0 - IF ( mINFI(I) .NE. 0 ) THEN - IF ( FINA .EQ. 1 ) THEN - AI = MAX( AI, mA(I) - TMP) - ELSE - AI = mA(I) - TMP - FINA = 1 - END IF - IF (FINB.EQ.1.AND.BI<=AI) GOTO 200 - END IF - IF ( mINFI(I) .NE. 1 ) THEN - IF ( FINB .EQ. 1 ) THEN - BI = MIN( BI, mB(I) - TMP) - ELSE - BI = mB(I) - TMP - FINB = 1 - END IF - IF (FINA.EQ.1.AND.BI<=AI) GOTO 200 - END IF - 100 isXd = (mNt gZERO ) THEN - IF (useC1C2) THEN -! Note: for J =I+1:N+1: Y(J) = conditional expectation, E(Yj|Y1,...Yk) - CALL C1C2(I+1,N+1,IK,mA,mB,mINFI,mY,mBIG,AI,BI,FINA,FINB) - ENDIF - CALL MVNLMS( AI, BI, 2*FINA+FINB-1, DI, EI ) - IF ( DI >= EI ) GO TO 200 - VAL = VAL * ( EI - DI ) - - IF ( I <= N .OR. (NdleftN < NdleftO)) THEN - mY(IK) = FIINV( DI + W(IK)*( EI - DI ) ) - IF (NdleftN < NdleftO ) THEN - mXd(NdleftN+1:NdleftO) = mCmXd(NdleftN+1:NdleftO)+ - & mY(IK) * mCDIXd(NdleftN+1:NdleftO) - NdleftO = NdleftN - ENDIF - useC1C2 = (IK+1<=mNc1c2) - IF (useC1C2) THEN - - ! E(Y(J) | Y(1),...Y(I))/STD(Y(J)|Y(1),,,,Y(I)) - mY(I+1:N+1) = mY(I+1:N+1) + mBIG(IK, I+1:N+1)*mY(IK) - ENDIF - ENDIF - IK = IK + 1 - FINA = 0 - FINB = 0 - END IF - END DO - IF (mNd>0) VAL = VAL * jacob(mXd,mXc) - RETURN - 200 VAL = gZERO - RETURN - END FUNCTION MVNFUN - - -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -!!******************* RINDD - the main program *********************!! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - SUBROUTINE RINDD(VALS,ERR,TERR,Big,Ex,Xc,Nt, - & indI,Blo,Bup,INFIN) - USE RCRUDEMOD - USE KRBVRCMOD - USE ADAPTMOD - USE KROBOVMOD - USE DKBVRCMOD - USE SSOBOLMOD - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(: ), INTENT(out):: VALS, ERR ,TERR - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: BIG - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: Xc - DOUBLE PRECISION, DIMENSION(:), INTENT(in) :: Ex - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: Blo, Bup - INTEGER, DIMENSION(:), INTENT(in) :: indI,INFIN - INTEGER, INTENT(in) :: Nt -! DOUBLE PRECISION, INTENT(in) :: XcScale -! local variables - INTEGER :: ix, INFORM, NDIM, MAXPTS, MINPTS - DOUBLE PRECISION :: VALUE,fxc,absERR,absERR2 - double precision :: LABSEPS,LRELEPS - - - VALS(:) = gZERO - ERR(:) = gONE - TERR(:) = gONE - - call preInit(BIG,Xc,Nt,inform) - IF (INFORM.GT.0) GOTO 110 ! degenerate case exit VALS=0 for all - ! (should perhaps return NaN instead??) - -! Now the loop over all different values of -! variables Xc (the one one is conditioning on) -! is started. The density f_{Xc}(xc(:,ix)) -! will be computed and denoted by fxc. - DO ix = 1, mNx - call initIntegrand(ix,Xc,Ex,indI,Blo,Bup,infin, - & fxc,value,abserr,NDIM,inform) - - - IF (INFORM.GT.0) GO TO 100 - - MAXPTS = mMAXPTS - MINPTS = mMINPTS - LABSEPS = max(mABSEPS-abserr,0.2D0*mABSEPS) !*fxc - LRELEPS = mRELEPS - ABSERR2 = mSmall - - SELECT CASE (mMethod) - CASE (:1) - IF (NDIM < 9) THEN - CALL SADAPT(NDIM,MAXPTS,MVNFUN,LABSEPS, - & LRELEPS,ABSERR2,VALUE,INFORM) - VALUE = MAX(VALUE,gZERO) - ELSE - CALL KRBVRC(NDIM, MINPTS, MAXPTS, MVNFUN,LABSEPS,LRELEPS, - & ABSERR2, VALUE, INFORM ) - ENDIF - CASE (2) -! Call the subregion adaptive integration subroutine - IF ( NDIM .GT. 19.) THEN -! print *, 'Ndim too large for SADMVN => Calling KRBVRC' - CALL KRBVRC( NDIM, MINPTS, MAXPTS, MVNFUN, LABSEPS, - & LRELEPS, ABSERR2, VALUE, INFORM ) - ELSE - CALL SADAPT(NDIM,MAXPTS,MVNFUN,LABSEPS, - & LRELEPS,ABSERR2,VALUE,INFORM) - VALUE = MAX(VALUE,gZERO) - ENDIF - CASE (3) ! Call the Lattice rule integration procedure - CALL KRBVRC( NDIM, MINPTS, MAXPTS, MVNFUN, LABSEPS, - & LRELEPS, ABSERR2, VALUE, INFORM ) - CASE (4) ! Call the Lattice rule - ! integration procedure - CALL KROBOV( NDIM, MINPTS, MAXPTS, MVNFUN, LABSEPS, - & LRELEPS,ABSERR2, VALUE, INFORM ) - CASE (5) ! Call Crude Monte Carlo integration procedure - CALL RANMC( NDIM, MAXPTS, MVNFUN, LABSEPS, - & LRELEPS, ABSERR2, VALUE, INFORM ) - CASE (6) ! Call the scrambled Sobol sequence rule integration procedure - CALL SOBNIED( NDIM, MINPTS, MAXPTS, MVNFUN, LABSEPS, LRELEPS, - & ABSERR2, VALUE, INFORM ) - CASE (7:) - CALL DKBVRC( NDIM, MINPTS, MAXPTS, MVNFUN, LABSEPS, LRELEPS, - & ABSERR2, VALUE, INFORM ) - END SELECT - -! IF (INFORM.gt.0) print *,'RIND, INFORM,error =',inform,error - 100 VALS(ix) = VALUE*fxc - IF (SIZE(ERR, DIM = 1).EQ.mNx) ERR(ix) = abserr2*fxc - IF (SIZE(TERR, DIM = 1).EQ.mNx) TERR(ix) = abserr*fxc - ENDDO !ix - - 110 CONTINUE - call cleanUp - RETURN - END SUBROUTINE RINDD - - SUBROUTINE setIntLimits(xc,indI,Blo,Bup,INFIN,inform) - IMPLICIT NONE - DOUBLE PRECISION, DIMENSION(: ), INTENT(in) :: xc - INTEGER, DIMENSION(: ), INTENT(in) :: indI,INFIN - DOUBLE PRECISION, DIMENSION(:,:), INTENT(in) :: Blo,Bup - integer, intent(out) :: inform -!Local variables - INTEGER :: I, J, K, L,Mb1,Nb,NI,Nc - DOUBLE PRECISION :: xCut, SQ0 -!this procedure set mA,mB and mInfi according to Blo/Bup and INFIN -! -! INFIN INTEGER, array of integration limits flags: -! if INFIN(I) < 0, Ith limits are (-infinity, infinity); -! if INFIN(I) = 0, Ith limits are (-infinity, mB(I)]; -! if INFIN(I) = 1, Ith limits are [mA(I), infinity); -! if INFIN(I) = 2, Ith limits are [mA(I), mB(I)]. -! Note on member variables: -! mXedni = indices to the variables new place after cvsrtXc. Size Ntdc -! mCm = E(Xt,Xd|Xc), i.e., conditional mean given Xc -! mBIG(:,1:Ntd) = Cov(Xt,Xd|Xc) - - xCut = ABS(mInfinity) - Mb1 = size(Blo,DIM=1)-1 - Nb = size(Blo,DIM=2) - NI = size(indI,DIM=1) - Nc = size(xc,DIM=1) - if (Mb1>Nc .or. Nb.NE.NI-1) then -! size of variables inconsistent - inform = 4 - return - endif - -! IF (Mb.GT.Nc+1) print *,'barrier: Mb,Nc =',Mb,Nc -! IF (Nb.NE.NI-1) print *,'barrier: Nb,NI =',Nb,NI - DO J = 2, NI - DO I = indI (J - 1) + 1 , indI (J) - L = mXedni(I) - mINFI(L) = INFIN(J-1) - SQ0 = SQRT(mBIG(L,L)) - mA(L) = -xCut*SQ0 - mB(L) = xCut*SQ0 - IF (mINFI(L).GE.0) THEN - IF (mINFI(L).NE.0) THEN - mA(L) = Blo (1, J - 1)-mCm(L) - DO K = 1, Mb1 - mA(L) = mA(L)+Blo(K+1,J-1)*xc(K) - ENDDO ! K - ! This can only be done if - if (mA(L)< -xCut*SQ0) mINFI(L) = mINFI(L)-2 - ENDIF - IF (mINFI(L).NE.1) THEN - mB(L) = Bup (1, J - 1)-mCm(L) - DO K = 1, Mb1 - mB(L) = mB(L)+Bup(K+1,J-1)*xc(K) - ENDDO - if (xCut*SQ0-1) THEN - IF (infi.NE.0)THEN - IF (A < -mXcutOff) THEN - infi = infi-2 -! CALL mexprintf('ADJ A') - ENDIF - ENDIF - IF (infi.NE.1) THEN - IF (mXCutOff < B) THEN - infi = infi-1 -! CALL mexprintf('ADJ B') - ENDIF - END IF - END IF - RETURN - END SUBROUTINE ADJLIMITS - SUBROUTINE C1C2(I0,I1,IK,A,B,INFIN, Cm, BIG, AJ, BJ, FINA,FINB) -! The regression equation for the conditional distr. of Y given X=x -! is equal to the conditional expectation of Y given X=x, i.e., -! -! E(Y|X=x) = E(Y) + Cov(Y,X)/Var(X)[x-E(X)] -! -! Let -! x1 = (x-E(X))/SQRT(Var(X)) be zero mean, -! C1< x1 B(I) or -! -! b) Cm(I)+x1*B1(I)+C*SQ(I)-1) THEN - !BdSQ0 = B1(I) - !CSQ = xCut * SQ(I) - BdSQ0 = BIG(IK,I) - CSQ = xCut * BIG(I,IK) - IF (BdSQ0 > LTOL) THEN - IF ( INFI .NE. 0 ) THEN - IF (FINA.EQ.1) THEN - AJ = MAX(AJ,(A(I) - Cm(I) - CSQ)/BdSQ0) - ELSE - AJ = (A(I) - Cm(I) - CSQ)/BdSQ0 - FINA = 1 - ENDIF - IF (FINB.GT.0) AJ = MIN(AJ,BJ) - END IF - IF ( INFI .NE. 1 ) THEN - IF (FINB.EQ.1) THEN - BJ = MIN(BJ,(B(I) - Cm(I) + CSQ)/BdSQ0) - ELSE - BJ = (B(I) - Cm(I) + CSQ)/BdSQ0 - FINB = 1 - ENDIF - IF (FINA.GT.0) BJ = MAX(AJ,BJ) - END IF - ELSEIF (BdSQ0 < -LTOL) THEN - IF ( INFI .NE. 0 ) THEN - IF (FINB.EQ.1) THEN - BJ = MIN(BJ,(A(I) - Cm(I) - CSQ)/BdSQ0) - ELSE - BJ = (A(I) - Cm(I) - CSQ)/BdSQ0 - FINB = 1 - ENDIF - IF (FINA.GT.0) BJ = MAX(AJ,BJ) - END IF - IF ( INFI .NE. 1 ) THEN - IF (FINA.EQ.1) THEN - AJ = MAX(AJ,(B(I) - Cm(I) + CSQ)/BdSQ0) - ELSE - AJ = (B(I) - Cm(I) + CSQ)/BdSQ0 - FINA = 1 - ENDIF - IF (FINB.GT.0) AJ = MIN(AJ,BJ) - END IF - END IF - ENDIF - END DO -! IF (FINA>0 .AND. FINB>0) THEN -! IF (AJmaxSQ) maxSQ = SQ(I) - ENDDO - - XCEPS2 = Ntdc*mSmall*maxSQ - mXcEps2 = XCEPS2 - LTOL = mSmall - LO = 1 - K = Ntdc - DO I = 1, Nc ! Condsort Xc - m = K+1-MAXLOC(SQ(K:Ntd+1:-1)) - M1 = m(1) - IF (SQ(m1)<=XCEPS2) THEN -! PRINT *,'CVSRTXC: Degenerate case of Xc(Nc-J+1) for J=',ix - !CALL mexprintf('CVSRTXC: Degenerate case of Xc(Nc-J+1)') - INFORM = 1 - GOTO 200 ! RETURN !degenerate case - ENDIF - IF (M1.NE.K) THEN - ! Symmetric row column permuations - ! Swap row and columns, but only upper triangular part - CALL RCSWAP( M1, K, Ntdc,Ntd, R,INDEX1,SQ) - END IF - R(K,K) = SQRT(SQ(K)) - IF (K .EQ. LO) GOTO 200 - R(LO:K-1,K) = R(LO:K-1,K)/R(K,K) -! Cov(Xi,Xj|Xk,Xk+1,..,Xn) = .... -! Cov(Xi,Xj|Xk+1,..,Xn) - Cov(Xi,Xk|Xk+1,..Xn)*Cov(Xj,Xk|Xk+1,..Xn) - DO J = LO,K-1 - ! Var(Xj | Xk,Xk+1,...,Xn) - SQ(J) = R(J,J) - R(J,K)*R(J,K) - IF (SQ(J)<=LTOL.AND.J<=Ntd) THEN - IF (LO < J) THEN - CALL RCSWAP(LO, J, Ntdc,Ntd, R,INDEX1,SQ) - ENDIF - R(LO,LO:K-1) = gZERO - IF (SQ(LO) < -10.0D0*SQRT(LTOL)) THEN - ! inform = 2 - !R(LO,K) = gZERO - ! CALL mexprintf('Negative definit BIG!'//CHAR(10)) - ENDIF - SQ(LO) = gZERO - LO = LO + 1 - ELSE - R(J,J) = SQ(J) - R(LO:J-1,J) = R(LO:J-1,J) - R(LO:J-1,K)*R(J,K) - ENDIF - END DO - K = K - 1 - ENDDO - 200 DEALLOCATE(SQ) - RETURN - END SUBROUTINE CVSRTXC - - SUBROUTINE RCSCALE(chkLim,K,K0,N1,N,K1,INFIS,CDI,Cm, - & R,A,B,INFI,INDEX1,Y) - USE GLOBALCONST - USE SWAPMOD - IMPLICIT NONE -!RCSCALE: Scale covariance matrix and limits -! -! CALL RCSCALE( k, k0, N1, N,K1, CDI,Cm,R,A, B, INFIN,index1,Y) -! -! chkLim = TRUE if check if variable K is redundant -! FALSE -! K = index to variable which is deterministic,i.e., -! STD(Xk|X1,...Xr) = 0 -! N1 = Number of significant variables of [Xt,Xd] -! N = length(Xt)+length(Xd) -! K1 = index to current variable we are conditioning on. -! CDI = Cholesky diagonal elements which contains either -! CDI(J) = STD(Xj | X1,...,Xj-1,Xc) if Xj is stochastic given -! X1,...Xj, Xc -! or -! CDI(J) = COV(Xj,Xk | X1,..,Xk-1,Xc )/STD(Xk | X1,..,Xk-1,Xc) -! if Xj is determinstically determined given X1,..,Xk,Xc -! for some k1) then - ! Check if variable is redundant - ! TODO: this chklim-block does not work correctly yet - xCut = mInfinity - I = 1 - Ak = R(I,K)*xCut - Bk = - (R(I,K))*xCut - if (INFI(I)>=0) then - if (INFI(I).ne.0) then - Ak = -(R(I,K))*MAX(A(I),-xCut) - endif - if (INFI(I).ne.1) then - Bk = - (R(I,K))*MIN(B(I),xCut) - endif - endif - - if (R(I,K) LTOL) .OR. (isXt)) THEN - DO J = 1,I-1 - isXd = (INDEX1(J)>Nt) - IF ( (R(J,J) <= LTOL) .AND.isXd) THEN - CALL RCSWAP(J, I, N, N, R,INDEX1,Cm, A, B, INFI) - !GO TO 10 - CYCLE LP3 - ENDIF - END DO - ENDIF -! 10 - END DO LP3 -! -! Move any doubly infinite limits or any redundant of Xt to the next -! innermost positions. -! - LP4: DO I = N-INFISD, N1+1, -1 - isXd = (INDEX1(I)>Nt) - IF ( ((INFI(I) > -1).AND.(R(I,I) > LTOL)) - & .OR. isXd) THEN - DO J = 1,I-1 - isXt = (INDEX1(J)<=Nt) - IF ( (INFI(J) < 0 .OR. (R(J,J)<= LTOL)) - & .AND. (isXt)) THEN - CALL RCSWAP( J, I, N,N, R,INDEX1,Cm, A, B, INFI) - !GO TO 15 - CYCLE LP4 - ENDIF - END DO - ENDIF -!15 - END DO LP4 - -! CALL mexprintf('Before sorting') -! CALL PRINTCOF(N,A,B,INFI,R,INDEX1) -! CALL PRINTVEC(CDI,'CDI') -! CALL PRINTVEC(Cm,'Cm') - - IF ( N1 <= 0 ) GOTO 200 -! -! Sort remaining limits and determine Cholesky factor. -! - Y(1:N1) = gZERO - K = 1 - Ndleft = Nd - INFISD - Nullity = 0 - DO WHILE (K .LE. N1) - -! IF (Ndim.EQ.3) EPSL = MAX(EPS2,1D-10) -! Determine the integration limits for variable with minimum -! expected probability and interchange that variable with Kth. - - K0 = K - Nullity - PRBMIN = gTWO - JMIN = K - CVDIAG = ZERO - RMAX = ZERO - IF ((Ndleft>0) .OR. (NDIM < Nd+mNIT)) THEN - DO J = K, N1 - isXd = (INDEX1(J)>Nt) - isOK = ((NDIM <= Nd+mNIT).OR.isXd) - IF ( R(J,J) <= K0*K0*EPSL .OR. (.NOT. isOK)) THEN - RMAX = max(RMAX,ABS(R(J,J))) - ELSE - TMP = ZERO ! = conditional mean of Y(I) given Y(1:I-1) - DO I = 1, K0 - 1 - TMP = TMP + R(I,J)*Y(I) - END DO - SUMSQ = SQRT( R(J,J)) - - IF (INFI(J)>-1) THEN - ! May have infinite int. limits if Nd>0 - IF (INFI(J).NE.0) THEN - AJ = ( A(J) - TMP )/SUMSQ - ENDIF - IF (INFI(J).NE.1) THEN - BJ = ( B(J) - TMP )/SUMSQ - ENDIF - ENDIF - IF (isXd) THEN - AA = (Cm(J)+TMP)/SUMSQ ! inflection point - CALL EXLMS(AA,AJ,BJ,INFI(J),D,E,Ca,Pa) - PRBJ = E - D - ELSE - !CALL MVNLMS( AJ, BJ, INFI(J), D, E ) - CALL MVNLIMITS(AJ,BJ,INFI(J),APJ,PRBJ) - ENDIF - !IF ( EMIN + D .GE. E + DMIN ) THEN - IF ( PRBJ < PRBMIN ) THEN - JMIN = J - AMIN = AJ - BMIN = BJ - PRBMIN = MAX(PRBJ,ZERO) - CVDIAG = SUMSQ - ENDIF - ENDIF - END DO - END IF -! -! Compute Ith column of Cholesky factor. -! Compute expected value for Ith integration variable (without -! considering the jacobian) and -! scale Ith covariance matrix row and limits. -! -! 40 - IF ( CVDIAG.GT.TOL) THEN - isXd = (INDEX1(JMIN)>Nt) - IF (isXd) THEN - Ndleft = Ndleft - 1 - ELSEIF (BCVSRT.EQV..FALSE..AND.(PRBMIN+LTOL>=gONE)) THEN -!BCVSRT.EQ. - J = 1 - AJ = R(J,JMIN)*xCut - BJ = - (R(J,JMIN))*xCut - if (INFI(J)>=0) then - if (INFI(J).ne.0) then - AJ = -(R(J,JMIN))*MAX(A(J),-xCut) - endif - if (INFI(J).ne.1) then - BJ = - (R(J,JMIN))*MIN(B(J),xCut) - endif - endif - if (R(J,JMIN)Nt) - if (isXd) then - Ndleft = Ndleft - 1 - ELSEIF (BCVSRT.EQV..FALSE.) THEN -! BCVSRT.EQ. - J = 1 - AJ = R(J,I)*xCut - BJ = - (R(J,I))*xCut - if (INFI(J)>=0) then - if (INFI(J).ne.0) then - AJ = -(R(J,I))*MAX(A(J),-xCut) - endif - if (INFI(J).ne.1) then - BJ = - (R(J,I))*MIN(B(J),xCut) - endif - endif - if (R(J,I)100) THEN - R(I,K0) = gZERO - ELSE - R(I,K0) = MAX(SQRT(MAX(R(I,I), gZERO)),LTOL) - ENDIF - Nullity = Nullity + 1 - K = K + 1 - IF (K < I) THEN - CALL RCSWAP( K, I, N1,N,R,INDEX1,Cm, A, B, INFI) - ! SWAP conditional standarddeviations - DO J = 1, K0 - CALL SWAP(R(K,J),R(I,J)) - END DO - ENDIF - chkLim = .FALSE. !((.not.isXd).AND.(BCVSRT.EQ..FALSE.)) - L = INFIS - CALL RCSCALE(chkLim,K,K0,N1,N,K1,INFIS,CDI,Cm, - & R,A,B,INFI,INDEX1) - if (L.ne.INFIS) THEN - K = K - 1 - I = I - 1 - ENDIF - END IF - I = I + 1 - 75 CONTINUE - END DO - INFJ = INFI(K1) - - IF (K1 .EQ.1) THEN - FINA = 0 - FINB = 0 - IF (INFJ.GE.0) THEN - IF (INFJ.NE.0) FINA = 1 - IF (INFJ.NE.1) FINB = 1 - ENDIF - CALL C1C2(K1+1,N1,K0,A,B,INFI, Y, R, - & AMIN, BMIN, FINA,FINB) - INFJ = 2*FINA+FINB-1 - CALL MVNLIMITS(AMIN,BMIN,INFJ,APJ,PRBMIN) - ENDIF - - Y(K0) = gettmean(AMIN,BMIN,INFJ,PRBMIN) - - - R( K0, K1 ) = R( K0, K1 ) / CVDIAG - DO J = 1, K0 - 1 - ! conditional covariances - R( J, K1 ) = R( J, K1 ) / CVDIAG - ! conditional standard dev.s used in regression eq. - R( K1, J ) = R( K1, J ) / CVDIAG - END DO - - A( K1 ) = A( K1 )/CVDIAG - B( K1 ) = B( K1 )/CVDIAG - - K = K + 1 -100 CONTINUE - ELSE - covErr = RMAX - R(K:N1,K:N1) = gZERO - I = K - DO WHILE (I <= N1) -! Scale covariance matrix rows and limits -! If the conditional covariance matrix diagonal entry is zero, -! permute limits and/or rows, if necessary. - chkLim = ((index1(I)<=Nt).AND.(BCVSRT.EQV..FALSE.)) - L = INFIS - CALL RCSCALE(chkLim,I,K0-1,N1,N,K1,INFIS,CDI,Cm, - & R,A,B,INFI,INDEX1) - if (L.EQ.INFIS) I = I + 1 - END DO - Nullity = N1 - K0 + 1 - GOTO 200 !RETURN - END IF - END DO - 200 CONTINUE - IF (Ndim .GT. 0) THEN ! N10 - IF (INFI(J).NE.0) THEN - AJ = ( A(J) - TMP )/SUMSQ - ENDIF - IF (INFI(J).NE.1) THEN - BJ = ( B(J) - TMP )/SUMSQ - ENDIF - 30 IF (INDEX1(J).GT.Nt) THEN - AA = (Cm(J)+TMP)/SUMSQ ! inflection point - CALL EXLMS(AA,AJ,BJ,INFI(J),D,E,Ca,Pa) - PRBJ = E-D - ELSE - !CALL MVNLMS( AJ, BJ, INFI(J), D, E ) - CALL MVNLIMITS(AJ,BJ,INFI(J),APJ,PRBJ) - ENDIF - IF ( PRBJ < PRBMIN ) THEN - JMIN = J - AMIN = AJ - BMIN = BJ - PRBMIN = MAX(PRBJ,ZERO) - CVDIAG = SUMSQ - ENDIF - ENDIF - END DO - END IF -! -! Compute Ith column of Cholesky factor. -! Compute expected value for Ith integration variable (without -! considering the jacobian) and -! scale Ith covariance matrix row and limits. -! -!40 - IF ( CVDIAG.GT.TOL) THEN - IF (INDEX1(JMIN).GT.Nt) THEN - Ndleft = Ndleft-1 - ELSE - IF (BCVSRT.EQV..FALSE..AND.(PRBMIN+LTOL.GE.gONE)) THEN -!BCVSRT.EQ. - I = 1 - AJ = R(I,JMIN)*xCut - BJ = - (R(I,JMIN))*xCut - if (INFI(1)>=0) then - if (INFI(1).ne.0) then - AJ = -(R(I,JMIN))*MAX(A(I),-xCut) - endif - if (INFI(1).ne.1) then - BJ = - (R(I,JMIN))*MIN(B(I),xCut) - endif - endif - if (R(I,JMIN) -# Microsoft Developer Studio Generated Build File, Format Version 6.00 -# ** DO NOT EDIT ** - -# TARGTYPE "Win32 (x86) Console Application" 0x0103 - -CFG=test_fimod - Win32 Debug -!MESSAGE This is not a valid makefile. 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USE ERFCOREMOD - USE FIMOD -* -* Test program for fimod -* - DOUBLE PRECISION X, XI, XI2, VAL, P, Q, CORREL - DOUBLE PRECISION A(3), B(3), R(3), EPSI - INTEGER I, INFIN(3) - PRINT '('' Results for: FI'')' - X = -1.0 - DO I = 1,5 - VAL = FI(X) - CALL NORMPRB(X, P, Q) - XI = FIINV(VAL) - XI2 = -FIINV(Q) - PRINT *, 'X=',X, ' P=', VAL, ' XI=', XI - PRINT *, 'X=',X, ' P2=', P, ' XI2=', XI2, ' Q=', Q - X = X + I - !PRINT '('' Error Estimate : '', '' ('', F8.6'')'' )', ERR - ENDDO - - PRINT '('' Results for: BVNMVN'')' - CORREL = -0.2D0 - DO I = 1,6 - CORREL = CORREL + 0.2D0 - A(:) = 0.0D0 - B(:) = 5.0D0 - INFIN(:) = 1 - VAL = BVNMVN( A, B, INFIN, CORREL ) - PRINT *, ' P=', VAL, ' R=', CORREL - - END DO - - PRINT '('' Results for: TVNMVN'')' - EPSI = 1D-10 - CORREL = -0.2D0 - DO I = 1,6 - CORREL = CORREL + 0.2D0 - A(:) = 0.0D0 - B(:) = 5.0D0 - INFIN(:) = 1 - R(:) = CORREL !(/ 0.3D0, R13, R23 /) - VAL = TVNMVN(A, B, INFIN, R, EPSI) - PRINT *, ' P=', VAL, ' R=', CORREL - - END DO - END diff --git a/wafo/source/rind2007/test_rind71mod.f b/wafo/source/rind2007/test_rind71mod.f deleted file mode 100644 index 90ab2cc..0000000 --- a/wafo/source/rind2007/test_rind71mod.f +++ /dev/null @@ -1,85 +0,0 @@ - PROGRAM TST_RIND - USE RIND71MOD - USE FIMOD - IMPLICIT NONE - -* -* Test program for rind71 -* -* gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -o test_rind71.exe intmodule.f jacobmod.f fimod.f rind71.f test_rind71.f -* - DOUBLE PRECISION ABSEPS, RELEPS, VAL - INTEGER N, Nc,Nt,Nx, I, J, K, IJ, MAXPTS, IFT - PARAMETER ( N = 5, Nc=0, Nt=5, Nx=1, MAXPTS = 5000*N*N*N ) - PARAMETER ( ABSEPS = 0.00005, RELEPS = 0 ) - DOUBLE PRECISION CORREL(N,N), LOW(N), UP(N), BLOW(Nx,N),BUP(Nx,N) - DOUBLE PRECISION Ex(N), Vals(Nx),ERR(Nx), TERR(Nx),Xc(Nc,Nx) - INTEGER INFIN(N), INDI(N+1) -* Chen Problem - DATA ( UP(I), I=1,N) /.0, 1.5198, 9.7817, 9.4755, 1.5949/ - DATA (LOW(I), I=1,N) /.0, .0 ,-1.7817,-1.4755,-9.5949/ - DATA (INFIN(I), I=1,N)/ 1, 2 , 1 , 1 , 0 / - INDI = (/(I,I=0,N)/) - CORREL(:,:) = 0.0d0 - CORREL(1,2) = -0.707107 - CORREL(2,3) = 1.d0 - CORREL(2:3,4:5) = 0.5d0 - CORREL(4,5) = 0.5d0 - Ex(:) = 0.d0 - DO I = 1, N - CORREL(I,I) = 1.0d0 - DO j = I+1, N - CORREL(I,J) = 0.3 - CORREL(J,I) = CORREL(I,J) - ENDDO - ENDDO - val = FI(releps) - CALL initdata(1) - BLow(1,:) = LOW - Bup(1,:) = UP - - PRINT '('' Test of RIND71'')' - PRINT '(12X, ''Requested Accuracy '',F8.5)', MAX(ABSEPS,RELEPS) - PRINT '('' Number of Dimensions is '',I2)', N - PRINT '('' Maximum # of Function Values is '',I7)', MAXPTS -* - DO K = 1, 3 - PRINT '(/'' I Limits'')' - PRINT '(4X,''Lower Upper Lower Left of Correlation Matrix'')' - if (INFIN(1)==1) then - BUP(1,1) = 9.d0 - BLOW(1,1) = 0.d0 - elseif (INFIN(1)==0) then - BUP(1,1) = 0.d0 - BLOW(1,1) = -9.d0 - else - BUP(1,1) = 9.d0 - BLOW(1,1) = -9.d0 - endif - DO I = 1, N - IF ( INFIN(I) .LT. 0 ) THEN - PRINT '(I2, '' -infin infin '', 7F9.5)', - & I, ( CORREL(I,J), J = 1,I ) - ELSE IF ( INFIN(I) .EQ. 0 ) THEN - PRINT '(I2, '' -infin'', F7.4, 1X, 7F9.5)', - & I, UP(I), ( CORREL(I,J), J = 1,I) - ELSE IF ( INFIN(I) .EQ. 1 ) THEN - PRINT '(I2, F7.4, '' infin '', 7F9.5)', - & I, LOW(I), ( CORREL(I,J), J = 1,I) - ELSE - PRINT '(I2, 2F7.4, 1X, 7F9.5)', - & I, LOW(I), UP(I), ( CORREL(I,J), J = 1,I ) - ENDIF - END DO - - CALL RIND71(VALS, CORREL, Ex, Xc,Nt,indI,Blow,Bup) -! CALL RINDD(VALS,ERR,TERR,CORREL,Ex,Xc,Nt,indI,BLow,Bup,INFIN) - - - PRINT '('' Results for: RINDD'')' - PRINT '('' Value : '', F12.6, I5 )', VALS(1), IFT -! PRINT '('' Error Estimate : '', '' ('', F8.6'')'' )', ERR - INFIN(1) = INFIN(1) - 1 - - END DO - END diff --git a/wafo/source/rind2007/test_rindmod.f b/wafo/source/rind2007/test_rindmod.f deleted file mode 100644 index 5afa41f..0000000 --- a/wafo/source/rind2007/test_rindmod.f +++ /dev/null @@ -1,69 +0,0 @@ - PROGRAM TST_RIND - USE RINDMOD -* -* Test program for rindmod2007 -* gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -o test_rindmod.exe intmodule.f jacobmod.f swapmod.f fimod.f rindmod.f test_rindmod.f - -* - DOUBLE PRECISION ABSEPS, RELEPS - INTEGER N, Nc,Nt,Nx, I, J, K, MAXPTS - PARAMETER ( N = 5, Nc=0, Nt=5, Nx=1, MAXPTS = 5000*N*N*N ) - PARAMETER ( ABSEPS = 0.00005, RELEPS = 0 ) - DOUBLE PRECISION CORREL(N,N), LOW(N), UP(N), BLOW(Nx,N),BUP(Nx,N) - DOUBLE PRECISION Ex(N), Vals(Nx),ERR(Nx), TERR(Nx),Xc(Nc,Nx) - INTEGER INFIN(N), INDI(N+1) -* Chen Problem - DATA ( UP(I), I=1,N) /.0, 1.5198, 1.7817, 1.4755, 1.5949/ - DATA (LOW(I), I=1,N) /.0, .0 , -1.7817, -1.4755, -1.5949/ - DATA (INFIN(I), I=1,N)/ 1, 2 , 1 , 1 , 0 / - INDI = (/(I,I=0,N)/) - CORREL(:,:) = 0.0d0 - CORREL(1,2) = -0.707107 - CORREL(2,3) = 1.d0 - CORREL(2:3,4:5) = 0.5d0 - CORREL(4,5) = 0.5d0 - Ex(:) = 0.d0 - DO I = 1, N - CORREL(I,I) = 1.0d0 - DO j = I+1, N - CORREL(I,J) = 0.3 - CORREL(J,I) = CORREL(I,J) - ENDDO - ENDDO - CALL setConstants(METHOD=3,ABSEPS=abseps,RELEPS=releps, - ! MAXPTS=maxpts) - PRINT '('' Test of MVNDST'')' - PRINT '(12X, ''Requested Accuracy '',F8.5)', MAX(ABSEPS,RELEPS) - PRINT '('' Number of Dimensions is '',I2)', N - PRINT '('' Maximum # of Function Values is '',I7)', MAXPTS -* - DO K = 1, 3 - PRINT '(/'' I Limits'')' - PRINT '(4X,''Lower Upper Lower Left of Correlation Matrix'')' - - DO I = 1, N - IF ( INFIN(I) .LT. 0 ) THEN - PRINT '(I2, '' -infin infin '', 7F9.5)', - & I, ( CORREL(I,J), J = 1,I ) - ELSE IF ( INFIN(I) .EQ. 0 ) THEN - PRINT '(I2, '' -infin'', F7.4, 1X, 7F9.5)', - & I, UP(I), ( CORREL(I,J), J = 1,I) - ELSE IF ( INFIN(I) .EQ. 1 ) THEN - PRINT '(I2, F7.4, '' infin '', 7F9.5)', - & I, LOW(I), ( CORREL(I,J), J = 1,I) - ELSE - PRINT '(I2, 2F7.4, 1X, 7F9.5)', - & I, LOW(I), UP(I), ( CORREL(I,J), J = 1,I ) - ENDIF - END DO - BLow(1,:) = LOW - Bup(1,:) = UP - CALL RIND(VALS,ERR,TERR,CORREL,Ex,Xc,Nt,indI,BLow,Bup,INFIN) - - - PRINT '('' Results for: RINDD'')' - PRINT '('' Value : '', F12.6 )', VALS(1) - PRINT '('' Error Estimate : '', '' ('', F8.6'')'' )', ERR - INFIN(1) = INFIN(1) - 1 - END DO - END diff --git a/wafo/source/test_f90/hello.f90 b/wafo/source/test_f90/hello.f90 deleted file mode 100644 index 59c4831..0000000 --- a/wafo/source/test_f90/hello.f90 +++ /dev/null @@ -1,9 +0,0 @@ -module hello -use types -contains - subroutine foo(a) - integer(intdim) :: a - print*, "Hello from Fortran!" - print*, "a=",a - end subroutine foo -end module hello \ No newline at end of file diff --git a/wafo/source/test_f90/hello.txt b/wafo/source/test_f90/hello.txt deleted file mode 100644 index 769fc13..0000000 --- a/wafo/source/test_f90/hello.txt +++ /dev/null @@ -1,188 +0,0 @@ -[f2py] Confused with fortran 90 modules - -Dede ded.espaze at laposte.net -Fri Oct 19 11:45:36 EEST 2007 -Previous message: [f2py] Confused with fortran 90 modules -Next message: AW: [f2py] (no subject) -Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] -Hi Peter, - -I had recently the same problem with the program of a friend. He -had done a similar work but he was using reals. We succeeded to make -it work by using only "real(kind=8)" on the Python side, that's why I -have introduced a new file: hello_interface.f90. To reuse the Fortran -subroutines, we wrote a conversion function, so I have changed a -little types.f90. My files: - -types.f90 -!--------------------------! - module types - integer, parameter :: WP=4, intdim=selected_int_kind(8) - contains - function to_intdim(int_value) - integer(kind=8) :: int_value - integer(intdim) :: to_intdim - to_intdim = int_value - end function to_intdim - end module types -!--------------------------! - -hello.f90 -!--------------------------! - module hello - use types - contains - subroutine foo(a) - integer(intdim) :: a - print*, "Hello from Fortran!" - print*, "a=",a - end subroutine foo - end module hello -!--------------------------! - -hello_interface.f90 -!--------------------------! - module bindings - use types - use hello - contains - subroutine pyfoo(a) - integer(kind=8) :: a - call foo(to_intdim(a)) - end subroutine pyfoo - end module bindings -!--------------------------! - -For using the Fortran modules in Python, the code needs to be compiled -with dynamic flags, so -fPIC is introduced: - -gfortran -fPIC -c types.f90 -gfortran -fPIC -c hello.f90 - -The Python module needs to include the generated objects: - -f2py -m hello -c types.o hello.o hello_interface.f90 - -f2py -m hello -c types.o hello.o hello_interface.f90 --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 - -Now you should have the module "hello.so", and I hope you will get in -a python session: - -# ipython -. -. -In [1]: import hello - -In [2]: hello.bindings.pyfoo(4) - Hello from Fortran! - a= 4 - -Thanks to Python, it is then easy to write a module that hide the f2py -interface, so then by doing: - -import hello -hello.foo(4) - -you directly get the work done. - -Cheers, - -Dede - - -On Thu, 18 Oct 2007 01:08:07 -0600 -"Peter Schmitt" wrote: - -> I'm fairly new to Fortran, and I'm just starting out with f2py... I -> have a question which is best illustrated by example: -> -> In fortran, I have a program that calls a module, such as: -> -> hello.f90: -> ! -----------------------------------------! -> program hello -> use types -> -> call foo(5) -> -> contains -> subroutine foo (a) -> integer(intdim) :: a -> print*, "Hello from Fortran!" -> print*, "a=",a -> end subroutine foo -> -> end program hello -> ! -----------------------------------------! -> -> types.f90 -> ! -----------------------------------------! -> module types -> integer, parameter :: WP=4, intdim=selected_int_kind(8) -> end module types -> ! -----------------------------------------! -> -> To build this program in plain old fortran, I issue the following -> three commands to compile and link: -> gfortran -c types.f90 -> gfortran -c hello.f90 -> gfortran types.o hello.o -o HELLO -> -> -> Now if I want to call "foo(5)" in Python using f2py, I change -> hello.f90 as follows: -> -> hello.f90: -> ! -----------------------------------------! -> use types -> -> subroutine foo (a) -> integer(intdim) :: a -> print*, "Hello from Fortran!" -> print*, "a=",a -> end subroutine foo -> ! -----------------------------------------! -> -> Then compile types and hello -> f2py2.5 --fcompiler=gfortran -c -m types types.f90 -> f2py2.5 --fcompiler=gfortran -c -m hello hello.f90 -> -> but I can't compile hello.f90. I get the following error: -> -> > Traceback (most recent call last): -> > File -> > "/home/pschmitt/usr/local/lib/python2.5/site-packages/numpy/__init__.py", -> > line 31, in -> > from _import_tools import PackageLoader -> > File -> > "/home/pschmitt/usr/local/lib/python2.5/site-packages/numpy/_import_tools.py", -> > line 5, in -> > from glob import glob -> > File "/usr/lib/python2.5/glob.py", line 4, in -> > import fnmatch -> > File "/usr/lib/python2.5/fnmatch.py", line 13, in -> > import re -> > File "/usr/lib/python2.5/re.py", line 276, in -> > copy_reg.pickle(_pattern_type, _pickle, _compile) -> > AttributeError: 'module' object has no attribute 'pickle' -> > 'import site' failed; use -v for traceback -> > Traceback (most recent call last): -> > File "/home/pschmitt/usr/local/bin/f2py2.5", line 3, in -> > import os, sys -> > File "/usr/lib/python2.5/os.py", line 696, in -> > import copy_reg as _copy_reg -> > File "/usr/lib/python2.5/copy_reg.py", line 7, in -> > from types import ClassType as _ClassType -> > ImportError: cannot import name ClassType -> > -> -> I'm having a hard time wrapping my head around f2py and f90 -> modules... can someone offer any help? -> -> Thanks! -> -Pete - -Previous message: [f2py] Confused with fortran 90 modules -Next message: AW: [f2py] (no subject) -Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] -More information about the f2py-users mailing list \ No newline at end of file diff --git a/wafo/source/test_f90/hello_interface.f90 b/wafo/source/test_f90/hello_interface.f90 deleted file mode 100644 index 618a4e0..0000000 --- a/wafo/source/test_f90/hello_interface.f90 +++ /dev/null @@ -1,9 +0,0 @@ -module bindings -use types -use hello -contains - subroutine pyfoo(a) - integer(kind=8) :: a - call foo(to_intdim(a)) - end subroutine pyfoo -end module bindings \ No newline at end of file diff --git a/wafo/source/test_f90/mymod.f90 b/wafo/source/test_f90/mymod.f90 deleted file mode 100644 index 94220e8..0000000 --- a/wafo/source/test_f90/mymod.f90 +++ /dev/null @@ -1,47 +0,0 @@ -! f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m mymod -c mymod.f90 - -!module functionInterface -! INTERFACE -! FUNCTION F(Z) result (VAL) -! DOUBLE PRECISION, INTENT(IN) :: Z -! DOUBLE PRECISION :: VAL -! END FUNCTION F -! END INTERFACE -!end module functionInterface - -module mod1 - integer :: i = 5 - integer :: x(4) - double precision :: y = 5. - double precision, dimension(2,3) :: a - double precision, allocatable, dimension(:,:) :: b -end module mod1 -module mod -use mod1 -contains -!subroutine fun(f,x1) -!real(4) :: f -!double precision, intent(in) :: x1 -!external f -!print *, "x=[",x1,"]" -!print *, "f(x)=[",dexp(x1),"]" -!end subroutine fun - -subroutine foo(F) -!use functionInterface -integer k -real(4) :: f -!external f - print *, "i=",i - print *, "x=[",x,"]" - print *, "a=[" - print *, "[",a(1,1),",",a(1,2),",",a(1,3),"]" - print *, "[",a(2,1),",",a(2,2),",",a(2,3),"]" - print *, "]" - print *, "Setting a(1,2)=a(1,2)+3" - a(1,2) = a(1,2)+3 - i = i +1 -! print *, F(y), y -! call fun(2.0,y) -end subroutine foo -end module mod \ No newline at end of file diff --git a/wafo/source/test_f90/types.f90 b/wafo/source/test_f90/types.f90 deleted file mode 100644 index 55e2d08..0000000 --- a/wafo/source/test_f90/types.f90 +++ /dev/null @@ -1,11 +0,0 @@ - - -module types - integer, parameter :: WP=4, intdim=selected_int_kind(8) - contains - function to_intdim(int_value) - integer(kind=8) :: int_value - integer(intdim) :: to_intdim - to_intdim = int_value - end function to_intdim -end module types diff --git a/wafo/tests/__init__.py b/wafo/tests/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/wafo/tests/conftest.py b/wafo/tests/conftest.py deleted file mode 100644 index 5c8859b..0000000 --- a/wafo/tests/conftest.py +++ /dev/null @@ -1,12 +0,0 @@ -#!/usr/bin/env python -# -*- coding: utf-8 -*- -""" - Dummy conftest.py for wafo. - - If you don't know what this is for, just leave it empty. - Read more about conftest.py under: - https://pytest.org/latest/plugins.html -""" -from __future__ import print_function, absolute_import, division - -import pytest # @UnusedImport diff --git a/wafo/tests/test_bitwise.py b/wafo/tests/test_bitwise.py deleted file mode 100644 index af47fad..0000000 --- a/wafo/tests/test_bitwise.py +++ /dev/null @@ -1,38 +0,0 @@ -''' -Created on 14. feb. 2016 - -@author: pab -''' -import unittest -import wafo.bitwise as wb -import numpy as np -from numpy.testing import assert_array_equal - - -class Test(unittest.TestCase): - - def test_getbit(self): - - assert_array_equal(wb.getbit(13, np.arange(3, -1, -1)), - [1, 1, 0, 1]) - assert_array_equal(wb.getbit(5, np.r_[0:4]), [1, 0, 1, 0]) - - def test_setbit(self): - """ - Set bit fifth bit in the five bit binary binary representation - of 9 (01001) - """ - assert_array_equal(wb.setbit(9, 4), 25) - - def test_setbits(self): - assert_array_equal(wb.setbits([1, 1]), 3) - assert_array_equal(wb.setbits([1, 0]), 1) - - def test_getbits(self): - assert_array_equal(wb.getbits(3), [1, 1, 0, 0, 0, 0, 0, 0]) - assert_array_equal(wb.getbits(1), [1, 0, 0, 0, 0, 0, 0, 0]) - - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_containers.py b/wafo/tests/test_containers.py deleted file mode 100644 index 690b2ce..0000000 --- a/wafo/tests/test_containers.py +++ /dev/null @@ -1,58 +0,0 @@ -''' -Created on 29. jun. 2016 - -@author: pab -''' -import unittest -import numpy as np -from numpy.testing import assert_array_almost_equal -from wafo.containers import transformdata_1d, PlotData - - -class TestPlotData(unittest.TestCase): - - def setUp(self): - x = np.linspace(0, np.pi, 5) - self.d2 = PlotData(np.sin(x), x, - xlab='x', ylab='sin', title='sinus', - plot_args=['r.']) - self.x = x - - def tearDown(self): - pass - - def test_copy(self): - d3 = self.d2.copy() # shallow copy - self.d2.args = None - assert_array_almost_equal(d3.args, self.x) - - def test_labels_str(self): - txt = str(self.d2.labels) - self.assertEqual(txt, - 'AxisLabels(title=sinus, xlab=x, ylab=sin, zlab=)') - - -class TestTransform(unittest.TestCase): - def test_transformdata_1d(self): - expectations = \ - ([0.25, 0.4330127, 0.5, 0.4330127, 0.25], - [0.75, 0.5669873, 0.5, 0.5669873, 0.75], - [0.17881231, 0.42307446, 0.66733662, 0.84614892], - [0.82118769, 0.57692554, 0.33266338, 0.15385108], - [-1.38629436, -0.83698822, -0.69314718, -0.83698822, -1.38629436], - [-0.28768207, -0.56741838, -0.69314718, -0.56741838, -0.28768207], - [-1.72141859, -0.86020708, -0.40446069, -0.1670599], - [-0.19700358, -0.55004207, -1.10062416, -1.87177018], - [-6.0205999, -3.6349936, -3.0103, -3.6349936, -6.0205999]) - - x = np.linspace(0, np.pi, 7)[1:-1] - f = np.sin(x)/2 - for i, truth in enumerate(expectations): - plotflag = i * 10 - tf = transformdata_1d(x, f, plotflag) - print(tf) - assert_array_almost_equal(tf, truth) - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_dct_pack.py b/wafo/tests/test_dct_pack.py deleted file mode 100644 index bb05d14..0000000 --- a/wafo/tests/test_dct_pack.py +++ /dev/null @@ -1,67 +0,0 @@ -''' -Created on 14. feb. 2016 - -@author: pab -''' -import unittest -import numpy as np -from numpy.testing import assert_array_almost_equal -import wafo.dctpack as wd - - -class Test(unittest.TestCase): - def test_shiftdim(self): - a = np.arange(6).reshape((1, 1, 3, 1, 2)) - b = wd.shiftdim(a) - c = wd.shiftdim(b, -2) - assert_array_almost_equal(b.shape, (3, 1, 2)) - assert_array_almost_equal(c.shape, a.shape) - assert_array_almost_equal(c, a) - - def _test_3d(self, dct, idct, dctn, idctn): - a = np.array([[[0.51699637, 0.42946223, 0.89843545], - [0.27853391, 0.8931508, 0.34319118], - [0.51984431, 0.09217771, 0.78764716]], - [[0.25019845, 0.92622331, 0.06111409], - [0.81363641, 0.06093368, 0.13123373], - [0.47268657, 0.39635091, 0.77978269]], - [[0.86098829, 0.07901332, 0.82169182], - [0.12560088, 0.78210188, 0.69805434], - [0.33544628, 0.81540172, 0.9393219]]]) - d = dct(dct(dct(a).transpose(0, 2, 1)).transpose(2, 1, 0) - ).transpose(2, 1, 0).transpose(0, 2, 1) - d0 = dctn(a) - e0 = idctn(d0) - e = idct(idct(idct(d).transpose(0, 2, 1)).transpose(2, 1, 0) - ).transpose(2, 1, 0).transpose(0, 2, 1) - assert_array_almost_equal(d, d0) - assert_array_almost_equal(e, e0) - assert_array_almost_equal(a, e) - - def test_3d_dct_idct_dctn_idctn(self): - self._test_3d(wd.dct, wd.idct, wd.dctn, wd.idctn) - - def test_3d_dst_idst_dstn_idstn(self): - self._test_3d(wd.dst, wd.idst, wd.dstn, wd.idstn) - - def test_dct_and_dctn(self): - self._test_1d(wd.dct, wd.idct, wd.dctn, wd.idctn) - - def test_dst_and_dstn(self): - self._test_1d(wd.dst, wd.idst, wd.dstn, wd.idstn) - - def _test_1d(self, dct, idct, dctn, idctn): - a = np.arange(12) # .reshape((3, -1)) - y = dct(a) - yn = dctn(a) - x = idct(y) - xn = idctn(yn) - - assert_array_almost_equal(y, yn) - assert_array_almost_equal(x, a) - assert_array_almost_equal(xn, a) - - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_gaussian.py b/wafo/tests/test_gaussian.py deleted file mode 100644 index e043a5f..0000000 --- a/wafo/tests/test_gaussian.py +++ /dev/null @@ -1,170 +0,0 @@ -''' -Created on 17. juli 2010 - -@author: pab -''' -import unittest -import numpy as np -from numpy import pi, inf -from numpy.testing import assert_array_almost_equal -from wafo.gaussian import (Rind, prbnormtndpc, prbnormndpc, prbnormnd, - cdfnorm2d, prbnorm2d) - - -def test_rind(): - - Et = 0.001946 # exact prob. - n = 5 - Blo = -np.inf - Bup = -1.2 - indI = np.array([-1, n - 1], dtype=int) # Barriers - m = np.zeros(n) - rho = 0.3 - Sc = (np.ones((n, n)) - np.eye(n)) * rho + np.eye(n) - rind = Rind() - E0, err0, terr0 = rind(Sc, m, Blo, Bup, indI) - - assert(np.abs(E0 - Et) < 2*(err0 + terr0)) - - t = '%2.4f' % E0 - t_true = '%2.4f' % Et - assert(t == t_true) - - A = np.repeat(Blo, n) - B = np.repeat(Bup, n) # Integration limits - E1, err1, terr1 = rind(np.triu(Sc), m, A, B) # same as E0 - assert(np.abs(E1 - Et) < 2*(err1 + terr1)) - - t = '%2.4f' % E1 - assert(t == t_true) - - # Compute expectation E( abs(X1*X2*...*X5) ) - xc = np.zeros((0, 1)) - infinity = 37 - dev = np.sqrt(np.diag(Sc)) # std - ind = np.nonzero(indI[1:])[0] - Bup, Blo = np.atleast_2d(Bup, Blo) - Bup[0, ind] = np.minimum(Bup[0, ind], infinity * dev[indI[ind + 1]]) - Blo[0, ind] = np.maximum(Blo[0, ind], -infinity * dev[indI[ind + 1]]) - val, err, terr = rind(Sc, m, Blo, Bup, indI, xc, nt=0) - assert_array_almost_equal(val, 0.05494076, decimal=3) - assert(err < 0.0013) - assert_array_almost_equal(terr, 1.00000000e-10) - - # Compute expectation E( X1^{+}*X2^{+} ) with random - # correlation coefficient,Cov(X1,X2) = rho2. - m2 = [0, 0] - rho2 = 0.3 # np.random.rand(1) - Sc2 = [[1, rho2], [rho2, 1]] - Blo2 = 0 - Bup2 = np.inf - indI2 = [-1, 1] - rind2 = Rind(method=1) - - def g2(x): - return (x * (np.pi / 2 + np.arcsin(x)) + - np.sqrt(1 - x**2)) / (2 * np.pi) - assert_array_almost_equal(g2(rho2), 0.24137214191774381) # exact value - - E3, err3, terr3 = rind(Sc2, m2, Blo2, Bup2, indI2, nt=0) - assert_array_almost_equal(E3, 0.24127499) - assert_array_almost_equal(err3, 0.00013838) - assert_array_almost_equal(terr3, 1.00000000e-10) - - E4, err4, terr4 = rind2(Sc2, m2, Blo2, Bup2, indI2, nt=0) - assert_array_almost_equal(E4, 0.24127499) - assert_array_almost_equal(err4, 0.00013838) - assert_array_almost_equal(terr4, 1.00000000e-10) -# -# >>> E5, err5, terr5 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0,abseps=1e-4) -# array([ 0.24127499]) -# array([ 0.00013838]) -# array([ 1.00000000e-10]) - - -def test_prbnormtndpc(): - - rho2 = np.random.rand(2) - a2 = np.zeros(2) - b2 = np.repeat(np.inf, 2) - val2, err2, _ift2 = prbnormtndpc(rho2, a2, b2) - - def g2(x): - return 0.25 + np.arcsin(x[0] * x[1]) / (2 * pi) - E2 = g2(rho2) # exact value - assert(np.abs(E2 - val2) < err2) - - rho3 = np.random.rand(3) - a3 = np.zeros(3) - b3 = np.repeat(inf, 3) - val3, err3, _ift3 = prbnormtndpc(rho3, a3, b3) - - def g3(x): - return 0.5 - sum(np.sort(np.arccos([x[0] * x[1], x[0] * x[2], - x[1] * x[2]]))) / (4 * pi) - E3 = g3(rho3) # Exact value - assert(np.abs(E3 - val3) < err3) - - -def test_prbnormndpc(): - - rho2 = np.random.rand(2) - a2 = np.zeros(2) - b2 = np.repeat(np.inf, 2) - val2, err2, _ift2 = prbnormndpc(rho2, a2, b2) - - def g2(x): - return 0.25 + np.arcsin(x[0] * x[1]) / (2 * pi) - E2 = g2(rho2) # exact value - assert(np.abs(E2 - val2) < err2) - - rho3 = np.random.rand(3) - a3 = np.zeros(3) - b3 = np.repeat(inf, 3) - val3, err3, _ift3 = prbnormndpc(rho3, a3, b3) - - def g3(x): - return 0.5 - sum(np.sort(np.arccos([x[0] * x[1], x[0] * x[2], - x[1] * x[2]]))) / (4 * pi) - E3 = g3(rho3) # Exact value - assert(np.abs(E3 - val3) < err3) - - -def test_prbnormnd(): - - Et = 0.001946 # exact prob. - n = 5 - Blo = -np.inf - Bup = -1.2 - m = np.zeros(n) - rho = 0.3 - Sc = (np.ones((n, n)) - np.eye(n)) * rho + np.eye(n) - A = np.repeat(Blo, n) - B = np.repeat(Bup, n) - m - [val, err, _inform] = prbnormnd(Sc, A, B) - assert(np.abs(val - Et) < err) - - t = 'val = %2.5f' % val - assert(t == 'val = 0.00195') - - -def test_cdfnorm2d(): - x = np.linspace(-3, 3, 3) - [b1, b2] = np.meshgrid(x, x) - r = 0.3 - truth = [[2.38515157e-05, 1.14504149e-03, 1.34987703e-03], - [1.14504149e-03, 2.98493342e-01, 4.99795143e-01], - [1.34987703e-03, 4.99795143e-01, 9.97324055e-01]] - assert_array_almost_equal(cdfnorm2d(b1, b2, r), truth) - - -def test_prbnorm2d(): - - a = [-1, -2] - b = [1, 1] - r = 0.3 - assert_array_almost_equal(prbnorm2d(a, b, r), 0.56659121) - -if __name__ == '__main__': - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_integrate.py b/wafo/tests/test_integrate.py deleted file mode 100644 index 0f50435..0000000 --- a/wafo/tests/test_integrate.py +++ /dev/null @@ -1,124 +0,0 @@ -''' -Created on 23. okt. 2014 - -@author: pab -''' -import unittest -import numpy as np -from numpy import exp, Inf -from numpy.testing import assert_array_almost_equal -from wafo.integrate import gaussq, quadgr, clencurt, romberg - - -class TestIntegrators(unittest.TestCase): - def test_clencurt(self): - val, err = clencurt(np.exp, 0, 2) - assert_array_almost_equal(val, np.expm1(2)) - self.assert_(err < 1e-10) - - def test_romberg(self): - tol = 1e-7 - q, err = romberg(np.sqrt, 0, 10, 0, abseps=tol) - assert_array_almost_equal(q, 2.0/3 * 10**(3./2)) - self.assert_(err < tol) - - -class TestGaussq(unittest.TestCase): - ''' - 1 : p(x) = 1 a =-1, b = 1 Gauss-Legendre - 2 : p(x) = exp(-x^2) a =-inf, b = inf Hermite - 3 : p(x) = x^alpha*exp(-x) a = 0, b = inf Laguerre - 4 : p(x) = (x-a)^alpha*(b-x)^beta a =-1, b = 1 Jacobi - 5 : p(x) = 1/sqrt((x-a)*(b-x)), a =-1, b = 1 Chebyshev 1'st kind - 6 : p(x) = sqrt((x-a)*(b-x)), a =-1, b = 1 Chebyshev 2'nd kind - 7 : p(x) = sqrt((x-a)/(b-x)), a = 0, b = 1 - 8 : p(x) = 1/sqrt(b-x), a = 0, b = 1 - 9 : p(x) = sqrt(b-x), a = 0, b = 1 - ''' - - def test_gauss_legendre(self): - val, _err = gaussq(exp, 0, 1) - assert_array_almost_equal(val, exp(1)-exp(0)) - - a, b, y = [0, 0], [1, 1], np.array([1., 2.]) - val, _err = gaussq(lambda x, y: x * y, a, b, args=(y, )) - assert_array_almost_equal(val, 0.5*y) - - def test_gauss_hermite(self): - val, _err = gaussq(lambda x: x, -Inf, Inf, wfun=2) - assert_array_almost_equal(val, 0) - - def test_gauss_laguerre(self): - val, _err = gaussq(lambda x: x, 0, Inf, wfun=3, alpha=1) - assert_array_almost_equal(val, 2) - - def test_gauss_jacobi(self): - val, _err = gaussq(lambda x: x, -1, 1, wfun=4, alpha=-0.5, beta=-0.5) - assert_array_almost_equal(val, 0) - - def test_gauss_wfun5_6(self): - for i in [5, 6]: - val, _err = gaussq(lambda x: x, -1, 1, wfun=i) - assert_array_almost_equal(val, 0) - - def test_gauss_wfun7(self): - val, _err = gaussq(lambda x: x, 0, 1, wfun=7) - assert_array_almost_equal(val, 1.17809725) - - def test_gauss_wfun8(self): - val, _err = gaussq(lambda x: x, 0, 1, wfun=8) - assert_array_almost_equal(val, 1.33333333) - - def test_gauss_wfun9(self): - val, _err = gaussq(lambda x: x, 0, 1, wfun=9) - assert_array_almost_equal(val, 0.26666667) - - -class TestQuadgr(unittest.TestCase): - def test_log(self): - Q, err = quadgr(np.log, 0, 1) - assert_array_almost_equal(Q, -1) - self.assert_(err < 1e-5) - - def test_exp(self): - Q, err = quadgr(np.exp, 0, 9999*1j*np.pi) - assert_array_almost_equal(Q, -2.0000000000122662) - self.assert_(err < 1.0e-8) - - def test_integral3(self): - tol = 1e-12 - Q, err = quadgr(lambda x: np.sqrt(4-x**2), 0, 2, tol) - assert_array_almost_equal(Q, np.pi) - self.assert_(err < tol) - # (3.1415926535897811, 1.5809575870662229e-13) - - def test_integral4(self): - Q, err = quadgr(lambda x: 1./x**0.75, 0, 1) - assert_array_almost_equal(Q, 4) - self.assert_(err < 1.0e-12) - - def test_integrand4(self): - tol = 1e-10 - Q, err = quadgr(lambda x: 1./np.sqrt(1-x**2), -1, 1, tol) - assert_array_almost_equal(Q, np.pi) - self.assert_(err < tol) - # (3.141596056985029, 6.2146261559092864e-06) - - def test_integrand5(self): - tol = 1e-9 - Q, err = quadgr(lambda x: np.exp(-x**2), -np.inf, np.inf, tol) - - assert_array_almost_equal(Q, np.sqrt(np.pi)) - self.assert_(err < tol) - # (1.7724538509055152, 1.9722334876348668e-11) - - def test_integrand6(self): - tol = 1e-9 - Q, err = quadgr(lambda x: np.cos(x) * np.exp(-x), 0, np.inf, tol) - assert_array_almost_equal(Q, 0.5) - self.assert_(err < tol) - # (0.50000000000000044, 7.3296813063450372e-11) - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_integrate_oscillating.py b/wafo/tests/test_integrate_oscillating.py deleted file mode 100644 index 7e3ec02..0000000 --- a/wafo/tests/test_integrate_oscillating.py +++ /dev/null @@ -1,394 +0,0 @@ -''' -Created on 31. aug. 2015 - -@author: pab -''' -from __future__ import division -import numpy as np -import mpmath as mp -import unittest -from wafo.integrate_oscillating import (adaptive_levin_points, - chebyshev_extrema, - chebyshev_roots, tanh_sinh_nodes, - tanh_sinh_open_nodes, - AdaptiveLevin, poly_basis, - chebyshev_basis, - EvansWebster, QuadOsc) -# import numdifftools as nd -from numpy.testing import assert_allclose -from scipy.special import gamma, digamma -_EPS = np.finfo(float).eps - - -class TestBasis(unittest.TestCase): - def test_poly(self): - t = 1 - vals = [poly_basis.derivative(t, k, n=1) for k in range(3)] - assert_allclose(vals, range(3)) - vals = [poly_basis.derivative(0, k, n=1) for k in range(3)] - assert_allclose(vals, [0, 1, 0]) - vals = [poly_basis.derivative(0, k, n=2) for k in range(3)] - assert_allclose(vals, [0, 0, 2]) - - def test_chebyshev(self): - t = 1 - vals = [chebyshev_basis.derivative(t, k, n=1) for k in range(3)] - assert_allclose(vals, np.arange(3)**2) - vals = [chebyshev_basis.derivative(0, k, n=1) for k in range(3)] - assert_allclose(vals, [0, 1, 0]) - vals = [chebyshev_basis.derivative(0, k, n=2) for k in range(3)] - assert_allclose(vals, [0, 0, 4]) - - -class TestLevinPoints(unittest.TestCase): - - def test_adaptive(self): - M = 11 - delta = 100 - x = adaptive_levin_points(M, delta) - true_x = [-1., -0.99, -0.98, -0.97, -0.96, 0., - 0.96, 0.97, 0.98, 0.99, 1.] - assert_allclose(x, true_x) - - def test_chebyshev_extrema(self): - M = 11 - delta = 100 - x = chebyshev_extrema(M, delta) - true_x = [1.000000e+00, 9.510565e-01, 8.090170e-01, 5.877853e-01, - 3.090170e-01, 6.123234e-17, -3.090170e-01, -5.877853e-01, - -8.090170e-01, -9.510565e-01, -1.000000e+00] - assert_allclose(x, true_x) - - def test_chebyshev_roots(self): - M = 11 - delta = 100 - x = chebyshev_roots(M, delta) - - true_x = [9.89821442e-01, 9.09631995e-01, 7.55749574e-01, - 5.40640817e-01, 2.81732557e-01, 2.83276945e-16, - -2.81732557e-01, -5.40640817e-01, -7.55749574e-01, - -9.09631995e-01, -9.89821442e-01] - assert_allclose(x, true_x) - - def test_tanh_sinh_nodes(self): - for n in 2**np.arange(1, 5) + 1: - x = tanh_sinh_nodes(n) - # self.assertEqual(n, len(x)) - - def test_tanh_sinh_open_nodes(self): - for n in 2**np.arange(1, 5) + 1: - x = tanh_sinh_open_nodes(n) - # self.assertEqual(n, len(x)) - - -class LevinQuadrature(unittest.TestCase): - def test_exp_4t_exp_jw_gamma_t_exp_4t(self): - def f(t): - return np.exp(4 * t) # amplitude function - - def g(t): - return t + np.exp(4 * t) * gamma(t) # phase function - - def dg(t): - return 1 + (4 + digamma(t)) * np.exp(4 * t) * gamma(t) - a = 1 - b = 2 - omega = 100 - - def ftot(t): - exp4t = mp.exp(4*t) - return exp4t * mp.exp(1j * omega * (t+exp4t*mp.gamma(t))) - - _true_val, _err = mp.quadts(ftot, [a, (a+b)/2, b], error=True) - - true_val = 0.00435354129735323908804 + 0.00202865398517716214366j - # quad = AdaptiveLevin(f, g, dg, a=a, b=b, s=1, full_output=True) - for quadfun in [EvansWebster, QuadOsc, AdaptiveLevin]: - quad = quadfun(f, g, dg, a=a, b=b, full_output=True) - val, info = quad(omega) - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-11) - # assert_allclose(info.n, 9) - - def test_exp_jw_t(self): - def g(t): - return t - - def dg(t): - return np.ones(np.shape(t)) - - def true_F(t): - return np.exp(1j*omega*g(t))/(1j*omega) - - val, _err = mp.quadts(g, [0, 1], error=True) - a = 1 - b = 2 - omega = 1 - true_val = true_F(b)-true_F(a) - - for quadfun in [QuadOsc, AdaptiveLevin, EvansWebster]: - quad = quadfun(dg, g, dg, a, b, full_output=True) - val, info = quad(omega) - - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-12) - # assert_allclose(info.n, 21) - - def test_I1_1_p_ln_x_exp_jw_xlnx(self): - def g(t): - return t*np.log(t) - - def dg(t): - return 1 + np.log(t) - - def true_F(t): - return np.exp(1j*(omega*g(t)))/(1j*omega) - - a = 100 - b = 200 - omega = 1 - true_val = true_F(b)-true_F(a) - for quadfun in [AdaptiveLevin, QuadOsc, EvansWebster]: - quad = quadfun(dg, g, dg, a, b, full_output=True) - - val, info = quad(omega) - - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-10) - # assert_allclose(info.n, 11) - - def test_I4_ln_x_exp_jw_30x(self): - n = 7 - - def g(t): - return t**n - - def dg(t): - return n*t**(n-1) - - def f(t): - return dg(t)*np.log(g(t)) - - a = 0 - b = (2 * np.pi)**(1./n) - omega = 30 - - def ftot(t): - return n*t**(n-1)*mp.log(t**n) * mp.exp(1j * omega * t**n) - - _true_val, _err = mp.quadts(ftot, [a, b], error=True, maxdegree=8) - # true_val = (-0.052183048684992 - 0.193877275099872j) - true_val = (-0.0521830486849921 - 0.193877275099871j) - - for quadfun in [QuadOsc, EvansWebster, AdaptiveLevin]: - quad = quadfun(f, g, dg, a, b, full_output=True) - val, info = quad(omega) - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-5) - - def test_I5_coscost_sint_exp_jw_sint(self): - a = 0 - b = np.pi/2 - omega = 100 - - def f(t): - return np.cos(np.cos(t))*np.sin(t) - - def g(t): - return np.sin(t) - - def dg(t): - return np.cos(t) - - def ftot(t): - return mp.cos(mp.cos(t)) * mp.sin(t) * mp.exp(1j * omega * - mp.sin(t)) - - _true_val, _err = mp.quadts(ftot, [a, 0.5, 1, b], maxdegree=9, - error=True) - - true_val = 0.0325497765499959-0.121009052128827j - for quadfun in [QuadOsc, EvansWebster, AdaptiveLevin]: - quad = quadfun(f, g, dg, a, b, full_output=True) - - val, info = quad(omega) - - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-9) - - def test_I6_exp_jw_td_1_m_t(self): - a = 0 - b = 1 - omega = 1 - - def f(t): - return np.ones(np.shape(t)) - - def g(t): - return t/(1-t) - - def dg(t): - return 1./(1-t)**2 - - def ftot(t): - return mp.exp(1j * omega * t/(1-t)) - - true_val = (0.3785503757641866423607342717846606761068353230802945830 + - 0.3433779615564270328325330038583124340012440194999075192j) - for quadfun in [QuadOsc, EvansWebster, AdaptiveLevin]: - quad = quadfun(f, g, dg, a, b, endpoints=False, full_output=True) - - val, info = quad(omega) - - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-10) - - def test_I8_cos_47pix2d4_exp_jw_x(self): - def f(t): - return np.cos(47*np.pi/4*t**2) - - def g(t): - return t - - def dg(t): - return 1 - - a = -1 - b = 1 - omega = 451*np.pi/4 - - true_val = 2.3328690362927e-3 - s = 15 - for quadfun in [QuadOsc, EvansWebster]: # , AdaptiveLevin]: - quad = quadfun(f, g, dg, a, b, s=s, endpoints=False, - full_output=True) - val, _info = quad(omega) - assert_allclose(val.real, true_val) - s = 1 if s <= 2 else s // 2 - # self.assert_(info.error_estimate < 1e-10) - # assert_allclose(info.n, 11) - - def test_I9_exp_tant_sec2t_exp_jw_tant(self): - a = 0 - b = np.pi/2 - omega = 100 - - def f(t): - return np.exp(-np.tan(t))/np.cos(t)**2 - - def g(t): - return np.tan(t) - - def dg(t): - return 1./np.cos(t)**2 - - true_val = (0.0000999900009999000099990000999900009999000099990000999 + - 0.009999000099990000999900009999000099990000999900009999j) - for quadfun in [QuadOsc, EvansWebster, AdaptiveLevin]: - quad = quadfun(f, g, dg, a, b, endpoints=False, full_output=True) - - val, info = quad(omega) - - assert_allclose(val, true_val) - self.assert_(info.error_estimate < 1e-8) - - def test_exp_zdcos2t_dcos2t_exp_jw_cos_t_b_dcos2t(self): - x1 = 20 - y1 = 50 - z1 = 10 - beta = np.abs(np.arctan(y1/x1)) - R = np.sqrt(x1**2+y1**2) - - def f(t, beta, z1): - cos2t = np.cos(t)**2 - return np.where(cos2t == 0, 0, np.exp(-z1/cos2t)/cos2t) - - def g(t, beta, z1): - return np.cos(t-beta)/np.cos(t)**2 - - def dg(t, beta, z1=0): - cos3t = np.cos(t)**3 - return 0.5*(3*np.sin(beta)-np.sin(beta-2*t))/cos3t - - def append_dg_zero(zeros, g1, beta): - signs = [1, ] if np.abs(g1) <= _EPS else [-1, 1] - for sgn1 in signs: - tn = np.arccos(sgn1 * g1) - if -np.pi / 2 <= tn <= np.pi / 2: - for sgn2 in [-1, 1]: - t = sgn2 * tn - if np.abs(dg(t, beta)) < 10*_EPS: - zeros.append(t) - return zeros - - def zeros_dg(beta): - k0 = (9*np.cos(2*beta)-7) - if k0 < 0: # No stationary points - return () - k1 = 3*np.cos(2*beta)-5 - g0 = np.sqrt(2)*np.sqrt(np.cos(beta)**2*k0) - zeros = [] - - if g0+k1 < _EPS: - g1 = 1./2*np.sqrt(-g0-k1) - zeros = append_dg_zero(zeros, g1, beta) - if _EPS < g0-k1: - g2 = 1./2*np.sqrt(g0-k1) - zeros = append_dg_zero(zeros, g2, beta) - if np.abs(g0+k1) <= _EPS or np.abs(g0-k1) <= _EPS: - zeros = append_dg_zero(zeros, 0, beta) - return tuple(zeros) - - a = -np.pi/2 - b = np.pi/2 - omega = R - - def ftot(t): - cos2t = mp.cos(t)**2 - return (mp.exp(-z1/cos2t) / cos2t * - mp.exp(1j * omega * mp.cos(t-beta)/cos2t)) - - zdg = zeros_dg(beta) - ab = (a, ) + zdg + (b, ) - true_val, _err = mp.quadts(ftot, ab, maxdegree=9, error=True) - # true_val3, err3 = mp.quadgl(ftot, ab, maxdegree=9, error=True) - if False: - import matplotlib.pyplot as plt - t = np.linspace(a, b, 5*513) - plt.subplot(2, 1, 1) - f2 = f(t, beta, z1)*np.exp(1j*R*g(t, beta, z1)) - - true_val2 = np.trapz(f2, t) - plt.plot(t, f2.real, label='f.real') - plt.plot(t, f2.imag, 'r', label='f.imag') - plt.title('integral=%g+1j%g,\n' - '(%g+1j%g)' % (true_val2.real, true_val2.imag, - true_val.real, true_val.imag)) - plt.legend(loc='best', framealpha=0.5) - plt.subplot(2, 1, 2) - plt.plot(t, dg(t, beta, z1), 'r', - label='dg(t,b={},z={})'.format(beta, z1)) - plt.plot(t, g(t, beta, z1), label='g(t,b,z)') - plt.hlines(0, a, b) - plt.axis([a, b, -5, 5]) - plt.title('beta=%g' % beta) - print(np.trapz(f2, t)) - plt.legend(loc='best', framealpha=0.5) - plt.show('hold') - # true_val = 0.00253186684281+0.004314054498j - # s = 15 - for quadfun in [QuadOsc]: # , EvansWebster]: # , AdaptiveLevin]: - # EvansWebster]: # , AdaptiveLevin, ]: - quad = quadfun(f, g, dg, a, b, precision=10, endpoints=False, - full_output=True) - val, _info = quad(omega, beta, z1) # @UnusedVariable - print(quadfun.__name__) - assert_allclose(val, complex(true_val), rtol=1e-3) - # s = 1 if s<=1 else s//2 - pass - # assert(False) - - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_misc.py b/wafo/tests/test_misc.py deleted file mode 100644 index 78cdc92..0000000 --- a/wafo/tests/test_misc.py +++ /dev/null @@ -1,691 +0,0 @@ -from six import iteritems -from numpy.testing import (run_module_suite, assert_equal, assert_almost_equal, - assert_array_equal, assert_array_almost_equal, - TestCase, assert_, assert_raises,) - -import numpy as np -from numpy import array, cos, exp, linspace, pi, sin, diff, arange, ones -from wafo.data import sea -import wafo -from wafo.misc import (JITImport, Bunch, detrendma, DotDict, findcross, ecross, - findextrema, findrfc, rfcfilter, findtp, findtc, - findrfc_astm, - findoutliers, common_shape, argsreduce, stirlerr, - getshipchar, betaloge, - gravity, nextpow2, discretize, polar2cart, - cart2polar, tranproc, - rotation_matrix, rotate_2d, spaceline, - args_flat, sub2index, index2sub, piecewise, - parse_kwargs) - - -def test_disufq(): - d_inf = [[0., -144.3090093, -269.37681737, -375.20342419, -461.78882978, - -529.13303412, -577.23603722, -606.09783908, -615.7184397, - -606.09783908, -577.23603722, -529.13303412, -461.78882978, - -375.20342419, -269.37681737, -144.3090093, 0., 0., 0., 0., - 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], - [0.00000000e+00, 0.00000000e+00, 5.65917684e-01, 2.82958842e+00, - 7.92284757e+00, 1.69775305e+01, 3.11254726e+01, 5.14985092e+01, - 7.92284757e+01, 1.15447207e+02, 1.61286540e+02, 2.17878308e+02, - 2.86354348e+02, 3.67846494e+02, 4.63486583e+02, 5.74406449e+02, - 7.01737928e+02, 8.46612855e+02, 8.46046937e+02, 8.43783266e+02, - 8.38690007e+02, 8.29635324e+02, 8.15487382e+02, 7.95114345e+02, - 7.67384379e+02, 7.31165647e+02, 6.85326315e+02, 6.28734546e+02, - 5.60258507e+02, 4.78766360e+02, 3.83126272e+02, 2.72206406e+02]] - - # depth = 10 - d_10 = [[-3.43299449, -144.58425201, -269.97386241, -376.2314858, - -463.35503499, -531.34450329, -580.19988853, -609.92118976, - -620.50840653, -611.96153858, -584.28058577, -537.46554798, - -471.51642516, -386.43321726, -282.21592426, -158.8601612, 0., 0., - 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], - [0., 0., 0.87964472, 3.30251807, 8.7088916, 18.1892694, - 32.87215973, 53.88831991, 82.36912798, - 119.44619211, 166.25122204, 223.91597801, 293.57224772, - 376.35183479, 473.38655268, 585.80822113, 714.74866403, - 861.33970818, 846.05101255, 843.78326617, 838.69000702, - 829.63532408, 815.48738199, 795.11434539, 767.38437889, - 731.16564714, 685.32631478, 628.73454642, 560.25850671, - 478.76636028, 383.12627176, 272.20640579]] - - g = 9.81 - n = 32 - amp = np.ones(n) + 1j * 1 - f = np.linspace(0., 3.0, n // 2 + 1) - nmin = 2 - nmax = n // 2 + 1 - cases = 1 - ns = n - w = 2.0 * pi * f - from wafo import c_library - - d_truth = [d_10, d_inf] - for i, water_depth in enumerate([10.0, 10000000]): - kw = wafo.wave_theory.dispersion_relation.w2k(w, 0., water_depth, g)[0] - data2 = wafo.numba_misc.disufq(amp.real, amp.imag, w, kw, water_depth, - g, nmin, nmax, cases, ns) - data = c_library.disufq(amp.real, amp.imag, w, kw, water_depth, g, - nmin, nmax, cases, ns) - - # print(data[0]) - # print(data[1]) - # deep water - assert_array_almost_equal(data, data2) - assert_array_almost_equal(data, d_truth[i]) - # assert(False) - - -def test_JITImport(): - np = JITImport('numpy') - assert_equal(1.0, np.exp(0)) - - -def test_bunch(): - d = Bunch(test1=1, test2=3) - assert_equal(1, getattr(d, 'test1')) - assert_equal(3, getattr(d, 'test2')) - - -def test_dotdict(): - d = DotDict(test1=1, test2=3) - assert_equal(1, d.test1) - assert_equal(3, d.test2) - - -def test_detrendma(): - x = linspace(0, 1, 200) - y = exp(x) + 0.1 * cos(20 * 2 * pi * x) - y0 = detrendma(y, 20) - tr = y - y0 - print(y0[::40]) - print(tr[::40]) - assert_array_almost_equal( - y0[::40], [-0.01058152, 0.09386986, 0.0903801, 0.08510006, - 0.07803487]) - assert_array_almost_equal(tr[::40], [1.11058152, 1.22796459, 1.50127309, - 1.8354286, 2.24397967]) - - -def test_findcross_and_ecross(): - assert_array_equal(findcross([0, 0, 1, -1, 1], 0), np.array([1, 2, 3])) - assert_array_equal(findcross([0, 1, -1, 1], 0), np.array([0, 1, 2])) - - t = linspace(0, 7 * pi, 250) - x = sin(t) - ind = findcross(x, 0.75) - assert_array_equal(ind, np.array([9, 25, 80, 97, 151, 168, 223, 239])) - t0 = ecross(t, x, ind, 0.75) - assert_array_almost_equal(t0, np.array([0.84910514, 2.2933879, 7.13205663, - 8.57630119, 13.41484739, - 14.85909194, - 19.69776067, 21.14204343])) - - -def test_findextrema(): - t = linspace(0, 7 * pi, 250) - x = sin(t) - ind = findextrema(x) - assert_array_almost_equal(ind, np.array([18, 53, 89, 125, 160, 196, 231])) - - -def test_findrfc(): - t = linspace(0, 7 * pi, 250) - x = sin(t) + 0.1 * sin(50 * t) - ind = findextrema(x) - assert_array_almost_equal( - ind, - np.array( - [1, 3, 4, 6, 7, 9, 11, 13, 14, 16, 18, 19, 21, - 23, 25, 26, 28, 29, 31, 33, 35, 36, 38, 39, 41, 43, - 45, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, - 67, 68, 70, 71, 73, 75, 77, 78, 80, 81, 83, 85, 87, - 88, 90, 92, 93, 95, 97, 99, 100, 102, 103, 105, 107, 109, - 110, 112, 113, 115, 117, 119, 120, 122, 124, 125, 127, 129, 131, - 132, 134, 135, 137, 139, 141, 142, 144, 145, 147, 149, 151, 152, - 154, 156, 157, 159, 161, 162, 164, 166, 167, 169, 171, 173, 174, - 176, 177, 179, 181, 183, 184, 186, 187, 189, 191, 193, 194, 196, - 198, 199, 201, 203, 205, 206, 208, 209, 211, 213, 215, 216, 218, - 219, 221, 223, 225, 226, 228, 230, 231, 233, 235, 237, 238, 240, - 241, 243, 245, 247, 248])) - _ti, tp = t[ind], x[ind] - for method in ['clib', 2, 1, 0]: - ind1 = findrfc(tp, 0.3, method=method) - if method in [1, 0]: - ind1 = ind1[:-1] - assert_array_almost_equal( - ind1, - np.array([0, 9, 32, 53, 74, 95, 116, 137])) - assert_array_almost_equal( - tp[ind1], - np.array( - [-0.00743352, 1.08753972, -1.07206545, 1.09550837, -1.07940458, - 1.07849396, -1.0995006, 1.08094452])) - - -def test_rfcfilter(): - - # 1. Filtered signal y is the turning points of x. - x = sea() - y = rfcfilter(x[:, 1], h=0.0, method=1) - assert_array_almost_equal( - y[0:5], - np.array([-1.2004945, 0.83950546, -0.09049454, - -0.02049454, -0.09049454])) - - # 2. This removes all rainflow cycles with range less than 0.5. - y1 = rfcfilter(x[:, 1], h=0.5, method=0) - assert_array_almost_equal( - y1[0:5], - np.array([-1.2004945, 0.83950546, -0.43049454, - 0.34950546, -0.51049454])) - # return - t = linspace(0, 7 * pi, 250) - x = sin(t) + 0.1 * sin(50 * t) - ind = findextrema(x) - assert_array_almost_equal( - ind, - np.array( - [1, 3, 4, 6, 7, 9, 11, 13, 14, 16, 18, 19, 21, - 23, 25, 26, 28, 29, 31, 33, 35, 36, 38, 39, 41, 43, - 45, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, - 67, 68, 70, 71, 73, 75, 77, 78, 80, 81, 83, 85, 87, - 88, 90, 92, 93, 95, 97, 99, 100, 102, 103, 105, 107, 109, - 110, 112, 113, 115, 117, 119, 120, 122, 124, 125, 127, 129, 131, - 132, 134, 135, 137, 139, 141, 142, 144, 145, 147, 149, 151, 152, - 154, 156, 157, 159, 161, 162, 164, 166, 167, 169, 171, 173, 174, - 176, 177, 179, 181, 183, 184, 186, 187, 189, 191, 193, 194, 196, - 198, 199, 201, 203, 205, 206, 208, 209, 211, 213, 215, 216, 218, - 219, 221, 223, 225, 226, 228, 230, 231, 233, 235, 237, 238, 240, - 241, 243, 245, 247, 248])) - _ti, tp = t[ind], x[ind] - tp03 = rfcfilter(tp, 0.3) - assert_array_almost_equal( - tp03, - np.array( - [-0.00743352, 1.08753972, -1.07206545, 1.09550837, -1.07940458, - 1.07849396, -1.0995006, 1.08094452, 0.11983423])) - - tp3 = findrfc_astm(tp) - assert_array_almost_equal((77, 3), tp3.shape) - # print(tp3[-5:]) - assert_array_almost_equal(tp3[-5:], - [[0.01552179, 0.42313414, 1.], - [1.09750448, -0.00199612, 0.5], - [1.09022256, -0.00927804, 0.5], - [0.48055514, 0.60038938, 0.5], - [0.03200274, 0.15183698, 0.5]]) - assert_array_almost_equal(tp3[:5], - [[0.03578165, 0.28906389, 1.], - [0.03602834, 0.56726584, 1.], - [0.03816623, 0.76461446, 1.], - [0.0638364, 0.92381302, 1.], - [0.07759006, 0.99628738, 1.]]) - - # assert(False) - - -def test_findtp(): - x = sea() - x1 = x[0:200, :] - itp = findtp(x1[:, 1], 0, 'Mw') - itph = findtp(x1[:, 1], 0.3, 'Mw') - assert_array_almost_equal( - itp, - np.array( - [11, 21, 22, 24, 26, 28, 31, 39, 43, 45, 47, 51, 56, - 64, 70, 78, 82, 84, 89, 94, 101, 108, 119, 131, 141, 148, - 149, 150, 159, 173, 184, 190, 199])) - assert_array_almost_equal( - itph, - np.array( - [11, 28, 31, 39, 47, 51, 56, 64, 70, 78, 89, 94, 101, - 108, 119, 131, 141, 148, 159, 173, 184, 190, 199])) - - -def test_findtc(): - x = sea() - x1 = x[0:200, :] - itc, iv = findtc(x1[:, 1], 0, 'dw') - assert_array_almost_equal( - itc, - np.array( - [28, 31, 39, 56, 64, 69, 78, 82, 83, 89, 94, 101, 108, - 119, 131, 140, 148, 159, 173, 184])) - assert_array_almost_equal( - iv, - np.array( - [19, 29, 34, 53, 60, 67, 76, 81, 82, 84, 90, 99, 103, - 112, 127, 137, 143, 154, 166, 180, 185])) - - -def test_findoutliers(): - xx = sea() - dt = diff(xx[:2, 0]) - dcrit = 5 * dt - ddcrit = 9.81 / 2 * dt * dt - zcrit = 0 - [inds, indg] = findoutliers(xx[:, 1], zcrit, dcrit, ddcrit, verbose=False) - assert_array_almost_equal(inds[np.r_[0, 1, 2, -3, -2, -1]], - np.array([6, 7, 8, 9509, 9510, 9511])) - assert_array_almost_equal(indg[np.r_[0, 1, 2, -3, -2, -1]], - np.array([0, 1, 2, 9521, 9522, 9523])) - - -def test_common_shape(): - A = np.ones((4, 1)) - B = 2 - C = np.ones((1, 5)) * 5 - assert_array_equal(common_shape(A, B, C), (4, 5)) - assert_array_equal(common_shape(A, B, C, shape=(3, 4, 1)), (3, 4, 5)) - A = np.ones((4, 1)) - B = 2 - C = np.ones((1, 5)) * 5 - assert_array_equal(common_shape(A, B, C), (4, 5)) - assert_array_equal(common_shape(A, B, C, shape=(3, 4, 1)), (3, 4, 5)) - - -def test_argsreduce(): - A = np.reshape(linspace(0, 19, 20), (4, 5)) - B = 2 - C = range(5) - cond = np.ones(A.shape) - [_A1, B1, _C1] = argsreduce(cond, A, B, C) - assert_equal(B1.shape, (20,)) - cond[2, :] = 0 - [A2, B2, C2] = argsreduce(cond, A, B, C) - assert_equal(B2.shape, (15,)) - assert_array_equal(A2, - np.array([0., 1., 2., 3., 4., 5., 6., 7., - 8., 9., 15., 16., 17., 18., 19.])) - assert_array_equal( - B2, np.array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])) - assert_array_equal( - C2, np.array([0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4])) - - -def test_stirlerr(): - assert_array_almost_equal(stirlerr(range(5)), - np.array([np.inf, 0.08106147, 0.0413407, - 0.02767793, 0.02079067])) - - -def test_parse_kwargs(): - opt = dict(arg1=1, arg2=3) - opt = parse_kwargs(opt, arg1=5) - assert(opt['arg1'] == 5) - assert(opt['arg2'] == 3) - opt2 = dict(arg3=15) - - opt = parse_kwargs(opt, **opt2) - assert('arg3' not in opt) - - -def test_getshipchar(): - sc = getshipchar(service_speed=10) - true_sc = dict(beam=29, - beamSTD=2.9, - draught=9.6, - draughtSTD=2.112, - length=216, - lengthSTD=2.011309883194276, - max_deadweight=30969, - max_deadweightSTD=3096.9, - propeller_diameter=6.761165385916601, - propeller_diameterSTD=0.20267047566705432, - service_speed=10, - service_speedSTD=0) - - for name, val in iteritems(true_sc): - assert_almost_equal(val, sc[name]) - - -def test_betaloge(): - assert_array_almost_equal(betaloge(3, arange(4)), - np.array([np.inf, -1.09861229, -2.48490665, - -3.40119738])) - - -def test_gravity(): - phi = linspace(0, 45, 5) - assert_array_almost_equal(gravity(phi), - np.array([9.78049, 9.78245014, 9.78803583, - 9.79640552, 9.80629387])) - - -def test_nextpow2(): - assert_equal(nextpow2(10), 4) - assert_equal(nextpow2(np.arange(5)), 3) - - -def test_discretize(): - x, y = discretize(np.cos, 0, np.pi, tol=0.01) - assert_array_almost_equal( - x, - np.array( - [0., 0.19634954, 0.39269908, 0.58904862, 0.78539816, - 0.9817477, 1.17809725, 1.37444679, 1.57079633, 1.76714587, - 1.96349541, 2.15984495, 2.35619449, 2.55254403, 2.74889357, - 2.94524311, 3.14159265])) - assert_array_almost_equal( - y, np.array([1.00000000e+00, 9.80785280e-01, - 9.23879533e-01, - 8.31469612e-01, 7.07106781e-01, 5.55570233e-01, - 3.82683432e-01, 1.95090322e-01, 6.12323400e-17, - -1.95090322e-01, -3.82683432e-01, -5.55570233e-01, - -7.07106781e-01, -8.31469612e-01, -9.23879533e-01, - -9.80785280e-01, -1.00000000e+00])) - - -def test_discretize_adaptive(): - x, y = discretize(np.cos, 0, np.pi, method='adaptive') - assert_array_almost_equal( - x, - np.array( - [0., 0.19634954, 0.39269908, 0.58904862, 0.78539816, - 0.9817477, 1.17809725, 1.37444679, 1.57079633, 1.76714587, - 1.96349541, 2.15984495, 2.35619449, 2.55254403, 2.74889357, - 2.94524311, 3.14159265])) - assert_array_almost_equal( - y, - np.array( - [1.00000000e+00, 9.80785280e-01, 9.23879533e-01, - 8.31469612e-01, 7.07106781e-01, 5.55570233e-01, - 3.82683432e-01, 1.95090322e-01, 6.12323400e-17, - -1.95090322e-01, -3.82683432e-01, -5.55570233e-01, - -7.07106781e-01, -8.31469612e-01, -9.23879533e-01, - -9.80785280e-01, -1.00000000e+00])) - - -def test_polar2cart_n_cart2polar(): - r = 5 - t = linspace(0, pi, 20) - x, y = polar2cart(t, r) - assert_array_almost_equal( - x, - np.array( - [5., 4.93180652, 4.72908621, 4.39736876, 3.94570255, - 3.38640786, 2.73474079, 2.00847712, 1.22742744, 0.41289673, - -0.41289673, -1.22742744, -2.00847712, -2.73474079, -3.38640786, - -3.94570255, -4.39736876, -4.72908621, -4.93180652, -5.])) - assert_array_almost_equal( - y, - np.array( - [0.00000000e+00, 8.22972951e-01, 1.62349735e+00, - 2.37973697e+00, 3.07106356e+00, 3.67861955e+00, - 4.18583239e+00, 4.57886663e+00, 4.84700133e+00, - 4.98292247e+00, 4.98292247e+00, 4.84700133e+00, - 4.57886663e+00, 4.18583239e+00, 3.67861955e+00, - 3.07106356e+00, 2.37973697e+00, 1.62349735e+00, - 8.22972951e-01, 6.12323400e-16])) - ti, ri = cart2polar(x, y) - assert_array_almost_equal( - ti, - np.array( - [0., 0.16534698, 0.33069396, 0.49604095, 0.66138793, - 0.82673491, 0.99208189, 1.15742887, 1.32277585, 1.48812284, - 1.65346982, 1.8188168, 1.98416378, 2.14951076, 2.31485774, - 2.48020473, 2.64555171, 2.81089869, 2.97624567, 3.14159265])) - assert_array_almost_equal( - ri, - np.array( - [5., 5., 5., 5., 5., 5., 5., 5., 5., 5., 5., 5., 5., - 5., 5., 5., 5., 5., 5., 5.])) - - -def test_tranproc(): - import wafo.transform.models as wtm - tr = wtm.TrHermite() - x = linspace(-5, 5, 501) - g = tr(x) - y0, y1 = tranproc(x, g, range(5), ones(5)) - assert_array_almost_equal( - y0, - np.array([0.02659612, 1.00115284, 1.92872532, - 2.81453257, 3.66292878])) - assert_array_almost_equal( - y1, - np.array([1.00005295, 0.9501118, 0.90589954, - 0.86643821, 0.83096482])) - - -class TestPiecewise(TestCase): - - def test_condition_is_single_bool_list(self): - assert_raises(ValueError, piecewise, [True, False], [1], [0, 0]) - - def test_condition_is_list_of_single_bool_list(self): - x = piecewise([[True, False]], [1], [0, 0]) - assert_array_equal(x, [1, 0]) - - def test_conditions_is_list_of_single_bool_array(self): - x = piecewise([np.array([True, False])], [1], [0, 0]) - assert_array_equal(x, [1, 0]) - - def test_condition_is_single_int_array(self): - assert_raises(ValueError, piecewise, np.array([1, 0]), [1], [0, 0]) - - def test_condition_is_list_of_single_int_array(self): - x = piecewise([np.array([1, 0])], [1], [0, 0]) - assert_array_equal(x, [1, 0]) - - def test_simple(self): - x = piecewise([[False, True]], [lambda x:-1], [0, 0]) - assert_array_equal(x, [0, -1]) - - x = piecewise([[True, False], [False, True]], [3, 4], [1, 2]) - assert_array_equal(x, [3, 4]) - - def test_default(self): - # No value specified for x[1], should be 0 - x = piecewise([[True, False]], [2], [1, 2],) - assert_array_equal(x, [2, 0]) - - # Should set x[1] to 3 - x = piecewise([[True, False]], [2, 3], [1, 2]) - assert_array_equal(x, [2, 3]) - - def test_0d(self): - x = np.array(3) - y = piecewise([x > 3], [4, 0], x) - assert_(y.ndim == 0) - assert_(y == 0) - - x = 5 - y = piecewise([[True], [False]], [1, 0], x) - assert_(y == 1) - assert_(y.ndim == 0) - - def test_abs_function(self): - x = np.linspace(-2.5, 2.5, 6) - vals = piecewise([x < 0, x >= 0], [lambda x: -x, lambda x: x], (x,)) - assert_array_equal(vals, - [2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) - - def test_abs_function_with_scalar(self): - x = np.array(-2.5) - vals = piecewise([x < 0, x >= 0], [lambda x: -x, lambda x: x], (x,)) - assert_(vals == 2.5) - - def test_otherwise_condition(self): - x = np.linspace(-2.5, 2.5, 6) - vals = piecewise([x < 0, ], [lambda x: -x, lambda x: x], (x,)) - assert_array_equal(vals, [2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) - - def test_passing_further_args_to_fun(self): - def fun0(x, y, scale=1.): - return -x * y / scale - - def fun1(x, y, scale=1.): - return x * y / scale - x = np.linspace(-2.5, 2.5, 6) - vals = piecewise([x < 0, ], [fun0, fun1], (x,), args=(2.,), scale=2.) - assert_array_equal(vals, [2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) - - def test_step_function(self): - x = np.linspace(-2.5, 2.5, 6) - vals = piecewise([x < 0, x >= 0], [-1, 1], x) - assert_array_equal(vals, [-1., -1., -1., 1., 1., 1.]) - - def test_step_function_with_scalar(self): - x = 1 - vals = piecewise([x < 0, x >= 0], [-1, 1], x) - assert_(vals == 1) - - def test_function_with_two_args(self): - x = np.linspace(-2, 2, 5) - X, Y = np.meshgrid(x, x) - vals = piecewise( - [X * Y < 0, ], [lambda x, y: -x * y, lambda x, y: x * y], (X, Y)) - assert_array_equal(vals, [[4., 2., -0., 2., 4.], - [2., 1., -0., 1., 2.], - [-0., -0., 0., 0., 0.], - [2., 1., 0., 1., 2.], - [4., 2., 0., 2., 4.]]) - - def test_fill_value_and_function_with_two_args(self): - x = np.linspace(-2, 2, 5) - X, Y = np.meshgrid(x, x) - vals = piecewise([X * Y < -0.5, X * Y > 0.5], - [lambda x, y: -x * y, lambda x, y: x * y], (X, Y), - fillvalue=np.nan) - nan = np.nan - assert_array_equal(vals, [[4., 2., nan, 2., 4.], - [2., 1., nan, 1., 2.], - [nan, nan, nan, nan, nan], - [2., 1., nan, 1., 2.], - [4., 2., nan, 2., 4.]]) - - def test_fill_value2_and_function_with_two_args(self): - x = np.linspace(-2, 2, 5) - X, Y = np.meshgrid(x, x) - vals = piecewise([X * Y < -0.5, X * Y > 0.5], - [lambda x, y: -x * y, lambda x, y: x * y, np.nan], - (X, Y)) - nan = np.nan - assert_array_equal(vals, [[4., 2., nan, 2., 4.], - [2., 1., nan, 1., 2.], - [nan, nan, nan, nan, nan], - [2., 1., nan, 1., 2.], - [4., 2., nan, 2., 4.]]) - - -class TestRotationMatrix(TestCase): - - def test_h0_p0_r0(self): - vals = rotation_matrix(heading=0, pitch=0, roll=0).tolist() - truevals = [[1., 0., 0.], - [0., 1., 0.], - [0., 0., 1.]] - self.assertListEqual(vals, truevals) - - def test_h180_p0_r0(self): - vals = rotation_matrix(heading=180, pitch=0, roll=0).tolist() - truevals = [[-1.0, -1.2246467991473532e-16, 0.0], - [1.2246467991473532e-16, -1.0, 0.0], - [-0.0, 0.0, 1.0]] - self.assertListEqual(vals, truevals) - - def test_h0_p180_r0(self): - vals = rotation_matrix(heading=0, pitch=180, roll=0).tolist() - truevals = [[-1.0, 0.0, 1.2246467991473532e-16], - [-0.0, 1.0, 0.0], - [-1.2246467991473532e-16, -0.0, -1.0]] - self.assertListEqual(vals, truevals) - - def test_h0_p0_r180(self): - vals = rotation_matrix(heading=0, pitch=180, roll=0).tolist() - truevals = [[-1.0, 0.0, 1.2246467991473532e-16], - [-0.0, 1.0, 0.0], - [-1.2246467991473532e-16, -0.0, -1.0]] - self.assertListEqual(vals, truevals) - - -class TestRotate2d(TestCase): - - def test_rotate_0deg(self): - vals = list(rotate_2d(x=1, y=0, angle_deg=0)) - truevals = [1.0, 0.0] - self.assertListEqual(vals, truevals) - - def test_rotate_90deg(self): - vals = list(rotate_2d(x=1, y=0, angle_deg=90)) - truevals = [6.123233995736766e-17, 1.0] - self.assertListEqual(vals, truevals) - - def test_rotate_180deg(self): - vals = list(rotate_2d(x=1, y=0, angle_deg=180)) - truevals = [-1.0, 1.2246467991473532e-16] - self.assertListEqual(vals, truevals) - - def test_rotate_360deg(self): - vals = list(rotate_2d(x=1, y=0, angle_deg=360)) - truevals = [1.0, -2.4492935982947064e-16] - self.assertListEqual(vals, truevals) - - -class TestSpaceLine(TestCase): - - def test_space_line(self): - vals = spaceline((2, 0, 0), (3, 0, 0), num=5).tolist() - truevals = [[2., 0., 0.], - [2.25, 0., 0.], - [2.5, 0., 0.], - [2.75, 0., 0.], - [3., 0., 0.]] - self.assertListEqual(vals, truevals) - - -class TestArgsFlat(TestCase): - - def test_1_vector_and_2_scalar_args(self): - x = [1, 2, 3] - pos, c_shape = args_flat(x, 2, 3) - truepos = [[1, 2, 3], - [2, 2, 3], - [3, 2, 3]] - truec_shape = [3, ] - self.assertListEqual(pos.tolist(), truepos) - self.assertListEqual(list(c_shape), truec_shape) - - def test_1_vector_args(self): - pos1, c_shape1 = args_flat([1, 2, 3]) - truepos1 = [[1, 2, 3]] - truec_shape1 = None - self.assertListEqual(pos1.tolist(), truepos1) - self.assertIs(c_shape1, truec_shape1) - - def test_3_scalar_args(self): - pos1, c_shape1 = args_flat(1, 2, 3) - truepos1 = [[1, 2, 3]] - truec_shape1 = [] - self.assertListEqual(pos1.tolist(), truepos1) - self.assertListEqual(list(c_shape1), truec_shape1) - - def test_3_scalar_args_version2(self): - pos1, c_shape1 = args_flat([1], 2, 3) - truepos1 = [[1, 2, 3]] - truec_shape1 = [1, ] - self.assertListEqual(pos1.tolist(), truepos1) - self.assertListEqual(list(c_shape1), truec_shape1) - - -class TestSub2index2Sub(TestCase): - - def test_sub2index_and_index2sub(self): - shape = (3, 3, 4) - a = np.arange(np.prod(shape)).reshape(shape) - trueval = a[1, 2, 3] - order = 'C' - i = sub2index(shape, 1, 2, 3, order=order) - self.assertEquals(i, 23) - - val = a.ravel(order)[i] - self.assertEquals(val, trueval) - - sub = index2sub(shape, i, order=order) - for j, true_sub_j in enumerate([1, 2, 3]): - self.assertEquals(sub[j].tolist(), true_sub_j) - -if __name__ == '__main__': - run_module_suite() diff --git a/wafo/tests/test_objects.py b/wafo/tests/test_objects.py deleted file mode 100644 index aa5d02f..0000000 --- a/wafo/tests/test_objects.py +++ /dev/null @@ -1,190 +0,0 @@ -# -*- coding:utf-8 -*- -""" -Created on 5. aug. 2010 - -@author: pab -""" - -import unittest -from numpy.testing import TestCase, assert_array_almost_equal -import wafo.data -import wafo.objects as wo -import wafo.spectrum.models as sm -import wafo.transform.models as tm - - -class TestTimeSeries(TestCase): - def setUp(self): - x = wafo.data.sea() - self.ts = wo.mat2timeseries(x) - - def test_sampling_period(self): - ts = self.ts - assert_array_almost_equal(ts.sampling_period(), 0.25) - - def test_tospecdata(self): - S = self.ts.tospecdata(L=150) - print(S.data[:10].tolist()) - assert_array_almost_equal(S.data[:10], - [0.0050789888306202345, 0.0049411187454784225, - 0.004553923924951667, 0.003990722577978725, - 0.00335482379127744, 0.002755110296973988, - 0.002281782794825119, 0.0019941282234629933, - 0.0019329154962902488, 0.002164040256079313]) - -# [0.00913087, 0.00881073, 0.00791944, -# 0.00664244, 0.00522429, 0.00389816, -# 0.00282753, 0.00207843, 0.00162678, -# 0.0013916]) - def test_tocovdata(self): - rf = self.ts.tocovdata(lag=150) - assert_array_almost_equal(rf.data[:10], - [0.22368637, 0.20838473, 0.17110733, - 0.12237803, 0.07024054, 0.02064859, - -0.02218831, -0.0555993, -0.07859847, - -0.09166187]) - - def test_timeseries_trdata(self): - Hs = 7.0 - Sj = sm.Jonswap(Hm0=Hs) - S = Sj.tospecdata() # Make spectrum object from numerical values - S.tr = tm.TrOchi(mean=0, skew=0.16, kurt=0, sigma=Hs/4, ysigma=Hs/4) - xs = S.sim(ns=2**20, iseed=10) - ts = wo.mat2timeseries(xs) - g0, _gemp = ts.trdata(monitor=False) # Not Monitor the development - - # Equal weight on all points - g1, _gemp = ts.trdata(method='mnonlinear', gvar=0.5) - - # Less weight on the ends - g2, _gemp = ts.trdata(method='nonlinear', gvar=[3.5, 0.5, 3.5]) - self.assert_(1.2 < S.tr.dist2gauss() < 1.6) - self.assert_(1.65 < g0.dist2gauss() < 2.05) - self.assert_(0.54 < g1.dist2gauss() < 0.95) - self.assert_(1.5 < g2.dist2gauss() < 1.9) - - def test_timeseries_wave_periods(self): - true_t = ([-0.69, -0.86, -1.05], - [0.42, 0.78, 1.37], - [0.09, 0.51, -0.85], - [-0.27, -0.08, 0.32], - [3.84377468, 6.35707656, 4.15490909], - [6.25273295, 6.10295202, 3.36978685], - [2.48364668, 4.74282402, 1.75553431], - [3.76908628, 1.360128, 1.61425254], - [-5.05027968, -9.16405436, -15.60113092], - [7.53392635, 13.90687837, 17.35666522], - [-0.2811934, -7.11392635, -13.12687837], - [4.05027968, 8.47405436, 14.74113092], - [2.03999996, 0.07, 0.05], - [-0.93, -0.07, -0.12], - [1.10999996, 0., -0.07], - [-0.86, -0.02, 0.3], - [0.93, -0.8, -0.2], - [1.10999996, 0., -0.07], - [-0.02, 0.3, -0.34], - [6.10295202, 3.36978685, 3.58501107], - [6.25273295, 6.10295202, 3.36978685], - ) - - pdefs = ['t2c', 'c2t', 't2t', 'c2c', - 'd2d', 'u2u', 'd2u', 'u2d', - 'd2t', 't2u', 'u2c', 'c2d', - 'm2M', 'M2m', 'm2m', 'M2M', 'all', - ] - ts = wo.TimeSeries(self.ts.data[0:400, :2], self.ts.args[:400]) - for pdef, truth in zip(pdefs, true_t): - T, _ix = ts.wave_periods(vh=0.0, pdef=pdef) - # print(T[:3,]) - assert_array_almost_equal(T[:3], truth) - - true_t2 = ([1.10999996, 0., - 0.07], - [-0.02, 0.3, - 0.34], - [6.10295202, 3.369787, 3.585011], - [6.25273295, 6.102952, 3.369787], - [-0.27, -0.08, 0.32], - [-0.27, -0.08, 0.32]) - wdefs = ['mw', 'Mw', 'dw', 'uw', 'tw', 'cw', ] - for wdef, truth in zip(wdefs, true_t2): - pdef = '{0}2{0}'.format(wdef[0].lower()) - T, _ix = ts.wave_periods(vh=0.0, pdef=pdef, wdef=wdef) - print(T[:3]) - assert_array_almost_equal(T[:3], truth) - - -class TestObjects(TestCase): - def setUp(self): - x = wafo.data.sea() - self.ts = wo.mat2timeseries(x) - - def test_cycles_and_levelcrossings(self): - tp = self.ts.turning_points() - assert_array_almost_equal(tp.data[:10], - [-1.200495, 0.839505, -0.090495, -0.020495, - -0.090495, -0.040495, -0.160495, 0.259505, - -0.430495, -0.080495] - ) - - mm = tp.cycle_pairs() - assert_array_almost_equal(mm.data[:10], - [0.839505, -0.020495, -0.040495, 0.259505, - -0.080495, -0.080495, 0.349505, 0.859505, - 0.009505, 0.319505]) - true_lcs = (([0., 1., 2., 2., 3., 4., 5., 6., 7., 9.], - [-1.7504945, -1.4404945, -1.4204945, -1.4004945, - -1.3704945, -1.3204945, -1.2704945, -1.2604945, - -1.2504945, -1.2004945]), - ([0., 1., 2., 3., 3., 4., 5., 6., 7., 9.], - [-1.7504945, -1.4404945, -1.4204945, -1.4004945, - -1.3704945, -1.3204945, -1.2704945, -1.2604945, - -1.2504945, -1.2004945]), - ([1., 2., 3., 4., 4., 5., 6., 7., 9., 11.], - [-1.7504945, -1.4404945, -1.4204945, -1.4004945, - -1.3704945, -1.3204945, -1.2704945, -1.2604945, - -1.2504945, -1.2004945]), - ([1., 2., 3., 3., 4., 5., 6., 7., 9., 11.], - [-1.7504945, -1.4404945, -1.4204945, -1.4004945, - -1.3704945, -1.3204945, -1.2704945, -1.2604945, - -1.2504945, -1.2004945])) - for i, true_lc in enumerate(true_lcs): - true_count, true_levels = true_lc - lc = mm.level_crossings(kind=i+1) - assert_array_almost_equal(lc.data[:10], true_count) - assert_array_almost_equal(lc.args[:10], true_levels) - - def test_levelcrossings_extrapolate(self): - tp = self.ts.turning_points() - mm = tp.cycle_pairs() - lc = mm.level_crossings() - - s = lc.sigma # x[:, 1].std() - ix = slice(0, 1000, 100) - lc_ray = lc.extrapolate(-2 * s, 2 * s, dist='rayleigh') - - assert_array_almost_equal(lc_ray.data[ix], - [1.78925398e-37, 9.61028192e-23, - 2.05282628e-11, 1.74389448e-03, - 5.89169345e+01, 5.240000e+02, - 6.72609651e+01, 4.46086175e-01, - 2.23463577e-04, 8.45526153e-09]) - lc_exp = lc.extrapolate(-2 * s, 2 * s, dist='expon') - - lc_gpd = lc.extrapolate(-2 * s, 2 * s, dist='genpareto') - - assert_array_almost_equal(lc_exp.data[ix], - [6.51864195e-12, 1.13025876e-08, - 1.95974080e-05, 3.39796881e-02, - 5.89169345e+01, 5.24000000e+02, - 6.43476951e+01, 1.13478843e+00, - 2.00122906e-02, 3.52921977e-04]) - assert_array_almost_equal(lc_gpd.data[ix], - [0.00000000e+00, 0.00000000e+00, - 0.00000000e+00, 0.00000000e+00, - 5.89169345e+01, 5.24000000e+02, - 6.80484770e+01, 1.41019390e-01, - 0.00000000e+00, 0.00000000e+00]) - - -if __name__ == "__main__": - # import sys;sys.argv = ['', 'Test.testName'] - unittest.main() diff --git a/wafo/tests/test_padua.py b/wafo/tests/test_padua.py deleted file mode 100644 index e0e58e4..0000000 --- a/wafo/tests/test_padua.py +++ /dev/null @@ -1,101 +0,0 @@ - - -import unittest -import numpy as np -from numpy import cos, pi -import numpy.testing as npt -from numpy.testing import assert_array_almost_equal -from wafo.padua import (padua_points, example_functions, padua_fit, - # padua_fit2, - padua_cubature, padua_val) - - -class PaduaTestCase(unittest.TestCase): - - def test_padua_points_degree0(self): - pad = padua_points(0) - expected = [[-1], [-1]] - assert_array_almost_equal(pad, expected, 15) - - def test_padua_points_degree1(self): - pad = padua_points(1) - expected = [cos(np.r_[0, 1, 1] * pi), - cos(np.r_[1, 0, 2] * pi / 2)] - - assert_array_almost_equal(pad, expected, 15) - - def test_padua_points_degree2(self): - pad = padua_points(2, domain=[0, 1, 0, 2]) - expected = [(cos(np.r_[0, 0, 1, 1, 2, 2] * pi / 2) + 1) / 2, - cos(np.r_[1, 3, 0, 2, 1, 3] * pi / 3) + 1] - - assert_array_almost_equal(pad, expected, 15) - - def test_testfunct(self): - vals = [example_functions(0, 0, id_) for id_ in range(12)] - expected = [7.664205912849231e-01, 0.7071067811865476, 0, - 1.6487212707001282, 1.9287498479639178e-22, 1.0, - 1.0, 1.0, 1.0, 0.0, 1.0, 0.0] - assert_array_almost_equal(vals, expected, 15) - - def test_padua_fit_even_degree(self): - points = padua_points(10) - C0f, abs_error = padua_fit(points, example_functions, 6) - expected = np.zeros((11, 11)) - expected[0, 0] = 1 - assert_array_almost_equal(C0f, expected, 15) - assert_array_almost_equal(abs_error, 1.2168216554799264e-15) - - def test_padua_fit_odd_degree(self): - points = padua_points(9) - C0f, abs_error = padua_fit(points, example_functions, 6) - expected = np.zeros((10, 10)) - expected[0, 0] = 1 - assert_array_almost_equal(C0f, expected, 15) - assert_array_almost_equal(abs_error, 4.509537093983535e-17) - -# TODO: padua_fit2 does not work correctly -# def test_padua_fit_odd_degree2(self): -# points = padua_points(9) -# C0f, _abs_error = padua_fit2(points, example_functions, 6) -# expected = np.zeros((10, 10)) -# expected[0, 0] = 1 -# assert_array_almost_equal(C0f, expected, 15) - - def test_padua_cubature(self): - domain = [0, 1, 0, 1] - points = padua_points(500, domain) - C0f, abs_error = padua_fit(points, example_functions, 0) - val = padua_cubature(C0f, domain) - expected = 4.06969589491556e-01 - assert_array_almost_equal(val, expected, 15) - assert_array_almost_equal(abs_error, 3.66470417665e-16) - - def test_padua_val_unordered(self): - domain = [0, 1, 0, 1] - points = padua_points(20, domain) - C0f, abs_error = padua_fit(points, example_functions, 0) - X = np.array([0, 0.5, 1]) - # true_val = example_functions.franke(X, X) - val = padua_val(X, X, C0f, domain) - expected = [0.76642059128493, 0.32621734202885, 0.03587865112678] - assert_array_almost_equal(val, expected, 14) - assert_array_almost_equal(abs_error, 0.003897032262116954) - - def test_padua_val_grid(self): - domain = [0, 1, 0, 1] - a, b, c, d = domain - points = padua_points(21, domain) - C0f, abs_error = padua_fit(points, example_functions, 0) - X1 = np.linspace(a, b, 2) - X2 = np.linspace(c, d, 2) - val = padua_val(X1, X2, C0f, domain, use_meshgrid=True) - - expected = [[0.76642059128493, 0.10757071952145], - [0.27033716159114, 0.03573497102484]] - assert_array_almost_equal(val, expected, 14) - assert_array_almost_equal(abs_error, 0.0022486904061664046) - - -if __name__ == "__main__": - npt.run_module_suite()