commit 6f5bcd9eedbd0926f2b20842ff618c8ac849be96 Author: daviddrazen Date: Mon Feb 22 03:36:58 2010 +0000 Initial import of original WAFO code. diff --git a/gendocwafo.py b/gendocwafo.py new file mode 100755 index 0000000..a93850d --- /dev/null +++ b/gendocwafo.py @@ -0,0 +1,4 @@ + +import os + +os.system('epydoc --html -o html --name wafo --graph all src/wafo') \ No newline at end of file diff --git a/manifest b/manifest new file mode 100755 index 0000000..c64f3a8 --- /dev/null +++ b/manifest @@ -0,0 +1,22 @@ +setup.py +src\wafo\__init__.py +src\wafo\dctpack.py +src\wafo\definitions.py +src\wafo\demo_sg.py +src\wafo\info.py +src\wafo\interpolate.py +src\wafo\kdetools.py +src\wafo\misc.py +src\wafo\namedtuple.py +src\wafo\objects.py +src\wafo\plotbackend.py +src\wafo\polynomial.py +src\wafo\polynomial_old.py +src\wafo\sg_filter.py +src\wafo\data\__init__.py +src\wafo\data\info.py +src\wafo\spectrum\__init__.py +src\wafo\spectrum\dispersion_relation.py +src\wafo\spectrum\models.py +src\wafo\transform\__init__.py +src\wafo\transform\models.py diff --git a/setup.py b/setup.py new file mode 100755 index 0000000..465474e --- /dev/null +++ b/setup.py @@ -0,0 +1,56 @@ +""" +Install wafo + +Usage: + +python setup.py install [, --prefix=$PREFIX] + +python setup.py develop +python setup.py bdist_wininst +""" +#!/usr/bin/env python +import os, sys + +# make sure we import from WAFO in this package, not an installed one: +sys.path.insert(0, os.path.join('src')) +import wafo + +if __file__ == 'setupegg.py': + # http://peak.telecommunity.com/DevCenter/setuptools + from setuptools import setup, Extension +else: + from distutils.core import setup + +package_name = "wafo" +subpackages = ('spectrum','data','transform','covariance') +subpackagesfull = [os.path.join(package_name,f) for f in subpackages] +subtests = [os.path.join(subpkg,'test') for subpkg in subpackages] + +testscripts = [os.path.join(subtst, f) for subtst in subtests + for f in os.listdir(os.path.join('src',package_name,subtst)) + if not (f.startswith('.') or f.endswith('~') or + f.endswith('.old') or f.endswith('.bak'))] +datadir = 'data' +datafiles = [os.path.join(datadir, f) for f in os.listdir(os.path.join('src',package_name,datadir)) + if not (f.endswith('.py') or f.endswith('test') )] +#docs = [os.path.join('doc', f) for f in os.listdir('doc')] +packagedata = testscripts + datafiles + ['c_library.pyd'] #,'disufq1.c','diffsumfunq.pyd','diffsumfunq.pyf','findrfc.c','rfc.pyd','rfc.pyf'] + + +setup( + version = '0.11', + author='WAFO-group', + author_email='wafo@maths.lth.se', + description = wafo.__doc__, + license = "GPL", + url='http://www.maths.lth.se/matstat/wafo/', + name = package_name.upper(), + package_dir = {'': 'src'}, + packages = [package_name,] + list(subpackagesfull), + package_data = {package_name: packagedata}, + #package_data = {'': ['wafo.cfg']}, + #scripts = [os.path.join('bin', f) + # for f in os.listdir('bin') + # if not (f.startswith('.') or f.endswith('~') or + # f.endswith('.old') or f.endswith('.bak'))], + ) diff --git a/wafo/__init__.py b/wafo/__init__.py new file mode 100755 index 0000000..2d89078 --- /dev/null +++ b/wafo/__init__.py @@ -0,0 +1,9 @@ + +from info import __doc__ +import wafo.misc +import wafo.data +import wafo.objects +import wafo.spectrum +import wafo.transform +import wafo.definitions +import wafo.polynomial \ No newline at end of file diff --git a/wafo/c_library.pyd b/wafo/c_library.pyd new file mode 100755 index 0000000..9e014dd Binary files /dev/null and b/wafo/c_library.pyd differ diff --git a/wafo/covariance/__init__.py b/wafo/covariance/__init__.py new file mode 100755 index 0000000..603df5b --- /dev/null +++ b/wafo/covariance/__init__.py @@ -0,0 +1,7 @@ +""" +Covariance package in WAFO Toolbox. +""" + +from core import CovData1D +#import models +#import dispersion_relation \ No newline at end of file diff --git a/wafo/covariance/core.py b/wafo/covariance/core.py new file mode 100755 index 0000000..5a917f7 --- /dev/null +++ b/wafo/covariance/core.py @@ -0,0 +1,826 @@ +''' +CovData1D +--------- +data : Covariance function values. Size [ny nx nt], all singleton dim. removed. +args : Lag of first space dimension, length nx. +h : Water depth. +tr : Transformation function. +type : 'enc', 'rot' or 'none'. +v : Ship speed, if .type='enc' +phi : Rotation of coordinate system, e.g. direction of ship +norm : Normalization flag, Logical 1 if autocorrelation, 0 if covariance. +Rx, ... ,Rtttt : Obvious derivatives of .R. +note : Memorandum string. +date : Date and time of creation or change. +''' + +from __future__ import division +import warnings +#import numpy as np +from numpy import (zeros, sqrt, dot, newaxis, inf, where, pi, nan, #@UnresolvedImport + atleast_1d, hstack, vstack, r_, linspace, flatnonzero, size, #@UnresolvedImport + isnan, finfo, diag, ceil, floor, random) #@UnresolvedImport +from numpy.fft import fft +from numpy.random import randn +import scipy.interpolate as interpolate +from scipy.linalg import toeplitz, sqrtm, svd, cholesky, diagsvd, pinv +from scipy import sparse +from pylab import stineman_interp + +from wafo.wafodata import WafoData +from wafo.misc import sub_dict_select, nextpow2 #, JITImport +import wafo.spectrum as _wafospec +#_wafospec = JITImport('wafo.spectrum') + + +__all__ = ['CovData1D'] + +def _set_seed(iseed): + if iseed != None: + try: + random.set_state(iseed) + except: + random.seed(iseed) + + +#def rndnormnd(cov, mean=0.0, cases=1, method='svd'): +# ''' +# Random vectors from a multivariate Normal distribution +# +# Parameters +# ---------- +# mean, cov : array-like +# mean and covariance, respectively. +# cases : scalar integer +# number of sample vectors +# method : string +# defining squareroot method for covariance +# 'svd' : Singular value decomp. (stable, quite fast) (default) +# 'chol' : Cholesky decomposition (fast, but unstable) +# 'sqrtm' : sqrtm (stable and slow) +# +# Returns +# ------- +# r : matrix of random numbers from the multivariate normal +# distribution with the given mean and covariance matrix. +# +# The covariance must be a symmetric, semi-positive definite matrix with shape +# equal to the size of the mean. METHOD used for calculating the square root +# of COV is either svd, cholesky or sqrtm. (cholesky is fastest but least accurate.) +# When cholesky is chosen and S is not positive definite, the svd-method +# is used instead. +# +# Example +# ------- +# mu = [0, 5] +# S = [[1 0.45], [0.45 0.25]] +# r = rndnormnd(S, mu, 1) +# plot(r(:,1),r(:,2),'.') +# +# d = 40; rho = 2*rand(1,d)-1; +# mu = zeros(0,d); +# S = (rho.'*rho-diag(rho.^2))+eye(d); +# r = rndnormnd(S,mu,100,'genchol')'; +# +# See also +# -------- +# chol, svd, sqrtm, genchol +# ''' +# sa = np.atleast_2d(cov) +# mu = np.atleast_1d(mean).ravel() +# m, n = sa.shape +# if m != n: +# raise ValueError('Covariance must be square') +# def svdfun(sa): +# u, s, vh = svd(sa, full_matrices=False) +# sqt = diagsvd(sqrt(s)) +# return dot(u, dot(sqt, vh)) +# +# sqrtfuns = dict(sqrtm=sqrtm, svd=svdfun, cholesky=cholesky) +# sqrtfun = sqrtfuns[method] +# std = sqrtfun(sa) +# return dot(std,random.randn(n, cases)) + mu[:,newaxis] + + +class CovData1D(WafoData): + """ Container class for 1D covariance data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + type : string + spectrum type, one of 'freq', 'k1d', 'enc' (default 'freq') + lagtype : letter + lag type, one of: 'x', 'y' or 't' (default 't') + + + Examples + -------- + >>> import numpy as np + >>> import wafo.spectrum as sp + >>> Sj = sp.models.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = sp.SpecData1D(Sj(w),w) #Make spectrum object from numerical values + + See also + -------- + WafoData + CovData + """ + + def __init__(self,*args,**kwds): + super(CovData1D, self).__init__(*args,**kwds) + + self.name = 'WAFO Covariance Object' + self.type = 'time' + self.lagtype = 't' + self.h = inf + self.tr = None + self.phi = 0. + self.v = 0. + self.norm = 0 + somekeys = ['phi', 'name', 'h', 'tr', 'lagtype', 'v', 'type', 'norm'] + + self.__dict__.update(sub_dict_select(kwds,somekeys)) + + self.setlabels() + def setlabels(self): + ''' Set automatic title, x-,y- and z- labels + + based on type, + ''' + + N = len(self.type) + if N==0: + raise ValueError('Object does not appear to be initialized, it is empty!') + + labels = ['','ACF',''] + + if self.lagtype.startswith('t'): + labels[0] = 'Lag [s]' + else: + labels[0] = 'Lag [m]' + + if self.norm: + title = 'Auto Correlation Function ' + labels[0] = labels[0].split('[')[0] + else: + title = 'Auto Covariance Function ' + + self.labels.title = title + self.labels.xlab = labels[0] + self.labels.ylab = labels[1] + self.labels.zlab = labels[2] + + + +## def copy(self): +## kwds = self.__dict__.copy() +## wdata = CovData1D(**kwds) +## return wdata + + def tospecdata(self, rate=None, method='linear', nugget=0.0, trunc=1e-5, fast=True): + ''' + Computes spectral density from the auto covariance function + + Parameters + ---------- + rate = scalar, int + 1,2,4,8...2^r, interpolation rate for f (default 1) + + method: string + interpolation method 'stineman', 'linear', 'cubic' + + nugget = scalar, real + nugget effect to ensure that round off errors do not result in + negative spectral estimates. Good choice might be 10^-12. + + trunc : scalar, real + truncates all spectral values where S/max(S) < trunc + 0 <= trunc <1 This is to ensure that high frequency + noise is not added to the spectrum. (default 1e-5) + fast : bool + if True : zero-pad to obtain power of 2 length ACF (default) + otherwise no zero-padding of ACF, slower but more accurate. + + Returns + -------- + S = SpecData1D object + spectral density + + NB! This routine requires that the covariance is evenly spaced + starting from zero lag. Currently only capable of 1D matrices. + + Example: + >>> import wafo.spectrum.models as sm + >>> import numpy as np + >>> import scipy.signal.signaltools as st + >>> L = 129 + >>> t = np.linspace(0,75,L) + >>> R = np.zeros(L) + >>> win = st.parzen(41) + >>> R[0:21] = win[20:41] + >>> R0 = CovData1D(R,t) + >>> S0 = R0.tospecdata() + + >>> Sj = sm.Jonswap() + >>> S = Sj.tospecdata() + >>> R2 = S.tocovdata() + >>> S1 = R2.tospecdata() + >>> assert(all(abs(S1.data-S.data)<1e-4) ,'COV2SPEC') + + See also + -------- + spec2cov + datastructures + ''' + + dT = self.sampling_period() + # dT = time-step between data points. + + ACF, unused_ti = atleast_1d(self.data, self.args) + + if self.lagtype in 't': + spectype = 'freq' + ftype = 'w' + else: + spectype = 'k1d' + ftype = 'k' + + if rate is None: + rate = 1 ##interpolation rate + else: + rate = 2**nextpow2(rate) ##make sure rate is a power of 2 + + + ## add a nugget effect to ensure that round off errors + ## do not result in negative spectral estimates + ACF[0] = ACF[0] +nugget + n = ACF.size + # embedding a circulant vector and Fourier transform + if fast: + nfft = 2**nextpow2(2*n-2) + else: + nfft = 2*n-2 + + nf = nfft/2 ## number of frequencies + ACF = r_[ACF,zeros(nfft-2*n+2),ACF[n-1:0:-1]] + + Rper = (fft(ACF,nfft).real).clip(0) ## periodogram + RperMax = Rper.max() + Rper = where(Rper 1: + So.args = linspace(0, pi/dT, nf*rate) + if method=='stineman': + So.data = stineman_interp(So.args, w, S) + else: + intfun = interpolate.interp1d(w, S, kind=method) + So.data = intfun(So.args) + So.data = So.data.clip(0) # clip negative values to 0 + return So + + def sampling_period(self): + ''' + Returns sampling interval + + Returns + --------- + dt : scalar + sampling interval, unit: + [s] if lagtype=='t' + [m] otherwise + ''' + dt1 = self.args[1]-self.args[0] + n = size(self.args)-1 + t = self.args[-1]-self.args[0] + dt = t/n + if abs(dt-dt1) > 1e-10: + warnings.warn('Data is not uniformly sampled!') + return dt + + def sim(self, ns=None, cases=1, dt=None, iseed=None, derivative=False): + ''' + Simulates a Gaussian process and its derivative from ACF + + Parameters + ---------- + ns : scalar + number of simulated points. (default length(S)-1=n-1). + If ns>n-1 it is assummed that R(k)=0 for all k>n-1 + cases : scalar + number of replicates (default=1) + dt : scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : int or state + starting state/seed number for the random number generator + (default none is set) + derivative : bool + if true : return derivative of simulated signal as well + otherwise + + Returns + ------- + xs = a cases+1 column matrix ( t,X1(t) X2(t) ...). + xsder = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). + + Details + ------- + Performs a fast and exact simulation of stationary zero mean + Gaussian process through circulant embedding of the covariance matrix. + + If the ACF has a non-empty field .tr, then the transformation is + applied to the simulated data, the result is a simulation of a transformed + Gaussian process. + + Note: The simulation may give high frequency ripple when used with a + small dt. + + Example: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap() + >>> S = Sj.tospecdata() #Make spec + >>> R = S.tocovdata() + >>> x = R.sim(ns=1000,dt=0.2) + + See also + -------- + spec2sdat, gaus2dat + + Reference + ----------- + C.R Dietrich and G. N. Newsam (1997) + "Fast and exact simulation of stationary + Gaussian process through circulant embedding + of the Covariance matrix" + SIAM J. SCI. COMPT. Vol 18, No 4, pp. 1088-1107 + ''' + + # TODO fix it, it does not work + + # Add a nugget effect to ensure that round off errors + # do not result in negative spectral estimates + nugget = 0 # 10**-12 + + _set_seed(iseed) + + ACF = self.data.ravel() + n = ACF.size + + + I = ACF.argmax() + if I != 0: + raise ValueError('ACF does not have a maximum at zero lag') + + ACF.shape = (n, 1) + + dT = self.sampling_period() + + x = zeros((ns, cases+1)) + + if derivative: + xder = x.copy() + + ## add a nugget effect to ensure that round off errors + ## do not result in negative spectral estimates + ACF[0] = ACF[0] + nugget + + ## Fast and exact simulation of simulation of stationary + ## Gaussian process throug circulant embedding of the + ## Covariance matrix + floatinfo = finfo(float) + if (abs(ACF[-1]) > floatinfo.eps): ## assuming ACF(n+1)==0 + m2 = 2*n-1 + nfft = 2**nextpow2(max(m2, 2*ns)) + ACF = r_[ACF, zeros((nfft-m2,1)), ACF[-1:0:-1,:]] + #disp('Warning: I am now assuming that ACF(k)=0 ') + #disp('for k>MAXLAG.') + else: # # ACF(n)==0 + m2 = 2*n-2 + nfft = 2**nextpow2(max(m2, 2*ns)) + ACF = r_[ACF, zeros((nfft-m2, 1)), ACF[n-1:1:-1, :]] + + ##m2=2*n-2 + S = fft(ACF,nfft,axis=0).real ## periodogram + + I = S.argmax() + k = flatnonzero(S<0) + if k.size>0: + #disp('Warning: Not able to construct a nonnegative circulant ') + #disp('vector from the ACF. Apply the parzen windowfunction ') + #disp('to the ACF in order to avoid this.') + #disp('The returned result is now only an approximation.') + + # truncating negative values to zero to ensure that + # that this noise is not added to the simulated timeseries + + S[k] = 0. + + ix = flatnonzero(k>2*I) + if ix.size>0: +## # truncating all oscillating values above 2 times the peak +## # frequency to zero to ensure that +## # that high frequency noise is not added to +## # the simulated timeseries. + ix0 = k[ix[0]] + S[ix0:-ix0] =0.0 + + + + trunc = 1e-5 + maxS = S[I] + k = flatnonzero(S[I:-I]0: + S[k+I]=0. + ## truncating small values to zero to ensure that + ## that high frequency noise is not added to + ## the simulated timeseries + + cases1 = floor(cases/2) + cases2 = ceil(cases/2) +# Generate standard normal random numbers for the simulations + + #randn = np.random.randn + epsi = randn(nfft,cases2)+1j*randn(nfft,cases2) + Ssqr = sqrt(S/(nfft)) # #sqrt(S(wn)*dw ) + ephat = epsi*Ssqr #[:,np.newaxis] + y = fft(ephat,nfft,axis=0) + x[:, 1:cases+1] = hstack((y[2:ns+2, 0:cases2].real, y[2:ns+2, 0:cases1].imag)) + + x[:, 0] = linspace(0,(ns-1)*dT,ns) ##(0:dT:(dT*(np-1)))' + + if derivative: + Ssqr = Ssqr*r_[0:(nfft/2+1), -(nfft/2-1):0]*2*pi/nfft/dT + ephat = epsi*Ssqr #[:,newaxis] + y = fft(ephat,nfft,axis=0) + xder[:, 1:(cases+1)] = hstack((y[2:ns+2, 0:cases2].imag -y[2:ns+2, 0:cases1].real)) + xder[:, 0] = x[:,0] + + if self.tr is not None: + print(' Transforming data.') + g = self.tr + if derivative: + for ix in range(cases): + tmp = g.gauss2dat(x[:,ix+1], xder[:,ix+1]) + x[:,ix+1] = tmp[0] + xder[:,ix+1] = tmp[1] + else: + for ix in range(cases): + x[:, ix+1] = g.gauss2dat(x[:, ix+1]) + + if derivative: + return x, xder + else: + return x + + def simcond(self, xo, cases=1, method='approx', inds=None): + """ + Simulate values conditionally on observed known values + + Parameters + ---------- + x : array-like + datavector including missing data. + (missing data must be NaN if inds is not given) + Assumption: The covariance of x is equal to self and have the + same sample period. + cases : scalar integer + number of cases, i.e., number of columns of sample (default=1) + method : string + defining method used in the conditional simulation. Options are: + 'approximate': Condition only on the closest points. Pros: quite fast + 'pseudo': Use pseudo inverse to calculate conditional covariance matrix + 'exact' : Exact simulation. Cons: Slow for large data sets, may not + return any result due to near singularity of the covariance matrix. + inds : integers + indices to spurious or missing data in x + + Returns + ------- + sample : ndarray + a random sample of the missing values conditioned on the observed data. + mu, sigma : ndarray + mean and standard deviation, respectively, of the missing values + conditioned on the observed data. + + + Notes + ----- + SIMCOND generates the missing values from x conditioned on the observed + values assuming x comes from a multivariate Gaussian distribution + with zero expectation and Auto Covariance function R. + + See also + -------- + CovData1D.sim + TimeSeries.reconstruct, + rndnormnd + + Reference + --------- + Brodtkorb, P, Myrhaug, D, and Rue, H (2001) + "Joint distribution of wave height and wave crest velocity from + reconstructed data with application to ringing" + Int. Journal of Offshore and Polar Engineering, Vol 11, No. 1, pp 23--32 + + Brodtkorb, P, Myrhaug, D, and Rue, H (1999) + "Joint distribution of wave height and wave crest velocity from + reconstructed data" + in Proceedings of 9th ISOPE Conference, Vol III, pp 66-73 + """ + # TODO does not work yet. + + # secret methods: + # 'dec1-3': different decomposing algorithm's + # which is only correct for a variables + # having the Markov property + # Cons: 3 is not correct at all, but seems to give + # a reasonable result + # Pros: 1 is slow, 2 is quite fast and 3 is very fast + # Note: (mu1oStd is not given for method ='dec3') + compute_sigma = True + x = atleast_1d(xo).ravel() + acf = atleast_1d(self.data).ravel() + + N = len(x) + n = len(acf) + + i = acf.argmax() + if i != 0: + raise ValueError('This is not a valid ACF!!') + + + if not inds is None: + x[inds] = nan + inds = where(isnan(x))[0] #indices to the unknown observations + + Ns = len(inds) # # missing values + if Ns == 0: + warnings.warn('No missing data, unable to continue.') + return xo, zeros(Ns), zeros(Ns) + #end + if Ns == N:# simulated surface from the apriori distribution + txt = '''All data missing, + returning sample from the unconditional distribution.''' + warnings.warn(txt) + return self.sim(ns=N, cases=cases), zeros(Ns), zeros(Ns) + + indg = where(1-isnan(x))[0] #indices to the known observations + + #initializing variables + mu1o = zeros(Ns, 1) + mu1o_std = mu1o + sample = zeros((Ns, cases)) + if method[0] == 'd': + # simulated surface from the apriori distribution + xs = self.sim(ns=N, cases=cases) + mu1os = zeros((Ns, cases)) + + if method.startswith('dec1'): + # only correct for variables having the Markov property + # but still seems to give a reasonable answer. Slow procedure. + Sigma = sptoeplitz(hstack((acf, zeros(N-n)))) + + #Soo=Sigma(~inds,~inds); # covariance between known observations + #S11=Sigma(inds,inds); # covariance between unknown observations + #S1o=Sigma(inds,~inds);# covariance between known and unknown observations + #tmp=S1o*pinv(full(Soo)); + #tmp=S1o/Soo; # this is time consuming if Soo large + tmp = 2*Sigma[inds, indg]/(Sigma[indg, indg] + Sigma[indg, indg].T ) + + if compute_sigma: + #standard deviation of the expected surface + #mu1o_std=sqrt(diag(S11-tmp*S1o')); + mu1o_std = sqrt(diag(Sigma[inds, inds]-tmp*Sigma[indg, inds])) + + + #expected surface conditioned on the known observations from x + mu1o = tmp*x[indg] + #expected surface conditioned on the known observations from xs + mu1os = tmp*(xs[indg,:]) + # sampled surface conditioned on the known observations + sample = mu1o + xs[inds,:] - mu1os + + elif method.startswith('dec2'): + # only correct for variables having the Markov property + # but still seems to give a reasonable answer + # approximating the expected surfaces conditioned on + # the known observations from x and xs by only using the closest points + Sigma = sptoeplitz(hstack((acf,zeros(n)))) + n2 = int(floor(n/2)) + idx = r_[0:2*n] + max(0,inds[0]-n2) # indices to the points used + tmpinds = zeros(N,dtype=bool) + tmpinds[inds] = True # temporary storage of indices to missing points + tinds = where(tmpinds[idx])[0] # indices to the points used + tindg = where(1-tmpinds[idx])[0] + ns = len(tinds); # number of missing data in the interval + nprev = 0; # number of previously simulated points + xsinds = xs[inds,:] + while ns>0: + tmp=2*Sigma[tinds, tindg]/(Sigma[tindg, tindg]+Sigma[tindg, tindg].T) + if compute_sigma: + #standard deviation of the expected surface + #mu1o_std=sqrt(diag(S11-tmp*S1o')); + ix = slice(nprev+1,nprev+ns+1) + mu1o_std[ix] = max(mu1o_std[ix], + sqrt(diag(Sigma[tinds, tinds]-tmp*Sigma[tindg,tinds]))) + #end + + #expected surface conditioned on the closest known observations + # from x and xs2 + mu1o[(nprev+1):(nprev+ns+1)] = tmp*x[idx[tindg]] + mu1os[(nprev+1):(nprev+ns+1),:] = tmp*xs[idx[tindg],:] + + if idx[-1]==N-1:# + ns =0 # no more points to simulate + else: + # updating by putting expected surface into x + x[idx[tinds]] = mu1o[(nprev+1):(nprev+ns+1)] + xs[idx[tinds]] = mu1os[(nprev+1):(nprev+ns+1)] + + nw = sum(tmpinds[idx[-n2:]])# # data which we want to simulate once + tmpinds[idx[:-n2]] = False # removing indices to data .. + # which has been simulated + nprev = nprev+ns-nw # update # points simulated so far + + if (nw==0) and (nprev0: + #make sure MATLAB uses a symmetric matrix solver + tmp = 2*Sigma[tinds,tindg]/(Sigma[tindg,tindg]+Sigma[tindg,tindg].T) + Sigma1o = Sigma[tinds,tinds] - tmp*Sigma[tindg,tinds] + if compute_sigma: + #standard deviation of the expected surface + #mu1o_std=sqrt(diag(S11-tmp*S1o')); + mu1o_std[(nprev+1):(nprev+ns+1)] = max( mu1o_std[(nprev+1):(nprev+ns)] , + sqrt(diag(Sigma1o))) + #end + + #expected surface conditioned on the closest known observations from x + mu1o[(nprev+1):(nprev+ns+1)] = tmp*x2[idx[tindg]] + #sample conditioned on the known observations from x + sample[(nprev+1):(nprev+ns+1),:] = rndnormnd(tmp*x[idx[tindg]],Sigma1o, cases) + if idx[-1] == N-1: + ns = 0 # no more points to simulate + else: + # updating + x2[idx[tinds]] = mu1o[(nprev+1):(nprev+ns+1)] #expected surface + x[idx[tinds]] = sample[(nprev+1):(nprev+ns+1)]#sampled surface + nw = sum(tmpinds[idx[-n2::]]==True)# # data we want to simulate once more + tmpinds[idx[:-n2]] = False # removing indices to data .. + # which has been simulated + nprev = nprev+ns-nw # update # points simulated so far + + if (nw==0) and (nprev0.3*n: + return toeplitz(x) + else: + spdiags = sparse.dia_matrix + data = x[k].reshape(-1,1).repeat(n,axis=-1) + offsets = k + y = spdiags((data, offsets), shape=(n,n)) + if k[0]==0: + offsets = k[1::] + data = data[1::,:] + return y + spdiags((data, -offsets), shape=(n,n)) + +def test_covdata(): + import wafo.data + x = wafo.data.sea() + ts = wafo.objects.mat2timeseries(x) + rf = ts.tocovdata(lag=150) + rf.plot() + +def main(): + import wafo.spectrum.models as sm + import matplotlib + matplotlib.interactive(True) + Sj = sm.Jonswap() + S = Sj.tospecdata() #Make spec + S.plot() + R = S.tocovdata() + R.plot() + #x = R.sim(ns=1000,dt=0.2) + + +if __name__ == '__main__': + if True: #False : # + import doctest + doctest.testmod() + else: + main() \ No newline at end of file diff --git a/wafo/data/__init__.py b/wafo/data/__init__.py new file mode 100755 index 0000000..011591c --- /dev/null +++ b/wafo/data/__init__.py @@ -0,0 +1,3 @@ + +from wafo.data.info import __doc__ +from wafo.data.info import * diff --git a/wafo/data/atlantic.dat b/wafo/data/atlantic.dat new file mode 100755 index 0000000..7786ff1 --- /dev/null +++ b/wafo/data/atlantic.dat @@ -0,0 +1,582 @@ + 5.4829629629629641e+00 + 4.3614999999999986e+00 + 5.2602325581395339e+00 + 3.0619230769230770e+00 + 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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 + +""" +#from pylab import load +#from scipy.io import read_array +from numpy import (loadtxt,nan) +import os +__path2data = os.path.dirname( os.path.realpath(__file__)) + +__all__ =['atlantic','gfaks89','gfaksr89','japansea','northsea','sea','sfa89', + 'sn','yura87'] + +def _load(file): + """ local load function + """ + return loadtxt(os.path.join(__path2data,file)) + +def _tofloat(x): + if x=='nan' or x=='NaN': + y = nan + else: + y = float(x or 0) + return y +def _loadnan(file): + """ local load function accepting nan's + """ + myconverter = {0: _tofloat, 1: _tofloat} + return 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() + >>> 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() + >>> 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() + >>> 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() + >>> 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() + >>> 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() \ No newline at end of file diff --git a/wafo/data/japansea.dat b/wafo/data/japansea.dat new file mode 100755 index 0000000..a9fc01f --- /dev/null +++ b/wafo/data/japansea.dat @@ -0,0 +1,692 @@ +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 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+% 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 new file mode 100755 index 0000000..8411859 --- /dev/null +++ b/wafo/data/sfa89.dat @@ -0,0 +1,144 @@ + 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 2.0260000e+02 + 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+ 8.5544000e+04 1.0969470e+01 1.2073250e+01 9.2258770e+00 + 8.5545000e+04 1.1140410e+01 1.2986560e+01 9.7631170e+00 + 8.5546000e+04 1.1374840e+01 1.1213670e+01 1.0686190e+01 diff --git a/wafo/data_structures.py b/wafo/data_structures.py new file mode 100755 index 0000000..23d59dc --- /dev/null +++ b/wafo/data_structures.py @@ -0,0 +1,2659 @@ +""" +Class objects for data, spectrum, covariance function and time series in WAFO + + To represent data, spectra, covariance functions and time series + in WAFO, the classes WafoData, SpecData1D, CovData1D and TimeSeries is used. + Here follows a list of their attributes: + + WafoData + ---------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + date : Date and time of creation or change. + labels : AxisLabels + children : list of WafoData objects + + SpecData1D + ------------ + data : One sided Spectrum values + args : freguency values of freqtype + type :String: 'freq', 'dir', 'k2d', k1d', 'encdir' or 'enc'. + freqtype :'w' OR 'f' OR 'k' Frequency/wave number lag, length nf. + tr : Transformation function (default [] (none)). + h : Water depth (default inf). + norm : Normalization flag, Logical 1 if S is normalized, 0 if not + date :Date and time of creation or change. + v : Ship speed, if .type = 'enc' or 'encdir'. + phi angle of rotation of the coordinate system + (counter-clocwise) e.g. azymuth of a ship. + + + CovData1D + ---------- + data : Covariance function values. Size [ny nx nt], all singleton dim. removed. + args : Lag of first space dimension, length nx. + .h Water depth. + .tr Transformation function. + .type 'enc', 'rot' or 'none'. + .v Ship speed, if .type='enc' + .phi Rotation of coordinate system, e.g. direction of ship + .norm Normalization flag, Logical 1 if autocorrelation, 0 if covariance. + .Rx ... .Rtttt Obvious derivatives of .R. + .note Memorandum string. + .date Date and time of creation or change. + + + + +""" +#------------------------------------------------------------------------------- +# Name: module1 +# Purpose: +# +# Author: pab +# +# Created: 16.09.2008 +# Copyright: (c) pab 2008 +# Licence: +#------------------------------------------------------------------------------- +#!/usr/bin/env python + + +from __future__ import division +import warnings +import numpy +import numpy as np +from time import gmtime, strftime +from wafo.misc import nextpow2, discretize, findextrema, findrfc, sub_dict_select +#import wafo.spectrum.dispersion_relation as disp_rel +#from scipy import fft +from scipy.integrate import simps, trapz +from pylab import stineman_interp +import scipy.interpolate as interpolate + +import warnings +try: + import diffsumfunq +except: + pass + +from plotbackend import plotbackend + +__all__ = ['SpecData1D','SpecData2D','WafoData', 'AxisLabels','CovData1D', + 'TimeSeries','sensortypeid','sensortype'] +def empty_copy(obj): + class Empty(obj.__class__): + def __init__(self): + pass + newcopy = Empty() + newcopy.__class__ = obj.__class__ + return newcopy + +def _set_seed(iseed): + if iseed != None: + try: + np.random.set_state(iseed) + except: + np.random.seed(iseed) + +class WafoData(object): + '''Container class for data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + labels : AxisLabels + children : list of WafoData objects + + Member methods + -------------- + plot : + copy : + + + Example + ------- + >>> import numpy as np + >>> x = np.arange(-2,2,0.2) + + # Plot 2 objects in one call + >>> d2 = WafoData(np.sin(x),x,xlab='x',ylab='sin',title='sinus') + >>> d2.plot() + + % Plot with confidence interval + d3 = wdata(sin(x),x); + d3 = set(d3,'dataCI',[sin(x(:))*0.9 sin(x(:))*1.2]); + plot(d3) + + See also + -------- + wdata/plot, + specdata, + covdata + ''' + def __init__(self,data=None,args=None,**kwds): + self.data = data + self.args = args + self.date = strftime("%a, %d %b %Y %H:%M:%S", gmtime()) + self.plotter = None + self.children = None + self.labels = AxisLabels(**kwds) + self.setplotter() + + def plot(self,*args,**kwds): + if self.children!=None: + plotbackend.hold('on') + for child in self.children: + tmp = child.plot(*args,**kwds) + + tmp2 = self.plotter.plot(self,*args,**kwds) + return tmp2 + + def copy(self): + newcopy = empty_copy(self) + newcopy.__dict__.update(self.__dict__) + return newcopy + + + def setplotter(self): + ''' + Set plotter based on the data type data_1d, data_2d, data_3d or data_nd + ''' + + if isinstance(self.args,(list,tuple)): # Multidimensional data + ndim = len(self.args) + if ndim<2: + warnings.warn('Unable to determine plotter-type, because len(self.args)<2.') + print('If the data is 1D, then self.args should be a vector!') + print('If the data is 2D, then length(self.args) should be 2.') + print('If the data is 3D, then length(self.args) should be 3.') + print('Unless you fix this, the plot methods will not work!') + elif ndim==2: + self.plotter = Plotter_2d() + else: + warnings.warn('Plotter method not implemented for ndim>2') + + else: #One dimensional data + self.plotter = Plotter_1d() + + +class AxisLabels: + def __init__(self,title='',xlab='',ylab='',zlab='',**kwds): + self.title = title + self.xlab = xlab + self.ylab = ylab + self.zlab = zlab + def copy(self): + lbkwds = self.labels.__dict__.copy() + labels = AxisLabels(**lbkwds) + return labels + + def labelfig(self): + try: + plotbackend.title(self.title) + plotbackend.xlabel(self.xlab) + plotbackend.ylabel(self.ylab) + plotbackend.zlabel(self.zlab) + except: + pass + +class Plotter_1d(object): + """ + class comment + + bar + barh + loglog + semilogx + semilogy + plot + stem + scatter + + """ + + def __init__(self,plotmethod='plot'): + self.plotfun = None + self.plotbackend = plotbackend + try: + self.plotfun = plotbackend.__dict__[plotmethod] + except: + pass + def show(self): + plotbackend.show() + + def plot(self,wdata,*args,**kwds): + if isinstance(wdata.args,(list,tuple)): + args1 = tuple((wdata.args))+(wdata.data,)+args + else: + args1 = tuple((wdata.args,))+(wdata.data,)+args + self.plotfun(*args1,**kwds) + wdata.labels.labelfig() + +class Plotter_2d(Plotter_1d): + """ + class comment + + contour + mesh + surf + + + """ + + def __init__(self,plotmethod='contour'): + super(Plotter_2d,self).__init__(plotmethod) + #self.plotfun = plotbackend.__dict__[plotmethod] + +class TrGauss(WafoData): + def __init__(self,*args,**kwds): + super(TrGauss, self).__init__(*args,**kwds) + +class CycleCount(object): + def __init__(self,M,m): + self.M = M + self.m = m + + def amplitudes(self): + return (self.M-self.m)/2. + +class SpecData1D(WafoData): + """ Container class for 1D spectrum data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + type : string + spectrum type, one of 'freq', 'k1d', 'enc' (default 'freq') + freqtype : letter + frequency type, one of: 'f', 'w' or 'k' (default 'w') + + + Examples + -------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S1 = Sj.toSpecData(w) #Make spectrum object from numerical values + >>> S = SpecData1D(Sj(w),w) # Alternatively do it manually + + See also + -------- + WafoData + CovData + """ + + def __init__(self,*args,**kwds): + super(SpecData1D, self).__init__(*args,**kwds) + + self.name='WAFO Spectrum Object' + self.type='freq' + self.freqtype='w' + self.angletype='' + self.h=np.inf + self.tr=None + self.phi=0. + self.v=0. + self.norm=0 + somekeys = ['angletype', 'phi', 'name', 'h', 'tr', 'freqtype', 'v', 'type', 'norm'] + + self.__dict__.update(sub_dict_select(kwds,somekeys)) + + self.setlabels() +## def copy(self): +## newcopy = empty_copy(self) +## newcopy.update(self.__dict__) +## #kwds = self.__dict__.copy() +## #wdata = SpecData1D(**kwds) +## #wdata.labels = sel.labels.copy() +## return newcopy + def toacf_matrix(self,nr=0,Nt=None,dt=None): + ''' Computes covariance function and its derivatives, alternative version + + Parameters + ---------- + Nr = number of derivatives in output, Nr<=4 (default 0) + Nt = number in time grid, i.e., number of time-lags. + (default rate*(n-1)) where rate = round(1/(2*f(end)*dt)) or + rate = round(pi/(w(n)*dt)) depending on S. + dt = time spacing for R + + Returns + ------- + R = [R0, R1,...Rnr] matrix with autocovariance and its + derivatives, i.e., Ri (i=1:nr) are column vectors with + the 1'st to nr'th derivatives of R0. size Nt+1 x Nr+1 + + NB! This routine requires that the spectrum grid is equidistant + starting from zero frequency. + Example: + -------- + S = jonswap; + dt = 0.1; + R = spec2cov2(S,3,256,dt); + See also + -------- + spec2cov, specinterp, datastructures + ''' + + ftype = self.freqtype #; %options are 'f' and 'w' and 'k' + freq = self.args + n = length(freq) + dTold = self.sampling_period() + if dt is None: + dt = dTold + rate = 1 + else: + rate = np.maximum(np.round(dTold*1./dt),1.) + + + if Nt is None: + Nt = rate*(n-1) + else: #%check if Nt is ok + Nt = np.minimum(Nt,rate*(n-1)); + + + checkdt = 1.2*min(np.diff(freq))/2./np.pi; + if ftype in 'k': + lagtype = 'x' + else: + lagtype = 't' + if ftype in 'f': + checkdt = checkdt*2*np.pi + msg1 = 'The step dt = %g in computation of the density is too small.' % dt + msg2 = 'The step dt = %g step is small, may cause numerical inaccuracies.' % dt + + if (checkdt < 2.**-16/dt): + np.disp(msg1) + np.disp('The computed covariance (by FFT(2^K)) may differ from the theoretical.') + np.disp('Solution:') + raise ValueError('use larger dt or sparser grid for spectrum.') + + + #% Calculating covariances + #%~~~~~~~~~~~~~~~~~~~~~~~~ + S2 = self.copy() + S2.resample(dt) + + R2 = S2.toacf(nr,Nt,rate=1) + R = np.zeros((Nt+1,nr+1)) + R[:,0] = R2.data[0:Nt+1] + fieldname = 'R' + lagtype*nr + for ix in range(1,nr+1): + fn = fieldname[1:ix]; + R[:,0:Nt+1] = gettattr(R2,fn)[0:Nt+1]; + + + EPS0 = 0.0001 + cc = R[0,0]-R[1,0]*(R[1,0]/R[0,0]); + if Nt+1>=5: + #%cc1=R(1,1)-R(3,1)*(R(3,1)/R(1,1))+R(3,2)*(R(3,2)/R(1,3)); + #%cc3=R(1,1)-R(5,1)*(R(5,1)/R(1,1))+R(5,2)*(R(5,2)/R(1,3)); + + cc2 = R(0,0)-R(4,0)*(R(4,0)/R(0,0)); + if (cc2R(x,t); Nt and Ny set =>R(y,t) + 4) Any type, Nt, Nx and Ny set => R(x,y,t) + 5) Any type, Nt not set, Nx and/or Ny set => Nt set to default, goto 3) or 4) + + NB! This routine requires that the spectrum grid is equidistant + starting from zero frequency. + NB! If you are using a model spectrum, S, with sharp edges + to calculate covariances then you should probably round off the sharp + edges like this: + + Example: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap() + >>> S = Sj.toSpecData() + >>> S.data[0:40] = 0.0 + >>> S.data[100:-1] = 0.0 + >>> Nt = len(S.data)-1; + >>> R = S.toacf(nr=0,Nt=Nt) + + R = spec2cov(S,0,Nt); + win = parzen(2*Nt+1); + R.R = R.R.*win(Nt+1:end); + S1 = cov2spec(R); + R2 = spec2cov(S1); + figure(1) + plotspec(S),hold on, plotspec(S1,'r') + figure(2) + covplot(R), hold on, covplot(R2,[],[],'r') + figure(3) + semilogy(abs(R2.R-R.R)), hold on, + semilogy(abs(S1.S-S.S)+1e-7,'r') + + See also cov2spec, datastructures + ''' + + freq = self.args + n = freq.size + + if freq[0]>0: + raise ValueError('Spectrum does not start at zero frequency/wave number.\n Correct it with resample, for example.') + dw = np.abs(np.diff(freq,n=2,axis=0)) + if np.any(dw>1.0e-8): + raise ValueError('Not equidistant frequencies/wave numbers in spectrum.\n Correct it with resample, for example.') + + + if rate is None: + rate=1 #; %interpolation rate + elif rate>16: + rate=16 + else: # make sure rate is a power of 2 + rate=2**nextpow2(rate) + + if Nt is None: + Nt = rate*(n-1) + else: #check if Nt is ok + Nt = np.minimum(Nt,rate*(n-1)) + + S = self.copy() + + + if self.freqtype in 'k': + lagtype = 'x' + else: + lagtype = 't' + + dT = S.sampling_period() + #normalize spec so that sum(specn)/(n-1)=R(0)=var(X) + specn = S.data*freq[-1] + if S.freqtype in 'f': + w = freq*2*np.pi + else: + w = freq + + nfft = rate*2**nextpow2(2*n-2); + + Rper = np.r_[specn, np.zeros(nfft-(2*n)+2) , np.conj(specn[n-1:0:-1])] #; % periodogram + t = np.r_[0:Nt+1]*dT*(2*n-2)/nfft + + fft = np.fft.fft + + r = fft(Rper,nfft).real/(2*n-2) + R = CovData1D(r[0:Nt+1],t,lagtype=lagtype) + R.tr = S.tr; + R.h = S.h; + R.norm = S.norm; + + if nr>0: + w = np.r_[w , np.zeros(nfft-2*n+2) ,-w[n-1:0:-1] ] + fieldname = 'R' + lagtype*nr ; + for ix in range(1,nr+1): + Rper = (-1j*w*Rper) + r = fft(Rper,nfft).real/(2*n-2) + setattr(R,fieldname[0:ix+1],r[0:Nt+1]) + return R + + + + + def sim(self,ns=None,cases=1,dt=None,iseed=None,method='random',derivative=False): + ''' Simulates a Gaussian process and its derivative from spectrum + + Parameters + ---------- + ns : scalar + number of simulated points. (default length(S)-1=n-1). + If ns>n-1 it is assummed that R(k)=0 for all k>n-1 + cases : scalar + number of replicates (default=1) + dt : scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : int or state + starting state/seed number for the random number generator + (default none is set) + method : string + if 'exact' : simulation using cov2sdat + if 'random' : random phase and amplitude simulation (default) + derivative : bool + if true : return derivative of simulated signal as well + otherwise + + + Returns + ------- + xs = a cases+1 column matrix ( t,X1(t) X2(t) ...). + xsder = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). + + Details + ------- + Performs a fast and exact simulation of stationary zero mean + Gaussian process through circulant embedding of the covariance matrix + or by summation of sinus functions with random amplitudes and random + phase angle. + + If the spectrum has a non-empty field .tr, then the transformation is + applied to the simulated data, the result is a simulation of a transformed + Gaussian process. + + Note: The method 'exact' simulation may give high frequency ripple when + used with a small dt. In this case the method 'random' works better. + + Example: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap();S = Sj.toSpecData(); + >>> np =100; dt = .2; + >>> x1 = S.sim(np,dt=dt); + + waveplot(x1,'r',x2,'g',1,1) + + See also + -------- + cov2sdat, gaus2dat + + Reference + ----------- + C.R Dietrich and G. N. Newsam (1997) + "Fast and exact simulation of stationary + Gaussian process through circulant embedding + of the Covariance matrix" + SIAM J. SCI. COMPT. Vol 18, No 4, pp. 1088-1107 + + Hudspeth, R.T. and Borgman, L.E. (1979) + "Efficient FFT simulation of Digital Time sequences" + Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM2, + + ''' + + fft = np.fft.fft + + S = self.copy() + if dt is not None: + S.resample(dt) + + + ftype = S.freqtype + freq = S.args + + dT = S.sampling_period() + Nt = freq.size + + if ns is None: + ns=Nt-1 + + if method in 'exact': + + #nr=0,Nt=None,dt=None + R = S.toacf(nr=0); + T = Nt*dT + ix = np.flatnonzero(R.args>T); + + # Trick to avoid adding high frequency noise to the spectrum + if ix.size>0: + R.data[ix[0]::]=0.0 + + return R.sim(ns=ns,cases=cases,iseed=iseed,derivative=derivative) + + _set_seed(iseed) + + ns = ns+np.mod(ns,2) # make sure it is even + + fi = freq[1:-1] + Si = S.data[1:-1] + if ftype in ('w','k'): + fact = 2.*np.pi + Si = Si*fact; + fi = fi/fact; + + zeros = np.zeros + + x = zeros((ns,cases+1)); + + df = 1/(ns*dT) + + + # interpolate for freq. [1:(N/2)-1]*df and create 2-sided, uncentered spectra + # ---------------------------------------------------------------------------- + f = np.arange(1,ns/2.)*df + + Fs = np.hstack((0., fi, df*ns/2.)) + Su = np.hstack((0., np.abs(Si)/2., 0.)); + + + Si = np.interp(f,Fs,Su) + Su=np.hstack((0., Si,0, Si[(ns/2)-2::-1])) + del(Si, Fs) + + # Generate standard normal random numbers for the simulations + # ----------------------------------------------------------- + randn = np.random.randn + Zr = randn((ns/2)+1,cases) + Zi = np.vstack((zeros((1,cases)), randn((ns/2)-1,cases), zeros((1,cases)))); + + A = zeros((ns,cases),dtype=complex) + A[0:(ns/2+1),:] = Zr - 1j*Zi; + del(Zr, Zi) + A[(ns/2+1):ns,:] = A[ns/2-1:0:-1,:].conj(); + A[0,:] = A[0,:]*np.sqrt(2.); + A[(ns/2),:] = A[(ns/2),:]*np.sqrt(2.); + + + # Make simulated time series + # -------------------------- + + T = (ns-1)*dT + Ssqr = np.sqrt(Su*df/2.) + + # stochastic amplitude + A = A*Ssqr[:,np.newaxis]; + + + # Deterministic amplitude + #A = sqrt[1]*Ssqr(:,ones(1,cases)).*exp(sqrt(-1)*atan2(imag(A),real(A))); + del( Su, Ssqr) + + + x[:,1::] = fft(A,axis=0).real + x[:,0] = np.linspace(0,T,ns) #'; %(0:dT:(np-1)*dT).'; + + + if derivative: + xder=np.zeros(ns,cases+1) + w = 2.*np.pi*np.hstack((0, f, 0.,-f[-1::-1])) + A = -1j*A*w[:,newaxis] + xder[:,1:(cases+1)] = fft(A,axis=0).real; + xder[:,0] = x[:,0] + + + + if S.tr is not None: + np.disp(' Transforming data.') + g=S.tr; + G=np.fliplr(g); #% the invers of g + if derivative: + for ix in range(cases): + tmp=tranproc(np.hstack((x[:,ix+1], xder[:,ix+1])),G); + x[:,ix+1]=tmp[:,0]; + xder[:,ix+1]=tmp[:,1]; + + else: + for ix in range(cases): + x[:,ix+1]=tranproc(x[:,ix+1],G); + + + + if derivative: + return x,xder + else: + return x + +# function [x2,x,svec,dvec,A]=spec2nlsdat(S,np,dt,iseed,method,truncationLimit) + def sim_nl(self,ns=None,cases=1,dt=None,iseed=None,method='random', + fnlimit=1.4142,reltol=1e-3,g=9.81): + """ Simulates a Randomized 2nd order non-linear wave X(t) + + Parameters + ---------- + ns : scalar + number of simulated points. (default length(S)-1=n-1). + If ns>n-1 it is assummed that R(k)=0 for all k>n-1 + cases : scalar + number of replicates (default=1) + dt : scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : int or state + starting state/seed number for the random number generator + (default none is set) + method : string + 'apStochastic' : Random amplitude and phase (default) + 'aDeterministic' : Deterministic amplitude and random phase + 'apDeterministic' : Deterministic amplitude and phase + fnLimit : scalar + normalized upper frequency limit of spectrum for 2'nd order + components. The frequency is normalized with + sqrt(gravity*tanh(kbar*waterDepth)/Amax)/(2*pi) + (default sqrt(2), i.e., Convergence criterion [1]_). + Other possible values are: + sqrt(1/2) : No bump in trough criterion + sqrt(pi/7) : Wave steepness criterion + reltol : scalar + relative tolerance defining where to truncate spectrum for the + for sum and difference frequency effects + + + Returns + ------- + xs2 = a cases+1 column matrix ( t,X1(t) X2(t) ...). + xs1 = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). + + Details + ------- + Performs a Fast simulation of Randomized 2nd order non-linear + waves by summation of sinus functions with random amplitudes and + phase angles. The extent to which the simulated result are applicable + to real seastates are dependent on the validity of the assumptions: + + 1. Seastate is unidirectional + 2. Surface elevation is adequately represented by 2nd order random + wave theory + 3. The first order component of the surface elevation is a Gaussian + random process. + + If the spectrum does not decay rapidly enough towards zero, the + contribution from the 2nd order wave components at the upper tail can + be very large and unphysical. To ensure convergence of the perturbation + series, the upper tail of the spectrum is truncated at FNLIMIT in the + calculation of the 2nd order wave components, i.e., in the calculation + of sum and difference frequency effects. This may also be combined with + the elimination of second order effects from the spectrum, i.e., extract + the linear components from the spectrum. One way to do this is to use + SPEC2LINSPEC. + + Example + -------- + np =100; dt = .2; + [x1, x2] = spec2nlsdat(jonswap,np,dt); + waveplot(x1,'r',x2,'g',1,1) + + See also + -------- + spec2linspec, spec2sdat, cov2sdat + + References + ---------- + .. [1] Nestegaard, A and Stokka T (1995) + A Third Order Random Wave model. + In proc.ISOPE conf., Vol III, pp 136-142. + + .. [2] R. S Langley (1987) + A statistical analysis of non-linear random waves. + Ocean Engng, Vol 14, pp 389-407 + + .. [3] Marthinsen, T. and Winterstein, S.R (1992) + 'On the skewness of random surface waves' + In proc. ISOPE Conf., San Francisco, 14-19 june. + """ + + + # TODO % Check the methods: 'apdeterministic' and 'adeterministic' + + from wafo.spectrum import dispersion_relation as sm + + Hm0 = self.characteristic('Hm0')[0] + Tm02 = self.characteristic('Tm02')[0] + #Hm0 = spec2char(S,'Hm0'); + #Tm02 = spec2char(S,'Tm02'); + + _set_seed(iseed) + fft = np.fft.fft + + S = self.copy() + if dt is not None: + S.resample(dt) + + + ftype = S.freqtype + freq = S.args + + dT = S.sampling_period() + Nt = freq.size + + if ns is None: + ns = Nt-1 + + ns = ns+np.mod(ns,2) # make sure it is even + + fi = freq[1:-1] + Si = S.data[1:-1] + if ftype in ('w','k'): + fact = 2.*np.pi + Si = Si*fact; + fi = fi/fact; + + Smax = max(Si) + waterDepth = min(abs(S.h),10.**30); + + zeros = np.zeros + + x = zeros((ns,cases+1)); + + df = 1/(ns*dT) + + # interpolate for freq. [1:(N/2)-1]*df and create 2-sided, uncentered spectra + # ---------------------------------------------------------------------------- + f = np.arange(1,ns/2.)*df + Fs = np.hstack((0., fi, df*ns/2.)) + w = 2.*np.pi*Fs + kw = sm.w2k(w ,0.,waterDepth,g)[0] + Su = np.hstack((0., np.abs(Si)/2., 0.)); + + + + Si = np.interp(f,Fs,Su) + nmin = (Si>Smax*reltol).argmax() + nmax = np.flatnonzero(Si>0).max() + Su = np.hstack((0., Si,0, Si[(ns/2)-2::-1])) + del(Si, Fs) + + # Generate standard normal random numbers for the simulations + # ----------------------------------------------------------- + randn = np.random.randn + Zr = randn((ns/2)+1,cases) + Zi = np.vstack((zeros((1,cases)), randn((ns/2)-1,cases), zeros((1,cases)))); + + A = zeros((ns,cases),dtype=complex) + A[0:(ns/2+1),:] = Zr - 1j*Zi; + del(Zr, Zi) + A[(ns/2+1):ns,:] = A[ns/2-1:0:-1,:].conj(); + A[0,:] = A[0,:]*np.sqrt(2.); + A[(ns/2),:] = A[(ns/2),:]*np.sqrt(2.); + + + # Make simulated time series + # -------------------------- + + T = (ns-1)*dT + Ssqr = np.sqrt(Su*df/2.) + + + if method.startswith('apd') : # apdeterministic + # Deterministic amplitude and phase + A[1:(ns/2),:] = A[1,0]; + A[(ns/2+1):ns,:] = A[1,0].conj(); + A = sqrt(2)*Ssqr[:,np.newaxis]*exp(1J*atan2(A.imag,A.real)) + elif method.startswith('ade'): # adeterministic + # Deterministic amplitude and random phase + A = sqrt(2)*Ssqr[:,np.newaxis]*exp(1J*atan2(A.imag,A.real)); + else: + # stochastic amplitude + A = A*Ssqr[:,np.newaxis]; + # Deterministic amplitude + #A = sqrt(2)*Ssqr(:,ones(1,cases)).*exp(sqrt(-1)*atan2(imag(A),real(A))); + del( Su, Ssqr) + + + x[:,1::] = fft(A,axis=0).real + x[:,0] = np.linspace(0,T,ns) #'; %(0:dT:(np-1)*dT).'; + + + + x2 = x.copy() + + # If the spectrum does not decay rapidly enough towards zero, the + # contribution from the wave components at the upper tail can be very + # large and unphysical. + # To ensure convergence of the perturbation series, the upper tail of the + # spectrum is truncated in the calculation of sum and difference + # frequency effects. + # Find the critical wave frequency to ensure convergence. + + sqrt = np.sqrt + log = np.log + pi = np.pi + tanh = np.tanh + numWaves = 1000. # Typical number of waves in 3 hour seastate + kbar = sm.w2k(2.*np.pi/Tm02,0.,waterDepth)[0]; + Amax = sqrt(2*log(numWaves))*Hm0/4; #% Expected maximum amplitude for 1000 waves seastate + + fLimitUp = fnlimit*sqrt(g*tanh(kbar*waterDepth)/Amax)/(2*pi); + fLimitLo = sqrt(g*tanh(kbar*waterDepth)*Amax/waterDepth)/(2*pi*waterDepth); + + nmax = min(np.flatnonzero(f<=fLimitUp).max(),nmax)+1; + nmin = max(np.flatnonzero(fLimitLo<=f).min(),nmin)+1; + + #if isempty(nmax),nmax = np/2;end + #if isempty(nmin),nmin = 2;end % Must always be greater than 1 + fLimitUp = df*nmax; + fLimitLo = df*nmin; + + print('2nd order frequency Limits = %g,%g'% (fLimitLo, fLimitUp)) + + + +## if nargout>3, +## %compute the sum and frequency effects separately +## [svec, dvec] = disufq((A.'),w,kw,min(h,10^30),g,nmin,nmax); +## svec = svec.'; +## dvec = dvec.'; +## +## x2s = fft(svec); % 2'nd order sum frequency component +## x2d = fft(dvec); % 2'nd order difference frequency component +## +## % 1'st order + 2'nd order component. +## x2(:,2:end) =x(:,2:end)+ real(x2s(1:np,:))+real(x2d(1:np,:)); +## else + rvec,ivec = diffsumfunq.disufq(A.real,A.imag,w,kw,waterDepth,g,nmin,nmax) + + svec = rvec + 1J*ivec + x2o = fft(svec) # 2'nd order component + + + # 1'st order + 2'nd order component. + x2[:,1::] = x[:,1::]+ x2o[0:ns,:].real(); + + return x2, x + + + + + + + def moment(self,nr=2,even=True,j=0): + ''' Calculates spectral moments from spectrum + + Parameters + ---------- + nr : int + order of moments (recomended maximum 4) + even : bool + False for all moments, + True for only even orders + j : int + 0 or 1 + + Returns + ------- + m : list of moments + mtext : list of strings describing the elements of m, see below + + Details + ------- + Calculates spectral moments of up to order NR by use of + Simpson-integration. + + / / + mj_t^i = | w^i S(w)^(j+1) dw, or mj_x^i = | k^i S(k)^(j+1) dk + / / + + where k=w^2/gravity, i=0,1,...,NR + + The strings in output mtext have the same position in the list + as the corresponding numerical value has in output m + Notation in mtext: 'm0' is the variance, + 'm0x' is the first-order moment in x, + 'm0xx' is the second-order moment in x, + 'm0t' is the first-order moment in t, + etc. + For the calculation of moments see Baxevani et al. + + Example: + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + >>> S.moment() + ([0.56220770033914191, 0.35433180985851975], ['m0', 'm0tt']) + + References + ---------- + Baxevani A. et al. (2001) + Velocities for Random Surfaces + ''' + pi= np.pi + one_dim_spectra = ['freq','enc','k1d'] + if self.type not in one_dim_spectra: + raise ValueError('Unknown spectrum type!') + + f = np.ravel(self.args) + S = np.ravel(self.data) + if self.freqtype in ['f','w']: + vari = 't' + if self.freqtype=='f': + f = 2.*pi*f + S = S/(2.*pi) + else: + vari = 'x' + S1=np.abs(S)**(j+1.) + m = [simps(S1,x=f)] + mtxt = 'm%d' % j + mtext = [mtxt] + step = np.mod(even,2)+1 + df = f**step + for i in range(step,nr+1,step): + S1 = S1*df + m.append(simps(S1,x=f)) + mtext.append(mtxt+vari*i) + return m, mtext + + def sampling_period(self): + ''' Returns sampling interval from Nyquist frequency of spectrum + + Returns + --------- + dT : scalar + sampling interval, unit: + [m] if wave number spectrum, + [s] otherwise + + Let wm be maximum frequency/wave number in spectrum, + then dT=pi/wm if angular frequency, dT=1/(2*wm) if natural frequency (Hz) + + Example + ------- + S = jonswap; + dt = spec2dt(S) + + See also + ''' + + if self.freqtype in 'f': + wmdt = 0.5 # Nyquist to sampling interval factor + else: # ftype == w og ftype == k + wmdt = np.pi; + + wm = self.args[-1] #Nyquist frequency + dt = wmdt/wm; #sampling interval = 1/Fs + return dt + + def resample(self,dt=None,Nmin=0,Nmax=2**13+1,method='stineman'): + ''' Interpolate and zero-padd spectrum to change Nyquist freq. + + Parameters + ---------- + dt : scalar + wanted sampling interval (default as given by S, see spec2dt) + unit: [s] if frequency-spectrum, [m] if wave number spectrum + Nmin : scalar + minimum number of frequencies. + Nmax : scalar + minimum number of frequencies + method : string + interpolation method (options are 'linear', 'cubic' or 'stineman') + + To be used before simulation (e.g. spec2sdat) or evaluation of covariance + function (spec2cov) to directly get wanted sampling interval. + The input spectrum is interpolated and padded with zeros to reach + the right max-frequency, w(end)=pi/dt, f(end)=1/(2*dt), or k(end)=pi/dt. + The objective is that output frequency grid should be at least as dense + as the input grid, have equidistant spacing and length equal to + 2^k+1 (>=Nmin). If the max frequency is changed, the number of points + in the spectrum is maximized to 2^13+1. + + Note: Also zero-padding down to zero freq, if S does not start there. + If empty input dt, this is the only effect. + + See also + -------- + spec2cov, spec2sdat, covinterp, spec2dt + ''' + + + ftype = self.freqtype + w = self.args.ravel() + n = w.size + + #%doInterpolate = 0; + + if ftype=='f': + Cnf2dt = 0.5; # Nyquist to sampling interval factor + else: #% ftype == w og ftype == k + Cnf2dt = np.pi + + wnOld = w[-1] # Old Nyquist frequency + dTold = Cnf2dt/wnOld; # sampling interval=1/Fs + + + if dt is None: + dt=dTold + + + + # Find how many points that is needed + nfft = 2**nextpow2(max(n-1,Nmin-1)) + dttest = dTold*(n-1)/nfft + + while (dttest>dt) and (nfft0 or w[1]>0 or (nfft!=n) or dt!=dTold or any(abs(np.diff(w,axis=0))>1.0e-8); + + if doInterpolate>0: + S1 = self.data + + dw = min(np.diff(w)); + + if dWn>0: + #% add a zero just above old max-freq, and a zero at new max-freq + #% to get correct interpolation there + Nz = 1 + (dWn>dw) #; % Number of zeros to add + if Nz==2: + w = np.hstack((w, wnOld+dw, wnNew)) + else: + w = np.hstack((w, wnNew)) + + S1 = np.hstack((S1, np.zeros(Nz))) + + if w[0]>0: + #% add a zero at freq 0, and, if there is space, a zero just below min-freq + Nz = 1 + (w[0]>dw); #% Number of zeros to add + if Nz==2: + w=np.hstack((0, w[0]-dw, w)) + else: + w=np.hstack((0, w)) + + S1 = np.hstack((zeros(Nz), S1)) + + + #% Do a final check on spacing in order to check that the gridding is + #% sufficiently dense: + #np1 = S1.size + dwMin = np.finfo(float).max + #%wnc = min(wnNew,wnOld-1e-5); + wnc = wnNew; + specfun = lambda xi : stineman_interp(xi,w,S1) + + + x,y = discretize(specfun,0,wnc) + dwMin = np.minimum(min(np.diff(x)),dwMin) + + + newNfft = 2**nextpow2(np.ceil(wnNew/dwMin))+1 + if newNfft>nfft: + if (nfft<=2**15+1) and (newNfft>2**15+1): + warnings.warn('Spectrum matrix is very large (>33k). Memory problems may occur.') + + nfft = newNfft; + + + self.args = np.linspace(0,wnNew,nfft) + if method=='stineman': + self.data = stineman_interp(self.args,w,S1) + else: + intfun = interpolate.interp1d(w,S1,kind=method) + self.data = intfun(self.args) + self.data = self.data.clip(0) # clip negative values to 0 + + def normalize(self): + pass + def bandwidth(self,factors=0): + ''' Return some spectral bandwidth and irregularity factors + + + Returns + -------- + bw : arraylike + vector of bandwidth factors + + Parameters + ----------- + factors : array-like + Input vector 'factors' correspondence: + 0 alpha=m2/sqrt(m0*m4) (irregularity factor) + 1 eps2 = sqrt(m0*m2/m1^2-1) (narrowness factor) + 2 eps4 = sqrt(1-m2^2/(m0*m4))=sqrt(1-alpha^2) (broadness factor) + 3 Qp=(2/m0^2)int_0^inf f*S(f)^2 df (peakedness factor) + + Order of output is the same as order in 'factors' + + Example: + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + >>> S.bandwidth([0,1,2,3]) + array([ 0.65354446, 0.3975428 , 0.75688813, 2.00207912]) + ''' + + if self.freqtype in 'k': + vari = 'k'; + else: + vari = 'w'; + + m,mtxt = self.moment(nr=4,even=False) + sqrt = np.sqrt + fact = np.atleast_1d(factors) + alpha = m[2]/sqrt(m[0]*m[4]) + eps2 = sqrt(m[0]*m[2]/m[1]**2.-1.) + eps4 = sqrt(1.-m[2]**2./m[0]/m[4]); + f = self.args + S = self.data + Qp = 2/m[0]**2.*simps(f*S**2,x=f); + bw = np.array([alpha,eps2,eps4,Qp]) + return bw[fact] + + def characteristic(self,fact='Hm0',T=1200,g=9.81): + """Returns spectral characteristics and their covariance + + Parameters + ---------- + fact = vector with factor integers or a string or + a cellarray of strings, see below.(default [1]) + T : scalar + recording time (sec) (default 1200 sec = 20 min) + g : scalar + acceleration of gravity [m/s^2] + + Returns + ------- + ch = vector of spectral characteristics + R = matrix of the corresponding covariances given T + chtext = a list of strings describing the elements of ch, see example. + + + Description + ------------ + If input spectrum is of wave number type, output are factors for + corresponding 'k1D', else output are factors for 'freq'. + Input vector 'factors' correspondence: + 1 Hm0 = 4*sqrt(m0) Significant wave height + 2 Tm01 = 2*pi*m0/m1 Mean wave period + 3 Tm02 = 2*pi*sqrt(m0/m2) Mean zero-crossing period + 4 Tm24 = 2*pi*sqrt(m2/m4) Mean period between maxima + 5 Tm_10 = 2*pi*m_1/m0 Energy period + 6 Tp = 2*pi/{w | max(S(w))} Peak period + 7 Ss = 2*pi*Hm0/(g*Tm02^2) Significant wave steepness + 8 Sp = 2*pi*Hm0/(g*Tp^2) Average wave steepness + 9 Ka = abs(int S(w)*exp(i*w*Tm02) dw ) /m0 Groupiness parameter + 10 Rs = (S(0.092)+S(0.12)+S(0.15)/(3*max(S(w))) Quality control parameter + 11 Tp1 = 2*pi*int S(w)^4 dw Peak Period (robust estimate for Tp) + ------------------ + int w*S(w)^4 dw + + 12 alpha = m2/sqrt(m0*m4) Irregularity factor + 13 eps2 = sqrt(m0*m2/m1^2-1) Narrowness factor + 14 eps4 = sqrt(1-m2^2/(m0*m4))=sqrt(1-alpha^2) Broadness factor + 15 Qp = (2/m0^2)int_0^inf w*S(w)^2 dw Peakedness factor + + Order of output is same as order in 'factors' + The covariances are computed with a Taylor expansion technique + and is currently only available for factors 1, 2, and 3. Variances + are also available for factors 4,5,7,12,13,14 and 15 + + Quality control: + ---------------- + Critical value for quality control parameter Rs is Rscrit = 0.02 + for surface displacement records and Rscrit=0.0001 for records of + surface acceleration or slope. If Rs > Rscrit then probably there + are something wrong with the lower frequency part of S. + + Ss may be used as an indicator of major malfunction, by checking that + it is in the range of 1/20 to 1/16 which is the usual range for + locally generated wind seas. + + Examples: + --------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=5) + >>> S = Sj.toSpecData() #Make spectrum ob + >>> S.characteristic(1) + (array([ 8.59007646]), array([[ 0.03040216]]), ['Tm01']) + + >>> [ch, R, txt] = S.characteristic([1,2,3]) # fact a vector of integers + >>> S.characteristic('Ss') # fact a string + (array([ 0.04963112]), array([[ 2.63624782e-06]]), ['Ss']) + + >>> S.characteristic(['Hm0','Tm02']) # fact a list of strings + (array([ 4.99833578, 8.03139757]), + array([[ 0.05292989, 0.02511371], + [ 0.02511371, 0.0274645 ]]), + ['Hm0', 'Tm02']) + + See also + --------- + bandwidth, + moment + + References + ---------- + Krogstad, H.E., Wolf, J., Thompson, S.P., and Wyatt, L.R. (1999) + 'Methods for intercomparison of wave measurements' + Coastal Enginering, Vol. 37, pp. 235--257 + + Krogstad, H.E. (1982) + 'On the covariance of the periodogram' + Journal of time series analysis, Vol. 3, No. 3, pp. 195--207 + + Tucker, M.J. (1993) + 'Recommended standard for wave data sampling and near-real-time processing' + Ocean Engineering, Vol.20, No.5, pp. 459--474 + + Young, I.R. (1999) + "Wind generated ocean waves" + Elsevier Ocean Engineering Book Series, Vol. 2, pp 239 + """ + + #% TODO % Need more checking on computing the variances for Tm24,alpha, eps2 and eps4 + #% TODO % Covariances between Tm24,alpha, eps2 and eps4 variables are also needed + NaN = np.nan + tfact = dict(Hm0=0,Tm01=1,Tm02=2,Tm24=3, Tm_10=4,Tp=5,Ss=6, Sp=7, Ka=8, + Rs=9, Tp1=10,Alpha=11,Eps2=12,Eps4=13,Qp=14) + tfact1 = ('Hm0','Tm01','Tm02','Tm24', 'Tm_10','Tp','Ss', 'Sp', 'Ka', + 'Rs', 'Tp1','Alpha','Eps2','Eps4','Qp') + + if isinstance(fact,str): + fact = list((fact,)) + if isinstance(fact,(list,tuple)): + nfact = [] + for k in fact: + if isinstance(k,str): + nfact.append(tfact.get(k.capitalize(),15)) + else: + nfact.append(k) + else: + nfact = fact; + + nfact = np.atleast_1d(nfact) + + if np.any((nfact>14) | (nfact<0)): + raise ValueError('Factor outside range (0,...,14)') + + vari = self.freqtype + + f = self.args.ravel() + S1 = self.data.ravel() + m,mtxt = self.moment(nr=4,even=False) + + #% moments corresponding to freq in Hz + for k in range(1,5): + m[k] = m[k]/(2*np.pi)**k + + pi = np.pi + ind = np.flatnonzero(f>0) + m.append(simps(S1[ind]/f[ind],f[ind])*2.*np.pi) #; % = m_1 + m_10 = simps(S1[ind]**2/f[ind],f[ind])*(2*pi)**2/T # % = COV(m_1,m0|T=t0) + m_11 = simps(S1[ind]**2./f[ind]**2,f[ind])*(2*pi)**3/T #% = COV(m_1,m_1|T=t0) + + sqrt = np.sqrt + #% Hm0 Tm01 Tm02 Tm24 Tm_10 + Hm0 = 4.*sqrt(m[0]); + Tm01 = m[0]/m[1]; + Tm02 = sqrt(m[0]/m[2]); + Tm24 = sqrt(m[2]/m[4]); + Tm_10= m[5]/m[0]; + + Tm12 = m[1]/m[2] + + ind = S1.argmax() + maxS = S1[ind] + #[maxS ind] = max(S1); + Tp = 2.*pi/f[ind] # % peak period /length + Ss = 2.*pi*Hm0/g/Tm02**2 # % Significant wave steepness + Sp = 2.*pi*Hm0/g/Tp**2 #; % Average wave steepness + Ka = abs(simps(S1*np.exp(1J*f*Tm02),f))/m[0]; #% groupiness factor + + #% Quality control parameter + #% critical value is approximately 0.02 for surface displacement records + #% If Rs>0.02 then there are something wrong with the lower frequency part + #% of S. + Rs = np.sum(np.interp(np.r_[0.0146, 0.0195, 0.0244]*2*pi,f,S1))/3./maxS; + Tp2 = 2*pi*simps(S1**4,f)/simps(f*S1**4,f); + + + alpha1 = Tm24/Tm02 #; % m(3)/sqrt(m(1)*m(5)); + eps2 = sqrt(Tm01/Tm12-1.)# % sqrt(m(1)*m(3)/m(2)^2-1); + eps4 = sqrt(1.-alpha1**2) #; % sqrt(1-m(3)^2/m(1)/m(5)); + Qp = 2./m[0]**2*simps(f*S1**2,f); + + + + + ch = np.r_[Hm0, Tm01, Tm02, Tm24, Tm_10, Tp, Ss, Sp, Ka, Rs, Tp2, alpha1, eps2, eps4, Qp] + + + #% Select the appropriate values + ch = ch[nfact] + chtxt = [tfact1[i] for i in nfact] + + #if nargout>1, + #% covariance between the moments: + #%COV(mi,mj |T=t0) = int f^(i+j)*S(f)^2 df/T + mij,mijtxt = self.moment(nr=8,even=False,j=1) + for ix,tmp in enumerate(mij): + mij[ix] = tmp/T/((2.*pi)**(ix-1.0)) + + + #% and the corresponding variances for + #%{'hm0', 'tm01', 'tm02', 'tm24', 'tm_10','tp','ss', 'sp', 'ka', 'rs', 'tp1','alpha','eps2','eps4','qp'} + R = np.r_[4*mij[0]/m[0], + mij[0]/m[1]**2.-2.*m[0]*mij[1]/m[1]**3.+m[0]**2.*mij[2]/m[1]**4., + 0.25*(mij[0]/(m[0]*m[2])-2.*mij[2]/m[2]**2+m[0]*mij[4]/m[2]**3), + 0.25*(mij[4]/(m[2]*m[4])-2*mij[6]/m[4]**2+m[2]*mij[8]/m[4]**3) , + m_11/m[0]**2+(m[5]/m[0]**2)**2*mij[0]-2*m[5]/m[0]**3*m_10, + NaN, + (8*pi/g)**2*(m[2]**2/(4*m[0]**3)*mij[0]+mij[4]/m[0]-m[2]/m[0]**2*mij[2]), + NaN*np.ones(4), + m[2]**2*mij[0]/(4*m[0]**3*m[4])+mij[4]/(m[0]*m[4])+mij[8]*m[2]**2/(4*m[0]*m[4]**3)- + m[2]*mij[2]/(m[0]**2*m[4])+m[2]**2*mij[4]/(2*m[0]**2*m[4]**2)-m[2]*mij[6]/m[0]/m[4]**2, + (m[2]**2*mij[0]/4+(m[0]*m[2]/m[1])**2*mij[2]+m[0]**2*mij[4]/4-m[2]**2*m[0]*mij[1]/m[1]+ + m[0]*m[2]*mij[2]/2-m[0]**2*m[2]/m[1]*mij[3])/eps2**2/m[1]**4, + (m[2]**2*mij[0]/(4*m[0]**2)+mij[4]+m[2]**2*mij[8]/(4*m[4]**2)-m[2]*mij[2]/m[0]+ + m[2]**2*mij[4]/(2*m[0]*m[4])-m[2]*mij[6]/m[4])*m[2]**2/(m[0]*m[4]*eps4)**2, + NaN]; + + #% and covariances by a taylor expansion technique: + #% Cov(Hm0,Tm01) Cov(Hm0,Tm02) Cov(Tm01,Tm02) + S0 = np.r_[ 2./(sqrt(m[0])*m[1])*(mij[0]-m[0]*mij[1]/m[1]), + 1./sqrt(m[2])*(mij[0]/m[0]-mij[2]/m[2]), + 1./(2*m[1])*sqrt(m[0]/m[2])*(mij[0]/m[0]-mij[2]/m[2]-mij[1]/m[1]+m[0]*mij[3]/(m[1]*m[2]))] + + R1 = np.ones((15,15)); + R1[:,:] = NaN + for ix,Ri in enumerate(R): + R1[ix,ix] = Ri + + + + R1[0,2:4] = S0[:2]; + R1[1,2] = S0[2]; + for ix in [0,1]: #%make lower triangular equal to upper triangular part + R1[ix+1:,ix] = R1[ix,ix+1:] + + + R = R[nfact] + R1= R1[nfact,:][:,nfact] + + + #% Needs further checking: + #% Var(Tm24)= 0.25*(mij[4]/(m[2]*m[4])-2*mij[6]/m[4]**2+m[2]*mij[8]/m[4]**3) ... + return ch, R1, chtxt + + def setlabels(self): + ''' Set automatic title, x-,y- and z- labels on SPECDATA object + + based on type, angletype, freqtype + ''' + + N = len(self.type); + if N==0: + raise ValueError('Object does not appear to be initialized, it is empty!') + + labels = ['','',''] + if self.type.endswith('dir'): + title = 'Directional Spectrum' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[2] = 'S(w,\theta) [m^2 s / rad^2]' + else: + labels[0] = 'Frequency [Hz]' + labels[2] = 'S(f,\theta) [m^2 s / rad]' + + if self.angletype.startswith('r'): + labels[1] = 'Wave directions [rad]' + elif self.angletype.startswith('d'): + labels[1] = 'Wave directions [deg]' + elif self.type.endswith('freq'): + title = 'Spectral density' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[1] = 'S(w) [m^2 s/ rad]' + else: + labels[0] = 'Frequency [Hz]' + labels[1] = 'S(f) [m^2 s]' + else: + title = 'Wave Number Spectrum' + labels[0] = 'Wave number [rad/m]' + if self.type.endswith('k1d'): + labels[1] = 'S(k) [m^3/ rad]' + elif self.type.endswith('k2d'): + labels[1] = labels[0] + labels[2] = 'S(k1,k2) [m^4/ rad^2]' + else: + raise ValueError('Object does not appear to be initialized, it is empty!') + if self.norm!=0: + title = 'Normalized ' + title + labels[0] = 'Normalized ' + labels[0].split('[')[0] + if not self.type.endswith('dir'): + labels[1] = labels[1].split('[')[0] + labels[2] = labels[2].split('[')[0] + + self.labels.title = title + self.labels.xlab = labels[0] + self.labels.ylab = labels[1] + self.labels.zlab = labels[2] +class SpecData2D(WafoData): + """ Container class for 2D spectrum data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + type : string + spectrum type (default 'freq') + freqtype : letter + frequency type (default 'w') + angletype : string + angle type of directional spectrum (default 'radians') + + Examples + -------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + + See also + -------- + WafoData + CovData + """ + + def __init__(self,*args,**kwds): + super(SpecData2D, self).__init__(*args,**kwds) + + self.name='WAFO Spectrum Object' + self.type='freq' + self.freqtype='w' + self.angletype='' + self.h=np.inf + self.tr=None + self.phi=0. + self.v=0. + self.norm=0 + somekeys = ['angletype', 'phi', 'name', 'h', 'tr', 'freqtype', 'v', 'type', 'norm'] + + self.__dict__.update(sub_dict_select(kwds,somekeys)) + + if self.type.endswith('dir') and self.angletype=='': + self.angletype = 'radians' + + self.setlabels() + + def toacf(self): + pass + def sim(self): + pass + def sim_nl(self): + pass + def rotate(self): + pass + def moment(self,nr=2,vari='xt',even=True): + ''' Calculates spectral moments from spectrum + + Parameters + ---------- + nr : int + order of moments (maximum 4) + vari : string + variables in model, optional when two-dim.spectrum, + string with 'x' and/or 'y' and/or 't' + even : bool + False for all moments, + True for only even orders + + Returns + ------- + m : list of moments + mtext : list of strings describing the elements of m, see below + + Details + ------- + Calculates spectral moments of up to order four by use of + Simpson-integration. + + // + m_jkl=|| k1^j*k2^k*w^l S(w,th) dw dth + // + + where k1=w^2/gravity*cos(th-phi), k2=w^2/gravity*sin(th-phi) + and phi is the angle of the rotation in S.phi. If the spectrum + has field .g, gravity is replaced by S.g. + + The strings in output mtext have the same position in the cell array + as the corresponding numerical value has in output m + Notation in mtext: 'm0' is the variance, + 'mx' is the first-order moment in x, + 'mxx' is the second-order moment in x, + 'mxt' is the second-order cross moment between x and t, + 'myyyy' is the fourth-order moment in y + etc. + For the calculation of moments see Baxevani et al. + + Example: + S=demospec('dir') + [m,mtext]=spec2mom(S,2,'xyt') + + References + ---------- + Baxevani A. et al. (2001) + Velocities for Random Surfaces + ''' + +##% Tested on: Matlab 6.0 +##% Tested on: Matlab 5.3 +##% History: +##% Revised by I.R. 04.04.2001: Introducing the rotation angle phi. +##% Revised by A.B. 23.05.2001: Correcting 'mxxyy' and introducing +##% 'mxxyt','mxyyt' and 'mxytt'. +##% Revised by A.B. 21.10.2001: Correcting 'mxxyt'. +##% Revised by A.B. 21.10.2001: Adding odd-order moments. +##% By es 27.08.1999 + + + pi= np.pi + two_dim_spectra = ['dir','encdir','k2d'] + if self.type not in two_dim_spectra: + raise ValueError('Unknown 2D spectrum type!') + +## if (vari==None and nr<=1: +## vari='x' +## elif vari==None: +## vari='xt' +## else #% secure the mutual order ('xyt') +## vari=''.join(sorted(vari.lower())) +## Nv=len(vari) +## +## if vari[0]=='t' and Nv>1: +## vari = vari[1::]+ vari[0] +## +## Nv = len(vari) +## +## if not self.type.endswith('dir'): +## S1 = self.tospec(self.type[:-2]+'dir') +## else: +## S1 = self; +## w = np.ravel(S1.args[0]) +## theta = S1.args[1]-S1.phi +## S = S1.data +## Sw = simps(S,x=theta) +## m = [simps(Sw,x=w)] +## mtext=['m0'] +## +## if nr>0: +## +## nw=w.size +## if strcmpi(vari(1),'x') +## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).'; +## % integral S*cos(th) dth +## end +## if strcmpi(vari(1),'y') +## Ss=simpson(th,S1.S.*(sin(th)*ones(1,nw))).'; +## % integral S*sin(th) dth +## if strcmpi(vari(1),'x') +## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).'; +## end +## end +## if ~isfield(S1,'g') +## S1.g=gravity; +## end +## kx=w.^2/S1.g(1); % maybe different normalization in x and y => diff. g +## ky=w.^2/S1.g(end); +## +## if Nv>=1 +## switch vari +## case 'x' +## vec = kx.*Sc; +## mtext(end+1)={'mx'}; +## case 'y' +## vec = ky.*Ss; +## mtext(end+1)={'my'}; +## case 't' +## vec = w.*Sw; +## mtext(end+1)={'mt'}; +## end +## else +## vec = [kx.*Sc ky.*Ss w*Sw]; +## mtext(end+(1:3))={'mx', 'my', 'mt'}; +## end +## if nr>1 +## if strcmpi(vari(1),'x') +## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).'; +## % integral S*cos(th) dth +## Sc2=simpson(th,S1.S.*(cos(th).^2*ones(1,nw))).'; +## % integral S*cos(th)^2 dth +## end +## if strcmpi(vari(1),'y')||strcmpi(vari(2),'y') +## Ss=simpson(th,S1.S.*(sin(th)*ones(1,nw))).'; +## % integral S*sin(th) dth +## Ss2=simpson(th,S1.S.*(sin(th).^2*ones(1,nw))).'; +## % integral S*sin(th)^2 dth +## if strcmpi(vari(1),'x') +## Scs=simpson(th,S1.S.*((cos(th).*sin(th))*ones(1,nw))).'; +## % integral S*cos(th)*sin(th) dth +## end +## end +## if ~isfield(S1,'g') +## S1.g=gravity; +## end +## +## if Nv==2 +## switch vari +## case 'xy' +## vec=[kx.*Sc ky.*Ss kx.^2.*Sc2 ky.^2.*Ss2 kx.*ky.*Scs]; +## mtext(end+(1:5))={'mx','my','mxx', 'myy', 'mxy'}; +## case 'xt' +## vec=[kx.*Sc w.*Sw kx.^2.*Sc2 w.^2.*Sw kx.*w.*Sc]; +## mtext(end+(1:5))={'mx','mt','mxx', 'mtt', 'mxt'}; +## case 'yt' +## vec=[ky.*Ss w.*Sw ky.^2.*Ss2 w.^2.*Sw ky.*w.*Ss]; +## mtext(end+(1:5))={'my','mt','myy', 'mtt', 'myt'}; +## end +## else +## vec=[kx.*Sc ky.*Ss w.*Sw kx.^2.*Sc2 ky.^2.*Ss2 w.^2.*Sw kx.*ky.*Scs kx.*w.*Sc ky.*w.*Ss]; +## mtext(end+(1:9))={'mx','my','mt','mxx', 'myy', 'mtt', 'mxy', 'mxt', 'myt'}; +## end +## if nr>3 +## if strcmpi(vari(1),'x') +## Sc3=simpson(th,S1.S.*(cos(th).^3*ones(1,nw))).'; +## % integral S*cos(th)^3 dth +## Sc4=simpson(th,S1.S.*(cos(th).^4*ones(1,nw))).'; +## % integral S*cos(th)^4 dth +## end +## if strcmpi(vari(1),'y')||strcmpi(vari(2),'y') +## Ss3=simpson(th,S1.S.*(sin(th).^3*ones(1,nw))).'; +## % integral S*sin(th)^3 dth +## Ss4=simpson(th,S1.S.*(sin(th).^4*ones(1,nw))).'; +## % integral S*sin(th)^4 dth +## if strcmpi(vari(1),'x') %both x and y +## Sc2s=simpson(th,S1.S.*((cos(th).^2.*sin(th))*ones(1,nw))).'; +## % integral S*cos(th)^2*sin(th) dth +## Sc3s=simpson(th,S1.S.*((cos(th).^3.*sin(th))*ones(1,nw))).'; +## % integral S*cos(th)^3*sin(th) dth +## Scs2=simpson(th,S1.S.*((cos(th).*sin(th).^2)*ones(1,nw))).'; +## % integral S*cos(th)*sin(th)^2 dth +## Scs3=simpson(th,S1.S.*((cos(th).*sin(th).^3)*ones(1,nw))).'; +## % integral S*cos(th)*sin(th)^3 dth +## Sc2s2=simpson(th,S1.S.*((cos(th).^2.*sin(th).^2)*ones(1,nw))).'; +## % integral S*cos(th)^2*sin(th)^2 dth +## end +## end +## if Nv==2 +## switch vari +## case 'xy' +## vec=[vec kx.^4.*Sc4 ky.^4.*Ss4 kx.^3.*ky.*Sc3s ... +## kx.^2.*ky.^2.*Sc2s2 kx.*ky.^3.*Scs3]; +## mtext(end+(1:5))={'mxxxx','myyyy','mxxxy','mxxyy','mxyyy'}; +## case 'xt' +## vec=[vec kx.^4.*Sc4 w.^4.*Sw kx.^3.*w.*Sc3 ... +## kx.^2.*w.^2.*Sc2 kx.*w.^3.*Sc]; +## mtext(end+(1:5))={'mxxxx','mtttt','mxxxt','mxxtt','mxttt'}; +## case 'yt' +## vec=[vec ky.^4.*Ss4 w.^4.*Sw ky.^3.*w.*Ss3 ... +## ky.^2.*w.^2.*Ss2 ky.*w.^3.*Ss]; +## mtext(end+(1:5))={'myyyy','mtttt','myyyt','myytt','myttt'}; +## end +## else +## vec=[vec kx.^4.*Sc4 ky.^4.*Ss4 w.^4.*Sw kx.^3.*ky.*Sc3s ... +## kx.^2.*ky.^2.*Sc2s2 kx.*ky.^3.*Scs3 kx.^3.*w.*Sc3 ... +## kx.^2.*w.^2.*Sc2 kx.*w.^3.*Sc ky.^3.*w.*Ss3 ... +## ky.^2.*w.^2.*Ss2 ky.*w.^3.*Ss kx.^2.*ky.*w.*Sc2s ... +## kx.*ky.^2.*w.*Scs2 kx.*ky.*w.^2.*Scs]; +## mtext(end+(1:15))={'mxxxx','myyyy','mtttt','mxxxy','mxxyy',... +## 'mxyyy','mxxxt','mxxtt','mxttt','myyyt','myytt','myttt','mxxyt','mxyyt','mxytt'}; +## +## end % if Nv==2 ... else ... +## end % if nr>3 +## end % if nr>1 +## m=[m simpson(w,vec)]; +## end % if nr>0 +## % end; %%if Nv==1... else... to be removed +## end % ... else two-dim spectrum + + + + def interp(self): + pass + def normalize(self): + pass + def bandwidth(self): + pass + def setlabels(self): + ''' Set automatic title, x-,y- and z- labels on SPECDATA object + + based on type, angletype, freqtype + ''' + + N = len(self.type); + if N==0: + raise ValueError('Object does not appear to be initialized, it is empty!') + + labels = ['','',''] + if self.type.endswith('dir'): + title = 'Directional Spectrum' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[2] = 'S(w,\theta) [m**2 s / rad**2]' + else: + labels[0] = 'Frequency [Hz]' + labels[2] = 'S(f,\theta) [m**2 s / rad]' + + if self.angletype.startswith('r'): + labels[1] = 'Wave directions [rad]' + elif self.angletype.startswith('d'): + labels[1] = 'Wave directions [deg]' + elif self.type.endswith('freq'): + title = 'Spectral density' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[1] = 'S(w) [m**2 s/ rad]' + else: + labels[0] = 'Frequency [Hz]' + labels[1] = 'S(f) [m**2 s]' + else: + title = 'Wave Number Spectrum' + labels[0] = 'Wave number [rad/m]' + if self.type.endswith('k1d'): + labels[1] = 'S(k) [m**3/ rad]' + elif self.type.endswith('k2d'): + labels[1] = labels[0] + labels[2] = 'S(k1,k2) [m**4/ rad**2]' + else: + raise ValueError('Object does not appear to be initialized, it is empty!') + if self.norm!=0: + title = 'Normalized ' + title + labels[0] = 'Normalized ' + labels[0].split('[')[0] + if not self.type.endswith('dir'): + labels[1] = labels[1].split('[')[0] + labels[2] = labels[2].split('[')[0] + + self.labels.title = title + self.labels.xlab = labels[0] + self.labels.ylab = labels[1] + self.labels.zlab = labels[2] + +class CovData1D(WafoData): + """ Container class for 1D covariance data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + type : string + spectrum type, one of 'freq', 'k1d', 'enc' (default 'freq') + lagtype : letter + lag type, one of: 'x', 'y' or 't' (default 't') + + + Examples + -------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + + See also + -------- + WafoData + CovData + """ + + def __init__(self,*args,**kwds): + super(CovData1D, self).__init__(*args,**kwds) + + self.name='WAFO Covariance Object' + self.type='time' + self.lagtype='t' + self.h=np.inf + self.tr=None + self.phi=0. + self.v=0. + self.norm=0 + somekeys = ['phi', 'name', 'h', 'tr', 'lagtype', 'v', 'type', 'norm'] + + self.__dict__.update(sub_dict_select(kwds,somekeys)) + + #self.setlabels() + def copy(self): + kwds = self.__dict__.copy() + wdata = CovData1D(**kwds) + return wdata + + def tospec(self,rate=None,method='linear',nugget=0.0,trunc=1e-5,fast=True): + '''Computes spectral density from the auto covariance function + + Parameters + ---------- + rate = scalar, int + 1,2,4,8...2^r, interpolation rate for f (default 1) + + method: string + interpolation method 'stineman', 'linear', 'cubic' + + nugget = scalar, real + nugget effect to ensure that round off errors do not result in + negative spectral estimates. Good choice might be 10^-12. + + trunc : scalar, real + truncates all spectral values where S/max(S) < trunc + 0 <= trunc <1 This is to ensure that high frequency + noise is not added to the spectrum. (default 1e-5) + fast : bool + if True : zero-pad to obtain power of 2 length ACF (default) + otherwise no zero-padding of ACF, slower but more accurate. + + Returns + -------- + S = SpecData1D object + spectral density + + NB! This routine requires that the covariance is evenly spaced + starting from zero lag. Currently only capable of 1D matrices. + + Example: + >>> import wafo.spectrum.models as sm + >>> import numpy as np + >>> import scipy.signal.signaltools as st + >>> L = 129 + >>> t = np.linspace(0,75,L) + >>> R = np.zeros(L) + >>> win = st.parzen(41) + >>> R[0:20] = win[20:41] + >>> R0 = CovData1D(R,t) + >>> S0 = R0.tospec() + + >>> Sj = sm.Jonswap() + >>> S = Sj.toSpecData() + >>> R2 = S.toacf() + >>> S1 = R2.tospec() + >>> assert(all(abs(S1.data-S.data)<1e-4) ,'COV2SPEC') + + See also + -------- + spec2cov + datastructures + ''' + + dT = self.sampling_period() + # dT = time-step between data points.(default = T(2)-T1)). + + ACF, ti = np.atleast_1d(self.data,self.args) + + if self.lagtype in 't': + spectype = 'freq' + ftype = 'w' + else: + spectype = 'k1d' + ftype = 'k' + + if rate is None: + rate = 1 #;%interpolation rate + else: + rate = 2**nextpow2(rate) #;%make sure rate is a power of 2 + + + #% add a nugget effect to ensure that round off errors + #% do not result in negative spectral estimates + ACF[0] = ACF[0] +nugget + n = ACF.size + # embedding a circulant vector and Fourier transform + if fast: + nfft = 2**nextpow2(2*n-2) + else: + nfft = 2*n-2 + + nf = nfft/2 #;% number of frequencies + fft = np.fft.fft + ACF = np.r_[ACF,np.zeros(nfft-2*n+2),ACF[n-1:0:-1]] + + Rper = (fft(ACF,nfft).real).clip(0) #% periodogram + RperMax = Rper.max() + Rper = np.where(Rper1: + So.args = np.linspace(0,pi/dT,nf*rate); + if method=='stineman': + So.data = stineman_interp(So.args,w,S) + else: + intfun = interpolate.interp1d(w,S,kind=method) + So.data = intfun(So.args) + So.data = So.data.clip(0) # clip negative values to 0 + + return So + + + + + + def sampling_period(self): + ''' Returns sampling interval + + Returns + --------- + dT : scalar + sampling interval, unit: + [s] if lagtype=='t' + [m] otherwise + + + See also + ''' + dt1 = self.args[1]-self.args[0] + N = np.size(self.args)-1 + T = self.args[-1]-self.args[0] + dt = T/N + + return dt + + def sim(self,ns=None,cases=1,dt=None,iseed=None,derivative=False): + ''' Simulates a Gaussian process and its derivative from ACF + + Parameters + ---------- + ns : scalar + number of simulated points. (default length(S)-1=n-1). + If ns>n-1 it is assummed that R(k)=0 for all k>n-1 + cases : scalar + number of replicates (default=1) + dt : scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : int or state + starting state/seed number for the random number generator + (default none is set) + derivative : bool + if true : return derivative of simulated signal as well + otherwise + + + Returns + ------- + xs = a cases+1 column matrix ( t,X1(t) X2(t) ...). + xsder = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). + + Details + ------- + Performs a fast and exact simulation of stationary zero mean + Gaussian process through circulant embedding of the covariance matrix. + + If the ACF has a non-empty field .tr, then the transformation is + applied to the simulated data, the result is a simulation of a transformed + Gaussian process. + + Note: The simulation may give high frequency ripple when used with a + small dt. + + Example: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap() + >>> S = Sj.toSpecData() #Make spec + >>> R = S.toacf() + >>> x = R.sim(ns=1000,dt=0.2) + + See also + -------- + spec2sdat, gaus2dat + + Reference + ----------- + C.R Dietrich and G. N. Newsam (1997) + "Fast and exact simulation of stationary + Gaussian process through circulant embedding + of the Covariance matrix" + SIAM J. SCI. COMPT. Vol 18, No 4, pp. 1088-1107 + + ''' + + # TODO fix it, it does not work + #% add a nugget effect to ensure that round off errors + #% do not result in negative spectral estimates + nugget=0 #;%10^-12; + + _set_seed(iseed) + + ACF = self.data.ravel() + n = ACF.size + + + I = ACF.argmax() + if I!=0: + raise ValueError('ACF does not have a maximum at zero lag') + + ACF.shape = (n,1) + + dT = self.sampling_period() + + + fft = np.fft.fft + + x=np.zeros((ns,cases+1)) + + + if derivative: + xder=x.copy() + + + #% add a nugget effect to ensure that round off errors + #% do not result in negative spectral estimates + ACF[0]=ACF[0]+nugget; + + #% Fast and exact simulation of simulation of stationary + #% Gaussian process throug circulant embedding of the + #% Covariance matrix + floatinfo = numpy.finfo(float) + if (abs(ACF[-1])>floatinfo.eps): #% assuming ACF(n+1)==0 + m2=2*n-1; + nfft=2**nextpow2(max(m2,2*ns)); + ACF=np.r_[ACF,np.zeros((nfft-m2,1)),ACF[-1:0:-1,:]] + + #disp('Warning: I am now assuming that ACF(k)=0 ') + #disp('for k>MAXLAG.') + + else: # % ACF(n)==0 + m2=2*n-2; + nfft=2**nextpow2(max(m2,2*ns)) + ACF=np.r_[ACF,np.zeros((nfft-m2,1)),ACF[n-1:1:-1,:]] + + #%m2=2*n-2; + + S=fft(ACF,nfft,axis=0).real #;% periodogram + + + I=S.argmax() + k=np.flatnonzero(S<0); + if k.size>0: + #disp('Warning: Not able to construct a nonnegative circulant ') + #disp('vector from the ACF. Apply the parzen windowfunction ') + #disp('to the ACF in order to avoid this.') + #disp('The returned result is now only an approximation.') + + # truncating negative values to zero to ensure that + # that this noise is not added to the simulated timeseries + + S[k] = 0. + + ix = np.flatnonzero(k>2*I) + if ix.size>0: +## % truncating all oscillating values above 2 times the peak +## % frequency to zero to ensure that +## % that high frequency noise is not added to +## % the simulated timeseries. + ix0 = k[ix[0]] + S[ix0:-ix0] =0.0 + + + sqrt = np.sqrt + trunc = 1e-5; + maxS = S[I] + k=np.flatnonzero(S[I:-I]0: + S[k+I]=0. + #% truncating small values to zero to ensure that + #% that high frequency noise is not added to + #% the simulated timeseries + + cases1 = np.floor(cases/2); + cases2 = np.ceil(cases/2); +#% Generate standard normal random numbers for the simulations +#% ----------------------------------------------------------- + randn = np.random.randn + epsi = randn(nfft,cases2)+1j*randn(nfft,cases2); + Ssqr=sqrt(S/(nfft)) #; %sqrt(S(wn)*dw ) + ephat=epsi*Ssqr[:,np.newaxis] + y=fft(ephat,nfft); + x[:,1:cases+1]=np.hstack((y[2:ns+2,0:cases2].real, y[2:ns+2,0:cases1].imag)) + + + + x[:,0]=np.linspace(0,(ns-1)*dT,ns) #%(0:dT:(dT*(np-1)))'; + + if derivative: + Ssqr = Ssqr*np.r_[0:(nfft/2+1),-(nfft/2-1):0]*2*np.pi/nfft/dT + ephat = epsi*Ssqr[:,np.newaxis] + y = fft(ephat,nfft); + xder[:,1:(cases+1)]= np.hstack((y[2:ns+2,0:cases2].imag -y[2:ns+2,0:cases1].real)) + xder[:,0]=x[:,0] + + if self.tr is not None: + np.disp(' Transforming data.') + g=self.tr; + G=np.fliplr(g); #% the invers of g + if derivative: + for ix in range(cases): + tmp=tranproc(np.hstack((x[:,ix+1], xder[:,ix+1])),G); + x[:,ix+1]=tmp[:,0]; + xder[:,ix+1]=tmp[:,1]; + + else: + for ix in range(cases): + x[:,ix+1]=tranproc(x[:,ix+1],G); + + if derivative: + return x,xder + else: + return x + + + +class TimeSeries(WafoData): + ''' Container class for 1D TimeSeries data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + type : integer or string + sensor type for time series (default 'n' : Surface elevation) + see sensortype for more options + position : vector of size 3 + instrument position relative to the coordinate system + + ''' + def __init__(self,*args,**kwds): + super(TimeSeries, self).__init__(*args,**kwds) + self.name='WAFO TimeSeries Object' + self.type='n' + self.position = np.zeros(3) + somekeys = ['type', 'position'] + self.__dict__.update(sub_dict_select(kwds,somekeys)) + + #self.setlabels() + if not any(self.args): + n = len(self.data) + self.args = xrange(0,n) + + def sampling_period(self): + ''' Returns sampling interval + + Returns + --------- + dT : scalar + sampling interval, unit: + [s] if lagtype=='t' + [m] otherwise + + + See also + ''' + dt1 = self.args[1]-self.args[0] + N = np.size(self.args)-1 + T = self.args[-1]-self.args[0] + dt = T/N + + return dt + + def acf(self,lag=None,flag='biased',norm=False,dt = None): + ''' Return auto covariance function from data. + + + R = ACF vector length L+1 + t = time lags length L+1 + stdev = estimated large lag standard deviation of the estimate + assuming x is a Gaussian process: + if R(k)=0 for all lags k>q then an approximation + of the variance for large samples due to Bartlett + var(R(k))=1/N*(R(0)^2+2*R(1)^2+2*R(2)^2+ ..+2*R(q)^2) + for k>q and where N=length(x). Special case is + white noise where it equals R(0)^2/N for k>0 + norm = 0 indicating that R is not normalized + + x = a column data vector or two column data matrix with sampled times and values. + L = the maximum time-lag for which the ACF is estimated. + (Default L=n-1) + plotflag = 1 then the ACF is plotted vs lag + 2 then the ACF is plotted vs lag in seconds + 3 then the ACF is plotted vs lag and vs lag (sec + dT = time-step between data points (default xn(2,1)-xn(1,1) or 1 Hz). + flag = 'biased' : scales the raw cross-correlation by 1/n. (default) + 'unbiased': scales the raw correlation by 1/(n-abs(k)), + where k is the index into the result. + + + - x may contain NaN's (i.e. missing values). + + Example: + x = load('sea.dat'); + rf = dat2cov(x,150,2) + ''' + n = len(self.data) + if not lag: + lag = n-1 + + x = self.data.copy() + indnan = numpy.isnan(x) + if any(indnan): + x = x - numpy.mean(x[1-indnan]) # remove the mean pab 09.10.2000 + #indnan = find(indnan); + Ncens = n - sum(indnan) + x[indnan] = 0. # pab 09.10.2000 much faster for censored samples + else: + indnan = None + Ncens = n + x = x - numpy.mean(x) + + fft = numpy.fft.fft + nfft = 2**nextpow2(n) + Rper = abs(fft(x,nfft))**2/Ncens # Raw periodogram + + R = numpy.real(fft(Rper))/nfft # %ifft=fft/nfft since Rper is real! + lags = np.arange(0,lag+1) + if flag.startswith('unbiased'): + # unbiased result, i.e. divide by n-abs(lag) + R=R[lags]*Ncens/ np.arange(Ncens,Ncens-lag,-1) + #else % biased result, i.e. divide by n + # r=r(1:L+1)*Ncens/Ncens; + + #c0 = R[0] + dT = self.sampling_period() + t = numpy.linspace(0,lag*dT,lag+1) + cumsum = numpy.cumsum + acf = CovData1D(R[lags],t) + acf.stdev=numpy.sqrt(numpy.r_[ 0, 1 ,1+2*cumsum(R[1:]**2)]/Ncens) + acf.children = [WafoData(-2.*acf.stdev[lags],t),WafoData(2.*acf.stdev[lags],t)] + return acf + + def spec(self): + pass + def turning_points(self,h=0,wavetype=None,output='tp'): + ''' Return turning points (tp) from data, optionally rainflowfiltered. + + Parameters + ---------- + h : scalar + a threshold; + if h<0, then tp=x; + if h=0, then tp is a sequence of turning points (default); + if h>0, then all rainflow cycles with height smaller than + h are removed. + + wavetype : string + defines the type of wave. Possible options are + 'mw' 'Mw' or 'none'. + If None all rainflow filtered min and max + will be returned, otherwise only the rainflow filtered + min and max, which define a wave according to the + wave definition, will be returned. + output : string + 'tp' if only returning tp + 'all' if tp and ind + + Returns + ------- + tp : TimeSeries object + with times and turning points. + + ind : arraylike + indices to the turning points in the original sequence. + + + Example: + x = load('sea.dat'); x1 = x(1:200,:); + tp = dat2tp(x1,0,'Mw'); tph = dat2tp(x1,0.3,'Mw'); + plot(x1(:,1),x1(:,2),tp(:,1),tp(:,2),'ro',tph(:,1),tph(:,2),'k*') + + See also + --------- + findcross, findrfc + ''' + + if h<0: + tp = self.copy() + ind = np.arange(tp.args.size) + if output.startswith('tp'): + return tp + else: + return tp, ind + x2 = self.data + + n = len(x2) + ind = findextrema(x2) + + if ind.size<2: + tp = None + ind = None + return tp + + + #% In order to get the exact up-crossing intensity from rfc by + #% mm2lc(tp2mm(rfc)) we have to add the indices + #% to the last value (and also the first if the + #% sequence of turning points does not start with a minimum). + + if x2[ind[0]]>x2[ind[1]]: + #% adds indices to first and last value + ind = np.r_[0, ind ,n] + else: # adds index to the last value + ind = np.r_[ind, n] + + + if h>0: + ind1 = findrfc(x2[ind],h) + ind = ind[ind1] + + Nm =ind.size #% number of min and Max + + if wavetype in ('mw','Mw'): + + xor = lambda a,b : a^b + #% make sure that the first is a Max if wdef == 'Mw' + #% or make sure that the first is a min if wdef == 'mw' + removeFirst = xor((x2[ind[0]]>x2[ind[1]]),wavetype.startswith('Mw')) + if removeFirst: + ind = ind[1::] + Nm = Nm-1; + + + #% make sure the number of minima and Maxima are according to the wavedef. + #% i.e., make sure Nm=length(ind) is odd + if (mod(Nm,2))!=1: + ind = ind[:-1] + Nm = Nm-1 + try: + t = self.args + except: + t = ind + tp = TimeSeries(self.data[ind],t) + + return tp + + def lc_spectrum(self): + pass + def cycles(self): + pass + def trough_crest(self): + pass + def wave_period(self): + pass + def reconstruct(self): + pass + def plot_wave_idx(self): + ''' spwaveplot + ''' + pass + def findoutliers(self): + pass + + +def sensortypeid(*sensortypes): + ''' Return ID for sensortype name + + Parameter + --------- + sensortypes : list of strings defining the sensortype + + Returns + ------- + sensorids : list of integers defining the sensortype + + Valid senor-ids and -types for time series are as follows: + 0, 'n' : Surface elevation (n=Eta) + 1, 'n_t' : Vertical surface velocity + 2, 'n_tt' : Vertical surface acceleration + 3, 'n_x' : Surface slope in x-direction + 4, 'n_y' : Surface slope in y-direction + 5, 'n_xx' : Surface curvature in x-direction + 6, 'n_yy' : Surface curvature in y-direction + 7, 'n_xy' : Surface curvature in xy-direction + 8, 'P' : Pressure fluctuation about static MWL pressure + 9, 'U' : Water particle velocity in x-direction + 10, 'V' : Water particle velocity in y-direction + 11, 'W' : Water particle velocity in z-direction + 12, 'U_t' : Water particle acceleration in x-direction + 13, 'V_t' : Water particle acceleration in y-direction + 14, 'W_t' : Water particle acceleration in z-direction + 15, 'X_p' : Water particle displacement in x-direction from its mean position + 16, 'Y_p' : Water particle displacement in y-direction from its mean position + 17, 'Z_p' : Water particle displacement in z-direction from its mean position + + Example: + >>> sensortypeid('W','v') + [11, 10] + >>> sensortypeid('rubbish') + [-1.#IND] + + See also sensortype, id + ''' + + sensorid_table = dict(n=0,n_t=1,n_tt=2,n_x=3,n_y=4,n_xx=5, + n_yy=6,n_xy=7,p=8,u=9,v=10,w=11,u_t=12, + v_t=13,w_t=14,x_p=15,y_p=16,z_p=17) + try: + return [sensorid_table.get(name.lower(),np.NAN) for name in sensortypes] + except: + raise ValueError('Input must be a string!') + + + +def sensortype(*sensorids): + ''' Return sensortype name + + Parameter + --------- + sensorids : vector or list of integers defining the sensortype + + Returns + ------- + sensornames : list of strings defining the sensortype + + Valid senor-ids and -types for time series are as follows: + 0, 'n' : Surface elevation (n=Eta) + 1, 'n_t' : Vertical surface velocity + 2, 'n_tt' : Vertical surface acceleration + 3, 'n_x' : Surface slope in x-direction + 4, 'n_y' : Surface slope in y-direction + 5, 'n_xx' : Surface curvature in x-direction + 6, 'n_yy' : Surface curvature in y-direction + 7, 'n_xy' : Surface curvature in xy-direction + 8, 'P' : Pressure fluctuation about static MWL pressure + 9, 'U' : Water particle velocity in x-direction + 10, 'V' : Water particle velocity in y-direction + 11, 'W' : Water particle velocity in z-direction + 12, 'U_t' : Water particle acceleration in x-direction + 13, 'V_t' : Water particle acceleration in y-direction + 14, 'W_t' : Water particle acceleration in z-direction + 15, 'X_p' : Water particle displacement in x-direction from its mean position + 16, 'Y_p' : Water particle displacement in y-direction from its mean position + 17, 'Z_p' : Water particle displacement in z-direction from its mean position + + Example: + >>> sensortype(range(3)) + ['n', 'n_t', 'n_tt'] + + See also sensortypeid, tran + ''' + + + + validNames = ('n','n_t','n_tt','n_x','n_y','n_xx', + 'n_yy','n_xy','p','u','v','w','u_t', + 'v_t','w_t','x_p','y_p','z_p',np.NAN) + ids = np.atleast_1d(*sensorids) + if isinstance(ids,list): + ids = np.hstack(ids) + N = len(validNames)-1 + + try: + return [validNames[id] for id in ids.clip(0,N)] + except: + raise ValueError('Input must be an integer!') + + +def main(): + from wafo.spectrum import models as sm + sensortype(range(21)) + w = np.linspace(0,3,100) + Sj = sm.Jonswap() + S = Sj.toSpecData() + #S = SpecData1D(Sj(w),w) + R = S.toacf(nr=1) + S1 = S.copy() + Si = R.tospec() + ns =5000; + dt = .2; + x1 = S.sim_nl(ns= ns,dt=dt); + x2 = TimeSeries(x1[:,1],x1[:,0]) + R = x2.acf(lag=100) + R.plot() + + S.plot('ro') + t = S.moment() + t1 = S.bandwidth([0,1,2,3]) + S1 = S.copy() + S1.resample(dt=0.3,method='cubic') + S1.plot('k+') + x = S1.sim(ns=100) + import pylab + pylab.clf() + pylab.plot(x[:,0],x[:,1]) + pylab.show() + + pylab.close('all') + np.disp('done') + + +if __name__ == '__main__': + if False: #True: # + import doctest + doctest.testmod() + else: + #main() + import wafo.spectrum.models as sm + Sj = sm.Jonswap(); + S = Sj.toSpecData(); + + R = S.toacf() + x = R.sim(ns=1000,dt=0.2) + S.characteristic(['hm0','tm02']) + ns =1000; dt = .2; + x1 = S.sim_nl(ns,dt=dt); + + x = np.arange(-2,2,0.2) + + # Plot 2 objects in one call + d2 = WafoData(np.sin(x),x,xlab='x',ylab='sin',title='sinus') + + + d0 = d2.copy() + d0.data = d0.data*0.9 + d1 = d2.copy() + d1.data = d1.data*1.2 + d1.children = [d0] + d2.children = [d1] + + d2.plot() + print 'Done' \ No newline at end of file diff --git a/wafo/dctpack.py b/wafo/dctpack.py new file mode 100755 index 0000000..3ea245f --- /dev/null +++ b/wafo/dctpack.py @@ -0,0 +1,107 @@ +import numpy as np +__all__ = ['dct', 'idct'] +def dct(x, n=None): + """ + Discrete Cosine Transform + + N-1 + y[k] = 2* sum x[n]*cos(pi*k*(2n+1)/(2*N)), 0 <= k < N. + n=0 + + Examples + -------- + >>> import numpy as np + >>> x = np.arange(5) + >>> np.abs(x-idct(dct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + >>> np.abs(x-dct(idct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + + Reference + --------- + http://en.wikipedia.org/wiki/Discrete_cosine_transform + http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/ + """ + fft = np.fft.fft + x = np.atleast_1d(x) + + if n is None: + n = x.shape[-1] + + if x.shape[-1] < n: + n_shape = x.shape[:-1] + (n - x.shape[-1],) + xx = np.hstack((x, np.zeros(n_shape))) + else: + xx = x[..., :n] + + real_x = np.all(np.isreal(xx)) + if (real_x and (np.remainder(n, 2) == 0)): + xp = 2 * fft(np.hstack((xx[..., ::2], xx[..., ::-2]))) + else: + xp = fft(np.hstack((xx, xx[..., ::-1]))) + xp = xp[..., :n] + + w = np.exp(-1j * np.arange(n) * np.pi / (2 * n)) + + y = xp * w + + if real_x: + return y.real + else: + return y + +def idct(x, n=None): + """ + Inverse Discrete Cosine Transform + + N-1 + x[k] = 1/N sum w[n]*y[n]*cos(pi*k*(2n+1)/(2*N)), 0 <= k < N. + n=0 + + w(0) = 1/2 + w(n) = 1 for n>0 + + Examples + -------- + >>> import numpy as np + >>> x = np.arange(5) + >>> np.abs(x-idct(dct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + >>> np.abs(x-dct(idct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + + Reference + --------- + http://en.wikipedia.org/wiki/Discrete_cosine_transform + http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/ + """ + + ifft = np.fft.ifft + x = np.atleast_1d(x) + + if n is None: + n = x.shape[-1] + + w = np.exp(1j * np.arange(n) * np.pi / (2 * n)) + + if x.shape[-1] < n: + n_shape = x.shape[:-1] + (n - x.shape[-1],) + xx = np.hstack((x, np.zeros(n_shape))) * w + else: + xx = x[..., :n] * w + + real_x = np.all(np.isreal(x)) + if (real_x and (np.remainder(n, 2) == 0)): + xx[..., 0] = xx[..., 0] * 0.5 + yp = ifft(xx) + y = np.zeros(xx.shape, dtype=complex) + y[..., ::2] = yp[..., :n / 2] + y[..., ::-2] = yp[..., n / 2::] + else: + yp = ifft(np.hstack((xx, np.zeros_like(xx[..., 0]), np.conj(xx[..., :0:-1])))) + y = yp[..., :n] + + if real_x: + return y.real + else: + return y diff --git a/wafo/definitions.py b/wafo/definitions.py new file mode 100755 index 0000000..a6474e1 --- /dev/null +++ b/wafo/definitions.py @@ -0,0 +1,284 @@ +""" +WAFO defintions and numenclature + +crossings : +cycle_pairs : +turning_points : +wave_amplitudes : +wave_periods : +waves : +""" +def wave_amplitudes(): + r""" + Wave amplitudes and heights definitions and nomenclature + + Definition of wave amplitudes and wave heights + --------------------------------------------- + + <----- Direction of wave propagation + + + |..............c_..........| + | /| \ | + Hd | _/ | \ | Hu + M | / | \ | + / \ | M / Ac | \_ | c_ + F \ | / \m/ | \ | / \ + ------d----|---u------------------d---|---u----d------ level v + \ | /| \ | / \L + \_ | / | At \_|_/ + \|/..| t + t + + Parameters + ---------- + Ac : crest amplitude + At : trough amplitude + Hd : wave height as defined for down crossing waves + Hu : wave height as defined for up crossing waves + + See also + -------- + waves, crossings, turning_points + """ + print(wave_amplitudes.__doc__) + +def crossings(): + r""" + Level v crossing definitions and nomenclature + + Definition of level v crossings + ------------------------------- + M + . . M M + . . . . . . + F d . . L + -----------------------u-------d-------o----------------- level v + . . . . u + . m + m + + Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the + figure above denote local minimum, maximum, first value, last + value, down- and up-crossing, respectively. The remaining + sampled values are indicated with a '.'. Values that are identical + with v, but do not cross the level is indicated with the letter 'o'. + We have a level up-crossing at index, k, if + + x(k) < v and v < x(k+1) + or if + x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 + + where di is the index to the previous downcrossing. + Similarly there is a level down-crossing at index, k, if + + x(k) > v and v > x(k+1) + or if + x(k) == v and v > x(k+1) and x(r) > v for some ui < r <= k-1 + + where ui is the index to the previous upcrossing. + + The first (F) value is a up crossing if x(1) = v and x(2) > v. + Similarly, it is a down crossing if x(1) = v and x(2) < v. + + See also + -------- + wave_periods, waves, turning_points, findcross, findtp + """ + print(crossings.__doc__) + +def cycle_pairs(): + r""" + Cycle pairs definitions and numenclature + + Definition of Max2min and min2Max cycle pair + -------------------------------------------- + A min2Max cycle pair (mM) is defined as the pair of a minimum + and the following Maximum. Similarly a Max2min cycle pair (Mm) + is defined as the pair of a Maximum and the following minimum. + (all turning points possibly rainflowfiltered before pairing into cycles.) + + See also + -------- + turning_points + """ + print(cycle_pairs.__doc__) + +def wave_periods(): + r""" + Wave periods (lengths) definitions and nomenclature + + Definition of wave periods (lengths) + ------------------------------------ + + + <----- Direction of wave propagation + + <-------Tu---------> + : : + <---Tc-----> : + : : : <------Tcc----> + M : c : : : : + / \ : M / \_ : : c_ c + F \ :/ \m/ \: :/ \ / \ + ------d--------u----------d-------u----d--------u---d-------- level v + \ / \ / :\_ _/: :\_ L + \_ / \_t_/ : \t_/ : : \m/ + \t/ : : : : + : : <---Tt---> : + <--------Ttt-------> : : + <-----Td-----> + Tu = Up crossing period + Td = Down crossing period + Tc = Crest period, i.e., period between up crossing and + the next down crossing + Tt = Trough period, i.e., period between down crossing and + the next up crossing + Ttt = Trough2trough period + Tcc = Crest2crest period + + + <----- Direction of wave propagation + + <--Tcf-> Tuc + : : <-Tcb-> <-> + M : c : : : : + / \ : M / \_ c_ : : c + F \ :/ \m/ \ / \___: :/ \ + ------d---------u----------d---------u-------d--------u---d------ level v + :\_ / \ __/: \_ _/ \_ L + : \_ / \_t_/ : \t_/ \m/ + : \t/ : : + : : : : + <-Ttf-> <-Ttb-> + + + Tcf = Crest front period, i.e., period between up crossing and crest + Tcb = Crest back period, i.e., period between crest and down crossing + Ttf = Trough front period, i.e., period between down crossing and trough + Ttb = Trough back period, i.e., period between trough and up crossing + Also note that Tcf and Ttf can also be abbreviated by their crossing + marker, e.g. Tuc (u2c) and Tdt (d2t), respectively. Similar applies + to all the other wave periods and wave lengths. + + (The nomenclature for wave length is similar, just substitute T and + period with L and length, respectively) + + <----- Direction of wave propagation + + <--TMm--> + <-TmM-> : : + M : : M : + / \ : M /:\_ : M_ M + F \ : / \m/ : \ : /: \ / \ + \ : / : \ : / : \ / \ + \ : / : \ : / : \_ _/ \_ L + \_ : / : \_m_/ : \m_/ \m/ + \m/ : : : : + <-----TMM-----> <----Tmm-----> + + + TmM = Period between minimum and the following Maximum + TMm = Period between Maximum and the following minimum + TMM = Period between Maximum and the following Maximum + Tmm = Period between minimum and the following minimum + + See also + -------- + waves, + wave_amplitudes, + crossings, + turning_points + """ + print(wave_periods.__doc__) +def turning_points(): + r""" + Turning points definitions and numenclature + + Definition of turningpoints + --------------------------- + <----- Direction of wave propagation + + M M + / \ .... M /:\_ M_ M + F \ | / \m/ : \ /: \ / \ + \ h | / : \ / : \ / \ + \ | / : \ / : \_ _/ \_ L + \_ | / : \_m_/ : \m_/ \m/ + \m/ : : : : + <------Mw-----> <-----mw-----> + + Local minimum or maximum are indicated with the + letters 'm' or 'M'. Turning points in this connection are all + local max (M) and min (m) and the last (L) value and the + first (F) value if the first local extremum is a max. + + (This choice is made in order to get the exact up-crossing intensity + from rfc by mm2lc(tp2mm(rfc)) ) + + + See also + -------- + waves, + crossings, + cycle_pairs + findtp + + """ + print(turning_points.__doc__) +def waves(): + r""" + Wave definitions and nomenclature + + Definition of trough and crest + ------------------------------ + A trough (t) is defined as the global minimum between a + level v down-crossing (d) and the next up-crossing (u) + and a crest (c) is defined as the global maximum between a + level v up-crossing and the following down-crossing. + + Definition of down- and up -crossing waves + ------------------------------------------ + A level v-down-crossing wave (dw) is a wave from a + down-crossing to the following down-crossing. + Similarly, a level v-up-crossing wave (uw) is a wave from an up-crossing + to the next up-crossing. + + Definition of trough and crest waves + ------------------------------------ + A trough-to-trough wave (tw) is a wave from a trough (t) to the + following trough. The crest-to-crest wave (cw) is defined similarly. + + + Definition of min2min and Max2Max wave + -------------------------------------- + A min2min wave (mw) is defined starting from a minimum (m) and + ending in the following minimum. + Similarly a Max2Max wave (Mw) is thus a wave from a maximum (M) + to the next maximum (all waves optionally rainflow filtered). + + <----- Direction of wave propagation + + + <------Mw-----> <----mw----> + M : : c : + / \ M : / \_ : c_ c + F \ / \m/ \ : /: \ /:\ + ------d--------u----------d-------u----d--------u---d------ level v + \ /: \ : /: : :\_ _/ : :\_ L + \_ / : \_t_/ : : : \t_/ : : \m/ + \t/ <-------uw---------> : <-----dw-----> + : : : : + <--------tw--------> <------cw-----> + + (F=first value and L=last value). + + See also + -------- + turning_points, + crossings, + wave_periods + findtc, + findcross + """ + print(waves.__doc__) \ No newline at end of file diff --git a/wafo/definitions.~py b/wafo/definitions.~py new file mode 100755 index 0000000..1ec1a24 --- /dev/null +++ b/wafo/definitions.~py @@ -0,0 +1,281 @@ +""" +WAFO defintions and numenclature + +crossings : +cycle_pairs : +turning_points : +wave_amplitudes : +wave_periods : +waves : +""" +def wave_amplitudes(): + """ + Wave amplitudes and heights definitions and nomenclature + + Definition of wave amplitudes and wave heights + --------------------------------------------- + + <----- Direction of wave propagation + + + ...............c_.......... + | /| \ | + Hd | _/ | \ | Hu + M | / | \ | + / \ | M / Ac | \_ | c_ + F \ | / \m/ | \ | / \ + ------d----|---u------------------d---|---u----d------ level v + \ | /| \ | / \L + \_ | / | At \_|_/ + \|/..| t + t + + Parameters + ---------- + Ac : crest amplitude + At : trough amplitude + Hd : wave height as defined for down crossing waves + Hu : wave height as defined for up crossing waves + + See also + -------- + waves, crossings, turning_points + """ + pass +def crossings(): + """ + Level v crossing definitions and nomenclature + + Definition of level v crossings + ------------------------------- + M + . . M M + . . . . . . + F d . . L + -----------------------u-------d-------o----------------- level v + . . . . u + . m + m + + Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the + figure above denote local minimum, maximum, first value, last + value, down- and up-crossing, respectively. The remaining + sampled values are indicated with a '.'. Values that are identical + with v, but do not cross the level is indicated with the letter 'o'. + We have a level up-crossing at index, k, if + + x(k) < v and v < x(k+1) + or if + x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 + + where di is the index to the previous downcrossing. + Similarly there is a level down-crossing at index, k, if + + x(k) > v and v > x(k+1) + or if + x(k) == v and v > x(k+1) and x(r) > v for some ui < r <= k-1 + + where ui is the index to the previous upcrossing. + + The first (F) value is a up crossing if x(1) = v and x(2) > v. + Similarly, it is a down crossing if x(1) = v and x(2) < v. + + See also + -------- + wave_periods, waves, turning_points, findcross, findtp + """ + pass +def cycle_pairs(): + """ + Cycle pairs definitions and numenclature + + Definition of Max2min and min2Max cycle pair + -------------------------------------------- + A min2Max cycle pair (mM) is defined as the pair of a minimum + and the following Maximum. Similarly a Max2min cycle pair (Mm) + is defined as the pair of a Maximum and the following minimum. + (all turning points possibly rainflowfiltered before pairing into cycles.) + + See also + -------- + turning_points + """ + pass +def wave_periods(): + """ + Wave periods (lengths) definitions and nomenclature + + Definition of wave periods (lengths) + ------------------------------------ + + + <----- Direction of wave propagation + + <-------Tu---------> + : : + <---Tc-----> : + : : : <------Tcc----> + M : c : : : : + / \ : M / \_ : : c_ c + F \ :/ \m/ \: :/ \ / \ + ------d--------u----------d-------u----d--------u---d-------- level v + \ / \ / :\_ _/: :\_ L + \_ / \_t_/ : \t_/ : : \m/ + \t/ : : : : + : : <---Tt---> : + <--------Ttt-------> : : + <-----Td-----> + Tu = Up crossing period + Td = Down crossing period + Tc = Crest period, i.e., period between up crossing and + the next down crossing + Tt = Trough period, i.e., period between down crossing and + the next up crossing + Ttt = Trough2trough period + Tcc = Crest2crest period + + + <----- Direction of wave propagation + + <--Tcf-> Tuc + : : <-Tcb-> <-> + M : c : : : : + / \ : M / \_ c_ : : c + F \ :/ \m/ \ / \___: :/ \ + ------d---------u----------d---------u-------d--------u---d------ level v + :\_ / \ __/: \_ _/ \_ L + : \_ / \_t_/ : \t_/ \m/ + : \t/ : : + : : : : + <-Ttf-> <-Ttb-> + + + Tcf = Crest front period, i.e., period between up crossing and crest + Tcb = Crest back period, i.e., period between crest and down crossing + Ttf = Trough front period, i.e., period between down crossing and trough + Ttb = Trough back period, i.e., period between trough and up crossing + Also note that Tcf and Ttf can also be abbreviated by their crossing + marker, e.g. Tuc (u2c) and Tdt (d2t), respectively. Similar applies + to all the other wave periods and wave lengths. + + (The nomenclature for wave length is similar, just substitute T and + period with L and length, respectively) + + <----- Direction of wave propagation + + <--TMm--> + <-TmM-> : : + M : : M : + / \ : M /:\_ : M_ M + F \ : / \m/ : \ : /: \ / \ + \ : / : \ : / : \ / \ + \ : / : \ : / : \_ _/ \_ L + \_ : / : \_m_/ : \m_/ \m/ + \m/ : : : : + <-----TMM-----> <----Tmm-----> + + + TmM = Period between minimum and the following Maximum + TMm = Period between Maximum and the following minimum + TMM = Period between Maximum and the following Maximum + Tmm = Period between minimum and the following minimum + + See also + -------- + waves, + wave_amplitudes, + crossings, + turning_points + """ + pass +def turning_points(): + """ + Turning points definitions and numenclature + + Definition of turningpoints + --------------------------- + <----- Direction of wave propagation + + M M + / \ .... M /:\_ M_ M + F \ | / \m/ : \ /: \ / \ + \ h | / : \ / : \ / \ + \ | / : \ / : \_ _/ \_ L + \_ | / : \_m_/ : \m_/ \m/ + \m/ : : : : + <------Mw-----> <-----mw-----> + + Local minimum or maximum are indicated with the + letters 'm' or 'M'. Turning points in this connection are all + local max (M) and min (m) and the last (L) value and the + first (F) value if the first local extremum is a max. + + (This choice is made in order to get the exact up-crossing intensity + from rfc by mm2lc(tp2mm(rfc)) ) + + + See also + -------- + waves, + crossings, + cycle_pairs + findtp + + """ + pass +def waves(): + """ + Wave definitions and nomenclature + + Definition of trough and crest + ------------------------------ + A trough (t) is defined as the global minimum between a + level v down-crossing (d) and the next up-crossing (u) + and a crest (c) is defined as the global maximum between a + level v up-crossing and the following down-crossing. + + Definition of down- and up -crossing waves + ------------------------------------------ + A level v-down-crossing wave (dw) is a wave from a + down-crossing to the following down-crossing. + Similarly, a level v-up-crossing wave (uw) is a wave from an up-crossing + to the next up-crossing. + + Definition of trough and crest waves + ------------------------------------ + A trough-to-trough wave (tw) is a wave from a trough (t) to the + following trough. The crest-to-crest wave (cw) is defined similarly. + + + Definition of min2min and Max2Max wave + -------------------------------------- + A min2min wave (mw) is defined starting from a minimum (m) and + ending in the following minimum. + Similarly a Max2Max wave (Mw) is thus a wave from a maximum (M) + to the next maximum (all waves optionally rainflow filtered). + + <----- Direction of wave propagation + + + <------Mw-----> <----mw----> + M : : c : + / \ M : / \_ : c_ c + F \ / \m/ \ : /: \ /:\ + ------d--------u----------d-------u----d--------u---d------ level v + \ /: \ : /: : :\_ _/ : :\_ L + \_ / : \_t_/ : : : \t_/ : : \m/ + \t/ <-------uw---------> : <-----dw-----> + : : : : + <--------tw--------> <------cw-----> + + (F= first value and L=last value). + + See also + -------- + turning_points, + crossings, + wave_periods + findtc, + findcross + """ + pass \ No newline at end of file diff --git a/wafo/demo_sg.py b/wafo/demo_sg.py new file mode 100755 index 0000000..1f70688 --- /dev/null +++ b/wafo/demo_sg.py @@ -0,0 +1,43 @@ +from pylab import subplot, plot, title, savefig, figure, arange, sin, random #@UnresolvedImport +from sg_filter import calc_coeff, smooth + + +figure(figsize=(7,12)) + + +# generate chirp signal +tvec = arange(0, 6.28, .02) +signal = sin(tvec*(2.0+tvec)) + +# add noise to signal +noise = random.normal(size=signal.shape) +signal += (2000.+.15 * noise) + +# plot signal +subplot(311) +plot(signal) +title('signal') + +# smooth and plot signal +subplot(312) +coeff = calc_coeff(8, 4) +s_signal = smooth(signal, coeff) + +plot(s_signal) +title('smoothed signal') + +# smooth derivative of signal and plot it +subplot(313) +coeff = calc_coeff(8, 1, 1) +d_signal = smooth(signal, coeff) + +plot(d_signal) +title('smoothed derivative of signal') + +# show plot +savefig("savitzky.png") + + + + + diff --git a/wafo/diffsumfunq.pyd b/wafo/diffsumfunq.pyd new file mode 100755 index 0000000..6632819 Binary files /dev/null and b/wafo/diffsumfunq.pyd differ diff --git a/wafo/diffsumfunq.pyf b/wafo/diffsumfunq.pyf new file mode 100755 index 0000000..c8eb2c0 --- /dev/null +++ b/wafo/diffsumfunq.pyf @@ -0,0 +1,30 @@ +! File diffsumfunq.pyf +python module diffsumfunq +interface + 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==shape(iA,0)) :: n=shape(rA,0) + 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), 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==shape(iA,0)) :: n=shape(rA,0) + 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), 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 disufq + +end interface +end python module diffsumfunq \ No newline at end of file diff --git a/wafo/disufq.pyf b/wafo/disufq.pyf new file mode 100755 index 0000000..c8eb2c0 --- /dev/null +++ b/wafo/disufq.pyf @@ -0,0 +1,30 @@ +! File diffsumfunq.pyf +python module diffsumfunq +interface + 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==shape(iA,0)) :: n=shape(rA,0) + 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), 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==shape(iA,0)) :: n=shape(rA,0) + 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), 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 disufq + +end interface +end python module diffsumfunq \ No newline at end of file diff --git a/wafo/disufq1.c b/wafo/disufq1.c new file mode 100755 index 0000000..cae7868 --- /dev/null +++ b/wafo/disufq1.c @@ -0,0 +1,446 @@ +#include "math.h" +/* + * 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 *(y1+1)){ /* if first is a max*/ + y=&(*(y1+1)); /* ignore the first max*/ + NC=floor((n-1)/2); + Tstart=2; + } + else { + y=y1; + NC=floor(n/2); + Tstart=1; + } + + if (NC<1){ + info = 0; + return; /* No RFC cycles*/ + } + + + if (( *(y+0) > *(y+1)) && ( *(y+1) > *(y+2)) ){ + info = -1; + return; /*This is not a sequence of turningpoints, exit */ + } + if ((*(y+0) < *(y+1)) && (*(y+1)< *(y+2))){ + info=-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 = ix; + return ; +} + + + diff --git a/wafo/gaussian.py b/wafo/gaussian.py new file mode 100755 index 0000000..1f616a5 --- /dev/null +++ b/wafo/gaussian.py @@ -0,0 +1,367 @@ +import numpy as np +from numpy import (r_, minimum, maximum, atleast_1d, atleast_2d, mod, zeros, #@UnresolvedImport + ones, floor, random, eye, nonzero, repeat, sqrt, inf, diag, triu) #@UnresolvedImport +from scipy.special import ndtri as invnorm +import rindmod + + +class Rind(object): + ''' + RIND Computes multivariate normal expectations + + Parameters + ---------- + S : array-like, shape Ntdc x Ntdc + Covariance matrix of X=[Xt,Xd,Xc] (Ntdc = Nt+Nd+Nc) + m : array-like, size Ntdc + expectation of X=[Xt,Xd,Xc] + Blo, Bup : array-like, shape Mb x Nb + Lower and upper barriers used to compute the integration limits, Hlo and Hup, respectively. + indI : array-like, length Ni + vector of indices to the different barriers in the indicator function. + (NB! restriction indI(1)=0, indI(NI)=Nt+Nd, Ni = Nb+1) + (default indI = 0:Nt+Nd) + xc : values to condition on (default xc = zeros(0,1)), size Nc x Nx + Nt : size of Xt (default Nt = Ntdc - Nc) + + Returns + ------- + val: ndarray, size Nx + expectation/density as explained below + err, terr : ndarray, size Nx + estimated sampling error and estimated truncation error, respectively. + (err is with 99 confidence level) + + Notes + ----- + RIND computes multivariate normal expectations, i.e., + E[Jacobian*Indicator|Condition ]*f_{Xc}(xc(:,ix)) + where + "Indicator" = I{ Hlo(i) < X(i) < Hup(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) + + Multivariate probability is computed if Nd = 0. + + If Mb>> n = 5 + >>> Blo =-np.inf; Bup=-1.2; indI=[-1, n-1] # Barriers + >>> m = np.zeros(n); rho = 0.3; + >>> Sc =(np.ones((n,n))-np.eye(n))*rho+np.eye(n) + >>> rind = Rind() + >>> E0 = rind(Sc,m,Blo,Bup,indI) # exact prob. 0.001946 + + >>> A = np.repeat(Blo,n); B = np.repeat(Bup,n) # Integration limits + >>> E1 = rind(np.triu(Sc),m,A,B) #same as E0 + + 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]]) + >>> rind(Sc,m,Blo,Bup,indI, xc, nt=0) + (array([ 0.05494076]), array([ 0.00083066]), array([ 1.00000000e-10])) + + Compute expectation E( X1^{+}*X2^{+} ) with random + correlation coefficient,Cov(X1,X2) = rho2. + >>> m2 = [0, 0]; rho2 = np.random.rand(1) + >>> Sc2 = [[1, rho2], [rho2 ,1]] + >>> Blo2 = 0; Bup2 = np.inf; indI2 = [-1, 1] + >>> rind2 = Rind(method=1) + >>> g2 = lambda x : (x*(np.pi/2+np.arcsin(x))+np.sqrt(1-x**2))/(2*np.pi) + >>> E2 = g2(rho2) # exact value + >>> E3 = rind(Sc2,m2,Blo2,Bup2,indI2,nt=0) + >>> E4 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0) + >>> E5 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0,abseps=1e-4) + + See also + -------- + prbnormnd, prbnormndpc + + References + ---------- + Podgorski et al. (2000) + "Exact distributions for apparent waves in irregular seas" + Ocean Engineering, Vol 27, no 1, pp979-1016. + + P. A. Brodtkorb (2004), + 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. + + Per A. Brodtkorb (2006) + "Evaluating Nearly Singular Multinormal Expectations with Application to + Wave Distributions", + Methodology And Computing In Applied Probability, Volume 8, Number 1, pp. 65-91(27) + ''' + + + def __init__(self, **kwds): + ''' + Parameters + ---------- + method : integer, optional + defining the integration method + 0 Integrate by Gauss-Legendre quadrature (Podgorski et al. 1999) + 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 scalar, optional + scales the conditinal probability density, i.e., + f_{Xc} = exp(-0.5*Xc*inv(Sxc)*Xc + XcScale) (default XcScale=0) + abseps, releps : real scalars, optional + absolute and relative error tolerance. (default abseps=0, releps=1e-3) + coveps : real scalar, optional + error tolerance in Cholesky factorization (default 1e-13) + maxpts, minpts : scalar integers, optional + maximum and minimum number of function values allowed. The parameter, + maxpts, 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 maxpts=40000, minpts=0) + seed : scalar integer, optional + seed to the random generator used in the integrations + (Only for METHOD~=0)(default floor(rand*1e9)) + nit : scalar integer, optional + 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 scalar, optional + cut off value where the marginal normal distribution is truncated. + (Depends on requested accuracy. A value between 4 and 5 is reasonable.) + xsplit : real scalar + parameter controlling performance of quadrature integration: + if Hup>=xCutOff AND Hlo<-XSPLIT OR + Hup>=XSPLIT AND Hlo<=-xCutOff then + do a different integration to increase speed + in rind2 and rindnit. This give slightly different results + if XSPILT>=xCutOff => do the same integration always + (Only for METHOD==0)(default XSPLIT = 1.5) + quadno : scalar integer + Quadrature formulae number used in integration of Xd variables. + This number implicitly determines number of nodes + used. (Only for METHOD==0) + speed : scalar integer + defines accuracy of calculations by choosing different parameters, + possible values: 1,2...,9 (9 fastest, default []). + If not speed is None the parameters, ABSEPS, RELEPS, COVEPS, + XCUTOFF, MAXPTS and QUADNO will be set according to + INITOPTIONS. + nc1c2 : scalar integer, optional + number of times to use the regression equation to restrict integration + area. Nc1c2 = 1,2 is recommended. (default 2) + (note: works only for method >0) + ''' + self.method = 3 + self.xcscale = 0 + self.abseps = 0 + self.releps = 1e-3, + self.coveps = 1e-10 + self.maxpts = 40000 + self.minpts = 0 + self.seed = None + self.nit = 1000, + self.xcutoff = None + self.xsplit = 1.5 + self.quadno = 2 + self.speed = None + self.nc1c2 = 2 + + self.__dict__.update(**kwds) + self.initialize(self.speed) + self.set_constants() + + def initialize(self, speed=None): + ''' + Initializes member variables according to speed. + + Parameter + --------- + speed : scalar integer + defining accuracy of calculations. + Valid numbers: 1,2,...,10 + (1=slowest and most accurate,10=fastest, but less accuracy) + + + Member variables initialized according to speed: + ----------------------------------------------- + speed : Integer defining accuracy of calculations. + abseps : Absolute error tolerance. + releps : Relative error tolerance. + covep : Error tolerance in Cholesky factorization. + xcutoff : Truncation limit of the normal CDF + maxpts : Maximum number of function values allowed. + quadno : Quadrature formulae used in integration of Xd(i) + implicitly determining # nodes + ''' + if speed is None: + return + self.speed = min(max(speed, 1), 13) + + self.maxpts = 10000 + self.quadno = r_[1:4] + (10 - min(speed, 9)) + (speed == 1) + if speed in (11, 12, 13): + self.abseps = 1e-1 + elif speed == 10: + self.abseps = 1e-2 + elif speed in (7, 8, 9): + self.abseps = 1e-2 + elif speed in (4, 5, 6): + self.maxpts = 20000 + self.abseps = 1e-3 + elif speed in (1, 2, 3): + self.maxpts = 30000 + self.abseps = 1e-4 + + if speed < 12: + tmp = max(abs(11 - abs(speed)), 1) + expon = mod(tmp + 1, 3) + 1 + self.coveps = self.abseps * ((1.0e-1) ** expon) + elif speed < 13: + self.coveps = 0.1 + else: + self.coveps = 0.5 + + self.releps = min(self.abseps, 1.0e-2) + + if self.method == 0 : + # This gives approximately the same accuracy as when using + # RINDDND and RINDNIT + # xCutOff= MIN(MAX(xCutOff+0.5d0,4.d0),5.d0) + self.abseps = self.abseps * 1.0e-1 + trunc_error = 0.05 * max(0, self.abseps) + self.xcutoff = max(min(abs(invnorm(trunc_error)), 7), 1.2) + self.abseps = max(self.abseps - trunc_error, 0) + + def set_constants(self): + if self.xcutoff is None: + trunc_error = 0.1 * self.abseps + self.nc1c2 = max(1, self.nc1c2) + xcut = abs(invnorm(trunc_error / (self.nc1c2 * 2))) + self.xcutoff = max(min(xcut, 8.5), 1.2) + #self.abseps = max(self.abseps- truncError,0); + #self.releps = max(self.releps- truncError,0); + + if self.method > 0: + names = ['method', 'xcscale', 'abseps', 'releps', 'coveps', + 'maxpts', 'minpts', 'nit', 'xcutoff', 'nc1c2', 'quadno', + 'xsplit'] + + constants = [getattr(self, name) for name in names] + constants[0] = mod(constants[0], 10) + rindmod.set_constants(*constants) #@UndefinedVariable + + def __call__(self, cov, m, ab, bb, indI=None, xc=None, nt=None, **kwds): + if any(kwds): + self.__dict__.update(**kwds) + self.set_constants() + if xc is None: + xc = zeros((0, 1)) + + BIG, Blo, Bup, xc = atleast_2d(cov, ab, bb, xc) + Blo = Blo.copy() + Bup = Bup.copy() + + Ntdc = BIG.shape[0] + Nc = xc.shape[0] + if nt is None: + nt = Ntdc - Nc + + unused_Mb, Nb = Blo.shape + Nd = Ntdc - nt - Nc + Ntd = nt + Nd + + if indI is None: + if Nb != Ntd: + raise ValueError('Inconsistent size of Blo and Bup') + indI = r_[-1:Ntd] + + Ex, indI = atleast_1d(m, indI) + if self.seed is None: + seed = int(floor(random.rand(1) * 1e10)) #@UndefinedVariable + else: + seed = int(self.seed) + + # INFIN = INTEGER, array of integration limits flags: size 1 x Nb + # 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)]. + infinity = 37 + dev = sqrt(diag(BIG)) # std + ind = nonzero(indI[1:] > -1)[0] + infin = repeat(2, len(indI) - 1) + infin[ind] = (2 - (Bup[0, ind] > infinity * dev[indI[ind + 1]]) + - 2 * (Blo[0, ind] < -infinity * dev[indI[ind + 1]])) + + Bup[0, ind] = minimum(Bup[0, ind], infinity * dev[indI[ind + 1]]) + Blo[0, ind] = maximum(Blo[0, ind], -infinity * dev[indI[ind + 1]]) + ind2 = indI + 1 + return rindmod.rind(BIG, Ex, xc, nt, ind2, Blo, Bup, infin, seed) #@UndefinedVariable + +def test_rind(): + ''' Small test function + ''' + n = 5 + Blo = -inf + Bup = -1.2 + indI = [-1, n - 1] # Barriers +# A = np.repeat(Blo, n) +# B = np.repeat(Bup, n) # Integration limits + m = zeros(n) + rho = 0.3 + Sc = (ones((n, n)) - eye(n)) * rho + eye(n) + rind = Rind() + E0 = rind(Sc, m, Blo, Bup, indI) # exact prob. 0.001946 A) + print(E0) + + A = repeat(Blo, n) + B = repeat(Bup, n) # Integration limits + E1 = rind(triu(Sc), m, A, B) #same as E0 + + xc = zeros((0, 1)) + infinity = 37 + dev = sqrt(diag(Sc)) # std + ind = nonzero(indI[1:])[0] + Bup, Blo = atleast_2d(Bup, Blo) + Bup[0, ind] = minimum(Bup[0, ind], infinity * dev[indI[ind + 1]]) + Blo[0, ind] = maximum(Blo[0, ind], -infinity * dev[indI[ind + 1]]) + E3 = rind(Sc, m, Blo, Bup, indI, xc, nt=1) + + +if __name__ == '__main__': + if False: #True: # + test_rind() + else: + import doctest + doctest.testmod() diff --git a/wafo/info.py b/wafo/info.py new file mode 100755 index 0000000..0689094 --- /dev/null +++ b/wafo/info.py @@ -0,0 +1,83 @@ +""" +WAFO +===== + WAFO is a toolbox Python routines for statistical analysis and simulation of random waves and random loads. + WAFO is freely redistributable software, see WAFO licence, cf. the GNU General Public License (GPL) and + contain tools for: + +Fatigue Analysis +---------------- +-Fatigue life prediction for random loads +-Theoretical density of rainflow cycles + +Sea modelling +------------- +-Simulation of linear and non-linear Gaussian waves +-Estimation of seamodels (spectrums) +-Joint wave height, wave steepness, wave period distributions + +Statistics +------------ +-Extreme value analysis +-Kernel density estimation +-Hidden markov models + + WAFO consists of several modules with short descriptions below. + The modules SPECTRUM, COVARIANCE, TRANSFORM, WAVEMODELS, and MULTIDIM are + mainly for oceanographic applications. + The modules CYCLES, MARKOV, and DAMAGE are mainly for fatigue problems. + The contents file for each module is shown by typing 'help module-name' + Type 'help fatigue' for a presentation of all routines related to fatigue. + + The paths to the modules are initiated by the function 'initwafo'. + + ONEDIM - Data analysis of time series. Example: extraction of + turning points, estimation of spectrum and covariance function. + Estimation transformation used in transformed Gaussian model. + COVARIANCE - Computation of spectral functions, linear + and non-linear time series simulation. + SPECTRUM - Computation of spectral moments and covariance functions, linear + and non-linear time series simulation. + Ex: common spectra implemented, directional spectra, + bandwidth measures, exact distributions for wave characteristics. + TRANSFORM - Modelling with linear or transformed Gaussian waves. Ex: + + WAVEMODELS - Models for distributions of wave characteristics found in + the literature. Ex: parametric models for breaking + limited wave heights. + MULTIDIM - Multi-dimensional time series analysis. (Under construction) + CYCLES - Cycle counting, discretization, and crossings, calculation of + damage. Simulation of discrete Markov chains, switching Markov + chains, harmonic oscillator. Ex: Rainflow cycles and matrix, + discretization of loads. Damage of a rainflow count or + matrix, damage matrix, S-N plot. + MARKOV - Routines for Markov loads, switching Markov loads, and + their connection to rainflow cycles. + DAMAGE - Calculation of damage. Ex: Damage of a rainflow count or + matrix, damage matrix, S-N plot. + SIMTOOLS - Simulation of random processes. Ex: spectral simulation, + simulation of discrete Markov chains, switching Markov + chains, harmonic oscillator + STATISTICS - Statistical tools and extreme-value distributions. + Ex: generation of random numbers, estimation of parameters, + evaluation of pdf and cdf + KDETOOLS - Kernel-density estimation. + MISC - Miscellaneous routines. Ex: numerical integration, smoothing + spline, binomial coefficient, water density. + WDEMOS - WAFO demos. + DOCS - Documentation of toolbox, definitions. An overview is given + in the routine wafomenu. + DATA - Measurements from marine applications. + PAPERS - Commands that generate figures in selected scientific + publications. + SOURCE - Fortran and C files. Information on compilation. + EXEC - Executable files (cf. SOURCE), pre-compiled for Solaris, + Alpha-Dec or Windows. + + WAFO homepage: + On the WAFO home page you will find: + - The WAFO Tutorial + - New versions of WAFO to download. + - Reported bugs. + - List of publications related to WAFO. +""" \ No newline at end of file diff --git a/wafo/integrate.py b/wafo/integrate.py new file mode 100755 index 0000000..8618a02 --- /dev/null +++ b/wafo/integrate.py @@ -0,0 +1,1494 @@ +from __future__ import division +import warnings +import copy +import numpy as np +from numpy import pi, sqrt, ones, zeros #@UnresolvedImport +from scipy import integrate as intg +import scipy.special.orthogonal as ort +from scipy import special as sp +import matplotlib +import pylab as plb +matplotlib.interactive(True) +_POINTS_AND_WEIGHTS = {} + +def humps(x=None): + ''' + Computes a function that has three roots, and some humps. + ''' + if x is None: + y = np.linspace(0,1) + else: + y = np.asarray(x) + + return 1.0 / ( ( y - 0.3 )**2 + 0.01 ) + 1.0 / ( ( y - 0.9 )**2 + 0.04 ) + 2 * y - 5.2 + +def is_numlike(obj): + 'return true if *obj* looks like a number' + try: + obj+1 + except TypeError: return False + else: return True + +def dea3(v0, v1, v2): + ''' + Extrapolate a slowly convergent sequence + + Parameters + ---------- + v0,v1,v2 : array-like + 3 values of a convergent sequence to extrapolate + + Returns + ------- + result : array-like + extrapolated value + abserr : array-like + absolute error estimate + + Description + ----------- + DEA3 attempts to extrapolate nonlinearly to a better estimate + of the sequence's limiting value, thus improving the rate of + convergence. The routine is based on the epsilon algorithm of + P. Wynn, see [1]_. + + Example + ------- + # integrate sin(x) from 0 to pi/2 + + >>> import numpy as np + >>> Ei= np.zeros(3) + >>> linfun = lambda k : np.linspace(0, np.pi/2., 2.**(k+5)+1) + >>> for k in np.arange(3): + ... x = linfun(k) + ... Ei[k] = np.trapz(np.sin(x),x) + >>> En, err = dea3(Ei[0],Ei[1],Ei[2]) + >>> En, err + (array([ 1.]), array([ 0.00020081])) + >>> TrueErr = Ei-1. + >>> TrueErr + array([ -2.00805680e-04, -5.01999079e-05, -1.25498825e-05]) + + See also + -------- + dea + + Reference + --------- + .. [1] C. Brezinski (1977) + "Acceleration de la convergence en analyse numerique", + "Lecture Notes in Math.", vol. 584, + Springer-Verlag, New York, 1977. + ''' + + E0, E1, E2 = np.atleast_1d(v0, v1, v2) + abs = np.abs + max = np.maximum + ten = 10.0 + one = ones(1) + small = np.finfo(float).eps #1.0e-16 #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 + + result = zeros(E0.shape) + abserr = result.copy() + converged = ( err1 <= tol1) & (err2 <= tol2).ravel() + k0, = converged.nonzero() + if k0.size>0 : + #%C IF E0, E1 AND E2 ARE EQUAL TO WITHIN MACHINE + #%C ACCURACY, CONVERGENCE IS ASSUMED. + result[k0] = E2[k0] + abserr[k0] = err1[k0] + err2[k0] + E2[k0]*small*ten + + k1, = (1-converged).nonzero() + + if k1.size>0 : + ss = one/delta2[k1] - one/delta1[k1] + smallE2 = (abs(ss*E1[k1]) <= 1.0e-3).ravel() + k2 = k1[smallE2.nonzero()] + if k2.size>0 : + result[k2] = E2[k2] + abserr[k2] = err1[k2] + err2[k2] + E2[k2]*small*ten + + k4, = (1-smallE2).nonzero() + if k4.size>0 : + k3 = k1[k4] + result[k3] = E1[k3] + one/ss[k4] + abserr[k3] = err1[k3] + err2[k3] + abs(result[k3]-E2[k3]) + + return result, abserr + +def clencurt(fun,a,b,n0=5,trace=False,*args): + ''' + Numerical evaluation of an integral, Clenshaw-Curtis method. + + Parameters + ---------- + fun : callable + a, b : array-like + Lower and upper integration limit, respectively. + n : integer + defines number of evaluation points (default 5) + + Returns + ------- + Q = evaluated integral + tol = Estimate of the approximation error + + Notes + ----- + CLENCURT approximates the integral of f(x) from a to b + using an 2*n+1 points Clenshaw-Curtis formula. + The error estimate is usually a conservative estimate of the + approximation error. + The integral is exact for polynomials of degree 2*n or less. + + Example + ------- + >>> import numpy as np + >>> val,err = clencurt(np.exp,0,2) + >>> abs(val-np.expm1(2))< err, err<1e-10 + (array([ True], dtype=bool), array([ True], dtype=bool)) + + + See also + -------- + simpson, + gaussq + + References + ---------- + [1] Goodwin, E.T. (1961), + "Modern Computing Methods", + 2nd edition, New yourk: Philosophical Library, pp. 78--79 + + [2] Clenshaw, C.W. and Curtis, A.R. (1960), + Numerische Matematik, Vol. 2, pp. 197--205 + ''' + + + #% make sure n is even + n = 2*n0 + a,b = np.atleast_1d(a,b) + a_shape = a.shape + af = a.ravel() + bf = b.ravel() + + Na = np.prod(a_shape) + + s = np.r_[0:n+1] + s2 = np.r_[0:n+1:2] + s2.shape = (-1,1) + x1 = np.cos(np.pi*s/n) + x1.shape = (-1,1) + x = x1*(bf-af)/2.+(bf+af)/2 + + if hasattr(fun,'__call__'): + f = fun(x) + else: + x0 = np.flipud(fun[:, 0]) + n = len(x0)-1 + if abs(x-x0) > 1e-8: + raise ValueError('Input vector x must equal cos(pi*s/n)*(b-a)/2+(b+a)/2') + + f = np.flipud(fun[:, 1::]) + + if trace: + plb.plot(x, f,'+') + + # using a Gauss-Lobatto variant, i.e., first and last + # term f(a) and f(b) is multiplied with 0.5 + f[0, :] = f[0, :]/2 + f[n, :] = f[n, :]/2 + +## % x = cos(pi*0:n/n) +## % f = f(x) +## % +## % N+1 +## % c(k) = (2/N) sum f''(n)*cos(pi*(2*k-2)*(n-1)/N), 1 <= k <= N/2+1. +## % n=1 + fft = np.fft.fft + tmp = np.real(fft(f[:n, :], axis=0)) + c = 2/n*(tmp[0:n/2+1, :]+np.cos(np.pi*s2)*f[n, :]) +## % old call +## % c = 2/n * cos(s2*s'*pi/n) * f + c[0, :] = c[0, :]/2 + c[n/2, :] = c[n/2, :]/2 + +## % alternative call +## % c = dct(f) + + + c = c[0:n/2+1, :]/((s2-1)*(s2+1)) + Q = (af-bf)*np.sum(c,axis=0) + #Q = (a-b).*sum( c(1:n/2+1,:)./repmat((s2-1).*(s2+1),1,Na)) + + abserr = (bf-af)*np.abs(c[n/2, :]) + + if Na>1: + abserr = np.reshape(abserr, a_shape) + Q = np.reshape(Q, a_shape) + return Q, abserr + +def romberg(fun, a, b, releps=1e-3, abseps=1e-3): + ''' + Numerical integration with the Romberg method + + Parameters + ---------- + fun : callable + function to integrate + a, b : real scalars + lower and upper integration limits, respectively. + releps, abseps : scalar, optional + requested relative and absolute error, respectively. + + Returns + ------- + Q : scalar + value of integral + abserr : scalar + estimated absolute error of integral + + ROMBERG approximates the integral of F(X) from A to B + using Romberg's method of integration. The function F + must return a vector of output values if a vector of input values is given. + + + Example + ------- + >>> import numpy as np + >>> [q,err] = romberg(np.sqrt,0,10,0,1e-4) + >>> q,err + (array([ 21.08185107]), array([ 6.61635466e-05])) + ''' + h = b-a + hMin = 1.0e-9 + # Max size of extrapolation table + tableLimit = max(min(np.round(np.log2(h/hMin)),30),3) + + rom = zeros((2,tableLimit)) + + rom[0,0] = h * (fun(a)+fun(b))/2 + ipower = 1 + fp = ones(tableLimit)*4 + + #Ih1 = 0 + Ih2 = 0. + Ih4 = rom[0,0] + abserr = Ih4 + #%epstab = zeros(1,decdigs+7) + #%newflg = 1 + #%[res,abserr,epstab,newflg] = dea(newflg,Ih4,abserr,epstab) + two = 1 + one = 0 + for i in xrange(1,tableLimit): + h *= 0.5 + Un5 = np.sum(fun(a + np.arange(1,2*ipower,2)*h))*h + + # trapezoidal approximations + #T2n = 0.5 * (Tn + Un) = 0.5*Tn + Un5 + rom[two,0] = 0.5 * rom[one,0] + Un5 + + fp[i] = 4 * fp[i-1] + # Richardson extrapolation + for k in xrange(i): + #rom(2,k+1)=(fp(k)*rom(2,k)-rom(1,k))/(fp(k)-1) + rom[two,k+1] = rom[two,k]+(rom[two,k]-rom[one,k])/(fp[k]-1) + + Ih1 = Ih2 + Ih2 = Ih4 + + Ih4 = rom[two,i] + + if (2<=i): + [res,abserr] = dea3(Ih1,Ih2,Ih4) + #%Ih4 = res + if (abserr <= max(abseps,releps*abs(res)) ): + break + + #%rom(1,1:i) = rom(2,1:i) + two = one + one = (one+1) % 2 + ipower *= 2 + return res, abserr + +def h_roots(n, method='newton'): + ''' + Returns the roots (x) of the nth order Hermite polynomial, + H_n(x), and weights (w) to use in Gaussian Quadrature over + [-inf,inf] with weighting function exp(-x**2). + + Parameters + ---------- + n : integer + number of roots + method : 'newton' or 'eigenvalue' + uses Newton Raphson to find zeros of the Hermite polynomial (Fast) + or eigenvalue of the jacobi matrix (Slow) to obtain the nodes and + weights, respectively. + + Returns + ------- + x : ndarray + roots + w : ndarray + weights + + Example + ------- + >>> import numpy as np + >>> [x,w] = h_roots(10) + >>> np.sum(x*w) + -5.2516042729766621e-019 + + See also + -------- + qrule, gaussq + + References + ---------- + [1] Golub, G. H. and Welsch, J. H. (1969) + 'Calculation of Gaussian Quadrature Rules' + Mathematics of Computation, vol 23,page 221-230, + + [2]. Stroud and Secrest (1966), 'gaussian quadrature formulas', + prentice-hall, Englewood cliffs, n.j. + ''' + + + if not method.startswith('n'): + return ort.h_roots(n) + else: + sqrt = np.sqrt + max_iter = 10 + releps = 3e-14 + C = [9.084064e-01, 5.214976e-02, 2.579930e-03, 3.986126e-03] + #PIM4=0.7511255444649425 + PIM4 = np.pi**(-1./4) + + # The roots are symmetric about the origin, so we have to + # find only half of them. + m = int(np.fix((n+1)/2)) + + # Initial approximations to the roots go into z. + anu = 2.0*n+1 + rhs = np.arange(3,4*m,4)*np.pi/anu + r3 = rhs**(1./3) + r2 = r3**2 + theta = r3*(C[0]+r2*(C[1]+r2*(C[2]+r2*C[3]))) + z = sqrt(anu)*np.cos(theta) + + L = zeros((3,len(z))) + k0 = 0 + kp1 = 1 + for its in xrange(max_iter): + #Newtons method carried out simultaneously on the roots. + L[k0,:] = 0 + L[kp1,:] = PIM4 + + for j in xrange(1,n+1): + #%Loop up the recurrence relation to get the Hermite + #%polynomials evaluated at z. + km1 = k0 + k0 = kp1 + kp1 = np.mod(kp1+1,3) + + L[kp1,:] =z*sqrt(2/j)*L[k0,:]-np.sqrt((j-1)/j)*L[km1,:] + + + # L now contains the desired Hermite polynomials. + # We next compute pp, the derivatives, + # by the relation (4.5.21) using p2, the polynomials + # of one lower order. + + pp = sqrt(2*n)*L[k0,:] + dz = L[kp1,:]/pp + + z = z-dz # Newtons formula. + + if not np.any(abs(dz) > releps): + break + else: + warnings.warn('too many iterations!') + + x = np.empty(n) + w = np.empty(n) + x[0:m] = z # Store the root + x[n-1:n-m-1:-1] = -z # and its symmetric counterpart. + w[0:m] = 2./pp**2 # Compute the weight + w[n-1:n-m-1:-1] = w[0:m] # and its symmetric counterpart. + return x, w + +def j_roots(n, alpha, beta, method='newton'): + ''' + Returns the roots (x) of the nth order Jacobi polynomial, P^(alpha,beta)_n(x) + and weights (w) to use in Gaussian Quadrature over [-1,1] with weighting + function (1-x)**alpha (1+x)**beta with alpha,beta > -1. + + Parameters + ---------- + n : integer + number of roots + alpha,beta : scalars + defining shape of Jacobi polynomial + method : 'newton' or 'eigenvalue' + uses Newton Raphson to find zeros of the Hermite polynomial (Fast) + or eigenvalue of the jacobi matrix (Slow) to obtain the nodes and + weights, respectively. + + Returns + ------- + x : ndarray + roots + w : ndarray + weights + + + Example + -------- + >>> [x,w]= j_roots(10,0,0) + >>> sum(x*w) + 2.7755575615628914e-016 + + See also + -------- + qrule, gaussq + + + Reference + --------- + [1] Golub, G. H. and Welsch, J. H. (1969) + 'Calculation of Gaussian Quadrature Rules' + Mathematics of Computation, vol 23,page 221-230, + + [2]. Stroud and Secrest (1966), 'gaussian quadrature formulas', + prentice-hall, Englewood cliffs, n.j. + ''' + + if not method.startswith('n'): + [x,w] = ort.j_roots(n,alpha,beta) + else: + + max_iter = 10 + releps = 3e-14 + + # Initial approximations to the roots go into z. + alfbet = alpha+beta + + + z = np.cos( np.pi*(np.arange(1,n+1) -0.25+0.5*alpha)/( n +0.5 *(alfbet+1) )) + + L = zeros((3,len(z))) + k0 = 0 + kp1 = 1 + for its in xrange(max_iter): + #Newton's method carried out simultaneously on the roots. + tmp = 2 + alfbet + L[k0,:] = 1 + L[kp1,:] = (alpha-beta+tmp*z)/2 + + for j in xrange(2,n+1): + #Loop up the recurrence relation to get the Jacobi + #polynomials evaluated at z. + km1 = k0 + k0 = kp1 + kp1 = np.mod(kp1+1,3) + + a = 2.*j*(j+alfbet)*tmp + tmp = tmp + 2 + c = 2*(j-1+alpha)*(j-1+beta)*tmp + + b = (tmp-1)*(alpha**2-beta**2+tmp*(tmp-2)*z) + + L[kp1,:] =(b*L[k0,:] - c*L[km1,:])/a + + #L now contains the desired Jacobi polynomials. + #We next compute pp, the derivatives with a standard + # relation involving the polynomials of one lower order. + + pp = (n*(alpha-beta-tmp*z)*L[kp1,:]+2*(n+alpha)*(n+beta)*L[k0,:])/(tmp*(1-z**2)) + dz = L[kp1,:]/pp + z = z-dz # Newton's formula. + + + if not any(abs(dz) > releps*abs(z)): + break + else: + warnings.warn('too many iterations in jrule') + + x = z # %Store the root and the weight. + w = np.exp(sp.gammaln(alpha+n)+sp.gammaln(beta+n)-sp.gammaln(n+1)- + sp.gammaln(alpha+beta+n+1) )*tmp*2**alfbet/(pp*L[k0,:]) + + return x, w + +def la_roots(n, alpha=0, method='newton'): + ''' + Returns the roots (x) of the nth order generalized (associated) Laguerre + polynomial, L^(alpha)_n(x), and weights (w) to use in Gaussian quadrature over + [0,inf] with weighting function exp(-x) x**alpha with alpha > -1. + + Parameters + ---------- + n : integer + number of roots + method : 'newton' or 'eigenvalue' + uses Newton Raphson to find zeros of the Laguerre polynomial (Fast) + or eigenvalue of the jacobi matrix (Slow) to obtain the nodes and + weights, respectively. + + Returns + ------- + x : ndarray + roots + w : ndarray + weights + + Example + ------- + >>> import numpy as np + >>> [x,w] = h_roots(10) + >>> np.sum(x*w) + -5.2516042729766621e-019 + + See also + -------- + qrule, gaussq + + References + ---------- + [1] Golub, G. H. and Welsch, J. H. (1969) + 'Calculation of Gaussian Quadrature Rules' + Mathematics of Computation, vol 23,page 221-230, + + [2]. Stroud and Secrest (1966), 'gaussian quadrature formulas', + prentice-hall, Englewood cliffs, n.j. + ''' + + if alpha<=-1: + raise ValueError('alpha must be greater than -1') + + if not method.startswith('n'): + return ort.la_roots(n,alpha) + else: + max_iter = 10 + releps = 3e-14 + C = [9.084064e-01, 5.214976e-02, 2.579930e-03, 3.986126e-03] + + # Initial approximations to the roots go into z. + anu = 4.0*n+2.0*alpha+2.0 + rhs = np.arange(4*n-1,2,-4)*np.pi/anu + r3 = rhs**(1./3) + r2 = r3**2 + theta = r3*(C[0]+r2*(C[1]+r2*(C[2]+r2*C[3]))) + z = anu*np.cos(theta)**2 + + dz = zeros(len(z)) + L = zeros((3,len(z))) + Lp = zeros((1,len(z))) + pp = zeros((1,len(z))) + k0 = 0 + kp1 = 1 + k = slice(len(z)) + for its in xrange(max_iter): + #%Newton's method carried out simultaneously on the roots. + L[k0,k] = 0. + L[kp1,k] = 1. + + for jj in xrange(1,n+1): + # Loop up the recurrence relation to get the Laguerre + # polynomials evaluated at z. + km1 = k0 + k0 = kp1 + kp1 = np.mod(kp1+1,3) + + L[kp1,k] =((2*jj-1+alpha-z[k])*L[k0,k]-(jj-1+alpha)*L[km1,k])/jj + #end + #%L now contains the desired Laguerre polynomials. + #%We next compute pp, the derivatives with a standard + #% relation involving the polynomials of one lower order. + + Lp[k] = L[k0,k] + pp[k] = (n*L[kp1,k]-(n+alpha)*Lp[k])/z[k] + + dz[k] = L[kp1,k]/pp[k] + z[k] = z[k]-dz[k]# % Newton?s formula. + #%k = find((abs(dz) > releps.*z)) + + + if not np.any(abs(dz) > releps): + break + else: + warnings.warn('too many iterations!') + + x = z + w = -np.exp(sp.gammaln(alpha+n)-sp.gammaln(n))/(pp*n*Lp) + return x,w + +def p_roots(n,method='newton', a=-1, b=1): + ''' + Returns the roots (x) of the nth order Legendre polynomial, P_n(x), + and weights (w) to use in Gaussian Quadrature over [-1,1] with weighting + function 1. + + Parameters + ---------- + n : integer + number of roots + method : 'newton' or 'eigenvalue' + uses Newton Raphson to find zeros of the Hermite polynomial (Fast) + or eigenvalue of the jacobi matrix (Slow) to obtain the nodes and + weights, respectively. + + Returns + ------- + x : ndarray + roots + w : ndarray + weights + + + Example + ------- + Integral of exp(x) from a = 0 to b = 3 is: exp(3)-exp(0)= + >>> import numpy as np + >>> [x,w] = p_roots(11,a=0,b=3) + >>> np.sum(np.exp(x)*w) + 19.085536923187668 + + See also + -------- + quadg. + + + References + ---------- + [1] Davis and Rabinowitz (1975) 'Methods of Numerical Integration', page 365, + Academic Press. + + [2] Golub, G. H. and Welsch, J. H. (1969) + 'Calculation of Gaussian Quadrature Rules' + Mathematics of Computation, vol 23,page 221-230, + + [3] Stroud and Secrest (1966), 'gaussian quadrature formulas', + prentice-hall, Englewood cliffs, n.j. + ''' + + if not method.startswith('n'): + x,w = ort.p_roots(n) + else: + + m = int(np.fix((n+1)/2)) + + mm = 4*m-1 + t = (np.pi/(4*n+2))*np.arange(3,mm+1,4) + nn = (1-(1-1/n)/(8*n*n)) + xo = nn*np.cos(t) + + if method.endswith('1'): + + # Compute the zeros of the N+1 Legendre Polynomial + # using the recursion relation and the Newton-Raphson method + + + #% Legendre-Gauss Polynomials + L = zeros((3,m)) + + # Derivative of LGP + Lp = zeros((m,)) + dx = zeros((m,)) + + releps = 1e-15 + max_iter = 100 + #% Compute the zeros of the N+1 Legendre Polynomial + #% using the recursion relation and the Newton-Raphson method + + #% Iterate until new points are uniformly within epsilon of old points + k = slice(m) + k0 = 0 + kp1 = 1 + for ix in xrange(max_iter): + L[k0,k] = 1 + L[kp1,k] = xo[k] + + for jj in xrange(2,n+1): + km1 = k0 + k0 = kp1 + kp1 = np.mod(k0+1,3) + L[kp1,k] = ( (2*jj-1)*xo[k]*L[k0,k]-(jj-1)*L[km1,k] )/jj + + Lp[k] = n*( L[k0,k]-xo[k]*L[kp1,k] )/(1-xo[k]**2) + + dx[k] = L[kp1,k]/Lp[k] + xo[k] = xo[k]-dx[k] + k, = np.nonzero((abs(dx)> releps*np.abs(xo))) + if len(k)==0: + break + else: + warnings.warn('Too many iterations!') + + x = -xo + w =2./((1-x**2)*(Lp**2)) + else: + # Algorithm given by Davis and Rabinowitz in 'Methods + # of Numerical Integration', page 365, Academic Press, 1975. + + e1 = n*(n+1) + + for j in xrange(2): + pkm1 = 1 + pk = xo + for k in xrange(2,n+1): + t1 = xo*pk + pkp1 = t1-pkm1-(t1-pkm1)/k+t1 + pkm1 = pk + pk = pkp1 + + den = 1.-xo*xo + d1 = n*(pkm1-xo*pk) + dpn = d1/den + d2pn = (2.*xo*dpn-e1*pk)/den + d3pn = (4.*xo*d2pn+(2-e1)*dpn)/den + d4pn = (6.*xo*d3pn+(6-e1)*d2pn)/den + u = pk/dpn + v = d2pn/dpn + h = -u*(1+(.5*u)*(v+u*(v*v-u*d3pn/(3*dpn)))) + p = pk+h*(dpn+(.5*h)*(d2pn+(h/3)*(d3pn+.25*h*d4pn))) + dp = dpn+h*(d2pn+(.5*h)*(d3pn+h*d4pn/3)) + h = h-p/dp + xo = xo+h + + x = -xo-h + fx = d1-h*e1*(pk+(h/2)*(dpn+(h/3)*(d2pn+(h/4)*(d3pn+(.2*h)*d4pn)))) + w = 2*(1-x**2)/(fx**2) + + if (m+m) > n: + x[m-1] = 0.0 + + if not ((m+m) == n): + m = m-1 + + x = np.hstack((x,-x[m-1::-1])) + w = np.hstack((w,w[m-1::-1])) + + + if (a!=-1) | (b!=1): + # Linear map from[-1,1] to [a,b] + dh = (b-a)/2 + x = dh*(x+1)+a + w = w*dh + + return x, w + +def qrule(n, wfun=1, alpha=0, beta=0): + ''' + Return nodes and weights for Gaussian quadratures. + + Parameters + ---------- + n : integer + number of base points + wfun : integer + defining the weight function, p(x). (default wfun = 1) + 1,11,21: p(x) = 1 a =-1, b = 1 Gauss-Legendre + 2,12 : p(x) = exp(-x^2) a =-inf, b = inf Hermite + 3,13 : p(x) = x^alpha*exp(-x) a = 0, b = inf Laguerre + 4,14 : 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 + + Returns + ------- + bp = base points (abscissas) + wf = weight factors + + The Gaussian Quadrature integrates a (2n-1)th order + polynomial exactly and the integral is of the form + b n + Int ( p(x)* F(x) ) dx = Sum ( wf_j* F( bp_j ) ) + a j=1 + where p(x) is the weight function. + For Jacobi and Laguerre: alpha, beta >-1 (default alpha=beta=0) + + Examples: + --------- + >>> [bp,wf] = qrule(10) + >>> sum(bp**2*wf) # integral of x^2 from a = -1 to b = 1 + 0.66666666666666641 + >>> [bp,wf] = qrule(10,2) + >>> sum(bp**2*wf) # integral of exp(-x.^2)*x.^2 from a = -inf to b = inf + 0.88622692545275772 + >>> [bp,wf] = qrule(10,4,1,2) + >>> sum(bp*wf) # integral of (x+1)*(1-x)^2 from a = -1 to b = 1 + 0.26666666666666844 + + See also + -------- + gaussq + + Reference + --------- + Abromowitz and Stegun (1954) + (for method 5 to 9) + ''' + + if (alpha<=-1) | (beta <=-1): + raise ValueError('alpha and beta must be greater than -1') + + if wfun==1: # Gauss-Legendre + [bp,wf] = p_roots(n) + elif wfun==2: # Hermite + [bp,wf] = h_roots(n) + elif wfun==3: # Generalized Laguerre + [bp,wf] = la_roots(n,alpha) + elif wfun==4: #Gauss-Jacobi + [bp,wf] = j_roots(n,alpha,beta) + elif wfun==5: # p(x)=1/sqrt((x-a)*(b-x)), a=-1 and b=1 (default) + jj = np.arange(1,n+1) + wf = ones(n) * np.pi / n + bp = np.cos( (2*jj-1)*np.pi / (2*n) ) + + elif wfun==6: # p(x)=sqrt((x-a)*(b-x)), a=-1 and b=1 + jj = np.arange(1,n+1) + xj = jj * np.pi / (n+1) + wf = np.pi / (n+1) * np.sin( xj )**2 + bp = np.cos( xj ) + + elif wfun==7: # p(x)=sqrt((x-a)/(b-x)), a=0 and b=1 + jj = np.arange(1,n+1) + xj = (jj-0.5)*pi / (2*n+1) + bp = np.cos( xj )**2 + wf = 2*np.pi*bp/(2*n+1) + + elif wfun==8: # p(x)=1/sqrt(b-x), a=0 and b=1 + [bp1, wf1] = p_roots(2*n) + k, = np.where(0<=bp1) + wf = 2*wf1[k] + bp = 1-bp1[k]**2 + + elif wfun==9: # p(x)=np.sqrt(b-x), a=0 and b=1 + [bp1, wf1] = p_roots(2*n+1) + k, = np.where(0-1) (default alpha=beta=0) + + Returns + ------- + val : ndarray + evaluated integral + err : ndarray + error estimate, absolute tolerance abs(int-intold) + + Notes + ----- + GAUSSQ numerically evaluate integral using a Gauss quadrature. + The Quadrature integrates a (2m-1)th order polynomial exactly and the + integral is of the form + b + Int (p(x)* Fun(x)) dx + a + GAUSSQ is vectorized to accept integration limits A, B and + coefficients P1,P2,...Pn, as matrices or scalars and the + result is the common size of A, B and P1,P2,...,Pn. + + Examples + --------- + integration of x**2 from 0 to 2 and from 1 to 4 + + >>> from scitools import numpyutils as npt + scitools.easyviz backend is gnuplot + >>> A = [0, 1]; B = [2,4] + >>> fun = npt.wrap2callable('x**2') + >>> [val1,err1] = gaussq(fun,A,B) + >>> val1 + array([ 2.66666667, 21. ]) + >>> err1 + array([ 1.77635684e-15, 1.06581410e-14]) + + Integration of x^2*exp(-x) from zero to infinity: + >>> fun2 = npt.wrap2callable('1') + >>> val2, err2 = gaussq(fun2, 0, npt.inf, wfun=3, alpha=2) + >>> val3, err3 = gaussq(lambda x: x**2,0, npt.inf, wfun=3, alpha=0) + >>> val2, err2 + (array([ 2.]), array([ 6.66133815e-15])) + >>> val3, err3 + (array([ 2.]), array([ 1.77635684e-15])) + + Integrate humps from 0 to 2 and from 1 to 4 + >>> val4, err4 = gaussq(humps,A,B) + + See also + -------- + qrule + gaussq2d + ''' + global _POINTS_AND_WEIGHTS + max_iter = 11 + gn = 2 + if not hasattr(fun,'__call__'): + raise ValueError('Function must be callable') + + A, B = np.atleast_1d(a,b) + a_shape = np.atleast_1d(A.shape) + b_shape = np.atleast_1d(B.shape) + + if np.prod(a_shape)==1: # make sure the integration limits have correct size + A = A*ones(b_shape) + a_shape = b_shape + elif np.prod(b_shape)==1: + B = B*ones(a_shape) + elif any( a_shape!=b_shape): + raise ValueError('The integration limits must have equal size!') + + + if args is None: + num_parameters = 0 + else: + num_parameters = len(args) + P0 = copy.deepcopy(args) + isvector1 = zeros(num_parameters) + + nk = np.prod(a_shape) #% # of integrals we have to compute + for ix in xrange(num_parameters): + if is_numlike(P0[ix]): + p0_shape = np.shape(P0[ix]) + Np0 = np.prod(p0_shape) + isvector1[ix] = (Np0 > 1) + if isvector1[ix]: + if nk == 1: + a_shape = p0_shape + nk = Np0 + A = A*ones(a_shape) + B = B*ones(a_shape) + elif nk!=Np0: + raise ValueError('The input must have equal size!') + + P0[ix].shape = (-1,1) # make sure it is a column + + + k = np.arange(nk) + val = zeros(nk) + val_old = zeros(nk) + abserr = zeros(nk) + + + #setup mapping parameters + A.shape = (-1, 1) + B.shape = (-1, 1) + jacob = (B-A)/2 + + shift = 1 + if wfun == 1:# Gauss-legendre + dx = jacob + elif wfun==2 or wfun==3: + shift = 0 + jacob = ones((nk,1)) + A = zeros((nk,1)) + dx = jacob + elif wfun==4: + dx = jacob**(alpha+beta+1) + elif wfun==5: + dx = ones((nk,1)) + elif wfun==6: + dx = jacob**2 + elif wfun==7: + shift = 0 + jacob = jacob*2 + dx = jacob + elif wfun==8: + shift = 0 + jacob = jacob*2 + dx = sqrt(jacob) + elif wfun==9: + shift = 0 + jacob = jacob*2 + dx = sqrt(jacob)**3 + else: + raise ValueError('unknown option') + + dx = dx.ravel() + + if trace: + x_trace = [0,]*max_iter + y_trace = [0,]*max_iter + + + if num_parameters>0: + ix_vec, = np.where(isvector1) + if len(ix_vec): + P1 = copy.copy(P0) + + #% Break out of the iteration loop for three reasons: + #% 1) the last update is very small (compared to int and compared to reltol) + #% 2) There are more than 11 iterations. This should NEVER happen. + + + for ix in xrange(max_iter): + x_and_w = 'wfun%d_%d_%g_%g' % (wfun,gn,alpha,beta) + if x_and_w in _POINTS_AND_WEIGHTS: + xn,w = _POINTS_AND_WEIGHTS[x_and_w] + else: + xn,w = qrule(gn,wfun,alpha,beta) + _POINTS_AND_WEIGHTS[x_and_w] = (xn,w) + + # calculate the x values + x = (xn+shift)*jacob[k,:] + A[k,:] + + + # calculate function values y=fun(x,p1,p2,....,pn) + if num_parameters>0: + if len(ix_vec): + #% Expand vector to the correct size + for iy in ix_vec: + P1[iy] = P0[iy][k,:] + + y = fun(x, **P1) + else: + y = fun(x, **P0) + else: + y = fun(x) + + + val[k] = np.sum(w*y,axis=1)*dx[k] # do the integration sum(y.*w) + + + if trace: + x_trace.append(x.ravel()) + y_trace.append(y.ravel()) + + hfig = plb.plot(x,y,'r.') + #hold on + #drawnow,shg + #if trace>1: + # pause + + plb.setp(hfig,'color','b') + + + abserr[k] = abs(val_old[k]-val[k]) #absolute tolerance + if ix > 1: + + k, = np.where(abserr > np.maximum(abs(reltol*val),abstol)) # abserr > abs(abstol))%indices to integrals which did not converge + nk = len(k)# of integrals we have to compute again + if nk : + val_old[k] = val[k] + else: + break + + gn *= 2 #double the # of basepoints and weights + else: + if nk>1: + if (nk==np.prod(a_shape)): + tmptxt = 'All integrals did not converge--singularities likely!' + else: + tmptxt = '%d integrals did not converge--singularities likely!' % (nk,) + + else: + tmptxt = 'Integral did not converge--singularity likely!' + warnings.warn(tmptxt) + + val.shape = a_shape # make sure int is the same size as the integration limits + abserr.shape = a_shape + + if trace>0: + plb.clf() + plb.plot(np.hstack(x_trace), np.hstack(y_trace),'+') + return val, abserr + +def richardson(Q,k): + #% Richardson extrapolation with parameter estimation + c = np.real((Q[k-1]-Q[k-2])/(Q[k]-Q[k-1])) - 1. + #% The lower bound 0.07 admits the singularity x.^-0.9 + c = max(c,0.07) + R = Q[k] + (Q[k] - Q[k-1])/c + return R + +def quadgr(fun,a,b,abseps=1e-5): + ''' + Gauss-Legendre quadrature with Richardson extrapolation. + + [Q,ERR] = QUADGR(FUN,A,B,TOL) approximates the integral of a function + FUN from A to B with an absolute error tolerance TOL. FUN is a function + handle and must accept vector arguments. TOL is 1e-6 by default. Q is + the integral approximation and ERR is an estimate of the absolute error. + + QUADGR uses a 12-point Gauss-Legendre quadrature. The error estimate is + based on successive interval bisection. Richardson extrapolation + accelerates the convergence for some integrals, especially integrals + with endpoint singularities. + + Examples + -------- + >>> import numpy as np + >>> Q, err = quadgr(np.log,0,1) + >>> quadgr(np.exp,0,9999*1j*np.pi) + (-2.0000000000122617, 2.1933275196062141e-009) + + >>> quadgr(lambda x: np.sqrt(4-x**2),0,2,1e-12) + (3.1415926535897811, 1.5809575870662229e-013) + + >>> quadgr(lambda x: x**-0.75,0,1) + (4.0000000000000266, 5.6843418860808015e-014) + + >>> quadgr(lambda x: 1./np.sqrt(1-x**2),-1,1) + (3.141596056985029, 6.2146261559092864e-006) + + >>> quadgr(lambda x: np.exp(-x**2),-np.inf,np.inf,1e-9) #% sqrt(pi) + (1.7724538509055152, 1.9722334876348668e-011) + + >>> quadgr(lambda x: np.cos(x)*np.exp(-x),0,np.inf,1e-9) + (0.50000000000000044, 7.3296813063450372e-011) + + See also + -------- + QUAD, + QUADGK + ''' + #% Author: jonas.lundgren@saabgroup.com, 2009. + + + # Order limits (required if infinite limits) + if a == b: + Q = b - a + err = b - a + return Q, err + elif np.real(a) > np.real(b): + reverse = True + a, b = b, a + else: + reverse = False + + + #% Infinite limits + if np.isinf(a) | np.isinf(b): + # Check real limits + if ~np.isreal(a) | ~np.isreal(b) | np.isnan(a) | np.isnan(b): + raise ValueError('Infinite intervals must be real.') + + #% Change of variable + if np.isfinite(a) & np.isinf(b): + #% a to inf + fun1 = lambda t : fun(a + t/(1-t))/(1-t)**2 + [Q,err] = quadgr(fun1,0,1,abseps) + elif np.isinf(a) & np.isfinite(b): + #% -inf to b + fun2 = lambda t: fun(b + t/(1+t))/(1+t)**2 + [Q,err] = quadgr(fun2,-1,0,abseps) + else: #% -inf to inf + fun1 = lambda t: fun(t/(1-t))/(1-t)**2 + fun2 = lambda t: fun(t/(1+t))/(1+t)**2 + [Q1,err1] = quadgr(fun1,0,1,abseps/2) + [Q2,err2] = quadgr(fun2,-1,0,abseps/2) + Q = Q1 + Q2 + err = err1 + err2 + + #% Reverse direction + if reverse: + Q = -Q + return Q, err + + #% Gauss-Legendre quadrature (12-point) + xq = np.asarray([0.12523340851146894, 0.36783149899818018, 0.58731795428661748, + 0.76990267419430469, 0.9041172563704748, 0.98156063424671924]) + wq = np.asarray([0.24914704581340288, 0.23349253653835478, 0.20316742672306584, + 0.16007832854334636, 0.10693932599531818, 0.047175336386511842]) + xq = np.hstack((xq, -xq)) + wq = np.hstack((wq, wq)) + nq = len(xq) + + #% Initiate vectors + max_iter = 17 # Max number of iterations + Q0 = zeros(max_iter) # Quadrature + Q1 = zeros(max_iter) # First Richardson extrapolation + Q2 = zeros(max_iter) # Second Richardson extrapolation + + # One interval + hh = (b - a)/2 # Half interval length + x = (a + b)/2 + hh*xq # Nodes + # Quadrature + Q0[0] = hh*np.sum(wq*fun(x),axis=0) + + # Successive bisection of intervals + for k in xrange(1,max_iter): + + # Interval bisection + hh = hh/2 + x = np.hstack([x + a, x + b])/2 + # Quadrature + Q0[k] = hh*np.sum(wq*np.sum(np.reshape(fun(x),(-1,nq)),axis=0),axis=0) + + # Richardson extrapolation + if k >= 5: + Q1[k] = richardson(Q0,k) + Q2[k] = richardson(Q1,k) + elif k >= 3: + Q1[k] = richardson(Q0,k) + + + #% Estimate absolute error + if k >= 6: + Qv = np.hstack((Q0[k], Q1[k], Q2[k])) + Qw = np.hstack((Q0[k-1], Q1[k-1], Q2[k-1])) + elif k >= 4: + Qv = np.hstack((Q0[k], Q1[k])) + Qw = np.hstack((Q0[k-1], Q1[k-1])) + else: + Qv = np.atleast_1d(Q0[k]) + Qw = Q0[k-1] + + errors = np.atleast_1d(abs(Qv - Qw)) + j = errors.argmin() + err = errors[j] + Q = Qv[j] + if k>=2: + val,err1 = dea3(Q0[k-2],Q0[k-1],Q0[k]) + + # Convergence + if (err < abseps) | ~np.isfinite(Q): + break + else: + warnings.warn('Max number of iterations reached without convergence.') + + if ~np.isfinite(Q): + warnings.warn('Integral approximation is Infinite or NaN.') + + + # The error estimate should not be zero + err = err + 2*np.finfo(Q).eps + # Reverse direction + if reverse: + Q = -Q + + return Q, err + +def qdemo(f,a,b): + ''' + Compares different quadrature rules. + + Parameters + ---------- + f : callable + function + a,b : scalars + lower and upper integration limits + + Details + ------- + qdemo(f,a,b) computes and compares various approximations to + the integral of f from a to b. Three approximations are used, + the composite trapezoid, Simpson's, and Boole's rules, all with + equal length subintervals. + In a case like qdemo(exp,0,3) one can see the expected + convergence rates for each of the three methods. + In a case like qdemo(sqrt,0,3), the convergence rate is limited + not by the method, but by the singularity of the integrand. + + Example + ------- + >>> import numpy as np + >>> qdemo(np.exp,0,3) + true value = 19.08553692 + ftn Trapezoid Simpsons Booles + evals approx error approx error approx error + 3, 22.5366862979, 3.4511493747, 19.5061466023, 0.4206096791, 19.4008539142, 0.3153169910 + 5, 19.9718950387, 0.8863581155, 19.1169646189, 0.0314276957, 19.0910191534, 0.0054822302 + 9, 19.3086731081, 0.2231361849, 19.0875991312, 0.0020622080, 19.0856414320, 0.0001045088 + 17, 19.1414188470, 0.0558819239, 19.0856674267, 0.0001305035, 19.0855386464, 0.0000017232 + 33, 19.0995135407, 0.0139766175, 19.0855451052, 0.0000081821, 19.0855369505, 0.0000000273 + 65, 19.0890314614, 0.0034945382, 19.0855374350, 0.0000005118, 19.0855369236, 0.0000000004 + 129, 19.0864105817, 0.0008736585, 19.0855369552, 0.0000000320, 19.0855369232, 0.0000000000 + 257, 19.0857553393, 0.0002184161, 19.0855369252, 0.0000000020, 19.0855369232, 0.0000000000 + 513, 19.0855915273, 0.0000546041, 19.0855369233, 0.0000000001, 19.0855369232, 0.0000000000 + ftn Clenshaw Chebychev Gauss-L + evals approx error approx error approx error + 3, 19.5061466023, 0.4206096791, 0.0000000000, 1.0000000000, 19.0803304585, 0.0052064647 + 5, 19.0834145766, 0.0021223465, 0.0000000000, 1.0000000000, 19.0855365951, 0.0000003281 + 9, 19.0855369150, 0.0000000082, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + 17, 19.0855369232, 0.0000000000, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + 33, 19.0855369232, 0.0000000000, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + 65, 19.0855369232, 0.0000000000, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + 129, 19.0855369232, 0.0000000000, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + 257, 19.0855369232, 0.0000000000, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + 513, 19.0855369232, 0.0000000000, 0.0000000000, 1.0000000000, 19.0855369232, 0.0000000000 + + ''' + # use quad8 with small tolerance to get "true" value + #true1 = quad8(f,a,b,1e-10) + #[true tol]= gaussq(f,a,b,1e-12) + #[true tol] = agakron(f,a,b,1e-13) + true_val, tol = intg.quad(f, a, b) + print('true value = %12.8f' % (true_val,)) + kmax = 9 + neval = zeros(kmax,dtype=int) + qt = zeros(kmax) + qs = zeros(kmax) + qb = zeros(kmax) + qc = zeros(kmax) + qc2 = zeros(kmax) + qg = zeros(kmax) + + et = ones(kmax) + es = ones(kmax) + eb = ones(kmax) + ec = ones(kmax) + ec2 = ones(kmax) + ec3 = ones(kmax) + eg = ones(kmax) + # try various approximations + + for k in xrange(kmax): + n = 2**(k+1) + 1 + neval[k] = n + h = (b-a)/(n-1) + x = np.linspace(a,b,n) + y = f(x) + + # trapezoid approximation + q = np.trapz(y,x) + #h*( (y(1)+y(n))/2 + sum(y(2:n-1)) ) + qt[k] = q + et[k] = abs(q - true_val) + # Simpson approximation + q = intg.simps(y,x) + #(h/3)*( y(1)+y(n) + 4*sum(y(2:2:n-1)) + 2*sum(y(3:2:n-2)) ) + qs[k] = q + es[k] = abs(q - true_val) + # Boole's rule + #q = boole(x,y) + q = (2*h/45)*(7*(y[0]+y[-1]) + 12*np.sum(y[2:n-1:4]) + + 32*np.sum(y[1:n-1:2]) + 14*np.sum(y[4:n-3:4])) + qb[k] = q + eb[k] = abs(q - true_val) + + # Clenshaw-Curtis + [q, ec3[k]] = clencurt(f,a,b,(n-1)/2) + qc[k] = q + ec[k] = abs(q - true_val) + + # Chebychev + #ck = chebfit(f,n,a,b) + #q = chebval(b,chebint(ck,a,b),a,b) + #qc2[k] = q; ec2[k] = abs(q - true) + + # Gauss-Legendre quadrature + q = intg.fixed_quad(f,a,b,n=n)[0] + #[x, w]=qrule(n,1) + #x = (b-a)/2*x + (a+b)/2 % Transform base points X. + #w = (b-a)/2*w % Adjust weigths. + #q = sum(feval(f,x).*w) + qg[k] = q + eg[k] = abs(q - true_val) + + + #% display results + formats = ['%4.0f, ',] + ['%10.10f, ',]*6 + formats[-1] = formats[-1].split(',')[0] + data = np.vstack((neval,qt,et,qs,es,qb,eb)).T + print(' ftn Trapezoid Simpson''s Boole''s') + print('evals approx error approx error approx error') + + for k in xrange(kmax): + tmp = data[k].tolist() + print(''.join(fi % t for fi, t in zip(formats,tmp))) + + # display results + data = np.vstack((neval,qc,ec,qc2,ec2,qg,eg)).T + print(' ftn Clenshaw Chebychev Gauss-L') + print('evals approx error approx error approx error') + for k in xrange(kmax): + tmp = data[k].tolist() + print(''.join(fi % t for fi, t in zip(formats,tmp))) + + + plb.loglog(neval,np.vstack((et,es,eb,ec,ec2,eg)).T) + plb.xlabel('number of function evaluations') + plb.ylabel('error') + plb.legend(('Trapezoid','Simpsons','Booles','Clenshaw','Chebychev','Gauss-L')) + #ec3' + + + + +def main(): + val,err = clencurt(np.exp,0,2) + valt = np.exp(2)-np.exp(0) + [Q,err] = quadgr(lambda x: x**2,1,4,1e-9) + [Q,err] = quadgr(humps,1,4,1e-9) + + [x,w] = h_roots(11,'newton') + sum(w) + [x2,w2] = la_roots(11,1,'t') + + from scitools import numpyutils as npu + fun = npu.wrap2callable('x**2') + p0 = fun(0) + A = [0, 1,1]; B = [2,4,3] + area,err = gaussq(fun,A,B) + + fun = npu.wrap2callable('x**2') + [val1,err1] = gaussq(fun,A,B) + + + #Integration of x^2*exp(-x) from zero to infinity: + fun2 = npu.wrap2callable('1') + [val2,err2] = gaussq(fun2,0,np.inf,wfun=3, alpha=2) + [val2,err2] = gaussq(lambda x: x**2,0,np.inf,wfun=3,alpha=0) + + #Integrate humps from 0 to 2 and from 1 to 4 + [val3,err3] = gaussq(humps,A,B) + + [x,w] = p_roots(11,'newton',1,3) + y = np.sum(x**2*w) + + x = np.linspace(0,np.pi/2) + q0 = np.trapz(humps(x),x) + [q,err] = romberg(humps,0,np.pi/2,1e-4) + print q,err + +if __name__=='__main__': + import doctest + doctest.testmod() + #main() diff --git a/wafo/interpolate.py b/wafo/interpolate.py new file mode 100755 index 0000000..24743ef --- /dev/null +++ b/wafo/interpolate.py @@ -0,0 +1,418 @@ +#------------------------------------------------------------------------------- +# Name: module1 +# Purpose: +# +# Author: pab +# +# Created: 30.12.2008 +# Copyright: (c) pab 2008 +# Licence: +#------------------------------------------------------------------------------- +#!/usr/bin/env python +from __future__ import division +import numpy as np +import scipy.sparse as sp +import scipy.sparse.linalg #@UnusedImport +from numpy.ma.core import ones, zeros, prod, sin +from numpy import diff, pi, inf #@UnresolvedImport +from numpy.lib.shape_base import vstack +from numpy.lib.function_base import linspace +import polynomial as pl + +class PPform1(object): + """The ppform of the piecewise polynomials is given in terms of coefficients + and breaks. The polynomial in the ith interval is + x_{i} <= x < x_{i+1} + + S_i = sum(coefs[m,i]*(x-breaks[i])^(k-m), m=0..k) + where k is the degree of the polynomial. + + Example + ------- + >>> coef = np.array([[1,1]]) # unit step function + >>> coef = np.array([[1,1],[0,1]]) # linear from 0 to 2 + >>> coef = np.array([[1,1],[1,1],[0,2]]) # linear from 0 to 2 + >>> breaks = [0,1,2] + >>> self = PPform(coef, breaks) + >>> x = linspace(-1,3) + >>> plot(x,self(x)) + """ + def __init__(self, coeffs, breaks, fill=0.0, sort=False, a=None, b=None): + if sort: + self.breaks = np.sort(breaks) + else: + self.breaks = np.asarray(breaks) + if a is None: + a = self.breaks[0] + if b is None: + b = self.breaks[-1] + self.coeffs = np.asarray(coeffs) + self.order = self.coeffs.shape[0] + self.fill = fill + self.a = a + self.b = b + + def __call__(self, xnew): + saveshape = np.shape(xnew) + xnew = np.ravel(xnew) + res = np.empty_like(xnew) + mask = (self.a <= xnew) & (xnew <= self.b) + res[~mask] = self.fill + xx = xnew.compress(mask) + indxs = np.searchsorted(self.breaks[:-1], xx) - 1 + indxs = indxs.clip(0, len(self.breaks)) + pp = self.coeffs + dx = xx - self.breaks.take(indxs) + if True: + v = pp[0, indxs] + for i in xrange(1, self.order): + v = dx * v + pp[i, indxs] + values = v + else: + V = np.vander(dx, N=self.order) + # values = np.diag(dot(V,pp[:,indxs])) + dot = np.dot + values = np.array([dot(V[k, :], pp[:, indxs[k]]) for k in xrange(len(xx))]) + + res[mask] = values + res.shape = saveshape + return res + + def linear_extrapolate(self, output=True): + ''' + Return a 1D PPform which extrapolate linearly outside its basic interval + ''' + + max_order = 2 + + if self.order <= max_order: + if output: + return self + else: + return + breaks = self.breaks.copy() + coefs = self.coeffs.copy() + #pieces = len(breaks) - 1 + + # Add new breaks beyond each end + breaks2add = breaks[[0, -1]] + np.array([-1, 1]) + newbreaks = np.hstack([breaks2add[0], breaks, breaks2add[1]]) + + dx = newbreaks[[0, -2]] - breaks[[0, -2]] + + dx = dx.ravel() + + # Get coefficients for the new last polynomial piece (a_n) + # by just relocate the previous last polynomial and + # then set all terms of order > maxOrder to zero + + a_nn = coefs[:, -1] + dxN = dx[-1] + + a_n = pl.polyreloc(a_nn, -dxN) # Relocate last polynomial + #set to zero all terms of order > maxOrder + a_n[0:self.order - max_order] = 0 + + #Get the coefficients for the new first piece (a_1) + # by first setting all terms of order > maxOrder to zero and then + # relocate the polynomial. + + + #Set to zero all terms of order > maxOrder, i.e., not using them + a_11 = coefs[self.order - max_order::, 0] + dx1 = dx[0] + + a_1 = pl.polyreloc(a_11, -dx1) # Relocate first polynomial + a_1 = np.hstack([zeros(self.order - max_order), a_1]) + + newcoefs = np.hstack([ a_1.reshape(-1, 1), coefs, a_n.reshape(-1, 1)]) + if output: + return PPform(newcoefs, newbreaks, a= -inf, b=inf) + else: + self.coeffs = newcoefs + self.breaks = newbreaks + self.a = -inf + self.b = inf + + def derivative(self): + """ + Return first derivative of the piecewise polynomial + """ + + cof = pl.polyder(self.coeffs) + brks = self.breaks.copy() + return PPform(cof, brks, fill=self.fill) + + + def integrate(self): + """ + Return the indefinite integral of the piecewise polynomial + """ + cof = pl.polyint(self.coeffs) + + pieces = len(self.breaks) - 1 + if 1 < pieces : + # evaluate each integrated polynomial at the right endpoint of its interval + xs = diff(self.breaks[:-1, ...], axis=0) + index = np.arange(pieces - 1) + + vv = xs * cof[0, index] + k = self.order + for i in xrange(1, k): + vv = xs * (vv + cof[i, index]) + + cof[-1] = np.hstack((0, vv)).cumsum() + + return PPform(cof, self.breaks, fill=self.fill) + + + +## def fromspline(cls, xk, cvals, order, fill=0.0): +## N = len(xk)-1 +## sivals = np.empty((order+1,N), dtype=float) +## for m in xrange(order,-1,-1): +## fact = spec.gamma(m+1) +## res = _fitpack._bspleval(xk[:-1], xk, cvals, order, m) +## res /= fact +## sivals[order-m,:] = res +## return cls(sivals, xk, fill=fill) + +class SmoothSpline(PPform): + """ + Cubic Smoothing Spline. + + Parameters + ---------- + x : array-like + x-coordinates of data. (vector) + y : array-like + y-coordinates of data. (vector or matrix) + p : real scalar + smoothing parameter between 0 and 1: + 0 -> LS-straight line + 1 -> cubic spline interpolant + lin_extrap : bool + if False regular smoothing spline + if True a smoothing spline with a constraint on the ends to + ensure linear extrapolation outside the range of the data (default) + var : array-like + variance of each y(i) (default 1) + + Returns + ------- + pp : ppform + If xx is not given, return self-form of the spline. + + Given the approximate values + + y(i) = g(x(i))+e(i) + + of some smooth function, g, where e(i) is the error. SMOOTH tries to + recover g from y by constructing a function, f, which minimizes + + p * sum (Y(i) - f(X(i)))^2/d2(i) + (1-p) * int (f'')^2 + + + Example + ------- + >>> import numpy as np + >>> x = np.linspace(0,1) + >>> y = exp(x)+1e-1*np.random.randn(x.shape) + >>> pp9 = SmoothSpline(x, y, p=.9) + >>> pp99 = SmoothSpline(x, y, p=.99, var=0.01) + >>> plot(x,y, x,pp99(x),'g', x,pp9(x),'k', x,exp(x),'r') + + See also + -------- + lc2tr, dat2tr + + + References + ---------- + Carl de Boor (1978) + 'Practical Guide to Splines' + Springer Verlag + Uses EqXIV.6--9, self 239 + """ + def __init__(self, xx, yy, p=None, lin_extrap=True, var=1): + coefs, brks = self._compute_coefs(xx, yy, p, var) + super(SmoothSpline, self).__init__(coefs, brks) + if lin_extrap: + self.linear_extrapolate(output=False) + + def _compute_coefs(self, xx, yy, p=None, var=1): + x, y = np.atleast_1d(xx, yy) + x = x.ravel() + dx = np.diff(x) + must_sort = (dx < 0).any() + if must_sort: + ind = x.argsort() + x = x[ind] + y = y[..., ind] + dx = np.diff(x) + + n = len(x) + + #ndy = y.ndim + szy = y.shape + + nd = prod(szy[:-1]) + ny = szy[-1] + + if n < 2: + raise ValueError('There must be >=2 data points.') + elif (dx <= 0).any(): + raise ValueError('Two consecutive values in x can not be equal.') + elif n != ny: + raise ValueError('x and y must have the same length.') + + dydx = np.diff(y) / dx + + if (n == 2) : #% straight line + coefs = np.vstack([dydx.ravel(), y[0, :]]) + else: + + dx1 = 1. / dx + D = sp.spdiags(var * ones(n), 0, n, n) # The variance + + u, p = self._compute_u(p, D, dydx, dx, dx1, n) + dx1.shape = (n - 1, -1) + dx.shape = (n - 1, -1) + zrs = zeros(nd) + if p < 1: + ai = (y - (6 * (1 - p) * D * diff(vstack([zrs, + diff(vstack([zrs, u, zrs]), axis=0) * dx1, + zrs]), axis=0)).T).T #faster than yi-6*(1-p)*Q*u + else: + ai = y.reshape(n, -1) + + # The piecewise polynominals are written as + # fi=ai+bi*(x-xi)+ci*(x-xi)^2+di*(x-xi)^3 + # where the derivatives in the knots according to Carl de Boor are: + # ddfi = 6*p*[0;u] = 2*ci; + # dddfi = 2*diff([ci;0])./dx = 6*di; + # dfi = diff(ai)./dx-(ci+di.*dx).*dx = bi; + + ci = np.vstack([zrs, 3 * p * u]) + di = (diff(vstack([ci, zrs]), axis=0) * dx1 / 3); + bi = (diff(ai, axis=0) * dx1 - (ci + di * dx) * dx) + ai = ai[:n - 1, ...] + if nd > 1: + di = di.T + ci = ci.T + ai = ai.T + #end + if not any(di): + if not any(ci): + coefs = vstack([bi.ravel(), ai.ravel()]) + else: + coefs = vstack([ci.ravel(), bi.ravel(), ai.ravel()]) + #end + else: + coefs = vstack([di.ravel(), ci.ravel(), bi.ravel(), ai.ravel()]) + + return coefs, x + + def _compute_u(self, p, D, dydx, dx, dx1, n): + if p is None or p != 0: + data = [dx[1:n - 1], 2 * (dx[:n - 2] + dx[1:n - 1]), dx[:n - 2]] + R = sp.spdiags(data, [-1, 0, 1], n - 2, n - 2) + + if p is None or p < 1: + Q = sp.spdiags([dx1[:n - 2], -(dx1[:n - 2] + dx1[1:n - 1]), dx1[1:n - 1]], [0, -1, -2], n, n - 2) + QDQ = (Q.T * D * Q) + if p is None or p < 0: + # Estimate p + p = 1. / (1. + QDQ.diagonal().sum() / (100. * R.diagonal().sum()** 2)); + + if p == 0: + QQ = 6 * QDQ + else: + QQ = (6 * (1 - p)) * (QDQ) + p * R + else: + QQ = R + + # Make sure it uses symmetric matrix solver + ddydx = diff(dydx, axis=0) + sp.linalg.use_solver(useUmfpack=True) + u = 2 * sp.linalg.spsolve((QQ + QQ.T), ddydx) + #faster than u=QQ\(Q' * yi); + return u.reshape(n - 2, -1), p + + +def test_smoothing_spline(): + x = linspace(0, 2 * pi + pi / 4, 20) + y = sin(x) #+ np.random.randn(x.size) + pp = SmoothSpline(x, y, p=1) + x1 = linspace(-1, 2 * pi + pi / 4 + 1, 20) + y1 = pp(x1) + pp1 = pp.derivative() + pp0 = pp1.integrate() + dy1 = pp1(x1) + y01 = pp0(x1) + #dy = y-y1 + import pylab as plb + + plb.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-') + plb.show() + pass + #tck = interpolate.splrep(x, y, s=len(x)) + +def main(): + from scipy import interpolate + import matplotlib.pyplot as plt + import matplotlib + matplotlib.interactive(True) + + coef = np.array([[1, 1], [0, 1]]) # linear from 0 to 2 + #coef = np.array([[1,1],[1,1],[0,2]]) # linear from 0 to 2 + breaks = [0, 1, 2] + pp = PPform(coef, breaks, a= -100, b=100) + x = linspace(-1, 3, 20) + y = pp(x) + + x = linspace(0, 2 * pi + pi / 4, 20) + y = x + np.random.randn(x.size) + tck = interpolate.splrep(x, y, s=len(x)) + xnew = linspace(0, 2 * pi, 100) + ynew = interpolate.splev(xnew, tck, der=0) + tck0 = interpolate.splmake(xnew, ynew, order=3, kind='smoothest', conds=None) + pp = interpolate.ppform.fromspline(*tck0) + + plt.plot(x, y, "x", xnew, ynew, xnew, sin(xnew), x, y, "b") + plt.legend(['Linear', 'Cubic Spline', 'True']) + plt.title('Cubic-spline interpolation') + + + t = np.arange(0, 1.1, .1) + x = np.sin(2 * np.pi * t) + y = np.cos(2 * np.pi * t) + tck1, u = interpolate.splprep([t, y], s=0) + tck2 = interpolate.splrep(t, y, s=len(t), task=0) + #interpolate.spl + tck = interpolate.splmake(t, y, order=3, kind='smoothest', conds=None) + self = interpolate.ppform.fromspline(*tck2) + plt.plot(t, self(t)) + pass + +def test_pp(): + import polynomial as pl + coef = np.array([[1, 1], [0, 0]]) # linear from 0 to 2 + + coef = np.array([[1, 1], [1, 1], [0, 2]]) # quadratic from 0 to 1 and 1 to 2. + dc = pl.polyder(coef, 1) + c2 = pl.polyint(dc, 1) + breaks = [0, 1, 2] + pp = PPform(coef, breaks) + pp(0.5) + pp(1) + pp(1.5) + dpp = pp.derivative() + import pylab as plb + x = plb.linspace(-1, 3) + plb.plot(x, pp(x), x, dpp(x), '.') + plb.show() + +if __name__ == '__main__': + #main() + test_smoothing_spline() diff --git a/wafo/kdetools.py b/wafo/kdetools.py new file mode 100755 index 0000000..f71d4fe --- /dev/null +++ b/wafo/kdetools.py @@ -0,0 +1,609 @@ +#------------------------------------------------------------------------------- +# Name: kdetools +# Purpose: +# +# Author: pab +# +# Created: 01.11.2008 +# Copyright: (c) pab2 2008 +# Licence: LGPL +#------------------------------------------------------------------------------- +#!/usr/bin/env python +#import numpy as np +from scipy.special import gamma +from numpy import pi, atleast_2d #@UnresolvedImport +from misc import tranproc, trangood +def sphere_volume(d, r=1.0): + """ + Returns volume of d-dimensional sphere with radius r + + Parameters + ---------- + d : scalar or array_like + dimension of sphere + r : scalar or array_like + radius of sphere (default 1) + + Reference + --------- + Wand,M.P. and Jones, M.C. (1995) + 'Kernel smoothing' + Chapman and Hall, pp 105 + """ + return (r**d)* 2.*pi**(d/2.)/(d*gamma(d/2.)) + + +class kde(object): + """ Representation of a kernel-density estimate using Gaussian kernels. + + Parameters + ---------- + dataset : (# of dims, # of data)-array + datapoints to estimate from + + Members + ------- + d : int + number of dimensions + n : int + number of datapoints + + Methods + ------- + kde.evaluate(points) : array + evaluate the estimated pdf on a provided set of points + kde(points) : array + same as kde.evaluate(points) + kde.integrate_gaussian(mean, cov) : float + multiply pdf with a specified Gaussian and integrate over the whole domain + kde.integrate_box_1d(low, high) : float + integrate pdf (1D only) between two bounds + kde.integrate_box(low_bounds, high_bounds) : float + integrate pdf over a rectangular space between low_bounds and high_bounds + kde.integrate_kde(other_kde) : float + integrate two kernel density estimates multiplied together + + Internal Methods + ---------------- + kde.covariance_factor() : float + computes the coefficient that multiplies the data covariance matrix to + obtain the kernel covariance matrix. Set this method to + kde.scotts_factor or kde.silverman_factor (or subclass to provide your + own). The default is scotts_factor. + """ + + def __init__(self, dataset,**kwds): + self.kernel='gauss' + self.hs = None + self.hsmethod=None + self.L2 = None + self.__dict__.update(kwds) + + self.dataset = atleast_2d(dataset) + self.d, self.n = self.dataset.shape + + + self._compute_covariance() + + + def evaluate(self, points): + """Evaluate the estimated pdf on a set of points. + + Parameters + ---------- + points : (# of dimensions, # of points)-array + Alternatively, a (# of dimensions,) vector can be passed in and + treated as a single point. + + Returns + ------- + values : (# of points,)-array + The values at each point. + + Raises + ------ + ValueError if the dimensionality of the input points is different than + the dimensionality of the KDE. + """ + + points = atleast_2d(points).astype(self.dataset.dtype) + + d, m = points.shape + if d != self.d: + if d == 1 and m == self.d: + # points was passed in as a row vector + points = reshape(points, (self.d, 1)) + m = 1 + else: + msg = "points have dimension %s, dataset has dimension %s" % (d, + self.d) + raise ValueError(msg) + + result = zeros((m,), points.dtype) + + if m >= self.n: + # there are more points than data, so loop over data + for i in range(self.n): + diff = self.dataset[:,i,newaxis] - points + tdiff = dot(self.inv_cov, diff) + energy = sum(diff*tdiff,axis=0)/2.0 + result += exp(-energy) + else: + # loop over points + for i in range(m): + diff = self.dataset - points[:,i,newaxis] + tdiff = dot(self.inv_cov, diff) + energy = sum(diff*tdiff,axis=0)/2.0 + result[i] = sum(exp(-energy),axis=0) + + result /= self._norm_factor + + return result + + __call__ = evaluate + +##function [f, hs,lambda]= kdefun(A,options,varargin) +##%KDEFUN Kernel Density Estimator. +##% +##% CALL: [f, hs] = kdefun(data,options,x1,x2,...,xd) +##% +##% f = kernel density estimate evaluated at x1,x2,...,xd. +##% data = data matrix, size N x D (D = # dimensions) +##% options = kdeoptions-structure or cellvector of named parameters with +##% corresponding values, see kdeoptset for details. +##% x1,x2..= vectors/matrices defining the points to evaluate the density +##% +##% KDEFUN gives a slow, but exact kernel density estimate evaluated at x1,x2,...,xd. +##% Notice that densities close to normality appear to be the easiest for the kernel +##% estimator to estimate and that the degree of estimation difficulty increases with +##% skewness, kurtosis and multimodality. +##% +##% If D > 1 KDE calculates quantile levels by integration. An +##% alternative is to calculate them by ranking the kernel density +##% estimate obtained at the points DATA i.e. use the commands +##% +##% f = kde(data); +##% r = kdefun(data,[],num2cell(data,1)); +##% f.cl = qlevels2(r,f.PL); +##% +##% The first is probably best when estimating the pdf and the latter is the +##% easiest and most robust for multidimensional data when only a visualization +##% of the data is needed. +##% +##% For faster estimates try kdebin. +##% +##% Examples: +##% data = rndray(1,500,1); +##% x = linspace(sqrt(eps),5,55); +##% plotnorm((data).^(.5)) % gives a straight line => L2 = 0.5 reasonable +##% f = kdefun(data,{'L2',.5},x); +##% plot(x,f,x,pdfray(x,1),'r') +##% +##% See also kde, mkernel, kdebin +## +##% Reference: +##% B. W. Silverman (1986) +##% 'Density estimation for statistics and data analysis' +##% Chapman and Hall , pp 100-110 +##% +##% Wand, M.P. and Jones, M.C. (1995) +##% 'Kernel smoothing' +##% Chapman and Hall, pp 43--45 +## +## +## +## +##%Tested on: matlab 5.2 +##% History: +##% revised pab Feb2004 +##% -options moved into a structure +##% revised pab Dec2003 +##% -removed some code +##% revised pab 27.04.2001 +##% - changed call from mkernel to mkernel2 (increased speed by 10%) +##% revised pab 01.01.2001 +##% - added the possibility that L2 is a cellarray of parametric +##% or non-parametric transformations (secret option) +##% revised pab 14.12.1999 +##% - fixed a small error in example in help header +##% revised pab 28.10.1999 +##% - added L2 +##% revised pab 21.10.99 +##% - added alpha to input arguments +##% - made it fully general for d dimensions +##% - HS may be a smoothing matrix +##% revised pab 21.09.99 +##% - adapted from kdetools by Christian Beardah +## +## defaultoptions = kdeoptset; +##% If just 'defaults' passed in, return the default options in g +##if ((nargin==1) && (nargout <= 1) && isequal(A,'defaults')), +## f = defaultoptions; +## return +##end +##error(nargchk(1,inf, nargin)) +## +##[n, d]=size(A); % Find dimensions of A, +## % n=number of data points, +## % d=dimension of the data. +##if (nargin<2 || isempty(options)) +## options = defaultoptions; +##else +## switch lower(class(options)) +## case {'char','struct'}, +## options = kdeoptset(defaultoptions,options); +## case {'cell'} +## +## options = kdeoptset(defaultoptions,options{:}); +## otherwise +## error('Invalid options') +## end +##end +##kernel = options.kernel; +##h = options.hs; +##alpha = options.alpha; +##L2 = options.L2; +##hsMethod = options.hsMethod; +## +##if isempty(h) +## h=zeros(1,d); +##end +## +##L22 = cell(1,d); +##k3=[]; +##if isempty(L2) +## L2=ones(1,d); % default no transformation +##elseif iscell(L2) % cellarray of non-parametric and parametric transformations +## Nl2 = length(L2); +## if ~(Nl2==1||Nl2==d), error('Wrong size of L2'), end +## [L22{1:d}] = deal(L2{1:min(Nl2,d)}); +## L2 = ones(1,d); % default no transformation +## for ix=1:d, +## if length(L22{ix})>1, +## k3=[k3 ix]; % Non-parametric transformation +## else +## L2(ix) = L22{ix}; % Parameter to the Box-Cox transformation +## end +## end +##elseif length(L2)==1 +## L2=L2(:,ones(1,d)); +##end +## +##amin=min(A); +##if any((amin(L2~=1)<=0)) , +## error('DATA cannot be negative or zero when L2~=1') +##end +## +## +##nv=length(varargin); +##if nv0 +## Xn = num2cell(lA,1); +## opt1 = kdeoptset('kernel',kernel,'hs',h,'alpha',0,'L2',1); +## f2 = kdefun(lA,opt1,Xn{:}); % get a pilot estimate by regular KDE (alpha=0) +## g = exp(sum(log(f2))/n); +## +## lambda=(f2(:)/g).^(-alpha); +##else +## lambda=ones(n,1); +##end +## +## +## +## +## +##f=zeros(Nx,1); +##if (min(hsiz)==1)||(d==1) +## for ix=1:n, % Sum over all data points +## Avec=lA(ix,:); +## Xnn=(lX-Avec(ones(Nx,1),:))./(h(ones(Nx,1),:) *lambda(ix)); +## f = f + mkernel2(Xnn,kernel)/lambda(ix)^d; +## end +##else % fully general +## h1=inv(h); +## for ix=1:n, % Sum over all data points +## Avec=lA(ix,:); +## Xnn=(lX-Avec(ones(Nx,1),:))*(h1/lambda(ix)); +## f = f + mkernel2(Xnn,kernel)/lambda(ix)^d; +## end +##end +##f=f/(n*deth); +## +##% transforming back +##if any(k1), % L2=0 i.e. logaritmic transformation +## for ix=k1 +## f=f./X(:,ix); +## end +## if any(max(abs(diff(f)))>10) +## disp('Warning: Numerical problems may have occured due to the logaritmic') +## disp('transformation. Check the KDE for spurious spikes') +## end +##end +##if any(k2) % L2~=0 i.e. power transformation +## for ix=k2 +## f=f.*(X(:,ix).^(L2(ix)-1))*L2(ix)*sign(L2(ix)); +## end +## if any(max(abs(diff(f)))>10) +## disp('Warning: Numerical problems may have occured due to the power') +## disp('transformation. Check the KDE for spurious spikes') +## end +##end +##if any(k3), % non-parametric transformation +## oneC = ones(Nx,1); +## for ix=k3 +## gn = L22{ix}; +## %Gn = fliplr(L22{ix}); +## %x0 = tranproc(lX(:,ix),Gn); +## if any(isnan(X(:,ix))), +## error('The transformation does not have a strictly positive derivative.') +## end +## hg1 = tranproc([X(:,ix) oneC],gn); +## der1 = abs(hg1(:,2)); % dg(X)/dX = 1/(dG(Y)/dY) +## % alternative 2 +## %pp = smooth(Gn(:,1),Gn(:,2),1,[],1); +## %dpp = diffpp(pp); +## %der1 = 1./abs(ppval(dpp,f.x{ix})); +## % Alternative 3 +## %pp = smooth(gn(:,1),gn(:,2),1,[],1); +## %dpp = diffpp(pp); +## %%plot(hg1(:,1),der1-abs(ppval(dpp,x0))) +## %der1 = abs(ppval(dpp,x0)); +## if any(der1<=0), +## error('The transformation must have a strictly positive derivative') +## end +## f = f.*der1; +## end +## if any(max(abs(diff(f)))>10) +## disp('Warning: Numerical problems may have occured due to the power') +## disp('transformation. Check the KDE for spurious spikes') +## end +##end +## +##f=reshape(f,xsiz); % restore original shape +##if nargout>1 +## hs=h; +##end +## +## +## +## +## +## +## +## +## +## +##function [z,c]=mkernel(varargin) +##%MKERNEL Multivariate Kernel Function. +##% +##% CALL: z = mkernel(x1,x2,...,xd,kernel); +##% z = mkernel(X,kernel); +##% +##% +##% z = kernel function values evaluated at x1,x2,...,xd +##% x1,x2..= input arguments, vectors or matrices with common size +##% or +##% X = cellarray of vector/matrices with common size +##% (i.e. X{1}=x1, X{2}=x2....) +##% +##% kernel = 'epanechnikov' - Epanechnikov kernel. +##% 'epa1' - product of 1D Epanechnikov kernel. +##% 'biweight' - Bi-weight kernel. +##% 'biw1' - product of 1D Bi-weight kernel. +##% 'triweight' - Tri-weight kernel. +##% 'triangular' - Triangular kernel. +##% 'gaussian' - Gaussian kernel +##% 'rectangular' - Rectangular kernel. +##% 'laplace' - Laplace kernel. +##% 'logistic' - Logistic kernel. +##% +##% Note that only the first 4 letters of the kernel name is needed. +##% +##% See also kde, kdefun, kdebin +## +##% Reference: +##% B. W. Silverman (1986) +##% 'Density estimation for statistics and data analysis' +##% Chapman and Hall, pp. 43, 76 +##% +##% Wand, M. P. and Jones, M. C. (1995) +##% 'Density estimation for statistics and data analysis' +##% Chapman and Hall, pp 31, 103, 175 +## +##%Tested on: matlab 5.3 +##% History: +##% Revised pab sep2005 +##% -replaced reference to kdefft with kdebin +##% revised pab aug2005 +##% -Fixed some bugs +##% revised pab Dec2003 +##% removed some old code +##% revised pab 27.04.2001 +##% - removed some old calls +##% revised pab 01.01.2001 +##% - speeded up tri3 +##% revised pab 01.12.1999 +##% - added four weight, sphere +##% - made comparison smarter => faster execution for d>1 +##% revised pab 26.10.1999 +##% fixed normalization fault in epan +##% by pab 21.09.99 +##% added multivariate epan, biweight and triweight +##% +##% collected all knorm,kepan ... into this file +##% adapted from kdetools CB +## +##d=length(varargin)-1; +##kstr=varargin{d+1}; % kernel string +##if iscell(varargin{1}) +## X=varargin{1}; +## d=numel(X); +##else +## X=varargin; +##end +## +##switch lower(kstr(1:4)) +## case {'sphe','epan','biwe','triw','four'} +## switch lower(kstr(1:4)) +## case 'sphe', r=0; %Sphere = rect for 1D +## case 'epan', r=1; %Multivariate Epanechnikov kernel. +## case 'biwe', r=2; %Multivariate Bi-weight Kernel +## case 'triw', r=3; %Multi variate Tri-weight Kernel +## case 'four', r=4; %Multi variate Four-weight Kernel +## % as r -> infty, b -> infty => kernel -> Gaussian distribution +## end +## b=1;% radius of the kernel +## b2=b^2; +## s=X{1}.^2; +## k=find(s<=b2); +## z=zeros(size(s)); +## ix=2; +## while (any(k) && (ix<=d)), +## s(k)=s(k)+X{ix}(k).^2; +## k1=(s(k)<=b2); +## k=k(k1); +## ix=ix+1; +## end; +## if any(k) +## c=2^r*prod(1:r)*vsph(d,b)/prod((d+2):2:(d+2*r)); % normalizing constant +## %c=beta(r+1,r+1)*vsph(d,b)*(2^(2*r)); % Wand and Jones pp 31 +## % the commented c above does note yield the right scaling +## % for d>1 +## z(k)=((1-s(k)/b2).^r)/c; +## end +## +## case 'rect', % 1D product Rectangular Kernel +## z=zeros(size(X{1})); +## k=find(abs(X{1})<=1); +## ix=2; +## while (any(k) && (ix<=d)), +## k1 =(abs(X{ix}(k))<=1); +## k=k(k1); +## ix=ix+1; +## end +## if any(k) +## z(k)=(0.5^d); +## end +## case {'epa1','biw1','triw1','fou1'} +## switch lower(kstr(1:4)) +## %case 'rect', r=0; %rectangular +## case 'epa1', r=1; %1D product Epanechnikov kernel. +## case 'biw1', r=2; %1D product Bi-weight Kernel +## case 'tri1', r=3; %1D product Tri-weight Kernel +## case 'fou1', r=4; %1D product Four-weight Kernel +## end +## b=1; +## b2=b^2; +## b21=1/b2; +## z=zeros(size(X{1})); +## k=find(abs(X{1})<=b); +## ix=2; +## while (any(k) && (ix<=d)), +## %for ix=2:d +## k1 =(abs(X{ix}(k))<=b); +## k = k(k1); +## ix=ix+1; +## end +## if any(k) +## c=2^r*prod(1:r)*vsph(1,b)/prod((1+2):2:(1+2*r)); % normalizing constant +## z(k) = (1-X{1}(k).^2*b21).^r; +## for ix=2:d +## z(k)=z(k).*(1-X{ix}(k).^2*b21).^r; +## end; +## z(k)=z(k)/c^d; +## end +## case 'tria',% 1D product Triangular Kernel +## z=zeros(size(X{1})); +## k=find(abs(X{1})<1); +## ix=2; +## while (any(k) && (ix<=d)), +## %for ix=2:d +## k1 =(abs(X{ix}(k))<1); +## k = k(k1); +## ix=ix+1; +## end +## if any(k) +## z(k) = (1-abs(X{1}(k))); +## for ix=2:d +## z(k)=z(k).*(1-abs(X{ix}(k))); +## end +## end +## case {'norm','gaus'},% multivariate gaussian Density Function. +## s=X{1}.^2; +## for ix=2:d +## s=s+X{ix}.^2; +## end; +## z=(2*pi)^(-d/2)*exp(-0.5*s); +## case 'lapl' % Laplace Kernel +## z=0.5*exp(-abs(X{1})); +## for ix=2:d +## z=z.*0.5*exp(-abs(X{ix})); +## end +## case 'logi', % Logistic Kernel +## z1=exp(X{1}); +## z=z1./(z1+1).^2; +## for ix=2:d +## z1=exp(X{ix}); +## z=z.*z1./(z1+1).^2; +## end +## +## otherwise, error('unknown kernel') +## end +## +## + + diff --git a/wafo/meshgrid.py b/wafo/meshgrid.py new file mode 100755 index 0000000..a3081d9 --- /dev/null +++ b/wafo/meshgrid.py @@ -0,0 +1,132 @@ +import numpy as np +def meshgrid(*xi,**kwargs): + """ + Return coordinate matrices from one or more coordinate vectors. + + Make N-D coordinate arrays for vectorized evaluations of + N-D scalar/vector fields over N-D grids, given + one-dimensional coordinate arrays x1, x2,..., xn. + + Parameters + ---------- + x1, x2,..., xn : array_like + 1-D arrays representing the coordinates of a grid. + indexing : 'xy' or 'ij' (optional) + cartesian ('xy', default) or matrix ('ij') indexing of output + sparse : True or False (default) (optional) + If True a sparse grid is returned in order to conserve memory. + copy : True (default) or False (optional) + If False a view into the original arrays are returned in order to + conserve memory + + Returns + ------- + X1, X2,..., XN : ndarray + For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` , + return ``(N1, N2, N3,...Nn)`` shaped arrays if indexing='ij' + or ``(N2, N1, N3,...Nn)`` shaped arrays if indexing='xy' + with the elements of `xi` repeated to fill the matrix along + the first dimension for `x1`, the second for `x2` and so on. + + See Also + -------- + index_tricks.mgrid : Construct a multi-dimensional "meshgrid" + using indexing notation. + index_tricks.ogrid : Construct an open multi-dimensional "meshgrid" + using indexing notation. + + Examples + -------- + >>> x = np.linspace(0,1,3) # coordinates along x axis + >>> y = np.linspace(0,1,2) # coordinates along y axis + >>> xv, yv = meshgrid(x,y) # extend x and y for a 2D xy grid + >>> xv + array([[ 0. , 0.5, 1. ], + [ 0. , 0.5, 1. ]]) + >>> yv + array([[ 0., 0., 0.], + [ 1., 1., 1.]]) + >>> xv, yv = meshgrid(x,y, sparse=True) # make sparse output arrays + >>> xv + array([[ 0. , 0.5, 1. ]]) + >>> yv + array([[ 0.], + [ 1.]]) + + >>> meshgrid(x,y,sparse=True,indexing='ij') # change to matrix indexing + [array([[ 0. ], + [ 0.5], + [ 1. ]]), array([[ 0., 1.]])] + >>> meshgrid(x,y,indexing='ij') + [array([[ 0. , 0. ], + [ 0.5, 0.5], + [ 1. , 1. ]]), + array([[ 0., 1.], + [ 0., 1.], + [ 0., 1.]])] + + >>> meshgrid(0,1,5) # just a 3D point + [array([[[0]]]), array([[[1]]]), array([[[5]]])] + >>> map(np.squeeze,meshgrid(0,1,5)) # just a 3D point + [array(0), array(1), array(5)] + >>> meshgrid(3) + array([3]) + >>> meshgrid(y) # 1D grid; y is just returned + array([ 0., 1.]) + + `meshgrid` is very useful to evaluate functions on a grid. + + >>> x = np.arange(-5, 5, 0.1) + >>> y = np.arange(-5, 5, 0.1) + >>> xx, yy = meshgrid(x, y, sparse=True) + >>> z = np.sin(xx**2+yy**2)/(xx**2+yy**2) + """ + copy = kwargs.get('copy',True) + args = np.atleast_1d(*xi) + if not isinstance(args, list): + if args.size>0: + return args.copy() if copy else args + else: + raise TypeError('meshgrid() take 1 or more arguments (0 given)') + + sparse = kwargs.get('sparse',False) + indexing = kwargs.get('indexing','xy') # 'ij' + + + ndim = len(args) + s0 = (1,)*ndim + output = [x.reshape(s0[:i]+(-1,)+s0[i+1::]) for i, x in enumerate(args)] + + shape = [x.size for x in output] + + if indexing == 'xy': + # switch first and second axis + output[0].shape = (1,-1) + (1,)*(ndim-2) + output[1].shape = (-1, 1) + (1,)*(ndim-2) + shape[0],shape[1] = shape[1],shape[0] + + if sparse: + if copy: + return [x.copy() for x in output] + else: + return output + else: + # Return the full N-D matrix (not only the 1-D vector) + if copy: + mult_fact = np.ones(shape,dtype=int) + return [x*mult_fact for x in output] + else: + return np.broadcast_arrays(*output) + + +def ndgrid(*args,**kwargs): + """ + Same as calling meshgrid with indexing='ij' (see meshgrid for + documentation). + """ + kwargs['indexing'] = 'ij' + return meshgrid(*args,**kwargs) + +if __name__=='__main__': + import doctest + doctest.testmod() diff --git a/wafo/misc.py b/wafo/misc.py new file mode 100755 index 0000000..e854e60 --- /dev/null +++ b/wafo/misc.py @@ -0,0 +1,1895 @@ +''' +Misc lsdkfalsdflasdfl +''' +from __future__ import division + +import sys + +import numpy as np +from numpy import abs +from numpy import amax +from numpy import any +from numpy import arange +from numpy import arctan2 +from numpy import array +from numpy import asarray +from numpy import atleast_1d +from numpy import broadcast_arrays +from numpy import ceil +from numpy import cos +from numpy import diff +from numpy import empty_like +from numpy import exp +from numpy import extract +from numpy import finfo +from numpy import floor +from numpy import frexp +from numpy import hstack +from numpy import hypot +from numpy import inf +from numpy import interp +from numpy import isnan +from numpy import isscalar +from numpy import linspace +from numpy import log +from numpy import logical_and +from numpy import mod +from numpy import nonzero +from numpy import ones +from numpy import pi +from numpy import r_ +from numpy import sign +from numpy import sin +from numpy import sqrt +from numpy import unique1d +from numpy import vstack +from numpy import where +from numpy import zeros +from scipy.special import gammaln +import types +import warnings + +try: + import wafo.c_library as clib +except: + clib = None +floatinfo = finfo(float) + + +__all__ = ['JITImport', 'DotDict', 'Bunch', 'printf', 'sub_dict_select', + 'parse_kwargs', 'ecross', 'findtc', 'findtp', 'findcross', + 'findextrema', 'findrfc', 'rfcfilter', 'common_shape', 'argsreduce', + 'stirlerr', 'getshipchar', 'betaloge', 'gravity', 'nextpow2', + 'discretize', 'pol2cart', 'cart2pol', 'ndgrid', 'meshgrid'] + +class JITImport(object): + ''' + Just In Time Import of module + + Example + ------- + >>> np = JITImport('numpy') + >>> np.exp(0)==1.0 + True + ''' + def __init__(self, module_name): + self._module_name = module_name + self._module = None + def __getattr__(self, attr): + try: + return getattr(self._module, attr) + except: + if self._module is None: + self._module = __import__(self._module_name, None, None, ['*']) + assert(isinstance(self._module, types.ModuleType), 'module') + return getattr(self._module, attr) + else: + raise + +class DotDict(dict): + ''' Implement dot access to dict values + + Example + ------- + >>> d = DotDict(test1=1,test2=3) + >>> d.test1 + 1 + ''' + __getattr__ = dict.__getitem__ + +class Bunch(object): + ''' Implement keyword argument initialization of class + + ''' + def __init__(self, ** kwargs): + self.__dict__.update(kwargs) + def keys(self): + return self.__dict__.keys() + def update(self, ** kwargs): + self.__dict__.update(kwargs) + +def printf(format, * args): + sys.stdout.write(format % args) + + +def sub_dict_select(somedict, somekeys): + ''' + Extracting a Subset from Dictionary + + Example + -------- + # Update options dict from keyword arguments if + # the keyword exists in options + >>> opt = dict(arg1=2, arg2=3) + >>> kwds = dict(arg2=100,arg3=1000) + >>> sub_dict = sub_dict_select(kwds,opt.keys()) + >>> opt.update(sub_dict) + >>> opt + {'arg1': 2, 'arg2': 100} + + See also + -------- + dict_intersection + ''' + #slower: validKeys = set(somedict).intersection(somekeys) + return dict((k, somedict[k]) for k in somekeys if k in somedict) + + +def parse_kwargs(options, ** kwargs): + ''' Update options dict from keyword arguments if the keyword exists in options + + Example + >>> opt = dict(arg1=2, arg2=3) + >>> opt = parse_kwargs(opt,arg2=100) + >>> print opt + {'arg1': 2, 'arg2': 100} + >>> opt2 = dict(arg2=101) + >>> opt = parse_kwargs(opt,**opt2) + + See also sub_dict_select + ''' + + newopts = sub_dict_select(kwargs, options.keys()) + if len(newopts) > 0: + options.update(newopts) + return options + +def testfun(*args, ** kwargs): + opts = dict(opt1=1, opt2=2) + if len(args) == 1 and len(kwargs) == 0 and type(args[0]) is str and args[0].startswith('default'): + return opts + opts = parse_kwargs(opts, ** kwargs) + return opts + +def detrendma(x, L): + """ + Removes a trend from data using a moving average + of size 2*L+1. If 2*L+1 > len(x) then the mean is removed + + Parameters + ---------- + x : vector or matrix of column vectors + of data + L : scalar, integer + defines the size of the moving average window + + Returns + ------- + y : ndarray + detrended data + + Examples + -------- + >>> import pylab as plb + >>> exp = plb.exp; cos = plb.cos; randn = plb.randn + >>> x = plb.linspace(0,1,200) + >>> y = exp(x)+cos(5*2*pi*x)+1e-1*randn(x.size) + >>> y0 = detrendma(y,20); tr = y-y0 + >>> h = plb.plot(x, y, x, y0, 'r', x, exp(x), 'k', x, tr, 'm') + + >>> plb.close('all') + + See also + -------- + Reconstruct + """ + + if L <= 0: + raise ValueError('L must be positive') + if L != round(L): + raise ValueError('L must be an integer') + + x1 = atleast_1d(x) + if x1.shape[0] == 1: + x1 = x1.ravel() + + n = x1.shape[0] + if n < 2 * L + 1: # only able to remove the mean + return x1 - x1.mean(axis=0) + + + mn = x1[0:2 * L + 1].mean(axis=0) + y = empty_like(x1) + y[0:L] = x1[0:L] - mn + + ix = r_[L:(n - L)] + trend = ((x1[ix + L] - x1[ix - L]) / (2 * L + 1)).cumsum(axis=0) + mn + y[ix] = x1[ix] - trend + y[n - L::] = x1[n - L::] - trend[-1] + return y + +def ecross(t, f, ind, v): + ''' + Extracts exact level v crossings + + ECROSS interpolates t and f linearly to find the exact level v + crossings, i.e., the points where f(t0) = v + + Parameters + ---------- + t,f : vectors + of arguments and functions values, respectively. + ind : ndarray of integers + indices to level v crossings as found by findcross. + v : scalar or vector (of size(ind)) + defining the level(s) to cross. + + Returns + ------- + t0 : vector + of exact level v crossings. + + Example + ------- + >>> from matplotlib import pylab as plb + >>> ones = plb.ones + >>> t = plb.linspace(0,7*plb.pi,250) + >>> x = plb.sin(t) + >>> ind = findcross(x,0.75) + >>> ind + array([ 9, 25, 80, 97, 151, 168, 223, 239]) + >>> t0 = ecross(t,x,ind,0.75) + >>> t0 + array([ 0.84910514, 2.2933879 , 7.13205663, 8.57630119, + 13.41484739, 14.85909194, 19.69776067, 21.14204343]) + >>> a = plb.plot(t, x, '.', t[ind], x[ind], 'r.', t, ones(t.shape)*0.75, + ... t0, ones(t0.shape)*0.75, 'g.') + + >>> plb.close('all') + + See also + -------- + findcross + ''' + return t[ind] + (v - f[ind]) * (t[ind + 1] - t[ind]) / (f[ind + 1] - f[ind]) + +def _findcross(xn): + '''Return indices to zero up and downcrossings of a vector + ''' + if clib is not None: + ind, m = clib.findcross(xn, 0.0) + return ind[:m] + + n = len(xn) + iz, = (xn == 0).nonzero() + if any(iz): + # Trick to avoid turning points on the crossinglevel. + if iz[0] == 0: + if len(iz) == n: + warnings.warn('All values are equal to crossing level!') + return zeros(0, dtype=np.int) + + diz = diff(iz) + ix = iz((diz > 1).argmax()) + if not any(ix): + ix = iz[-1] + + #x(ix) is a up crossing if x(1:ix) = v and x(ix+1) > v. + #x(ix) is a downcrossing if x(1:ix) = v and x(ix+1) < v. + xn[0:ix] = -xn[ix + 1] + iz = iz[ix::] + + for ix in iz.tolist(): + xn[ix] = xn[ix - 1] + + #% indices to local level crossings ( without turningpoints) + ind, = (xn[:n - 1] * xn[1:] < 0).nonzero() + return ind + +def findcross(x, v=0.0, kind=None): + ''' + Return indices to level v up and/or downcrossings of a vector + + Parameters + ---------- + x : array_like + vector with sampled values. + v : scalar, real + level v. + kind : string + defines type of wave or crossing returned. Possible options are + 'dw' : downcrossing wave + 'uw' : upcrossing wave + 'cw' : crest wave + 'tw' : trough wave + 'd' : downcrossings only + 'u' : upcrossings only + None : All crossings will be returned + + Returns + ------- + ind : array-like + indices to the crossings in the original sequence x. + + Example + ------- + >>> from matplotlib import pylab as plb + >>> ones = plb.ones + >>> v = 0.75 + >>> t = plb.linspace(0,7*plb.pi,250) + >>> x = plb.sin(t) + >>> ind = findcross(x,v) # all crossings + >>> ind + array([ 9, 25, 80, 97, 151, 168, 223, 239]) + >>> t0 = plb.plot(t,x,'.',t[ind],x[ind],'r.', t, ones(t.shape)*v) + >>> ind2 = findcross(x,v,'u') + >>> ind2 + array([ 9, 80, 151, 223]) + >>> t0 = plb.plot(t[ind2],x[ind2],'o') + >>> plb.close('all') + + See also + -------- + crossdef + wavedef + ''' + xn = np.int8(sign(atleast_1d(x).ravel() - v)) #@UndefinedVariable + ind = _findcross(xn) + if ind.size == 0: + warnings.warn('No level v = %0.5g crossings found in x' % v) + return ind + + if kind not in ('du', 'all', None): + if kind == 'd': #downcrossings only + t_0 = int(xn[ind[0] + 1] > 0) + ind = ind[t_0::2] + elif kind == 'u': #upcrossings only + t_0 = int(xn[ind[0] + 1] < 0) + ind = ind[t_0::2] + elif kind in ('dw', 'uw', 'tw', 'cw'): + #make sure that the first is a level v down-crossing if wdef=='dw' + #or make sure that the first is a level v up-crossing if wdef=='uw' + #make sure that the first is a level v down-crossing if wdef=='tw' + #or make sure that the first is a level v up-crossing if wdef=='cw' + xor = lambda a, b: a ^ b + first_is_down_crossing = int(xn[ind[0]] > xn[ind[0] + 1]) + if xor(first_is_down_crossing, kind in ('dw', 'tw')): + ind = ind[1::] + + n_c = ind.size # number of level v crossings + # make sure the number of troughs and crests are according to the + # wavedef, i.e., make sure length(ind) is odd if dw or uw + # and even if tw or cw + is_odd = mod(n_c, 2) + if xor(is_odd, kind in ('dw', 'uw')): + ind = ind[:-1] + else: + raise ValueError('Unknown wave/crossing definition!') + return ind + +def findextrema(x): + ''' + Return indices to minima and maxima of a vector + + Parameters + ---------- + x : vector with sampled values. + + Returns + ------- + ind : indices to minima and maxima in the original sequence x. + + Examples + -------- + >>> import numpy as np + >>> import pylab as pb + >>> t = np.linspace(0,7*np.pi,250) + >>> x = np.sin(t) + >>> ind = findextrema(x) + >>> a = pb.plot(t,x,'.',t[ind],x[ind],'r.') + >>> pb.close('all') + + See also + -------- + findcross + crossdef + ''' + xn = atleast_1d(x).ravel() + return findcross(diff(xn), 0.0) + 1 + +def findrfc(tp, hmin=0.0): + ''' + Return indices to rainflow cycles of a sequence of TP. + + Parameters + ----------- + tp : array-like + vector of turningpoints (NB! Only values, not sampled times) + h : real scalar + rainflow threshold. If h>0, then all rainflow cycles with height + smaller than h are removed. + + Returns + ------- + ind : ndarray of int + indices to the rainflow cycles of the original sequence TP. + + Example: + -------- + >>> import pylab as pb + >>> t = pb.linspace(0,7*np.pi,250) + >>> x = pb.sin(t)+0.1*np.sin(50*t) + >>> ind = findextrema(x) + >>> ti, tp = t[ind], x[ind] + >>> a = pb.plot(t,x,'.',ti,tp,'r.') + >>> ind1 = findrfc(tp,0.3) + >>> a = pb.plot(ti[ind1],tp[ind1]) + >>> pb.close('all') + + See also + -------- + rfcfilter, + findtp. + ''' + # TODO merge rfcfilter and findrfc + y1 = atleast_1d(tp).ravel() + n = len(y1) + ind = zeros(0, dtype=np.int) + ix = 0 + if y1[0] > y1[1]: + #first is a max, ignore it + y = y1[1::] + NC = floor((n - 1) / 2) - 1 + Tstart = 1 + else: + y = y1 + NC = floor(n / 2) - 1 + Tstart = 0 + + if (NC < 1): + return ind #No RFC cycles*/ + + if (y[0] > y[1]) and (y[1] > y[2]): + warnings.warn('This is not a sequence of turningpoints, exit') + return ind + + if (y[0] < y[1]) and (y[1] < y[2]): + warnings.warn('This is not a sequence of turningpoints, exit') + return ind + + if clib is None: + ind = zeros(n, dtype=np.int) + NC = np.int(NC) + for i in xrange(NC): + Tmi = Tstart + 2 * i + Tpl = Tstart + 2 * i + 2 + xminus = y[2 * i] + xplus = y[2 * i + 2] + + if(i != 0): + j = i - 1 + while ((j >= 0) and (y[2 * j + 1] <= y[2 * i + 1])): + if (y[2 * j] < xminus): + xminus = y[2 * j] + Tmi = Tstart + 2 * j + j -= 1 + if (xminus >= xplus): + if (y[2 * i + 1] - xminus >= hmin): + ind[ix] = Tmi + ix += 1 + ind[ix] = (Tstart + 2 * i + 1) + ix += 1 + #goto L180 continue + else: + j = i + 1 + while (j < NC): + if (y[2 * j + 1] >= y[2 * i + 1]): + break #goto L170 + if((y[2 * j + 2] <= xplus)): + xplus = y[2 * j + 2] + Tpl = (Tstart + 2 * j + 2) + j += 1 + else: + if ((y[2 * i + 1] - xminus) >= hmin): + ind[ix] = Tmi + ix += 1 + ind[ix] = (Tstart + 2 * i + 1) + ix += 1 + #iy = i + continue + + + #goto L180 + #L170: + if (xplus <= xminus): + if ((y[2 * i + 1] - xminus) >= hmin): + ind[ix] = Tmi + ix += 1 + ind[ix] = (Tstart + 2 * i + 1) + ix += 1 + elif ((y[2 * i + 1] - xplus) >= hmin): + ind[ix] = (Tstart + 2 * i + 1) + ix += 1 + ind[ix] = Tpl + ix += 1 + + #L180: + #iy=i + # /* for i */ + else: + ind, ix = clib.findrfc(y, hmin) + return ind[:ix] + +def rfcfilter(x, h, method=0): + """ + Rainflow filter a signal. + + Parameters + ----------- + x : vector + Signal. [nx1] + h : real, scalar + Threshold for rainflow filter. + method : scalar, integer + 0 : removes cycles with range < h. (default) + 1 : removes cycles with range <= h. + + Returns + -------- + y = Rainflow filtered signal. + + Examples: + --------- + # 1. Filtered signal y is the turning points of x. + >>> import wafo.data + >>> x = wafo.data.sea() + >>> y = rfcfilter(x[:,1], h=0, method=1) + >>> y[0:5] + 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) + >>> y1[0:5] + array([-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454]) + + See also + -------- + findrfc + """ + # TODO merge rfcfilter and findrfc + y = atleast_1d(x).ravel() + n = len(y) + t = zeros(n, dtype=np.int) + j = 0 + t0 = 0 + y0 = y[t0] + + z0 = 0 + if method == 0: + cmpfun1 = lambda a, b: a <= b + cmpfun2 = lambda a, b: a < b + else: + cmpfun1 = lambda a, b: a < b + cmpfun2 = lambda a, b: a <= b + + #% The rainflow filter + for tim1, yi in enumerate(y[1::]): + fpi = y0 + h + fmi = y0 - h + ti = tim1 + 1 + #yi = y[ti] + + if z0 == 0: + if cmpfun1(yi, fmi): + z1 = -1 + elif cmpfun1(fpi, yi): + z1 = + 1 + else: + z1 = 0 + t1, y1 = (t0, y0) if z1 == 0 else (ti, yi) + else: + if (((z0 == + 1) & cmpfun1(yi, fmi)) | ((z0 == -1) & cmpfun2(yi, fpi))): + z1 = -1 + elif (((z0 == + 1) & cmpfun2(fmi, yi)) | ((z0 == -1) & cmpfun1(fpi, yi))): + z1 = + 1 + else: + warnings.warn('Something wrong, i=%d' % tim1) + + #% Update y1 + if z1 != z0: + t1, y1 = ti, yi + elif z1 == -1: + #% y1 = min([y0 xi]) + t1, y1 = (t0, y0) if y0 < yi else (ti, yi) + elif z1 == + 1: + #% y1 = max([y0 xi]) + t1, y1 = (t0, y0) if y0 > yi else (ti, yi) + + #% Update y if y0 is a turning point + if abs(z0 - z1) == 2: + j += 1 + t[j] = t0 + + #% Update t0, y0, z0 + t0, y0, z0 = t1, y1, z1 + #end + + #% Update y if last y0 is greater than (or equal) threshold + if cmpfun1(h, abs(y0 - y[t[j]])): + j += 1 + t[j] = t0 + return y[t[:j]] + +def findtp(x, h=0.0, kind=None): + ''' + Return indices to turning points (tp) of data, optionally rainflowfiltered. + + Parameters + ---------- + x : vector + signal + h : real, scalar + rainflow threshold + if h<0, then ind = range(len(x)) + if h=0, then tp is a sequence of turning points (default) + if h>0, then all rainflow cycles with height smaller than + h are removed. + kind : string + defines the type of wave. Possible options are + 'mw' 'Mw' or 'none'. + If None all rainflow filtered min and max + will be returned, otherwise only the rainflow filtered + min and max, which define a wave according to the + wave definition, will be returned. + + Returns + ------- + ind : arraylike + indices to the turning points in the original sequence. + + Example: + -------- + >>> import wafo.data + >>> import pylab + >>> x = wafo.data.sea() + >>> x1 = x[0:200,:] + >>> itp = findtp(x1[:,1],0,'Mw') + >>> itph = findtp(x1[:,1],0.3,'Mw') + >>> tp = x1[itp,:] + >>> tph = x1[itph,:] + >>> a = pylab.plot(x1[:,0],x1[:,1],tp[:,0],tp[:,1],'ro',tph[:,1],tph[:,1],'k.') + >>> pylab.close('all') + + See also + --------- + findtc + findcross + findextrema + findrfc + ''' + n = len(x) + if h < 0.0: + return arange(n) + + ind = findextrema(x) + + if ind.size < 2: + return None + + + #% In order to get the exact up-crossing intensity from rfc by + #% mm2lc(tp2mm(rfc)) we have to add the indices + #% to the last value (and also the first if the + #% sequence of turning points does not start with a minimum). + + if x[ind[0]] > x[ind[1]]: + #% adds indices to first and last value + ind = r_[0, ind, n - 1] + else: # adds index to the last value + ind = r_[ind, n - 1] + + if h > 0.0: + ind1 = findrfc(x[ind], h) + ind = ind[ind1] + + if kind in ('mw', 'Mw'): + xor = lambda a, b: a ^ b + # make sure that the first is a Max if wdef == 'Mw' + # or make sure that the first is a min if wdef == 'mw' + first_is_max = (x[ind[0]] > x[ind[1]]) + + remove_first = xor(first_is_max, kind.startswith('Mw')) + if remove_first: + ind = ind[1::] + + # make sure the number of minima and Maxima are according to the wavedef. + # i.e., make sure Nm=length(ind) is odd + if (mod(ind.size, 2)) != 1: + ind = ind[:-1] + return ind + +def findtc(x_in, v=None, kind=None): + """ + Return indices to troughs and crests of data. + + Parameters + ---------- + x : vector + surface elevation. + v : real scalar + reference level (default v = mean of x). + + kind : string + defines the type of wave. Possible options are + 'dw', 'uw', 'tw', 'cw' or None. + If None indices to all troughs and crests will be returned, + otherwise only the paired ones will be returned + according to the wavedefinition. + + Returns + -------- + tc_ind : vector of ints + indices to the trough and crest turningpoints of sequence x. + v_ind : vector of ints + indices to the level v crossings of the original + sequence x. (d,u) + + Example: + -------- + >>> import wafo.data + >>> import pylab + >>> x = wafo.data.sea() + >>> x1 = x[0:200,:] + >>> itc, iv = findtc(x1[:,1],0,'dw') + >>> tc = x1[itc,:] + >>> a = pylab.plot(x1[:,0],x1[:,1],tc[:,0],tc[:,1],'ro') + >>> pylab.close('all') + + See also + -------- + findtp + findcross, + wavedef + """ + + x = atleast_1d(x_in) + if v is None: + v = x.mean() + + v_ind = findcross(x, v, kind) + n_c = v_ind.size + if n_c <= 2: + warnings.warn('There are no waves!') + return zeros(0, dtype=np.int), zeros(0, dtype=np.int) + + # determine the number of trough2crest (or crest2trough) cycles + isodd = mod(n_c, 2) + if isodd: + n_tc = int((n_c - 1) / 2) + else: + n_tc = int((n_c - 2) / 2) + + #% allocate variables before the loop increases the speed + ind = zeros(n_c - 1, dtype=np.int) + + first_is_down_crossing = (x[v_ind[0]] > x[v_ind[0] + 1]) + if first_is_down_crossing: + for i in xrange(n_tc): + #% trough + j = 2 * i + ind[j] = x[v_ind[j] + 1:v_ind[j + 1] + 1].argmin() + #% crest + ind[j + 1] = x[v_ind[j + 1] + 1:v_ind[j + 2] + 1].argmax() + + if (2 * n_tc + 1 < n_c) and (kind in (None, 'tw')): + #% trough + ind[n_c - 2] = x[v_ind[n_c - 2] + 1:v_ind[n_c - 1]].argmin() + + else: # %%%% the first is a up-crossing + for i in xrange(n_tc): + #% trough + j = 2 * i + ind[j] = x[v_ind[j] + 1:v_ind[j + 1] + 1].argmax() + #% crest + ind[j + 1] = x[v_ind[j + 1] + 1:v_ind[j + 2] + 1].argmin() + + if (2 * n_tc + 1 < n_c) and (kind in (None, 'cw')): + #% trough + ind[n_c - 2] = x[v_ind[n_c - 2] + 1:v_ind[n_c - 1]].argmax() + + return v_ind[:n_c - 1] + ind + 1, v_ind + +def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False): + """ + Return indices to spurious points of data + + Parameters + ---------- + x : vector + of data values. + zcrit : real scalar + critical distance between consecutive points. + dcrit : real scalar + critical distance of Dx used for determination of spurious + points. (Default 1.5 standard deviation of x) + ddcrit : real scalar + critical distance of DDx used for determination of spurious + points. (Default 1.5 standard deviation of x) + + Returns + ------- + inds : ndarray of integers + indices to spurious points. + indg : ndarray of integers + indices to the rest of the points. + + Notes + ----- + Consecutive points less than zcrit apart are considered as spurious. + The point immediately after and before are also removed. Jumps greater than + dcrit in Dxn and greater than ddcrit in D^2xn are also considered as spurious. + (All distances to be interpreted in the vertical direction.) + Another good choice for dcrit and ddcrit are: + + dcrit = 5*dT and ddcrit = 9.81/2*dT**2 + + where dT is the timestep between points. + + Examples + -------- + >>> import numpy as np + >>> import wafo + >>> xx = wafo.data.sea() + >>> dt = np.diff(xx[:2,0]) + >>> dcrit = 5*dt + >>> ddcrit = 9.81/2*dt*dt + >>> zcrit = 0 + >>> [inds, indg] = findoutliers(xx[:,1],zcrit,dcrit,ddcrit,verbose=True) + Found 0 spurious positive jumps of Dx + Found 0 spurious negative jumps of Dx + Found 37 spurious positive jumps of D^2x + Found 200 spurious negative jumps of D^2x + Found 244 consecutive equal values + Found the total of 1152 spurious points + + #waveplot(xx,'-',xx(inds,:),1,1,1) + + See also + -------- + waveplot, reconstruct + """ + + + # finding outliers + findjumpsDx = True # find jumps in Dx + # two point spikes and Spikes dcrit above/under the + # previous and the following point are spurios. + findSpikes = False #find spikes + findDspikes = False # find double (two point) spikes + findjumpsD2x = True # find jumps in D^2x + findNaN = True # % find missing values + + xn = asarray(x).flatten() + + if xn.size < 2: + raise ValueError('The vector must have more than 2 elements!') + + + ind = zeros(0, dtype=int) + #indg=[] + indmiss = isnan(xn) + if findNaN and indmiss.any(): + ind, = nonzero(indmiss) + if verbose: + print('Found %d missing points' % ind.size) + xn[indmiss] = 0. #%set NaN's to zero + + if dcrit is None: + dcrit = 1.5 * xn.std() + if verbose: + print('dcrit is set to %g' % dcrit) + + if ddcrit is None: + ddcrit = 1.5 * xn.std() + if verbose: + print('ddcrit is set to %g' % ddcrit) + + dxn = diff(xn) + ddxn = diff(dxn) + + if findSpikes: # finding spurious spikes + tmp, = nonzero((dxn[:-1] > dcrit) * (dxn[1::] < -dcrit) | + (dxn[:-1] < -dcrit) * (dxn[1::] > dcrit)) + if tmp.size > 0: + tmp = tmp + 1 + ind = hstack((ind, tmp)) + if verbose: + print('Found %d spurious spikes' % tmp.size) + + if findDspikes: #,% finding spurious double (two point) spikes + tmp, = nonzero((dxn[:-2] > dcrit) * (dxn[2::] < -dcrit) | + (dxn[:-2] < -dcrit) * (dxn[2::] > dcrit)) + if tmp.size > 0: + tmp = tmp + 1 + ind = hstack((ind, tmp, tmp + 1)) #%removing both points + if verbose: + print('Found %d spurious two point (double) spikes' % tmp.size) + + if findjumpsDx: # ,% finding spurious jumps in Dx + tmp, = nonzero(dxn > dcrit) + if verbose: + print('Found %d spurious positive jumps of Dx' % tmp.size) + if tmp.size > 0: + ind = hstack((ind, tmp + 1)) #removing the point after the jump + + tmp, = nonzero(dxn < -dcrit) + if verbose: + print('Found %d spurious negative jumps of Dx' % tmp.size) + if tmp.size > 0: + ind = hstack((ind, tmp)) #removing the point before the jump + + if findjumpsD2x: # ,% finding spurious jumps in D^2x + tmp, = nonzero(ddxn > ddcrit) + if tmp.size > 0: + tmp = tmp + 1 + ind = hstack((ind, tmp)) # removing the jump + + if verbose: + print('Found %d spurious positive jumps of D^2x' % tmp.size) + + tmp, = nonzero(ddxn < -ddcrit) + if tmp.size > 0: + tmp = tmp + 1 + ind = hstack((ind, tmp)) # removing the jump + + if verbose: + print('Found %d spurious negative jumps of D^2x' % tmp.size) + + if zcrit >= 0.0: + #% finding consecutive values less than zcrit apart. + indzeros = (abs(dxn) <= zcrit) + indz, = nonzero(indzeros) + if indz.size > 0: + indz = indz + 1 + #%finding the beginning and end of consecutive equal values + indtr, = nonzero((diff(indzeros))) + indtr = indtr + 1 + #%indices to consecutive equal points + if True: # removing the point before + all equal points + the point after + ind = hstack((ind, indtr - 1, indz, indtr, indtr + 1)) + else: # % removing all points + the point after + ind = hstack((ind, indz, indtr, indtr + 1)) + + if verbose: + if zcrit == 0.: + print('Found %d consecutive equal values' % indz.size) + else: + print('Found %d consecutive values less than %g apart.' % (indz.size, zcrit)) + indg = ones(xn.size, dtype=bool) + + if ind.size > 1: + ind = unique1d(ind) + indg[ind] = 0 + indg, = nonzero(indg) + + if verbose: + print('Found the total of %d spurious points' % ind.size) + + return ind, indg + +def common_shape(*args, ** kwds): + ''' + Return the common shape of a sequence of arrays + + Parameters + ----------- + *args : arraylike + sequence of arrays + **kwds : + shape + + Returns + ------- + shape : tuple + common shape of the elements of args. + + Raises + ------ + An error is raised if some of the arrays do not conform + to the common shape according to the broadcasting rules in numpy. + + Examples + -------- + >>> import numpy as np + >>> A = np.ones((4,1)) + >>> B = 2 + >>> C = np.ones((1,5))*5 + >>> common_shape(A,B,C) + (4, 5) + >>> common_shape(A,B,C,shape=(3,4,1)) + (3, 4, 5) + + See also + -------- + broadcast, broadcast_arrays + ''' + args = map(asarray, args) + shapes = [x.shape for x in args] + shape = kwds.get('shape') + if shape is not None: + if not isinstance(shape, (list, tuple)): + shape = (shape, ) + shapes.append(tuple(shape)) + if len(set(shapes)) == 1: + # Common case where nothing needs to be broadcasted. + return tuple(shapes[0]) + shapes = [list(s) for s in shapes] + nds = [len(s) for s in shapes] + biggest = max(nds) + # Go through each array and prepend dimensions of length 1 to each of the + # shapes in order to make the number of dimensions equal. + for i in range(len(shapes)): + diff = biggest - nds[i] + if diff > 0: + shapes[i] = [1] * diff + shapes[i] + + # Check each dimension for compatibility. A dimension length of 1 is + # accepted as compatible with any other length. + c_shape = [] + for axis in range(biggest): + lengths = [s[axis] for s in shapes] + unique = set(lengths + [1]) + if len(unique) > 2: + # There must be at least two non-1 lengths for this axis. + raise ValueError("shape mismatch: two or more arrays have " + "incompatible dimensions on axis %r." % (axis, )) + elif len(unique) == 2: + # There is exactly one non-1 length. The common shape will take this + # value. + unique.remove(1) + new_length = unique.pop() + c_shape.append(new_length) + else: + # Every array has a length of 1 on this axis. Strides can be left + # alone as nothing is broadcasted. + c_shape.append(1) + + return tuple(c_shape) + +def argsreduce(condition, * args): + """ Return the elements of each input array that satisfy some condition. + + Parameters + ---------- + condition : array_like + An array whose nonzero or True entries indicate the elements of each + input array to extract. The shape of 'condition' must match the common + shape of the input arrays according to the broadcasting rules in numpy. + arg1, arg2, arg3, ... : array_like + one or more input arrays. + + Returns + ------- + narg1, narg2, narg3, ... : ndarray + sequence of extracted copies of the input arrays converted to the same + size as the nonzero values of condition. + + Example + ------- + >>> import numpy as np + >>> rand = np.random.random_sample + >>> A = rand((4,5)) + >>> B = 2 + >>> C = rand((1,5)) + >>> cond = np.ones(A.shape) + >>> [A1,B1,C1] = argsreduce(cond,A,B,C) + >>> B1.shape + (20,) + >>> cond[2,:] = 0 + >>> [A2,B2,C2] = argsreduce(cond,A,B,C) + >>> B2.shape + (15,) + + See also + -------- + numpy.extract + """ + newargs = atleast_1d(*args) + if not isinstance(newargs, list): + newargs = [newargs,] + expand_arr = (condition == condition) + return [extract(condition, arr1 * expand_arr) for arr1 in newargs] + + +def stirlerr(n): + ''' + Return error of Stirling approximation, i.e., log(n!) - log( sqrt(2*pi*n)*(n/exp(1))**n ) + + Example + ------- + >>> stirlerr(2) + array([ 0.0413407]) + + See also + --------- + binom + + + Reference + ----------- + Catherine Loader (2000). + Fast and Accurate Computation of Binomial Probabilities + + + ''' + + S0 = 0.083333333333333333333 # /* 1/12 */ + S1 = 0.00277777777777777777778 # /* 1/360 */ + S2 = 0.00079365079365079365079365 # /* 1/1260 */ + S3 = 0.000595238095238095238095238 # /* 1/1680 */ + S4 = 0.0008417508417508417508417508 # /* 1/1188 */ + + n1 = atleast_1d(n) + + y = gammaln(n1 + 1) - log(sqrt(2 * pi * n1) * (n1 / exp(1)) ** n1) + + + nn = n1 * n1 + + n500 = 500 < n1 + y[n500] = (S0 - S1 / nn[n500]) / n1[n500] + n80 = logical_and(80 < n1, n1 <= 500) + if any(n80): + y[n80] = (S0 - (S1 - S2 / nn[n80]) / nn[n80]) / n1[n80] + n35 = logical_and(35 < n1, n1 <= 80) + if any(n35): + nn35 = nn[n35] + y[n35] = (S0 - (S1 - (S2 - S3 / nn35) / nn35) / nn35) / n1[n35] + + n15 = logical_and(15 < n1, n1 <= 35) + if any(n15): + nn15 = nn[n15] + y[n15] = (S0 - (S1 - (S2 - (S3 - S4 / nn15) / nn15) / nn15) / nn15) / n1[n15] + + return y + +def getshipchar(value, property="max_deadweight"): + ''' + Return ship characteristics from value of one ship-property + + Parameters + ---------- + value : scalar + value to use in the estimation. + property : string + defining the ship property used in the estimation. Options are: + 'max_deadweight','length','beam','draft','service_speed', + 'propeller_diameter'. + The length was found from statistics of 40 vessels of size 85 to + 100000 tonn. An exponential curve through 0 was selected, and the + factor and exponent that minimized the standard deviation of the relative + error was selected. (The error returned is the same for any ship.) The + servicespeed was found for ships above 1000 tonns only. + The propeller diameter formula is from [1]_. + + Returns + ------- + sc : dict + containing estimated mean values and standard-deviations of ship characteristics: + max_deadweight [kkg], (weight of cargo, fuel etc.) + length [m] + beam [m] + draught [m] + service_speed [m/s] + propeller_diameter [m] + + Example + --------- + >>> getshipchar(10,'service_speed') + {'beam': 29.0, + 'beamSTD': 2.9000000000000004, + 'draught': 9.5999999999999996, + 'draughtSTD': 2.1120000000000001, + 'length': 216.0, + 'lengthSTD': 2.0113098831942762, + 'max_deadweight': 30969.0, + 'max_deadweightSTD': 3096.9000000000001, + 'propeller_diameter': 6.761165385916601, + 'propeller_diameterSTD': 0.20267047566705432, + 'service_speed': 10.0, + 'service_speedSTD': 0} + + Other units: 1 ft = 0.3048 m and 1 knot = 0.5144 m/s + + + Reference + --------- + .. [1] Gray and Greeley, (1978), + "Source level model for propeller blade rate radiation for the world's merchant + fleet", Bolt Beranek and Newman Technical Memorandum No. 458. + ''' + valid_props = dict(l='length', b='beam', d='draught', m='max_deadweigth', + s='service_speed', p='propeller_diameter') + prop = valid_props[property[0]] + + prop2max_dw = dict(length=lambda x: (x / 3.45) ** (2.5), + beam=lambda x: ((x / 1.78) ** (1 / 0.27)), + draught=lambda x: ((x / 0.8) ** (1 / 0.24)), + service_speed=lambda x: ((x / 1.14) ** (1 / 0.21)), + propeller_diameter=lambda x: (((x / 0.12) ** (4 / 3) / 3.45) ** (2.5))) + + max_deadweight = prop2max_dw.get(prop, lambda x: x)(value) + propertySTD = prop + 'STD' + + length = round(3.45 * max_deadweight ** 0.40) + length_err = length ** 0.13 + + beam = round(1.78 * max_deadweight ** 0.27 * 10) / 10 + beam_err = beam * 0.10 + + draught = round(0.80 * max_deadweight ** 0.24 * 10) / 10 + draught_err = draught * 0.22 + + #S = round(2/3*(L)**0.525) + speed = round(1.14 * max_deadweight ** 0.21 * 10) / 10 + speed_err = speed * 0.10 + + + p_diam = 0.12 * length ** (3.0 / 4.0) + p_diam_err = 0.12 * length_err ** (3.0 / 4.0) + + max_deadweight = round(max_deadweight) + max_deadweightSTD = 0.1 * max_deadweight + + shipchar = {'max_deadweight':max_deadweight, 'max_deadweightSTD':max_deadweightSTD, + 'length':length, 'lengthSTD':length_err, 'beam':beam, 'beamSTD':beam_err, + 'draught':draught, 'draughtSTD':draught_err, + 'service_speed':speed, 'service_speedSTD':speed_err, + 'propeller_diameter':p_diam, 'propeller_diameterSTD':p_diam_err} + + shipchar[propertySTD] = 0 + return shipchar + +def betaloge(z, w): + ''' + Natural Logarithm of beta function. + + CALL betaloge(z,w) + + BETALOGE computes the natural logarithm of the beta + function for corresponding elements of Z and W. The arrays Z and + W must be real and nonnegative. Both arrays must be the same size, + or either can be scalar. BETALOGE is defined as: + + y = LOG(BETA(Z,W)) = gammaln(Z)+gammaln(W)-gammaln(Z+W) + + and is obtained without computing BETA(Z,W). Since the beta + function can range over very large or very small values, its + logarithm is sometimes more useful. + This implementation is more accurate than the BETALN implementation + for large arguments + + Example + + + + See also + -------- + betaln, beta + ''' + # y = gammaln(z)+gammaln(w)-gammaln(z+w) + zpw = z + w + return (stirlerr(z) + stirlerr(w) + 0.5 * log(2 * pi) + (w - 0.5) * log(w) + + (z - 0.5) * log(z) - stirlerr(zpw) - (zpw - 0.5) * log(zpw)) + + # stirlings approximation: + # (-(zpw-0.5).*log(zpw) +(w-0.5).*log(w)+(z-0.5).*log(z) +0.5*log(2*pi)) + #return y + +def gravity(phi=45): + ''' Returns the constant acceleration of gravity + + GRAVITY calculates the acceleration of gravity + using the international gravitational formulae [1]_: + + g = 9.78049*(1+0.0052884*sin(phir)**2-0.0000059*sin(2*phir)**2) + where + phir = phi*pi/180 + + Parameters + ---------- + phi : {float, int} + latitude in degrees + + Returns + -------- + g : ndarray + acceleration of gravity [m/s**2] + + Examples + -------- + >>> import numpy as np + >>> phi = np.linspace(0,45,5) + >>> gravity(phi) + array([ 9.78049 , 9.78245014, 9.78803583, 9.79640552, 9.80629387]) + + See also + -------- + wdensity + + References + ---------- + .. [1] Irgens, Fridtjov (1987) + "Formelsamling i mekanikk: + statikk, fasthetsl?re, dynamikk fluidmekanikk" + tapir forlag, University of Trondheim, + ISBN 82-519-0786-1, pp 19 + + ''' + + phir = phi * pi / 180. # change from degrees to radians + return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2. - 0.0000059 * sin(2 * phir) ** 2.) + +def nextpow2(x): + ''' + Return next higher power of 2 + + Example + ------- + >>> nextpow2(10) + 4 + >>> nextpow2(np.arange(5)) + 3 + ''' + t = isscalar(x) or len(x) + if (t > 1): + f, n = frexp(t) + else: + f, n = frexp(abs(x)) + + if (f == 0.5): + n = n - 1 + return n + +def discretize(fun, a, b, tol=0.005, n=5): + ''' + Automatic discretization of function + + Parameters + ---------- + fun : callable + function to discretize + a,b : real scalars + evaluation limits + tol : real, scalar + absoute error tolerance + n : scalar integer + number of values + + Returns + ------- + x : discretized values + y : fun(x) + + Example + ------- + >>> import numpy as np + >>> import pylab as plb + >>> x,y = discretize(np.cos,0,np.pi) + >>> t = plb.plot(x,y) + >>> plb.show() + + >>> plb.close('all') + + ''' + tiny = floatinfo.tiny + + + x = linspace(a, b, n) + y = fun(x) + + err0 = inf + err = 10000 + nmax = 2 ** 20 + while (err != err0 and err > tol and n < nmax): + err0 = err + x0 = x + y0 = y + n = 2 * (n - 1) + 1 + x = linspace (a, b, n) + y = fun(x) + y00 = interp(x, x0, y0) + err = 0.5 * amax(abs((y00 - y) / (abs(y00 + y) + tiny))) + return x, y + + +def pol2cart(theta, rho): + ''' + Transform polar coordinates into 2D cartesian coordinates. + + Returns + ------- + x, y : array-like + Cartesian coordinates, x = rho*cos(theta), y = rho*sin(theta) + + See also + -------- + cart2pol + ''' + return rho * cos(theta), rho * sin(theta) + +def cart2pol(x, y): + ''' Transform 2D cartesian coordinates into polar coordinates. + + Returns + ------- + theta : array-like + arctan2(y,x) + rho : array-like + sqrt(x**2+y**2) + + See also + -------- + pol2cart + ''' + return arctan2(y, x), hypot(x, y) + +def meshgrid(*xi, ** kwargs): + """ + Return coordinate matrices from one or more coordinate vectors. + + Make N-D coordinate arrays for vectorized evaluations of + N-D scalar/vector fields over N-D grids, given + one-dimensional coordinate arrays x1, x2,..., xn. + + Parameters + ---------- + x1, x2,..., xn : array_like + 1-D arrays representing the coordinates of a grid. + indexing : 'xy' or 'ij' (optional) + cartesian ('xy', default) or matrix ('ij') indexing of output + sparse : True or False (default) (optional) + If True a sparse grid is returned in order to conserve memory. + copy : True (default) or False (optional) + If False a view into the original arrays are returned in order to + conserve memory + + Returns + ------- + X1, X2,..., XN : ndarray + For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` , + return ``(N1, N2, N3,...Nn)`` shaped arrays if indexing='ij' + or ``(N2, N1, N3,...Nn)`` shaped arrays if indexing='xy' + with the elements of `xi` repeated to fill the matrix along + the first dimension for `x1`, the second for `x2` and so on. + + See Also + -------- + index_tricks.mgrid : Construct a multi-dimensional "meshgrid" + using indexing notation. + index_tricks.ogrid : Construct an open multi-dimensional "meshgrid" + using indexing notation. + + Examples + -------- + >>> x = np.linspace(0,1,3) # coordinates along x axis + >>> y = np.linspace(0,1,2) # coordinates along y axis + >>> xv, yv = meshgrid(x,y) # extend x and y for a 2D xy grid + >>> xv + array([[ 0. , 0.5, 1. ], + [ 0. , 0.5, 1. ]]) + >>> yv + array([[ 0., 0., 0.], + [ 1., 1., 1.]]) + >>> xv, yv = meshgrid(x,y, sparse=True) # make sparse output arrays + >>> xv + array([[ 0. , 0.5, 1. ]]) + >>> yv + array([[ 0.], + [ 1.]]) + + >>> meshgrid(x,y,sparse=True,indexing='ij') # change to matrix indexing + [array([[ 0. ], + [ 0.5], + [ 1. ]]), array([[ 0., 1.]])] + >>> meshgrid(x,y,indexing='ij') + [array([[ 0. , 0. ], + [ 0.5, 0.5], + [ 1. , 1. ]]), array([[ 0., 1.], + [ 0., 1.], + [ 0., 1.]])] + + >>> meshgrid(0,1,5) # just a 3D point + [array([[[0]]]), array([[[1]]]), array([[[5]]])] + >>> map(np.squeeze,meshgrid(0,1,5)) # just a 3D point + [array(0), array(1), array(5)] + >>> meshgrid(3) + array([3]) + >>> meshgrid(y) # 1D grid y is just returned + array([ 0., 1.]) + + `meshgrid` is very useful to evaluate functions on a grid. + + >>> x = np.arange(-5, 5, 0.1) + >>> y = np.arange(-5, 5, 0.1) + >>> xx, yy = meshgrid(x, y, sparse=True) + >>> z = np.sin(xx**2+yy**2)/(xx**2+yy**2) + """ + copy = kwargs.get('copy', True) + args = atleast_1d(*xi) + if not isinstance(args, list): + if args.size > 0: + return args.copy() if copy else args + else: + raise TypeError('meshgrid() take 1 or more arguments (0 given)') + + sparse = kwargs.get('sparse', False) + indexing = kwargs.get('indexing', 'xy') # 'ij' + + + ndim = len(args) + s0 = (1, ) * ndim + output = [x.reshape(s0[:i] + (-1, ) + s0[i + 1::]) for i, x in enumerate(args)] + + shape = [x.size for x in output] + + if indexing == 'xy': + # switch first and second axis + output[0].shape = (1, -1) + (1, ) * (ndim - 2) + output[1].shape = (-1, 1) + (1, ) * (ndim - 2) + shape[0], shape[1] = shape[1], shape[0] + + if sparse: + if copy: + return [x.copy() for x in output] + else: + return output + else: + # Return the full N-D matrix (not only the 1-D vector) + if copy: + mult_fact = ones(shape, dtype=int) + return [x * mult_fact for x in output] + else: + return broadcast_arrays(*output) + + +def ndgrid(*args, ** kwargs): + """ + Same as calling meshgrid with indexing='ij' (see meshgrid for + documentation). + """ + kwargs['indexing'] = 'ij' + return meshgrid(*args, ** kwargs) + +def trangood(x, f, min_n=None, min_x=None, max_x=None, max_n=inf): + """ + Make sure transformation is efficient. + + Parameters + ------------ + x, f : array_like + input transform function, (x,f(x)). + min_n : scalar, int + minimum number of points in the good transform. + (Default x.shape[0]) + min_x : scalar, real + minimum x value to transform. (Default min(x)) + max_x : scalar, real + maximum x value to transform. (Default max(x)) + max_n : scalar, int + maximum number of points in the good transform + (default inf) + Returns + ------- + x, f : array_like + the good transform function. + + TRANGOOD interpolates f linearly and optionally + extrapolate it linearly outside the range of x + with X uniformly spaced. + + See also + --------- + tranproc, + numpy.interp + """ + xo, fo = atleast_1d(x, f) + #n = xo.size + if (xo.ndim != 1): + raise ValueError('x must be a vector.') + if (fo.ndim != 1): + raise ValueError('f must be a vector.') + + i = xo.argsort() + xo = xo[i] + fo = fo[i] + del i + dx = diff(xo) + if (any(dx <= 0)): + raise ValueError('Duplicate x-values not allowed.') + + nf = fo.shape[0] + + if max_x is None: + max_x = xo[-1] + if min_x is None: + min_x = xo[0] + if min_n is None: + min_n = nf + if (min_n < 2): + min_n = 2 + if (max_n < 2): + max_n = 2 + + ddx = diff(dx) + xn = xo[-1] + x0 = xo[0] + L = float(xn - x0) + eps = floatinfo.eps + if ((nf < min_n) or (max_n < nf) or any(abs(ddx) > 10 * eps * (L))): +## % pab 07.01.2001: Always choose the stepsize df so that +## % it is an exactly representable number. +## % This is important when calculating numerical derivatives and is +## % accomplished by the following. + dx = L / (min(min_n, max_n) - 1) + dx = (dx + 2.) - 2. + xi = arange(x0, xn + dx / 2., dx) + #% New call pab 11.11.2000: This is much quicker + fo = interp(xi, xo, fo) + xo = xi + +# x is now uniformly spaced + dx = xo[1] - xo[0] + + # Extrapolate linearly outside the range of ff + if (min_x < xo[0]): + x1 = dx * arange(floor((min_x - xo[0]) / dx), -2) + f2 = fo[0] + x1 * (fo[1] - fo[0]) / (xo[1] - xo[0]) + fo = hstack((f2, fo)) + xo = hstack((x1 + xo[0], xo)) + + if (max_x > xo[-1]): + x1 = dx * arange(1, ceil((max_x - xo[-1]) / dx) + 1) + f2 = f[-1] + x1 * (f[-1] - f[-2]) / (xo[-1] - xo[-2]) + fo = hstack((fo, f2)) + xo = hstack((xo, x1 + xo[-1])) + + return xo, fo + +def tranproc(x, f, x0, * xi): + """ + Transforms process X and up to four derivatives + using the transformation f. + + Parameters + ---------- + x,f : array-like + [x,f(x)], transform function, y = f(x). + x0, x1,...,xn : vectors + where xi is the i'th time derivative of x0. 0<=N<=4. + + Returns + ------- + y0, y1,...,yn : vectors + where yi is the i'th time derivative of y0 = f(x0). + + By the basic rules of derivation: + Y1 = f'(X0)*X1 + Y2 = f''(X0)*X1^2 + f'(X0)*X2 + Y3 = f'''(X0)*X1^3 + f'(X0)*X3 + 3*f''(X0)*X1*X2 + Y4 = f''''(X0)*X1^4 + f'(X0)*X4 + 6*f'''(X0)*X1^2*X2 + + f''(X0)*(3*X2^2 + 4*X1*X3) + + The derivation of f is performed numerically with a central difference + method with linear extrapolation towards the beginning and end of f, + respectively. + + Example + -------- + Derivative of g and the transformed Gaussian model. + >>> import pylab as plb + >>> import wafo.transform.models as wtm + >>> tr = wtm.TrHermite() + >>> x = linspace(-5,5,501) + >>> g = tr(x) + >>> gder = tranproc(x, g, x, ones(g.shape[0])) + >>> h = plb.plot(x, g, x, gder[1]) + + plb.plot(x,pdfnorm(g)*gder[1],x,pdfnorm(x)) + plb.legend('Transformed model','Gaussian model') + + >>> plb.close('all') + + See also + -------- + trangood. + """ + + eps = floatinfo.eps + xo, fo, x0 = atleast_1d(x, f, x0) + xi = atleast_1d(*xi) + if not isinstance(xi, list): + xi = [xi,] + N = len(xi) # N = number of derivatives + nmax = ceil((xo.ptp()) * 10 ** (7. / max(N, 1))) + xo, fo = trangood(xo, fo, min_x=min(x0), max_x=max(x0), max_n=nmax) + + n = f.shape[0] + #y = x0.copy() + xu = (n - 1) * (x0 - xo[0]) / (xo[-1] - xo[0]) + + fi = asarray(floor(xu), dtype=int) + fi = where(fi == n - 1, fi - 1, fi) + + xu = xu - fi + y0 = fo[fi] + (fo[fi + 1] - fo[fi]) * xu + + y = y0 + + if N > 0: + y = [y0] + hn = xo[1] - xo[0] + if hn ** N < sqrt(eps): + print('Numerical problems may occur for the derivatives in tranproc.') + warnings.warn('The sampling of the transformation may be too small.') + + #% Transform X with the derivatives of f. + fxder = zeros((N, x0.size)) + fder = vstack((xo, fo)).T + for k in range(N): #% Derivation of f(x) using a difference method. + n = fder.shape[0] + #%fder = [(fder(1:n-1,1)+fder(2:n,1))/2 diff(fder(:,2))./diff(fder(:,1))] + fder = vstack([(fder[0:n - 1, 0] + fder[1:n, 0]) / 2, diff(fder[:, 1]) / hn]) + fxder[k] = tranproc(fder[0], fder[1], x0) + + #% Calculate the transforms of the derivatives of X. + #% First time derivative of y: y1 = f'(x)*x1 + + y1 = fxder[0] * xi[0] + y.append(y1) + if N > 1: + + # Second time derivative of y: + # y2 = f''(x)*x1.^2+f'(x)*x2 + y2 = fxder[1] * xi[0] ** 2. + fxder[0] * xi[1] + y.append(y2) + if N > 2: + # Third time derivative of y: + # y3 = f'''(x)*x1.^3+f'(x)*x3 +3*f''(x)*x1*x2 + y3 = fxder[2] * xi[0] ** 3 + fxder[0] * xi[2] + \ + 3 * fxder[1] * xi[0] * xi[1] + y.append(y3) + if N > 3: + # Fourth time derivative of y: + # y4 = f''''(x)*x1.^4+f'(x)*x4 + # +6*f'''(x)*x1^2*x2+f''(x)*(3*x2^2+4x1*x3) + y4 = (fxder[3] * xi[0] ** 4. + fxder[0] * xi[3] + \ + 6. * fxder[2] * xi[0] ** 2. * xi[1] + \ + fxder[1] * (3. * xi[1] ** 2. + 4. * xi[0] * xi[1])) + y.append(y4) + if N > 4: + warnings.warn('Transformation of derivatives of order>4 not supported.') + return y #0,y1,y2,y3,y4 + + +def test_common_shape(): + + A = ones((4, 1)) + B = 2 + C = ones((1, 5)) * 5 + common_shape(A, B, C) + + common_shape(A, B, C, shape=(3, 4, 1)) + + A = ones((4, 1)) + B = 2 + C = ones((1, 5)) * 5 + common_shape(A, B, C, shape=(4, 5)) + + +def test_meshgrid(): + x = array([-1, -0.5, 1, 4, 5], float) + y = array([0, -2, -5], float) + xv, yv = meshgrid(x, y, sparse=False) + print(xv) + print(yv) + xv, yv = meshgrid(x, y, sparse=True) # make sparse output arrays + print(xv) + print(yv) + print(meshgrid(0, 1, 5, sparse=True)) # just a 3D point + print(meshgrid([0, 1, 5], sparse=True)) # just a 3D point + xv, yv = meshgrid(y, y) + yv[0, 0] = 10 + print(xv) + print(yv) +## >>> xv +## array([[ 0. , 0.5, 1. ]]) +## >>> yv +## array([[ 0.], +## [ 1.]]) +## array([[-1. , -0.5, 1. , 4. , 5. ], +## [-1. , -0.5, 1. , 4. , 5. ], +## [-1. , -0.5, 1. , 4. , 5. ]]) +## +## array([[ 0., 0., 0., 0., 0.], +## [-2., -2., -2., -2., -2.], +## [-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) + gder = tranproc(x, g, x, ones(g.size)) + pass + #>>> gder(:,1) = g(:,1) + #>>> plot(g(:,1),[g(:,2),gder(:,2)]) + #>>> plot(g(:,1),pdfnorm(g(:,2)).*gder(:,2),g(:,1),pdfnorm(g(:,1))) + #>>> legend('Transformed model','Gaussian model') +def _test_detrend(): + import pylab as plb + cos = plb.cos;randn = plb.randn + x = linspace(0, 1, 200) + y = exp(x) + cos(5 * 2 * pi * x) + 1e-1 * randn(x.size) + y0 = detrendma(y, 20);tr = y - y0 + plb.plot(x, y, x, y0, 'r', x, exp(x), 'k', x, tr, 'm') + +def _test_extrema(): + import pylab as pb + from pylab import plot + t = pb.linspace(0, 7 * pi, 250) + x = pb.sin(t) + 0.1 * sin(50 * t) + ind = findextrema(x) + ti, tp = t[ind], x[ind] + plot(t, x, '.', ti, tp, 'r.') + ind1 = findrfc(tp, 0.3) + + + +def _test_discretize(): + import pylab as plb + x, y = discretize(cos, 0, pi) + plb.plot(x, y) + plb.show() + + plb.close('all') +def _test_stirlerr(): + x = linspace(1, 5, 6) + print stirlerr(x) + print stirlerr(1) + print getshipchar(1000) + print betaloge(3, 2) + +def _test_parse_kwargs(): + opt = dict(arg1=1, arg2=3) + print opt + opt = parse_kwargs(opt, arg1=5) + print opt + opt2 = dict(arg3=15) + opt = parse_kwargs(opt, **opt2) + print opt + + opt0 = testfun('default') + print opt0 + opt0.update(opt1=100) + print opt0 + opt0 = parse_kwargs(opt0, opt2=200) + print opt0 + out1 = testfun(opt0['opt1'], **opt0) + print out1 + +if __name__ == "__main__": + if True:# False: # + import doctest + doctest.testmod() + else: + _test_tranproc() diff --git a/wafo/mvn.pyd b/wafo/mvn.pyd new file mode 100755 index 0000000..b656b23 Binary files /dev/null and b/wafo/mvn.pyd differ diff --git a/wafo/mvn.pyf b/wafo/mvn.pyf new file mode 100755 index 0000000..8a3d5f1 --- /dev/null +++ b/wafo/mvn.pyf @@ -0,0 +1,39 @@ +! -*- f90 -*- +! Note: the context of this file is case sensitive. + +python module mvn ! in + interface ! in :mvn + subroutine mvnun(d,n,lower,upper,means,covar,maxpts,abseps,releps,value,inform) ! in :mvn:mvndst.f + integer intent(hide) :: d=shape(means,0) + integer intent(hide) :: n=shape(means,1) + double precision dimension(d) :: lower + double precision dimension(d) :: upper + double precision dimension(d,n) :: means + double precision dimension(d,d) :: covar + integer intent(optional) :: maxpts=d*1000 + double precision intent(optional) :: abseps=1e-6 + double precision intent(optional) :: releps=1e-6 + double precision intent(out) :: value + integer intent(out) :: inform + end subroutine mvnun + + subroutine mvndst(n,lower,upper,infin,correl,maxpts,abseps,releps,error,value,inform) ! in :mvn:mvndst.f + integer intent(hide) :: n=len(lower) + double precision dimension(n) :: lower + double precision dimension(n) :: upper + integer dimension(n) :: infin + double precision dimension(n*(n-1)/2) :: correl + integer intent(optional) :: maxpts=2000 + double precision intent(optional) :: abseps=1e-6 + double precision intent(optional) :: releps=1e-6 + double precision intent(out) :: error + double precision intent(out) :: value + integer intent(out) :: inform + integer :: ivls + common /dkblck/ ivls + end subroutine mvndst + end interface +end python module mvn + +! This file was auto-generated with f2py (version:2.39.235_1752). +! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/mvn1.pyf b/wafo/mvn1.pyf new file mode 100755 index 0000000..817b9e5 --- /dev/null +++ b/wafo/mvn1.pyf @@ -0,0 +1,129 @@ +! -*- f90 -*- +! Note: the context of this file is case sensitive. + +python module mvn2 ! in + interface ! in :mvn2 + subroutine mvnun(d,n,lower,upper,means,covar,maxpts,abseps,releps,value,inform) ! in :mvn2:mvndst.f + integer optional,check(len(lower)>=d),depend(lower) :: d=len(lower) + integer optional,check(shape(means,1)==n),depend(means) :: n=shape(means,1) + double precision dimension(d) :: lower + double precision dimension(d),depend(d) :: upper + double precision dimension(d,n),depend(d) :: means + double precision dimension(d,d),depend(d,d) :: covar + integer :: maxpts + double precision :: abseps + double precision :: releps + double precision :: value + integer :: inform + end subroutine mvnun + subroutine mvndst(n,lower,upper,infin,correl,maxpts,abseps,releps,error,value,inform) ! in :mvn2:mvndst.f + integer :: n + double precision dimension(*) :: lower + double precision dimension(*) :: upper + integer dimension(*) :: infin + double precision dimension(*) :: correl + integer :: maxpts + double precision :: abseps + double precision :: releps + double precision :: error + double precision :: value + integer :: inform + integer :: ivls + common /dkblck/ ivls + end subroutine mvndst + function mvndfn(n,w) ! in :mvn2:mvndst.f + integer :: n + double precision dimension(*) :: w + double precision dimension(*) :: upper + integer dimension(*) :: infin + integer :: infis + double precision :: e + double precision dimension(*) :: lower + double precision :: d + double precision dimension(*) :: correl + double precision :: mvndfn + double precision :: mvndnt + entry mvndnt(n,correl,lower,upper,infin,infis,d,e) + end function mvndfn + subroutine mvnlms(a,b,infin,lower,upper) ! in :mvn2:mvndst.f + double precision :: a + double precision :: b + integer :: infin + double precision :: lower + double precision :: upper + end subroutine mvnlms + subroutine covsrt(n,lower,upper,correl,infin,y,infis,a,b,cov,infi) ! in :mvn2:mvndst.f + integer :: n + double precision dimension(*) :: lower + double precision dimension(*) :: upper + double precision dimension(*) :: correl + integer dimension(*) :: infin + double precision dimension(*) :: y + integer :: infis + double precision dimension(*) :: a + double precision dimension(*) :: b + double precision dimension(*) :: cov + integer dimension(*) :: infi + end subroutine covsrt + subroutine dkswap(x,y) ! in :mvn2:mvndst.f + double precision :: x + double precision :: y + end subroutine dkswap + subroutine rcswp(p,q,a,b,infin,n,c) ! in :mvn2:mvndst.f + integer :: p + integer :: q + double precision dimension(*) :: a + double precision dimension(*) :: b + integer dimension(*) :: infin + integer :: n + double precision dimension(*) :: c + end subroutine rcswp + subroutine dkbvrc(ndim,minvls,maxvls,functn,abseps,releps,abserr,finest,inform) ! in :mvn2:mvndst.f + integer :: ndim + integer :: minvls + integer :: maxvls + external functn + double precision :: abseps + double precision :: releps + double precision :: abserr + double precision :: finest + integer :: inform + end subroutine dkbvrc + subroutine dksmrc(ndim,klim,sumkro,prime,vk,functn,x) ! in :mvn2:mvndst.f + integer :: ndim + integer :: klim + double precision :: sumkro + integer :: prime + double precision dimension(*) :: vk + external functn + double precision dimension(*) :: x + end subroutine dksmrc + function mvnphi(z) ! in :mvn2:mvndst.f + double precision :: z + double precision :: mvnphi + end function mvnphi + function phinvs(p) ! in :mvn2:mvndst.f + double precision :: p + double precision :: phinvs + end function phinvs + function bvnmvn(lower,upper,infin,correl) ! in :mvn2:mvndst.f + double precision dimension(*) :: lower + double precision dimension(*) :: upper + integer dimension(*) :: infin + double precision :: correl + double precision :: bvnmvn + end function bvnmvn + function bvu(sh,sk,r) ! in :mvn2:mvndst.f + double precision :: sh + double precision :: sk + double precision :: r + double precision :: bvu + end function bvu + function mvnuni() ! in :mvn2:mvndst.f + double precision :: mvnuni + end function mvnuni + end interface +end python module mvn2 + +! This file was auto-generated with f2py (version:2_5972). +! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/wafo/mvndst.f b/wafo/mvndst.f new file mode 100755 index 0000000..255efff --- /dev/null +++ b/wafo/mvndst.f @@ -0,0 +1,1130 @@ +C f2py -m -h mvn1.pyf mvndst.f +C f2py mvn.pyf mvndst.f -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 +! f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m mvnprd -c mvnprd.f + +* Note: The test program has been removed and a utlity routine mvnun has been +* added. RTK 2004-08-10 +* +* Copyright 2000 by Alan Genz. +* Copyright 2004-2005 by Enthought, Inc. +* +* The subroutine MVNUN is copyrighted by Enthought, Inc. +* The rest of the file is copyrighted by Alan Genz and has kindly been offered +* to the Scipy project under it's BSD-style license. +* +* This file contains a short test program and MVNDST, a subroutine +* for computing multivariate normal distribution function values. +* The file is self contained and should compile without errors on (77) +* standard Fortran compilers. The test program demonstrates the use of +* MVNDST for computing MVN distribution values for a five dimensional +* example problem, with three different integration limit combinations. +* +* Alan Genz +* Department of Mathematics +* Washington State University +* Pullman, WA 99164-3113 +* Email : alangenz@wsu.edu +* + SUBROUTINE mvnun(d, n, lower, upper, means, covar, maxpts, + & abseps, releps, value, inform) +* Parameters +* +* d integer, dimensionality of the data +* n integer, the number of data points +* lower double(2), the lower integration limits +* upper double(2), the upper integration limits +* means double(n), the mean of each kernel +* covar double(2,2), the covariance matrix +* maxpts integer, the maximum number of points to evaluate at +* abseps double, absolute error tolerance +* releps double, relative error tolerance +* value double intent(out), integral value +* inform integer intent(out), +* if inform == 0: error < eps +* elif inform == 1: error > 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 = 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 ) + 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 + 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/namedtuple.py b/wafo/namedtuple.py new file mode 100755 index 0000000..9a634f3 --- /dev/null +++ b/wafo/namedtuple.py @@ -0,0 +1,132 @@ +from operator import itemgetter as _itemgetter +from keyword import iskeyword as _iskeyword +import sys as _sys + +def namedtuple(typename, field_names, verbose=False): + """Returns a new subclass of tuple with named fields. + + >>> Point = namedtuple('Point', 'x y') + >>> Point.__doc__ # docstring for the new class + 'Point(x, y)' + >>> p = Point(11, y=22) # instantiate with positional args or keywords + >>> p[0] + p[1] # indexable like a plain tuple + 33 + >>> x, y = p # unpack like a regular tuple + >>> x, y + (11, 22) + >>> p.x + p.y # fields also accessable by name + 33 + >>> d = p._asdict() # convert to a dictionary + >>> d['x'] + 11 + >>> Point(**d) # convert from a dictionary + Point(x=11, y=22) + >>> p._replace(x=100) # _replace() is like str.replace() but targets named fields + Point(x=100, y=22) + + """ + + # Parse and validate the field names. Validation serves two purposes, + # generating informative error messages and preventing template injection attacks. + if isinstance(field_names, basestring): + field_names = field_names.replace(',', ' ').split() # names separated by whitespace and/or commas + field_names = tuple(field_names) + for name in (typename,) + field_names: + if not min(c.isalnum() or c=='_' for c in name): + raise ValueError('Type names and field names can only contain alphanumeric characters and underscores: %r' % name) + if _iskeyword(name): + raise ValueError('Type names and field names cannot be a keyword: %r' % name) + if name[0].isdigit(): + raise ValueError('Type names and field names cannot start with a number: %r' % name) + seen_names = set() + for name in field_names: + if name.startswith('_'): + raise ValueError('Field names cannot start with an underscore: %r' % name) + if name in seen_names: + raise ValueError('Encountered duplicate field name: %r' % name) + seen_names.add(name) + + # Create and fill-in the class template + numfields = len(field_names) + argtxt = repr(field_names).replace("'", "")[1:-1] # tuple repr without parens or quotes + reprtxt = ', '.join('%s=%%r' % name for name in field_names) + dicttxt = ', '.join('%r: t[%d]' % (name, pos) for pos, name in enumerate(field_names)) + template = '''class %(typename)s(tuple): + '%(typename)s(%(argtxt)s)' \n + __slots__ = () \n + _fields = %(field_names)r \n + def __new__(cls, %(argtxt)s): + return tuple.__new__(cls, (%(argtxt)s)) \n + @classmethod + def _make(cls, iterable, new=tuple.__new__, len=len): + 'Make a new %(typename)s object from a sequence or iterable' + result = new(cls, iterable) + if len(result) != %(numfields)d: + raise TypeError('Expected %(numfields)d arguments, got %%d' %% len(result)) + return result \n + def __repr__(self): + return '%(typename)s(%(reprtxt)s)' %% self \n + def _asdict(t): + 'Return a new dict which maps field names to their values' + return {%(dicttxt)s} \n + def _replace(self, **kwds): + 'Return a new %(typename)s object replacing specified fields with new values' + result = self._make(map(kwds.pop, %(field_names)r, self)) + if kwds: + raise ValueError('Got unexpected field names: %%r' %% kwds.keys()) + return result \n\n''' % locals() + for i, name in enumerate(field_names): + template += ' %s = property(itemgetter(%d))\n' % (name, i) + if verbose: + print template + + # Execute the template string in a temporary namespace + namespace = dict(itemgetter=_itemgetter) + try: + exec template in namespace + except SyntaxError, e: + raise SyntaxError(e.message + ':\n' + template) + result = namespace[typename] + + # For pickling to work, the __module__ variable needs to be set to the frame + # where the named tuple is created. Bypass this step in enviroments where + # sys._getframe is not defined (Jython for example). + if hasattr(_sys, '_getframe'): + result.__module__ = _sys._getframe(1).f_globals['__name__'] + + return result + + + + + + +if __name__ == '__main__': + # verify that instances can be pickled + from cPickle import loads, dumps + Point = namedtuple('Point', 'x, y', True) + p = Point(x=10, y=20) + assert p == loads(dumps(p)) + + # test and demonstrate ability to override methods + class Point(namedtuple('Point', 'x y')): + @property + def hypot(self): + return (self.x ** 2 + self.y ** 2) ** 0.5 + def __str__(self): + return 'Point: x=%6.3f y=%6.3f hypot=%6.3f' % (self.x, self.y, self.hypot) + + for p in Point(3,4), Point(14,5), Point(9./7,6): + print p + + class Point(namedtuple('Point', 'x y')): + 'Point class with optimized _make() and _replace() without error-checking' + _make = classmethod(tuple.__new__) + def _replace(self, _map=map, **kwds): + return self._make(_map(kwds.get, ('x', 'y'), self)) + + print Point(11, 22)._replace(x=100) + + import doctest + TestResults = namedtuple('TestResults', 'failed attempted') + print TestResults(*doctest.testmod()) \ No newline at end of file diff --git a/wafo/objects.py b/wafo/objects.py new file mode 100755 index 0000000..9883db4 --- /dev/null +++ b/wafo/objects.py @@ -0,0 +1,1454 @@ + +#------------------------------------------------------------------------------- +# Name: module1 +# Purpose: +# +# Author: pab +# +# Created: 16.09.2008 +# Copyright: (c) pab 2008 +# Licence: +#------------------------------------------------------------------------------- +#!/usr/bin/env python + + +from __future__ import division +import warnings +import numpy as np + +from numpy import (inf, pi, zeros, ones, sqrt, where, log, exp, sin, arcsin, mod, #@UnresolvedImport + newaxis, linspace, arange, sort, all, abs, linspace, vstack, hstack, atleast_1d, #@UnresolvedImport + polyfit, r_, nonzero, cumsum, ravel, size, isnan, nan, floor, ceil, diff, array) #@UnresolvedImport +from numpy.fft import fft +from numpy.random import randn +from scipy.integrate import trapz +from pylab import stineman_interp +from matplotlib.mlab import psd +import scipy.signal + +from scipy.special import erf + +from wafo.misc import (nextpow2, findtp, findtc, findcross, sub_dict_select, + ecross, JITImport) +from wafodata import WafoData +from plotbackend import plotbackend +import matplotlib +matplotlib.interactive(True) +_wafocov = JITImport('wafo.covariance') +_wafospec = JITImport('wafo.spectrum') + +__all__ = ['TimeSeries','LevelCrossings','CyclePairs','TurningPoints', + 'sensortypeid','sensortype'] + + + +class LevelCrossings(WafoData): + ''' + Container class for Level crossing data objects in WAFO + + Member variables + ---------------- + data : array-like + number of upcrossings + args : array-like + crossing levels + + ''' + def __init__(self,*args,**kwds): + super(LevelCrossings, self).__init__(*args,**kwds) + self.labels.title = 'Level crossing spectrum' + self.labels.xlab = 'Levels' + self.labels.ylab = 'Count' + self.stdev = kwds.get('stdev',None) + self.mean = kwds.get('mean',None) + self.setplotter(plotmethod='step') + + icmax = self.data.argmax() + if self.data != None: + if self.stdev is None or self.mean is None: + logcros = where(self.data==0.0, inf, -log(self.data)) + logcmin = logcros[icmax] + logcros = sqrt(2*abs(logcros-logcmin)) + logcros[0:icmax+1] = 2*logcros[icmax]-logcros[0:icmax+1] + p = polyfit(self.args[10:-9], logcros[10:-9],1) #least square fit + if self.stdev is None: + self.stdev = 1.0/p[0] #estimated standard deviation of x + if self.mean is None: + self.mean = -p[1]/p[0] #self.args[icmax] + cmax = self.data[icmax] + x = (self.args-self.mean)/self.stdev + y = cmax*exp(-x**2/2.0) + self.children = [WafoData(y,self.args)] + + def sim(self,ns,alpha): + """ + Simulates process with given irregularity factor and crossing spectrum + + Parameters + ---------- + ns : scalar, integer + number of sample points. + alpha : real scalar + irregularity factor, 0>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=7) + >>> S = Sj.tospecdata() #Make spectrum object from numerical values + >>> alpha = S.characteristic('alpha')[0] + >>> n = 10000 + >>> xs = S.sim(ns=n) + >>> ts = mat2timeseries(xs) + >>> tp = ts.turning_points() + >>> mm = tp.cycle_pairs() + >>> lc = mm.level_crossings() + + xs2 = lc.sim(n,alpha) + ts2 = mat2timeseries(xs2) + Se = ts2.tospecdata() + + S.plot('b') + Se.plot('r') + alpha2 = Se.characteristic('alpha')[0] + alpha-alpha2 + + spec2char(Se,'alpha') + lc2 = dat2lc(xs2) + figure(gcf+1) + subplot(211) + lcplot(lc2) + subplot(212) + lcplot(lc) + """ + + # TODO % add a good example + f = linspace(0,0.49999,1000) + rho_st = 2.*sin(f*pi)**2-1. + tmp = alpha*arcsin(sqrt((1.+rho_st)/2)) + tmp = sin(tmp)**2 + a2 = (tmp-rho_st)/(1-tmp) + y = vstack((a2+rho_st,1-a2)).min(axis=0) + maxidx = y.argmax() + #[maximum,maxidx]=max(y) + + rho_st = rho_st[maxidx] + a2 = a2[maxidx] + a1 = 2.*rho_st+a2-1. + r0 = 1. + r1 = -a1/(1.+a2) + r2 = (a1**2-a2-a2**2)/(1+a2) + sigma2 = r0+a1*r1+a2*r2 + #randn = np.random.randn + e = randn(ns)*sqrt(sigma2) + e[:1] = 0.0 + L0 = randn(1) + L0 = vstack((L0,r1*L0+sqrt(1-r2**2)*randn(1))) + #%Simulate the process, starting in L0 + lfilter = scipy.signal.lfilter + L = lfilter(1,[1, a1, a2],e,lfilter([1, a1, a2],1,L0)) + + epsilon = 1.01 + min_L = min(L) + max_L = max(L) + maxi = max(abs(r_[min_L, max_L]))*epsilon + mini = -maxi + + u = linspace(mini,maxi,101) + G = (1+erf(u/sqrt(2)))/2 + G = G*(1-G) + + x = linspace(0,r1,100) + factor1 = 1./sqrt(1-x**2) + factor2 = 1./(1+x) + integral = zeros(u.shape, dtype=float) + for i in range(len(integral)): + y = factor1*exp(-u[i]*u[i]*factor2) + integral[i] = trapz(x,y) + #end + G = G-integral/(2*pi) + G = G/max(G) + + Z = ((u>=0)*2-1)*sqrt(-2*log(G)) + +## sumcr = trapz(lc(:,1),lc(:,2)) +## lc(:,2) = lc(:,2)/sumcr +## mcr = trapz(lc(:,1),lc(:,1).*lc(:,2)) +## scr = trapz(lc(:,1),lc(:,1).^2.*lc(:,2)) +## scr = sqrt(scr-mcr^2) +## g = lc2tr(lc,mcr,scr) +## +## f = [u u] +## f(:,2) = tranproc(Z,fliplr(g)) +## +## process = tranproc(L,f) +## process = [(1:length(process)) process] +## +## +## %Check the result without reference to getrfc: +## LCe = dat2lc(process) +## max(lc(:,2)) +## max(LCe(:,2)) +## +## clf +## plot(lc(:,1),lc(:,2)/max(lc(:,2))) +## hold on +## plot(LCe(:,1),LCe(:,2)/max(LCe(:,2)),'-.') +## title('Relative crossing intensity') +## +## %% Plot made by the function funplot_4, JE 970707 +## %param = [min(process(:,2)) max(process(:,2)) 100] +## %plot(lc(:,1),lc(:,2)/max(lc(:,2))) +## %hold on +## %plot(levels(param),mu/max(mu),'--') +## %hold off +## %title('Crossing intensity') +## %watstamp +## +## % Temporarily +## %funplot_4(lc,param,mu) + + + def trdata(self, mean=None, sigma=None, **options): + ''' + Estimate transformation, g, from observed crossing intensity, version2. + + Assumption: a Gaussian process, Y, is related to the + non-Gaussian process, X, by Y = g(X). + + Parameters + ---------- + options = structure with the fields: + csm, gsm - defines the smoothing of the crossing intensity and the + transformation g. Valid values must be + 0<=csm,gsm<=1. (default csm = 0.9 gsm=0.05) + Smaller values gives smoother functions. + param - vector which defines the region of variation of the data X. + (default [-5 5 513]). + + monitor monitor development of estimation + linextrap - 0 use a regular smoothing spline + 1 use a smoothing spline with a constraint on the ends to + ensure linear extrapolation outside the range of the data. + (default) + cvar - Variances for the crossing intensity. (default 1) + gvar - Variances for the empirical transformation, g. (default 1) + ne - Number of extremes (maxima & minima) to remove from the + estimation of the transformation. This makes the + estimation more robust against outliers. (default 7) + Ntr - Maximum length of empirical crossing intensity. + The empirical crossing intensity is interpolated + linearly before smoothing if the length exceeds Ntr. + A reasonable NTR will significantly speed up the + estimation for long time series without loosing any + accuracy. NTR should be chosen greater than + PARAM(3). (default 1000) + Returns + ------- + gs, ge : TrData objects + smoothed and empirical estimate of the transformation g. + ma,sa = mean and standard deviation of the process + + Notes + ----- + The empirical crossing intensity is usually very irregular. + More than one local maximum of the empirical crossing intensity + may cause poor fit of the transformation. In such case one + should use a smaller value of GSM or set a larger variance for GVAR. + If X(t) is likely to cross levels higher than 5 standard deviations + then the vector param has to be modified. For example if X(t) is + unlikely to cross a level of 7 standard deviations one can use + param = [-7 7 513]. + + Example + ------- + Hm0 = 7 + S = jonswap([],Hm0); g=ochitr([],[Hm0/4]); + S.tr = g; S.tr(:,2)=g(:,2)*Hm0/4; + xs = spec2sdat(S,2^13); + lc = dat2lc(xs) + g0 = lc2tr2(lc,0,Hm0/4,'plot','iter'); % Monitor the development + g1 = lc2tr2(lc,0,Hm0/4,troptset('gvar', .5 )); % Equal weight on all points + g2 = lc2tr2(lc,0,Hm0/4,'gvar', [3.5 .5 3.5]); % Less weight on the ends + hold on, trplot(g1,g) % Check the fit + trplot(g2) + + See also troptset, dat2tr, trplot, findcross, smooth + + NB! the transformated data will be N(0,1) + + Reference + --------- + Rychlik , I., Johannesson, P., and Leadbetter, M.R. (1997) + "Modelling and statistical analysis of ocean wavedata + using a transformed Gaussian process", + Marine structures, Design, Construction and Safety, + Vol 10, pp 13--47 + ''' + + + # Tested on: Matlab 5.3, 5.2, 5.1 + # History: + # by pab 29.12.2000 + # based on lc2tr, but the inversion is faster. + # by IR and PJ + pass + +# opt = troptset('chkder','on','plotflag','off','csm',.9,'gsm',.05,.... +# 'param',[-5 5 513],'delay',2,'linextrap','on','ntr',1000,'ne',7,'cvar',1,'gvar',1); +# # If just 'defaults' passed in, return the default options in g +# if nargin==1 && nargout <= 1 && isequal(cross,'defaults') +# g = opt; +# return +# end +# error(nargchk(3,inf,nargin)) +# if nargin>=4 , opt = troptset(opt,varargin{:}); end +# csm2 = opt.gsm; +# param = opt.param; +# ptime = opt.delay; +# Ne = opt.ne; +# switch opt.chkder; +# case 'off', chkder = 0; +# case 'on', chkder = 1; +# otherwise, chkder = opt.chkder; +# end +# switch opt.linextrap; +# case 'off', def = 0; +# case 'on', def = 1; +# otherwise, def = opt.linextrap; +# end +# switch opt.plotflag +# case {'none','off'}, plotflag = 0; +# case 'final', plotflag = 1; +# case 'iter', plotflag = 2; +# otherwise, plotflag = opt.plotflag; +# end +# ncr = length(cross); +# if ncr>opt.ntr && opt.ntr>0, +# x0 = linspace(cross(1+Ne,1),cross(end-Ne,1),opt.ntr)'; +# cros = [ x0,interp1q(cross(:,1),cross(:,2),x0)]; +# Ne = 0; +# Ner = opt.ne; +# ncr = opt.ntr; +# else +# Ner = 0; +# cros=cross; +# end +# +# ng = length(opt.gvar); +# if ng==1 +# gvar = opt.gvar(ones(ncr,1)); +# else +# gvar = interp1(linspace(0,1,ng)',opt.gvar(:),linspace(0,1,ncr)','*linear'); +# end +# ng = length(opt.cvar); +# if ng==1 +# cvar = opt.cvar(ones(ncr,1)); +# else +# cvar = interp1(linspace(0,1,ng)',opt.cvar(:),linspace(0,1,ncr)','*linear'); +# end +# +# g = zeros(param(3),2); +# +# uu = levels(param); +# +# g(:,1) = sa*uu' + ma; +# +# g2 = cros; +# +# if Ner>0, # Compute correction factors +# cor1 = trapz(cross(1:Ner+1,1),cross(1:Ner+1,2)); +# cor2 = trapz(cross(end-Ner-1:end,1),cross(end-Ner-1:end,2)); +# else +# cor1 = 0; +# cor2 = 0; +# end +# cros(:,2) = cumtrapz(cros(:,1),cros(:,2))+cor1; +# cros(:,2) = (cros(:,2)+.5)/(cros(end,2) + cor2 +1); +# cros(:,1) = (cros(:,1)-ma)/sa; +# +# # find the mode +# [tmp,imin]= min(abs(cros(:,2)-.15)); +# [tmp,imax]= min(abs(cros(:,2)-.85)); +# inde = imin:imax; +# tmp = smooth(cros(inde,1),g2(inde,2),opt.csm,cros(inde,1),def,cvar(inde)); +# +# [tmp imax] = max(tmp); +# u0 = cros(inde(imax),1); +# #u0 = interp1q(cros(:,2),cros(:,1),.5) +# +# +# cros(:,2) = invnorm(cros(:,2),-u0,1); +# +# g2(:,2) = cros(:,2); +# # NB! the smooth function does not always extrapolate well outside the edges +# # causing poor estimate of g +# # We may alleviate this problem by: forcing the extrapolation +# # to be linear outside the edges or choosing a lower value for csm2. +# +# inds = 1+Ne:ncr-Ne;# indices to points we are smoothing over +# scros2 = smooth(cros(inds,1),cros(inds,2),csm2,uu,def,gvar(inds)); +# +# g(:,2) = scros2';#*sa; #multiply with stdev +# +# if chkder~=0 +# for ix = 1:5 +# dy = diff(g(:,2)); +# if any(dy<=0) +# warning('WAFO:LCTR2','The empirical crossing spectrum is not sufficiently smoothed.') +# disp(' The estimated transfer function, g, is not ') +# disp(' a strictly increasing function.') +# dy(dy>0)=eps; +# gvar = -([dy;0]+[0;dy])/2+eps; +# g(:,2) = smooth(g(:,1),g(:,2),1,g(:,1),def,ix*gvar); +# else +# break +# end +# end +# end +# if 0, #either +# test = sqrt((param(2)-param(1))/(param(3)-1)*sum((uu-scros2).^2)); +# else # or +# #test=sqrt(simpson(uu,(uu-scros2).^2)); +# # or +# test=sqrt(trapz(uu,(uu-scros2).^2)); +# end +# +# +# if plotflag>0, +# trplot(g ,g2,ma,sa) +# #legend(['Smoothed (T=' num2str(test) ')'],'g(u)=u','Not smoothed',0) +# #ylabel('Transfer function g(u)') +# #xlabel('Crossing level u') +# +# if plotflag>1,pause(ptime),end +# end + + +class CyclePairs(WafoData): + ''' + Container class for Cycle Pairs data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D + + + ''' + def __init__(self, *args, **kwds): + super(CyclePairs, self).__init__(*args, **kwds) + self.type_ = kwds.get('type_', 'max2min') + self.stdev = kwds.get('stdev', None) + self.mean = kwds.get('mean', None) + + self.labels.title = self.type_+ ' cycle pairs' + self.labels.xlab = 'min' + self.labels.ylab = 'max' + + def amplitudes(self): + return (self.data-self.args)/2. + + def damage(self, beta, K=1): + """ + Calculates the total Palmgren-Miner damage of cycle pairs. + + Parameters + ---------- + beta : array-like, size m + Beta-values, material parameter. + K : scalar, optional + K-value, material parameter. + + Returns + ------- + D : ndarray, size m + Damage. + + Notes + ----- + The damage is calculated according to + D[i] = sum ( K * a**beta[i] ), with a = (max-min)/2 + + Examples + -------- + >>> import wafo + >>> from matplotlib import pyplot as plt + >>> ts = wafo.objects.mat2timeseries(wafo.data.sea()) + >>> tp = ts.turning_points() + >>> mm = tp.cycle_pairs() + >>> h = mm.plot('.') + >>> bv = range(3,9) + >>> D = mm.damage(beta=bv) + >>> D + array([ 138.5238799 , 117.56050788, 108.99265423, 107.86681126, + 112.3791076 , 122.08375071]) + >>> h = plt.plot(bv,D,'x-') + + See also + -------- + SurvivalCycleCount + """ + amp = abs(self.amplitudes()) + return atleast_1d([K*np.sum(amp**betai) for betai in beta]) + + def level_crossings(self, type_='uM'): + """ Return number of upcrossings from a cycle count. + + Parameters + ---------- + type_ : int or string + defining crossing type, options are + 0,'u' : only upcrossings. + 1,'uM' : upcrossings and maxima (default). + 2,'umM': upcrossings, minima, and maxima. + 3,'um' :upcrossings and minima. + Return + ------ + lc : level crossing object + with levels and number of upcrossings. + + + Calculates the number of upcrossings from a cycle pairs, e.g. + min2Max cycles or rainflow cycles. + + Example: + -------- + >>> import wafo + >>> ts = wafo.objects.mat2timeseries(wafo.data.sea()) + >>> tp = ts.turning_points() + >>> mm = tp.cycle_pairs() + >>> h = mm.plot('.') + >>> lc = mm.level_crossings() + >>> h2 = lc.plot() + + See also + -------- + TurningPoints + LevelCrossings + """ + + if isinstance(type_, str): + t = dict(u=0, uM=1, umM=2, um=3) + defnr = t.get(type_, 1) + else: + defnr = type_ + + if ((defnr<0) or (defnr>3)): + raise ValueError('type_ must be one of (1,2,3,4).') + + index, = nonzero(self.args <= self.data) + if index.size == 0: + index, = nonzero(self.args >= self.data) + M = self.args[index] + m = self.data[index] + else: + m = self.args[index] + M = self.data[index] + +#if isempty(index) +# error('Error in input cc.') +#end + ncc = len(m) + #ones = np.ones + #zeros = np.zeros + #cumsum = np.cumsum + minima = vstack((m, ones(ncc), zeros(ncc), ones(ncc))) + maxima = vstack((M, -ones(ncc), ones(ncc), zeros(ncc))) + + extremes = hstack((maxima, minima)) + index = extremes[0].argsort() + extremes = extremes[:, index] + + ii = 0 + n = extremes.shape[1] + extr = zeros((4, n)) + extr[:, 0] = extremes[:, 0] + for i in xrange(1, n): + if extremes[0, i] == extr[0, ii]: + extr[1:4, ii] = extr[1:4, ii] + extremes[1:4, i] + else: + ii += 1 + extr[:, ii] = extremes[:, i] + + #[xx nx]=max(extr(:,1)) + nx = extr[0].argmax()+1 + levels = extr[0, 0:nx] + if defnr == 2: ## This are upcrossings + maxima + dcount = cumsum(extr[1, 0:nx]) + extr[2, 0:nx]-extr[3, 0:nx] + elif defnr == 4: # # This are upcrossings + minima + dcount = cumsum(extr[1, 0:nx]) + dcount[nx-1] = dcount[nx-2] + elif defnr == 1: ## This are only upcrossings + dcount = cumsum(extr[1, 0:nx]) - extr[3, 0:nx] + elif defnr == 3: ## This are upcrossings + minima + maxima + dcount = cumsum(extr[1, 0:nx]) + extr[2, 0:nx] + return LevelCrossings(dcount, levels, stdev=self.stdev) + +class TurningPoints(WafoData): + ''' + Container class for Turning Points data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D + + + ''' + def __init__(self, *args, **kwds): + super(TurningPoints, self).__init__(*args, **kwds) + self.name='WAFO TurningPoints Object' + somekeys = ['name'] + self.__dict__.update(sub_dict_select(kwds, somekeys)) + + #self.setlabels() + if not any(self.args): + n = len(self.data) + self.args = range(0, n) + else: + self.args = ravel(self.args) + self.data= ravel(self.data) + + def cycle_pairs(self, type_='min2max'): + """ Return min2Max or Max2min cycle pairs from turning points + + Parameters + ---------- + type_ : string + type of cycles to return options are 'min2max' or 'max2min' + + Return + ------ + mm : cycles object + with min2Max or Max2min cycle pairs. + + Example + ------- + >>> import wafo + >>> x = wafo.data.sea() + >>> ts = wafo.objects.mat2timeseries(x) + >>> tp = ts.turning_points() + >>> mM = tp.cycle_pairs() + >>> h = mM.plot('.') + + + See also + -------- + TurningPoints + SurvivalCycleCount + """ + if self.data[0]>self.data[1]: + im = 1 + iM = 0 + else: + im = 0 + iM = 1 + + # Extract min-max and max-min cycle pairs + #n = len(self.data) + if type_.lower().startswith('min2max'): + m = self.data[im:-1:2] + M = self.data[im+1::2] + else: + type_ = 'max2min' + M = self.data[iM:-1:2] + m = self.data[iM+1::2] + + return CyclePairs(M, m, type=type_) + +def mat2timeseries(x): + """ + Convert 2D arrays to TimeSeries object + assuming 1st column is time and the remaining columns contain data. + """ + return TimeSeries(x[:, 1::], x[:, 0].ravel()) + +class TimeSeries(WafoData): + ''' + Container class for 1D TimeSeries data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + sensortypes : list of integers or strings + sensor type for time series (default ['n'] : Surface elevation) + see sensortype for more options + position : vector of size 3 + instrument position relative to the coordinate system + + Examples + -------- + >>> import wafo.data + >>> x = wafo.data.sea() + >>> ts = mat2timeseries(x) + >>> rf = ts.tocovdata(lag=150) + >>> h = rf.plot() + + ''' + def __init__(self, *args, **kwds): + super(TimeSeries, self).__init__(*args, **kwds) + self.name = 'WAFO TimeSeries Object' + self.sensortypes = ['n', ] + self.position = zeros(3) + somekeys = ['sensortypes', 'position'] + self.__dict__.update(sub_dict_select(kwds, somekeys)) + + #self.setlabels() + if not any(self.args): + n = len(self.data) + self.args = range(0, n) + + def sampling_period(self): + ''' + Returns sampling interval + + Returns + ------- + dt : scalar + sampling interval, unit: + [s] if lagtype=='t' + [m] otherwise + + See also + ''' + dt1 = self.args[1]-self.args[0] + n = size(self.args)-1 + t = self.args[-1]-self.args[0] + dt = t/n + if abs(dt-dt1) > 1e-10: + warnings.warn('Data is not uniformly sampled!') + return dt + + def tocovdata(self, lag=None, flag='biased', norm=False, dt = None): + ''' + Return auto covariance function from data. + + Parameters + ---------- + lag : scalar, int + maximum time-lag for which the ACF is estimated. (Default lag=n-1) + flag : string, 'biased' or 'unbiased' + If 'unbiased' scales the raw correlation by 1/(n-abs(k)), + where k is the index into the result, otherwise scales the raw + cross-correlation by 1/n. (default) + norm : bool + True if normalize output to one + dt : scalar + time-step between data points (default see sampling_period). + + Return + ------- + R : CovData1D object + with attributes: + data : ACF vector length L+1 + args : time lags length L+1 + stdev : estimated large lag standard deviation of the estimate + assuming x is a Gaussian process: + if R(k)=0 for all lags k>q then an approximation + of the variance for large samples due to Bartlett + var(R(k))=1/N*(R(0)^2+2*R(1)^2+2*R(2)^2+ ..+2*R(q)^2) + for k>q and where N=length(x). Special case is + white noise where it equals R(0)^2/N for k>0 + norm : bool + If false indicating that R is not normalized + + Example: + -------- + >>> import wafo.data + >>> x = wafo.data.sea() + >>> ts = mat2timeseries(x) + >>> acf = ts.tocovdata(150) + >>> h = acf.plot() + ''' + n = len(self.data) + if not lag: + lag = n-1 + + x = self.data.flatten() + indnan = isnan(x) + if any(indnan): + x = x - x[1-indnan].mean() # remove the mean pab 09.10.2000 + #indnan = find(indnan) + Ncens = n - sum(indnan) + x[indnan] = 0. # pab 09.10.2000 much faster for censored samples + else: + indnan = None + Ncens = n + x = x - x.mean() + + #fft = np.fft.fft + nfft = 2**nextpow2(n) + Rper = abs(fft(x,nfft))**2/Ncens # Raw periodogram + + R = np.real(fft(Rper))/nfft # %ifft=fft/nfft since Rper is real! + lags = range(0,lag+1) + if flag.startswith('unbiased'): + # unbiased result, i.e. divide by n-abs(lag) + R = R[lags]*Ncens/arange(Ncens, Ncens-lag, -1) + #else % biased result, i.e. divide by n + # r=r(1:L+1)*Ncens/Ncens + + c0 = R[0] + if norm: + R = R/c0 + if dt is None: + dt = self.sampling_period() + t = linspace(0,lag*dt,lag+1) + #cumsum = np.cumsum + acf = _wafocov.CovData1D(R[lags],t) + acf.stdev=sqrt(r_[ 0, 1 ,1+2*cumsum(R[1:]**2)]/Ncens) + acf.children = [WafoData(-2.*acf.stdev[lags],t),WafoData(2.*acf.stdev[lags],t)] + acf.norm = norm + return acf + + def tospecdata(self,*args,**kwargs): + """ + Return power spectral density by Welches average periodogram method. + + Parameters + ---------- + NFFT : int, scalar + if len(data) < NFFT, it will be zero padded to `NFFT` + before estimation. Must be even; a power 2 is most efficient. + detrend : function + Fs : real, scalar + sampling frequency (samples per time unit). + + window : vector of length NFFT or function + To create window vectors see numpy.blackman, numpy.hamming, + numpy.bartlett, scipy.signal, scipy.signal.get_window etc. + noverlap : scalar int + gives the length of the overlap between segments. + + Returns + ------- + S : SpecData1D + Power Spectral Density + + Notes + ----- + The data vector is divided into NFFT length segments. Each segment + is detrended by function detrend and windowed by function window. + noverlap gives the length of the overlap between segments. The + absolute(fft(segment))**2 of each segment are averaged to compute Pxx, + with a scaling to correct for power loss due to windowing. + + Reference + --------- + Bendat & Piersol (1986) Random Data: Analysis and Measurement + Procedures, John Wiley & Sons + """ + fs = 1./(2*self.sampling_period()) + S, f = psd(self.data.ravel(), Fs=fs, *args, **kwargs) + fact = 2.0*pi + w = fact*f + return _wafospec.SpecData1D(S/fact, w) + + def turning_points(self,h=0.0,wavetype=None): + ''' + Return turning points (tp) from data, optionally rainflowfiltered. + + Parameters + ---------- + h : scalar + a threshold + if h<=0, then tp is a sequence of turning points (default) + if h>0, then all rainflow cycles with height smaller than + h are removed. + + wavetype : string + defines the type of wave. Possible options are + 'mw' 'Mw' or 'none'. + If None all rainflow filtered min and max + will be returned, otherwise only the rainflow filtered + min and max, which define a wave according to the + wave definition, will be returned. + + Returns + ------- + tp : TurningPoints object + with times and turning points. + + Example: + >>> import wafo.data + >>> x = wafo.data.sea() + >>> x1 = x[:200,:] + >>> ts1 = mat2timeseries(x1) + >>> tp = ts1.turning_points(wavetype='Mw') + >>> tph = ts1.turning_points(h=0.3,wavetype='Mw') + >>> hs = ts1.plot() + >>> hp = tp.plot('ro') + >>> hph = tph.plot('k.') + + See also + --------- + findcross, + findrfc + findtp + ''' + ind = findtp(self.data, max(h,0.0), wavetype) + try: + t = self.args[ind] + except: + t = ind + return TurningPoints(self.data[ind],t) + + def trough_crest(self,v=None,wavetype=None): + """ + Return trough and crest turning points + + Parameters + ----------- + v : scalar + reference level (default v = mean of x). + + wavetype : string + defines the type of wave. Possible options are + 'dw', 'uw', 'tw', 'cw' or None. + If None indices to all troughs and crests will be returned, + otherwise only the paired ones will be returned + according to the wavedefinition. + + Returns + -------- + tc : TurningPoints object + with trough and crest turningpoints + """ + ind = findtc(self.data, v, wavetype)[0] + try: + t = self.args[ind] + except: + t = ind + return TurningPoints(self.data[ind], t) + + def wave_periods(self, vh=None, pdef='d2d', wdef=None, index=None, rate=1): + """ + Return sequence of wave periods/lengths from data. + + Parameters + ---------- + vh : scalar + reference level ( default v=mean(x(:,2)) ) or + rainflow filtering height (default h=0) + pdef : string + defining type of waveperiod (wavelength) returned: + Level v separated 't2c', 'c2t', 't2t' or 'c2c' -waveperiod. + Level v 'd2d', 'u2u', 'd2u' or 'u2d' -waveperiod. + Rain flow filtered (with height greater than h) + 'm2M', 'M2m', 'm2m' or 'M2M' -waveperiod. + Explanation to the abbreviations: + M=Max, m=min, d=down-crossing, u=up-crossing , + t=trough and c=crest. + Thus 'd2d' means period between a down-crossing to the + next down-crossing and 'u2c' means period between a + u-crossing to the following crest. + wdef : string + defining type of wave. Possible options are + 'mw','Mw','dw', 'uw', 'tw', 'cw' or None. + If wdef is None all troughs and crests will be used, + otherwise only the troughs and crests which define a + wave according to the wavedefinition are used. + + index : vector + index sequence of one of the following : + -level v-crossings (indices to "du" are required to + calculate 'd2d', 'd2u', 'u2d' or 'u2u' waveperiods) + -level v separated trough and crest turningpoints + (indices to 'tc' are required to calculate + 't2t', 't2c', 'c2t' or 'c2c' waveperiods) + -level v crossings and level v separated trough and + crest turningpoints (indices to "dutc" are + required to calculate t2u, u2c, c2d or d2t + waveperiods) + -rainflow filtered turningpoints with minimum rfc height h + (indices to "mMtc" are required to calculate + 'm2m', 'm2M', 'M2m' or 'M2M' waveperiods) + + rate : scalar + interpolation rate. If rate larger than one, then x is + interpolated before extrating T + + Returns + -------- + T : vector + sequence of waveperiods (or wavelengths). + index : vector + of indices + + + Example: + -------- + >>> import wafo + >>> x = wafo.data.sea() + >>> ts = wafo.objects.mat2timeseries(x[0:400,:]) + >>> T = ts.wave_periods(vh=0.0,pdef='c2c') + + T = dat2wa(x1,0,'c2c') #% Returns crest2crest waveperiods + subplot(121), waveplot(x1,'-',1,1),subplot(122),histgrm(T) + + See also: + -------- + findtp, + findtc, + findcross, perioddef + """ + +##% This is a more flexible version than the dat2hwa or tp2wa routines. +##% There is a secret option: if pdef='all' the function returns +##% all the waveperiods 'd2t', 't2u', 'u2c' and 'c2d' in sequence. +##% It is up to the user to extract the right waveperiods. +##% If the first is a down-crossing then the first is a 'd2t' waveperiod. +##% If the first is a up-crossing then the first is a 'u2c' waveperiod. +##% +##% Example: +##% [T ind]=dat2wa(x,0,'all') %returns all waveperiods +##% nn = length(T) +##% % want to extract all t2u waveperiods +##% if x(ind(1),2)>0 % if first is down-crossing +##% Tt2u=T(2:4:nn) +##% else % first is up-crossing +##% Tt2u=T(4:4:nn) +##% end + + if rate>1: #% interpolate with spline + n = ceil(self.data.size*rate) + ti = linspace(self.args[0], self.args[-1], n) + x = stineman_interp(ti, self.args, self.data) + else: + x = self.data + ti = self.args + + + if vh is None: + if pdef[0] in ('m','M'): + vh = 0 + print(' The minimum rfc height, h, is set to: %g' % vh) + else: + vh = x.mean() + print(' The level l is set to: %g' % vh) + + + if index is None: + if pdef in ('m2m', 'm2M', 'M2m','M2M'): + index = findtp(x, vh, wdef) + elif pdef in ('u2u','u2d','d2u', 'd2d'): + index = findcross(x, vh, wdef) + elif pdef in ('t2t','t2c','c2t', 'c2c'): + index = findtc(x,vh,wdef)[0] + elif pdef in ('d2t','t2u', 'u2c', 'c2d','all'): + index, v_ind = findtc(x, vh, wdef) + index = sort(r_[index, v_ind]) #% sorting crossings and tp in sequence + else: + raise ValueError('Unknown pdef option!') + + if (x[index[0]]>x[index[1]]): #% if first is down-crossing or max + if pdef in ('d2t', 'M2m', 'c2t', 'd2u' , 'M2M', 'c2c', 'd2d', 'all'): + start = 1 + elif pdef in ('t2u', 'm2M', 't2c', 'u2d' ,'m2m', 't2t', 'u2u'): + start = 2 + elif pdef in ('u2c'): + start = 3 + elif pdef in ('c2d'): + start = 4 + else: + raise ValueError('Unknown pdef option!') + # else first is up-crossing or min + elif pdef in ('all', 'u2c', 'm2M', 't2c', 'u2d', 'm2m', 't2t', 'u2u'): + start = 0 + elif pdef in ('c2d', 'M2m', 'c2t', 'd2u', 'M2M', 'c2c', 'd2d'): + start = 1 + elif pdef in ('d2t'): + start = 2 + elif pdef in ('t2u'): + start = 3 + else: + raise ValueError('Unknown pdef option!') + + # determine the steps between wanted periods + if pdef in ('d2t', 't2u', 'u2c', 'c2d' ): + step = 4 + elif pdef in ('all'): + step = 1 #% secret option! + else: + step = 2 + + #% determine the distance between min2min, t2t etc.. + if pdef in ('m2m', 't2t', 'u2u', 'M2M', 'c2c', 'd2d'): + dist = 2 + else: + dist = 1 + + nn = len(index) + #% New call: (pab 28.06.2001) + if pdef[0] in ('u', 'd'): + t0 = ecross(ti, x, index[start:(nn-dist):step], vh) + else: # % min, Max, trough, crest or all crossings wanted + t0 = x[index[start:(nn-dist):step]] + + if pdef[2] in ('u','d'): + t1 = ecross(ti, x, index[(start+dist):nn:step], vh) + else: # % min, Max, trough, crest or all crossings wanted + t1 = x[index[(start+dist):nn:step]] + + T = t1 - t0 +## if False: #% Secret option: indices to the actual crossings used. +## index=index.ravel() +## ind = [index(start:(nn-dist):step) index((start+dist):nn:step)].' +## ind = ind(:) + + + return T, index + + #% Old call: kept just in case + #%T = x(index((start+dist):step:nn),1)-x(index(start:step:(nn-dist)),1) + + + + def reconstruct(self): + pass + def plot_wave(self, sym1='k.', ts=None, sym2='k+', nfig=None, nsub=None, + stdev=None, vfact=3): + ''' + Plots the surface elevation of timeseries. + + Parameters + ---------- + sym1, sym2 : string + plot symbol and color for data and ts, respectively + (see PLOT) (default 'k.' and 'k+') + ts : TimeSeries or TurningPoints object + to overplot data. default zero-separated troughs and crests. + nsub : scalar integer + Number of subplots in each figure. By default nsub is such that + there are about 20 mean down crossing waves in each subplot. + If nfig is not given and nsub is larger than 6 then nsub is + changed to nsub=min(6,ceil(nsub/nfig)) + nfig : scalar integer + Number of figures. By default nfig=ceil(Nsub/6). + stdev : real scalar + standard deviation of data. + vfact : real scalar + how large in stdev the vertical scale should be (default 3) + + + Example + ------- + Plot x1 with red lines and mark troughs and crests with blue circles. + >>> import wafo + >>> x = wafo.data.sea() + >>> ts150 = wafo.objects.mat2timeseries(x[:150,:]) + >>> h = ts150.plot_wave('r-', sym2='bo') + + See also + -------- + findtc, plot + ''' + # TODO: finish reconstruct + nw = 20 + tn = self.args + xn = self.data.ravel() + indmiss = isnan(xn) # indices to missing points + indg = where(1-indmiss)[0] + if ts is None: + tc_ix = findtc(xn[indg],0,'tw')[0] + xn2 = xn[tc_ix] + tn2 = tn[tc_ix] + else: + xn2 = ts.data + tn2 = ts.args + + if stdev is None: + stdev = xn[indg].std() + + if nsub is None: + nsub = int(floor(len(xn2)/(2*nw)))+1 # about Nw mdc waves in each plot + if nfig is None: + nfig = int(ceil(nsub/6)) + nsub = min(6,int(ceil(nsub/nfig))) + + n = len(xn) + Ns = int(floor(n/(nfig*nsub))) + ind = r_[0:Ns] + if all(xn>=0): + vscale = [0, 2*stdev*vfact] + else: + vscale = array([-1, 1])*vfact*stdev + + + XlblTxt = 'Time [sec]' + dT = 1 + timespan = tn[ind[-1]]-tn[ind[0]] + if abs(timespan)>18000: # more than 5 hours + dT = 1/(60*60) + XlblTxt = 'Time (hours)' + elif abs(timespan)>300:# more than 5 minutes + dT = 1/60 + XlblTxt = 'Time (minutes)' + + if np.max(abs(xn[indg]))>5*stdev: + XlblTxt = XlblTxt +' (Spurious data since max > 5 std.)' + + plot = plotbackend.plot + subplot = plotbackend.subplot + figs = [] + for iz in xrange(nfig): + figs.append(plotbackend.figure()) + plotbackend.title('Surface elevation from mean water level (MWL).') + for ix in xrange(nsub): + if nsub>1: + subplot(nsub,1,ix) + + h_scale = array([tn[ind[0]], tn[ind[-1]]]) + ind2 = where((h_scale[0]<=tn2) & (tn2<=h_scale[1]))[0] + plot(tn[ind]*dT, xn[ind], sym1) + if len(ind2)>0: + plot(tn2[ind2]*dT,xn2[ind2],sym2) + plot(h_scale*dT, [0, 0], 'k-') + #plotbackend.axis([h_scale*dT, v_scale]) + + for iy in [-2, 2]: + plot(h_scale*dT, iy*stdev*ones(2), ':') + + ind = ind + Ns + #end + plotbackend.xlabel(XlblTxt) + + return figs + + + def plot_sp_wave(self, wave_idx_, tz_idx=None, *args, **kwds): + """ + Plot specified wave(s) from timeseries + + wave_idx : integer vector + of indices to waves we want to plot, i.e., wave numbers. + tz_idx : integer vector + of indices to the beginning, middle and end of + defining wave, i.e. for zero-downcrossing waves, indices to + zerocrossings (default trough2trough wave) + + Examples + -------- + Plot waves nr. 6,7,8 and waves nr. 12,13,...,17 + >>> import wafo + >>> x = wafo.data.sea() + >>> ts = wafo.objects.mat2timeseries(x[0:500,...]) + >>> h = ts.plot_sp_wave(np.r_[6:9,12:18]) + + + See also + -------- + plot_wave, findtc + """ + wave_idx = atleast_1d(wave_idx_).flatten() + if tz_idx is None: + tc_ind, tz_idx = findtc(self.data,0,'tw') # finding trough to trough waves + + dw = nonzero(abs(diff(wave_idx))>1)[0] + Nsub = dw.size+1 + Nwp = zeros(Nsub, dtype=int) + if Nsub>1: + dw = dw + 1 + Nwp[Nsub-1] = wave_idx[-1]-wave_idx[dw[-1]]+1 + wave_idx[dw[-1]+1:] = -2 + for ix in range(Nsub-2,1,-2): + Nwp[ix] = wave_idx[dw[ix]-1] - wave_idx[dw[ix-1]]+1 # # of waves pr subplot + wave_idx[dw[ix-1]+1:dw[ix]] = -2 + + Nwp[0] = wave_idx[dw[0]-1] - wave_idx[0]+1 + wave_idx[1:dw[0]] = -2 + wave_idx = wave_idx[wave_idx>-1] + else: + Nwp[0] = wave_idx[-1]-wave_idx[0]+1 + #end + + Nsub = min(6,Nsub) + Nfig = int(ceil(Nsub/6)) + Nsub = min(6,int(ceil(Nsub/Nfig))) + figs = [] + for iy in range(Nfig): + figs.append(plotbackend.figure()) + for ix in range(Nsub): + plotbackend.subplot(Nsub,1,mod(ix,Nsub)+1) + ind = r_[tz_idx[2*wave_idx[ix]-1]:tz_idx[2*wave_idx[ix]+2*Nwp[ix]-1]] + ## indices to wave + plotbackend.plot(self.args[ind],self.data[ind],*args,**kwds) + plotbackend.hold('on') + xi = [self.args[ind[0]],self.args[ind[-1]]] + plotbackend.plot(xi,[0, 0]) + + if Nwp[ix]==1: + plotbackend.ylabel('Wave %d' % wave_idx[ix]) + else: + plotbackend.ylabel('Wave %d - %d' % (wave_idx[ix], wave_idx[ix]+Nwp[ix]-1)) + + plotbackend.xlabel('Time [sec]') + #wafostamp + return figs + +def sensortypeid(*sensortypes): + ''' Return ID for sensortype name + + Parameter + --------- + sensortypes : list of strings defining the sensortype + + Returns + ------- + sensorids : list of integers defining the sensortype + + Valid senor-ids and -types for time series are as follows: + 0, 'n' : Surface elevation (n=Eta) + 1, 'n_t' : Vertical surface velocity + 2, 'n_tt' : Vertical surface acceleration + 3, 'n_x' : Surface slope in x-direction + 4, 'n_y' : Surface slope in y-direction + 5, 'n_xx' : Surface curvature in x-direction + 6, 'n_yy' : Surface curvature in y-direction + 7, 'n_xy' : Surface curvature in xy-direction + 8, 'P' : Pressure fluctuation about static MWL pressure + 9, 'U' : Water particle velocity in x-direction + 10, 'V' : Water particle velocity in y-direction + 11, 'W' : Water particle velocity in z-direction + 12, 'U_t' : Water particle acceleration in x-direction + 13, 'V_t' : Water particle acceleration in y-direction + 14, 'W_t' : Water particle acceleration in z-direction + 15, 'X_p' : Water particle displacement in x-direction from its mean position + 16, 'Y_p' : Water particle displacement in y-direction from its mean position + 17, 'Z_p' : Water particle displacement in z-direction from its mean position + + Example: + >>> sensortypeid('W','v') + [11, 10] + >>> sensortypeid('rubbish') + [1.#QNAN] + + See also + -------- + sensortype + ''' + + sensorid_table = dict(n=0, n_t=1, n_tt=2, n_x=3, n_y=4, n_xx=5, + n_yy=6, n_xy=7, p=8, u=9, v=10, w=11, u_t=12, + v_t=13, w_t=14, x_p=15, y_p=16, z_p=17) + try: + return [sensorid_table.get(name.lower(), nan) for name in sensortypes] + except: + raise ValueError('Input must be a string!') + + + +def sensortype(*sensorids): + ''' + Return sensortype name + + Parameter + --------- + sensorids : vector or list of integers defining the sensortype + + Returns + ------- + sensornames : tuple of strings defining the sensortype + Valid senor-ids and -types for time series are as follows: + 0, 'n' : Surface elevation (n=Eta) + 1, 'n_t' : Vertical surface velocity + 2, 'n_tt' : Vertical surface acceleration + 3, 'n_x' : Surface slope in x-direction + 4, 'n_y' : Surface slope in y-direction + 5, 'n_xx' : Surface curvature in x-direction + 6, 'n_yy' : Surface curvature in y-direction + 7, 'n_xy' : Surface curvature in xy-direction + 8, 'P' : Pressure fluctuation about static MWL pressure + 9, 'U' : Water particle velocity in x-direction + 10, 'V' : Water particle velocity in y-direction + 11, 'W' : Water particle velocity in z-direction + 12, 'U_t' : Water particle acceleration in x-direction + 13, 'V_t' : Water particle acceleration in y-direction + 14, 'W_t' : Water particle acceleration in z-direction + 15, 'X_p' : Water particle displacement in x-direction from its mean position + 16, 'Y_p' : Water particle displacement in y-direction from its mean position + 17, 'Z_p' : Water particle displacement in z-direction from its mean position + + Example: + >>> sensortype(range(3)) + ('n', 'n_t', 'n_tt') + + See also + -------- + sensortypeid, tran + ''' + valid_names = ('n', 'n_t', 'n_tt', 'n_x', 'n_y', 'n_xx', 'n_yy', 'n_xy', + 'p', 'u', 'v', 'w', 'u_t', 'v_t', 'w_t', 'x_p', 'y_p', 'z_p', + nan) + ids = atleast_1d(*sensorids) + if isinstance(ids, list): + ids = hstack(ids) + n = len(valid_names) - 1 + ids = where(((ids<0) | (n>> p = np.poly1d([1,1,1]) + >>> P = np.polyint(p) + >>> P + poly1d([ 0.33333333, 0.5 , 1. , 0. ]) + >>> np.polyder(P) == p + True + + The integration constants default to zero, but can be specified: + + >>> P = np.polyint(p, 3) + >>> P(0) + 0.0 + >>> np.polyder(P)(0) + 0.0 + >>> np.polyder(P, 2)(0) + 0.0 + >>> P = np.polyint(p, 3, k=[6,5,3]) + >>> P + poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) + + Note that 3 = 6 / 2!, and that the constants are given in the order of + integrations. Constant of the highest-order polynomial term comes first: + + >>> np.polyder(P, 2)(0) + 6.0 + >>> np.polyder(P, 1)(0) + 5.0 + >>> P(0) + 3.0 + + """ + m = int(m) + if m < 0: + raise ValueError, "Order of integral must be positive (see polyder)" + if k is None: + k = zeros(m, float) + k = atleast_1d(k) + if len(k) == 1 and m > 1: + k = k[0] * ones(m, float) + if len(k) < m: + raise ValueError, \ + "k must be a scalar or a rank-1 array of length 1 or >m." + truepoly = isinstance(p, poly1d) + p = asarray(p) + if m == 0: + if truepoly: + return poly1d(p) + return p + else: + ix = arange(len(p), 0, -1) + if p.ndim > 1: + ix = ix[..., newaxis] + pieces = p.shape[-1] + k0 = k[0] * ones((1, pieces), dtype=int) + else: + k0 = [k[0]] + y = np.concatenate((p.__truediv__(ix), k0), axis=0) + + val = polyint(y, m - 1, k=k[1:]) + if truepoly: + return poly1d(val) + return val + +def polyder(p, m=1): + """ + Return the derivative of the specified order of a polynomial. + + Parameters + ---------- + p : poly1d or sequence + Polynomial to differentiate. + A sequence is interpreted as polynomial coefficients, see `poly1d`. + m : int, optional + Order of differentiation (default: 1) + + Returns + ------- + der : poly1d + A new polynomial representing the derivative. + + See Also + -------- + polyint : Anti-derivative of a polynomial. + poly1d : Class for one-dimensional polynomials. + + Examples + -------- + The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is: + + >>> p = np.poly1d([1,1,1,1]) + >>> p2 = np.polyder(p) + >>> p2 + poly1d([3, 2, 1]) + + which evaluates to: + + >>> p2(2.) + 17.0 + + We can verify this, approximating the derivative with + ``(f(x + h) - f(x))/h``: + + >>> (p(2. + 0.001) - p(2.)) / 0.001 + 17.007000999997857 + + The fourth-order derivative of a 3rd-order polynomial is zero: + + >>> np.polyder(p, 2) + poly1d([6, 2]) + >>> np.polyder(p, 3) + poly1d([6]) + >>> np.polyder(p, 4) + poly1d([ 0.]) + + """ + m = int(m) + if m < 0: + raise ValueError, "Order of derivative must be positive (see polyint)" + truepoly = isinstance(p, poly1d) + p = asarray(p) + if m == 0: + if truepoly: + return poly1d(p) + return p + else: + n = len(p) - 1 + ix = arange(n, 0, -1) + if p.ndim > 1: + ix = ix[..., newaxis] + y = ix * p[:-1] + val = polyder(y, m - 1) + if truepoly: + return poly1d(val) + return val + +def polyreloc(p, x, y=0.0): + """ + Relocate polynomial + + The polynomial `p` is relocated by "moving" it `x` + units along the x-axis and `y` units along the y-axis. + So the polynomial `r` is relative to the point (x,y) as + the polynomial `p` is relative to the point (0,0). + + Parameters + ---------- + p : array-like, poly1d + vector or matrix of column vectors of polynomial coefficients to relocate. + (Polynomial coefficients are in decreasing order.) + x : scalar + distance to relocate P along x-axis + y : scalar + distance to relocate P along y-axis (default 0) + + Returns + ------- + r : ndarray, poly1d + vector/matrix/poly1d of relocated polynomial coefficients. + + See also + -------- + polyrescl + + Example + ------- + >>> import numpy as np + >>> p = np.arange(6); p.shape = (2,-1) + >>> np.polyval(p,0) + array([3, 4, 5]) + >>> np.polyval(p,1) + array([3, 5, 7]) + >>> r = polyreloc(p,-1) # move to the left along x-axis + >>> np.polyval(r,-1) # = polyval(p,0) + array([3, 4, 5]) + >>> np.polyval(r,0) # = polyval(p,1) + array([3, 5, 7]) + """ + + truepoly = isinstance(p, poly1d) + r = atleast_1d(p).copy() + n = r.shape[0] + + # Relocate polynomial using Horner's algorithm + for ii in range(n, 1, -1): + for i in range(1, ii): + r[i] = r[i] - x * r[i - 1] + r[-1] = r[-1] + y + if r.ndim > 1 and r.shape[-1] == 1: + r.shape = (r.size,) + if truepoly: + r = poly1d(r) + return r + +def polyrescl(p, x, y=1.0): + """ + Rescale polynomial. + + Parameters + ---------- + p : array-like, poly1d + vector or matrix of column vectors of polynomial coefficients to rescale. + (Polynomial coefficients are in decreasing order.) + x,y : scalars + defining the factors to rescale the polynomial `p` in + x-direction and y-direction, respectively. + + Returns + ------- + r : ndarray, poly1d + vector/matrix/poly1d of rescaled polynomial coefficients. + + See also + -------- + polyreloc + + Example + ------- + >>> import numpy as np + >>> p = np.arange(6); p.shape = (2,-1) + >>> np.polyval(p,0) + array([3, 4, 5]) + >>> np.polyval(p,1) + array([3, 5, 7]) + >>> r = polyrescl(p,2) # scale by 2 along x-axis + >>> np.polyval(r,0) # = polyval(p,0) + array([ 3., 4., 5.]) + >>> np.polyval(r,2) # = polyval(p,1) + array([ 3., 5., 7.]) + """ + + truepoly = isinstance(p, poly1d) + r = atleast_1d(p) + n = r.shape[0] + + xscale = (float(x) ** arange(1 - n , 1)) + if r.ndim == 1: + q = y * r * xscale + else: + q = y * r * xscale[:, newaxis] + if truepoly: + q = poly1d(q) + return q + +def polytrim(p): + """ + Trim polynomial by stripping off leading zeros. + + Parameters + ---------- + p : array-like, poly1d + vector or matrix of column vectors of polynomial coefficients in + decreasing order. + + Returns + ------- + r : ndarray, poly1d + vector/matrix/poly1d of trimmed polynomial coefficients. + + Example + ------- + >>> p = [0,1,2] + >>> polytrim(p) + array([1, 2]) + >>> p1 = [[0,0],[1,2],[3,4]] + >>> polytrim(p1) + array([[1, 2], + [3, 4]]) + """ + + truepoly = isinstance(p, poly1d) + if truepoly: + return p + else: + r = atleast_1d(p).copy() + # Remove leading zeros + is_not_lead_zeros = logical_or.accumulate(r != 0, axis=0) + if r.ndim == 1: + r = r[is_not_lead_zeros] + else: + is_not_lead_zeros = any(is_not_lead_zeros, axis=1) + r = r[is_not_lead_zeros, :] + return r + +def poly2hstr(p, variable='x'): + """ + Return polynomial as a Horner represented string. + + Parameters + ---------- + p : array-like poly1d + vector of polynomial coefficients in decreasing order. + variable : string + display character for variable + + Returns + ------- + p_str : string + consisting of the polynomial coefficients in the vector P multiplied + by powers of the given `variable`. + + Examples + -------- + >>> poly2hstr([1, 1, 2], 's' ) + '(s + 1)*s + 2' + + See also + -------- + poly2str + """ + var = variable + + coefs = polytrim(atleast_1d(p)) + order = len(coefs) - 1 # Order of polynomial. + s = '' # Initialize output string. + ix = 1; + for expon in range(order, -1, -1): + coef = coefs[order - expon] + #% There is no point in adding a zero term (except if it's the only + #% term, but we'll take care of that later). + if coef == 0: + ix += 1 + else: + #% Append exponent if necessary. + if ix > 1: + exponstr = '%.0f' % ix + s = '%s**%s' % (s, exponstr); + ix = 1 + #% Is it the first term? + isfirst = s == '' + + # We need the coefficient only if it is different from 1 or -1 or + # when it is the constant term. + needcoef = ((abs(coef) != 1) | (expon == 0) & isfirst) | 1 - isfirst + + # We need the variable except in the constant term. + needvar = (expon != 0) + + #% Add sign, but we don't need a leading plus-sign. + if isfirst: + if coef < 0: + s = '-' # % Unary minus. + else: + if coef < 0: + s = '%s - ' % s # % Binary minus (subtraction). + else: + s = '%s + ' % s # % Binary plus (addition). + + + #% Append the coefficient if it is different from one or when it is + #% the constant term. + if needcoef: + coefstr = '%.20g' % abs(coef) + s = '%s%s' % (s, coefstr) + + #% Append variable if necessary. + if needvar: + #% Append a multiplication sign if necessary. + if needcoef: + if 1 - isfirst: + s = '(%s)' % s + s = '%s*' % s + s = '%s%s' % (s, var) + + #% Now treat the special case where the polynomial is zero. + if s == '': + s = '0' + return s + +def poly2str(p, variable='x'): + """ + Return polynomial as a string. + + Parameters + ---------- + p : array-like poly1d + vector of polynomial coefficients in decreasing order. + variable : string + display character for variable + + Returns + ------- + p_str : string + consisting of the polynomial coefficients in the vector P multiplied + by powers of the given `variable`. + + See also + -------- + poly2hstr + + Examples + -------- + >>> poly2str([1, 1, 2], 's' ) + 's**2 + s + 2' + """ + thestr = "0" + var = variable + + # Remove leading zeros + coeffs = polytrim(atleast_1d(p)) + + N = len(coeffs) - 1 + + for k in range(len(coeffs)): + coefstr = '%.4g' % abs(coeffs[k]) + if coefstr[-4:] == '0000': + coefstr = coefstr[:-5] + power = (N - k) + if power == 0: + if coefstr != '0': + newstr = '%s' % (coefstr,) + else: + if k == 0: + newstr = '0' + else: + newstr = '' + elif power == 1: + if coefstr == '0': + newstr = '' + elif coefstr == 'b' or coefstr == '1': + newstr = var + else: + newstr = '%s*%s' % (coefstr, var) + else: + if coefstr == '0': + newstr = '' + elif coefstr == 'b' or coefstr == '1': + newstr = '%s**%d' % (var, power,) + else: + newstr = '%s*%s**%d' % (coefstr, var, power) + + if k > 0: + if newstr != '': + if coeffs[k] < 0: + thestr = "%s - %s" % (thestr, newstr) + else: + thestr = "%s + %s" % (thestr, newstr) + elif (k == 0) and (newstr != '') and (coeffs[k] < 0): + thestr = "-%s" % (newstr,) + else: + thestr = newstr + return thestr + +def polyshift(py, a= -1, b=1): + """ + Polynomial coefficient shift + + Polyshift shift the polynomial coefficients by a variable shift: + + Y = 2*(X-.5*(b+a))/(b-a) + + i.e., the interval -1 <= Y <= 1 is mapped to the interval a <= X <= b + + Parameters + ---------- + py : array-like + polynomial coefficients for the variable y. + a,b : scalars + lower and upper limit. + + Returns + ------- + px : ndarray + polynomial coefficients for the variable x. + + See also + -------- + polyishift + + Example + ------- + >>> py = [1, 0] + >>> px = polyshift(py,0,5) + >>> polyval(px,[0, 2.5, 5]) #% This is the same as the line below + array([-1., 0., 1.]) + >>> polyval(py,[-1, 0, 1 ]) + array([-1, 0, 1]) + """ + + if (a == -1) & (b == 1): + return py + L = b - a + return polyishift(py, -(2. + b + a) / L, (2. - b - a) / L) + +def polyishift(px, a= -1, b=1): + """ + Inverse polynomial coefficient shift + + Polyishift does the inverse of Polyshift, + shift the polynomial coefficients by a variable shift: + + Y = 2*(X-.5*(b+a)/(b-a) + + i.e., the interval a <= X <= b is mapped to the interval -1 <= Y <= 1 + + Parameters + ---------- + px : array-like + polynomial coefficients for the variable x. + a,b : scalars + lower and upper limit. + + Returns + ------- + py : ndarray + polynomial coefficients for the variable y. + + See also + -------- + polyishift + + Example + ------- + >>> px = [1, 0] + >>> py = polyishift(px,0,5); + >>> polyval(px,[0, 2.5, 5]) #% This is the same as the line below + array([ 0. , 2.5, 5. ]) + >>> polyval(py,[-1, 0, 1]) + array([ 0. , 2.5, 5. ]) + """ + if (a == -1) & (b == 1): + return px + L = b - a + xscale = 2. / L + xloc = -float(a + b) / L + return polyreloc(polyrescl(px, xscale), xloc) + +def map_from_interval(x, a, b) : + """F(x), where F: [a,b] -> [-1,1].""" + return (x - (b + a) / 2.0) * (2.0 / (b - a)) + +def map_to_interval(x, a, b) : + """F(x), where F: [-1,1] -> [a,b].""" + return (x * (b - a) + (b + a)) / 2.0 + +def poly2cheb(p, a= -1, b=1): + """ + Convert polynomial coefficients into Chebyshev coefficients + + Parameters + ---------- + p : array-like + polynomial coefficients + a,b : real scalars + lower and upper limits (Default -1,1) + + Returns + ------- + ck : ndarray + Chebychef coefficients + + POLY2CHEB do the inverse of CHEB2POLY: given a vector of polynomial + coefficients AK, returns an equivalent vector of Chebyshev + coefficients CK. + + This is useful for economization of power series. + The steps for doing so: + 1. Convert polynomial coefficients to Chebychev coefficients, CK. + 2. Truncate the CK series to a smaller number of terms, using the + coefficient of the first neglected Chebychev polynomial as an error + estimate. + 3 Convert back to a polynomial by CHEB2POLY + + See also + -------- + cheb2poly + chebval + chebfit + + Examples + -------- + >>> import numpy as np + >>> p = np.arange(5) + >>> ck = poly2cheb(p) + >>> cheb2poly(ck) + array([ 1., 2., 3., 4.]) + + Reference + --------- + William H. Press, Saul Teukolsky, + William T. Wetterling and Brian P. Flannery (1997) + "Numerical recipes in Fortran 77", Vol. 1, pp 184-194 + """ + f = poly1d(p) + n = len(f.coeffs) + return chebfit(f, n, a, b) + +def cheb2poly(ck, a= -1, b=1): + """ + Converts Chebyshev coefficients to polynomial coefficients + + Parameters + ---------- + ck : array-like + Chebychef coefficients + a,b : real, scalars + lower and upper limits (Default -1,1) + + Returns + ------- + p : ndarray + polynomial coefficients + + It is not advised to do this for len(ck)>10 due to numerical cancellations. + + See also + -------- + chebval + chebfit + + Examples + -------- + >>> import numpy as np + >>> p = np.arange(5) + >>> ck = poly2cheb(p) + >>> cheb2poly(ck) + array([ 1., 2., 3., 4.]) + + + References + ---------- + http://en.wikipedia.org/wiki/Chebyshev_polynomials + http://en.wikipedia.org/wiki/Chebyshev_form + http://en.wikipedia.org/wiki/Clenshaw_algorithm + """ + + n = len(ck) + + b_Nmi = zeros(1) + b_Nmip1 = zeros(1) + y = r_[2 / (b - a), -(a + b) / (b - a)] + y2 = 2. * y + + # Clenshaw recurence + for ix in xrange(n - 1): + tmp = b_Nmi + b_Nmi = polymul(y2, b_Nmi) # polynomial multiplication + nb = len(b_Nmip1) + b_Nmip1[-1] = b_Nmip1[-1] - ck[ix] + b_Nmi[-nb::] = b_Nmi[-nb::] - b_Nmip1 + b_Nmip1 = tmp + + p = polymul(y, b_Nmi) # polynomial multiplication + nb = len(b_Nmip1) + b_Nmip1[-1] = b_Nmip1[-1] - ck[n - 1] + p[-nb::] = p[-nb::] - b_Nmip1 + return polytrim(p) + +def chebextr(n): + """ + Return roots of derivative of Chebychev polynomial of the first kind. + + All local extreme values of the polynomial are either -1 or 1. So, + CHEBPOLY( N, CHEBEXTR(N) ) ) return the same as (-1).^(N:-1:0) + except for the numerical noise in the former. + + Because the extreme values of Chebychev polynomials of the first + kind are either -1 or 1, their roots are often used as starting + values for the nodes in minimax approximations. + + + Parameters + ---------- + n : scalar, integer + degree of Chebychev polynomial. + + Examples + -------- + >>> x = chebextr(4) + >>> chebpoly(4,x) + array([ 1., -1., 1., -1., 1.]) + + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_nodes + http://en.wikipedia.org/wiki/Chebyshev_polynomials + """ + return - cos((pi * arange(n + 1)) / n); + +def chebroot(n, kind=1): + """ + Return roots of Chebychev polynomial of the first or second kind. + + The roots of the Chebychev polynomial of the first kind form a particularly + good set of nodes for polynomial interpolation because the resulting + interpolation polynomial minimizes the problem of Runge's phenomenon. + + Parameters + ---------- + n : scalar, integer + degree of Chebychev polynomial. + kind: 1 or 2, optional + kind of Chebychev polynomial (default 1) + + Examples + -------- + >>> import numpy as np + >>> x = chebroot(3) + >>> np.abs(chebpoly(3,x))<1e-15 + array([ True, True, True], dtype=bool) + >>> chebpoly(3) + array([ 4., 0., -3., 0.]) + >>> x2 = chebroot(4,kind=2) + >>> np.abs(chebpoly(4,x2,kind=2))<1e-15 + array([ True, True, True, True], dtype=bool) + >>> chebpoly(4,kind=2) + array([ 16., 0., -12., 0., 1.]) + + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_nodes + http://en.wikipedia.org/wiki/Chebyshev_polynomials + """ + if kind not in (1, 2): + raise ValueError('kind must be 1 or 2') + return - cos(pi * (arange(n) + 0.5 * kind) / (n + kind - 1)); + + +def chebpoly(n, x=None, kind=1): + """ + Return Chebyshev polynomial of the first or second kind. + + These polynomials are orthogonal on the interval [-1,1], with + respect to the weight function w(x) = (1-x^2)^(-1/2+kind-1). + + chebpoly(n) returns the coefficients of the Chebychev polynomial of degree N. + chebpoly(n,x) returns the Chebychev polynomial of degree N evaluated in X. + + Parameters + ---------- + n : integer, scalar + degree of Chebychev polynomial. + x : array-like, optional + evaluation points + kind: 1 or 2, optional + kind of Chebychev polynomial (default 1) + + Returns + ------- + p : ndarray + polynomial coefficients if x is None. + Chebyshev polynomial evaluated at x otherwise + + Examples + -------- + >>> import numpy as np + >>> x = chebroot(3) + >>> np.abs(chebpoly(3,x))<1e-15 + array([ True, True, True], dtype=bool) + >>> chebpoly(3) + array([ 4., 0., -3., 0.]) + >>> x2 = chebroot(4,kind=2) + >>> np.abs(chebpoly(4,x2,kind=2))<1e-15 + array([ True, True, True, True], dtype=bool) + >>> chebpoly(4,kind=2) + array([ 16., 0., -12., 0., 1.]) + + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_polynomials + """ + if x is None: # Calculate coefficients. + if n == 0: + p = ones(1) + else: + p = round(pow(2, n - 2 + kind) * poly(chebroot(n, kind=kind))) + p[1::2] = 0; + return p + else: # Evaluate polynomial in chebychev form + ck = zeros(n + 1) + ck[0] = 1. + return _chebval(atleast_1d(x), ck, kind=kind) + +def chebfit(fun, n=10, a= -1, b=1, trace=False): + """ + Computes the Chebyshevs coefficients + + so that f(x) can be approximated by: + + n-1 + f(x) = sum ck*Tk(x) + k=0 + + where Tk is the k'th Chebyshev polynomial of the first kind. + + Parameters + ---------- + fun : callable + function to approximate + n : integer, scalar, optional + number of base points (abscissas). Default n=10 (maximum 50) + a,b : real, scalars, optional + integration limits + + Returns + ------- + ck : ndarray + polynomial coefficients in Chebychev form. + + Examples + -------- + Fit exp(x) + + >>> import pylab as pb + >>> a = 0; b = 2 + >>> ck = chebfit(pb.exp,7,a,b); + >>> x = pb.linspace(0,4); + >>> h=pb.plot(x,pb.exp(x),'r',x,chebval(x,ck,a,b),'g.') + >>> x1 = chebroot(9)*(b-a)/2+(b+a)/2 + >>> ck1 = chebfit(pb.exp(x1)) + >>> h=pb.plot(x,pb.exp(x),'r',x,chebval(x,ck1,a,b),'g.') + + >>> pb.close() + + See also + -------- + chebval + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_nodes + http://mathworld.wolfram.com/ChebyshevApproximationFormula.html + + W. Fraser (1965) + "A Survey of Methods of Computing Minimax and Near-Minimax Polynomial + Approximations for Functions of a Single Independent Variable" + Journal of the ACM (JACM), Vol. 12 , Issue 3, pp 295 - 314 + """ + + if (n > 50): + warnings.warn('CHEBFIT should only be used for n<50') + + if hasattr(fun, '__call__'): + x = map_to_interval(chebroot(n), a, b) + f = fun(x); + if trace: + plb.plot(x, f, '+') + else: + f = fun + n = len(f) + #raise ValueError('Function must be callable!') + # N-1 + # c(k) = (2/N) sum w(n) f(n)*cos(pi*k*(2n+1)/(2N)), 0 <= k < N. + # n=0 + # + # w(0) = 0.5, w(n)=1 for n>0 + ck = dct(f[::-1]) / n + ck[0] = ck[0] / 2. + return ck[::-1] + +def dct(x, n=None): + """ + Discrete Cosine Transform + + N-1 + y[k] = 2* sum x[n]*cos(pi*k*(2n+1)/(2*N)), 0 <= k < N. + n=0 + + Examples + -------- + >>> import numpy as np + >>> x = np.arange(5) + >>> np.abs(x-idct(dct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + >>> np.abs(x-dct(idct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + + Reference + --------- + http://en.wikipedia.org/wiki/Discrete_cosine_transform + http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/ + """ + + x = atleast_1d(x) + + if n is None: + n = x.shape[-1] + + if x.shape[-1] < n: + n_shape = x.shape[:-1] + (n - x.shape[-1],) + xx = hstack((x, zeros(n_shape))) + else: + xx = x[..., :n] + + real_x = all(isreal(xx)) + if (real_x and (remainder(n, 2) == 0)): + xp = 2 * fft(hstack((xx[..., ::2], xx[..., ::-2]))) + else: + xp = fft(hstack((xx, xx[..., ::-1]))) + xp = xp[..., :n] + + w = exp(-1j * arange(n) * pi / (2 * n)) + + y = xp * w + + if real_x: + return y.real + else: + return y + +def idct(x, n=None): + """ + Inverse Discrete Cosine Transform + + N-1 + x[k] = 1/N sum w[n]*y[n]*cos(pi*k*(2n+1)/(2*N)), 0 <= k < N. + n=0 + + w(0) = 1/2 + w(n) = 1 for n>0 + + Examples + -------- + >>> import numpy as np + >>> x = np.arange(5) + >>> np.abs(x-idct(dct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + >>> np.abs(x-dct(idct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + + Reference + --------- + http://en.wikipedia.org/wiki/Discrete_cosine_transform + http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/ + """ + + + x = atleast_1d(x) + + if n is None: + n = x.shape[-1] + + w = exp(1j * arange(n) * pi / (2 * n)) + + if x.shape[-1] < n: + n_shape = x.shape[:-1] + (n - x.shape[-1],) + xx = hstack((x, zeros(n_shape))) * w + else: + xx = x[..., :n] * w + + real_x = all(isreal(x)) + if (real_x and (remainder(n, 2) == 0)): + xx[..., 0] = xx[..., 0] * 0.5 + yp = ifft(xx) + y = zeros(xx.shape, dtype=complex) + y[..., ::2] = yp[..., :n / 2] + y[..., ::-2] = yp[..., n / 2::] + else: + yp = ifft(hstack((xx, zeros_like(xx[..., 0]), conj(xx[..., :0:-1])))) + y = yp[..., :n] + + if real_x: + return y.real + else: + return y + +def _chebval(x, ck, kind=1): + """ + Evaluate polynomial in Chebyshev form. + + A polynomial of degree N in Chebyshev form is a polynomial p(x) of the form: + + N + p(x) = sum ck*Tk(x) + k=0 + or + N + p(x) = sum ck*Uk(x) + k=0 + + where Tk and Uk are the k'th Chebyshev polynomial of the first and second + kind, respectively. + + References + ---------- + http://en.wikipedia.org/wiki/Clenshaw_algorithm + http://mathworld.wolfram.com/ClenshawRecurrenceFormula.html + """ + n = len(ck) + b_Nmi = zeros(x.shape) # b_(N-i) + b_Nmip1 = b_Nmi.copy() # b_(N-i+1) + x2 = 2 * x + # Clenshaw reccurence + for ix in xrange(n - 1): + tmp = b_Nmi + b_Nmi = x2 * b_Nmi - b_Nmip1 + ck[ix] + b_Nmip1 = tmp + return kind * x * b_Nmi - b_Nmip1 + ck[n - 1] + + +def chebval(x, ck, a= -1, b=1, kind=1, fill=None): + """ + Evaluate polynomial in Chebyshev form at X + + A polynomial of degree N in Chebyshev form is a polynomial p(x) of the form: + + N + p(x) = sum ck*Tk(x) + k=0 + + where Tk is the k'th Chebyshev polynomial of the first or second kind. + + Paramaters + ---------- + x : array-like + points to evaluate + ck : array-like + polynomial coefficients in Chebyshev form ordered from highest degree to zero + a,b : real, scalars, optional + limits for polynomial (Default -1,1) + kind: 1 or 2, optional + kind of Chebychev polynomial (default 1) + fill : scalar, optional + If provided, define value to return for `x < a` or `b < x`. + + Examples + -------- + Plot Chebychev polynomial of the first kind and order 4: + >>> import pylab as pb + >>> x = pb.linspace(-1,1) + >>> ck = pb.zeros(5); ck[-1]=1 + >>> h = pb.plot(x,chebval(x,ck),x,chebpoly(4,x),'.') + >>> pb.close() + + Fit exponential function: + >>> import pylab as pb + >>> ck = chebfit(pb.exp,7,0,2) + >>> x = pb.linspace(0,4); + >>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x)) + >>> pb.close() + + See also + -------- + chebfit + + References + ---------- + http://en.wikipedia.org/wiki/Clenshaw_algorithm + http://mathworld.wolfram.com/ClenshawRecurrenceFormula.html + """ + + y = map_from_interval(atleast_1d(x), a, b) + if fill is None: + f = _chebval(y, ck, kind=kind) + else: + cond = (abs(y) <= 1) + f = where(cond, 0, fill) + if any(cond): + yk = extract(cond, y) + f[cond] = _chebval(yk, ck, kind=kind) + return f + + +def chebder(ck, a= -1, b=1): + """ + Differentiate Chebyshev polynomial + + Parameters + ---------- + ck : array-like + polynomial coefficients in Chebyshev form of function to differentiate + a,b : real, scalars + limits for polynomial(Default -1,1) + + Return + ------ + cder : ndarray + polynomial coefficients in Chebyshev form of the derivative + + Examples + -------- + + Fit exponential function: + >>> import pylab as pb + >>> ck = chebfit(pb.exp,7,0,2) + >>> x = pb.linspace(0,4) + >>> ck2 = chebder(ck,0,2); + >>> h = pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x),'r') + >>> pb.close() + + See also + -------- + chebint + chebfit + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_polynomials + + W. Fraser (1965) + "A Survey of Methods of Computing Minimax and Near-Minimax Polynomial + Approximations for Functions of a Single Independent Variable" + Journal of the ACM (JACM), Vol. 12 , Issue 3, pp 295 - 314 + """ + + n = len(ck) - 1 + cder = zeros(n, dtype=asarray(ck).dtype) + cder[0] = 2 * n * ck[0] + cder[1] = 2 * (n - 1) * ck[1] + for j in xrange(2, n): + cder[j] = cder[j - 2] + 2 * (n - j) * ck[j] + + return cder * 2. / (b - a) # Normalize to the interval b-a. + +def chebint(ck, a= -1, b=1): + """ + Integrate Chebyshev polynomial + + Parameters + ---------- + ck : array-like + polynomial coefficients in Chebyshev form of function to integrate. + a,b : real, scalars + limits for polynomial(Default -1,1) + + Return + ------ + cint : ndarray + polynomial coefficients in Chebyshev form of the integrated function + + Examples + -------- + Fit exponential function: + >>> import pylab as pb + >>> ck = chebfit(pb.exp,7,0,2) + >>> x = pb.linspace(0,4) + >>> ck2 = chebint(ck,0,2); + >>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x),'r.') + >>> pb.close() + + See also + -------- + chebder + chebfit + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_polynomials + + W. Fraser (1965) + "A Survey of Methods of Computing Minimax and Near-Minimax Polynomial + Approximations for Functions of a Single Independent Variable" + Journal of the ACM (JACM), Vol. 12 , Issue 3, pp 295 - 314 + """ + +# int T0(x) = T1(x)+1 +# int T1(x) = 0.5*(T2(x)/2-T0/2) +# int Tn(x) dx = 0.5*{Tn+1(x)/(n+1) - Tn-1(x)/(n-1)} +# N +# p(x) = sum cn*Tn(x) +# n=0 + +# int p(x) dx = sum cn * int(Tn(x)dx) = 0.5*sum cn *{Tn+1(x)/(n+1) - Tn-1(x)/(n-1)} +# = 0.5 sum (cn-1-cn+1)*Tn/n n>0 + + n = len(ck) + + cint = zeros(n) + con = 0.25 * (b - a) + + dif1 = diff(ck[-1::-2]) + ix1 = r_[1:n - 1:2] + cint[ix1] = -(con * dif1) / ix1 + if n > 3: + dif2 = diff(ck[-2::-2]) + ix2 = r_[2:n - 1:2] + cint[ix2] = -(con * dif2) / ix2 + cint = cint[::-1] + #% cint(n) is a special case + cint[-1] = (con * ck[n - 2]) / (n - 1) + cint[0] = 2 * np.sum((-1) ** r_[0:n - 1] * cint[-2::-1]) # Set integration constant + return cint + +class Cheb1d(object): + coeffs = None + order = None + a = None + b = None + kind = None + def __init__(self, ck, a= -1, b=1, kind=1): + if isinstance(ck, Cheb1d): + for key in ck.__dict__.keys(): + self.__dict__[key] = ck.__dict__[key] + return + cki = trim_zeros(atleast_1d(ck), 'b') + if len(cki.shape) > 1: + raise ValueError, "Polynomial must be 1d only." + self.__dict__['coeffs'] = cki + self.__dict__['order'] = len(cki) - 1 + self.__dict__['a'] = a + self.__dict__['b'] = b + self.__dict__['kind'] = kind + + + def __call__(self, x): + return chebval(x, self.coeffs, self.a, self.b, self.kind) + + def __array__(self, t=None): + if t: + return asarray(self.coeffs, t) + else: + return asarray(self.coeffs) + + def __repr__(self): + vals = repr(self.coeffs) + vals = vals[6:-1] + return "Cheb1d(%s)" % vals + + def __len__(self): + return self.order + + def __str__(self): + pass + def __neg__(self): + new = Cheb1d(self) + new.coeffs = -self.coeffs + return new + + def __pos__(self): + return self + + + def __add__(self, other): + other = Cheb1d(other) + new = Cheb1d(self) + new.coeffs = polyadd(self.coeffs, other.coeffs) + return new + + def __radd__(self, other): + return self.__add__(other) + + def __sub__(self, other): + other = Cheb1d(other) + new = Cheb1d(self) + new.coeffs = polysub(self.coeffs, other.coeffs) + return new + + def __rsub__(self, other): + other = Cheb1d(other) + new = Cheb1d(self) + new.coeffs = polysub(other.coeffs, new.coeffs) + return new + + def __eq__(self, other): + other = Cheb1d(other) + return (all(self.coeffs == other.coeffs) and (self.a == other.a) + and (self.b == other.b) and (self.kind == other.kind)) + + def __ne__(self, other): + return any(self.coeffs != other.coeffs) or (self.a != other.a) or (self.b != other.b) or (self.kind != other.kind) + + def __setattr__(self, key, val): + raise ValueError, "Attributes cannot be changed this way." + + def __getattr__(self, key): + if key in ['c', 'coef', 'coefficients']: + return self.coeffs + elif key in ['o']: + return self.order + elif key in ['a']: + return self.a + elif key in ['b']: + return self.b + elif key in ['k']: + return self.kind + else: + try: + return self.__dict__[key] + except KeyError: + raise AttributeError("'%s' has no attribute '%s'" % (self.__class__, key)) + def __getitem__(self, val): + if val > self.order: + return 0 + if val < 0: + return 0 + return self.coeffs[val] + + def __setitem__(self, key, val): + #ind = self.order - key + if key < 0: + raise ValueError, "Does not support negative powers." + if key > self.order: + zr = zeros(key - self.order, self.coeffs.dtype) + self.__dict__['coeffs'] = concatenate((self.coeffs, zr)) + self.__dict__['order'] = key + self.__dict__['coeffs'][key] = val + return + + def __iter__(self): + return iter(self.coeffs) + + def integ(self, m=1): + """ + Return an antiderivative (indefinite integral) of this polynomial. + + Refer to `chebint` for full documentation. + + See Also + -------- + chebint : equivalent function + + """ + integ = Cheb1d(self) + integ.coeffs = chebint(self.coeffs, self.a, self.b) + return integ + + def deriv(self, m=1): + """ + Return a derivative of this polynomial. + + Refer to `chebder` for full documentation. + + See Also + -------- + chebder : equivalent function + + """ + der = Cheb1d(self) + der.coeffs = chebder(self.coeffs, self.a, self.b) + return der + +def padefit(c, m=None): + """ + Rational polynomial fitting from polynomial coefficients + + Parameters + ---------- + c : array-like + coefficients of power series expansion from highest degree to zero. + m : scalar integer + order of denominator polynomial. (Default floor((len(c)-1)/2)) + + Returns + ------- + num, den : poly1d + numerator and denominator polynomials for the pade approximation + + If the function is well approximated by + M+N+1 + f(x) = sum c(2*n+2-k)*x^k + k=0 + + then the pade approximation is given by + M + sum c1(n-k+1)*x^k + k=0 + f(x) = ------------------------ + N + sum c2(n-k+1)*x^k + k=0 + + Note: c must be ordered for direct use with polyval + + Example + ------- + Pade approximation to exp(x) + >>> import scipy.special as sp + >>> import pylab as plb + >>> c = poly1d(1./sp.gamma(plb.r_[6+1:0:-1])) #polynomial coeff exponential function + >>> [p, q] = padefit(c) + >>> p; q + poly1d([ 0.00277778, 0.03333333, 0.2 , 0.66666667, 1. ]) + poly1d([ 0.03333333, -0.33333333, 1. ]) + + >>> x = plb.linspace(0,4); + >>> h = plb.plot(x,c(x),x,p(x)/q(x),'g-', x,plb.exp(x),'r.') + >>> plb.close() + + See also + -------- + scipy.misc.pade + + """ + if not m: + m = int(floor((len(c) - 1) * 0.5)) + c = asarray(c) + return pade(c[::-1], m) + +def test_pade(): + cof = array(([1.0, 1.0, 1.0 / 2, 1. / 6, 1. / 24])) + p, q = pade(cof, 2) + t = arange(0, 2, 0.1) + assert(all(abs(p(t) / q(t) - exp(t)) < 0.3)) + +def padefitlsq(fun, m, k, a= -1, b=1, trace=False, x=None, end_points=True): + """ + Rational polynomial fitting. A minimax solution by least squares. + + Parameters + ---------- + fun : callable or or a two column matrix + f=[x,f(x)] where length(x)>(m+k+1)*8. + m, k : integer + number of coefficients of the numerator and denominater, respectively. + a, b : real scalars + evaluation limits, (default a=-1,b=1) + + Returns + ------- + num, den : poly1d + numerator and denominator polynomials for the pade approximation + dev : ndarray + maximum absolute deviation of the approximation + + The pade approximation is given by + m + sum c1[m-i]*x**i + i=0 + f(x) = ------------------------ + k + sum c2[k-i]*x**i + i=0 + + If F is a two column matrix, [x f(x)], a good choice for x is: + + x = cos(pi/(N-1)*(N-1:-1:0))*(b-a)/2+ (a+b)/2, where N = (m+k+1)*8; + + Note: c1 and c2 are ordered for direct use with polyval + + Example + ------- + + Pade approximation to exp(x) between 0 and 2 + >>> import pylab as plb + >>> [c1, c2] = padefitlsq(plb.exp,3,3,0,2) + >>> c1; c2 + poly1d([ 0.01443847, 0.128842 , 0.55284547, 0.99999962]) + poly1d([-0.0049658 , 0.07610473, -0.44716929, 1. ]) + + >>> x = plb.linspace(0,4) + >>> h = plb.plot(x, polyval(c1,x)/polyval(c2,x),'g') + >>> h = plb.plot(x, plb.exp(x), 'r') + + See also + -------- + padefit + + Reference + --------- + William H. Press, Saul Teukolsky, + William T. Wetterling and Brian P. Flannery (1997) + "Numerical recipes in Fortran 77", Vol. 1, pp 197-20 + """ + + NFAC = 8 + BIG = 1e30 + MAXIT = 5 + + smallest_devmax = BIG + ncof = m + k + 1 + npt = NFAC * ncof # % Number of points where function is evaluated, i.e. fineness of mesh + + if x is None: + if end_points: + # Use the location of the local extreme values of + # the Chebychev polynomial of the first kind of degree NPT-1. + x = map_to_interval(chebextr(npt - 1), a, b) + else: + # Use the roots of the Chebychev polynomial of the first kind of degree NPT. + # Note this is useful if there are singularities close to the endpoints. + x = map_to_interval(chebroot(npt, kind=1), a, b) + + + if hasattr(fun, '__call__'): + fs = fun(x) + else: + fs = fun + n = len(fs) + if n < npt: + warnings.warn('Check the result! Number of function values should be at least: %d' % npt) + + if trace: + import pylab as plb + plb.plot(x, fs, '+') + + wt = ones((npt)) + ee = ones((npt)) + mad = 0 + + u = zeros((npt, ncof)) + for ix in xrange(MAXIT): + #% Set up design matrix for least squares fit. + pow = wt + bb = pow * (fs + abs(mad) * sign(ee)) + + for jx in xrange(m + 1): + u[:, jx] = pow + pow = pow * x + + pow = -bb + for jx in xrange(m + 1, ncof): + pow = pow * x + u[:, jx] = pow + + + [u1, w, v] = linalg.svd(u, full_matrices=False) + cof = where(w == 0, 0.0, dot(bb, u1) / w) + cof = dot(cof, v) + + #% Tabulate the deviations and revise the weights + ee = polyval(cof[m::-1], x) / polyval(cof[ncof:m:-1].tolist() + [1, ], x) - fs + + wt = abs(ee) + devmax = max(wt) + mad = wt.mean() #% mean absolute deviation + + if (devmax <= smallest_devmax): #% Save only the best coefficients found + smallest_devmax = devmax + c1 = cof[m::-1] + c2 = cof[ncof:m:-1].tolist() + [1, ] + + if trace: + print('Iteration=%d, max error=%g' % (ix, devmax)) + plb.plot(x, fs, x, ee + fs) + #c1=c1(:) + #c2=c2(:) + return poly1d(c1), poly1d(c2) + + + + + +def main(): + + [c1, c2] = padefitlsq(exp, 3, 3, 0, 2) + + x = linspace(0, 4) + plb.plot(x, polyval(c1, x) / polyval(c2, x), 'g') + plb.plot(x, exp(x), 'r') + + import scipy.special as sp + + p = [[1, 1, 1], [2, 2, 2]] + pi = polyint(p, 1) + pr = polyreloc(p, 2) + pd = polyder(p) + st = poly2str(p) + c = poly1d(1. / sp.gamma(plb.r_[6 + 1:0:-1])) #polynomial coeff exponential function + [p, q] = padefit(c) + x = linspace(0, 4); + plb.plot(x, c(x), x, p(x) / q(x), 'g-', x, exp(x), 'r.') + plb.close() + x = arange(4) + dx = dct(x) + idx = idct(dx) + + a = 0; + b = 2; + ck = chebfit(exp, 6, a, b); + t = chebval(0, ck, a, b) + x = linspace(0, 2, 6); + plb.plot(x, exp(x), 'r', x, chebval(x, ck, a, b), 'g.') + #x1 = chebroot(9).'*(b-a)/2+(b+a)/2 ; + #ck1 =chebfit([x1 exp(x1)],9,a,b); + #plot(x,exp(x),'r'), hold on + #plot(x,chebval(x,ck1,a,b),'g'), hold off + + + t = poly2hstr([1, 1, 2]) + py = [1, 0] + px = polyshift(py, 0, 5); + t1 = polyval(px, [0, 2.5, 5]) #% This is the same as the line below + t2 = polyval(py, [-1, 0, 1 ]) + + px = [1, 0] + py = polyishift(px, 0, 5); + t1 = polyval(px, [0, 2.5, 5]) #% This is the same as the line below + t2 = polyval(py, [-1, 0, 1 ]) + print(t1, t2) + +if __name__ == '__main__': + if False: + main() + else: + import doctest + doctest.testmod() diff --git a/wafo/polynomial_old.py b/wafo/polynomial_old.py new file mode 100755 index 0000000..fbe9c70 --- /dev/null +++ b/wafo/polynomial_old.py @@ -0,0 +1,1207 @@ +#------------------------------------------------------------------------------- +# Name: polynomial +# Purpose: Functions to operate on polynomials. +# +# Author: pab +# polyXXX functions are based on functions found in the matlab toolbox polyutil written by +# Author: Peter J. Acklam +# E-mail: pjacklam@online.no +# WWW URL: http://home.online.no/~pjacklam +# +# Created: 30.12.2008 +# Copyright: (c) pab 2008 +# Licence: LGPL +#------------------------------------------------------------------------------- +#!/usr/bin/env python + +""" + Extended functions to operate on polynomials +""" +import warnings +import numpy as np +from numpy.lib.polynomial import * +__all__ = np.lib.polynomial.__all__ +__all__ = __all__ + ['polyreloc', 'polyrescl', 'polytrim', 'poly2hstr', 'poly2str', + 'polyshift', 'polyishift', 'map_from_intervall', 'map_to_intervall', + 'cheb2poly', 'chebextr', 'chebroot', 'chebpoly', 'chebfit', 'chebval', + 'chebder', 'chebint', 'Cheb1d', 'dct', 'idct'] + +def polyreloc(p,x,y=0.0): + """ + Relocate polynomial + + The polynomial `p` is relocated by "moving" it `x` + units along the x-axis and `y` units along the y-axis. + So the polynomial `r` is relative to the point (x,y) as + the polynomial `p` is relative to the point (0,0). + + Parameters + ---------- + p : array-like, poly1d + vector or matrix of column vectors of polynomial coefficients to relocate. + (Polynomial coefficients are in decreasing order.) + x : scalar + distance to relocate P along x-axis + y : scalar + distance to relocate P along y-axis (default 0) + + Returns + ------- + r : ndarray, poly1d + vector/matrix/poly1d of relocated polynomial coefficients. + + See also + -------- + polyrescl + + Example + ------- + >>> import numpy as np + >>> p = np.arange(6); p.shape = (2,-1) + >>> np.polyval(p,0) + array([3, 4, 5]) + >>> np.polyval(p,1) + array([3, 5, 7]) + >>> r = polyreloc(p,-1) # move to the left along x-axis + >>> np.polyval(r,-1) # = polyval(p,0) + array([3, 4, 5]) + >>> np.polyval(r,0) # = polyval(p,1) + array([3, 5, 7]) + """ + + truepoly = isinstance(p, poly1d) + r = np.atleast_1d(p).copy() + n = r.shape[0] + + # Relocate polynomial using Horner's algorithm + for ii in range(n,1,-1): + for i in range(1,ii): + r[i] = r[i] - x*r[i-1] + r[-1] = r[-1] + y + if r.ndim>1 and r.shape[-1]==1: + r.shape = (r.size,) + if truepoly: + r = poly1d(r) + return r + +def polyrescl(p, x, y=1.0): + """ + Rescale polynomial. + + Parameters + ---------- + p : array-like, poly1d + vector or matrix of column vectors of polynomial coefficients to rescale. + (Polynomial coefficients are in decreasing order.) + x,y : scalars + defining the factors to rescale the polynomial `p` in + x-direction and y-direction, respectively. + + Returns + ------- + r : ndarray, poly1d + vector/matrix/poly1d of rescaled polynomial coefficients. + + See also + -------- + polyreloc + + Example + ------- + >>> import numpy as np + >>> p = np.arange(6); p.shape = (2,-1) + >>> np.polyval(p,0) + array([3, 4, 5]) + >>> np.polyval(p,1) + array([3, 5, 7]) + >>> r = polyrescl(p,2) # scale by 2 along x-axis + >>> np.polyval(r,0) # = polyval(p,0) + array([ 3., 4., 5.]) + >>> np.polyval(r,2) # = polyval(p,1) + array([ 3., 5., 7.]) + """ + + truepoly = isinstance(p, poly1d) + r = np.atleast_1d(p).copy() + n = r.shape[0] + + xscale =(float(x)**np.arange(1-n , 1)) + if r.ndim==1: + q = y*r*xscale + else: + q = y*r*xscale[:,np.newaxis] + if truepoly: + q = poly1d(q) + return q + +def polytrim(p): + """ + Trim polynomial by stripping off leading zeros. + + Parameters + ---------- + p : array-like, poly1d + vector of polynomial coefficients in decreasing order. + + Returns + ------- + r : ndarray, poly1d + vector/matrix/poly1d of trimmed polynomial coefficients. + + Example + ------- + >>> p = [0,1,2] + >>> polytrim(p) + array([1, 2]) + """ + + truepoly = isinstance(p, poly1d) + if truepoly: + return p + else: + r = np.atleast_1d(p).copy() + # Remove leading zeros + is_not_lead_zeros =np.logical_or.accumulate(r != 0,axis=0) + if r.ndim==1: + r = r[is_not_lead_zeros] + else: + is_not_lead_zeros = np.any(is_not_lead_zeros,axis=1) + r = r[is_not_lead_zeros,:] + return r + +def poly2hstr(p, variable='x' ): + """ + Return polynomial as a Horner represented string. + + Parameters + ---------- + p : array-like poly1d + vector of polynomial coefficients in decreasing order. + variable : string + display character for variable + + Returns + ------- + p_str : string + consisting of the polynomial coefficients in the vector P multiplied + by powers of the given `variable`. + + Examples + -------- + >>> poly2hstr([1, 1, 2], 's' ) + '(s + 1)*s + 2' + + See also + -------- + poly2str + """ + var = variable + + coefs = polytrim(np.atleast_1d(p)) + order = len(coefs)-1 # Order of polynomial. + s = '' # Initialize output string. + ix = 1; + for expon in range(order,-1,-1): + coef = coefs[order-expon] + #% There is no point in adding a zero term (except if it's the only + #% term, but we'll take care of that later). + if coef == 0: + ix = ix+1 + else: + #% Append exponent if necessary. + if ix>1: + exponstr = '%.0f' % ix + s = '%s**%s' % (s,exponstr); + ix = 1 + #% Is it the first term? + isfirst = s == '' + + # We need the coefficient only if it is different from 1 or -1 or + # when it is the constant term. + needcoef = (( abs(coef) != 1 ) | ( expon == 0 ) & isfirst) | 1-isfirst + + # We need the variable except in the constant term. + needvar = ( expon != 0 ) + + #% Add sign, but we don't need a leading plus-sign. + if isfirst: + if coef < 0: + s = '-' # % Unary minus. + else: + if coef < 0: + s = '%s - ' % s # % Binary minus (subtraction). + else: + s = '%s + ' % s # % Binary plus (addition). + + + #% Append the coefficient if it is different from one or when it is + #% the constant term. + if needcoef: + coefstr = '%.20g' % abs(coef) + s = '%s%s' % (s,coefstr) + + #% Append variable if necessary. + if needvar: + #% Append a multiplication sign if necessary. + if needcoef: + if 1-isfirst: + s = '(%s)' % s + s = '%s*' % s + s = '%s%s' % ( s, var ) + + #% Now treat the special case where the polynomial is zero. + if s=='': + s = '0' + return s + +def poly2str(p,variable='x'): + """ + Return polynomial as a string. + + Parameters + ---------- + p : array-like poly1d + vector of polynomial coefficients in decreasing order. + variable : string + display character for variable + + Returns + ------- + p_str : string + consisting of the polynomial coefficients in the vector P multiplied + by powers of the given `variable`. + + See also + -------- + poly2hstr + + Examples + -------- + >>> poly2str([1, 1, 2], 's' ) + 's**2 + s + 2' + """ + thestr = "0" + var = variable + + # Remove leading zeros + coeffs = polytrim(np.atleast_1d(p)) + + N = len(coeffs)-1 + + for k in range(len(coeffs)): + coefstr = '%.4g' % abs(coeffs[k]) + if coefstr[-4:] == '0000': + coefstr = coefstr[:-5] + power = (N-k) + if power == 0: + if coefstr != '0': + newstr = '%s' % (coefstr,) + else: + if k == 0: + newstr = '0' + else: + newstr = '' + elif power == 1: + if coefstr == '0': + newstr = '' + elif coefstr == 'b' or coefstr == '1': + newstr = var + else: + newstr = '%s*%s' % (coefstr, var) + else: + if coefstr == '0': + newstr = '' + elif coefstr == 'b' or coefstr == '1': + newstr = '%s**%d' % (var, power,) + else: + newstr = '%s*%s**%d' % (coefstr, var, power) + + if k > 0: + if newstr != '': + if coeffs[k] < 0: + thestr = "%s - %s" % (thestr, newstr) + else: + thestr = "%s + %s" % (thestr, newstr) + elif (k == 0) and (newstr != '') and (coeffs[k] < 0): + thestr = "-%s" % (newstr,) + else: + thestr = newstr + return thestr + +def polyshift(py,a=-1,b=1): + """ + Polynomial coefficient shift + + Polyshift shift the polynomial coefficients by a variable shift: + + Y = 2*(X-.5*(b+a))/(b-a) + + i.e., the interval -1 <= Y <= 1 is mapped to the interval a <= X <= b + + Parameters + ---------- + py : array-like + polynomial coefficients for the variable y. + a,b : scalars + lower and upper limit. + + Returns + ------- + px : ndarray + polynomial coefficients for the variable x. + + See also + -------- + polyishift + + Example + ------- + >>> py = [1, 0] + >>> px = polyshift(py,0,5) + >>> polyval(px,[0, 2.5, 5]) #% This is the same as the line below + array([-1., 0., 1.]) + >>> polyval(py,[-1, 0, 1 ]) + array([-1, 0, 1]) + """ + + if (a==-1) & (b ==1): + return py + L = b-a + return polyishift(py,-(2.+b+a)/L,(2.-b-a)/L) + +def polyishift(px,a=-1,b=1): + """ + Inverse polynomial coefficient shift + + Polyishift does the inverse of Polyshift, + shift the polynomial coefficients by a variable shift: + + Y = 2*(X-.5*(b+a)/(b-a) + + i.e., the interval a <= X <= b is mapped to the interval -1 <= Y <= 1 + + Parameters + ---------- + px : array-like + polynomial coefficients for the variable x. + a,b : scalars + lower and upper limit. + + Returns + ------- + py : ndarray + polynomial coefficients for the variable y. + + See also + -------- + polyishift + + Example + ------- + >>> px = [1, 0] + >>> py = polyishift(px,0,5); + >>> polyval(px,[0, 2.5, 5]) #% This is the same as the line below + array([ 0. , 2.5, 5. ]) + >>> polyval(py,[-1, 0, 1]) + array([ 0. , 2.5, 5. ]) + """ + if (a==-1) & (b ==1): + return px + L = b-a + xscale = 2./L + xloc = -float(a+b)/L + return polyreloc( polyrescl(px,xscale),xloc) + +def map_from_interval(x,a,b) : + """F(x), where F: [a,b] -> [-1,1].""" + return (x - (b + a)/2.0)*(2.0/(b - a)) + +def map_to_interval(x,a,b) : + """F(x), where F: [-1,1] -> [a,b].""" + return (x*(b - a) + (b + a))/2.0 + +def poly2cheb(p,a=-1,b=1): + """ + Convert polynomial coefficients into Chebyshev coefficients + + Parameters + ---------- + p : array-like + polynomial coefficients + a,b : real scalars + lower and upper limits (Default -1,1) + + Returns + ------- + ck : ndarray + Chebychef coefficients + + POLY2CHEB do the inverse of CHEB2POLY: given a vector of polynomial + coefficients AK, returns an equivalent vector of Chebyshev + coefficients CK. + + This is useful for economization of power series. + The steps for doing so: + 1. Convert polynomial coefficients to Chebychev coefficients, CK. + 2. Truncate the CK series to a smaller number of terms, using the + coefficient of the first neglected Chebychev polynomial as an error + estimate. + 3 Convert back to a polynomial by CHEB2POLY + + See also + -------- + cheb2poly + chebval + chebfit + + Examples + -------- + >>> import numpy as np + >>> p = np.arange(5) + >>> ck = poly2cheb(p) + >>> cheb2poly(ck) + array([ 1., 2., 3., 4.]) + + Reference + --------- + William H. Press, Saul Teukolsky, + William T. Wetterling and Brian P. Flannery (1997) + "Numerical recipes in Fortran 77", Vol. 1, pp 184-194 + """ + f = poly1d(p) + n = len(f.coeffs) + return chebfit(f,n,a,b) + +def cheb2poly(ck,a=-1,b=1): + """ + Converts Chebyshev coefficients to polynomial coefficients + + Parameters + ---------- + ck : array-like + Chebychef coefficients + a,b : real, scalars + lower and upper limits (Default -1,1) + + Returns + ------- + p : ndarray + polynomial coefficients + + It is not advised to do this for len(ck)>10 due to numerical cancellations. + + See also + -------- + chebval + chebfit + + Examples + -------- + >>> import numpy as np + >>> p = np.arange(5) + >>> ck = poly2cheb(p) + >>> cheb2poly(ck) + array([ 1., 2., 3., 4.]) + + + References + ---------- + http://en.wikipedia.org/wiki/Chebyshev_polynomials + http://en.wikipedia.org/wiki/Chebyshev_form + http://en.wikipedia.org/wiki/Clenshaw_algorithm + """ + + n = len(ck) + + b_Nmi = np.zeros(1) + b_Nmip1 = np.zeros(1) + y = np.r_[2/(b-a), -(a+b)/(b-a)] + y2 = 2.*y + + # Clenshaw recurence + for ix in range(n-1,0,-1): + tmp = b_Nmi + b_Nmi = polymul(y2,b_Nmi) # polynomial multiplication + nb = len(b_Nmip1) + b_Nmip1[-1] = b_Nmip1[-1]-ck[ix] + b_Nmi[-nb::] = b_Nmi[-nb::]-b_Nmip1 + b_Nmip1 = tmp + + p = polymul(y,b_Nmi) # polynomial multiplication + nb = len(b_Nmip1) + b_Nmip1[-1] = b_Nmip1[-1]-ck[0] + p[-nb::] = p[-nb::]-b_Nmip1 + return polytrim(p) + +def chebextr(n): + """ + Return roots of derivative of Chebychev polynomial of the first kind. + + All local extreme values of the polynomial are either -1 or 1. So, + CHEBPOLY( N, CHEBEXTR(N) ) ) return the same as (-1).^(N:-1:0) + except for the numerical noise in the former. + + Because the extreme values of Chebychev polynomials of the first + kind are either -1 or 1, their roots are often used as starting + values for the nodes in minimax approximations. + + + Parameters + ---------- + n : scalar, integer + degree of Chebychev polynomial. + + Examples + -------- + >>> x = chebextr(4) + >>> chebpoly(4,x) + array([ 1., -1., 1., -1., 1.]) + + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_nodes + http://en.wikipedia.org/wiki/Chebyshev_polynomials + """ + return -np.cos((np.pi*np.arange(n+1))/n); + +def chebroot(n,kind=1): + """ + Return roots of Chebychev polynomial of the first or second kind. + + The roots of the Chebychev polynomial of the first kind form a particularly + good set of nodes for polynomial interpolation because the resulting + interpolation polynomial minimizes the problem of Runge's phenomenon. + + Parameters + ---------- + n : scalar, integer + degree of Chebychev polynomial. + kind: 1 or 2, optional + kind of Chebychev polynomial (default 1) + + Examples + -------- + >>> import numpy as np + >>> x = chebroot(3) + >>> np.abs(chebpoly(3,x))<1e-15 + array([ True, True, True], dtype=bool) + >>> chebpoly(3) + array([ 4., 0., -3., 0.]) + >>> x2 = chebroot(4,kind=2) + >>> np.abs(chebpoly(4,x2,kind=2))<1e-15 + array([ True, True, True, True], dtype=bool) + >>> chebpoly(4,kind=2) + array([ 16., 0., -12., 0., 1.]) + + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_nodes + http://en.wikipedia.org/wiki/Chebyshev_polynomials + """ + if kind not in (1,2): + raise ValueError('kind must be 1 or 2') + return -np.cos(np.pi*(np.arange(n)+0.5*kind)/(n+kind-1)); + + +def chebpoly(n, x=None, kind=1): + """ + Return Chebyshev polynomial of the first or second kind. + + These polynomials are orthogonal on the interval [-1,1], with + respect to the weight function w(x) = (1-x^2)^(-1/2+kind-1). + + chebpoly(n) returns the coefficients of the Chebychev polynomial of degree N. + chebpoly(n,x) returns the Chebychev polynomial of degree N evaluated in X. + + Parameters + ---------- + n : integer, scalar + degree of Chebychev polynomial. + x : array-like, optional + evaluation points + kind: 1 or 2, optional + kind of Chebychev polynomial (default 1) + + Returns + ------- + p : ndarray + polynomial coefficients if x is None. + Chebyshev polynomial evaluated at x otherwise + + Examples + -------- + >>> import numpy as np + >>> x = chebroot(3) + >>> np.abs(chebpoly(3,x))<1e-15 + array([ True, True, True], dtype=bool) + >>> chebpoly(3) + array([ 4., 0., -3., 0.]) + >>> x2 = chebroot(4,kind=2) + >>> np.abs(chebpoly(4,x2,kind=2))<1e-15 + array([ True, True, True, True], dtype=bool) + >>> chebpoly(4,kind=2) + array([ 16., 0., -12., 0., 1.]) + + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_polynomials + """ + if x is None: # Calculate coefficients. + if n == 0: + p = np.ones(1) + else: + p = np.round( pow(2,n-2+kind) * np.poly( chebroot(n,kind=kind) ) ) + p[1::2] = 0; + return p + else: # Evaluate polynomial in chebychev form + ck = np.zeros(n+1) + ck[n] = 1. + return _chebval(np.atleast_1d(x),ck,kind=kind) + +def chebfit(fun,n=10,a=-1,b=1,trace=False): + """ + Computes the Chebyshevs coefficients + + so that f(x) can be approximated by: + + n-1 + f(x) = sum ck*Tk(x) + k=0 + + where Tk is the k'th Chebyshev polynomial of the first kind. + + Parameters + ---------- + fun : callable + function to approximate + n : integer, scalar, optional + number of base points (abscissas). Default n=10 (maximum 50) + a,b : real, scalars, optional + integration limits + + Returns + ------- + ck : ndarray + polynomial coefficients in Chebychev form. + + Examples + -------- + Fit exp(x) + + >>> import pylab as pb + >>> a = 0; b = 2 + >>> ck = chebfit(pb.exp,7,a,b); + >>> x = pb.linspace(0,4); + >>> h=pb.plot(x,pb.exp(x),'r',x,chebval(x,ck,a,b),'g.') + >>> x1 = chebroot(9)*(b-a)/2+(b+a)/2 + >>> ck1 = chebfit(pb.exp(x1)) + >>> h=pb.plot(x,pb.exp(x),'r',x,chebval(x,ck1,a,b),'g.') + + >>> pb.close() + + See also + -------- + chebval + + Reference + --------- + http://en.wikipedia.org/wiki/Chebyshev_nodes + http://mathworld.wolfram.com/ChebyshevApproximationFormula.html + + W. Fraser (1965) + "A Survey of Methods of Computing Minimax and Near-Minimax Polynomial + Approximations for Functions of a Single Independent Variable" + Journal of the ACM (JACM), Vol. 12 , Issue 3, pp 295 - 314 + + William H. Press, Saul Teukolsky, + William T. Wetterling and Brian P. Flannery (1997) + "Numerical recipes in Fortran 77", Vol. 1, pp 184-194 + """ + + if (n>50): + warnings.warn('CHEBFIT should only be used for n<50') + + if hasattr(fun,'__call__'): + x = map_to_interval(chebroot(n),a,b) + f = fun(x); + if trace: + import pylab as plb + plb.plot(x,f,'+') + else: + f = fun + n = len(f) + #raise ValueError('Function must be callable!') + # N-1 + # c(k) = (2/N) sum w(n) f(n)*cos(pi*k*(2n+1)/(2N)), 0 <= k < N. + # n=0 + # + # w(0) = 0.5, w(n)=1 for n>0 + ck = dct(f[::-1])/n + ck[0] = ck[0]/2. + return ck + +def dct(x,n=None): + """ + Discrete Cosine Transform + + N-1 + y[k] = 2* sum x[n]*cos(pi*k*(2n+1)/(2*N)), 0 <= k < N. + n=0 + + Examples + -------- + >>> import numpy as np + >>> x = np.arange(5) + >>> np.abs(x-idct(dct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + >>> np.abs(x-dct(idct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + + Reference + --------- + http://en.wikipedia.org/wiki/Discrete_cosine_transform + http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/ + """ + fft = np.fft.fft + x = np.atleast_1d(x) + + if n is None: + n = x.shape[-1] + + if x.shape[-1]0 + + Examples + -------- + >>> import numpy as np + >>> x = np.arange(5) + >>> np.abs(x-idct(dct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + >>> np.abs(x-dct(idct(x)))<1e-14 + array([ True, True, True, True, True], dtype=bool) + + Reference + --------- + http://en.wikipedia.org/wiki/Discrete_cosine_transform + http://users.ece.utexas.edu/~bevans/courses/ee381k/lectures/ + """ + + ifft = np.fft.ifft + x = np.atleast_1d(x) + + if n is None: + n = x.shape[-1] + + w = np.exp(1j * np.arange(n) * np.pi/(2*n)) + + if x.shape[-1]>> import pylab as pb + >>> x = pb.linspace(-1,1) + >>> ck = pb.zeros(5); ck[-1]=1 + >>> h = pb.plot(x,chebval(x,ck),x,chebpoly(4,x),'.') + >>> pb.close() + + Fit exponential function: + >>> import pylab as pb + >>> ck = chebfit(pb.exp,7,0,2) + >>> x = pb.linspace(0,4); + >>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x)) + >>> pb.close() + + See also + -------- + chebfit + + References + ---------- + http://en.wikipedia.org/wiki/Clenshaw_algorithm + http://mathworld.wolfram.com/ClenshawRecurrenceFormula.html + """ + + y = map_from_interval(np.atleast_1d(x),a,b) + if fill is None: + f = _chebval(y,ck,kind=kind) + else: + cond = (np.abs(y)<=1) + f = np.where(cond,0,fill) + if np.any(cond): + yk = np.extract(cond,y) + f[cond] = _chebval(yk,ck,kind=kind) + return f + + +def chebder(ck,a=-1,b=1): + """ + Differentiate Chebyshev polynomial + + Parameters + ---------- + ck : array-like + polynomial coefficients in Chebyshev form of function to differentiate + a,b : real, scalars + limits for polynomial(Default -1,1) + + Return + ------ + cder : ndarray + polynomial coefficients in Chebyshev form of the derivative + + Examples + -------- + + Fit exponential function: + >>> import pylab as pb + >>> ck = chebfit(pb.exp,7,0,2) + >>> x = pb.linspace(0,4) + >>> ck2 = chebder(ck,0,2); + >>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x),'r') + >>> pb.close() + + See also + -------- + chebint + chebfit + """ + + n = len(ck) + cder = np.zeros(n) + # n and n-1 are special cases. + # cder(n-1)=0; + cder[-2] = 2*(n-1)*ck[-1] + for j in range(n-3,-1,-1): + cder[j] = cder[j+2]+2*j*ck[j+1] + + return cder*2./(b-a) # Normalize to the interval b-a. + +def chebint(ck,a=-1,b=1): + """ + Integrate Chebyshef polynomial + + Parameters + ---------- + ck : array-like + polynomial coefficients in Chebyshev form of function to integrate. + a,b : real, scalars + limits for polynomial(Default -1,1) + + Return + ------ + cint : ndarray + polynomial coefficients in Chebyshev form of the integrated function + + Examples + -------- + Fit exponential function: + >>> import pylab as pb + >>> ck = chebfit(pb.exp,7,0,2) + >>> x = pb.linspace(0,4) + >>> ck2 = chebint(ck,0,2); + >>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x),'r.') + >>> pb.close() + + See also + -------- + chebder + chebfit + """ + + + n = len(ck) + + cint = np.zeros(n); + con = 0.25*(b-a); + + dif1 = np.diff(ck[::2]) + ix1= np.r_[1:n-1:2] + cint[ix1] = -(con*dif1)/(ix1-1) + if n>3: + dif2 = np.diff(ck[1::2]) + ix2=np.r_[2:n-1:2] + cint[ix2] = -(con*dif2)/(ix2-1) + + #% cint(n) is a special case + cint[-1] = (con*ck[n-2])/(n-1) + cint[0] = np.sum((-1)**np.r_[1:n]*cint[1::]) # Set constant of integration + + + return cint + +class Cheb1d(object): + coeffs = None + order = None + a = None + b = None + def __init__(self,ck,a=-1,b=1): + if isinstance(ck, poly1d): + for key in ck.__dict__.keys(): + self.__dict__[key] = ck.__dict__[key] + return + cki = np.trim_zeros(np.atleast_1d(ck),'b') + if len(cki.shape) > 1: + raise ValueError, "Polynomial must be 1d only." + self.__dict__['coeffs'] = cki + self.__dict__['order'] = len(cki) - 1 + self.__dict__['a'] = a + self.__dict__['b'] = b + + + def __call__(self,x): + return chebval(x,self.coeffs,self.a,self.b) + + def __array__(self, t=None): + if t: + return np.asarray(self.coeffs, t) + else: + return np.asarray(self.coeffs) + + def __repr__(self): + vals = repr(self.coeffs) + vals = vals[6:-1] + return "Cheb1d(%s)" % vals + + def __len__(self): + return self.order + + def __str__(self): + pass + def __neg__(self): + return Cheb1d(-self.coeffs,self.a,self.b) + + def __pos__(self): + return self + + + def __add__(self, other): + other = poly1d(other) + return poly1d(polyadd(self.coeffs, other.coeffs)) + + def __radd__(self, other): + other = poly1d(other) + return poly1d(polyadd(self.coeffs, other.coeffs)) + + def __sub__(self, other): + other = poly1d(other) + return poly1d(polysub(self.coeffs, other.coeffs)) + + def __rsub__(self, other): + other = poly1d(other) + return poly1d(polysub(other.coeffs, self.coeffs)) + + def __eq__(self, other): + return np.alltrue(self.coeffs == other.coeffs) + + def __ne__(self, other): + return np.any(self.coeffs != other.coeffs) or (self.a!=other.a) or (self.b !=other.b) + + def __setattr__(self, key, val): + raise ValueError, "Attributes cannot be changed this way." + + def __getattr__(self, key): + if key in ['c','coef','coefficients']: + return self.coeffs + elif key in ['o']: + return self.order + elif key in ['a']: + return self.a + elif key in ['b']: + return self.b + else: + try: + return self.__dict__[key] + except KeyError: + raise AttributeError("'%s' has no attribute '%s'" % (self.__class__, key)) + def __getitem__(self, val): + if val > self.order: + return 0 + if val < 0: + return 0 + return self.coeffs[val] + + def __setitem__(self, key, val): + ind = self.order - key + if key < 0: + raise ValueError, "Does not support negative powers." + if key > self.order: + zr = NX.zeros(key-self.order, self.coeffs.dtype) + self.__dict__['coeffs'] = NX.concatenate((self.coeffs,zr)) + self.__dict__['order'] = key + self.__dict__['coeffs'][key] = val + return + + def __iter__(self): + return iter(self.coeffs) + def integ(self, m=1): + """ + Return an antiderivative (indefinite integral) of this polynomial. + + Refer to `chebint` for full documentation. + + See Also + -------- + chebint : equivalent function + + """ + return Cheb1d(chebint(self.coeffs, self.a,self.b)) + + def deriv(self, m=1): + """ + Return a derivative of this polynomial. + + Refer to `chebder` for full documentation. + + See Also + -------- + chebder : equivalent function + + """ + return Cheb1d(chebder(self.coeffs,self.a,self.b)) +def main(): + if False: #True: # + x = np.arange(4) + dx = dct(x) + idx = idct(dx) + import pylab as plb + a = 0; + b = 2; + ck = chebfit(np.exp,6,a,b); + t = chebval(0,ck,a,b) + x=np.linspace(0,2,6); + plb.plot(x,np.exp(x),'r', x,chebval(x,ck,a,b),'g.') + #x1 = chebroot(9).'*(b-a)/2+(b+a)/2 ; + #ck1 =chebfit([x1 exp(x1)],9,a,b); + #plot(x,exp(x),'r'), hold on + #plot(x,chebval(x,ck1,a,b),'g'), hold off + + + t = poly2hstr([1,1,2]) + py = [1, 0] + px = polyshift(py,0,5); + t1=polyval(px,[0, 2.5, 5]) #% This is the same as the line below + t2=polyval(py,[-1, 0, 1 ]) + + px = [1, 0] + py = polyishift(px,0,5); + t1 = polyval(px,[0, 2.5, 5]) #% This is the same as the line below + t2 = polyval(py,[-1, 0, 1 ]) + print(t1,t2) + else: + import doctest + doctest.testmod() +if __name__== '__main__': + main() diff --git a/wafo/rfcmodule.pyf b/wafo/rfcmodule.pyf new file mode 100755 index 0000000..3f25fab --- /dev/null +++ b/wafo/rfcmodule.pyf @@ -0,0 +1,14 @@ +! File rfcmodule.pyf +python module rfcmodule +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(y) :: n=len(y) + double precision dimension(n), intent(in) :: y1 ! input array + double precision intent(in) :: hmin + integer dimension(n), intent(out) :: ind ! output array, + integer intent(out) :: info + end subroutine findrfc +end interface +end python module rfcmodule \ No newline at end of file diff --git a/wafo/rindmod.pyd b/wafo/rindmod.pyd new file mode 100755 index 0000000..d71a97f Binary files /dev/null and b/wafo/rindmod.pyd differ diff --git a/wafo/sg_filter.py b/wafo/sg_filter.py new file mode 100755 index 0000000..4c6216e --- /dev/null +++ b/wafo/sg_filter.py @@ -0,0 +1,84 @@ +#from math import * +from numpy import zeros, convolve, dot, linalg, size #@UnresolvedImport + +all = ['calc_coeff','smooth'] + +def _resub(D, rhs): + """ solves D D^T = rhs by resubstituion. + D is lower triangle-matrix from cholesky-decomposition """ + + M = D.shape[0] + x1= zeros((M,),float) + x2= zeros((M,),float) + + # resub step 1 + for l in range(M): + sum = rhs[l] + for n in range(l): + sum -= D[l,n]*x1[n] + x1[l] = sum/D[l,l] + + # resub step 2 + for l in range(M-1,-1,-1): + sum = x1[l] + for n in range(l+1,M): + sum -= D[n,l]*x2[n] + x2[l] = sum/D[l,l] + + return x2 + + +def calc_coeff(num_points, pol_degree, diff_order=0): + + """ + Calculates filter coefficients for symmetric savitzky-golay filter. + see: http://www.nrbook.com/a/bookcpdf/c14-8.pdf + + Parameters + ---------- + num_points : scalar, integer + means that 2*num_points+1 values contribute to the smoother. + pol_degree : scalar, integer + is degree of fitting polynomial + diff_order : scalar, integer + is degree of implicit differentiation. + 0 means that filter results in smoothing of function + 1 means that filter results in smoothing the first + derivative of function. + and so on ... + + """ + + # setup normal matrix + A = zeros((2*num_points+1, pol_degree+1), float) + for i in range(2*num_points+1): + for j in range(pol_degree+1): + A[i,j] = pow(i-num_points, j) + + # calculate diff_order-th row of inv(A^T A) + ATA = dot(A.transpose(), A) + rhs = zeros((pol_degree+1,), float) + rhs[diff_order] = 1 + D = linalg.cholesky(ATA) + wvec = _resub(D, rhs) + + # calculate filter-coefficients + coeff = zeros((2*num_points+1,), float) + for n in range(-num_points, num_points+1): + x = 0.0 + for m in range(pol_degree+1): + x += wvec[m]*pow(n, m) + coeff[n+num_points] = x + return coeff + +def smooth(signal, coeff): + """ + applies coefficients calculated by calc_coeff() + to signal + """ + + N = size(coeff-1)/2 + res = convolve(signal, coeff) + return res[N:-N] + + diff --git a/wafo/source/c_codes/build_all.py b/wafo/source/c_codes/build_all.py new file mode 100755 index 0000000..03c43b2 --- /dev/null +++ b/wafo/source/c_codes/build_all.py @@ -0,0 +1,19 @@ +""" +f2py c_library.pyf c_functions.c -c +""" +import os + +def compile_all(): + # 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/c_codes/c_functions.c b/wafo/source/c_codes/c_functions.c new file mode 100755 index 0000000..ac37a56 --- /dev/null +++ b/wafo/source/c_codes/c_functions.c @@ -0,0 +1,615 @@ +#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; /* 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=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 v){ + dcross=1; /* first is a down-crossing*/ + } + start=0; + if ( *(y +0)== v){ + /* Find out what type of crossing we have next time.. */ + for (i=1; i v){ + *(ind + ix) = i; /* first crossing is a up-crossing*/ + ix++; + dcross=1; /*The next crossing is a down-crossing*/ + break; + } + } + } + + for (i=start; i h) ) || ((dcross==1 ) && (*(y +i)>=h) && (*(y+i+1) < h) ) ) { + + *(ind + ix) = i+1 ; + ix++; + dcross=-dcross; + } + } + info = ix + return; +} + + diff --git a/wafo/source/c_codes/old/findrfc.c b/wafo/source/c_codes/old/findrfc.c new file mode 100755 index 0000000..ac0b7d2 --- /dev/null +++ b/wafo/source/c_codes/old/findrfc.c @@ -0,0 +1,118 @@ +#include "math.h" +/* + * findrfc.c - + * + * Returns indices to RFC turningpoints of a vector + * of turningpoints + * + * Install gfortran and run the following to build the module: + * f2py rfc.pyf findrfc.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 +* + * 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; + + if (*(y1+0)> *(y1+1)){ + /* if first is a max , ignore the first max*/ + y=&(*(y1+1)); + NC=floor((n-1)/2); + Tstart=2; + } + else { + y=y1; + NC=floor(n/2); + Tstart=1; + } + + if (NC<1){ + info = 0; + return; /* No RFC cycles*/ + } + + + if (( *(y+0) > *(y+1)) && ( *(y+1) > *(y+2)) ){ + info = -1; + return; /*This is not a sequence of turningpoints, exit */ + } + if ((*(y+0) < *(y+1)) && (*(y+1)< *(y+2))){ + info=-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 = ix; + return ; +} + + + diff --git a/wafo/source/c_codes/old/rfc.pyd b/wafo/source/c_codes/old/rfc.pyd new file mode 100755 index 0000000..89343f3 Binary files /dev/null and b/wafo/source/c_codes/old/rfc.pyd differ diff --git a/wafo/source/c_codes/old/rfc.pyf b/wafo/source/c_codes/old/rfc.pyf new file mode 100755 index 0000000..e129557 --- /dev/null +++ b/wafo/source/c_codes/old/rfc.pyf @@ -0,0 +1,14 @@ +! File rfc.pyf +python module rfc +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 intent(out) :: info + end subroutine findrfc +end interface +end python module rfc \ No newline at end of file diff --git a/wafo/source/cov2XXXpdf/bounds/cov2acdfb.f b/wafo/source/cov2XXXpdf/bounds/cov2acdfb.f new file mode 100755 index 0000000..b6a85b4 --- /dev/null +++ b/wafo/source/cov2XXXpdf/bounds/cov2acdfb.f @@ -0,0 +1,450 @@ + 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 new file mode 100755 index 0000000..2d9aee7 --- /dev/null +++ b/wafo/source/cov2XXXpdf/bounds/cov2mmpdfb.f @@ -0,0 +1,356 @@ + 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 new file mode 100755 index 0000000..9f77d29 --- /dev/null +++ b/wafo/source/cov2XXXpdf/bounds/cov2tccpdfb.f @@ -0,0 +1,504 @@ + 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 new file mode 100755 index 0000000..c925525 --- /dev/null +++ b/wafo/source/cov2XXXpdf/bounds/cov2tthpdfb.f @@ -0,0 +1,497 @@ + 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 new file mode 100755 index 0000000..2877fec --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2acdf.f @@ -0,0 +1,445 @@ + 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 new file mode 100755 index 0000000..6046c5a --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2mmpdf.f @@ -0,0 +1,357 @@ + 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 new file mode 100755 index 0000000..6cf7c9a --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2mmtpdf.f @@ -0,0 +1,769 @@ + 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 new file mode 100755 index 0000000..3582432 --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2tccpdf.f @@ -0,0 +1,498 @@ + 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 new file mode 100755 index 0000000..094e339 --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2tcpdf.f @@ -0,0 +1,440 @@ + 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 new file mode 100755 index 0000000..8d6f01a --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2thpdf.f @@ -0,0 +1,569 @@ + 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 new file mode 100755 index 0000000..95e8c22 --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2thpdfalan.f @@ -0,0 +1,632 @@ + 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 new file mode 100755 index 0000000..c0230de --- /dev/null +++ b/wafo/source/cov2XXXpdf/cov2tthpdf.f @@ -0,0 +1,505 @@ + 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 new file mode 100755 index 0000000..6575b70 --- /dev/null +++ b/wafo/source/mreg/build_all.py @@ -0,0 +1,35 @@ +""" +f2py c_library.pyf c_functions.c -c + +gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -c dsvdc.f mregmodule.f + +""" +import os + +def compile_all(): + files = ['mregmodule', 'dsvdc'] + 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) + #f2py --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71 -m mymod -c mymod.f90 + + os.system('f2py -m cov2mod -c %s cov2mmpdfreg_intfc.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71' % file_objects) + #compile1_txt = 'gfortran -fPIC -c mvnprd.f' + #compile2_txt = 'f2py -m mvnprdmod -c mvnprd.o mvnprd_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/mreg/checkmod.mod b/wafo/source/mreg/checkmod.mod new file mode 100755 index 0000000..cd61cae --- /dev/null +++ b/wafo/source/mreg/checkmod.mod @@ -0,0 +1,46 @@ +GFORTRAN module version '0' created from mregmodule.f on Wed Aug 05 19:15:05 2009 +MD5:9338abc0e14d4bf13175cb874e9f7ea5 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'checkmod' 'checkmod' 'checkmod' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() () 0 0) +3 'iii0' 'checkmod' 'iii0' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +4 'iii01' 'checkmod' 'iii01' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +5 'iii101' 'checkmod' 'iii101' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'iii11' 'checkmod' 'iii11' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'iii21' 'checkmod' 'iii21' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +8 'iii31' 'checkmod' 'iii31' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +9 'iii41' 'checkmod' 'iii41' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +10 'iii51' 'checkmod' 'iii51' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +11 'iii61' 'checkmod' 'iii61' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +12 'iii71' 'checkmod' 'iii71' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +13 'iii81' 'checkmod' 'iii81' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'iii91' 'checkmod' 'iii91' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +) + +('checkmod' 0 2 'iii0' 0 3 'iii01' 0 4 'iii101' 0 5 'iii11' 0 6 'iii21' +0 7 'iii31' 0 8 'iii41' 0 9 'iii51' 0 10 'iii61' 0 11 'iii71' 0 12 'iii81' +0 13 'iii91' 0 14) diff --git a/wafo/source/mreg/cov2mmpdfmod.mod b/wafo/source/mreg/cov2mmpdfmod.mod new file mode 100755 index 0000000..b04ec1e --- /dev/null +++ b/wafo/source/mreg/cov2mmpdfmod.mod @@ -0,0 +1,151 @@ +GFORTRAN module version '0' created from cov2mmpdfreg_intfc.f on Thu Aug 06 03:39:39 2009 +MD5:983e75e1f187678a4601b92db2a3f449 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () +() () () () () () () () () () () () () () ()) + +() + +() + +() + +() + +(2 'c_' 'cov2mmpdfmod' 'c_' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +3 'cov2mmpdfmod' 'cov2mmpdfmod' 'cov2mmpdfmod' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() () 0 0) +4 'cov2mmpdfreg' 'cov2mmpdfmod' 'cov2mmpdfreg' 1 ((PROCEDURE +UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 +UNKNOWN ()) 5 0 (6 7 8 9 10 11 12 13 14 15 16 17) () 0 () () () 0 0) +18 'covg' 'cov2mmpdfmod' 'covg' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 UNKNOWN ()) 19 0 (20 21 22 23 24 +25) () 0 () () () 0 0) +26 'eps0_' 'cov2mmpdfmod' 'eps0_' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +27 'eps_' 'cov2mmpdfmod' 'eps_' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +28 'epss_' 'cov2mmpdfmod' 'epss_' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +29 'iac_' 'cov2mmpdfmod' 'iac_' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +30 'initinteg' 'cov2mmpdfmod' 'initinteg' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () +0 () () () 0 0) +31 'initlevels' 'cov2mmpdfmod' 'initlevels' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 +UNKNOWN ()) 32 0 (33 34 35 36 37 38) () 0 () () () 0 0) +39 'isq_' 'cov2mmpdfmod' 'isq_' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +40 'sple' 'cov2mmpdfmod' 'sple' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 41 0 (42 43 +44 45) () 40 () () () 0 0) +46 'transf' 'cov2mmpdfmod' 'transf' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 +UNKNOWN ()) 47 0 (48 49 50 51 52 53) () 0 () () () 0 0) +9 'ulev' '' 'ulev' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +14 ())) 0 () () () 0 0) +10 'vlev' '' 'vlev' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +15 ())) 0 () () () 0 0) +11 'tg' '' 'tg' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 16 ())) 0 () () +() 0 0) +12 'xg' '' 'xg' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 16 ())) 0 () () +() 0 0) +13 'nt' '' 'nt' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'nu' '' 'nu' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +15 'nv' '' 'nv' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +16 'ng' '' 'ng' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +17 'nit' '' 'nit' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'uvdens' '' 'uvdens' 5 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +14 ()) (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 +0 0 INTEGER ()) 0 15 ())) 0 () () () 0 0) +7 't' '' 't' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 13 ())) 0 () () +() 0 0) +8 'cov' '' 'cov' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 13 ()) ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '5')) 0 () () () 0 0) +33 't' '' 't' 32 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +34 'ht' '' 'ht' 32 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +35 'n' '' 'n' 32 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +36 'ng' '' 'ng' 32 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +37 'nu' '' 'nu' 32 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +38 'nv' '' 'nv' 32 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +48 'n' '' 'n' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +49 't' '' 't' 47 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +50 'a' '' 'a' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +51 'timev' '' 'timev' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +52 'value' '' 'value' 47 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +53 'der' '' 'der' 47 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +42 'n' '' 'n' 41 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +43 't' '' 't' 41 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +44 'a' '' 'a' 41 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +45 'timev' '' 'timev' 41 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +20 'xl0' '' 'xl0' 19 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +21 'xl2' '' 'xl2' 19 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +22 'xl4' '' 'xl4' 19 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +23 'cov' '' 'cov' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ()) (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '5')) 0 () () () 0 0) +24 't' '' 't' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 25 ())) 0 () () +() 0 0) +25 'n' '' 'n' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +) + +('c_' 0 2 'cov2mmpdfmod' 0 3 'cov2mmpdfreg' 0 4 'covg' 0 18 'eps0_' 0 26 +'eps_' 0 27 'epss_' 0 28 'iac_' 0 29 'initinteg' 0 30 'initlevels' 0 31 +'isq_' 0 39 'sple' 0 40 'transf' 0 46) diff --git a/wafo/source/mreg/cov2mmpdfreg.f b/wafo/source/mreg/cov2mmpdfreg.f new file mode 100755 index 0000000..ff9d0d8 --- /dev/null +++ b/wafo/source/mreg/cov2mmpdfreg.f @@ -0,0 +1,651 @@ +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 new file mode 100755 index 0000000..d156065 --- /dev/null +++ b/wafo/source/mreg/cov2mmpdfreg_intfc.f @@ -0,0 +1,559 @@ +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 + + module cov2mmpdfmod + IMPLICIT NONE + PRIVATE + PUBLIC cov2mmpdfreg, EPS_, EPSS_, EPS0_, C_, IAC_, ISQ_ + DOUBLE PRECISION :: EPS_ = 1.d-2 + DOUBLE PRECISION :: EPSS_ = 5.d-5 +! used in GAUSSLE1 to implicitly ! determ. # nodes + DOUBLE PRECISION :: EPS0_ = 5.d-5 + DOUBLE PRECISION :: C_ = 4.5d0 + INTEGER :: IAC_=1 + INTEGER :: ISQ_=0 + + contains + + subroutine cov2mmpdfreg(UVdens,t,COV,ULev,VLev,Tg,Xg,Nt,Nu,Nv,Ng, + ! NIT) + USE SIZEMOD + USE EPSMOD + USE CHECKMOD + USE MREGMOD + 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,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,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 + 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. + +c + CALL INITLEVELS(T,HHT,Nt,NG,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' + stop + end if + DO IV=1,Nv + V=Vlev(IV) + CALL TRANSF(NG,V,Xg,Tg,VALUE,DER) + VT(IV)=VALUE + Vdd(IV)=DER +14 continue + 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 +16 CONTINUE + enddo + enddo + + CALL COVG(XL0,XL2,XL4,COV,T,Nt) + + + 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 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 + +10 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) +15 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)) + + 30 CONTINUE + 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)) + 50 CONTINUE + 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) + 51 CONTINUE + 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)) + + 40 CONTINUE + enddo + enddo + 41 CONTINUE + END IF + +C Here the covariance of the problem would be innitiated + + INF=0 + Print *,' Laps to go:',N-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 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 + + 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 + + SUBROUTINE INITLEVELS(T,HT,N,NG,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 + 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 + + IF (NG.GT.501) THEN + PRINT *,'Vector defining transformation of data > 501, stop' + STOP + 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 +10 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 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 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 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 FUNCTION SPLE + + + + SUBROUTINE COVG(XL0,XL2,XL4,COV,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(N,5), intent(in) :: COV + REAL*8, DIMENSION(N), intent(in) :: T + INTEGER, intent(in) :: N + + +C +C COV(Y(T),Y(0)) = COV(:,1) +C + XL0 = COV(1,1) +! XL0 = SPLE(NT,ZERO,COV(:,1),T) +C +C DERIVATIVE COV(Y(T),Y(0)) = COV(:,2) +C +C 2-DERIVATIVE COV(Y(T),Y(0)) = COV(:,3) + XL2 = -COV(1,3) +! XL2 = -SPLE(NT,ZERO,COV(:,3),T) +C 3-DERIVATIVE COV(Y(T),Y(0)) = COV(:,4) + +C 4-DERIVATIVE COV(Y(T),Y(0)) = COV(:,5) + + XL4 = COV(1,5) +! XL4 = SPLE(NT,ZERO,COV(:,5),T) + + RETURN + END SUBROUTINE COVG + + SUBROUTINE INITINTEG() + USE RINTMOD + USE EPSMOD + USE INFCMOD + USE MREGMOD +! 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 + + END module cov2mmpdfmod \ No newline at end of file diff --git a/wafo/source/mreg/dsvdc.f b/wafo/source/mreg/dsvdc.f new file mode 100755 index 0000000..9330beb --- /dev/null +++ b/wafo/source/mreg/dsvdc.f @@ -0,0 +1,613 @@ + 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/epsmod.mod b/wafo/source/mreg/epsmod.mod new file mode 100755 index 0000000..f8e3033 --- /dev/null +++ b/wafo/source/mreg/epsmod.mod @@ -0,0 +1,25 @@ +GFORTRAN module version '0' created from mregmodule.f on Wed Aug 05 19:15:05 2009 +MD5:67523ef735281684c8fb9aae15cdc0a3 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'eps' 'epsmod' 'eps' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +3 'eps0' 'epsmod' 'eps0' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +4 'epsmod' 'epsmod' 'epsmod' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () () 0 0) +5 'epss' 'epsmod' 'epss' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +) + +('eps' 0 2 'eps0' 0 3 'epsmod' 0 4 'epss' 0 5) diff --git a/wafo/source/mreg/expaccmod.mod b/wafo/source/mreg/expaccmod.mod new file mode 100755 index 0000000..1cc59bd --- /dev/null +++ b/wafo/source/mreg/expaccmod.mod @@ -0,0 +1,23 @@ +GFORTRAN module version '0' created from mregmodule.f on Wed Aug 05 19:15:05 2009 +MD5:2d868304b34a40918a05109c83ff1871 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'expaccmod' 'expaccmod' 'expaccmod' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() () 0 0) +3 'pmax' 'expaccmod' 'pmax' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.28000000000000@2') () 0 () () () 0 0) +) + +('expaccmod' 0 2 'pmax' 0 3) diff --git a/wafo/source/mreg/infcmod.mod b/wafo/source/mreg/infcmod.mod new file mode 100755 index 0000000..d78bd6b --- /dev/null +++ b/wafo/source/mreg/infcmod.mod @@ -0,0 +1,32 @@ +GFORTRAN module version '0' created from mregmodule.f on Wed Aug 05 19:15:05 2009 +MD5:806a8e6bde038d8bc47688d3b6e5277f -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'iac' 'infcmod' 'iac' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN EXPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +3 'inf' 'infcmod' 'inf' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '10')) 0 () () () 0 0) +4 'infcmod' 'infcmod' 'infcmod' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () () 0 0) +5 'info' 'infcmod' 'info' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT +(CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '10')) 0 () () () 0 0) +6 'isq' 'infcmod' 'isq' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +EXPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +) + +('iac' 0 2 'inf' 0 3 'infcmod' 0 4 'info' 0 5 'isq' 0 6) diff --git a/wafo/source/mreg/mregmod.mod b/wafo/source/mreg/mregmod.mod new file mode 100755 index 0000000..0cc4c8f --- /dev/null +++ b/wafo/source/mreg/mregmod.mod @@ -0,0 +1,97 @@ +GFORTRAN module version '0' created from mregmodule.f on Wed Aug 05 19:21:17 2009 +MD5:35f9c2506fae455bf63c0bcfadd75d2e -- If you edit this, you'll get what you deserve. + +(() +() () () () () () () () () () () () () () () () () () () () () () () () +() ()) + +() + +(('fi' 'mregmod' 2) ('rind' 'mregmod' 3) ('mreg' 'mregmod' 4)) + +() + +() + +(2 'fi' 'mregmod' 'fi' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 5 0 (6) () 2 () () () 0 0) +4 'mreg' 'mregmod' 'mreg' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 7 0 (8 9 10 11 12 +13 14 15 16 17 18 19 20) () 0 () () () 0 0) +3 'rind' 'mregmod' 'rind' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 21 0 (22 23 24 25 +26 27 28 29 30 31) () 0 () () () 0 0) +22 'xind' '' 'xind' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +23 'r' '' 'r' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '40401')) 0 () +() () 0 0) +24 'bu' '' 'bu' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'201')) 0 () () () 0 0) +25 'dbun' '' 'dbun' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +26 'db' '' 'db' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'201')) 0 () () () 0 0) +27 'sq' '' 'sq' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'201')) 0 () () () 0 0) +28 'vder' '' 'vder' 21 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +29 'nit' '' 'nit' 21 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +30 'n' '' 'n' 21 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +31 'infr' '' 'infr' 21 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'xx' '' 'xx' 5 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +8 'f' '' 'f' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'r' '' 'r' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '40401')) 0 () +() () 0 0) +10 'b' '' 'b' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '201')) 0 () () +() 0 0) +18 'n' '' 'n' 7 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +11 'db' '' 'db' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'201')) 0 () () () 0 0) +12 'aa' '' 'aa' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'4') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '4')) 0 () () () 0 0) +13 'bb' '' 'bb' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'7')) 0 () () () 0 0) +19 'nit' '' 'nit' 7 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'a' '' 'a' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1407')) 0 () +() () 0 0) +20 'infr' '' 'infr' 7 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +15 'da' '' 'da' 7 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 +'7')) 0 () () () 0 0) +16 'vder' '' 'vder' 7 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +17 'm' '' 'm' 7 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +) + +('fi' 0 2 'mreg' 0 4 'rind' 0 3) diff --git a/wafo/source/mreg/mregmodule.f b/wafo/source/mreg/mregmodule.f new file mode 100755 index 0000000..976b59b --- /dev/null +++ b/wafo/source/mreg/mregmodule.f @@ -0,0 +1,3044 @@ +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 +# 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. 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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, 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, 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 = 3.38713 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 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,INF,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, 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 new file mode 100755 index 0000000..2398238 --- /dev/null +++ b/wafo/source/mvnprd/mvnprd.pyf @@ -0,0 +1,23 @@ +! -*- 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 new file mode 100755 index 0000000..1f0715d --- /dev/null +++ b/wafo/source/mvnprd/mvnprd_interface.f @@ -0,0 +1,87 @@ + + 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,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 + + \ No newline at end of file diff --git a/wafo/source/mvnprd/mvnprodcorrprb_interface.f b/wafo/source/mvnprd/mvnprodcorrprb_interface.f new file mode 100755 index 0000000..190f081 --- /dev/null +++ b/wafo/source/mvnprd/mvnprodcorrprb_interface.f @@ -0,0 +1,33 @@ + +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/mvnprodcorrprbmod.mod b/wafo/source/mvnprd/mvnprodcorrprbmod.mod new file mode 100755 index 0000000..e57be0f --- /dev/null +++ b/wafo/source/mvnprd/mvnprodcorrprbmod.mod @@ -0,0 +1,45 @@ +GFORTRAN module version '0' created from mvnprodcorrprb.f on Fri Jul 31 00:49:14 2009 +MD5:f40d97ecb7391e1c401b4b2027719b7e -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () +() () () () () () () () () () () () () () () () () ()) + +() + +(('mvnprodcorrprb' 'mvnprodcorrprbmod' 2)) + +() + +() + +(2 'mvnprodcorrprb' 'mvnprodcorrprbmod' 'mvnprodcorrprb' 1 ((PROCEDURE +UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC +ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 3 0 (4 5 6 7 8 9 10 11 12 13) +() 0 () () () 0 0) +4 'rho' '' 'rho' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +5 'a' '' 'a' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +6 'b' '' 'b' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +7 'abseps' '' 'abseps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +8 'releps' '' 'releps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'usebreakpoints' '' 'usebreakpoints' 3 ((VARIABLE IN UNKNOWN-PROC +UNKNOWN UNKNOWN DUMMY) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () () 0 () () () 0 +0) +10 'usesimpson' '' 'usesimpson' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () () 0 () () () 0 0) +11 'abserr' '' 'abserr' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +12 'errflg' '' 'errflg' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +13 'prb' '' 'prb' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +) + +('mvnprodcorrprb' 0 2) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/adaptivegausskronrod.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/adaptivegausskronrod.mod new file mode 100755 index 0000000..7d21c23 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/adaptivegausskronrod.mod @@ -0,0 +1,112 @@ +GFORTRAN module created from mvnprodcorrprb.f on Thu Dec 04 12:55:42 2008 +MD5:6d500af6c301beba9c314ac587f06931 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('dqagpe' 'adaptivegausskronrod' 2) ('dqagp' 'adaptivegausskronrod' 3)) + +() + +() + +(3 'dqagp' 'adaptivegausskronrod' 'dqagp' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +4 0 (5 6 7 8 9 10 11 12 13 14 15 16) () 0 () () 0 0) +2 'dqagpe' 'adaptivegausskronrod' 'dqagpe' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +17 0 (18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38) () +0 () () 0 0) +10 'epsabs' '' 'epsabs' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +11 'epsrel' '' 'epsrel' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +12 'limit' '' 'limit' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +13 'result1' '' 'result1' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +14 'abserr' '' 'abserr' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +15 'neval' '' 'neval' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +16 'ier' '' 'ier' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +33 'elist' '' 'elist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +34 'pts' '' 'pts' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (OP (INTEGER 4 0 0 INTEGER ()) 0 PLUS ( +VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 21 ()) (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '2'))) 0 () () 0 0) +35 'iord' '' 'iord' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 +INTEGER ()) 0 25 ())) 0 () () 0 0) +36 'level' '' 'level' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 +INTEGER ()) 0 25 ())) 0 () () 0 0) +37 'ndin' '' 'ndin' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (OP (INTEGER 4 0 0 INTEGER ()) +0 PLUS (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 21 ()) (CONSTANT (INTEGER +4 0 0 INTEGER ()) 0 '2'))) 0 () () 0 0) +38 'last' '' 'last' 17 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +7 'b' '' 'b' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) (REAL 8 +0 0 REAL ()) 0 0 () () 0 () () 0 0) +8 'npts' '' 'npts' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +9 'points' '' 'points' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +8 ())) 0 () () 0 0) +5 'f' '' 'f' 4 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +6 'a' '' 'a' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) (REAL 8 +0 0 REAL ()) 0 0 () () 0 () () 0 0) +18 'f' '' 'f' 17 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +19 'a' '' 'a' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +20 'b' '' 'b' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +21 'npts' '' 'npts' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +22 'points' '' 'points' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +21 ())) 0 () () 0 0) +23 'epsabs' '' 'epsabs' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +24 'epsrel' '' 'epsrel' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +25 'limit' '' 'limit' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +26 'result' '' 'result' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +27 'abserr' '' 'abserr' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +28 'neval' '' 'neval' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +29 'ier' '' 'ier' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +30 'alist' '' 'alist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +31 'blist' '' 'blist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +32 'rlist' '' 'rlist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +) + +('dqagp' 0 3 'dqagpe' 0 2) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/build_all.py b/wafo/source/mvnprd/old/mvnprodcorrprb/build_all.py new file mode 100755 index 0000000..8b96b40 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/build_all.py @@ -0,0 +1,24 @@ +""" +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/erfcoremod.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/erfcoremod.mod new file mode 100755 index 0000000..62b1a08 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/erfcoremod.mod @@ -0,0 +1,51 @@ +GFORTRAN module created from mvnprodcorrprb.f on Thu Dec 04 11:05:50 2008 +MD5:3ad89711ff6ea0f8c745365231e1a1ea -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('derf' 'erfcoremod' 2) ('calerf' 'erfcoremod' 3) ('derfcx' 'erfcoremod' +4) ('derfc' 'erfcoremod' 5)) + +() + +() + +(3 'calerf' 'erfcoremod' 'calerf' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +6 0 (7 8 9) () 0 () () 0 0) +2 'derf' 'erfcoremod' 'derf' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 10 0 (11) () 12 () () +0 0) +5 'derfc' 'erfcoremod' 'derfc' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 13 0 (14) () 15 () () +0 0) +4 'derfcx' 'erfcoremod' 'derfcx' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 16 0 ( +17) () 18 () () 0 0) +19 'erfcoremod' 'erfcoremod' 'erfcoremod' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() 0 0) +11 'x' '' 'x' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +12 'value' '' 'value' 10 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +14 'x' '' 'x' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +15 'value' '' 'value' 13 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +17 'x' '' 'x' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +18 'value' '' 'value' 16 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +7 'arg' '' 'arg' 6 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +8 'result' '' 'result' 6 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +9 'jint' '' 'jint' 6 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +) + +('calerf' 0 3 'derf' 0 2 'derfc' 0 5 'derfcx' 0 4 'erfcoremod' 0 19) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/functioninterface.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/functioninterface.mod new file mode 100755 index 0000000..f5c7ab8 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/functioninterface.mod @@ -0,0 +1,27 @@ +GFORTRAN module created from mvnprodcorrprb.f on Wed Dec 03 15:55:57 2008 +MD5:2bffd45d12c9c1718b19499dd55e4953 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'f' 'functioninterface' 'f' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +BODY UNKNOWN EXTERNAL FUNCTION) (REAL 8 0 0 REAL ()) 3 0 (4) () 5 () () +0 0) +6 'functioninterface' 'functioninterface' 'functioninterface' 1 (( +MODULE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 +UNKNOWN ()) 0 0 () () 0 () () 0 0) +4 'z' '' 'z' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) (REAL 8 +0 0 REAL ()) 0 0 () () 0 () () 0 0) +5 'val' '' 'val' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +) + +('f' 0 2 'functioninterface' 0 6) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/integration1dmodule.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/integration1dmodule.mod new file mode 100755 index 0000000..698f6a9 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/integration1dmodule.mod @@ -0,0 +1,241 @@ +GFORTRAN module created from mvnprodcorrprb.f on Thu Dec 04 12:55:42 2008 +MD5:2001ac092337caac013ba2fcb5e647f3 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () +() () () () () () () () () () () () () () ()) + +() + +(('adaptivesimpson' 'integration1dmodule' 2 3) ('d1mach' +'integration1dmodule' 4) ('adaptivetrapz' 'integration1dmodule' 5 6) ( +'romberg' 'integration1dmodule' 7 8) ('dea' 'integration1dmodule' 9)) + +() + +() + +(10 'adaptiveintwithbreaks' 'integration1dmodule' 'adaptiveintwithbreaks' +1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE +ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 11 0 (12 13 14 15 16 17 18 +19 20) () 0 () () 0 0) +21 'adaptivesimpson1' 'integration1dmodule' 'adaptivesimpson1' 1 (( +PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 +0 0 UNKNOWN ()) 22 0 (23 24 25 26 27 28 29) () 0 () () 0 0) +3 'adaptivesimpson2' 'integration1dmodule' 'adaptivesimpson2' 1 (( +PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 +0 0 UNKNOWN ()) 30 0 (31 32 33 34 35 36 37) () 0 () () 0 0) +38 'adaptivesimpson3' 'integration1dmodule' 'adaptivesimpson3' 1 (( +PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 +0 0 UNKNOWN ()) 39 0 (40 41 42 43 44 45 46) () 0 () () 0 0) +2 'adaptivesimpsonwithbreaks' 'integration1dmodule' +'adaptivesimpsonwithbreaks' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 47 0 +(48 49 50 51 52 53 54 55 56) () 0 () () 0 0) +6 'adaptivetrapz1' 'integration1dmodule' 'adaptivetrapz1' 1 ((PROCEDURE +UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 +UNKNOWN ()) 57 0 (58 59 60 61 62 63 64) () 0 () () 0 0) +5 'adaptivetrapzwithbreaks' 'integration1dmodule' +'adaptivetrapzwithbreaks' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 65 0 (66 +67 68 69 70 71 72 73 74) () 0 () () 0 0) +4 'd1mach' 'integration1dmodule' 'd1mach' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 75 0 ( +76) () 4 () () 0 0) +9 'dea' 'integration1dmodule' 'dea' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +77 0 (78 79 80 81 82 83 84) () 0 () () 0 0) +85 'dea3' 'integration1dmodule' 'dea3' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 UNKNOWN ()) 86 0 ( +87 88 89 90 91) () 0 () () 0 0) +92 'integration1dmodule' 'integration1dmodule' 'integration1dmodule' 1 ( +(MODULE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 +UNKNOWN ()) 0 0 () () 0 () () 0 0) +8 'romberg1' 'integration1dmodule' 'romberg1' 1 ((PROCEDURE +UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 +UNKNOWN ()) 93 0 (94 95 96 97 98 99 100 101) () 0 () () 0 0) +7 'rombergwithbreaks' 'integration1dmodule' 'rombergwithbreaks' 1 (( +PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE +ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 102 0 (103 104 105 106 107 +108 109 110 111) () 0 () () 0 0) +78 'newflg' '' 'newflg' 77 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () () 0 () () 0 0) +79 'svalue' '' 'svalue' 77 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +80 'limexp' '' 'limexp' 77 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +81 'result' '' 'result' 77 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +82 'abserr' '' 'abserr' 77 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +87 'e0' '' 'e0' 86 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +88 'e1' '' 'e1' 86 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +83 'epstab' '' 'epstab' 77 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SIZE (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +84 'ierr' '' 'ierr' 77 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +89 'e2' '' 'e2' 86 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +90 'abserr' '' 'abserr' 86 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +91 'result' '' 'result' 86 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +17 'epsi' '' 'epsi' 11 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +18 'iflg' '' 'iflg' 11 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +19 'abserr' '' 'abserr' 11 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +20 'val' '' 'val' 11 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +48 'f' '' 'f' 47 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +49 'a' '' 'a' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +50 'b' '' 'b' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +51 'n' '' 'n' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +31 'f' '' 'f' 30 ((PROCEDURE UNKNOWN-INTENT DUMMY-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY FUNCTION) (REAL 8 0 0 REAL ()) 0 0 () () 31 () () 0 0) +32 'a' '' 'a' 30 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +33 'b' '' 'b' 30 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +34 'epsi' '' 'epsi' 30 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +13 'a' '' 'a' 11 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +14 'b' '' 'b' 11 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +15 'n' '' 'n' 11 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +16 'brks' '' 'brks' 11 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +58 'f' '' 'f' 57 ((PROCEDURE UNKNOWN-INTENT DUMMY-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY FUNCTION) (REAL 8 0 0 REAL ()) 0 0 () () 58 () () 0 0) +59 'a' '' 'a' 57 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +60 'b' '' 'b' 57 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +35 'iflg' '' 'iflg' 30 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +36 'abserr' '' 'abserr' 30 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +37 'val' '' 'val' 30 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +40 'f' '' 'f' 39 ((PROCEDURE UNKNOWN-INTENT DUMMY-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY FUNCTION) (REAL 8 0 0 REAL ()) 0 0 () () 40 () () 0 0) +52 'brks' '' 'brks' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +53 'epsi' '' 'epsi' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +54 'iflg' '' 'iflg' 47 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +55 'abserr' '' 'abserr' 47 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +56 'val' '' 'val' 47 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +23 'f' '' 'f' 22 ((PROCEDURE UNKNOWN-INTENT DUMMY-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY FUNCTION) (REAL 8 0 0 REAL ()) 0 0 () () 23 () () 0 0) +41 'a' '' 'a' 39 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +42 'b' '' 'b' 39 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +43 'epsi' '' 'epsi' 39 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +44 'iflg' '' 'iflg' 39 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +24 'a' '' 'a' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +25 'b' '' 'b' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +26 'epsi' '' 'epsi' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +27 'iflg' '' 'iflg' 22 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +28 'abserr' '' 'abserr' 22 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +29 'val' '' 'val' 22 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +66 'f' '' 'f' 65 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +76 'i' '' 'i' 75 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +12 'f' '' 'f' 11 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +45 'abserr' '' 'abserr' 39 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +46 'val' '' 'val' 39 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +72 'iflg' '' 'iflg' 65 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +73 'abserr' '' 'abserr' 65 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +74 'val' '' 'val' 65 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +71 'epsi' '' 'epsi' 65 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +67 'a' '' 'a' 65 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +68 'b' '' 'b' 65 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +69 'n' '' 'n' 65 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +70 'brks' '' 'brks' 65 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +61 'epsi' '' 'epsi' 57 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +62 'iflg' '' 'iflg' 57 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +63 'abserr' '' 'abserr' 57 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +64 'val' '' 'val' 57 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +103 'f' '' 'f' 102 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +104 'a' '' 'a' 102 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +105 'b' '' 'b' 102 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +106 'n' '' 'n' 102 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +107 'brks' '' 'brks' 102 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +108 'epsi' '' 'epsi' 102 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +109 'iflg' '' 'iflg' 102 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +110 'abserr' '' 'abserr' 102 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +111 'val' '' 'val' 102 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +94 'f' '' 'f' 93 ((PROCEDURE UNKNOWN-INTENT DUMMY-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY FUNCTION) (REAL 8 0 0 REAL ()) 0 0 () () 94 () () 0 0) +95 'a' '' 'a' 93 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +96 'b' '' 'b' 93 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +97 'decdigs' '' 'decdigs' 93 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +98 'abseps' '' 'abseps' 93 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +99 'errflg' '' 'errflg' 93 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +100 'abserr' '' 'abserr' 93 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +101 'val' '' 'val' 93 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +) + +('adaptiveintwithbreaks' 0 10 'adaptivesimpson1' 0 21 'adaptivesimpson2' +0 3 'adaptivesimpson3' 0 38 'adaptivesimpsonwithbreaks' 0 2 +'adaptivetrapz1' 0 6 'adaptivetrapzwithbreaks' 0 5 'd1mach' 0 4 'dea' 0 +9 'dea3' 0 85 'integration1dmodule' 0 92 'romberg1' 0 8 +'rombergwithbreaks' 0 7) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprdmod.pyd b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprdmod.pyd new file mode 100755 index 0000000..3b8605b Binary files /dev/null and b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprdmod.pyd differ diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb.f b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb.f new file mode 100755 index 0000000..8850562 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb.f @@ -0,0 +1,4335 @@ +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 new file mode 100755 index 0000000..190f081 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprb_interface.f @@ -0,0 +1,33 @@ + +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/mvnprodcorrprbmod.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprbmod.mod new file mode 100755 index 0000000..6f23eb4 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/mvnprodcorrprbmod.mod @@ -0,0 +1,44 @@ +GFORTRAN module created from mvnprodcorrprb.f on Thu Dec 04 12:55:42 2008 +MD5:52cce08f767867c5bd7250c82948c098 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () +() () () () () () () () () () () () () () () () ()) + +() + +(('mvnprodcorrprb' 'mvnprodcorrprbmod' 2)) + +() + +() + +(2 'mvnprodcorrprb' 'mvnprodcorrprbmod' 'mvnprodcorrprb' 1 ((PROCEDURE +UNKNOWN-INTENT MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC +ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 3 0 (4 5 6 7 8 9 10 11 12 13) +() 0 () () 0 0) +4 'rho' '' 'rho' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +9 'usebreakpoints' '' 'usebreakpoints' 3 ((VARIABLE IN UNKNOWN-PROC +UNKNOWN UNKNOWN DUMMY) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () () 0 () () 0 0) +10 'usesimpson' '' 'usesimpson' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () () 0 () () 0 0) +11 'abserr' '' 'abserr' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +12 'errflg' '' 'errflg' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +13 'prb' '' 'prb' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +5 'a' '' 'a' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +6 'b' '' 'b' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () 0 0) +7 'abseps' '' 'abseps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +8 'releps' '' 'releps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +) + +('mvnprodcorrprb' 0 2) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/AdaptiveGaussKronrod.f90 b/wafo/source/mvnprd/old/mvnprodcorrprb/old/AdaptiveGaussKronrod.f90 new file mode 100755 index 0000000..4c65537 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/AdaptiveGaussKronrod.f90 @@ -0,0 +1,1802 @@ +! 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.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.mod new file mode 100755 index 0000000..00fa45b --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.mod @@ -0,0 +1,112 @@ +GFORTRAN module created from mvnprodcorrprb.f on Tue Dec 02 13:32:39 2008 +MD5:5f0b454993ede1db4c4b6b9e47df36c4 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('dqagpe' 'adaptivegausskronrod' 2) ('dqagp' 'adaptivegausskronrod' 3)) + +() + +() + +(3 'dqagp' 'adaptivegausskronrod' 'dqagp' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +4 0 (5 6 7 8 9 10 11 12 13 14 15 16) () 0 () () 0 0) +2 'dqagpe' 'adaptivegausskronrod' 'dqagpe' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +17 0 (18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38) () +0 () () 0 0) +10 'epsabs' '' 'epsabs' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +11 'epsrel' '' 'epsrel' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +12 'limit' '' 'limit' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +13 'result1' '' 'result1' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +14 'abserr' '' 'abserr' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +15 'neval' '' 'neval' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +16 'ier' '' 'ier' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +9 'points' '' 'points' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +8 ())) 0 () () 0 0) +5 'f' '' 'f' 4 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +6 'a' '' 'a' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) (REAL 8 +0 0 REAL ()) 0 0 () () 0 () () 0 0) +7 'b' '' 'b' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) (REAL 8 +0 0 REAL ()) 0 0 () () 0 () () 0 0) +8 'npts' '' 'npts' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +18 'f' '' 'f' 17 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +EXTERNAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +19 'a' '' 'a' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +20 'b' '' 'b' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +21 'npts' '' 'npts' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +22 'points' '' 'points' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +21 ())) 0 () () 0 0) +23 'epsabs' '' 'epsabs' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +24 'epsrel' '' 'epsrel' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +25 'limit' '' 'limit' 17 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +26 'result' '' 'result' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +27 'abserr' '' 'abserr' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +28 'neval' '' 'neval' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +29 'ier' '' 'ier' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +30 'alist' '' 'alist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +31 'blist' '' 'blist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +32 'rlist' '' 'rlist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +33 'elist' '' 'elist' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 +25 ())) 0 () () 0 0) +34 'pts' '' 'pts' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') (OP (INTEGER 4 0 0 INTEGER ()) 0 PLUS ( +VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 21 ()) (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '2'))) 0 () () 0 0) +35 'iord' '' 'iord' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 +INTEGER ()) 0 25 ())) 0 () () 0 0) +36 'level' '' 'level' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (VARIABLE (INTEGER 4 0 0 +INTEGER ()) 0 25 ())) 0 () () 0 0) +37 'ndin' '' 'ndin' 17 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (OP (INTEGER 4 0 0 INTEGER ()) +0 PLUS (VARIABLE (INTEGER 4 0 0 INTEGER ()) 0 21 ()) (CONSTANT (INTEGER +4 0 0 INTEGER ()) 0 '2'))) 0 () () 0 0) +38 'last' '' 'last' 17 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +) + +('dqagp' 0 3 'dqagpe' 0 2) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyf b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyf new file mode 100755 index 0000000..03410ec --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyf @@ -0,0 +1,157 @@ +! -*- 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/adaptivegausskronrod.pyfo b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyfo new file mode 100755 index 0000000..31ea5ed --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/adaptivegausskronrod.pyfo @@ -0,0 +1,149 @@ +! -*- 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:AdaptiveGuassKronrod.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:AdaptiveGuassKronrod.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:AdaptiveGuassKronrod.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:AdaptiveGuassKronrod.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 adaptivegausskronrod ! in :adaptivegausskronrod:AdaptiveGuassKronrod.f90 + subroutine dea3(e0,e1,e2,abserr,result) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.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) :: result + end subroutine dea3 + subroutine dqagp(f,a,b,npts,points,epsabs,epsrel,limit,result1,abserr,neval,ier) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.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,result,abserr,neval,ier,alist,blist,rlist,elist,pts,iord,level,ndin,last) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.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) :: result + 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,result,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.f90:adaptivegausskronrod + use dqk21__user__routines + external f + double precision :: a + double precision :: b + double precision :: result + double precision :: abserr + double precision :: resabs + double precision :: resasc + end subroutine dqk21 + subroutine dqk15(f,a,b,result,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.f90:adaptivegausskronrod + use dqk15__user__routines + external f + double precision :: a + double precision :: b + double precision :: result + double precision :: abserr + double precision :: resabs + double precision :: resasc + end subroutine dqk15 + subroutine dqk9(f,a,b,result,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.f90:adaptivegausskronrod + use dqk9__user__routines + external f + double precision :: a + double precision :: b + double precision :: result + double precision :: abserr + double precision :: resabs + double precision :: resasc + end subroutine dqk9 + subroutine dqkl9(f,a,b,result,abserr,resabs,resasc) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.f90:adaptivegausskronrod + use dqkl9__user__routines + external f + double precision :: a + double precision :: b + double precision :: result + double precision :: abserr + double precision :: resabs + double precision :: resasc + end subroutine dqkl9 + subroutine dqpsrt(limit,last,maxerr,ermax,elist,iord,nrmax) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.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,result,abserr,res3la,nres) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.f90:adaptivegausskronrod + integer :: n + double precision dimension(52) :: epstab + double precision :: result + double precision :: abserr + double precision dimension(3) :: res3la + integer :: nres + end subroutine dqelg + function d1mach(i) ! in :adaptivegausskronrod:AdaptiveGuassKronrod.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 new file mode 100755 index 0000000..be04810 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/dea.f @@ -0,0 +1,390 @@ +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 new file mode 100755 index 0000000..83b9ecd --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/deamod.pyf @@ -0,0 +1,6 @@ +! -*- 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 new file mode 100755 index 0000000..138a8db --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcore.f90 @@ -0,0 +1,344 @@ +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/erfcore.pyd b/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcore.pyd new file mode 100755 index 0000000..4d78a99 Binary files /dev/null and b/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcore.pyd differ diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcoremod.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcoremod.mod new file mode 100755 index 0000000..a1d91e7 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/erfcoremod.mod @@ -0,0 +1,51 @@ +GFORTRAN module created from mvnprodcorrprb.f on Fri Nov 28 22:53:18 2008 +MD5:3ad89711ff6ea0f8c745365231e1a1ea -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('derf' 'erfcoremod' 2) ('calerf' 'erfcoremod' 3) ('derfcx' 'erfcoremod' +4) ('derfc' 'erfcoremod' 5)) + +() + +() + +(3 'calerf' 'erfcoremod' 'calerf' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +6 0 (7 8 9) () 0 () () 0 0) +2 'derf' 'erfcoremod' 'derf' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 10 0 (11) () 12 () () +0 0) +5 'derfc' 'erfcoremod' 'derfc' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 13 0 (14) () 15 () () +0 0) +4 'derfcx' 'erfcoremod' 'derfcx' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 16 0 ( +17) () 18 () () 0 0) +19 'erfcoremod' 'erfcoremod' 'erfcoremod' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() 0 0) +11 'x' '' 'x' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +12 'value' '' 'value' 10 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +14 'x' '' 'x' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +15 'value' '' 'value' 13 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +17 'x' '' 'x' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +18 'value' '' 'value' 16 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +7 'arg' '' 'arg' 6 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +8 'result' '' 'result' 6 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +9 'jint' '' 'jint' 6 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +) + +('calerf' 0 3 'derf' 0 2 'derfc' 0 5 'derfcx' 0 4 'erfcoremod' 0 19) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/functioninterface.mod b/wafo/source/mvnprd/old/mvnprodcorrprb/old/functioninterface.mod new file mode 100755 index 0000000..bd8697e --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/functioninterface.mod @@ -0,0 +1,27 @@ +GFORTRAN module created from mvnprodcorrprb.f on Fri Nov 28 22:53:18 2008 +MD5:2bffd45d12c9c1718b19499dd55e4953 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'f' 'functioninterface' 'f' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +BODY UNKNOWN EXTERNAL FUNCTION) (REAL 8 0 0 REAL ()) 3 0 (4) () 5 () () +0 0) +6 'functioninterface' 'functioninterface' 'functioninterface' 1 (( +MODULE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 +UNKNOWN ()) 0 0 () () 0 () () 0 0) +4 'z' '' 'z' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) (REAL 8 +0 0 REAL ()) 0 0 () () 0 () () 0 0) +5 'val' '' 'val' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () 0 0) +) + +('f' 0 2 'functioninterface' 0 6) diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/integration1Dmodule.f b/wafo/source/mvnprd/old/mvnprodcorrprb/old/integration1Dmodule.f new file mode 100755 index 0000000..c98497e --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/integration1Dmodule.f @@ -0,0 +1,1460 @@ +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 new file mode 100755 index 0000000..fa380b9 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprb.pyf @@ -0,0 +1,24 @@ +! -*- 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 new file mode 100755 index 0000000..7c6a8b2 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/mvnprodcorrprbmod.f90 @@ -0,0 +1,666 @@ + 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 new file mode 100755 index 0000000..9c291cc --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsp @@ -0,0 +1,97 @@ +# 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 new file mode 100755 index 0000000..95d7427 --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.dsw @@ -0,0 +1,29 @@ +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 new file mode 100755 index 0000000..018dc3a --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.f @@ -0,0 +1,39 @@ + 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/old/mvnprodcorrprb/old/test_mvnprodcorrprb.opt b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.opt new file mode 100755 index 0000000..015d2b2 Binary files /dev/null and b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.opt differ diff --git a/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.plg b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.plg new file mode 100755 index 0000000..8ea30dd --- /dev/null +++ b/wafo/source/mvnprd/old/mvnprodcorrprb/old/test_mvnprodcorrprb.plg @@ -0,0 +1,26 @@ + + +
+
Build Log

+

+--------------------Configuration: test_mvnprodcorrprb - Win32 Debug--------------------
+

+
Command Lines

+Creating temporary file "C:\DOCUME~1\pab.NTU\LOCALS~1\Temp\RSP265.tmp" with contents
+[
+/check:bounds /compile_only /debug:full /nologo /traceback /warn:argument_checking /warn:nofileopt /module:"Debug/" /object:"Debug/" /pdbfile:"Debug/DF60.PDB" 
+"C:\pab\workspace\PYWAFO\src\wafo\src\mvnprodcorrprb\test_mvnprodcorrprb.f"
+]
+Creating command line "link.exe kernel32.lib /nologo /subsystem:console /incremental:yes /pdb:"Debug/test_mvnprodcorrprb.pdb" /debug /machine:I386 /out:"Debug/test_mvnprodcorrprb.exe" /pdbtype:sept  .\Debug\mvnprodcorrprb.obj .\Debug\test_mvnprodcorrprb.obj "
+
Output Window

+Compiling Fortran...
+C:\pab\workspace\PYWAFO\src\wafo\src\mvnprodcorrprb\test_mvnprodcorrprb.f
+Linking...
+
+
+
+
Results

+test_mvnprodcorrprb.exe - 0 error(s), 0 warning(s)
+
+ + diff --git a/wafo/source/rind2007/.cproject b/wafo/source/rind2007/.cproject new file mode 100755 index 0000000..5bb1192 --- /dev/null +++ b/wafo/source/rind2007/.cproject @@ -0,0 +1,608 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +make + + +true +true +true + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +make + + +true +true +true + + + + + + + + + diff --git a/wafo/source/rind2007/.project b/wafo/source/rind2007/.project new file mode 100755 index 0000000..269ed5c --- /dev/null +++ b/wafo/source/rind2007/.project @@ -0,0 +1,81 @@ + + + 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/New File.txt b/wafo/source/rind2007/New File.txt new file mode 100755 index 0000000..ae0b9b7 --- /dev/null +++ b/wafo/source/rind2007/New File.txt @@ -0,0 +1,21 @@ + subroutine set_constants(method,xcscale,abseps,releps,coveps, + & maxpts,minpts,nit,xcutoff,Nc1c2) + use rindmod + double precision :: xcscale,abseps,releps,coveps,xcutoff + integer method, maxpts, minpts, nit, Nc1c2 +Cf2py double precision, optional :: xcscale = 0.0D0 +Cf2py double precision, optional :: abseps = 0.01D0 +Cf2py double precision, optional :: releps = 0.01D0 +Cf2py double precision, optional :: coveps = 1.0D-10 +Cf2py double precision, optional :: xcutoff = 5.0D0 + +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 + + call setconstants(method,xcscale,abseps,releps,coveps, + & maxpts,minpts,nit,xcutoff,Nc1c2) + return + end subroutine set_constants \ No newline at end of file diff --git a/wafo/source/rind2007/adaptmod.mod b/wafo/source/rind2007/adaptmod.mod new file mode 100755 index 0000000..26608ec --- /dev/null +++ b/wafo/source/rind2007/adaptmod.mod @@ -0,0 +1,69 @@ +GFORTRAN module version '0' created from intmodule.f on Wed Aug 05 06:33:27 2009 +MD5:4d2aeab527515248abfbe40787b2391c -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('adapt' 'adaptmod' 2) ('sadapt' 'adaptmod' 3)) + +() + +() + +(2 'adapt' 'adaptmod' 'adapt' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 4 0 (5 6 7 8 +9 10 11 12 13) () 0 () () () 0 0) +3 'sadapt' 'adaptmod' 'sadapt' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 14 0 (15 16 +17 18 19 20 21 22) () 0 () () () 0 0) +18 'abseps' '' 'abseps' 14 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +19 'releps' '' 'releps' 14 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +20 'error' '' 'error' 14 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +21 'value' '' 'value' 14 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +22 'inform' '' 'inform' 14 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +15 'n' '' 'n' 14 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +16 'maxpts' '' 'maxpts' 14 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +17 'functn' '' 'functn' 14 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC BODY +UNKNOWN DUMMY FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 23 0 (24 25) +() 17 () () () 0 0) +8 'functn' '' 'functn' 4 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC BODY +UNKNOWN DUMMY FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 26 0 (27 28) +() 8 () () () 0 0) +9 'absreq' '' 'absreq' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +10 'relreq' '' 'relreq' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'absest' '' 'absest' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +12 'finest' '' 'finest' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +5 'ndim' '' 'ndim' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'mincls' '' 'mincls' 4 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'maxcls' '' 'maxcls' 4 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +13 'inform' '' 'inform' 4 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +27 'n' '' 'n' 26 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +28 'z' '' 'z' 26 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +24 'n' '' 'n' 23 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +25 'z' '' 'z' 23 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +) + +('adapt' 0 2 'sadapt' 0 3) diff --git a/wafo/source/rind2007/build_all.py b/wafo/source/rind2007/build_all.py new file mode 100755 index 0000000..0cf452f --- /dev/null +++ b/wafo/source/rind2007/build_all.py @@ -0,0 +1,38 @@ +""" +f2py c_library.pyf c_functions.c -c + +g95 -W -Wall -pedantic-errors -fbounds-check -Werror -o test_fimod.exe fimod.f test_fimod.f +gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -o test_fimod.exe fimod.f test_fimod.f + +gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -o test_rindmod.exe intmodule.f jacobmod.f swapmod.f fimod.f rindmod2007.f test_rindmod.f +df %1 /check:all /fpe:0 /traceback /warn:argument checking /automatic /exe test_rindmod.exe intmodule.f jacobmod.f swapmod.f erfcoremod.f fimod.f rindmod.f test_rindmod.f +df /fast /fixed /transform_loops /exe test_rindmod.exe intmodule.f jacobmod.f swapmod.f erfcoremod.f fimod.f rindmod.f test_rindmod.f +""" +import os + +def compile_all(): + 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 -m rindmod -c %s rind_interface.f --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71' % file_objects) + #compile1_txt = 'gfortran -fPIC -c mvnprd.f' + #compile2_txt = 'f2py -m mvnprdmod -c mvnprd.o mvnprd_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/rind2007/c1c2mod.mod b/wafo/source/rind2007/c1c2mod.mod new file mode 100755 index 0000000..de6a79f --- /dev/null +++ b/wafo/source/rind2007/c1c2mod.mod @@ -0,0 +1,38 @@ +GFORTRAN module version '0' created from rind71mod.f on Wed Aug 05 06:26:34 2009 +MD5:b430fe7101e61f66883eafc0a9944272 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () +() () () () () () () () () () () () ()) + +() + +(('c1c2' 'c1c2mod' 2)) + +() + +() + +(2 'c1c2' 'c1c2mod' 'c1c2' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) 3 +0 (4 5 6 7 8 9) () 0 () () () 0 0) +10 'c1c2mod' 'c1c2mod' 'c1c2mod' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () () 0 0) +8 'sq' '' 'sq' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +9 'ind' '' 'ind' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +6 'cm' '' 'cm' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +4 'c1' '' 'c1' 3 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +5 'c2' '' 'c2' 3 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +7 'b1' '' 'b1' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +) + +('c1c2' 0 2 'c1c2mod' 0 10) diff --git a/wafo/source/rind2007/dkbvrcmod.mod b/wafo/source/rind2007/dkbvrcmod.mod new file mode 100755 index 0000000..6a36713 --- /dev/null +++ b/wafo/source/rind2007/dkbvrcmod.mod @@ -0,0 +1,44 @@ +GFORTRAN module version '0' created from intmodule.f on Wed Aug 05 05:35:49 2009 +MD5:a4e84422cfb5c96ca4a433837610753a -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('dkbvrc' 'dkbvrcmod' 2)) + +() + +() + +(2 'dkbvrc' 'dkbvrcmod' 'dkbvrc' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +3 0 (4 5 6 7 8 9 10 11 12) () 0 () () () 0 0) +4 'ndim' '' 'ndim' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +5 'minvls' '' 'minvls' 3 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'maxvls' '' 'maxvls' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'functn' '' 'functn' 3 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC BODY +UNKNOWN DUMMY FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 13 0 (14 15) +() 7 () () () 0 0) +8 'abseps' '' 'abseps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'releps' '' 'releps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +10 'abserr' '' 'abserr' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'finest' '' 'finest' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +12 'inform' '' 'inform' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'n' '' 'n' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +15 'z' '' 'z' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +) + +('dkbvrc' 0 2) diff --git a/wafo/source/rind2007/erfcoremod.f b/wafo/source/rind2007/erfcoremod.f new file mode 100755 index 0000000..47ca438 --- /dev/null +++ b/wafo/source/rind2007/erfcoremod.f @@ -0,0 +1,339 @@ + 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 new file mode 100755 index 0000000..ab7bd7d --- /dev/null +++ b/wafo/source/rind2007/fimod.f @@ -0,0 +1,1595 @@ + 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/fimod.mod b/wafo/source/rind2007/fimod.mod new file mode 100755 index 0000000..25ba753 --- /dev/null +++ b/wafo/source/rind2007/fimod.mod @@ -0,0 +1,216 @@ +GFORTRAN module version '0' created from fimod.f on Wed Aug 05 05:35:52 2009 +MD5:9b97aca95087f079d77ade04cc70d4e2 -- If you edit this, you'll get what you deserve. + +(() +() () () () () () () () () () () () () () () () () () () () () () () () +() ()) + +() + +(('bvu' 'fimod' 2) ('bvtl' 'fimod' 3) ('bvnmvn' 'fimod' 4) ('exlms' +'fimod' 5) ('fiinv' 'fimod' 6) ('fi' 'fimod' 7) ('gausint2' 'fimod' 8) ( +'mvnlms' 'fimod' 9) ('normprb' 'fimod' 10) ('mvnlimits' 'fimod' 11) ( +'gausint' 'fimod' 12) ('studnt' 'fimod' 13) ('tvtl' 'fimod' 14) ('exinv' +'fimod' 15)) + +() + +() + +(4 'bvnmvn' 'fimod' 'bvnmvn' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 16 0 +(17 18 19 20) () 21 () () () 0 0) +3 'bvtl' 'fimod' 'bvtl' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 22 0 (23 24 25 26) () 3 () +() () 0 0) +2 'bvu' 'fimod' 'bvu' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 27 0 (28 29 30) () 31 () +() () 0 0) +15 'exinv' 'fimod' 'exinv' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 32 0 (33 34 35 36) () 37 +() () () 0 0) +5 'exlms' 'fimod' 'exlms' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 38 0 (39 40 41 42 +43 44 45 46) () 0 () () () 0 0) +7 'fi' 'fimod' 'fi' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 47 0 (48) () 49 () () () +0 0) +6 'fiinv' 'fimod' 'fiinv' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 50 0 (51) () 52 () () () +0 0) +12 'gausint' 'fimod' 'gausint' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 53 0 (54 55 56 57 58 +59) () 60 () () () 0 0) +8 'gausint2' 'fimod' 'gausint2' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 61 0 (62 63 64 65) () +66 () () () 0 0) +11 'mvnlimits' 'fimod' 'mvnlimits' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 +0 0 UNKNOWN ()) 67 0 (68 69 70 71 72 73) () 0 () () () 0 0) +9 'mvnlms' 'fimod' 'mvnlms' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 74 0 (75 76 +77 78 79) () 0 () () () 0 0) +10 'normprb' 'fimod' 'normprb' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 80 0 (81 82 83) () 0 () () () 0 0) +13 'studnt' 'fimod' 'studnt' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC) (REAL 8 0 0 REAL ()) 84 0 (85 86) () 13 () +() () 0 0) +87 'tvnmvn' 'fimod' 'tvnmvn' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 88 0 (89 90 +91 92 93) () 94 () () () 0 0) +14 'tvtl' 'fimod' 'tvtl' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN FUNCTION GENERIC ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 95 0 (96 +97 98 99) () 14 () () () 0 0) +51 'p' '' 'p' 50 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +52 'val' '' 'val' 50 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +81 'z' '' 'z' 80 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +82 'p' '' 'p' 80 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +83 'q' '' 'q' 80 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN OPTIONAL +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +48 'z' '' 'z' 47 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +49 'value' '' 'value' 47 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +68 'a' '' 'a' 67 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +69 'b' '' 'b' 67 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +70 'infin' '' 'infin' 67 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +71 'ap' '' 'ap' 67 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +72 'prb' '' 'prb' 67 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +OPTIONAL DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +73 'aq' '' 'aq' 67 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN OPTIONAL +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +75 'a' '' 'a' 74 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +76 'b' '' 'b' 74 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +77 'infin' '' 'infin' 74 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +78 'lower' '' 'lower' 74 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +79 'upper' '' 'upper' 74 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +89 'a' '' 'a' 88 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +90 'b' '' 'b' 88 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +91 'infin' '' 'infin' 88 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 ASSUMED_SHAPE ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +92 'r' '' 'r' 88 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +93 'epsi' '' 'epsi' 88 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +94 'val' '' 'val' 88 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () +0 0) +17 'lower' '' 'lower' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +18 'upper' '' 'upper' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +19 'infin' '' 'infin' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 ASSUMED_SHAPE ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +20 'correl' '' 'correl' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +21 'val' '' 'val' 16 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () +0 0) +28 'sh' '' 'sh' 27 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +29 'sk' '' 'sk' 27 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +30 'r' '' 'r' 27 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +31 'val' '' 'val' 27 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +85 'nu' '' 'nu' 84 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +86 't' '' 't' 84 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +23 'nu' '' 'nu' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +24 'dh' '' 'dh' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +25 'dk' '' 'dk' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +26 'r' '' 'r' 22 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +96 'nu1' '' 'nu1' 95 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +97 'h' '' 'h' 95 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +98 'r' '' 'r' 95 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +99 'epsi' '' 'epsi' 95 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +54 'x1' '' 'x1' 53 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +55 'x2' '' 'x2' 53 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +56 'a' '' 'a' 53 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +57 'b' '' 'b' 53 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +58 'c' '' 'c' 53 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +59 'd' '' 'd' 53 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +60 'value' '' 'value' 53 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +62 'x1' '' 'x1' 61 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +63 'x2' '' 'x2' 61 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +64 'a' '' 'a' 61 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +65 'b' '' 'b' 61 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +66 'value' '' 'value' 61 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +39 'a' '' 'a' 38 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +40 'x1' '' 'x1' 38 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +41 'x2' '' 'x2' 38 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +42 'infin' '' 'infin' 38 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +43 'lower' '' 'lower' 38 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +44 'upper' '' 'upper' 38 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +45 'ca' '' 'ca' 38 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +46 'pa' '' 'pa' 38 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +33 'p' '' 'p' 32 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +34 'a' '' 'a' 32 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +35 'ca' '' 'ca' 32 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +36 'pa' '' 'pa' 32 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +37 'val' '' 'val' 32 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +) + +('bvnmvn' 0 4 'bvtl' 0 3 'bvu' 0 2 'exinv' 0 15 'exlms' 0 5 'fi' 0 7 +'fiinv' 0 6 'gausint' 0 12 'gausint2' 0 8 'mvnlimits' 0 11 'mvnlms' 0 9 +'normprb' 0 10 'studnt' 0 13 'tvnmvn' 0 87 'tvtl' 0 14) diff --git a/wafo/source/rind2007/funcmod.mod b/wafo/source/rind2007/funcmod.mod new file mode 100755 index 0000000..049abd3 --- /dev/null +++ b/wafo/source/rind2007/funcmod.mod @@ -0,0 +1,61 @@ +GFORTRAN module version '0' created from rind71mod.f on Wed Aug 05 05:36:49 2009 +MD5:d64139159f9b7d1a62e18500b19b3b23 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () +() () () ()) + +() + +(('mvnfun' 'funcmod' 2) ('mvnfun2' 'funcmod' 3)) + +() + +() + +(4 'big' 'funcmod' 'big' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (2 +DEFERRED () () () ()) 0 () () () 0 0) +5 'cm' 'funcmod' 'cm' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 DEFERRED () +()) 0 () () () 0 0) +6 'cmn' 'funcmod' 'cmn' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 DEFERRED () +()) 0 () () () 0 0) +7 'funcmod' 'funcmod' 'funcmod' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () () 0 0) +2 'mvnfun' 'funcmod' 'mvnfun' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 8 0 +(9 10) () 11 () () () 0 0) +3 'mvnfun2' 'funcmod' 'mvnfun2' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 12 0 +(13 14) () 15 () () () 0 0) +16 'pl1' 'funcmod' 'pl1' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +17 'pu1' 'funcmod' 'pu1' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +18 'xc' 'funcmod' 'xc' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 DEFERRED () +()) 0 () () () 0 0) +19 'xd' 'funcmod' 'xd' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 DEFERRED () +()) 0 () () () 0 0) +9 'ndim' '' 'ndim' 8 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +10 'w' '' 'w' 8 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +11 'xind' '' 'xind' 8 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () +0 0) +13 'ndim' '' 'ndim' 12 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'w' '' 'w' 12 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +15 'xind' '' 'xind' 12 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () +0 0) +) + +('big' 0 4 'cm' 0 5 'cmn' 0 6 'funcmod' 0 7 'mvnfun' 0 2 'mvnfun2' 0 3 +'pl1' 0 16 'pu1' 0 17 'xc' 0 18 'xd' 0 19) diff --git a/wafo/source/rind2007/globalconst.mod b/wafo/source/rind2007/globalconst.mod new file mode 100755 index 0000000..9d65c77 --- /dev/null +++ b/wafo/source/rind2007/globalconst.mod @@ -0,0 +1,64 @@ +GFORTRAN module version '0' created from rindmod.f on Wed Aug 05 05:35:53 2009 +MD5:28b9cfd26740ee7f785bb23117fdf8ea -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'ghalf' 'globalconst' 'ghalf' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.80000000000000@0') () 0 () () () 0 0) +3 'ginfinity' 'globalconst' 'ginfinity' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.25000000000000@2') () 0 () () () 0 0) +4 'globalconst' 'globalconst' 'globalconst' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() () 0 0) +5 'gone' 'globalconst' 'gone' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.10000000000000@1') () 0 () () () 0 0) +6 'gpi' 'globalconst' 'gpi' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.3243f6a8885a22@1') () 0 () () () 0 0) +7 'gpi1' 'globalconst' 'gpi1' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.517cc1b72721dc@0') () 0 () () () 0 0) +8 'gsqpi' 'globalconst' 'gsqpi' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.1c5bf891b4ef7d@1') () 0 () () () 0 0) +9 'gsqpi1' 'globalconst' 'gsqpi1' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.906eba8214dc78@0') () 0 () () () 0 0) +10 'gsqtw' 'globalconst' 'gsqtw' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.16a09e667f3be3@1') () 0 () () () 0 0) +11 'gsqtw1' 'globalconst' 'gsqtw1' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.b504f333f9df18@0') () 0 () () () 0 0) +12 'gsqtwpi' 'globalconst' 'gsqtwpi' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.281b263fec4e08@1') () 0 () () () 0 0) +13 'gsqtwpi1' 'globalconst' 'gsqtwpi1' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.662114cf50d880@0') () 0 () () () 0 0) +14 'gtwo' 'globalconst' 'gtwo' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.20000000000000@1') () 0 () () () 0 0) +15 'gtwpi' 'globalconst' 'gtwpi' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.6487ed5110b444@1') () 0 () () () 0 0) +16 'gzero' 'globalconst' 'gzero' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.00000000000000@0') () 0 () () () 0 0) +) + +('ghalf' 0 2 'ginfinity' 0 3 'globalconst' 0 4 'gone' 0 5 'gpi' 0 6 'gpi1' +0 7 'gsqpi' 0 8 'gsqpi1' 0 9 'gsqtw' 0 10 'gsqtw1' 0 11 'gsqtwpi' 0 12 +'gsqtwpi1' 0 13 'gtwo' 0 14 'gtwpi' 0 15 'gzero' 0 16) diff --git a/wafo/source/rind2007/globaldata.mod b/wafo/source/rind2007/globaldata.mod new file mode 100755 index 0000000..ad4c094 --- /dev/null +++ b/wafo/source/rind2007/globaldata.mod @@ -0,0 +1,160 @@ +GFORTRAN module version '0' created from rind71mod.f on Wed Aug 05 05:36:49 2009 +MD5:56b23d8cfb1ad898b2f43426b067c050 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 '__convert_r4_r8' '(intrinsic)' '__convert_r4_r8' 1 ((PROCEDURE +UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN FUNCTION ELEMENTAL PURE) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +3 'c1c2det' 'globaldata' 'c1c2det' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () ( +CONSTANT (LOGICAL 4 0 0 LOGICAL ()) 0 1) () 0 () () () 0 0) +4 'cepss' 'globaldata' 'cepss' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +5 'cov' 'globaldata' 'cov' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 +DEFERRED () ()) 0 () () () 0 0) +6 'covix' 'globaldata' 'covix' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'eps' 'globaldata' 'eps' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +8 'eps0' 'globaldata' 'eps0' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'eps2' 'globaldata' 'eps2' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +10 'epss' 'globaldata' 'epss' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'fxcepss' 'globaldata' 'fxcepss' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +12 'globaldata' 'globaldata' 'globaldata' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() () 0 0) +13 'hlo' 'globaldata' 'hlo' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 +DEFERRED () ()) 0 () () () 0 0) +14 'hup' 'globaldata' 'hup' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (1 +DEFERRED () ()) 0 () () () 0 0) +15 'index1' 'globaldata' 'index1' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (INTEGER 4 0 0 +INTEGER ()) 0 0 () (1 DEFERRED () ()) 0 () () () 0 0) +16 'indxtd' 'globaldata' 'indxtd' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (INTEGER 4 0 0 +INTEGER ()) 0 0 () (1 DEFERRED () ()) 0 () () () 0 0) +17 'mb' 'globaldata' 'mb' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +18 'nc' 'globaldata' 'nc' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +19 'nd' 'globaldata' 'nd' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +20 'ni' 'globaldata' 'ni' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +21 'nit' 'globaldata' 'nit' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +22 'nj' 'globaldata' 'nj' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +23 'njj' 'globaldata' 'njj' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +24 'nsimmax' 'globaldata' 'nsimmax' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () +0 () () () 0 0) +25 'nsimmin' 'globaldata' 'nsimmin' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () +0 () () () 0 0) +26 'nsxdj' 'globaldata' 'nsxdj' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () +(1 DEFERRED () ()) 0 () () () 0 0) +27 'nsxtmj' 'globaldata' 'nsxtmj' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (INTEGER 4 0 0 +INTEGER ()) 0 0 () (1 DEFERRED () ()) 0 () () () 0 0) +28 'nt' 'globaldata' 'nt' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +29 'ntd' 'globaldata' 'ntd' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +30 'ntdc' 'globaldata' 'ntdc' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +31 'ntscis' 'globaldata' 'ntscis' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () +0 () () () 0 0) +32 'nugget' 'globaldata' 'nugget' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +33 'nx' 'globaldata' 'nx' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +34 'pi' 'globaldata' 'pi' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.3243f6a8885a22@1') () 0 () () () 0 0) +35 'pi1' 'globaldata' 'pi1' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.517cc1b72721dc@0') () 0 () () () 0 0) +36 'plowgth' 'globaldata' 'plowgth' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.00000000000000@0') () 0 () () () 0 0) +37 'releps' 'globaldata' 'releps' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +38 'scis' 'globaldata' 'scis' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +39 'sq' 'globaldata' 'sq' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (REAL 8 0 0 REAL ()) 0 0 () (2 +DEFERRED () () () ()) 0 () () () 0 0) +40 'sqpi' 'globaldata' 'sqpi' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () (CONSTANT (REAL 8 0 0 +REAL ()) 0 '0.1c5bf891b4ef7d@1') () 0 () () () 0 0) +41 'sqpi1' 'globaldata' 'sqpi1' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.906eba8214dc78@0') () 0 () () () 0 0) +42 'sqtwo' 'globaldata' 'sqtwo' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.16a09e667f3be3@1') () 0 () () () 0 0) +43 'sqtwo1' 'globaldata' 'sqtwo1' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.b504f333f9df18@0') () 0 () () () 0 0) +44 'sqtwopi1' 'globaldata' 'sqtwopi1' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.662114cf50d880@0') () 0 () () () 0 0) +45 'twopi' 'globaldata' 'twopi' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () ( +CONSTANT (REAL 8 0 0 REAL ()) 0 '0.6487ed5110b444@1') () 0 () () () 0 0) +46 'usec1c2' 'globaldata' 'usec1c2' 1 ((PARAMETER UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (LOGICAL 4 0 0 LOGICAL ()) 0 0 () ( +CONSTANT (LOGICAL 4 0 0 LOGICAL ()) 0 1) () 0 () () () 0 0) +47 'xceps2' 'globaldata' 'xceps2' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +48 'xcscale' 'globaldata' 'xcscale' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +49 'xcutoff' 'globaldata' 'xcutoff' 1 ((VARIABLE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () +() () 0 0) +50 'xedni' 'globaldata' 'xedni' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN ALLOCATABLE DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () +(1 DEFERRED () ()) 0 () () () 0 0) +51 'xsplt' 'globaldata' 'xsplt' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +) + +('__convert_r4_r8' 0 2 'c1c2det' 0 3 'cepss' 0 4 'cov' 0 5 'covix' 0 6 +'eps' 0 7 'eps0' 0 8 'eps2' 0 9 'epss' 0 10 'fxcepss' 0 11 'globaldata' +0 12 'hlo' 0 13 'hup' 0 14 'index1' 0 15 'indxtd' 0 16 'mb' 0 17 'nc' 0 +18 'nd' 0 19 'ni' 0 20 'nit' 0 21 'nj' 0 22 'njj' 0 23 'nsimmax' 0 24 +'nsimmin' 0 25 'nsxdj' 0 26 'nsxtmj' 0 27 'nt' 0 28 'ntd' 0 29 'ntdc' 0 +30 'ntscis' 0 31 'nugget' 0 32 'nx' 0 33 'pi' 0 34 'pi1' 0 35 'plowgth' +0 36 'releps' 0 37 'scis' 0 38 'sq' 0 39 'sqpi' 0 40 'sqpi1' 0 41 'sqtwo' +0 42 'sqtwo1' 0 43 'sqtwopi1' 0 44 'twopi' 0 45 'usec1c2' 0 46 'xceps2' +0 47 'xcscale' 0 48 'xcutoff' 0 49 'xedni' 0 50 'xsplt' 0 51) diff --git a/wafo/source/rind2007/intmodule.f b/wafo/source/rind2007/intmodule.f new file mode 100755 index 0000000..b7e9e95 --- /dev/null +++ b/wafo/source/rind2007/intmodule.f @@ -0,0 +1,3856 @@ +! 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 new file mode 100755 index 0000000..7f4a193 --- /dev/null +++ b/wafo/source/rind2007/jacobmod.f @@ -0,0 +1,20 @@ + 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/jacobmod.mod b/wafo/source/rind2007/jacobmod.mod new file mode 100755 index 0000000..7281426 --- /dev/null +++ b/wafo/source/rind2007/jacobmod.mod @@ -0,0 +1,29 @@ +GFORTRAN module version '0' created from jacobmod.f on Wed Aug 05 05:35:52 2009 +MD5:4af662f7f9b6aea3cbe229e90aed063f -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('jacob' 'jacobmod' 2)) + +() + +() + +(2 'jacob' 'jacobmod' 'jacob' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN FUNCTION GENERIC ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 3 0 +(4 5) () 6 () () () 0 0) +4 'xd' '' 'xd' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +5 'xc' '' 'xc' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +6 'value1' '' 'value1' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN RESULT ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () +0 0) +) + +('jacob' 0 2) diff --git a/wafo/source/rind2007/krbvrcmod.mod b/wafo/source/rind2007/krbvrcmod.mod new file mode 100755 index 0000000..cc48e06 --- /dev/null +++ b/wafo/source/rind2007/krbvrcmod.mod @@ -0,0 +1,44 @@ +GFORTRAN module version '0' created from intmodule.f on Wed Aug 05 05:36:07 2009 +MD5:c734feac7a719b8cda518e46a6228370 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('krbvrc' 'krbvrcmod' 2)) + +() + +() + +(2 'krbvrc' 'krbvrcmod' 'krbvrc' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +3 0 (4 5 6 7 8 9 10 11 12) () 0 () () () 0 0) +4 'ndim' '' 'ndim' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +5 'minvls' '' 'minvls' 3 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'maxvls' '' 'maxvls' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'functn' '' 'functn' 3 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC BODY +UNKNOWN DUMMY FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 13 0 (14 15) +() 7 () () () 0 0) +8 'abseps' '' 'abseps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'releps' '' 'releps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +10 'abserr' '' 'abserr' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'finest' '' 'finest' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +12 'inform' '' 'inform' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'n' '' 'n' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +15 'z' '' 'z' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +) + +('krbvrc' 0 2) diff --git a/wafo/source/rind2007/krobovmod.mod b/wafo/source/rind2007/krobovmod.mod new file mode 100755 index 0000000..2a8be7c --- /dev/null +++ b/wafo/source/rind2007/krobovmod.mod @@ -0,0 +1,44 @@ +GFORTRAN module version '0' created from intmodule.f on Wed Aug 05 06:33:27 2009 +MD5:c2bbe88c382c1e5c407f55a156f093e2 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('krobov' 'krobovmod' 2)) + +() + +() + +(2 'krobov' 'krobovmod' 'krobov' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +3 0 (4 5 6 7 8 9 10 11 12) () 0 () () () 0 0) +4 'ndim' '' 'ndim' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +12 'inform' '' 'inform' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +10 'abserr' '' 'abserr' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'finest' '' 'finest' 3 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +7 'functn' '' 'functn' 3 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC BODY +UNKNOWN DUMMY FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 13 0 (14 15) +() 7 () () () 0 0) +8 'abseps' '' 'abseps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'releps' '' 'releps' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +6 'maxvls' '' 'maxvls' 3 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +5 'minvls' '' 'minvls' 3 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +15 'z' '' 'z' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +14 'n' '' 'n' 13 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +) + +('krobov' 0 2) diff --git a/wafo/source/rind2007/precisionmod.mod b/wafo/source/rind2007/precisionmod.mod new file mode 100755 index 0000000..f3e176a --- /dev/null +++ b/wafo/source/rind2007/precisionmod.mod @@ -0,0 +1,26 @@ +GFORTRAN module version '0' created from intmodule.f on Wed Aug 05 05:35:50 2009 +MD5:9a96cbd1faeb6554557f9d9308c50e28 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'gp' 'precisionmod' 'gp' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '8') () 0 () () () 0 0) +3 'precisionmod' 'precisionmod' 'precisionmod' 1 ((MODULE UNKNOWN-INTENT +UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () +() () 0 0) +4 'selected_real_kind' '(intrinsic)' 'selected_real_kind' 1 ((PROCEDURE +UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN FUNCTION) (UNKNOWN 0 0 0 +UNKNOWN ()) 0 0 () () 4 () () () 0 0) +) + +('gp' 0 2 'precisionmod' 0 3 'selected_real_kind' 0 4) diff --git a/wafo/source/rind2007/quad.mod b/wafo/source/rind2007/quad.mod new file mode 100755 index 0000000..c0469ec --- /dev/null +++ b/wafo/source/rind2007/quad.mod @@ -0,0 +1,271 @@ +GFORTRAN module version '0' created from rind71mod.f on Wed Aug 05 05:42:33 2009 +MD5:5fe7f8d121252e680c2bd7d7c177fa9d -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () +() () () () () ()) + +() + +(('gausshe0' 'quad' 2) ('gaussle0' 'quad' 3) ('gaussle1' 'quad' 4) ( +'gaussq' 'quad' 5) ('gaussle2' 'quad' 6) ('gaussla0' 'quad' 7)) + +() + +() + +(8 '__convert_r4_r8' '(intrinsic)' '__convert_r4_r8' 1 ((PROCEDURE +UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN FUNCTION ELEMENTAL PURE) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +2 'gausshe0' 'quad' 'gausshe0' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 9 0 (10 11 12 13 14 15) () 0 () () () 0 0) +7 'gaussla0' 'quad' 'gaussla0' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 16 0 (17 18 19 20 21 22) () 0 () () () 0 0) +3 'gaussle0' 'quad' 'gaussle0' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 23 0 (24 25 26 27 28 29) () 0 () () () 0 0) +4 'gaussle1' 'quad' 'gaussle1' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 30 0 (31 32 33 34 35) () 0 () () () 0 0) +6 'gaussle2' 'quad' 'gaussle2' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 36 0 (37 38 39 40 41 42) () 0 () () () 0 0) +5 'gaussq' 'quad' 'gaussq' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN ()) +43 0 (44 45 46 47 48 49) () 0 () () () 0 0) +50 'hebp' 'quad' 'hebp' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +51 'heind' 'quad' 'heind' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (ARRAY ( +INTEGER 4 0 0 INTEGER ()) 1 (((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '0') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '2') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '5') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '9') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '14') ()) ((CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '20') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '27') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '35') ()) (( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '44') ()) ((CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '54') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '66') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '82') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '102') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '126') ())) ('14')) (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '14')) 0 () () () 0 0) +52 'heqnr' 'quad' 'heqnr' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (ARRAY ( +INTEGER 4 0 0 INTEGER ()) 1 (((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '2') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '3') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '4') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '5') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '6') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '7') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '8') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '9') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '10') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '12') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '16') ()) (( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '20') ()) ((CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '24') ())) ('13')) (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '13')) 0 () () +() 0 0) +53 'hewf' 'quad' 'hewf' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +54 'i' 'quad' 'i' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +55 'labp0' 'quad' 'labp0' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT +(CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +56 'labp5' 'quad' 'labp5' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT +(CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +57 'laind' 'quad' 'laind' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (ARRAY ( +INTEGER 4 0 0 INTEGER ()) 1 (((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '0') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '2') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '5') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '9') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '14') ()) ((CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '20') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '27') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '35') ()) (( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '44') ()) ((CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '54') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '66') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '82') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '102') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '126') ())) ('14')) (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '14')) 0 () () () 0 0) +58 'laqnr' 'quad' 'laqnr' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (ARRAY ( +INTEGER 4 0 0 INTEGER ()) 1 (((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '2') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '3') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '4') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '5') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '6') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '7') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '8') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '9') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '10') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '12') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '16') ()) (( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '20') ()) ((CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '24') ())) ('13')) (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '13')) 0 () () +() 0 0) +59 'lawf0' 'quad' 'lawf0' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT +(CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +60 'lawf5' 'quad' 'lawf5' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT +(CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +61 'le2qnr' 'quad' 'le2qnr' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +62 'lebp' 'quad' 'lebp' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +63 'leind' 'quad' 'leind' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (ARRAY ( +INTEGER 4 0 0 INTEGER ()) 1 (((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '0') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '2') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '5') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '9') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '14') ()) ((CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '20') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '27') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '35') ()) (( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '44') ()) ((CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '54') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '66') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '82') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '102') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '126') ())) ('14')) (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '14')) 0 () () () 0 0) +64 'leqnr' 'quad' 'leqnr' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (ARRAY ( +INTEGER 4 0 0 INTEGER ()) 1 (((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '2') +()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '3') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '4') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '5') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '6') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '7') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '8') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '9') ()) ((CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '10') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER +()) 0 '12') ()) ((CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '16') ()) (( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '20') ()) ((CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '24') ())) ('13')) (1 EXPLICIT (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '13')) 0 () () +() 0 0) +65 'lewf' 'quad' 'lewf' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DIMENSION DATA) (REAL 8 0 0 REAL ()) 0 0 () (1 EXPLICIT ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '126')) 0 () () () 0 0) +66 'minqnr' 'quad' 'minqnr' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 +0) +67 'nhew' 'quad' 'nhew' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '13') () 0 () () () 0 0) +68 'nint1' 'quad' 'nint1' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DIMENSION) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 EXPLICIT +(CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '13')) 0 () () () 0 0) +69 'nlaw' 'quad' 'nlaw' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '13') () 0 () () () 0 0) +70 'nlew' 'quad' 'nlew' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '13') () 0 () () () 0 0) +71 'pmax' 'quad' 'pmax' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '24') () 0 () () () 0 0) +72 'quad' 'quad' 'quad' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () () 0 0) +73 'siznint' 'quad' 'siznint' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '13') () 0 () () () 0 0) +31 'n' '' 'n' 30 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +32 'wfout' '' 'wfout' 30 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +33 'bpout' '' 'bpout' 30 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +34 'xmi' '' 'xmi' 30 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +35 'xma' '' 'xma' 30 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +24 'n' '' 'n' 23 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +25 'wfout' '' 'wfout' 23 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +26 'bpout' '' 'bpout' 23 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +27 'xmi' '' 'xmi' 23 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +28 'xma' '' 'xma' 23 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +29 'n0' '' 'n0' 23 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +37 'n' '' 'n' 36 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +38 'wfout' '' 'wfout' 36 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +39 'bpout' '' 'bpout' 36 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +40 'xmi' '' 'xmi' 36 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +41 'xma' '' 'xma' 36 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +42 'n0' '' 'n0' 36 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +10 'n' '' 'n' 9 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +11 'wfout' '' 'wfout' 9 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +12 'bpout' '' 'bpout' 9 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +13 'xmi' '' 'xmi' 9 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +14 'xma' '' 'xma' 9 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +15 'n0' '' 'n0' 9 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +17 'n' '' 'n' 16 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +18 'wfout' '' 'wfout' 16 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +19 'bpout' '' 'bpout' 16 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +20 'xmi' '' 'xmi' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +21 'xma' '' 'xma' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +22 'n0' '' 'n0' 16 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +44 'n' '' 'n' 43 ((VARIABLE INOUT UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +45 'wf' '' 'wf' 43 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +46 'bp' '' 'bp' 43 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +47 'xmi' '' 'xmi' 43 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +48 'xma' '' 'xma' 43 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +49 'n0' '' 'n0' 43 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +) + +('__convert_r4_r8' 0 8 'gausshe0' 0 2 'gaussla0' 0 7 'gaussle0' 0 3 +'gaussle1' 0 4 'gaussle2' 0 6 'gaussq' 0 5 'hebp' 0 50 'heind' 0 51 +'heqnr' 0 52 'hewf' 0 53 'i' 0 54 'labp0' 0 55 'labp5' 0 56 'laind' 0 57 +'laqnr' 0 58 'lawf0' 0 59 'lawf5' 0 60 'le2qnr' 0 61 'lebp' 0 62 'leind' +0 63 'leqnr' 0 64 'lewf' 0 65 'minqnr' 0 66 'nhew' 0 67 'nint1' 0 68 +'nlaw' 0 69 'nlew' 0 70 'pmax' 0 71 'quad' 0 72 'siznint' 0 73) diff --git a/wafo/source/rind2007/rcrudemod.mod b/wafo/source/rind2007/rcrudemod.mod new file mode 100755 index 0000000..24beb95 --- /dev/null +++ b/wafo/source/rind2007/rcrudemod.mod @@ -0,0 +1,42 @@ +GFORTRAN module version '0' created from intmodule.f on Wed Aug 05 05:36:07 2009 +MD5:240f214ef2031c1b04fc7d9aaa35265b -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +(('ranmc' 'rcrudemod' 2)) + +() + +() + +(2 'ranmc' 'rcrudemod' 'ranmc' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) 3 0 (4 5 6 7 +8 9 10 11) () 0 () () () 0 0) +4 'n' '' 'n' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +5 'maxpts' '' 'maxpts' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +6 'functn' '' 'functn' 3 ((PROCEDURE UNKNOWN-INTENT UNKNOWN-PROC BODY +UNKNOWN DUMMY FUNCTION ALWAYS_EXPLICIT) (REAL 8 0 0 REAL ()) 12 0 (13 14) +() 6 () () () 0 0) +7 'abseps' '' 'abseps' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +8 'releps' '' 'releps' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'error' '' 'error' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +10 'value' '' 'value' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'inform' '' 'inform' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +13 'n' '' 'n' 12 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +14 'z' '' 'z' 12 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +) + +('ranmc' 0 2) diff --git a/wafo/source/rind2007/rind71mod.f b/wafo/source/rind2007/rind71mod.f new file mode 100755 index 0000000..8f9b9bd --- /dev/null +++ b/wafo/source/rind2007/rind71mod.f @@ -0,0 +1,4157 @@ +!**************************************************************************** +! 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/rind71mod.mod b/wafo/source/rind2007/rind71mod.mod new file mode 100755 index 0000000..267e4f4 --- /dev/null +++ b/wafo/source/rind2007/rind71mod.mod @@ -0,0 +1,81 @@ +GFORTRAN module version '0' created from rind71mod.f on Wed Aug 05 06:26:36 2009 +MD5:4c69b3be4f1e6c8e1aedc15a8c988682 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () +() () () ()) + +() + +(('echo' 'rind71mod' 2) ('initdata' 'rind71mod' 3) ('rind71' 'rind71mod' +4) ('setdata' 'rind71mod' 5)) + +() + +() + +(2 'echo' 'rind71mod' 'echo' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 6 0 (7) () 0 () () () 0 0) +3 'initdata' 'rind71mod' 'initdata' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +8 0 (9) () 0 () () () 0 0) +4 'rind71' 'rind71mod' 'rind71' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC +DECL UNKNOWN SUBROUTINE GENERIC ALWAYS_EXPLICIT) (UNKNOWN 0 0 0 UNKNOWN +()) 10 0 (11 12 13 14 15 16 17 18) () 0 () () () 0 0) +5 'setdata' 'rind71mod' 'setdata' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN SUBROUTINE GENERIC) (UNKNOWN 0 0 0 UNKNOWN ()) +19 0 (20 21 22 23 24 25 26 27 28) () 0 () () () 0 0) +24 'deps2' '' 'deps2' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +25 'dnit' '' 'dnit' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +26 'dxc' '' 'dxc' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +27 'dnint' '' 'dnint' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +28 'dxsplt' '' 'dxsplt' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +20 'method' '' 'method' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +21 'scale' '' 'scale' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +22 'depss' '' 'depss' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +23 'dreps' '' 'dreps' 19 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'speed' '' 'speed' 8 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) +(INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'array' '' 'array' 6 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 ASSUMED_SHAPE ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') () (CONSTANT (INTEGER 4 0 0 +INTEGER ()) 0 '1') ()) 0 () () () 0 0) +11 'fxind' '' 'fxind' 10 ((VARIABLE OUT UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +18 'bup' '' 'bup' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') () (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') ()) 0 () () () 0 0) +12 'big1' '' 'big1' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') () (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') ()) 0 () () () 0 0) +13 'ex' '' 'ex' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DIMENSION +DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (1 ASSUMED_SHAPE (CONSTANT (INTEGER 4 +0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +14 'xc1' '' 'xc1' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') () (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') ()) 0 () () () 0 0) +15 'nt1' '' 'nt1' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN DUMMY) ( +INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +16 'indi' '' 'indi' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () (1 ASSUMED_SHAPE ( +CONSTANT (INTEGER 4 0 0 INTEGER ()) 0 '1') ()) 0 () () () 0 0) +17 'blo' '' 'blo' 10 ((VARIABLE IN UNKNOWN-PROC UNKNOWN UNKNOWN +DIMENSION DUMMY) (REAL 8 0 0 REAL ()) 0 0 () (2 ASSUMED_SHAPE (CONSTANT +(INTEGER 4 0 0 INTEGER ()) 0 '1') () (CONSTANT (INTEGER 4 0 0 INTEGER ()) +0 '1') ()) 0 () () () 0 0) +) + +('echo' 0 2 'initdata' 0 3 'rind71' 0 4 'setdata' 0 5) diff --git a/wafo/source/rind2007/rind_interface.f b/wafo/source/rind2007/rind_interface.f new file mode 100755 index 0000000..a8960c9 --- /dev/null +++ b/wafo/source/rind2007/rind_interface.f @@ -0,0 +1,222 @@ +! 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,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 new file mode 100755 index 0000000..5b4f064 --- /dev/null +++ b/wafo/source/rind2007/rindmod.f @@ -0,0 +1,2435 @@ +! 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. To build this project using NMAKE, +!MESSAGE use the Export Makefile command and run +!MESSAGE +!MESSAGE NMAKE /f "test_fimod.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_fimod.mak" CFG="test_fimod - Win32 Debug" +!MESSAGE +!MESSAGE Possible choices for configuration are: +!MESSAGE +!MESSAGE "test_fimod - Win32 Release" (based on "Win32 (x86) Console Application") +!MESSAGE "test_fimod - 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 "$(CFG)" == "test_fimod - Win32 Release" + +# PROP BASE Use_MFC 0 +# PROP BASE Use_Debug_Libraries 0 +# PROP BASE Output_Dir "Release" +# PROP BASE Intermediate_Dir "Release" +# PROP BASE Target_Dir "" +# PROP Use_MFC 0 +# PROP Use_Debug_Libraries 0 +# PROP Output_Dir "Release" +# PROP Intermediate_Dir "Release" +# PROP Target_Dir "" +# ADD BASE F90 /compile_only /nologo /warn:nofileopt +# ADD F90 /compile_only /nologo /warn:nofileopt +# ADD BASE CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c +# ADD CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c +# ADD BASE RSC /l 0x414 /d "NDEBUG" +# ADD RSC /l 0x414 /d "NDEBUG" +BSC32=bscmake.exe +# ADD BASE BSC32 /nologo +# ADD BSC32 /nologo +LINK32=link.exe +# ADD BASE LINK32 kernel32.lib /nologo /subsystem:console /machine:I386 +# ADD LINK32 kernel32.lib /nologo /subsystem:console /machine:I386 + +!ELSEIF "$(CFG)" == "test_fimod - 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_fimod - Win32 Release" +# Name "test_fimod - Win32 Debug" +# Begin Source File + +SOURCE=.\fimod.f +# End Source File +# Begin Source File + +SOURCE=.\test_fimod.f +DEP_F90_TEST_=\ + ".\FIMOD.mod"\ + +NODEP_F90_TEST_=\ + ".\ERFCOREMOD.mod"\ + +# End Source File +# End Target +# End Project diff --git a/wafo/source/rind2007/test_fimod.dsw b/wafo/source/rind2007/test_fimod.dsw new file mode 100755 index 0000000..349f8b4 --- /dev/null +++ b/wafo/source/rind2007/test_fimod.dsw @@ -0,0 +1,29 @@ +Microsoft Developer Studio Workspace File, Format Version 6.00 +# WARNING: DO NOT EDIT OR DELETE THIS WORKSPACE FILE! + +############################################################################### + +Project: "test_fimod"=.\test_fimod.dsp - Package Owner=<4> + +Package=<5> +{{{ +}}} + +Package=<4> +{{{ +}}} + +############################################################################### + +Global: + +Package=<5> +{{{ +}}} + +Package=<3> +{{{ +}}} + +############################################################################### + diff --git a/wafo/source/rind2007/test_fimod.exe b/wafo/source/rind2007/test_fimod.exe new file mode 100755 index 0000000..65adab4 Binary files /dev/null and b/wafo/source/rind2007/test_fimod.exe differ diff --git a/wafo/source/rind2007/test_fimod.f b/wafo/source/rind2007/test_fimod.f new file mode 100755 index 0000000..36c6276 --- /dev/null +++ b/wafo/source/rind2007/test_fimod.f @@ -0,0 +1,48 @@ + PROGRAM TST_FIMOD +! 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.exe b/wafo/source/rind2007/test_rind71mod.exe new file mode 100755 index 0000000..6bac866 Binary files /dev/null and b/wafo/source/rind2007/test_rind71mod.exe differ diff --git a/wafo/source/rind2007/test_rind71mod.f b/wafo/source/rind2007/test_rind71mod.f new file mode 100755 index 0000000..90ab2cc --- /dev/null +++ b/wafo/source/rind2007/test_rind71mod.f @@ -0,0 +1,85 @@ + 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.exe b/wafo/source/rind2007/test_rindmod.exe new file mode 100755 index 0000000..4df9702 Binary files /dev/null and b/wafo/source/rind2007/test_rindmod.exe differ diff --git a/wafo/source/rind2007/test_rindmod.f b/wafo/source/rind2007/test_rindmod.f new file mode 100755 index 0000000..5afa41f --- /dev/null +++ b/wafo/source/rind2007/test_rindmod.f @@ -0,0 +1,69 @@ + 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/rind2007/test_rindmod2007.exe b/wafo/source/rind2007/test_rindmod2007.exe new file mode 100755 index 0000000..8fb3712 Binary files /dev/null and b/wafo/source/rind2007/test_rindmod2007.exe differ diff --git a/wafo/source/rind2007/test_rindmod2007.opt b/wafo/source/rind2007/test_rindmod2007.opt new file mode 100755 index 0000000..e3e59f7 Binary files /dev/null and b/wafo/source/rind2007/test_rindmod2007.opt differ diff --git a/wafo/source/rind2007/test_rindmod2007.plg b/wafo/source/rind2007/test_rindmod2007.plg new file mode 100755 index 0000000..d4e54ce --- /dev/null +++ b/wafo/source/rind2007/test_rindmod2007.plg @@ -0,0 +1,39 @@ + + +
+
Build Log

+

+--------------------Configuration: test_rindmod2007 - Win32 Debug--------------------
+

+
Command Lines

+Creating temporary file "C:\DOCUME~1\pab2\LOCALS~1\Temp\RSP391.tmp" with contents
+[
+/check:bounds /compile_only /debug:full /nologo /traceback /warn:argument_checking /warn:nofileopt /module:"Debug/" /object:"Debug/" /pdbfile:"Debug/DF60.PDB" 
+"C:\pab\workspace\PYWAFO\src\wafo\src\rind2007\split\fimod.f"
+"C:\pab\workspace\PYWAFO\src\wafo\src\rind2007\split\test_rindmod2007.f"
+]
+Creating temporary file "C:\DOCUME~1\pab2\LOCALS~1\Temp\RSP392.tmp" with contents
+[
+kernel32.lib /nologo /subsystem:console /incremental:yes /pdb:"Debug/test_rindmod2007.pdb" /debug /machine:I386 /out:"Debug/test_rindmod2007.exe" /pdbtype:sept 
+.\Debug\erfcoremod.obj
+.\Debug\fimod.obj
+.\Debug\intmodule.obj
+.\Debug\jacobmod.obj
+.\Debug\rindmod2007.obj
+.\Debug\swapmod.obj
+.\Debug\test_rindmod2007.obj
+]
+Creating command line "link.exe @C:\DOCUME~1\pab2\LOCALS~1\Temp\RSP392.tmp"
+
Output Window

+Compiling Fortran...
+C:\pab\workspace\PYWAFO\src\wafo\src\rind2007\split\fimod.f
+C:\pab\workspace\PYWAFO\src\wafo\src\rind2007\split\test_rindmod2007.f
+Linking...
+
+
+
+
Results

+test_rindmod2007.exe - 0 error(s), 0 warning(s)
+
+ + diff --git a/wafo/source/rind2007/trivariatevar.mod b/wafo/source/rind2007/trivariatevar.mod new file mode 100755 index 0000000..be1559e --- /dev/null +++ b/wafo/source/rind2007/trivariatevar.mod @@ -0,0 +1,39 @@ +GFORTRAN module version '0' created from fimod.f on Wed Aug 05 05:35:52 2009 +MD5:b833d1aae3d99e187e27ad8342187b63 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'ar' 'trivariatevar' 'ar' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +3 'h1' 'trivariatevar' 'h1' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +4 'h2' 'trivariatevar' 'h2' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +5 'h3' 'trivariatevar' 'h3' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +6 'nu' 'trivariatevar' 'nu' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () () 0 0) +7 'r23' 'trivariatevar' 'r23' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +8 'rua' 'trivariatevar' 'rua' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +9 'rub' 'trivariatevar' 'rub' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +10 'ruc' 'trivariatevar' 'ruc' 1 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (REAL 8 0 0 REAL ()) 0 0 () () 0 () () () 0 0) +11 'trivariatevar' 'trivariatevar' 'trivariatevar' 1 ((MODULE +UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) +0 0 () () 0 () () () 0 0) +) + +('ar' 0 2 'h1' 0 3 'h2' 0 4 'h3' 0 5 'nu' 0 6 'r23' 0 7 'rua' 0 8 'rub' +0 9 'ruc' 0 10 'trivariatevar' 0 11) diff --git a/wafo/source/test_f90/hello.f90 b/wafo/source/test_f90/hello.f90 new file mode 100755 index 0000000..59c4831 --- /dev/null +++ b/wafo/source/test_f90/hello.f90 @@ -0,0 +1,9 @@ +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.mod b/wafo/source/test_f90/hello.mod new file mode 100755 index 0000000..df2c0fe --- /dev/null +++ b/wafo/source/test_f90/hello.mod @@ -0,0 +1,41 @@ +GFORTRAN module created from hello.f90 on Wed Jul 15 21:22:12 2009 +MD5:e42897d3921cc8627fe4ea5bfb648729 -- If you edit this, you'll get what you deserve. + + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'foo' 'hello' 'foo' 1 ((PROCEDURE UNKNOWN-INTENT MODULE-PROC DECL +UNKNOWN SUBROUTINE) (UNKNOWN 0 0 0 UNKNOWN ()) 3 0 (4) () 0 () () 0 0) +5 'hello' 'hello' 'hello' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () 0 0) +6 'intdim' 'types' 'intdim' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '4') () 0 () () 0 0) +7 'selected_int_kind' '(intrinsic)' 'selected_int_kind' 1 ((PROCEDURE +UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN FUNCTION) (REAL 4 0 0 REAL ()) +0 0 () () 7 () () 0 0) +8 'to_intdim' 'types' 'to_intdim' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN FUNCTION) (INTEGER 4 0 0 INTEGER ()) 9 0 (10) () +8 () () 0 0) +11 'types' 'types' 'types' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () 0 0) +12 'wp' 'types' 'wp' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '4') () 0 () () 0 0) +4 'a' '' 'a' 3 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN +DUMMY) (INTEGER 4 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +10 'int_value' '' 'int_value' 9 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DUMMY) (INTEGER 8 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +) + +('foo' 0 2 'hello' 0 5 'intdim' 0 6 'selected_int_kind' 0 7 'to_intdim' +0 8 'types' 0 11 'wp' 0 12) diff --git a/wafo/source/test_f90/hello.pyd b/wafo/source/test_f90/hello.pyd new file mode 100755 index 0000000..0cd5db6 Binary files /dev/null and b/wafo/source/test_f90/hello.pyd differ diff --git a/wafo/source/test_f90/hello.txt b/wafo/source/test_f90/hello.txt new file mode 100755 index 0000000..769fc13 --- /dev/null +++ b/wafo/source/test_f90/hello.txt @@ -0,0 +1,188 @@ +[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 new file mode 100755 index 0000000..618a4e0 --- /dev/null +++ b/wafo/source/test_f90/hello_interface.f90 @@ -0,0 +1,9 @@ +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 new file mode 100755 index 0000000..94220e8 --- /dev/null +++ b/wafo/source/test_f90/mymod.f90 @@ -0,0 +1,47 @@ +! 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/mymod.pyd b/wafo/source/test_f90/mymod.pyd new file mode 100755 index 0000000..99d5811 Binary files /dev/null and b/wafo/source/test_f90/mymod.pyd differ diff --git a/wafo/source/test_f90/types.f90 b/wafo/source/test_f90/types.f90 new file mode 100755 index 0000000..55e2d08 --- /dev/null +++ b/wafo/source/test_f90/types.f90 @@ -0,0 +1,11 @@ + + +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/source/test_f90/types.mod b/wafo/source/test_f90/types.mod new file mode 100755 index 0000000..54d66ad --- /dev/null +++ b/wafo/source/test_f90/types.mod @@ -0,0 +1,34 @@ +GFORTRAN module created from types.f90 on Wed Jul 15 21:21:44 2009 +MD5:e10521533cef217cbd18f79ca3dd5909 -- If you edit this, you'll get what you deserve. + +(() () () () () () () () () () () () () () () () () () () () () () () () +() () ()) + +() + +() + +() + +() + +(2 'intdim' 'types' 'intdim' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT ( +INTEGER 4 0 0 INTEGER ()) 0 '4') () 0 () () 0 0) +3 'selected_int_kind' '(intrinsic)' 'selected_int_kind' 1 ((PROCEDURE +UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN UNKNOWN FUNCTION) (REAL 4 0 0 REAL ()) +0 0 () () 3 () () 0 0) +4 'to_intdim' 'types' 'to_intdim' 1 ((PROCEDURE UNKNOWN-INTENT +MODULE-PROC DECL UNKNOWN FUNCTION) (INTEGER 4 0 0 INTEGER ()) 5 0 (6) () +4 () () 0 0) +7 'types' 'types' 'types' 1 ((MODULE UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +UNKNOWN) (UNKNOWN 0 0 0 UNKNOWN ()) 0 0 () () 0 () () 0 0) +8 'wp' 'types' 'wp' 1 ((PARAMETER UNKNOWN-INTENT UNKNOWN-PROC UNKNOWN +IMPLICIT-SAVE) (INTEGER 4 0 0 INTEGER ()) 0 0 () (CONSTANT (INTEGER 4 0 +0 INTEGER ()) 0 '4') () 0 () () 0 0) +6 'int_value' '' 'int_value' 5 ((VARIABLE UNKNOWN-INTENT UNKNOWN-PROC +UNKNOWN UNKNOWN DUMMY) (INTEGER 8 0 0 INTEGER ()) 0 0 () () 0 () () 0 0) +) + +('intdim' 0 2 'selected_int_kind' 0 3 'to_intdim' 0 4 'types' 0 7 'wp' 0 +8) diff --git a/wafo/spectrum/__init__.py b/wafo/spectrum/__init__.py new file mode 100755 index 0000000..9cfd44c --- /dev/null +++ b/wafo/spectrum/__init__.py @@ -0,0 +1,11 @@ +""" +Spectrum package in WAFO Toolbox. + + Readme - Readme file for module SPEC in WAFO Toolbox + +""" + +from wafo.spectrum.core import SpecData1D +import wafo.spectrum.models +import wafo.spectrum.dispersion_relation +#from wafo.data_structures import SpecData1D \ No newline at end of file diff --git a/wafo/spectrum/core.py b/wafo/spectrum/core.py new file mode 100755 index 0000000..8265a35 --- /dev/null +++ b/wafo/spectrum/core.py @@ -0,0 +1,2485 @@ +from __future__ import division +import warnings +import numpy as np +from numpy import (pi, inf, meshgrid, zeros, ones, where, nonzero, #@UnresolvedImport + flatnonzero, ceil, sqrt, exp, log, arctan2, #@UnresolvedImport + tanh, cosh, sinh, random, atleast_1d, maximum, #@UnresolvedImport + minimum, diff, isnan, any, r_, conj, mod, #@UnresolvedImport + hstack, vstack, interp, ravel, finfo, linspace, #@UnresolvedImport + arange, array, nan, newaxis, fliplr, sign) #@UnresolvedImport +from numpy.fft import fft +from scipy.integrate import simps, trapz +from scipy.special import erf +from scipy.linalg import toeplitz +import scipy.interpolate as interpolate +from pylab import stineman_interp + +from dispersion_relation import w2k #, k2w +from wafo.wafodata import WafoData, now +from wafo.misc import sub_dict_select, nextpow2, discretize, JITImport +from wafo.gaussian import Rind +from wafo.transform import TrData +from wafo.plotbackend import plotbackend +from wafo import c_library +# Trick to avoid error due to circular import +_WAFOCOV = JITImport('wafo.covariance') + + +__all__ = ['SpecData1D', 'SpecData2D'] + +def _set_seed(iseed): + '''Set seed of random generator''' + if iseed != None: + try: + random.set_state(iseed) + except: + random.seed(iseed) + +def qtf(w, h=inf, g=9.81): + """ + Return Quadratic Transfer Function + + Parameters + ------------ + w : array-like + angular frequencies + h : scalar + water depth + g : scalar + acceleration of gravity + + Returns + ------- + h_s = sum frequency effects + h_d = difference frequency effects + h_dii = diagonal of h_d + """ + w = atleast_1d(w) + num_w = w.size + + k_w = w2k(w, theta=0, h=h, g=g)[0] + + k_1, k_2 = meshgrid(k_w, k_w) + + if h == inf: # go here for faster calculations + h_s = 0.25 * (abs(k_1) + abs(k_2)) + h_d = -0.25 * abs(abs(k_1) - abs(k_2)) + h_dii = zeros(num_w) + return h_s, h_d , h_dii + + [w_1, w_2] = meshgrid(w, w) + + + + w12 = (w_1 * w_2) + w1p2 = (w_1 + w_2) + w1m2 = (w_1 - w_2) + k12 = (k_1 * k_2) + k1p2 = (k_1 + k_2) + k1m2 = abs(k_1 - k_2) + + if 0: # Langley + p_1 = (-2 * w1p2 * (k12 * g ** 2. - w12 ** 2.) + + w_1 * (w_2 ** 4. - g ** 2 * k_2 ** 2) + + w_2 * (w_1 ** 4 - g * 2. * k_1 ** 2)) / (4. * w12) + p_2 = w1p2 ** 2. * cosh((k1p2) * h) - g * (k1p2) * sinh((k1p2) * h) + + h_s = (-p_1 / p_2 * w1p2 * cosh((k1p2) * h) / g - + (k12 * g ** 2 - w12 ** 2.) / (4 * g * w12) + + (w_1 ** 2 + w_2 ** 2) / (4 * g)) + + p_3 = (-2 * w1m2 * (k12 * g ** 2 + w12 ** 2) - + w_1 * (w_2 ** 4 - g ** 2 * k_2 ** 2) + + w_2 * (w_1 ** 4 - g ** 2 * k_1 ** 2)) / (4. * w12) + p_4 = w1m2 ** 2. * cosh(k1m2 * h) - g * (k1m2) * sinh((k1m2) * h) + + + h_d = (-p_3 / p_4 * (w1m2) * cosh((k1m2) * h) / g - + (k12 * g ** 2 + w12 ** 2) / (4 * g * w12) + + (w_1 ** 2. + w_2 ** 2.) / (4. * g)) + + else: # # Marthinsen & Winterstein + tmp1 = 0.5 * g * k12 / w12 + tmp2 = 0.25 / g * (w_1 ** 2. + w_2 ** 2. + w12) + h_s = (tmp1 - tmp2 + 0.25 * g * (w_1 * k_2 ** 2. + w_2 * k_1 ** 2) / + (w12 * (w1p2))) / (1. - g * (k1p2) / (w1p2) ** 2. * + tanh((k1p2) * h)) + tmp2 - 0.5 * tmp1 ## OK + + tmp2 = 0.25 / g * (w_1 ** 2 + w_2 ** 2 - w12) # #OK + h_d = (tmp1 - tmp2 - 0.25 * g * (w_1 * k_2 ** 2 - w_2 * k_1 ** 2) / + (w12 * (w1m2))) / (1. - g * (k1m2) / (w1m2) ** 2. * + tanh((k1m2) * h)) + tmp2 - 0.5 * tmp1 # # OK + + + ##tmp1 = 0.5*g*k_w./(w.*sqrt(g*h)) + ##tmp2 = 0.25*w.^2/g + +# Wave group velocity + c_g = 0.5 * g * (tanh(k_w * h) + k_w * h * (1.0 - tanh(k_w * h) ** 2)) / w + h_dii = (0.5 * (0.5 * g * (k_w / w) ** 2. - 0.5 * w ** 2 / g + + g * k_w / (w * c_g)) + / (1. - g * h / c_g ** 2.) - 0.5 * k_w / sinh(2 * k_w * h))# # OK + h_d.flat[0::num_w + 1] = h_dii + + ##k = find(w_1==w_2) + ##h_d(k) = h_dii + + #% The NaN's occur due to division by zero. => Set the isnans to zero + + h_dii = where(isnan(h_dii), 0, h_dii) + h_d = where(isnan(h_d), 0, h_d) + h_s = where(isnan(h_s), 0, h_s) + + return h_s, h_d , h_dii + +class SpecData1D(WafoData): + """ + Container class for 1D spectrum data objects in WAFO + + Member variables + ---------------- + data : array-like + One sided Spectrum values, size nf + args : array-like + freguency/wave-number-lag values of freqtype, size nf + type : String + spectrum type, one of 'freq', 'k1d', 'enc' (default 'freq') + freqtype : letter + frequency type, one of: 'f', 'w' or 'k' (default 'w') + tr : Transformation function (default (none)). + h : real scalar + Water depth (default inf). + v : real scalar + Ship speed, if type = 'enc'. + norm : bool + Normalization flag, True if S is normalized, False if not + date : string + Date and time of creation or change. + + Examples + -------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S1 = Sj.tospecdata(w) #Make spectrum object from numerical values + >>> S = SpecData1D(Sj(w),w) # Alternatively do it manually + + See also + -------- + WafoData + CovData + """ + + def __init__(self, *args, **kwds): + super(SpecData1D, self).__init__(*args, **kwds) + self.name = 'WAFO Spectrum Object' + self.type = 'freq' + self.freqtype = 'w' + self.angletype = '' + self.h = inf + self.tr = None + self.phi = 0.0 + self.v = 0.0 + self.norm = False + somekeys = ['angletype', 'phi', 'name', 'h', 'tr', 'freqtype', 'v', + 'type', 'norm'] + + self.__dict__.update(sub_dict_select(kwds, somekeys)) + + self.setlabels() + + def tocov_matrix(self, nr=0, nt=None, dt=None): + ''' + Computes covariance function and its derivatives, alternative version + + Parameters + ---------- + nr : scalar integer + number of derivatives in output, nr<=4 (default 0) + nt : scalar integer + number in time grid, i.e., number of time-lags. + (default rate*(n_f-1)) where rate = round(1/(2*f(end)*dt)) or + rate = round(pi/(w(n_f)*dt)) depending on S. + dt : real scalar + time spacing for acfmat + + Returns + ------- + acfmat : [R0, R1,...Rnr], shape Nt+1 x Nr+1 + matrix with autocovariance and its derivatives, i.e., Ri (i=1:nr) + are column vectors with the 1'st to nr'th derivatives of R0. + + NB! This routine requires that the spectrum grid is equidistant + starting from zero frequency. + + Example + ------- + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap() + >>> S = Sj.tospecdata() + >>> acfmat = S.tocov_matrix(nr=3, nt=256, dt=0.1) + >>> acfmat[:2,:] + array([[ 3.06075987, 0. , -1.67750289, 0. ], + [ 3.05246132, -0.16662376, -1.66819445, 0.18634189]]) + + See also + -------- + cov, + resample, + objects + ''' + + ftype = self.freqtype # %options are 'f' and 'w' and 'k' + freq = self.args + n_f = len(freq) + dt_old = self.sampling_period() + if dt is None: + dt = dt_old + rate = 1 + else: + rate = max(round(dt_old * 1. / dt), 1.) + + + if nt is None: + nt = rate * (n_f - 1) + else: #%check if Nt is ok + nt = minimum(nt, rate * (n_f - 1)) + + + checkdt = 1.2 * min(diff(freq)) / 2. / pi + if ftype in 'k': + lagtype = 'x' + else: + lagtype = 't' + if ftype in 'f': + checkdt = checkdt * 2 * pi + msg1 = 'Step dt = %g in computation of the density is too small.' % dt + msg2 = 'Step dt = %g is small, and may cause numerical inaccuracies.' % dt + + if (checkdt < 2. ** -16 / dt): + print(msg1) + print('The computed covariance (by FFT(2^K)) may differ from the') + print('theoretical. Solution:') + raise ValueError('use larger dt or sparser grid for spectrum.') + + + # Calculating covariances + #~~~~~~~~~~~~~~~~~~~~~~~~ + spec = self.copy() + spec.resample(dt) + + acf = spec.tocovdata(nr, nt, rate=1) + acfmat = zeros((nt + 1, nr + 1), dtype=float) + acfmat[:, 0] = acf.data[0:nt + 1] + fieldname = 'R' + lagtype * nr + for i in range(1, nr + 1): + fname = fieldname[:i + 1] + r_i = getattr(acf, fname) + acfmat[:, i] = r_i[0:nt + 1] + + eps0 = 0.0001 + if nt + 1 >= 5: + cc2 = acfmat[0, 0] - acfmat[4, 0] * (acfmat[4, 0] / acfmat[0, 0]) + if (cc2 < eps0): + warnings.warn(msg1) + cc1 = acfmat[0, 0] - acfmat[1, 0] * (acfmat[1, 0] / acfmat[0, 0]) + if (cc1 < eps0): + warnings.warn(msg2) + return acfmat + + def tocovdata(self, nr=0, nt=None, rate=None): + ''' + Computes covariance function and its derivatives + + Parameters + ---------- + nr : number of derivatives in output, nr<=4 (default = 0). + nt : number in time grid, i.e., number of time-lags + (default rate*(length(S.data)-1)). + rate = 1,2,4,8...2**r, interpolation rate for R + (default = 1, no interpolation) + + Returns + ------- + R : CovData1D + auto covariance function + + The input 'rate' gives together with the spectrum + the time-grid-spacing: dt=pi/(S.w[-1]*rate), S.w[-1] is the Nyquist freq. + This results in the time-grid: 0:dt:Nt*dt. + + What output is achieved with different S and choices of Nt,Nx and Ny: + 1) S.type='freq' or 'dir', Nt set, Nx,Ny not set: then result R(time) (one-dim) + 2) S.type='k1d' or 'k2d', Nt set, Nx,Ny not set: then result R(x) (one-dim) + 3) Any type, Nt and Nx set =>R(x,time); Nt and Ny set =>R(y,time) + 4) Any type, Nt, Nx and Ny set => R(x,y,time) + 5) Any type, Nt not set, Nx and/or Ny set => Nt set to default, goto 3) or 4) + + NB! This routine requires that the spectrum grid is equidistant + starting from zero frequency. + NB! If you are using a model spectrum, spec, with sharp edges + to calculate covariances then you should probably round off the sharp + edges like this: + + Example: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap() + >>> S = Sj.tospecdata() + >>> S.data[0:40] = 0.0 + >>> S.data[100:-1] = 0.0 + >>> Nt = len(S.data)-1 + >>> acf = S.tocovdata(nr=0, nt=Nt) + + R = spec2cov(spec,0,Nt) + win = parzen(2*Nt+1) + R.data = R.data.*win(Nt+1:end) + S1 = cov2spec(acf) + R2 = spec2cov(S1) + figure(1) + plotspec(S),hold on, plotspec(S1,'r') + figure(2) + covplot(R), hold on, covplot(R2,[],[],'r') + figure(3) + semilogy(abs(R2.data-R.data)), hold on, + semilogy(abs(S1.data-S.data)+1e-7,'r') + + See also + -------- + cov2spec + ''' + + freq = self.args + n_f = len(freq) + + if freq[0] > 0: + txt = '''Spectrum does not start at zero frequency/wave number. + Correct it with resample, for example.''' + raise ValueError(txt) + d_w = abs(diff(freq, n_f=2, axis=0)) + if any(d_w > 1.0e-8): + txt = '''Not equidistant frequencies/wave numbers in spectrum. + Correct it with resample, for example.''' + raise ValueError(txt) + + + if rate is None: + rate = 1 # %interpolation rate + elif rate > 16: + rate = 16 + else: # make sure rate is a power of 2 + rate = 2 ** nextpow2(rate) + + if nt is None: + nt = rate * (n_f - 1) + else: #check if Nt is ok + nt = minimum(nt, rate * (n_f - 1)) + + spec = self.copy() + + if self.freqtype in 'k': + lagtype = 'x' + else: + lagtype = 'time' + + d_t = spec.sampling_period() + #normalize spec so that sum(specn)/(n_f-1)=acf(0)=var(X) + specn = spec.data * freq[-1] + if spec.freqtype in 'f': + w = freq * 2 * pi + else: + w = freq + + nfft = rate * 2 ** nextpow2(2 * n_f - 2) + + # periodogram + rper = r_[specn, zeros(nfft - (2 * n_f) + 2), conj(specn[n_f - 1:0:-1])] + time = r_[0:nt + 1] * d_t * (2 * n_f - 2) / nfft + + r = fft(rper, nfft).real / (2 * n_f - 2) + acf = _WAFOCOV.CovData1D(r[0:nt + 1], time, lagtype=lagtype) + acf.tr = spec.tr + acf.h = spec.h + acf.norm = spec.norm + + if nr > 0: + w = r_[w , zeros(nfft - 2 * n_f + 2) , -w[n_f - 1:0:-1] ] + fieldname = 'R' + lagtype * nr + for i in range(1, nr + 1): + rper = -1j * w * rper + d_acf = fft(rper, nfft).real / (2 * n_f - 2) + setattr(acf, fieldname[0:i + 1], d_acf[0:nt + 1]) + return acf + + def to_linspec(self, ns=None, dt=None, cases=20, iseed=None, + fn_limit=sqrt(2), gravity=9.81): + ''' + Split the linear and non-linear component from the Spectrum + according to 2nd order wave theory + + Returns + ------- + SL, SN : SpecData1D objects + with linear and non-linear components only, respectively. + + Parameters + ---------- + ns : scalar integer + giving ns load points. (default length(S)-1=n-1). + If np>n-1 it is assummed that S(k)=0 for all k>n-1 + cases : scalar integer + number of cases (default=20) + dt : real scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : scalar integer + starting seed number for the random number generator + (default none is set) + fnLimit : real scalar + normalized upper frequency limit of spectrum for 2'nd order + components. The frequency is normalized with + sqrt(gravity*tanh(kbar*water_depth)/Amax)/(2*pi) + (default sqrt(2), i.e., Convergence criterion). + Generally this should be the same as used in the final + non-linear simulation (see example below). + + SPEC2LINSPEC separates the linear and non-linear component of the + spectrum according to 2nd order wave theory. This is useful when + simulating non-linear waves because: + If the spectrum does not decay rapidly enough towards zero, the + contribution from the 2nd order wave components at the upper tail can + be very large and unphysical. Another option to ensure convergence of + the perturbation series in the simulation, is to truncate the upper tail + of the spectrum at FNLIMIT in the calculation of the 2nd order wave + components, i.e., in the calculation of sum and difference frequency effects. + + Example: + -------- + np = 10000; + iseed = 1; + pflag = 2; + S = jonswap(10); + fnLimit = inf; + [SL,SN] = spec2linspec(S,np,[],[],fnLimit); + x0 = spec2nlsdat(SL,8*np,[],iseed,[],fnLimit); + x1 = spec2nlsdat(S,8*np,[],iseed,[],fnLimit); + x2 = spec2nlsdat(S,8*np,[],iseed,[],sqrt(2)); + Se0 = dat2spec(x0); + Se1 = dat2spec(x1); + Se2 = dat2spec(x2); + clf + plotspec(SL,'r',pflag), % Linear components + hold on + plotspec(S,'b',pflag) % target spectrum for simulated data + plotspec(Se0,'m',pflag), % approx. same as S + plotspec(Se1,'g',pflag) % unphysical spectrum + plotspec(Se2,'k',pflag) % approx. same as S + axis([0 10 -80 0]) + hold off + + See also + -------- + spec2nlsdat + + References + ---------- + P. A. Brodtkorb (2004), + The probability of Occurrence of dangerous Wave Situations at Sea. + Dr.Ing thesis, Norwegian University of Science and Technolgy, NTNU, + Trondheim, Norway. + + Nestegaard, A and Stokka T (1995) + A Third Order Random Wave model. + In proc.ISOPE conf., Vol III, pp 136-142. + + R. S Langley (1987) + A statistical analysis of non-linear random waves. + Ocean Engng, Vol 14, pp 389-407 + + Marthinsen, T. and Winterstein, S.R (1992) + 'On the skewness of random surface waves' + In proc. ISOPE Conf., San Francisco, 14-19 june. + ''' + + # by pab 13.08.2002 + + # TODO % Replace inputs with options structure + # TODO % Can be improved further. + + method = 'apstochastic' + trace = 1 #% trace the convergence + max_sim = 30 + tolerance = 5e-4 + + L = 200 #%maximum lag size of the window function used in + #%spectral estimate + #ftype = self.freqtype #options are 'f' and 'w' and 'k' +# switch ftype +# case 'f', +# ftype = 'w'; +# S = ttspec(S,ftype); +# end + Hm0 = self.characteristic('Hm0') + Tm02 = self.characteristic('Tm02') + + + if not iseed is None: + _set_seed(iseed) #% set the the seed + + n = len(self.data) + if ns is None: + ns = max(n - 1, 5000) + if dt is None: + S = self.interp(dt) # interpolate spectrum + else: + S = self.copy() + + ns = ns + mod(ns, 2) # make sure np is even + + water_depth = abs(self.h); + kbar = w2k(2 * pi / Tm02, 0, water_depth)[0] + + # Expected maximum amplitude for 1000 waves seastate + num_waves = 10000 + Amax = sqrt(2 * log(num_waves)) * Hm0 / 4 + + fLimitLo = sqrt(gravity * tanh(kbar * water_depth) * Amax / water_depth ** 3); + + + freq = S.args + eps = finfo(float).eps + freq[-1] = freq[-1] - sqrt(eps) + Hw2 = 0 + + SL = S + + indZero = nonzero(freq < fLimitLo)[0] + if len(indZero): + SL.data[indZero] = 0 + + maxS = max(S.data); + #Fs = 2*freq(end)+eps; % sampling frequency + + for ix in xrange(max_sim): + [x2, x1] = spec2nlsdat(SL, [np, cases], [], iseed, method, fnLimit) + #%x2(:,2:end) = x2(:,2:end) -x1(:,2:end); + S2 = dat2spec(x2, L) + S1 = dat2spec(x1, L) + #%[tf21,fi] = tfe(x2(:,2),x1(:,2),1024,Fs,[],512); + #%Hw11 = interp1q(fi,tf21.*conj(tf21),freq); + if True: + Hw1 = exp(interp1q(S2.args, log(abs(S1.data / S2.data)), freq)) + else: + # Geometric mean + Hw1 = exp((interp1q(S2.args, log(abs(S1.data / S2.data)), freq) + log(Hw2)) / 2) + #end + #Hw1 = (interp1q( S2.w,abs(S1.S./S2.S),freq)+Hw2)/2; + #plot(freq, abs(Hw11-Hw1),'g') + #title('diff') + #pause + #clf + + #d1 = interp1q( S2.w,S2.S,freq);; + + SL.data = (Hw1 * S.data) + + if len(indZero): + SL.data[indZero] = 0 + #end + k = nonzero(SL.data < 0)[0] + if len(k): # Make sure that the current guess is larger than zero + #%k + #Hw1(k) + Hw1[k] = min(S1.data[k] * 0.9, S.data[k]) + SL.data[k] = max(Hw1[k] * S.data[k], eps) + #end + Hw12 = Hw1 - Hw2 + maxHw12 = max(abs(Hw12)) + if trace == 1: + plotbackend.figure(1), + plotbackend.semilogy(freq, Hw1, 'r') + plotbackend.title('Hw') + plotbackend.figure(2), + plotbackend.semilogy(freq, abs(Hw12), 'r') + plotbackend.title('Hw-HwOld') + + #pause(3) + plotbackend.figure(1), + plotbackend.semilogy(freq, Hw1, 'b') + plotbackend.title('Hw') + plotbackend.figure(2), + plotbackend.semilogy(freq, abs(Hw12), 'b') + plotbackend.title('Hw-HwOld') + #figtile + #end + + print('Iteration : %d, Hw12 : %g Hw12/maxS : %g' % (ix, maxHw12, (maxHw12 / maxS))) + if (maxHw12 < maxS * tolerance) and (Hw1[-1] < Hw2[-1]) : + break + #end + Hw2 = Hw1 + #end + + #%Hw1(end) + #%maxS*1e-3 + #%if Hw1(end)*S.>maxS*1e-3, + #% warning('The Nyquist frequency of the spectrum may be too low') + #%end + + SL.date = now() #datestr(now) + #if nargout>1 + SN = SL.copy() + SN.data = S.data - SL.data + SN.note = SN.note + ' non-linear component (spec2linspec)' + #end + SL.note = SL.note + ' linear component (spec2linspec)' + + return SL, SN + + + def to_t_pdf(self, u=None, pdef='Tc', paramt=None, **options): + ''' + Density of crest/trough- period or length, version 2. + + Parameters + ---------- + u : real scalar + reference level (default the most frequently crossed level). + pdef : string, 'Tc', Tt', 'Lc' or 'Lt' + 'Tc', gives half wave period, Tc (default). + 'Tt', gives half wave period, Tt + 'Lc' and 'Lt' ditto for wave length. + paramt : [t0, tn, nt] + where t0, tn and nt is the first value, last value and the number + of points, respectively, for which the density will be computed. + paramt= [5, 5, 51] implies that the density is computed only for + T=5 and using 51 equidistant points in the interval [0,5]. + options : optional parameters + controlling the performance of the integration. See Rind for details. + + Notes + ----- + SPEC2TPDF2 calculates pdf of halfperiods Tc, Tt, Lc or Lt + in a stationary Gaussian transform process X(t), + where Y(t) = g(X(t)) (Y zero-mean Gaussian with spectrum given in S). + The transformation, g, can be estimated using LC2TR, + DAT2TR, HERMITETR or OCHITR. + + Example + ------- + The density of Tc is computed by: + >>> import pylab as plb + >>> from wafo.spectrum import models as sm + >>> w = np.linspace(0,3,100) + >>> Sj = sm.Jonswap() + >>> S = Sj.tospecdata() + >>> f = S.to_t_pdf(pdef='Tc', paramt=(0, 10, 51), speed=7) + >>> h = f.plot() + + estimated error bounds + >>> h2 = plb.plot(f.args, f.data+f.err, 'r', f.args, f.data-f.err, 'r') + + >>> plb.close('all') + + See also + -------- + Rind, spec2cov2, specnorm, dat2tr, dat2gaus, + definitions.wave_periods, + definitions.waves + + ''' + + opts = dict(speed=9) + opts.update(options) + if pdef[0] in ('l', 'L'): + if self.type != 'k1d': + raise ValueError('Must be spectrum of type: k1d') + elif pdef[0] in ('t', 'T'): + if self.type != 'freq': + raise ValueError('Must be spectrum of type: freq') + else: + raise ValueError('pdef must be Tc,Tt or Lc, Lt') +# if strncmpi('l',def,1) +# spec=spec2spec(spec,'k1d') +# elseif strncmpi('t',def,1) +# spec=spec2spec(spec,'freq') +# else +# error('Unknown def') +# end + pdef2defnr = dict(tc=1, lc=1, tt= -1, lt= -1) + defnr = pdef2defnr[pdef.lower()] + + S = self.copy() + S.normalize() + m, unused_mtxt = self.moment(nr=2, even=True) + A = sqrt(m[0] / m[1]) + + + if self.tr is None: + y = linspace(-5, 5, 513) + #g = _wafotransform. + g = TrData(y, sqrt(m[0]) * y) + else: + g = self.tr + + + if u is None: + u = g.gauss2dat(0) #% most frequently crossed level + + # transform reference level into Gaussian level + un = g.dat2gauss(u) + + #disp(['The level u for Gaussian process = ', num2str(u)]) + + if paramt is None: + #% z2 = u^2/2 + z = -sign(defnr) * un / sqrt(2) + expectedMaxPeriod = 2 * ceil(2 * pi * A * exp(z) * (0.5 + erf(z) / 2)) + paramt = [0, expectedMaxPeriod, 51] + + t0 = paramt[0] + tn = paramt[1] + Ntime = paramt[2] + t = linspace(0, tn / A, Ntime) #normalized times + Nstart = max(round(t0 / tn * (Ntime - 1)), 1) #% index to starting point to + #% evaluate + + dt = t[1] - t[0] + nr = 2 + R = S.tocov_matrix(nr, Ntime - 1, dt) + #R = spec2cov2(S,nr,Ntime-1,dt) + + + xc = vstack((un, un)) + indI = -ones(4, dtype=int) + Nd = 2 + Nc = 2 + XdInf = 100.e0 * sqrt(-R[0, 2]) + XtInf = 100.e0 * sqrt(R[0, 0]) + + B_up = hstack([un + XtInf, XdInf, 0]) + B_lo = hstack([un, 0, -XdInf]) + #%INFIN = [1 1 0] + #BIG = zeros((Ntime+2,Ntime+2)) + ex = zeros(Ntime + 2, dtype=float) + #%CC = 2*pi*sqrt(-R(1,1)/R(1,3))*exp(un^2/(2*R(1,1))) + #% XcScale = log(CC) + opts['xcscale'] = log(2 * pi * sqrt(-R[0, 0] / R[0, 2])) + (un ** 2 / (2 * R[0, 0])) + + f = zeros(Ntime, dtype=float) + err = zeros(Ntime, dtype=float) + + rind = Rind(**opts) + #h11 = fwaitbar(0,[],sprintf('Please wait ...(start at: %s)',datestr(now))) + for pt in xrange(Nstart, Ntime): + Nt = pt - Nd + 1 + Ntd = Nt + Nd + Ntdc = Ntd + Nc + indI[1] = Nt - 1 + indI[2] = Nt + indI[3] = Ntd - 1 + + #% positive wave period + BIG = self._covinput(pt, R) + + tmp = rind(BIG, ex[:Ntdc], B_lo, B_up, indI, xc, Nt) + f[pt], err[pt] = tmp[:2] + #fwaitbar(pt/Ntime,h11,sprintf('%s Ready: %d of %d',datestr(now),pt,Ntime)) + #end + #close(h11) + + + titledict = dict(tc='Density of Tc', tt='Density of Tt', lc='Density of Lc', lt='Density of Lt') + Htxt = titledict.get(pdef.lower()) + + if pdef[0].lower() == 'l': + xtxt = 'wave length [m]' + else: + xtxt = 'period [s]' + + Htxt = '%s_{v =%2.5g}' % (Htxt, u) + pdf = WafoData(f / A, t * A, title=Htxt, xlab=xtxt) + pdf.err = err / A + pdf.u = u + pdf.options = opts + return pdf + + + def _covinput(self, pt, R): + """ + Return covariance matrix for Tc or Tt period problems + + Parameters + ---------- + pt : scalar integer + time + R : array-like, shape Ntime x 3 + [R0,R1,R2] column vectors with autocovariance and its derivatives, + i.e., Ri (i=1:2) are vectors with the 1'st and 2'nd derivatives of R0. + + The order of the variables in the covariance matrix are organized as follows: + For pt>1: + ||X(t2)..X(ts),..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 + + 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|) + + """ + # cov(Xd) + Sdd = -toeplitz(R[[0, pt], 2]) + # cov(Xc) + Scc = toeplitz(R[[0, pt], 0]) + # cov(Xc,Xd) + Scd = array([[0, R[pt, 1]], [ -R[pt, 1], 0]]) + + if pt > 1 : + #%cov(Xt) + Stt = toeplitz(R[:pt - 1, 0]) # Cov(X(tn),X(ts)) = r(ts-tn) = r(|ts-tn|) + #%cov(Xc,Xt) + Sct = R[1:pt, 0] # Cov(X(tn),X(ts)) = r(ts-tn) = r(|ts-tn|) + Sct = vstack((Sct, Sct[::-1])) + #%Cov(Xd,Xt) + Sdt = -R[1:pt, 1] # Cov(X'(t1),X(ts)) = -r'(ts-t1) = r(|s-t|) + Sdt = vstack((Sdt, -Sdt[::-1])) + #N = pt + 3 + big = vstack((hstack((Stt, Sdt.T, Sct.T)), + hstack((Sdt, Sdd, Scd.T)), + hstack((Sct, Scd, Scc)))) + else: + #N = 4 + big = vstack((hstack((Sdd, Scd.T)), + hstack((Scd, Scc)))) + return big + + def to_specnorm(self): + S = self.copy() + S.normalize() + return S + + def sim(self, ns=None, cases=1, dt=None, iseed=None, method='random', derivative=False): + ''' Simulates a Gaussian process and its derivative from spectrum + + Parameters + ---------- + ns : scalar + number of simulated points. (default length(spec)-1=n-1). + If ns>n-1 it is assummed that acf(k)=0 for all k>n-1 + cases : scalar + number of replicates (default=1) + dt : scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : int or state + starting state/seed number for the random number generator + (default none is set) + method : string + if 'exact' : simulation using cov2sdat + if 'random' : random phase and amplitude simulation (default) + derivative : bool + if true : return derivative of simulated signal as well + otherwise + + Returns + ------- + xs = a cases+1 column matrix ( t,X1(t) X2(t) ...). + xsder = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). + + Details + ------- + Performs a fast and exact simulation of stationary zero mean + Gaussian process through circulant embedding of the covariance matrix + or by summation of sinus functions with random amplitudes and random + phase angle. + + If the spectrum has a non-empty field .tr, then the transformation is + applied to the simulated data, the result is a simulation of a transformed + Gaussian process. + + Note: The method 'exact' simulation may give high frequency ripple when + used with a small dt. In this case the method 'random' works better. + + Example: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap();S = Sj.tospecdata() + >>> ns =100; dt = .2 + >>> x1 = S.sim(ns,dt=dt) + + >>> import numpy as np + >>> import scipy.stats as st + >>> x2 = S.sim(20000,20) + >>> truth1 = [0,np.sqrt(S.moment(1)[0]),0., 0.] + >>> funs = [np.mean,np.std,st.skew,st.kurtosis] + >>> for fun,trueval in zip(funs,truth1): + ... res = fun(x2[:,1::],axis=0) + ... m = res.mean() + ... sa = res.std() + ... assert(np.abs(m-trueval) T) + + # Trick to avoid adding high frequency noise to the spectrum + if i.size > 0: + acf.data[i[0]::] = 0.0 + + return acf.sim(ns=ns, cases=cases, iseed=iseed, derivative=derivative) + + _set_seed(iseed) + + ns = ns + mod(ns, 2) # make sure it is even + + f_i = freq[1:-1] + s_i = spec.data[1:-1] + if ftype in ('w', 'k'): + fact = 2. * pi + s_i = s_i * fact + f_i = f_i / fact + + x = zeros((ns, cases + 1)) + + d_f = 1 / (ns * d_t) + + + # interpolate for freq. [1:(N/2)-1]*d_f and create 2-sided, uncentered spectra + f = arange(1, ns / 2.) * d_f + + f_u = hstack((0., f_i, d_f * ns / 2.)) + s_u = hstack((0., abs(s_i) / 2., 0.)) + + + s_i = interp(f, f_u, s_u) + s_u = hstack((0., s_i, 0, s_i[(ns / 2) - 2::-1])) + del(s_i, f_u) + + # Generate standard normal random numbers for the simulations + randn = random.randn + z_r = randn((ns / 2) + 1, cases) + z_i = vstack((zeros((1, cases)), randn((ns / 2) - 1, cases), zeros((1, cases)))) + + amp = zeros((ns, cases), dtype=complex) + amp[0:(ns / 2 + 1), :] = z_r - 1j *z_i + del(z_r, z_i) + amp[(ns / 2 + 1):ns, :] = amp[ns / 2 - 1:0:-1, :].conj() + amp[0, :] = amp[0, :]*sqrt(2.) + amp[(ns / 2), :] = amp[(ns / 2), :]*sqrt(2.) + + + # Make simulated time series + T = (ns - 1) * d_t + Ssqr = sqrt(s_u * d_f / 2.) + + # stochastic amplitude + amp = amp * Ssqr[:, newaxis] + + + # Deterministic amplitude + #amp = sqrt[1]*Ssqr(:,ones(1,cases)).*exp(sqrt(-1)*atan2(imag(amp),real(amp))) + del(s_u, Ssqr) + + + x[:, 1::] = fft(amp, axis=0).real + x[:, 0] = linspace(0, T, ns) #' %(0:d_t:(np-1)*d_t).' + + + if derivative: + xder = zeros(ns, cases + 1) + w = 2. * pi * hstack((0, f, 0., -f[-1::-1])) + amp = -1j * amp * w[:, newaxis] + xder[:, 1:(cases + 1)] = fft(amp, axis=0).real + xder[:, 0] = x[:, 0] + + if spec.tr is not None: + print(' Transforming data.') + g = spec.tr + G = fliplr(g) #% the invers of g + if derivative: + for i in range(cases): + tmp = tranproc(hstack((x[:, i + 1], xder[:, i + 1])), G) + x[:, i + 1] = tmp[:, 0] + xder[:, i + 1] = tmp[:, 1] + + else: + for i in range(cases): + x[:, i + 1] = tranproc(x[:, i + 1], G) + + if derivative: + return x, xder + else: + return x + +# function [x2,x,svec,dvec,amp]=spec2nlsdat(spec,np,dt,iseed,method,truncationLimit) + def sim_nl(self, ns=None, cases=1, dt=None, iseed=None, method='random', + fnlimit=1.4142, reltol=1e-3, g=9.81): + """ + Simulates a Randomized 2nd order non-linear wave X(t) + + Parameters + ---------- + ns : scalar + number of simulated points. (default length(spec)-1=n-1). + If ns>n-1 it is assummed that R(k)=0 for all k>n-1 + cases : scalar + number of replicates (default=1) + dt : scalar + step in grid (default dt is defined by the Nyquist freq) + iseed : int or state + starting state/seed number for the random number generator + (default none is set) + method : string + 'apStochastic' : Random amplitude and phase (default) + 'aDeterministic' : Deterministic amplitude and random phase + 'apDeterministic' : Deterministic amplitude and phase + fnlimit : scalar + normalized upper frequency limit of spectrum for 2'nd order + components. The frequency is normalized with + sqrt(gravity*tanh(kbar*water_depth)/amp_max)/(2*pi) + (default sqrt(2), i.e., Convergence criterion [1]_). + Other possible values are: + sqrt(1/2) : No bump in trough criterion + sqrt(pi/7) : Wave steepness criterion + reltol : scalar + relative tolerance defining where to truncate spectrum for the + sum and difference frequency effects + + + Returns + ------- + xs2 = a cases+1 column matrix ( t,X1(t) X2(t) ...). + xs1 = a cases+1 column matrix ( t,X1'(t) X2'(t) ...). + + Details + ------- + Performs a Fast simulation of Randomized 2nd order non-linear + waves by summation of sinus functions with random amplitudes and + phase angles. The extent to which the simulated result are applicable + to real seastates are dependent on the validity of the assumptions: + + 1. Seastate is unidirectional + 2. Surface elevation is adequately represented by 2nd order random + wave theory + 3. The first order component of the surface elevation is a Gaussian + random process. + + If the spectrum does not decay rapidly enough towards zero, the + contribution from the 2nd order wave components at the upper tail can + be very large and unphysical. To ensure convergence of the perturbation + series, the upper tail of the spectrum is truncated at FNLIMIT in the + calculation of the 2nd order wave components, i.e., in the calculation + of sum and difference frequency effects. This may also be combined with + the elimination of second order effects from the spectrum, i.e., extract + the linear components from the spectrum. One way to do this is to use + SPEC2LINSPEC. + + Example + -------- + np =100; dt = .2 + [x1, x2] = spec2nlsdat(jonswap,np,dt) + waveplot(x1,'r',x2,'g',1,1) + + See also + -------- + spec2linspec, spec2sdat, cov2sdat + + References + ---------- + .. [1] Nestegaard, amp and Stokka T (1995) + amp Third Order Random Wave model. + In proc.ISOPE conf., Vol III, pp 136-142. + + .. [2] R. spec Langley (1987) + amp statistical analysis of non-linear random waves. + Ocean Engng, Vol 14, pp 389-407 + + .. [3] Marthinsen, T. and Winterstein, spec.R (1992) + 'On the skewness of random surface waves' + In proc. ISOPE Conf., San Francisco, 14-19 june. + """ + + # TODO % Check the methods: 'apdeterministic' and 'adeterministic' + Hm0, Tm02 = self.characteristic(['Hm0', 'Tm02'])[0].tolist() + + _set_seed(iseed) + + spec = self.copy() + if dt is not None: + spec.resample(dt) + + + ftype = spec.freqtype + freq = spec.args + + d_t = spec.sampling_period() + Nt = freq.size + + if ns is None: + ns = Nt - 1 + + ns = ns + mod(ns, 2) # make sure it is even + + f_i = freq[1:-1] + s_i = spec.data[1:-1] + if ftype in ('w', 'k'): + fact = 2. * pi + s_i = s_i * fact + f_i = f_i / fact + + s_max = max(s_i) + water_depth = min(abs(spec.h), 10. ** 30) + + x = zeros((ns, cases + 1)) + + df = 1 / (ns * d_t) + + # interpolate for freq. [1:(N/2)-1]*df and create 2-sided, uncentered spectra + f = arange(1, ns / 2.) * df + f_u = hstack((0., f_i, df * ns / 2.)) + w = 2. * pi * hstack((0., f, df * ns / 2.)) + kw = w2k(w , 0., water_depth, g)[0] + s_u = hstack((0., abs(s_i) / 2., 0.)) + + + + s_i = interp(f, f_u, s_u) + nmin = (s_i > s_max * reltol).argmax() + nmax = flatnonzero(s_i > 0).max() + s_u = hstack((0., s_i, 0, s_i[(ns / 2) - 2::-1])) + del(s_i, f_u) + + # Generate standard normal random numbers for the simulations + randn = random.randn + z_r = randn((ns / 2) + 1, cases) + z_i = vstack((zeros((1, cases)), + randn((ns / 2) - 1, cases), + zeros((1, cases)))) + + amp = zeros((ns, cases), dtype=complex) + amp[0:(ns / 2 + 1), :] = z_r - 1j * z_i + del(z_r, z_i) + amp[(ns / 2 + 1):ns, :] = amp[ns / 2 - 1:0:-1, :].conj() + amp[0, :] = amp[0, :]*sqrt(2.) + amp[(ns / 2), :] = amp[(ns / 2), :]*sqrt(2.) + + + # Make simulated time series + + T = (ns - 1) * d_t + Ssqr = sqrt(s_u * df / 2.) + + + if method.startswith('apd') : # apdeterministic + # Deterministic amplitude and phase + amp[1:(ns / 2), :] = amp[1, 0] + amp[(ns / 2 + 1):ns, :] = amp[1, 0].conj() + amp = sqrt(2) * Ssqr[:, newaxis] * exp(1J * arctan2(amp.imag, amp.real)) + elif method.startswith('ade'): # adeterministic + # Deterministic amplitude and random phase + amp = sqrt(2) * Ssqr[:, newaxis] * exp(1J * arctan2(amp.imag, amp.real)) + else: + # stochastic amplitude + amp = amp * Ssqr[:, newaxis] + # Deterministic amplitude + #amp = sqrt(2)*Ssqr(:,ones(1,cases)).*exp(sqrt(-1)*atan2(imag(amp),real(amp))) + del(s_u, Ssqr) + + + x[:, 1::] = fft(amp, axis=0).real + x[:, 0] = linspace(0, T, ns) #' %(0:d_t:(np-1)*d_t).' + + + + x2 = x.copy() + + # If the spectrum does not decay rapidly enough towards zero, the + # contribution from the wave components at the upper tail can be very + # large and unphysical. + # To ensure convergence of the perturbation series, the upper tail of + # the spectrum is truncated in the calculation of sum and difference + # frequency effects. + # Find the critical wave frequency to ensure convergence. + + num_waves = 1000. # Typical number of waves in 3 hour seastate + kbar = w2k(2. * pi / Tm02, 0., water_depth)[0] + amp_max = sqrt(2 * log(num_waves)) * Hm0 / 4 #% Expected maximum amplitude for 1000 waves seastate + + f_limit_up = fnlimit * sqrt(g * tanh(kbar * water_depth) / amp_max) / (2 * pi) + f_limit_lo = sqrt(g * tanh(kbar * water_depth) * amp_max / water_depth) / (2 * pi * water_depth) + + nmax = min(flatnonzero(f <= f_limit_up).max(), nmax) + 1 + nmin = max(flatnonzero(f_limit_lo <= f).min(), nmin) + 1 + + #if isempty(nmax),nmax = np/2end + #if isempty(nmin),nmin = 2end % Must always be greater than 1 + f_limit_up = df * nmax + f_limit_lo = df * nmin + + print('2nd order frequency Limits = %g,%g' % (f_limit_lo, f_limit_up)) + + + +## if nargout>3, +## %compute the sum and frequency effects separately +## [svec, dvec] = disufq((amp.'),w,kw,min(h,10^30),g,nmin,nmax) +## svec = svec.' +## dvec = dvec.' +## +## x2s = fft(svec) % 2'nd order sum frequency component +## x2d = fft(dvec) % 2'nd order difference frequency component +## +## % 1'st order + 2'nd order component. +## x2(:,2:end) =x(:,2:end)+ real(x2s(1:np,:))+real(x2d(1:np,:)) +## else + amp = amp.T + rvec, ivec = c_library.disufq(amp.real, amp.imag, w, kw, water_depth, g, nmin, nmax, cases, ns) + + svec = rvec + 1J * ivec + svec.shape = (cases, ns) + x2o = fft(svec, axis=1).T # 2'nd order component + + + # 1'st order + 2'nd order component. + x2[:, 1::] = x[:, 1::] + x2o[0:ns, :].real + + return x2, x + + + + def stats_nl(self, h=None, moments='sk', method='approximate', g=9.81): + """ + Statistics of 2'nd order waves to the leading order. + + Parameters + ---------- + h : scalar + water depth (default self.h) + moments : string (default='sk') + composed of letters ['mvsk'] specifying which moments to compute: + 'm' = mean, + 'v' = variance, + 's' = (Fisher's) skew, + 'k' = (Fisher's) kurtosis. + method : string + 'approximate' method due to Marthinsen & Winterstein (default) + 'eigenvalue' method due to Kac and Siegert + + Skewness = kurtosis-3 = 0 for a Gaussian process. + The mean, sigma, skewness and kurtosis are determined as follows: + method == 'approximate': due to Marthinsen and Winterstein + mean = 2 * int Hd(w1,w1)*S(w1) dw1 + sigma = sqrt(int S(w1) dw1) + skew = 6 * int int [Hs(w1,w2)+Hd(w1,w2)]*S(w1)*S(w2) dw1*dw2/m0^(3/2) + kurt = (4*skew/3)^2 + + where Hs = sum frequency effects and Hd = difference frequency effects + + method == 'eigenvalue' + + mean = sum(E) + sigma = sqrt(sum(C^2)+2*sum(E^2)) + skew = sum((6*C^2+8*E^2).*E)/sigma^3 + kurt = 3+48*sum((C^2+E^2).*E^2)/sigma^4 + + where + h1 = sqrt(S*dw/2) + C = (ctranspose(V)*[h1;h1]) + and E and V is the eigenvalues and eigenvectors, respectively, of the 2'order + transfer matrix. S is the spectrum and dw is the frequency spacing of S. + + Example: + -------- + #Simulate a Transformed Gaussian process: + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap() + >>> S = Sj.tospecdata() + >>> me, va, sk, ku = S.stats_nl(moments='mvsk') + + + Hm0=7;Tp=11 + S = jonswap([],[Hm0 Tp]); [sk, ku, me]=spec2skew(S) + g=hermitetr([],[Hm0/4 sk ku me]); g2=[g(:,1), g(:,2)*Hm0/4] + ys = spec2sdat(S,15000) % Simulated in the Gaussian world + xs = gaus2dat(ys,g2) % Transformed to the real world + + See also + --------- + hermitetr, ochitr, lc2tr, dat2tr + + References: + ----------- + Langley, RS (1987) + 'A statistical analysis of nonlinear random waves' + Ocean Engineering, Vol 14, No 5, pp 389-407 + + Marthinsen, T. and Winterstein, S.R (1992) + 'On the skewness of random surface waves' + In proceedings of the 2nd ISOPE Conference, San Francisco, 14-19 june. + + Winterstein, S.R, Ude, T.C. and Kleiven, G. (1994) + 'Springing and slow drift responses: + predicted extremes and fatigue vs. simulation' + In Proc. 7th International behaviour of Offshore structures, (BOSS) + Vol. 3, pp.1-15 + """ + + #% default options + if h is None: + h = self.h + + #S = ttspec(S,'w') + w = ravel(self.args) + S = ravel(self.data) + if self.freqtype in ['f', 'w']: + vari = 't' + if self.freqtype == 'f': + w = 2. * pi * w + S = S / (2. * pi) + #m0 = self.moment(nr=0) + m0 = simps(S, w) + sa = sqrt(m0) + Nw = w.size + + Hs, Hd, Hdii = qtf(w, h, g) + + #%return + #%skew=6/sqrt(m0)^3*simpson(S.w,simpson(S.w,(Hs+Hd).*S1(:,ones(1,Nw))).*S1.') + + Hspd = trapz(trapz((Hs + Hd) * S[newaxis, :], w) * S, w) + output = [] + if method[0] == 'a': # %approx : Marthinsen, T. and Winterstein, S.R (1992) method + if 'm' in moments: + output.append(2. * trapz(Hdii * S, w)) + if 'v' in moments: + output.append(m0) + skew = 6. / sa ** 3 * Hspd + if 's' in moments: + output.append(skew) + if 'k' in moments: + output.append((4. * skew / 3.) ** 2. + 3.) + else: + raise ValueError('Unknown option!') + +## elif method[0]== 'q': #, #% quasi method +## Fn = self.nyquist_freq() +## dw = Fn/Nw +## tmp1 =sqrt(S[:,newaxis]*S[newaxis,:])*dw +## Hd = Hd*tmp1 +## Hs = Hs*tmp1 +## k = 6 +## stop = 0 +## while !stop: +## E = eigs([Hd,Hs;Hs,Hd],[],k) +## %stop = (length(find(abs(E)<1e-4))>0 | k>1200) +## %stop = (any(abs(E(:))<1e-4) | k>1200) +## stop = (any(abs(E(:))<1e-4) | k>=min(2*Nw,1200)) +## k = min(2*k,2*Nw) +## #end +## +## +## m02=2*sum(E.^2) % variance of 2'nd order contribution +## +## %Hstd = 16*trapz(S.w,(Hdii.*S1).^2) +## %Hstd = trapz(S.w,trapz(S.w,((Hs+Hd)+ 2*Hs.*Hd).*S1(:,ones(1,Nw))).*S1.') +## ma = 2*trapz(S.w,Hdii.*S1) +## %m02 = Hstd-ma^2% variance of second order part +## sa = sqrt(m0+m02) +## skew = 6/sa^3*Hspd +## kurt = (4*skew/3).^2+3 +## elif method[0]== 'e': #, % Kac and Siegert eigenvalue analysis +## Fn = self.nyquist_freq() +## dw = Fn/Nw +## tmp1 =sqrt(S[:,newaxis]*S[newaxis,:])*dw +## Hd = Hd*tmp1 +## Hs = Hs*tmp1 +## k = 6 +## stop = 0 +## +## +## while (not stop): +## [V,D] = eigs([Hd,HsHs,Hd],[],k) +## E = diag(D) +## %stop = (length(find(abs(E)<1e-4))>0 | k>=min(2*Nw,1200)) +## stop = (any(abs(E(:))<1e-4) | k>=min(2*Nw,1200)) +## k = min(2*k,2*Nw) +## #end +## +## +## h1 = sqrt(S*dw/2) +## C = (ctranspose(V)*[h1;h1]) +## +## E2 = E.^2 +## C2 = C.^2 +## +## ma = sum(E) % mean +## sa = sqrt(sum(C2)+2*sum(E2)) % standard deviation +## skew = sum((6*C2+8*E2).*E)/sa^3 % skewness +## kurt = 3+48*sum((C2+E2).*E2)/sa^4 % kurtosis + return output + + def moment(self, nr=2, even=True, j=0): + ''' Calculates spectral moments from spectrum + + Parameters + ---------- + nr : int + order of moments (recomended maximum 4) + even : bool + False for all moments, + True for only even orders + j : int + 0 or 1 + + Returns + ------- + m : list of moments + mtext : list of strings describing the elements of m, see below + + Details + ------- + Calculates spectral moments of up to order NR by use of + Simpson-integration. + + / / + mj_t^i = | w^i S(w)^(j+1) dw, or mj_x^i = | k^i S(k)^(j+1) dk + / / + + where k=w^2/gravity, i=0,1,...,NR + + The strings in output mtext have the same position in the list + as the corresponding numerical value has in output m + Notation in mtext: 'm0' is the variance, + 'm0x' is the first-order moment in x, + 'm0xx' is the second-order moment in x, + 'm0t' is the first-order moment in t, + etc. + For the calculation of moments see Baxevani et al. + + Example: + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + >>> S.moment() + ([0.56220770033914191, 0.35433180985851975], ['m0', 'm0tt']) + + References + ---------- + Baxevani A. et al. (2001) + Velocities for Random Surfaces + ''' + one_dim_spectra = ['freq', 'enc', 'k1d'] + if self.type not in one_dim_spectra: + raise ValueError('Unknown spectrum type!') + + f = ravel(self.args) + S = ravel(self.data) + if self.freqtype in ['f', 'w']: + vari = 't' + if self.freqtype == 'f': + f = 2. * pi * f + S = S / (2. * pi) + else: + vari = 'x' + S1 = abs(S) ** (j + 1.) + m = [simps(S1, x=f)] + mtxt = 'm%d' % j + mtext = [mtxt] + step = mod(even, 2) + 1 + df = f ** step + for i in range(step, nr + 1, step): + S1 = S1 * df + m.append(simps(S1, x=f)) + mtext.append(mtxt + vari * i) + return m, mtext + + def nyquist_freq(self): + """ + Return Nyquist frequency + """ + return self.args[-1] + + def sampling_period(self): + ''' Returns sampling interval from Nyquist frequency of spectrum + + Returns + --------- + dT : scalar + sampling interval, unit: + [m] if wave number spectrum, + [s] otherwise + + Let wm be maximum frequency/wave number in spectrum, + then dT=pi/wm if angular frequency, dT=1/(2*wm) if natural frequency (Hz) + + Example + ------- + S = jonswap + dt = spec2dt(S) + + See also + ''' + + if self.freqtype in 'f': + wmdt = 0.5 # Nyquist to sampling interval factor + else: # ftype == w og ftype == k + wmdt = pi + + wm = self.args[-1] #Nyquist frequency + dt = wmdt / wm #sampling interval = 1/Fs + return dt + + def resample(self, dt=None, Nmin=0, Nmax=2 ** 13 + 1, method='stineman'): + ''' + Interpolate and zero-padd spectrum to change Nyquist freq. + + Parameters + ---------- + dt : scalar + wanted sampling interval (default as given by S, see spec2dt) + unit: [s] if frequency-spectrum, [m] if wave number spectrum + Nmin : scalar + minimum number of frequencies. + Nmax : scalar + minimum number of frequencies + method : string + interpolation method (options are 'linear', 'cubic' or 'stineman') + + To be used before simulation (e.g. spec2sdat) or evaluation of covariance + function (spec2cov) to directly get wanted sampling interval. + The input spectrum is interpolated and padded with zeros to reach + the right max-frequency, w(end)=pi/dt, f(end)=1/(2*dt), or k(end)=pi/dt. + The objective is that output frequency grid should be at least as dense + as the input grid, have equidistant spacing and length equal to + 2^k+1 (>=Nmin). If the max frequency is changed, the number of points + in the spectrum is maximized to 2^13+1. + + Note: Also zero-padding down to zero freq, if S does not start there. + If empty input dt, this is the only effect. + + See also + -------- + spec2cov, spec2sdat, covinterp, spec2dt + ''' + + ftype = self.freqtype + w = self.args.ravel() + n = w.size + + #%doInterpolate = 0 + + if ftype == 'f': + Cnf2dt = 0.5 # Nyquist to sampling interval factor + else: #% ftype == w og ftype == k + Cnf2dt = pi + + wnOld = w[-1] # Old Nyquist frequency + dTold = Cnf2dt / wnOld # sampling interval=1/Fs + + + if dt is None: + dt = dTold + + # Find how many points that is needed + nfft = 2 ** nextpow2(max(n - 1, Nmin - 1)) + dttest = dTold * (n - 1) / nfft + + while (dttest > dt) and (nfft < Nmax - 1): + nfft = nfft * 2 + dttest = dTold * (n - 1) / nfft + + nfft = nfft + 1 + + wnNew = Cnf2dt / dt #% New Nyquist frequency + dWn = wnNew - wnOld + doInterpolate = dWn > 0 or w[1] > 0 or (nfft != n) or dt != dTold or any(abs(diff(w, axis=0)) > 1.0e-8) + + if doInterpolate > 0: + S1 = self.data + + dw = min(diff(w)) + + if dWn > 0: + #% add a zero just above old max-freq, and a zero at new max-freq + #% to get correct interpolation there + Nz = 1 + (dWn > dw) # % Number of zeros to add + if Nz == 2: + w = hstack((w, wnOld + dw, wnNew)) + else: + w = hstack((w, wnNew)) + + S1 = hstack((S1, zeros(Nz))) + + if w[0] > 0: + #% add a zero at freq 0, and, if there is space, a zero just below min-freq + Nz = 1 + (w[0] > dw) #% Number of zeros to add + if Nz == 2: + w = hstack((0, w[0] - dw, w)) + else: + w = hstack((0, w)) + + S1 = hstack((zeros(Nz), S1)) + + + #% Do a final check on spacing in order to check that the gridding is + #% sufficiently dense: + #np1 = S1.size + dwMin = finfo(float).max + #%wnc = min(wnNew,wnOld-1e-5) + wnc = wnNew + specfun = lambda xi : stineman_interp(xi, w, S1) + + x, unused_y = discretize(specfun, 0, wnc) + dwMin = minimum(min(diff(x)), dwMin) + + newNfft = 2 ** nextpow2(ceil(wnNew / dwMin)) + 1 + if newNfft > nfft: + if (nfft <= 2 ** 15 + 1) and (newNfft > 2 ** 15 + 1): + warnings.warn('Spectrum matrix is very large (>33k). Memory problems may occur.') + + nfft = newNfft + self.args = linspace(0, wnNew, nfft) + if method == 'stineman': + self.data = stineman_interp(self.args, w, S1) + else: + intfun = interpolate.interp1d(w, S1, kind=method) + self.data = intfun(self.args) + self.data = self.data.clip(0) # clip negative values to 0 + + def normalize(self, gravity=9.81): + ''' + Normalize a spectral density such that m0=m2=1 + + Paramter + -------- + gravity=9.81 + + Notes + ----- + Normalization performed such that + INT S(freq) dfreq = 1 INT freq^2 S(freq) dfreq = 1 + where integration limits are given by freq and S(freq) is the + spectral density; freq can be frequency or wave number. + The normalization is defined by + A=sqrt(m0/m2); B=1/A/m0; freq'=freq*A; S(freq')=S(freq)*B + + If S is a directional spectrum then a normalized gravity (.g) is added + to Sn, such that mxx normalizes to 1, as well as m0 and mtt. + (See spec2mom for notation of moments) + + If S is complex-valued cross spectral density which has to be + normalized, then m0, m2 (suitable spectral moments) should be given. + + Example: + ------- + S = jonswap + [Sn,mn4] = specnorm(S) + mts = spec2mom(S,2) % Should be equal to one! + ''' + mom, unused_mtext = self.moment(nr=4, even=True) + m0 = mom[0] + m2 = mom[1] + m4 = mom[2] + + SM0 = sqrt(m0) + SM2 = sqrt(m2) + A = SM0 / SM2 + B = SM2 / (SM0 * m0) + + if self.freqtype == 'f': + self.args = self.args * A / 2 / pi + self.data = self.data * B * 2 * pi + elif self.freqtype == 'w' : + self.args = self.args * A + self.data = self.data * B + m02 = m4 / gravity ** 2 + m20 = m02 + self.g = gravity * sqrt(m0 * m20) / m2 + self.A = A + self.norm = True + self.date = now() + + def bandwidth(self, factors=0): + ''' + Return some spectral bandwidth and irregularity factors + + Parameters + ----------- + factors : array-like + Input vector 'factors' correspondence: + 0 alpha=m2/sqrt(m0*m4) (irregularity factor) + 1 eps2 = sqrt(m0*m2/m1^2-1) (narrowness factor) + 2 eps4 = sqrt(1-m2^2/(m0*m4))=sqrt(1-alpha^2) (broadness factor) + 3 Qp=(2/m0^2)int_0^inf f*S(f)^2 df (peakedness factor) + + Returns + -------- + bw : arraylike + vector of bandwidth factors + Order of output is the same as order in 'factors' + + Example: + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + >>> S.bandwidth([0,1,2,3]) + array([ 0.65354446, 0.3975428 , 0.75688813, 2.00207912]) + ''' + +# if self.freqtype in 'k': +# vari = 'k' +# else: +# vari = 'w' + + m, unused_mtxt = self.moment(nr=4, even=False) + + fact = atleast_1d(factors) + alpha = m[2] / sqrt(m[0] * m[4]) + eps2 = sqrt(m[0] * m[2] / m[1] ** 2. - 1.) + eps4 = sqrt(1. - m[2] ** 2. / m[0] / m[4]) + f = self.args + S = self.data + Qp = 2 / m[0] ** 2. * simps(f * S ** 2, x=f) + bw = array([alpha, eps2, eps4, Qp]) + return bw[fact] + + def characteristic(self, fact='Hm0', T=1200, g=9.81): + """ + Returns spectral characteristics and their covariance + + Parameters + ---------- + fact : vector with factor integers or a string or a list of strings + defining spectral characteristic, see description below. + T : scalar + recording time (sec) (default 1200 sec = 20 min) + g : scalar + acceleration of gravity [m/s^2] + + Returns + ------- + ch : vector + of spectral characteristics + R : matrix + of the corresponding covariances given T + chtext : a list of strings + describing the elements of ch, see example. + + + Description + ------------ + If input spectrum is of wave number type, output are factors for + corresponding 'k1D', else output are factors for 'freq'. + Input vector 'factors' correspondence: + 1 Hm0 = 4*sqrt(m0) Significant wave height + 2 Tm01 = 2*pi*m0/m1 Mean wave period + 3 Tm02 = 2*pi*sqrt(m0/m2) Mean zero-crossing period + 4 Tm24 = 2*pi*sqrt(m2/m4) Mean period between maxima + 5 Tm_10 = 2*pi*m_1/m0 Energy period + 6 Tp = 2*pi/{w | max(S(w))} Peak period + 7 Ss = 2*pi*Hm0/(g*Tm02^2) Significant wave steepness + 8 Sp = 2*pi*Hm0/(g*Tp^2) Average wave steepness + 9 Ka = abs(int S(w)*exp(i*w*Tm02) dw ) /m0 Groupiness parameter + 10 Rs = (S(0.092)+S(0.12)+S(0.15)/(3*max(S(w))) Quality control parameter + 11 Tp1 = 2*pi*int S(w)^4 dw Peak Period (robust estimate for Tp) + ------------------ + int w*S(w)^4 dw + + 12 alpha = m2/sqrt(m0*m4) Irregularity factor + 13 eps2 = sqrt(m0*m2/m1^2-1) Narrowness factor + 14 eps4 = sqrt(1-m2^2/(m0*m4))=sqrt(1-alpha^2) Broadness factor + 15 Qp = (2/m0^2)int_0^inf w*S(w)^2 dw Peakedness factor + + Order of output is same as order in 'factors' + The covariances are computed with a Taylor expansion technique + and is currently only available for factors 1, 2, and 3. Variances + are also available for factors 4,5,7,12,13,14 and 15 + + Quality control: + ---------------- + Critical value for quality control parameter Rs is Rscrit = 0.02 + for surface displacement records and Rscrit=0.0001 for records of + surface acceleration or slope. If Rs > Rscrit then probably there + are something wrong with the lower frequency part of S. + + Ss may be used as an indicator of major malfunction, by checking that + it is in the range of 1/20 to 1/16 which is the usual range for + locally generated wind seas. + + Examples: + --------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=5) + >>> S = Sj.tospecdata() #Make spectrum ob + >>> S.characteristic(1) + (array([ 8.59007646]), array([[ 0.03040216]]), ['Tm01']) + + >>> [ch, R, txt] = S.characteristic([1,2,3]) # fact a vector of integers + >>> S.characteristic('Ss') # fact a string + (array([ 0.04963112]), array([[ 2.63624782e-06]]), ['Ss']) + + >>> S.characteristic(['Hm0','Tm02']) # fact a list of strings + (array([ 4.99833578, 8.03139757]), array([[ 0.05292989, 0.02511371], + [ 0.02511371, 0.0274645 ]]), ['Hm0', 'Tm02']) + + See also + --------- + bandwidth, + moment + + References + ---------- + Krogstad, H.E., Wolf, J., Thompson, S.P., and Wyatt, L.R. (1999) + 'Methods for intercomparison of wave measurements' + Coastal Enginering, Vol. 37, pp. 235--257 + + Krogstad, H.E. (1982) + 'On the covariance of the periodogram' + Journal of time series analysis, Vol. 3, No. 3, pp. 195--207 + + Tucker, M.J. (1993) + 'Recommended standard for wave data sampling and near-real-time processing' + Ocean Engineering, Vol.20, No.5, pp. 459--474 + + Young, I.R. (1999) + "Wind generated ocean waves" + Elsevier Ocean Engineering Book Series, Vol. 2, pp 239 + """ + + #% TODO % Need more checking on computing the variances for Tm24,alpha, eps2 and eps4 + #% TODO % Covariances between Tm24,alpha, eps2 and eps4 variables are also needed + + tfact = dict(Hm0=0, Tm01=1, Tm02=2, Tm24=3, Tm_10=4, Tp=5, Ss=6, Sp=7, Ka=8, + Rs=9, Tp1=10, Alpha=11, Eps2=12, Eps4=13, Qp=14) + tfact1 = ('Hm0', 'Tm01', 'Tm02', 'Tm24', 'Tm_10', 'Tp', 'Ss', 'Sp', 'Ka', + 'Rs', 'Tp1', 'Alpha', 'Eps2', 'Eps4', 'Qp') + + if isinstance(fact, str): + fact = list((fact,)) + if isinstance(fact, (list, tuple)): + nfact = [] + for k in fact: + if isinstance(k, str): + nfact.append(tfact.get(k.capitalize(), 15)) + else: + nfact.append(k) + else: + nfact = fact + + nfact = atleast_1d(nfact) + + if any((nfact > 14) | (nfact < 0)): + raise ValueError('Factor outside range (0,...,14)') + + #vari = self.freqtype + + f = self.args.ravel() + S1 = self.data.ravel() + m, unused_mtxt = self.moment(nr=4, even=False) + + #% moments corresponding to freq in Hz + for k in range(1, 5): + m[k] = m[k] / (2 * pi) ** k + + #pi = np.pi + ind = flatnonzero(f > 0) + m.append(simps(S1[ind] / f[ind], f[ind]) * 2. * pi) # % = m_1 + m_10 = simps(S1[ind] ** 2 / f[ind], f[ind]) * (2 * pi) ** 2 / T # % = COV(m_1,m0|T=t0) + m_11 = simps(S1[ind] ** 2. / f[ind] ** 2, f[ind]) * (2 * pi) ** 3 / T #% = COV(m_1,m_1|T=t0) + + #sqrt = np.sqrt + #% Hm0 Tm01 Tm02 Tm24 Tm_10 + Hm0 = 4. * sqrt(m[0]) + Tm01 = m[0] / m[1] + Tm02 = sqrt(m[0] / m[2]) + Tm24 = sqrt(m[2] / m[4]) + Tm_10 = m[5] / m[0] + + Tm12 = m[1] / m[2] + + ind = S1.argmax() + maxS = S1[ind] + #[maxS ind] = max(S1) + Tp = 2. * pi / f[ind] # % peak period /length + Ss = 2. * pi * Hm0 / g / Tm02 ** 2 # % Significant wave steepness + Sp = 2. * pi * Hm0 / g / Tp ** 2 # % Average wave steepness + Ka = abs(simps(S1 * exp(1J * f * Tm02), f)) / m[0] #% groupiness factor + + #% Quality control parameter + #% critical value is approximately 0.02 for surface displacement records + #% If Rs>0.02 then there are something wrong with the lower frequency part + #% of S. + Rs = np.sum(interp(r_[0.0146, 0.0195, 0.0244] * 2 * pi, f, S1)) / 3. / maxS + Tp2 = 2 * pi * simps(S1 ** 4, f) / simps(f * S1 ** 4, f) + + + alpha1 = Tm24 / Tm02 # % m(3)/sqrt(m(1)*m(5)) + eps2 = sqrt(Tm01 / Tm12 - 1.)# % sqrt(m(1)*m(3)/m(2)^2-1) + eps4 = sqrt(1. - alpha1 ** 2) # % sqrt(1-m(3)^2/m(1)/m(5)) + Qp = 2. / m[0] ** 2 * simps(f * S1 ** 2, f) + + ch = r_[Hm0, Tm01, Tm02, Tm24, Tm_10, Tp, Ss, Sp, Ka, Rs, Tp2, alpha1, eps2, eps4, Qp] + + #% Select the appropriate values + ch = ch[nfact] + chtxt = [tfact1[i] for i in nfact] + + #if nargout>1, + #% covariance between the moments: + #%COV(mi,mj |T=t0) = int f^(i+j)*S(f)^2 df/T + mij, unused_mijtxt = self.moment(nr=8, even=False, j=1) + for ix, tmp in enumerate(mij): + mij[ix] = tmp / T / ((2. * pi) ** (ix - 1.0)) + + + #% and the corresponding variances for + #%{'hm0', 'tm01', 'tm02', 'tm24', 'tm_10','tp','ss', 'sp', 'ka', 'rs', 'tp1','alpha','eps2','eps4','qp'} + R = r_[4 * mij[0] / m[0], + mij[0] / m[1] ** 2. - 2. * m[0] * mij[1] / m[1] ** 3. + m[0] ** 2. * mij[2] / m[1] ** 4., + 0.25 * (mij[0] / (m[0] * m[2]) - 2. * mij[2] / m[2] ** 2 + m[0] * mij[4] / m[2] ** 3), + 0.25 * (mij[4] / (m[2] * m[4]) - 2 * mij[6] / m[4] ** 2 + m[2] * mij[8] / m[4] ** 3) , + m_11 / m[0] ** 2 + (m[5] / m[0] ** 2) ** 2 * mij[0] - 2 * m[5] / m[0] ** 3 * m_10, + nan, + (8 * pi / g) ** 2 * (m[2] ** 2 / (4 * m[0] ** 3) * mij[0] + mij[4] / m[0] - m[2] / m[0] ** 2 * mij[2]), + nan * ones(4), + m[2] ** 2 * mij[0] / (4 * m[0] ** 3 * m[4]) + mij[4] / (m[0] * m[4]) + mij[8] * m[2] ** 2 / (4 * m[0] * m[4] ** 3) - + m[2] * mij[2] / (m[0] ** 2 * m[4]) + m[2] ** 2 * mij[4] / (2 * m[0] ** 2 * m[4] ** 2) - m[2] * mij[6] / m[0] / m[4] ** 2, + (m[2] ** 2 * mij[0] / 4 + (m[0] * m[2] / m[1]) ** 2 * mij[2] + m[0] ** 2 * mij[4] / 4 - m[2] ** 2 * m[0] * mij[1] / m[1] + + m[0] * m[2] * mij[2] / 2 - m[0] ** 2 * m[2] / m[1] * mij[3]) / eps2 ** 2 / m[1] ** 4, + (m[2] ** 2 * mij[0] / (4 * m[0] ** 2) + mij[4] + m[2] ** 2 * mij[8] / (4 * m[4] ** 2) - m[2] * mij[2] / m[0] + + m[2] ** 2 * mij[4] / (2 * m[0] * m[4]) - m[2] * mij[6] / m[4]) * m[2] ** 2 / (m[0] * m[4] * eps4) ** 2, + nan] + + #% and covariances by a taylor expansion technique: + #% Cov(Hm0,Tm01) Cov(Hm0,Tm02) Cov(Tm01,Tm02) + S0 = r_[ 2. / (sqrt(m[0]) * m[1]) * (mij[0] - m[0] * mij[1] / m[1]), + 1. / sqrt(m[2]) * (mij[0] / m[0] - mij[2] / m[2]), + 1. / (2 * m[1]) * sqrt(m[0] / m[2]) * (mij[0] / m[0] - mij[2] / m[2] - mij[1] / m[1] + m[0] * mij[3] / (m[1] * m[2]))] + + R1 = ones((15, 15)) + R1[:, :] = nan + for ix, Ri in enumerate(R): + R1[ix, ix] = Ri + + + + R1[0, 2:4] = S0[:2] + R1[1, 2] = S0[2] + for ix in [0, 1]: #%make lower triangular equal to upper triangular part + R1[ix + 1:, ix] = R1[ix, ix + 1:] + + + R = R[nfact] + R1 = R1[nfact, :][:, nfact] + + + #% Needs further checking: + #% Var(Tm24)= 0.25*(mij[4]/(m[2]*m[4])-2*mij[6]/m[4]**2+m[2]*mij[8]/m[4]**3) ... + return ch, R1, chtxt + + def setlabels(self): + ''' Set automatic title, x-,y- and z- labels on SPECDATA object + + based on type, angletype, freqtype + ''' + + N = len(self.type) + if N == 0: + raise ValueError('Object does not appear to be initialized, it is empty!') + + labels = ['', '', ''] + if self.type.endswith('dir'): + title = 'Directional Spectrum' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[2] = 'S(w,\theta) [m^2 s / rad^2]' + else: + labels[0] = 'Frequency [Hz]' + labels[2] = 'S(f,\theta) [m^2 s / rad]' + + if self.angletype.startswith('r'): + labels[1] = 'Wave directions [rad]' + elif self.angletype.startswith('d'): + labels[1] = 'Wave directions [deg]' + elif self.type.endswith('freq'): + title = 'Spectral density' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[1] = 'S(w) [m^2 s/ rad]' + else: + labels[0] = 'Frequency [Hz]' + labels[1] = 'S(f) [m^2 s]' + else: + title = 'Wave Number Spectrum' + labels[0] = 'Wave number [rad/m]' + if self.type.endswith('k1d'): + labels[1] = 'S(k) [m^3/ rad]' + elif self.type.endswith('k2d'): + labels[1] = labels[0] + labels[2] = 'S(k1,k2) [m^4/ rad^2]' + else: + raise ValueError('Object does not appear to be initialized, it is empty!') + if self.norm != 0: + title = 'Normalized ' + title + labels[0] = 'Normalized ' + labels[0].split('[')[0] + if not self.type.endswith('dir'): + labels[1] = labels[1].split('[')[0] + labels[2] = labels[2].split('[')[0] + + self.labels.title = title + self.labels.xlab = labels[0] + self.labels.ylab = labels[1] + self.labels.zlab = labels[2] + +class SpecData2D(WafoData): + """ Container class for 2D spectrum data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + + type : string + spectrum type (default 'freq') + freqtype : letter + frequency type (default 'w') + angletype : string + angle type of directional spectrum (default 'radians') + + Examples + -------- + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=3) + >>> w = np.linspace(0,4,256) + >>> S = SpecData1D(Sj(w),w) #Make spectrum object from numerical values + + See also + -------- + WafoData + CovData + """ + + def __init__(self, *args, **kwds): + super(SpecData2D, self).__init__(*args, **kwds) + + self.name = 'WAFO Spectrum Object' + self.type = 'freq' + self.freqtype = 'w' + self.angletype = '' + self.h = inf + self.tr = None + self.phi = 0. + self.v = 0. + self.norm = 0 + somekeys = ['angletype', 'phi', 'name', 'h', 'tr', 'freqtype', 'v', 'type', 'norm'] + + self.__dict__.update(sub_dict_select(kwds, somekeys)) + + if self.type.endswith('dir') and self.angletype == '': + self.angletype = 'radians' + + self.setlabels() + + def toacf(self): + pass + def sim(self): + pass + def sim_nl(self): + pass + def rotate(self): + pass + def moment(self, nr=2, vari='xt', even=True): + ''' + Calculates spectral moments from spectrum + + Parameters + ---------- + nr : int + order of moments (maximum 4) + vari : string + variables in model, optional when two-dim.spectrum, + string with 'x' and/or 'y' and/or 't' + even : bool + False for all moments, + True for only even orders + + Returns + ------- + m : list of moments + mtext : list of strings describing the elements of m, see below + + Details + ------- + Calculates spectral moments of up to order four by use of + Simpson-integration. + + // + m_jkl=|| k1^j*k2^k*w^l S(w,th) dw dth + // + + where k1=w^2/gravity*cos(th-phi), k2=w^2/gravity*sin(th-phi) + and phi is the angle of the rotation in S.phi. If the spectrum + has field .g, gravity is replaced by S.g. + + The strings in output mtext have the same position in the cell array + as the corresponding numerical value has in output m + Notation in mtext: 'm0' is the variance, + 'mx' is the first-order moment in x, + 'mxx' is the second-order moment in x, + 'mxt' is the second-order cross moment between x and t, + 'myyyy' is the fourth-order moment in y + etc. + For the calculation of moments see Baxevani et al. + + Example: + S=demospec('dir') + [m,mtext]=spec2mom(S,2,'xyt') + + References + ---------- + Baxevani A. et al. (2001) + Velocities for Random Surfaces + ''' + +##% Tested on: Matlab 6.0 +##% Tested on: Matlab 5.3 +##% History: +##% Revised by I.R. 04.04.2001: Introducing the rotation angle phi. +##% Revised by A.B. 23.05.2001: Correcting 'mxxyy' and introducing +##% 'mxxyt','mxyyt' and 'mxytt'. +##% Revised by A.B. 21.10.2001: Correcting 'mxxyt'. +##% Revised by A.B. 21.10.2001: Adding odd-order moments. +##% By es 27.08.1999 + + + pi = pi + two_dim_spectra = ['dir', 'encdir', 'k2d'] + if self.type not in two_dim_spectra: + raise ValueError('Unknown 2D spectrum type!') + +## if (vari==None and nr<=1: +## vari='x' +## elif vari==None: +## vari='xt' +## else #% secure the mutual order ('xyt') +## vari=''.join(sorted(vari.lower())) +## Nv=len(vari) +## +## if vari[0]=='t' and Nv>1: +## vari = vari[1::]+ vari[0] +## +## Nv = len(vari) +## +## if not self.type.endswith('dir'): +## S1 = self.tospecdata(self.type[:-2]+'dir') +## else: +## S1 = self +## w = ravel(S1.args[0]) +## theta = S1.args[1]-S1.phi +## S = S1.data +## Sw = simps(S,x=theta) +## m = [simps(Sw,x=w)] +## mtext=['m0'] +## +## if nr>0: +## +## nw=w.size +## if strcmpi(vari(1),'x') +## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).' +## % integral S*cos(th) dth +## end +## if strcmpi(vari(1),'y') +## Ss=simpson(th,S1.S.*(sin(th)*ones(1,nw))).' +## % integral S*sin(th) dth +## if strcmpi(vari(1),'x') +## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).' +## end +## end +## if ~isfield(S1,'g') +## S1.g=gravity +## end +## kx=w.^2/S1.g(1) % maybe different normalization in x and y => diff. g +## ky=w.^2/S1.g(end) +## +## if Nv>=1 +## switch vari +## case 'x' +## vec = kx.*Sc +## mtext(end+1)={'mx'} +## case 'y' +## vec = ky.*Ss +## mtext(end+1)={'my'} +## case 't' +## vec = w.*Sw +## mtext(end+1)={'mt'} +## end +## else +## vec = [kx.*Sc ky.*Ss w*Sw] +## mtext(end+(1:3))={'mx', 'my', 'mt'} +## end +## if nr>1 +## if strcmpi(vari(1),'x') +## Sc=simpson(th,S1.S.*(cos(th)*ones(1,nw))).' +## % integral S*cos(th) dth +## Sc2=simpson(th,S1.S.*(cos(th).^2*ones(1,nw))).' +## % integral S*cos(th)^2 dth +## end +## if strcmpi(vari(1),'y')||strcmpi(vari(2),'y') +## Ss=simpson(th,S1.S.*(sin(th)*ones(1,nw))).' +## % integral S*sin(th) dth +## Ss2=simpson(th,S1.S.*(sin(th).^2*ones(1,nw))).' +## % integral S*sin(th)^2 dth +## if strcmpi(vari(1),'x') +## Scs=simpson(th,S1.S.*((cos(th).*sin(th))*ones(1,nw))).' +## % integral S*cos(th)*sin(th) dth +## end +## end +## if ~isfield(S1,'g') +## S1.g=gravity +## end +## +## if Nv==2 +## switch vari +## case 'xy' +## vec=[kx.*Sc ky.*Ss kx.^2.*Sc2 ky.^2.*Ss2 kx.*ky.*Scs] +## mtext(end+(1:5))={'mx','my','mxx', 'myy', 'mxy'} +## case 'xt' +## vec=[kx.*Sc w.*Sw kx.^2.*Sc2 w.^2.*Sw kx.*w.*Sc] +## mtext(end+(1:5))={'mx','mt','mxx', 'mtt', 'mxt'} +## case 'yt' +## vec=[ky.*Ss w.*Sw ky.^2.*Ss2 w.^2.*Sw ky.*w.*Ss] +## mtext(end+(1:5))={'my','mt','myy', 'mtt', 'myt'} +## end +## else +## vec=[kx.*Sc ky.*Ss w.*Sw kx.^2.*Sc2 ky.^2.*Ss2 w.^2.*Sw kx.*ky.*Scs kx.*w.*Sc ky.*w.*Ss] +## mtext(end+(1:9))={'mx','my','mt','mxx', 'myy', 'mtt', 'mxy', 'mxt', 'myt'} +## end +## if nr>3 +## if strcmpi(vari(1),'x') +## Sc3=simpson(th,S1.S.*(cos(th).^3*ones(1,nw))).' +## % integral S*cos(th)^3 dth +## Sc4=simpson(th,S1.S.*(cos(th).^4*ones(1,nw))).' +## % integral S*cos(th)^4 dth +## end +## if strcmpi(vari(1),'y')||strcmpi(vari(2),'y') +## Ss3=simpson(th,S1.S.*(sin(th).^3*ones(1,nw))).' +## % integral S*sin(th)^3 dth +## Ss4=simpson(th,S1.S.*(sin(th).^4*ones(1,nw))).' +## % integral S*sin(th)^4 dth +## if strcmpi(vari(1),'x') %both x and y +## Sc2s=simpson(th,S1.S.*((cos(th).^2.*sin(th))*ones(1,nw))).' +## % integral S*cos(th)^2*sin(th) dth +## Sc3s=simpson(th,S1.S.*((cos(th).^3.*sin(th))*ones(1,nw))).' +## % integral S*cos(th)^3*sin(th) dth +## Scs2=simpson(th,S1.S.*((cos(th).*sin(th).^2)*ones(1,nw))).' +## % integral S*cos(th)*sin(th)^2 dth +## Scs3=simpson(th,S1.S.*((cos(th).*sin(th).^3)*ones(1,nw))).' +## % integral S*cos(th)*sin(th)^3 dth +## Sc2s2=simpson(th,S1.S.*((cos(th).^2.*sin(th).^2)*ones(1,nw))).' +## % integral S*cos(th)^2*sin(th)^2 dth +## end +## end +## if Nv==2 +## switch vari +## case 'xy' +## vec=[vec kx.^4.*Sc4 ky.^4.*Ss4 kx.^3.*ky.*Sc3s ... +## kx.^2.*ky.^2.*Sc2s2 kx.*ky.^3.*Scs3] +## mtext(end+(1:5))={'mxxxx','myyyy','mxxxy','mxxyy','mxyyy'} +## case 'xt' +## vec=[vec kx.^4.*Sc4 w.^4.*Sw kx.^3.*w.*Sc3 ... +## kx.^2.*w.^2.*Sc2 kx.*w.^3.*Sc] +## mtext(end+(1:5))={'mxxxx','mtttt','mxxxt','mxxtt','mxttt'} +## case 'yt' +## vec=[vec ky.^4.*Ss4 w.^4.*Sw ky.^3.*w.*Ss3 ... +## ky.^2.*w.^2.*Ss2 ky.*w.^3.*Ss] +## mtext(end+(1:5))={'myyyy','mtttt','myyyt','myytt','myttt'} +## end +## else +## vec=[vec kx.^4.*Sc4 ky.^4.*Ss4 w.^4.*Sw kx.^3.*ky.*Sc3s ... +## kx.^2.*ky.^2.*Sc2s2 kx.*ky.^3.*Scs3 kx.^3.*w.*Sc3 ... +## kx.^2.*w.^2.*Sc2 kx.*w.^3.*Sc ky.^3.*w.*Ss3 ... +## ky.^2.*w.^2.*Ss2 ky.*w.^3.*Ss kx.^2.*ky.*w.*Sc2s ... +## kx.*ky.^2.*w.*Scs2 kx.*ky.*w.^2.*Scs] +## mtext(end+(1:15))={'mxxxx','myyyy','mtttt','mxxxy','mxxyy',... +## 'mxyyy','mxxxt','mxxtt','mxttt','myyyt','myytt','myttt','mxxyt','mxyyt','mxytt'} +## +## end % if Nv==2 ... else ... +## end % if nr>3 +## end % if nr>1 +## m=[m simpson(w,vec)] +## end % if nr>0 +## % end %%if Nv==1... else... to be removed +## end % ... else two-dim spectrum + + + + def interp(self): + pass + def normalize(self): + pass + def bandwidth(self): + pass + def setlabels(self): + ''' Set automatic title, x-,y- and z- labels on SPECDATA object + + based on type, angletype, freqtype + ''' + + N = len(self.type) + if N == 0: + raise ValueError('Object does not appear to be initialized, it is empty!') + + labels = ['', '', ''] + if self.type.endswith('dir'): + title = 'Directional Spectrum' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[2] = 'S(w,\theta) [m**2 s / rad**2]' + else: + labels[0] = 'Frequency [Hz]' + labels[2] = 'S(f,\theta) [m**2 s / rad]' + + if self.angletype.startswith('r'): + labels[1] = 'Wave directions [rad]' + elif self.angletype.startswith('d'): + labels[1] = 'Wave directions [deg]' + elif self.type.endswith('freq'): + title = 'Spectral density' + if self.freqtype.startswith('w'): + labels[0] = 'Frequency [rad/s]' + labels[1] = 'S(w) [m**2 s/ rad]' + else: + labels[0] = 'Frequency [Hz]' + labels[1] = 'S(f) [m**2 s]' + else: + title = 'Wave Number Spectrum' + labels[0] = 'Wave number [rad/m]' + if self.type.endswith('k1d'): + labels[1] = 'S(k) [m**3/ rad]' + elif self.type.endswith('k2d'): + labels[1] = labels[0] + labels[2] = 'S(k1,k2) [m**4/ rad**2]' + else: + raise ValueError('Object does not appear to be initialized, it is empty!') + if self.norm != 0: + title = 'Normalized ' + title + labels[0] = 'Normalized ' + labels[0].split('[')[0] + if not self.type.endswith('dir'): + labels[1] = labels[1].split('[')[0] + labels[2] = labels[2].split('[')[0] + + self.labels.title = title + self.labels.xlab = labels[0] + self.labels.ylab = labels[1] + self.labels.zlab = labels[2] + +def test_specdata(): + import wafo.spectrum.models as sm + Sj = sm.Jonswap() + S = Sj.tospecdata() + me, va, sk, ku = S.stats_nl(moments='mvsk') + +def main(): + import matplotlib + matplotlib.interactive(True) + from wafo.spectrum import models as sm + + w = linspace(0, 3, 100) + Sj = sm.Jonswap() + S = Sj.tospecdata() + + f = S.to_t_pdf(pdef='Tc', paramt=(0, 10, 51), speed=7) + f.err + f.plot() + f.show() + #pdfplot(f) + #hold on, + #plot(f.x{:}, f.f+f.err,'r',f.x{:}, f.f-f.err) estimated error bounds + #hold off + #S = SpecData1D(Sj(w),w) + R = S.tocovdata(nr=1) + S1 = S.copy() + Si = R.tospecdata() + ns = 5000 + dt = .2 + x1 = S.sim_nl(ns=ns, dt=dt) + x2 = TimeSeries(x1[:, 1], x1[:, 0]) + R = x2.tocovdata(lag=100) + R.plot() + + S.plot('ro') + t = S.moment() + t1 = S.bandwidth([0, 1, 2, 3]) + S1 = S.copy() + S1.resample(dt=0.3, method='cubic') + S1.plot('k+') + x = S1.sim(ns=100) + import pylab + pylab.clf() + pylab.plot(x[:, 0], x[:, 1]) + pylab.show() + + pylab.close('all') + print('done') + +if __name__ == '__main__': + if True: #False : # + import doctest + doctest.testmod() + else: + main() diff --git a/wafo/spectrum/dispersion_relation.py b/wafo/spectrum/dispersion_relation.py new file mode 100755 index 0000000..d8ef652 --- /dev/null +++ b/wafo/spectrum/dispersion_relation.py @@ -0,0 +1,203 @@ +""" +Dispersion relation module +-------------------------- +k2w - Translates from wave number to frequency +w2k - Translates from frequency to wave number +""" +import warnings +#import numpy as np +from numpy import (atleast_1d, sqrt, zeros_like, arctan2, where, tanh, any, #@UnresolvedImport + sin, cos, sign, inf, flatnonzero, finfo, cosh, abs) #@UnresolvedImport + +__all__ = ['k2w', 'w2k'] + +def k2w(k1, k2=0e0, h=inf, g=9.81, u1=0e0, u2=0e0): + ''' Translates from wave number to frequency + using the dispersion relation + + Parameters + ---------- + k1 : array-like + wave numbers [rad/m]. + k2 : array-like, optional + second dimension wave number + h : real scalar, optional + water depth [m]. + g : real scalar, optional + acceleration of gravity, see gravity + u1, u2 : real scalars, optional + current velocity [m/s] along dimension 1 and 2. + note: when u1!=0 | u2!=0 then theta is not calculated correctly + + Returns + ------- + w : ndarray + angular frequency [rad/s]. + theta : ndarray + direction [rad]. + + Dispersion relation + ------------------- + w = sqrt(g*K*tanh(K*h)) ( 0 < w < inf) + theta = arctan2(k2,k1) (-pi < theta < pi) + where + K = sqrt(k1**2+k2**2) + + The shape of w and theta is the common shape of k1 and k2 according to the + numpy broadcasting rules. + + See also + -------- + w2k + + Example + ------- + >>> from numpy import arange + >>> k2w(arange(0.01,.5,0.2))[0] + array([ 0.3132092 , 1.43530485, 2.00551739]) + >>> k2w(arange(0.01,.5,0.2),h=20)[0] + array([ 0.13914927, 1.43498213, 2.00551724]) + ''' + + k1i, k2i, hi, gi, u1i, u2i = atleast_1d(k1, k2, h, g, u1, u2) + + if k1i.size == 0: + return zeros_like(k1i) + ku1 = k1i*u1i + ku2 = k2i*u2i + + theta = arctan2(k2, k1) + + k = sqrt(k1i**2+k2i**2) + w = where(k>0, ku1+ku2+sqrt(gi*k*tanh(k*hi)), 0.0) + + cond = (w<0) + if any(cond): + txt0 = ''' + Waves and current are in opposite directions + making some of the frequencies negative. + Here we are forcing the negative frequencies to zero. + ''' + warnings.warn(txt0) + w = where(cond, 0.0, w) # force w to zero + + return w, theta + +def w2k(w, theta=0.0, h=inf, g=9.81, count_limit=100): + ''' + Translates from frequency to wave number + using the dispersion relation + + Parameters + ---------- + w : array-like + angular frequency [rad/s]. + theta : array-like, optional + direction [rad]. + h : real scalar, optional + water depth [m]. + g : real scalar or array-like of size 2. + constant of gravity [m/s**2] or 3D normalizing constant + + Returns + ------- + k1, k2 : ndarray + wave numbers [rad/m] along dimension 1 and 2. + + Description + ----------- + Uses Newton Raphson method to find the wave number k in the dispersion relation + w**2= g*k*tanh(k*h). + The solution k(w) => k1 = k(w)*cos(theta) + k2 = k(w)*sin(theta) + The size of k1,k2 is the common shape of w and theta according to numpy + broadcasting rules. If w or theta is scalar it functions as a constant + matrix of the same shape as the other. + + Example + ------- + >>> import pylab as plb + >>> w = plb.linspace(0,3); + >>> h = plb.plot(w,w2k(w)[0]) + >>> w2k(range(4))[0] + array([ 0. , 0.1019368 , 0.4077472 , 0.91743119]) + >>> w2k(range(4),h=20)[0] + array([ 0. , 0.10503601, 0.40774726, 0.91743119]) + + >>> plb.close('all') + + See also + -------- + k2w + ''' + wi, th, gi = atleast_1d(w, theta, g) + + if wi.size == 0: + return zeros_like(wi) + + k = 1.0*sign(wi)*wi**2.0 #% deep water + if h == inf: + k2 = k*sin(th)/gi[-1] #%size np x nf + k1 = k*cos(th)/gi[0] + return k1, k2 + + + if gi.size > 1: + txt0 = ''' + Finite depth in combination with 3D normalization (len(g)=2) is not implemented yet. + ''' + raise ValueError(txt0) + + + find = flatnonzero + eps = finfo(float).eps + + oshape = k.shape + wi, k = wi.ravel(), k.ravel() + + # Newton's Method + # Permit no more than count_limit iterations. + + hn = zeros_like(k) + ix = find((wi<0) | (00 and count < count_limit): + ki = k[ix] + hn[ix] = (ki*tanh(ki*h)-wi[ix]**2.0/gi)/(tanh(ki*h)+ki*h/(cosh(ki*h)**2.0)) + knew = ki - hn[ix] + # Make sure that the current guess is not zero. + # When Newton's Method suggests steps that lead to zero guesses + # take a step 9/10ths of the way to zero: + ksmall = find(abs(knew)==0) + if ksmall.size>0: + knew[ksmall] = ki[ksmall] / 10.0 + hn[ix[ksmall]] = ki[ksmall]-knew[ksmall] + + k[ix] = knew + # disp(['Iteration ',num2str(count),' Number of points left: ' num2str(length(ix)) ]), + + ix = find((abs(hn) > sqrt(eps)*abs(k)) * abs(hn) > sqrt(eps)) + count += 1 + + if count == count_limit: + txt1 = ''' W2K did not converge. + The maximum error in the last step was: %13.8f''' % max(hn[ix]) + warnings.warn(txt1) + + k.shape = oshape + + k2 = k*sin(th) + k1 = k*cos(th) + return k1, k2 + +def main(): + import doctest + doctest.testmod() + +if __name__ == '__main__': + main() \ No newline at end of file diff --git a/wafo/spectrum/models.py b/wafo/spectrum/models.py new file mode 100755 index 0000000..139c1ad --- /dev/null +++ b/wafo/spectrum/models.py @@ -0,0 +1,1997 @@ +""" +Models module +------------- + +Dispersion relation +------------------- +k2w - Translates from wave number to frequency +w2k - Translates from frequency to wave number + +Model spectra +------------- +Bretschneider - Bretschneider spectral density. +Jonswap - JONSWAP spectral density +McCormick - McCormick spectral density. +OchiHubble - OchiHubble bimodal spectral density model. +Tmaspec - JONSWAP spectral density for finite water depth +Torsethaugen - Torsethaugen double peaked (swell + wind) spectrum model +Wallop - Wallop spectral density. +demospec - Loads a precreated spectrum of chosen type +jonswap_peakfact - Jonswap peakedness factor Gamma given Hm0 and Tp +jonswap_seastate - jonswap seastate from windspeed and fetch + +Directional spreading functions +------------------------------- +Spreading - Directional spreading function. + +""" + + +#------------------------------------------------------------------------------- +# Name: models +# Purpose: Interface to various spectrum models +# +# Author: pab +# +# Created: 29.08.2008 +# Copyright: (c) pab 2008 +# Licence: +#------------------------------------------------------------------------------- +#!/usr/bin/env python +from __future__ import division + +import warnings +from scipy.interpolate import interp1d +import scipy.optimize as optimize +import scipy.integrate as integrate +import scipy.special as sp +from scipy.fftpack import fft +#from scipy.misc import ppimport +#import numpy as np +from numpy import (inf, atleast_1d, newaxis, any, minimum, maximum, array, #@UnresolvedImport + asarray, exp, log, sqrt, where, pi, arange, linspace, sin, cos, abs, sinh, #@UnresolvedImport + isfinite, mod, expm1, tanh, cosh, finfo, ones, ones_like, isnan, #@UnresolvedImport + zeros_like, flatnonzero, sinc, hstack, vstack, real, flipud, clip) #@UnresolvedImport +from dispersion_relation import w2k +#ppimport.enable() +#_wafospectrum = ppimport.ppimport('wafo.spectrum') +from core import SpecData1D +sech = lambda x: 1.0/cosh(x) + +eps = finfo(float).eps + + +__all__ = ['Bretschneider','Jonswap','Torsethaugen','Wallop','McCormick','OchiHubble', + 'Tmaspec','jonswap_peakfact','jonswap_seastate','spreading', + 'w2k','k2w','phi1'] + +# Model spectra + +def _gengamspec(wn, N=5, M=4): + ''' Return Generalized gamma spectrum in dimensionless form + + Parameters + ---------- + wn : arraylike + normalized frequencies, w/wp. + N : scalar + defining the decay of the high frequency part. + M : scalar + defining the spectral width around the peak. + + Returns + ------- + S : arraylike + spectral values, same size as wn. + + The generalized gamma spectrum in non- + dimensional form is defined as: + + S = G0.*wn.**(-N).*exp(-B*wn.**(-M)) for wn > 0 + = 0 otherwise + where + B = N/M + C = (N-1)/M + G0 = B**C*M/gamma(C), Normalizing factor related to Bretschneider form + + Note that N = 5, M = 4 corresponds to a normalized + Bretschneider spectrum. + + Examples + -------- + >>> import numpy as np + >>> wn = np.linspace(0,4,5) + >>> _gengamspec(wn, N=6, M=2) + array([ 0. , 1.16765216, 0.17309961, 0.02305179, 0.00474686]) + + See also + -------- + Bretschneider + Jonswap, + Torsethaugen + + + References + ---------- + Torsethaugen, K. (2004) + "Simplified Double Peak Spectral Model for Ocean Waves" + In Proc. 14th ISOPE + ''' + w = atleast_1d(wn) + S = zeros_like(w) + + ##for w>0 # avoid division by zero + k = flatnonzero(w>0.0) + if k.size>0: + B = N/M + C = (N-1.0)/M + + # # A = Normalizing factor related to Bretschneider form + # A = B**C*M/gamma(C) + # S(k) = A*wn(k)**(-N)*exp(-B*wn(k)**(-M)) + logwn = log(w.take(k)) + logA = (C*log(B)+log(M)-sp.gammaln(C)) + S.put(k,exp(logA-N*logwn-B*exp(-M*logwn))) + return S + +class ModelSpectrum(object): + def __init__(self, Hm0=7.0, Tp=11.0, **kwds): + self.Hm0 = Hm0 + self.Tp = Tp + self.type = 'ModelSpectrum' + def tospecdata(self, w=None, wc=None, nw=257): + ''' + Return SpecData1D object from ModelSpectrum + + Parameter + --------- + w : arraylike + vector of angular frequencies used in the discretization of spectrum + wc : scalar + cut off frequency (default 33/Tp) + nw : int + number of frequencies + + Returns + ------- + S : SpecData1D object + member attributes of model spectrum are copied to S.workspace + ''' + + if w is None: + if wc is None: + wc = 33./self.Tp + w = linspace(0,wc,nw) + S = SpecData1D(self.__call__(w),w) + try: + h = self.h + S.h = h + except: + pass + S.labels.title = self.type + ' ' + S.labels.title + S.workspace = self.__dict__.copy() + return S + + def chk_seastate(self): + ''' Check if seastate is valid + ''' + + if self.Hm0<0: + raise ValueError('Hm0 can not be negative!') + + if self.Tp<=0: + raise ValueError('Tp must be positve!') + + if self.Hm0==0.0: + warnings.warn('Hm0 is zero!') + + self._chk_extra_param() + + def _chk_extra_param(self): + pass + +class Bretschneider(ModelSpectrum): + ''' + Bretschneider spectral density model + + Member variables + ---------------- + Hm0 : significant wave height (default 7 (m)) + Tp : peak period (default 11 (sec)) + N : scalar defining decay of high frequency part. (default 5) + M : scalar defining spectral width around the peak. (default 4) + + Parameters + ---------- + w : array-like + angular frequencies [rad/s] + + + The Bretschneider spectrum is defined as + + S(w) = A * G0 * wn**(-N)*exp(-N/(M*wn**M)) + where + G0 = Normalizing factor related to Bretschneider form + A = (Hm0/4)**2 / wp (Normalization factor) + wn = w/wp + wp = 2*pi/Tp, angular peak frequency + + This spectrum is a suitable model for fully developed sea, + i.e. a sea state where the wind has been blowing long enough over a + sufficiently open stretch of water, so that the high-frequency waves have + reached an equilibrium. In the part of the spectrum where the frequency is + greater than the peak frequency (w>wp), the energy distribution is + proportional to w**-5. + The spectrum is identical with ITTC (International Towing Tank + Conference), ISSC (International Ship and Offshore Structures Congress) + and Pierson-Moskowitz, wave spectrum given Hm0 and Tm01. It is also identical + with JONSWAP when the peakedness factor, gamma, is one. + For this spectrum, the following relations exist between the mean + period Tm01 = 2*pi*m0/m1, the peak period Tp and the mean + zero-upcrossing period Tz: + + Tm01 = 1.086*Tz, Tp = 1.408*Tz and Tp=1.2965*Tm01 + + Examples + -------- + >>> S = Bretschneider(Hm0=6.5,Tp=10) + >>> S((0,1,2,3)) + array([ 0. , 1.69350993, 0.06352698, 0.00844783]) + + See also + -------- + Jonswap, + Torsethaugen + ''' + def __init__(self, Hm0=7.0, Tp=11.0, N=5, M=4, chk_seastate=True, **kwds): + self.type = 'Bretschneider' + self.Hm0 = Hm0 + self.Tp = Tp + self.N = N + self.M = M + if chk_seastate: + self.chk_seastate() + + + def __call__(self,wi): + ''' Return Bretschnieder spectrum + ''' + w = atleast_1d(wi) + if self.Hm0>0: + wp = 2*pi/self.Tp + wn = w/wp + S = (self.Hm0/4.0)**2/wp * _gengamspec(wn,self.N,self.M) + else: + S = zeros_like(w) + return S + +def jonswap_peakfact(Hm0,Tp): + ''' Jonswap peakedness factor, gamma, given Hm0 and Tp + + Parameters + ---------- + Hm0 : significant wave height [m]. + Tp : peak period [s] + + Returns + ------- + gamma : Peakedness parameter of the JONSWAP spectrum + + Details + ------- + A standard value for GAMMA is 3.3. However, a more correct approach is + to relate GAMMA to Hm0 and Tp: + D = 0.036-0.0056*Tp/sqrt(Hm0) + gamma = exp(3.484*(1-0.1975*D*Tp**4/(Hm0**2))) + This parameterization is based on qualitative considerations of deep water + wave data from the North Sea, see Torsethaugen et. al. (1984) + Here GAMMA is limited to 1..7. + + NOTE: The size of GAMMA is the common shape of Hm0 and Tp. + + Examples + -------- + >>> import pylab as plb + >>> Tp,Hs = plb.meshgrid(range(4,8),range(2,6)) + >>> gam = jonswap_peakfact(Hs,Tp) + + >>> Hm0 = plb.linspace(1,20) + >>> Tp = Hm0 + >>> [T,H] = plb.meshgrid(Tp,Hm0) + >>> gam = jonswap_peakfact(H,T) + >>> v = plb.arange(0,8) + >>> h = plb.contourf(Tp,Hm0,gam,v);h=plb.colorbar() + + >>> Hm0 = plb.arange(1,11) + >>> Tp = plb.linspace(2,16) + >>> T,H = plb.meshgrid(Tp,Hm0) + >>> gam = jonswap_peakfact(H,T) + >>> h = plb.plot(Tp,gam.T) + >>> h = plb.xlabel('Tp [s]') + >>> h = plb.ylabel('Peakedness parameter') + + >>> plb.close('all') + + See also + -------- + jonswap + ''' + Hm0,Tp = atleast_1d(Hm0,Tp) + + x = Tp/sqrt(Hm0) + + gam = ones_like(x) + + k1 = flatnonzero(x<=5.14285714285714) + if k1.size>0: # #limiting gamma to [1 7] + xk = x.take(k1) + D = 0.036-0.0056*xk # # approx 5.061*Hm0**2/Tp**4*(1-0.287*log(gam)) + gam.put(k1,minimum(exp(3.484*( 1.0-0.1975*D*xk**4.0 ) ),7.0)) # # gamma + + return gam +def jonswap_seastate(u10, fetch=150000., method='lewis', g=9.81, output='dict'): + ''' + Return Jonswap seastate from windspeed and fetch + + Parameters + ---------- + U10 : real scalar + windspeed at 10 m above mean water surface [m/s] + fetch : real scalar + fetch [m] + method : 'hasselman73' seastate according to Hasselman et. al. 1973 + 'hasselman76' seastate according to Hasselman et. al. 1976 + 'lewis' seastate according to Lewis and Allos 1990 + g : real scalar + accelaration of gravity [m/s**2] + output : 'dict' or 'list' + + Returns + ------- + seastate: dict where + Hm0 : significant wave height [m] + Tp : peak period [s] + gamma : jonswap peak enhancement factor. + sigmaA, + sigmaB : jonswap spectral width parameters. + Ag : jonswap alpha, normalization factor. + + Example + -------- + >>> fetch = 10000; u10 = 10 + >>> ss = jonswap_seastate(u10, fetch, output='dict') + >>> ss + {'Ag': 0.016257903375341734, + 'Hm0': 0.51083679198275533, + 'Tp': 2.7727680999585265, + 'gamma': 2.4824142635861119, + 'sigmaA': 0.075317331395172021, + 'sigmaB': 0.091912084512251344} + >>> S = Jonswap(**ss) + >>> S.Hm0 + 0.51083679198275533 + + # Alternatively + >>> ss1 = jonswap_seastate(u10, fetch, output='list') + >>> S1 = Jonswap(*ss1) + >>> S1.Hm0 + 0.51083679198275533 + + See also + -------- + Jonswap + + + References + ---------- + Lewis, A. W. and Allos, R.N. (1990) + JONSWAP's parameters: sorting out the inconscistencies. + Ocean Engng, Vol 17, No 4, pp 409-415 + + Hasselmann et al. (1973) + Measurements of Wind-Wave Growth and Swell Decay during the Joint + North Sea Project (JONSWAP). + Ergansungsheft, Reihe A(8), Nr. 12, Deutschen Hydrografischen Zeitschrift. + + Hasselmann et al. (1976) + A parametric wave prediction model. + J. phys. oceanogr. Vol 6, pp 200-228 + + ''' + + # The following formulas are from Lewis and Allos 1990: + + zeta = g*fetch/(u10**2) # dimensionless fetch, Table 1 + #zeta = min(zeta, 2.414655013429281e+004) + if method.startswith('h'): + if method[-1]=='3': # Hasselman et.al (1973) + A = 0.076*zeta**(-0.22) + ny= 3.5*zeta**(-0.33) # dimensionless peakfrequency, Table 1 + epsilon1 = 9.91e-8*zeta**1.1 # dimensionless surface variance, Table 1 + else: # Hasselman et.al (1976) + A = 0.0662*zeta**(-0.2) + ny = 2.84*zeta**(-0.3) # dimensionless peakfrequency, Table 1 + epsilon1 = 1.6e-7*zeta # dimensionless surface variance, Eq.4 + + sa = 0.07 + sb = 0.09 + gam = 3.3 + else: + A = 0.074*zeta**(-0.22) # Eq. 10 + ny = 3.57*zeta**(-0.33) # dimensionless peakfrequency, Eq. 11 + epsilon1 = 3.512e-4*A*ny**(-4.)*zeta**(-0.1) # dimensionless surface variance, Eq.12 + sa = 0.05468*ny**(-0.32) # Eq. 13 + sb = 0.078314*ny**(-0.16) # Eq. 14 + gam = maximum(17.54*zeta**(-0.28384),1) # Eq. 15 + + Tp = u10/(ny*g) # Table 1 + Hm0 = 4*sqrt(epsilon1)*u10**2./g # Table 1 + if output[0]=='l': + return Hm0,Tp,gam,sa,sb,A + else: + return dict(Hm0=Hm0,Tp=Tp,gamma=gam,sigmaA=sa,sigmaB=sb,Ag=A) + +class Jonswap(ModelSpectrum): + ''' + Jonswap spectral density model + + Member variables + ---------------- + Hm0 : significant wave height (default 7 (m)) + Tp : peak period (default 11 (sec)) + gamma : peakedness factor determines the concentraton + of the spectrum on the peak frequency. + Usually in the range 1 <= gamma <= 7. + default depending on Hm0, Tp, see jonswap_peakedness) + sigmaA : spectral width parameter for w1: + N : scalar defining decay of high frequency part. (default 5) + M : scalar defining spectral width around the peak. (default 4) + method : String defining method used to estimate Ag when gamma>1 + 'integrate' : Ag = 1/gaussq(Gf*ggamspec(wn,N,M),0,wnc) (default) + 'parametric': Ag = (1+f1(N,M)*log(gamma)**f2(N,M))/gamma + 'custom' : Ag = Ag + wnc : wc/wp normalized cut off frequency used when calculating Ag + by integration (default 6) + Parameters + ---------- + w : array-like + angular frequencies [rad/s] + + Description + ----------- + The JONSWAP spectrum is defined as + + S(w) = A * Gf * G0 * wn**(-N)*exp(-N/(M*wn**M)) + where + G0 = Normalizing factor related to Bretschneider form + A = Ag * (Hm0/4)**2 / wp (Normalization factor) + Gf = j**exp(-.5*((wn-1)/s)**2) (Peak enhancement factor) + wn = w/wp + wp = angular peak frequency + s = sigmaA for wn <= 1 + sigmaB for 1 < wn + j = gamma, (j=1, => Bretschneider spectrum) + + The JONSWAP spectrum is assumed to be especially suitable for the North Sea, + and does not represent a fully developed sea. It is a reasonable model for + wind generated sea when the seastate is in the so called JONSWAP range, i.e., + 3.6*sqrt(Hm0) < Tp < 5*sqrt(Hm0) + + The relation between the peak period and mean zero-upcrossing period + may be approximated by + Tz = Tp/(1.30301-0.01698*gamma+0.12102/gamma) + + Examples + --------- + >>> import pylab as plb + >>> S = Jonswap(Hm0=7, Tp=11,gamma=1) + >>> w = plb.linspace(0,5) + >>> h = plb.plot(w,S(w)) + + >>> S2 = Bretschneider(Hm0=7, Tp=11) + >>> assert(all(abs(S(w)-S2(w))<1.e-7),'JONSWAP with gamma=1 differs from Bretscneider, should be equal!') + >>> plb.close('all') + + See also + -------- + Bretschneider + Tmaspec + Torsethaugen + + References + ----------- + Torsethaugen et al. (1984) + Characteristica for extreme Sea States on the Norwegian continental shelf. + Report No. STF60 A84123. Norwegian Hydrodyn. Lab., Trondheim + + Hasselmann et al. (1973) + Measurements of Wind-Wave Growth and Swell Decay during the Joint + North Sea Project (JONSWAP). + Ergansungsheft, Reihe A(8), Nr. 12, Deutschen Hydrografischen Zeitschrift. + ''' + def __init__(self, Hm0=7.0, Tp=11.0, gamma=None, sigmaA=0.07, sigmaB=0.09, + Ag=None, N=5, M=4, method='integration', wnc=6.0, + chk_seastate=True): + + self.type = 'Jonswap' + self.Hm0 = Hm0 + self.Tp = Tp + self.N = N + self.M = M + self.sigmaA = sigmaA + self.sigmaB = sigmaB + self.gamma = gamma + self.Ag = Ag + self.method = method + self.wnc = wnc + + if self.gamma==None or not isfinite(self.gamma) or self.gamma<1: + self.gamma = jonswap_peakfact(Hm0,Tp) + + self._preCalculateAg() + + if chk_seastate: + self.chk_seastate() + + def _chk_extra_param(self): + Tp = self.Tp + Hm0 = self.Hm0 + gam = self.gamma + outsideJonswapRange = Tp>5*sqrt(Hm0) or Tp<3.6*sqrt(Hm0) + if outsideJonswapRange: + txt0 = ''' + Hm0,Tp is outside the JONSWAP range. + The validity of the spectral density is questionable. + ''' + warnings.warn(txt0) + + if gam<1 or 7 < gam: + txt = ''' + The peakedness factor, gamma, is possibly too large. + The validity of the spectral density is questionable. + ''' + warnings.warn(txt) + + + def _localspec(self,wn): + Gf = self.peak_e_factor(wn) + return Gf*_gengamspec(wn,self.N, self.M) + + def _preCalculateAg(self): + ''' PRECALCULATEAG Precalculate normalization. + ''' + if self.gamma==1: + self.Ag = 1.0 + self.method = 'parametric' + elif self.Ag != None: + self.method = 'custom' + if self.Ag<=0: + raise ValueError('Ag must be larger than 0!') + elif self.method[0]=='i': + # normalizing by integration + self.method = 'integration' + if self.wnc<1.0: + raise ValueError('Normalized cutoff frequency, wnc, must be larger than one!') + area1, unused_err1 = integrate.quad(self._localspec, 0, 1) + area2, unused_err2 = integrate.quad(self._localspec, 1, self.wnc) + area = area1 + area2 + self.Ag = 1.0/area + elif self.method[1]=='p': + self.method = 'parametric' + ## # Original normalization + ## # NOTE: that Hm0**2/16 generally is not equal to intS(w)dw + ## # with this definition of Ag if sa or sb are changed from the + ## # default values + N = self.N + M = self.M + gammai = self.gamma + parametersOK = (3<=N and N<=50) or (2<=M and M <=9.5) and (1<= gammai and gammai<=20) + if parametersOK: + f1NM = 4.1*(N-2*M**0.28+5.3)**(-1.45*M**0.1+0.96) + f2NM = (2.2*M**(-3.3) + 0.57)*N**(-0.58*M**0.37+0.53)-1.04*M**(-1.9)+0.94 + self.Ag = (1+ f1NM*log(gammai)**f2NM)/gammai + + ### elseif N == 5 && M == 4, + ### options.Ag = (1+1.0*log(gammai).**1.16)/gammai + ### #options.Ag = (1-0.287*log(gammai)) + ### options.normalizeMethod = 'Three' + ### elseif N == 4 && M == 4, + ### options.Ag = (1+1.1*log(gammai).**1.19)/gammai + else: + raise ValueError('Not knowing the normalization because N, M or peakedness parameter is out of bounds!') + + if self.sigmaA!=0.07 or self.sigmaB!=0.09: + warnings.warn('Use integration to calculate Ag when sigmaA~=0.07 or sigmaB~=0.09') + + + + def peak_e_factor(self,wn): + ''' PEAKENHANCEMENTFACTOR + ''' + w = maximum(atleast_1d(wn),0.0) + sab = where(w>1,self.sigmaB,self.sigmaA) + + wnm12 = 0.5*((w-1.0)/sab)**2.0 + Gf = self.gamma**(exp(-wnm12)) + return Gf + + def __call__(self,wi): + ''' JONSWAP spectral density + ''' + w = atleast_1d(wi) + if (self.Hm0>0.0): + + N = self.N + M = self.M + wp = 2*pi/self.Tp + wn = w/wp + Ag = self.Ag + Hm0 = self.Hm0 + Gf = self.peak_e_factor(wn) + S = ((Hm0/4.0)**2/wp*Ag)*Gf*_gengamspec(wn,N,M) + else: + S = zeros_like(w) + return S + +def phi1(wi, h, g=9.81): + ''' Factor transforming spectra to finite water depth spectra. + + CALL: tr = phi1(w,h) + + Input + ----- + w : arraylike + angular frequency [rad/s] + h : scalar + water depth [m] + g : scalar + acceleration of gravity [m/s**2] + Returns + ------- + tr : arraylike + transformation factors + + Example: + ------- + Transform a JONSWAP spectrum to a spectrum for waterdepth = 30 m + + >>> S = Jonswap() + >>> w = range(3.0) + >>> S(w)*phi1(w,30.0) + array([ 0. , 1.0358056 , 0.03796281]) + + + Reference + --------- + Buows, E., Gunther, H., Rosenthal, W. and Vincent, C.L. (1985) + 'Similarity of the wind wave spectrum in finite depth water: 1 spectral form.' + J. Geophys. Res., Vol 90, No. C1, pp 975-986 + + ''' + w = atleast_1d(wi) + if h == inf: # % special case infinite water depth + return ones_like(w) + + k1 = w2k(w,0,inf,g=g)[0] + dw1 = 2.0*w/g # % dw/dk|h=inf + k2 = w2k(w,0,h,g=g)[0] + + k2h = k2*h + dw2 = where(k1!=0,dw1/(tanh(k2h)+k2h/cosh(k2h)**2.0),0) # dw/dk|h=h0 + + return where(k1!=0,(k1/k2)**3.0*dw2/dw1,0) + +class Tmaspec(Jonswap): + ''' JONSWAP spectrum for finite water depth + + Member variables + ---------------- + h = water depth (default 42 [m]) + g : acceleration of gravity [m/s**2] + Hm0 = significant wave height (default 7 [m]) + Tp = peak period (default 11 (sec)) + gamma = peakedness factor determines the concentraton + of the spectrum on the peak frequency. + Usually in the range 1 <= gamma <= 7. + default depending on Hm0, Tp, see getjonswappeakedness) + sigmaA = spectral width parameter for w1: + N = scalar defining decay of high frequency part. (default 5) + M = scalar defining spectral width around the peak. (default 4) + method = String defining method used to estimate Ag when gamma>1 + 'integrate' : Ag = 1/gaussq(Gf.*ggamspec(wn,N,M),0,wnc) (default) + 'parametric': Ag = (1+f1(N,M)*log(gamma)^f2(N,M))/gamma + 'custom' : Ag = Ag + wnc = wc/wp normalized cut off frequency used when calculating Ag + by integration (default 6) + Parameters + ---------- + w : array-like + angular frequencies [rad/s] + + Description + ------------ + The evaluated spectrum is + S(w) = Sj(w)*phi(w,h) + where + Sj = jonswap spectrum + phi = modification due to water depth + + The concept is based on a similarity law, and its validity is verified + through analysis of 3 data sets from: TEXEL, MARSEN projects (North + Sea) and ARSLOE project (Duck, North Carolina, USA). The data include + observations at water depths ranging from 6 m to 42 m. + + Example + -------- + >>> import pylab as plb + >>> w = plb.linspace(0,2.5) + >>> S = Tmaspec(h=10,gamma=1) # Bretschneider spectrum Hm0=7, Tp=11 + >>> o=plb.plot(w,S(w)) + >>> o=plb.plot(w,S(w,h=21)) + >>> o=plb.plot(w,S(w,h=42)) + >>> plb.show() + >>> plb.close('all') + + See also + --------- + Bretschneider, + Jonswap, + phi1, + Torsethaugen + + References: + Buows, E., Gunther, H., Rosenthal, W., and Vincent, C.L. (1985) + 'Similarity of the wind wave spectrum in finite depth water: 1 spectral form.' + J. Geophys. Res., Vol 90, No. C1, pp 975-986 + + Hasselman et al. (1973) + Measurements of Wind-Wave Growth and Swell Decay during the Joint + North Sea Project (JONSWAP). + Ergansungsheft, Reihe A(8), Nr. 12, deutschen Hydrografischen + Zeitschrift. + + ''' + def __init__(self, Hm0=7.0, Tp=11.0, gamma=None, sigmaA=0.07, sigmaB=0.09, + Ag=None, N=5, M=4, method='integration', wnc=6.0, + chk_seastate=True, h=42, g=9.81): + self.g = g + self.h = h + super(Tmaspec, self).__init__(Hm0,Tp,gamma,sigmaA,sigmaB,Ag,N,M,method,wnc,chk_seastate) + self.type = 'TMA' + + def phi(self,w,h=None,g=None): + if h==None: + h = self.h + if g==None: + g = self.g + return phi1(w,h,g) + + def __call__(self,w,h=None,g=None): + jonswap = super(Tmaspec, self).__call__(w) + return jonswap*self.phi(w,h,g) + +class Torsethaugen(ModelSpectrum): + ''' + Torsethaugen double peaked (swell + wind) spectrum model + + Member variables + ---------------- + Hm0 : significant wave height (default 7 (m)) + Tp : peak period (default 11 (sec)) + wnc : wc/wp normalized cut off frequency used when calculating Ag + by integration (default 6) + method : String defining method used to estimate normalization factors, Ag, + in the the modified JONSWAP spectra when gamma>1 + 'integrate' : Ag = 1/quad(Gf.*gengamspec(wn,N,M),0,wnc) + 'parametric': Ag = (1+f1(N,M)*log(gamma)**f2(N,M))/gamma + Parameters + ---------- + w : array-like + angular frequencies [rad/s] + + Description + ----------- + The double peaked (swell + wind) Torsethaugen spectrum is + modelled as S(w) = Ss(w) + Sw(w) where Ss and Sw are modified + JONSWAP spectrums for swell and wind peak, respectively. + The energy is divided between the two peaks according + to empirical parameters, which peak that is primary depends on parameters. + The empirical parameters are found for classes of Hm0 and Tp, + originating from a dataset consisting of 20 000 spectra divided + into 146 different classes of Hm0 and Tp. (Data measured at the + Statfjord field in the North Sea in a period from 1980 to 1989.) + The range of the measured Hm0 and Tp for the dataset + are from 0.5 to 11 meters and from 3.5 to 19 sec, respectively. + + Preliminary comparisons with spectra from other areas indicate that + some of the empirical parameters are dependent on geographical location. + Thus the model must be used with care for other areas than the + North Sea and sea states outside the area where measured data + are available. + + Example + ------- + >>> import pylab as plb + >>> w = plb.linspace(0,4) + >>> S = Torsethaugen(Hm0=6, Tp=8) + >>> h=plb.plot(w,S(w),w,S.wind(w),w,S.swell(w)) + + See also + -------- + Bretschneider + Jonswap + + + References + ---------- + Torsethaugen, K. (2004) + "Simplified Double Peak Spectral Model for Ocean Waves" + In Proc. 14th ISOPE + + Torsethaugen, K. (1996) + Model for a doubly peaked wave spectrum + Report No. STF22 A96204. SINTEF Civil and Environm. Engineering, Trondheim + + Torsethaugen, K. (1994) + 'Model for a doubly peaked spectrum. Lifetime and fatigue strength + estimation implications.' + International Workshop on Floating Structures in Coastal zone, + Hiroshima, November 1994. + + Torsethaugen, K. (1993) + 'A two peak wave spectral model.' + In proceedings OMAE, Glasgow + + ''' + + def __init__(self, Hm0=7, Tp=11, method='integration', wnc=6, gravity=9.81, + chk_seastate=True, **kwds): + self.type = 'Torsethaugen' + self.Hm0 = Hm0 + self.Tp = Tp + self.method = method + self.wnc = wnc + self.gravity = gravity + self.wind = None + self.swell = None + if chk_seastate: + self.chk_seastate() + + self._init_spec() + + def __call__(self,w): + ''' TORSETHAUGEN spectral density + ''' + return self.wind(w)+self.swell(w) + + def _chk_extra_param(self): + Hm0 = self.Hm0 + Tp = self.Tp + if Hm0>11 or Hm0>max((Tp/3.6)**2, (Tp-2)*12/11): + txt0 = '''Hm0 is outside the valid range. + The validity of the spectral density is questionable''' + warnings.warn(txt0) + + if Tp>20 or Tp<3: + txt1 = '''Tp is outside the valid range. + The validity of the spectral density is questionable''' + warnings.warn(txt1) + + def _init_spec(self): + ''' Initialize swell and wind part of Torsethaugen spectrum + ''' + monitor = 0 + Hm0 = self.Hm0 + Tp = self.Tp + gravity1 = self.gravity # m/s**2 + + min = minimum + max = maximum + + # The parameter values below are found comparing the + # model to average measured spectra for the Statfjord Field + # in the Northern North Sea. + Af = 6.6 #m**(-1/3)*sec + AL = 2 #sec/sqrt(m) + Au = 25 #sec + KG = 35 + KG0 = 3.5 + KG1 = 1 # m + r = 0.857 # 6/7 + K0 = 0.5 #1/sqrt(m) + K00 = 3.2 + + M0 = 4 + B1 = 2 #sec + B2 = 0.7 + B3 = 3.0 #m + S0 = 0.08 #m**2*s + S1 = 3 #m + + # Preliminary comparisons with spectra from other areas indicate that + # the parameters on the line below can be dependent on geographical location + A10 = 0.7; A1 = 0.5; A20 = 0.6; A2 = 0.3; A3 = 6 + + Tf = Af*(Hm0)**(1.0/3.0) + Tl = AL*sqrt(Hm0) # lower limit + Tu = Au # upper limit + + #Non-dimensional scales + # New call pab April 2005 + El = min(max((Tf-Tp)/(Tf-Tl),0),1) #wind sea + Eu = min(max((Tp-Tf)/(Tu-Tf),0),1) #Swell + + + + if Tp 0.1: + print(' Spectrum for Wind dominated sea') + else: + print(' Spectrum for pure wind sea') + else: #swell dominated seas + + # Primary peak (swell) + Ns = K0*sqrt(Hm0)+K00 #high frequency exponent + Ms = M0 #spectral width exponent + Rps = min((1-A20)*exp(-(Eu/A2)**2)+A20,1) + Hps = Rps*Hm0 # significant waveheight swell + Tps = Tp # primary peak period + # peak enhancement factor + gammas = KG*(1+KG0*exp(-Hm0/KG1))*(2*pi/gravity1*Hm0/(Tf**2))**r*(1+A3*Eu) + gammas = max(gammas,1) + + # Secondary peak (wind) + Nw = Ns # high frequency exponent + Mw = M0*(1-B2*exp(-Hm0/B3)) # spectral width exponent + Rpw = sqrt(1-Rps**2) + Hpw = Rpw*Hm0 # significant waveheight wind + + C = (Nw-1)/Mw + B = Nw/Mw + G0w = B**C*Mw/sp.gamma(C)#normalizing factor + #G0w = exp(C*log(B)+log(Mw)-gammaln(C)) + #G0w = Mw/((B)**(-C)*gamma(C)) + + if Hpw>0: + Tpw = (16*S0*(1-exp(-Hm0/S1))*(0.4)**Nw/( G0w*Hpw**2))**(-1.0/(Nw-1.0)) + else: + Tpw = inf + + #Tpw = max(Tpw,2.5) + gammaw = 1 + if monitor: + if Rpw > 0.1: + print(' Spectrum for swell dominated sea') + else: + print(' Spectrum for pure swell sea') + + + if monitor: + if (3.6*sqrt(Hm0)<= Tp & Tp<=5*sqrt(Hm0)): + print(' Jonswap range') + + print('Hm0 = %g' % Hm0) + print('Ns, Ms = %g, %g Nw, Mw = %g, %g' % (Ns, Ms, Nw, Mw)) + print('gammas = %g gammaw = ' % (gammas,gammaw)) + print('Rps = %g Rpw = %g' % (Rps,Rpw)) + print('Hps = %g Hpw = %g' % (Hps, Hpw)) + print('Tps = %g Tpw = %g' % (Tps, Tpw)) + + + #G0s=Ms/((Ns/Ms)**(-(Ns-1)/Ms)*gamma((Ns-1)/Ms )) #normalizing factor + + # Wind part + self.wind = Jonswap(Hm0=Hpw, Tp=Tpw, gamma=gammaw, N=Nw, M=Mw, + method=self.method, chk_seastate=False) + # Swell part + self.swell = Jonswap(Hm0=Hps, Tp=Tps, gamma=gammas, N=Ns, M=Ms, + method=self.method, chk_seastate=False) + +class McCormick(Bretschneider): + ''' McCormick spectral density model + + Member variables + ---------------- + Hm0 = significant wave height (default 7 (m)) + Tp = peak period (default 11 (sec)) + Tz = zero-down crossing period (default 0.8143*Tp) + M = scalar defining spectral width around the peak. + (default depending on Tp and Tz) + + Parameters + ---------- + w : array-like + angular frequencies [rad/s] + + Description + ----------- + The McCormick spectrum parameterization is a modification of the Bretschneider + spectrum and defined as + + S(w) = (M+1)*(Hm0/4)^2/wp*(wp./w)^(M+1)*exp(-(M+1)/M*(wp/w)^M) + where + Tp/Tz=(1+1/M)^(1/M)/gamma(1+1/M) + + + Example: + -------- + >>> S = McCormick(Hm0=6.5,Tp=10) + >>> S(range(4)) + array([ 0. , 1.87865908, 0.15050447, 0.02994663]) + + + See also + -------- + Bretschneider + Jonswap, + Torsethaugen + + + References: + ----------- + M.E. McCormick (1999) + "Application of the Generic Spectral Formula to Fetch-Limited Seas" + Marine Technology Society, Vol 33, No. 3, pp 27-32 + ''' + + def __init__(self, Hm0=7, Tp=11, Tz=None, M=None, chk_seastate=True): + self.type = 'McCormick' + self.Hm0 = Hm0 + self.Tp = Tp + if Tz==None: + Tz = 0.8143*Tp + + self.Tz = Tz + if chk_seastate: + self.chk_seastate() + + if M==None and self.Hm0>0: + self._TpdTz = Tp/Tz + M = 1.0/optimize.fminbound(self._localoptfun,0.01,5) + self.M = M + self.N = M+1.0 + + def _localoptfun(self,x): + #LOCALOPTFUN Local function to optimize. + y = 1.0+x + return (y**(x)/sp.gamma(y)-self._TpdTz)**2.0 + +class OchiHubble(ModelSpectrum): + ''' OchiHubble bimodal spectral density model. + + Member variables + ---------------- + + Hm0 : significant wave height (default 7 (m)) + par : integer defining the parametrization (default 0) + 0 : The most probable spectrum + 1,2,...10 : gives 95% Confidence spectra + + The OchiHubble bimodal spectrum is modelled as + S(w) = Ss(w) + Sw(w) where Ss and Sw are modified Bretschneider + spectra for swell and wind peak, respectively. + + The OH spectrum is a six parameter spectrum, all functions of Hm0. + The values of these parameters are determined from a analysis of data + obtained in the North Atlantic. The source of the data is the same as + that for the development of the Pierson-Moskowitz spectrum, but + analysis is carried out on over 800 spectra including those in + partially developed seas and those having a bimodal shape. From a + statistical analysis of the data, a family of wave spectra consisting + of 11 members is generated for a desired sea severity (Hm0) with the + coefficient of 0.95. + A significant advantage of using a family of spectra for design of + marine systems is that one of the family members yields the largest + response such as motions or wave induced forces for a specified sea + severity, while another yields the smallest response with confidence + coefficient of 0.95. + + Examples + -------- + >>> S = OchiHubble(par=2) + >>> S(range(4)) + array([ 0. , 0.90155636, 0.04185445, 0.00583207]) + + + See also + -------- + Bretschneider, + Jonswap, + Torsethaugen + + References: + ---------- + Ochi, M.K. and Hubble, E.N. (1976) + 'On six-parameter wave spectra.' + In Proc. 15th Conf. Coastal Engng., Vol.1, pp301-328 + + ''' + + def __init__(self, Hm0=7, par=1, chk_seastate=True): + self.type = 'Ochi Hubble' + self.Hm0 = Hm0 + self.Tp = 1 + self.par = par + self.wind = None + self.swell = None + + if chk_seastate: + self.chk_seastate() + self._init_spec() + + def __call__(self,w): + return self.wind(w)+self.swell(w) + + + def _init_spec(self): + + hp = array([[0.84, 0.54], + [0.84, 0.54], + [0.84, 0.54], + [0.84, 0.54], + [0.84, 0.54], + [0.95, 0.31], + [0.65, 0.76], + [0.90, 0.44], + [0.77, 0.64], + [0.73,0.68], + [0.92, 0.39]]) + wa = array([ [0.7, 1.15], + [0.93, 1.5], + [0.41, 0.88], + [0.74, 1.3], + [0.62, 1.03], + [0.70, 1.50], + [0.61, 0.94], + [0.81, 1.60], + [0.54, 0.61], + [0.70, 0.99], + [0.70, 1.37]]) + wb = array([ [0.046, 0.039], + [0.056, 0.046], + [0.016, 0.026], + [0.052, 0.039], + [0.039, 0.030], + [0.046, 0.046], + [0.039, 0.036], + [0.052, 0.033], + [0.039, 0.000], + [0.046, 0.039], + [0.046, 0.039]]) + Lpar = array([[3.00, 1.54,-0.062], + [3.00, 2.77,-0.112], + [2.55, 1.82,-0.089], + [2.65, 3.90,-0.085], + [2.60, 0.53,-0.069], + [1.35, 2.48,-0.102], + [4.95, 2.48,-0.102], + [1.80, 2.95,-0.105], + [4.50, 1.95,-0.082], + [6.40, 1.78,-0.069], + [0.70, 1.78,-0.069]]) + Hm0 = self.Hm0 + Lpari = Lpar[self.par] + Li = hstack((Lpari[0],Lpari[1]*exp(Lpari[2]*Hm0))) + + Hm0i = hp[self.par]*Hm0 + Tpi = 2*pi*exp(wb[self.par]*Hm0)/wa[self.par] + Ni = 4*Li+1 + Mi = [4, 4] + + self.swell = Bretschneider(Hm0=Hm0i[0], Tp=Tpi[0], N=Ni[0], M=Mi[0]) + self.wind = Bretschneider(Hm0=Hm0i[1], Tp=Tpi[1], N=Ni[1], M=Mi[1]) + + def _chk_extra_param(self): + if self.par<0 or 10>> S = Wallop(Hm0=6.5, Tp=10) + >>> S(range(4)) + array([ 0.00000000e+00, 9.36921871e-01, 2.76991078e-03, + 7.72996150e-05]) + + See also + -------- + Bretschneider + Jonswap, + Torsethaugen + + References: + ----------- + Huang, N.E., Long, S.R., Tung, C.C, Yuen, Y. and Bilven, L.F. (1981) + "A unified two parameter wave spectral model for a generous sea state" + J. Fluid Mechanics, Vol.112, pp 203-224 + ''' + + def __init__(self, Hm0=7, Tp=11, N=None, chk_seastate=True): + self.type = 'Wallop' + self.Hm0 = Hm0 + self.Tp = Tp + self.M = 4 + if N is None: + wp = 2.*pi/Tp + kp = w2k(wp,0,inf)[0] # wavenumber at peak frequency + Lp = 2.*pi/kp # wave length at the peak frequency + N = abs((log(2.*pi**2.)+2*log(Hm0/4)-2.0*log(Lp))/log(2)) + + self.N = N + + if chk_seastate: + self.chk_seastate() + +class Spreading(object): + ''' + Directional spreading function. + + Member variables + ---------------- + Returns + -------- + D = Directional spreading function returning + S = D(theta,w,wc) where S is a Nt X Nw matrix with the principal + direction always along the x-axis. + Member varialbes + ---------------- + type = type of spreading function, see options below (default 'cos2s') + 'cos2s' : cos-2s spreading N(S)*[cos((theta-theta0)/2)]**(2*S) (0 < S) + 'box' : Box-car spreading N(A)*I( -A < theta-theta0 < A) (0 < A < pi) + 'mises' : von Mises spreading N(K)*exp(K*cos(theta-theta0)) (0 < K) + 'poisson': Poisson spreading N(X)/(1-2*X*cos(theta-theta0)+X**2) (0 < X < 1) + 'sech2' : sech-2 spreading N(B)*sech(B*(theta-theta0))**2 (0 < B) + 'wnormal': Wrapped Normal + [1 + 2*sum exp(-(n*D1)^2/2)*cos(n*(theta-theta0))]/(2*pi) (0 < D1) + (N(.) = normalization factor) + (the first letter is enough for unique identification) + + theta0 = function handle, inline object, matrix or a scalar defining + average direction given in radians at every angular frequency. + (length 1 or length == length(wn)) (default 0) + method = Defines function used for direcional spreading parameter: + 0, None : S(wn) = spa, frequency independent + 1, 'mitsuyasu': S(wn) frequency dependent (default) + 2, 'donelan' : B(wn) frequency dependent + 3, 'banner' : B(wn) frequency dependent + S(wn) = spa *(wn)^ma, : wnlo <= wn < wnc + = spb *(wn)^mb, : wnc <= wn < wnup + = 0 : wnup <= wn + B(wn) = S(wn) : wnlo <= wn < wnup + = spb*wnup^mb : wnup <= wn, method = 2 + = sc*F(wn) : wnup <= wn , method = 3 + where F(wn) = 10^(-0.4+0.8393*exp(-0.567*log(wn^2))) and sc is + scalefactor to make the spreading funtion continous. + wnlimits = [wnlo wnc wnup] limits used in the function defining the + directional spreading parameter. + wnc is the normalized cutover frequency (default [0 1 inf]) + sp = [spa,spb] maximum spread parameters (default [15 15]) + m = [ma,mb] shape parameters (default [5 -2.5]) + + SPREADING Return function handle to a Directional spreading function. + Here the S- or B-parameter, of the COS-2S and SECH-2 spreading function, + respectively, is used as a measure of spread. All the parameters of the + other distributions are related to this parameter through the first Fourier + coefficient, R1, of the directional distribution as follows: + R1 = S/(S+1) or S = R1/(1-R1). + where + Box-car spreading : R1 = sin(A)/A + Von Mises spreading: R1 = besseli(1,K)/besseli(0,K), + Poisson spreading : R1 = X + sech-2 spreading : R1 = pi/(2*B*sinh(pi/(2*B)) + Wrapped Normal : R1 = exp(-D1^2/2) + + A value of S = 15 corresponds to + 'box' : A=0.62, 'sech2' : B=0.89 + 'mises' : K=8.3, 'poisson': X=0.94 + 'wnormal': D=0.36 + + The COS2S is the most frequently used spreading in engineering practice. + Apart from the current meter/pressure cell data in WADIC all + instruments seem to support the 'cos2s' distribution for heavier sea + states, (Krogstad and Barstow, 1999). For medium sea states + a spreading function between COS2S and POISSON seem appropriate, + while POISSON seems appropriate for swell. + For the COS2S Mitsuyasu et al. parameterized SPa = SPb = + 11.5*(U10/Cp) where Cp = g/wp is the deep water phase speed at wp and + U10 the wind speed at reference height 10m. Hasselman et al. (1980) + parameterized mb = -2.33-1.45*(U10/Cp-1.17). + Mitsuyasu et al. (1975) showed that SP for wind waves varies from + 5 to 30 being a function of dimensionless wind speed. + However, Goda and Suzuki (1975) proposed SP = 10 for wind waves, SP = 25 + for swell with short decay distance and SP = 75 for long decay distance. + Compared to experiments Krogstad et al. (1998) found that ma = 5 +/- eps and + that -1< mb < -3.5. + Values given in the litterature: [spa spb ma mb wlim(1:3) ] + (Mitsuyasu: spa == spb) (cos-2s) [15 15 5 -2.5 0 1 3 ] + (Hasselman: spa ~= spb) (cos-2s) [6.97 9.77 4.06 -2.3 0 1.05 3 ] + (Banner : spa ~= spb) (sech2) [2.61 2.28 1.3 -1.3 0.56 0.95 1.6] + + Examples : + + >>> import pylab as plb + >>> D = Spreading('cos2s',s_a=10.0) + + >>> w = plb.linspace(0,3,257) + >>> theta = plb.linspace(-pi,pi,129) + >>> t = plb.contour(D(theta,w)[0].squeeze()) + + # Make frequency dependent direction + >>> theta0 = lambda w: w*plb.pi/6.0 + >>> D2 = Spreading('cos2s',theta0=theta0) + >>> t = plb.contour(D2(theta,w)[0]) + + # Plot all spreading functions + >>> alltypes = ('cos2s','box','mises','poisson','sech2','wrap_norm') + >>> for ix in range(len(alltypes)): + ... D3 = Spreading(alltypes[ix]) + ... t = plb.figure(ix) + ... t = plb.contour(D3(theta,w)[0]) + ... t = plb.title(alltypes[ix]) + >>> plb.close('all') + + + See also mkdspec, plotspec, spec2spec + + References + Krogstad, H.E. and Barstow, S.F. (1999) + "Directional Distributions in Ocean Wave Spectra" + Proceedings of the 9th ISOPE Conference, Vol III, pp. 79-86 + + Goda, Y. (1999) + "Numerical simulation of ocean waves for statistical analysis" + Marine Tech. Soc. Journal, Vol. 33, No. 3, pp 5--14 + + Banner, M.L. (1990) + "Equilibrium spectra of wind waves." + J. Phys. Ocean, Vol 20, pp 966--984 + Donelan M.A., Hamilton J, Hui W.H. (1985) + "Directional spectra of wind generated waves." + Phil. Trans. Royal Soc. London, Vol A315, pp 387--407 + + Hasselmann D, Dunckel M, Ewing JA (1980) + "Directional spectra observed during JONSWAP." + J. Phys. Ocean, Vol.10, pp 1264--1280 + + Mitsuyasu, H, et al. (1975) + "Observation of the directional spectrum of ocean waves using a + coverleaf buoy." + J. Physical Oceanography, Vol.5, No.4, pp 750--760 + Some of this might be included in help header: + cos-2s: + NB! The generally strong frequency dependence in directional spread + makes it questionable to run load tests of ships and structures with a + directional spread independent of frequency (Krogstad and Barstow, 1999). + ''' +##% Parameterization of B +##% def = 2 Donelan et al freq. parametrization for 'sech2' +##% def = 3 Banner freq. parametrization for 'sech2' +##% (spa ~= spb) (sech-2) [2.61 2.28 1.3 -1.3 0.56 0.95 1.6] +## +## +##% Tested on: Matlab 7.0 +##% History: +##% revised pab jan 2007 +##% - renamed from spreading to mkspreading +##% - the function now return a function handle to the actual spreading function. +##% - removed wc, the cut over frequency -> input is now assumed as normalized frequency, w/wc. +##% revised pab 17.06.2001 +##% - added wrapped normal spreading +##% revised pab 6 April 2001 +##% - added fourier2distpar +##% - Fixed the normalization of sech2 spreading +##% revised by PAB and IR 1 April 2001: Introducing the azymuth as a +##% standard parameter in order to avoid rotations of the directions +##% theta. The x-axis is always pointing into the principal direction +##% as defined in the spreading function D(omega,theta). The actual +##% principal direction is defined by means of field D.phi. +##% revised es 06.06.2000, commented away: if ((ma==0) & (mb==0)), ..., +##% hoping that the check is unnecessary +##% revised pab 13.06.2000 +##% - fixed a serious bug: made sure -pi<= th-th0 <=pi +##% revised pab 16.02.2000 +##% -fixed default value for Hasselman parametrization +##% revised pab 02.02.2000 +##% - Nt or th may be specified + check on th +##% - added frequency dependence for sech-2 +##% - th0 as separate input +##% - updated header info +##% - changed check for nargins +##% - added the possibility of nan's in data vector +##% Revised by jr 2000.01.25 +##% - changed check of nargins +##% - frequency dependence only for cos-2s +##% - updated information +##% By es, jr 1999.11.25 + + + def __init__(self,type='cos2s',theta0=0,method='mitsuyasu',s_a=15.,s_b=15.,m_a=5.,m_b=-2.5,wn_lo=0.0,wn_c=1.,wn_up=inf): + + self.type = type + self.theta0 = theta0 + self.method = method + self.s_a = s_a + self.s_b = s_b + self.m_a = m_a + self.m_b = m_b + self.wn_lo = wn_lo + self.wn_c = wn_c + self.wn_up = wn_up + + methods = dict(n=None, m='mitsuyasu', d='donelan', b='banner') + methodslist = (None, 'mitsuyasu', 'donelan', 'banner') + + if isinstance(self.method,str): + if not self.method[0] in methods: + raise ValueError('Unknown method') + self.method = methods[self.method[0]] + elif self.method == None: + pass + else: + if method<0 or 3=1): + raise ValueError('POISSON spreading: X value must be less than 1') + return X + + def fourier2a(self,r1): + ''' Returns the solution of R1 = sin(A)/A. + ''' + A0 = flipud(linspace(0,pi+0.1,1025)) + funA = interp1d(sinc(A0/pi),A0) + A0 = funA(r1.ravel()) + A = asarray(A0) + + # Newton-Raphson + da = ones_like(r1) + + max_count = 100 + ix = flatnonzero(A) + for unused_iy in range(max_count): + Ai = A[ix] + da[ix] = (sin(Ai) -Ai*r1[ix])/(cos(Ai)-r1[ix]) + Ai = Ai - da[ix] + # Make sure that the current guess is larger than zero and less than pi + #x(ix) = xi + 0.1*(dx(ix) - 9*xi).*(xi<=0) + 0.38*(dx(ix)-6.2*xi +6.2).*(xi>pi) + # Make sure that the current guess is larger than zero. + A[ix] = Ai + 0.5*(da[ix] - Ai)*(Ai<=0.0) + + ix = flatnonzero((abs(da) > sqrt(eps)*abs(A))*(abs(da) > sqrt(eps))) + if ix.size==0: + if any(A>pi): + raise ValueError('BOX-CAR spreading: The A value must be less than pi') + return A.clip(min=1e-16,max=pi) + + + warnings.warn('Newton raphson method did not converge.') + return A.clip(min=1e-16) # Avoid division by zero + + def fourier2k(self, r1): + ''' + Returns the solution of R1 = besseli(1,K)/besseli(0,K), + ''' + K0 = hstack((linspace(0,10,513), linspace(10.00001,100))) + fun0 = lambda x : sp.ive(1,x)/sp.ive(0,x) + funK = interp1d(fun0(K0),K0) + K0 = funK(r1.ravel()) + k1 = flatnonzero(isnan(K0)) + if (k1.size>0): + K0[k1] = 0.0 + K0[k1] = K0.max() + + ix0 = flatnonzero(r1!=0.0) + K = zeros_like(r1) + fun = lambda x : fun0(x)-r1[ix] + for ix in ix0: + K[ix] = optimize.fsolve(fun,K0[ix]) + return K + + def fourier2b(self,r1): + ''' Returns the solution of R1 = pi/(2*B*sinh(pi/(2*B)). + ''' + B0 = hstack((linspace(eps,5,513), linspace(5.0001,100))) + funB = interp1d(self._r1ofsech2(B0),B0) + + B0 = funB(r1.ravel()) + k1 = flatnonzero(isnan(B0)) + if (k1.size>0): + B0[k1] = 0.0 + B0[k1] = max(B0) + + ix0 = flatnonzero(r1!=0.0) + B = zeros_like(r1) + fun = lambda x : 0.5*pi/(sinh(.5*pi/x))-x*r1[ix] + for ix in ix0: + B[ix] = abs(optimize.fsolve(fun,B0[ix])) + return B + + def fourier2d(self,r1): + ''' Returns the solution of R1 = exp(-D**2/2). + ''' + r = clip(r1,0.,1.0) + return where(r<=0,inf,sqrt(-2.0*log(r))) + + + + + + def spread_par_s(self,wn): + ''' Return spread parameter, S, of COS2S function + + Parameters + ---------- + wn : array_like + normalized frequencies. + Returns + ------- + S : ndarray + spread parameter of COS2S functions + ''' + if self.method==None: + # no frequency dependent spreading, + # but possible frequency dependent direction + s = atleast_1d(self.s_a) + else: + wn_lo = self.wn_lo + wn_up = self.wn_up + wn_c = self.wn_c + + spa = self.s_a + spb = self.s_b + ma = self.m_a + mb = self.m_b + + + # Mitsuyasu et. al and Hasselman et. al parametrization of + # frequency dependent spreading + s = where(wn<=wn_c,spa*wn**ma,spb*wn**mb) + s[wn<=wn_lo] = 0.0 + + k = flatnonzero(wn_up0: + if self.method[0]=='d': + # Donelan et. al. parametrization for B in SECH-2 + s[k] = spb*(wn_up)**mb + + # Convert to S-paramater in COS-2S distribution + r1 = self.r1ofsech2(s) + s = r1/(1.-r1) + + elif self.method[0]=='b': + # Banner parametrization for B in SECH-2 + s3m = spb*(wn_up)**mb + s3p = self._donelan(wn_up) + scale = s3m/s3p #% Scale so that parametrization will be continous + s[k] = scale*self.donelan(wn[k]) + r1 = self.r1ofsech2(s) + + #% Convert to S-paramater in COS-2S distribution + s = r1/(1.-r1) + else: + s[k] = 0.0 + + if any(s<0): + raise ValueError('The COS2S spread parameter, S(w), value must be larger than 0') + return s + + + def _donelan(self, wn): + ''' High frequency decay of B of sech2 paramater + ''' + return 10.0**(-0.4+0.8393*exp(-0.567*log(wn**2))) + + def _r1ofsech2(self, B): + ''' R1OFSECH2 Computes R1 = pi./(2*B.*sinh(pi./(2*B))) + ''' + realmax = finfo(float).max + tiny = 1./realmax + x = clip(2.*B,tiny,realmax) + xk = pi/x + return where(x<100.,xk/sinh(xk),-2.*xk/(exp(xk)*expm1(-2.*xk))) + + + +def test_some_spectra(): + S = Jonswap() + + w = arange(3.0) + S(w)*phi1(w,30.0) + S1 = S.tospecdata(w) + S1.plot() + + + import pylab as plb + w = plb.linspace(0,2.5) + S = Tmaspec(h=10,gamma=1) # Bretschneider spectrum Hm0=7, Tp=11 + plb.plot(w,S(w)) + plb.plot(w,S(w,h=21)) + plb.plot(w,S(w,h=42)) + plb.show() + plb.close('all') + + + + import pylab as plb + #w = plb.linspace(0,3) + w,th = plb.ogrid[0:4,0:6] + k,k2 = w2k(w,th) + k1,k12 = w2k(w,th,h=20) + plb.plot(w,k,w,k2) + + plb.show() + + plb.close('all') + w = plb.linspace(0,2,100) + S = Torsethaugen(Hm0=6, Tp=8) + plb.plot(w,S(w),w,S.wind(w),w,S.swell(w)) + + S1 = Jonswap(Hm0=7, Tp=11,gamma=1) + w = plb.linspace(0,2,100) + plb.plot(w,S1(w)) + plb.show() + plb.close('all') + + + Hm0 = plb.arange(1,11) + Tp = plb.linspace(2,16) + T,H = plb.meshgrid(Tp,Hm0) + gam = jonswap_peakfact(H,T) + plb.plot(Tp,gam.T) + plb.xlabel('Tp [s]') + plb.ylabel('Peakedness parameter') + + Hm0 = plb.linspace(1,20) + Tp = Hm0 + [T,H] = plb.meshgrid(Tp,Hm0) + gam = jonswap_peakfact(H,T) + v = plb.arange(0,8) + plb.contourf(Tp,Hm0,gam,v) + plb.colorbar() + plb.show() + plb.close('all') + +def test_spreading(): + import pylab as plb + pi = plb.pi + w = plb.linspace(0,3,257) + theta = plb.linspace(-pi,pi,129) + theta0 = lambda w: w*plb.pi/6.0 + D2 = Spreading('cos2s',theta0=theta0) + d1 =D2(theta,w)[0] + t = plb.contour(d1.squeeze()) + + pi = plb.pi + D = Spreading('wrap_norm',s_a=10.0) + + w = plb.linspace(0,3,257) + theta = plb.linspace(-pi,pi,129) + d1 = D(theta,w) + plb.contour(d1[0]) + plb.show() + +def main(): + if False: # True: # + test_some_spectra() + else: + import doctest + doctest.testmod() + +if __name__ == '__main__': + main() \ No newline at end of file diff --git a/wafo/transform/__init__.py b/wafo/transform/__init__.py new file mode 100755 index 0000000..735d08c --- /dev/null +++ b/wafo/transform/__init__.py @@ -0,0 +1,6 @@ +""" +Transform package in WAFO Toolbox. + +""" +from wafo.transform.core import * +import wafo.transform.models diff --git a/wafo/transform/core.py b/wafo/transform/core.py new file mode 100755 index 0000000..96ffcfe --- /dev/null +++ b/wafo/transform/core.py @@ -0,0 +1,192 @@ +''' +''' +from __future__ import division +#import numpy as np +from numpy import trapz, sqrt, linspace #@UnresolvedImport + +from wafo.wafodata import WafoData +from wafo.misc import tranproc #, trangood + +__all__ = ['TrData', 'TrCommon'] + +class TrCommon(object): + """ + transformation model, g. + + Information about the moments of the process can be obtained by site + specific data, laboratory measurements or by resort to theoretical models. + + Assumption + ---------- + The Gaussian process, Y, distributed N(0,1) is related to the + non-Gaussian process, X, by Y = g(X). + + Methods + ------- + dist2gauss : Returns a measure of departure from the Gaussian model, i.e., + int (g(x)-xn)**2 dx where int. limits are given by X. + dat2gauss : Transform non-linear data to Gaussian scale + gauss2dat : Transform Gaussian data to non-linear scale + + Member variables + ---------------- + mean, sigma, skew, kurt : real, scalar + mean, standard-deviation, skewness and kurtosis, respectively, of the + non-Gaussian process. Default mean=0, sigma=1, skew=0.16, kurt=3.04. + skew=kurt-3=0 for a Gaussian process. + """ + + def __init__(self, mean=0.0, var=1.0, skew=0.16, kurt=3.04, *args, **kwds): + sigma = kwds.get('sigma',None) + if sigma is None: + sigma = sqrt(var) + self.mean = mean + self.sigma = sigma + self.skew = skew + self.kurt = kurt + # Mean and std in the Gaussian world: + self.ymean = kwds.get('ymean', 0e0) + self.ysigma = kwds.get('ysigma', 1e0) + + def __call__(self, x): + return self._dat2gauss(x) + + def dist2gauss(self, x=None, xnmin=-5, xnmax=5, n=513): + """ + Return a measure of departure from the Gaussian model. + + Parameters + ---------- + x : vector (default sigma*linspace(xnmin,xnmax,n)+mean) + xnmin : real, scalar + minimum on normalized scale + xnmax : real, scalar + maximum on normalized scale + n : integer, scalar + number of evaluation points + + + Returns + ------- + t0 : real, scalar + a measure of departure from the Gaussian model calculated as + trapz(xn,(xn-g(x))**2.) where int. limits is given by X. + """ + if x is None: + xn = linspace(xnmin, xnmax, n) + x = self.sigma*xn+self.mean + else: + xn = (x-self.mean)/self.sigma + + yn = (self._dat2gauss(x)-self.ymean)/self.ysigma + t0 = trapz(xn,(xn-yn)**2.) + return t0 + + def gauss2dat(self,y, *yi): + """ + Transforms Gaussian data, y, to non-linear scale. + + Parameters + ---------- + y, y1,..., yn : array-like + input vectors with Gaussian data values, where yi is the i'th time + derivative of y. (n<=4) + Returns + ------- + x, x1,...,xn : array-like + transformed data to a non-linear scale + + See also + -------- + dat2gauss + tranproc + """ + return self._gauss2dat(y, *yi) + def _gauss2dat(self, y, *yi): + pass + def dat2gauss(self, x, *xi): + """ + Transforms non-linear data, x, to Gaussian scale. + + Parameters + ---------- + x, x1,...,xn : array-like + input vectors with non-linear data values, where xi is the i'th time + derivative of x. (n<=4) + Returns + ------- + y, y1,...,yn : array-like + transformed data to a Gaussian scale + + See also + -------- + gauss2dat + tranproc. + """ + return self._dat2gauss(x, *xi) + def _dat2gauss(self, x, *xi): + pass + +class TrData(WafoData, TrCommon): + __doc__ = TrCommon.__doc__.split('mean')[0].replace('','Data') + """ + data : array-like + Gaussian values, Y + args : array-like + non-Gaussian values, X + ymean, ysigma : real, scalars (default ymean=0, ysigma=1) + mean and standard-deviation, respectively, of the process in Gaussian world. + mean, sigma : real, scalars + mean and standard-deviation, respectively, of the non-Gaussian process. + Default: + mean = self.gauss2dat(ymean), + sigma = (self.gauss2dat(ysigma)-self.gauss2dat(-ysigma))/2 + + Example + ------- + Construct a linear transformation model + >>> import numpy as np + >>> sigma = 5; mean = 1 + >>> u = np.linspace(-5,5); x = sigma*u+mean; y = u + >>> g = TrData(y,x) + >>> g.mean + array([ 1.]) + >>> g.sigma + array([ 5.]) + + Check that the departure from a Gaussian model is zero + >>> g.dist2gauss() < 1e-16 + True + """ + def __init__(self, *args, **kwds): + WafoData.__init__(self, *args, **kwds) + self.labels.title = 'Transform' + self.labels.ylab = 'g(x)' + self.labels.xlab = 'x' + self.ymean = kwds.get('ymean', 0e0) + self.ysigma = kwds.get('ysigma', 1e0) + self.mean = kwds.get('mean', None) + self.sigma = kwds.get('sigma', None) + + if self.mean is None: + #self.mean = np.mean(self.args) # + self.mean = self.gauss2dat(self.ymean) + if self.sigma is None: + yp = self.ymean+self.ysigma + ym = self.ymean-self.ysigma + self.sigma = (self.gauss2dat(yp)-self.gauss2dat(ym))/2. + + def _gauss2dat(self, y, *yi): + return tranproc(self.data, self.args, y, *yi) + + def _dat2gauss(self, x, *xi): + return tranproc(self.args, self.data, x, *xi) + +def main(): + pass + +if __name__ == '__main__': + if True: #False : # + import doctest + doctest.testmod() + else: + main() \ No newline at end of file diff --git a/wafo/transform/models.py b/wafo/transform/models.py new file mode 100755 index 0000000..abeed05 --- /dev/null +++ b/wafo/transform/models.py @@ -0,0 +1,469 @@ +''' +Transform Gaussian models +------------------------- +TrHermite +TrOchi +''' +#------------------------------------------------------------------------------- +# Name: transform.models +# Purpose: +# +# Author: pab +# +# Created: 24.11.2008 +# Copyright: (c) pab 2008 +# Licence: +#------------------------------------------------------------------------------- +#!/usr/bin/env python + +from scipy.optimize import brentq +from numpy import (sqrt, atleast_1d, abs, imag, sign, where, cos, arccos, ceil, #@UnresolvedImport + expm1, log1p, pi) #@UnresolvedImport +import numpy as np +import warnings +from core import TrCommon +__all__=['TrHermite','TrOchi'] + +_example = ''' + >>> std = 7./4 + >>> g = (sigma=std, ysigma=std) + >>> g.dist2gauss() + 3.9858776379926808 + + Simulate a Transformed Gaussian process: + >>> import numpy as np + >>> import wafo.spectrum.models as sm + >>> Sj = sm.Jonswap(Hm0=4*std, Tp=11) + >>> w = np.linspace(0,4,256) + >>> S = Sj.tospecdata(w) #Make spectrum object from numerical values + >>> ys = S.sim(ns=15000) # Simulated in the Gaussian world + + >>> me, va, sk, ku = S.stats_nl(moments='mvsk') + >>> g2 = (mean=me, var=va, skew=sk, kurt=ku, ysigma=std) + >>> xs = g2.gauss2dat(ys[:,1:]) # Transformed to the real world + ''' + +class TrHermite(TrCommon): + __doc__ = TrCommon.__doc__.replace('','Hermite') + """ + pardef : scalar, integer + 1 Winterstein et. al. (1994) parametrization [1]_ (default) + 2 Winterstein (1988) parametrization [2]_ + + Description + ----------- + The hermite transformation model is monotonic cubic polynomial, calibrated + such that the first 4 moments of the transformed model G(y)=g^-1(y) match + the moments of the true process. The model is given as: + + g(x) = xn - c3(xn**2-1) - c4*(xn**3-3*xn) + + for kurt<3 (hardening model) where + xn = (x-mean)/sigma + c3 = skew/6 + c4 = (kurt-3)/24. + + or + G(y) = mean + K*sigma*[ y + c3(y**2-1) + c4*(y**3-3*y) ] + + for kurt>=3 (softening model) where + y = g(x) = G**-1(x) + K = 1/sqrt(1+2*c3^2+6*c4^2) + If pardef = 1 : + c3 = skew/6*(1-0.015*abs(skew)+0.3*skew^2)/(1+0.2*(kurt-3)) + c4 = 0.1*((1+1.25*(kurt-3))^(1/3)-1)*c41 + c41 = (1-1.43*skew^2/(kurt-3))^(1-0.1*(kurt)^0.8) + If pardef = 2 : + c3 = skew/(6*(1+6*c4)) + c4 = [sqrt(1+1.5*(kurt-3))-1]/18 + + + Example: + -------- + """ + _example.replace('','TrHermite') + """ + + See also + -------- + spec2skew, ochitr, lc2tr, dat2tr + + References + ---------- + .. [1] Winterstein, S.R, Ude, T.C. and Kleiven, G. (1994) + "Springing and slow drift responses: + predicted extremes and fatigue vs. simulation" + In Proc. 7th International behaviour of Offshore structures, (BOSS) + Vol. 3, pp.1-15 + .. [2] Winterstein, S.R. (1988) + 'Nonlinear vibration models for extremes and fatigue.' + J. Engng. Mech., ASCE, Vol 114, No 10, pp 1772-1790 + """ + def __init__(self,*args, **kwds): + super(TrHermite, self).__init__(*args, **kwds) + self.pardef = kwds.get('pardef',1) + self._c3 = None + self._c4 = None + self._forward = None + self._backward = None + self._x_limit = None + self.set_poly() + + def _poly_par_from_stats(self): + skew = self.skew + ga2 = self.kurt-3.0 + if ga2 <= 0: + self._c4 = ga2/24. + self._c3 = skew/6. + elif self.pardef == 2: + # Winterstein 1988 parametrization + if skew**2>8*(ga2+3.)/9.: + warnings.warn('Kurtosis too low compared to the skewness') + + self._c4 = (sqrt(1.+1.5*ga2)-1.)/18. + self._c3 = skew/(6.*(1+6.*self._c4)) + else: + # Winterstein et. al. 1994 parametrization intended to + # apply for the range: 0 <= ga2 < 12 and 0<= skew^2 < 2*ga2/3 + if skew**2 > 2*(ga2)/3: + warnings.warn('Kurtosis too low compared to the skewness') + + if (ga2 < 0) or (12 < ga2): + warnings.warn('Kurtosis must be between 0 and 12') + + self._c3 = skew/6*(1-0.015*abs(skew)+0.3*skew**2)/(1+0.2*ga2) + if ga2 == 0.: + self._c4 = 0.0 + else: + c41 = (1.-1.43*skew**2./ga2)**(1.-0.1*(ga2+3.)**0.8) + self._c4 = 0.1*((1.+1.25*ga2)**(1./3.)-1.)*c41 + + if not np.isfinite(self._c3) or not np.isfinite(self._c4): + raise ValueError('Unable to calculate the polynomial') + + def set_poly(self): + ''' + Set poly function from stats (i.e., mean, sigma, skew and kurt) + ''' + + if self._c3 is None: + self._poly_par_from_stats() + eps = np.finfo(float).eps + c3 = self._c3 + c4 = self._c4 + ma = self.mean + sa = self.sigma + if abs(c4)0: + # Compute where it is possible to invert the polynomial + if self.kurt<3.: + self._x_limit = r + else: + self._x_limit = sa*p(r)+ma + txt1 = ''' + The polynomial is not a strictly increasing function. + The derivative of g(x) is infinite at x = %g''' % self._x_limit + warnings.warn(txt1) + return + def check_forward(self, x): + if not (self._x_limit is None): + x00 = self._x_limit + txt2 = 'for the given interval x = [%g, %g]' % (x[0],x[-1]) + + if any(np.logical_and(x[0]<= x00, x00 <= x[-1])): + cdef = 1 + else: + cdef = sum( np.logical_xor(x00 <= x[0] , x00 <= x[-1])) + + if np.mod(cdef,2): + errtxt = 'Unable to invert the polynomial \n %s' % txt2 + raise ValueError(errtxt) + np.disp('However, successfully inverted the polynomial\n %s' % txt2) + + + def _dat2gauss(self,x, *xi): + if len(xi)>0: + raise ValueError('Transforming derivatives is not implemented!') + xn = atleast_1d(x) + self.check_forward(xn) + + xn = (xn-self.mean)/self.sigma + + if self._forward is None: + #Inverting the polynomial + yn = self._poly_inv(self._backward,xn) + else: + yn = self._forward(xn) + return yn*self.ysigma + self.ymean + + def _gauss2dat(self, y, *yi): + if len(yi)>0: + raise ValueError('Transforming derivatives is not implemented!') + yn = (atleast_1d(y)-self.mean)/self.ysigma + #self.check_forward(y) + + if self._backward is None: + #% Inverting the polynomial + #%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + xn = self._poly_inv(self._forward,yn) + else: + xn = self._backward(yn) + return self.sigma*xn + self.mean + + def _poly_inv(self, p, xn): + ''' + Invert polynomial + ''' + if p.order<2: + return xn + elif p.order==2: + # Quadratic: Solve a*u**2+b*u+c = xn + coefs = p.coeffs + a = coefs[0] + b = coefs[1] + c = coefs[2]-xn + t = 0.5*(b+sign(b)*sqrt(b**2-4*a*c)) + #so1 = t/a # largest solution + so2 = -c/t # smallest solution + return so2 + elif p.order==3: + # Solve + # K*(c4*u^3+c3*u^2+(1-3*c4)*u-c3) = xn = (x-ma)/sa + # -c4*xn^3-c3*xn^2+(1+3*c4)*xn+c3 = u + coefs = p.coeffs[1::]/p.coeffs[0] + a = coefs[0] + b = coefs[1] + c = coefs[2]-xn/p.coeffs[0] + + x0 = a/3. + #% substitue xn = z-x0 and divide by c4 => z^3 + 3*p1*z+2*q0 = 0 + p1 = b/3-x0**2 + #p1 = (b-a**2/3)/3 + + + #q0 = (c + x0*(2.*x0/3.-b))/2. + #q0 = x0**3 -a*b/6 +c/2 + q0 = x0*(x0**2-b/2)+c/2 +## # z^3+3*p1*z+2*q0=0 + +## c3 = self._c3 +## c4 = self._c4 +## b1 = 1./(3.*c4) +## #x0 = c3*b1 +## #% substitue u = z-x0 and divide by c4 => z^3 + 3*c*z+2*q0 = 0 +## #p1 = b1-1.-x0**2. +## Km1 = np.sqrt(1.+2.*c3**2+6*c4**2) +## q0 = x0**3-1.5*b1*(x0+xn*Km1) + #q0 = x0**3-1.5*b1*(x0+xn) + if not (self._x_limit is None): # % Three real roots + d = sqrt(-p1) + theta1 = arccos(-q0/d**3)/3 + th2 = np.r_[0, -2*pi/3, 2*pi/3] + x1 = abs(2*d*cos(theta1[ceil(len(xn)/2)] + th2)-x0) + ix = x1.argmin() # % choose the smallest solution + return 2.*d*cos(theta1 + th2[ix])-x0 + else: # %Only one real root exist + q1 = sqrt((q0)**2+p1**3) + #% Find the real root of the monic polynomial + A0 = (q1-q0)**(1./3.) + B0 = -(q1+q0)**(1./3.) + return A0+B0-x0 #% real root + #%% The other complex roots are given by + #%x= -(A0+B0)/2+(A0-B0)*sqrt(3)/2-x0 + #%x=-(A0+B0)/2+(A0-B0)*sqrt(-3)/2-x0 + + +class TrOchi(TrCommon): + __doc__ = TrCommon.__doc__.replace('','Ochi') + """ + + Description + ----------- + The Ochi transformation model is a monotonic exponential function, + calibrated such that the first 3 moments of the transformed model + G(y)=g^-1(y) match the moments of the true process. However, the + skewness is limited by ABS(SKEW)<2.82. According to Ochi it is + appropriate for a process with very strong non-linear characteristics. + The model is given as: + g(x) = ((1-exp(-gamma*(x-mean)/sigma))/gamma-mean2)/sigma2 + where + gamma = 1.28*a for x>=mean + 3*a otherwise + mean, + sigma = standard deviation and mean, respectively, of the process. + mean2, + sigma2 = normalizing parameters in the transformed world, i.e., to + make the gaussian process in the transformed world is N(0,1). + + The unknown parameters a, mean2 and sigma2 are found by solving the + following non-linear equations: + + a*(sigma2^2+mean2^2)+mean2 = 0 + sigma2^2-2*a^2*sigma2^4 = 1 + 2*a*sigma2^4*(3-8*a^2*sigma2^2) = skew + + Note + ---- + Transformation, g, does not have continous derivatives of 2'nd order or higher. + + Example + ------- + """ + _example.replace('','TrOchi') + """ + + See also + -------- + spec2skew, hermitetr, lc2tr, dat2tr + + References + ---------- + Ochi, M.K. and Ahn, K. (1994) + 'Non-Gaussian probability distribution of coastal waves.' + In Proc. 24th Conf. Coastal Engng, Vol. 1, pp 482-496 + + Michel K. Ochi (1998), + "OCEAN WAVES, The stochastic approach", + OCEAN TECHNOLOGY series 6, Cambridge, pp 255-275. + """ + + def __init__(self, *args, **kwds): + super(TrOchi, self).__init__(*args, **kwds) + self.kurt = None + self._phat = None + self._par_from_stats() + + def _par_from_stats(self): + skew = self.skew + if abs(skew)>2.82842712474619: + raise ValueError('Skewness must be less than 2.82842') + + mean1 = self.mean + sigma1 = self.sigma + + if skew==0: + self._phat = [sigma1, mean1, 0, 0, 1, 0] + return + + # Solve the equations to obtain the gamma parameters: + #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + # a*(sig2^2+ma2^2)+ma2 = 0 + # sig2^2-2*a^2*sig2^4 = E(y^2) % =1 + # 2*a*sig2^4*(3-8*a^2*sig2^2) = E(y^3) % = skew + + # Let x = [a sig2^2 ] + # Set up the 2D non-linear equations for a and sig2^2: + # g1='[x(2)-2.*x(1).^2.*x(2).^2-P1, 2.*x(1).*x(2).^2.*(3-8.*x(1).^2.*x(2))-P2 ]' + # Or solve the following 1D non-linear equation for sig2^2: + g2 = lambda x: -sqrt(abs(x-1)*2)*(3.*x-4*abs(x-1))+abs(skew) + + + a1 = 1. # % Start interval where sig2^2 is located. + a2 = 2. + + sig22 = brentq(g2,a1,a2) #% smallest solution for sig22 + a = sign(skew)*sqrt(abs(sig22-1)/2)/sig22 + gam_a = 1.28*a + gam_b = 3*a + sigma2 = sqrt(sig22) + + #% Solve the following 2nd order equation to obtain ma2 + #% a*(sig2^2+ma2^2)+ma2 = 0 + my2 = (-1.-sqrt(1.-4.*a**2*sig22))/a #% Largest mean + mean2 = a*sig22/my2 #% choose the smallest mean + + self._phat = [sigma1, mean1, gam_a, gam_b, sigma2, mean2] + return + + def _get_par(self): + ''' + Returns ga, gb, sigma2, mean2 + ''' + if (self._phat is None or self.sigma!=self._phat[0] + or self.mean!=self._phat[1]): + self._par_from_stats() + #sigma1 = self._phat[0] + #mean1 = self._phat[1] + ga = self._phat[2] + gb = self._phat[3] + sigma2 = self._phat[4] + mean2 = self._phat[5] + return ga, gb, sigma2, mean2 + + def _dat2gauss(self,x, *xi): + if len(xi)>0: + raise ValueError('Transforming derivatives is not implemented!') + ga, gb, sigma2, mean2 = self._get_par() + mean = self.mean + sigma = self.sigma + xn = atleast_1d(x) + xn = (xn-mean)/sigma + igp, = where(0 <= xn) + igm, = where(xn < 0) + + g = xn.copy() + + if ga!=0: + np.put(g,igp,(-expm1(-ga*xn[igp]))/ga) + + if gb!=0: + np.put(g,igm,(-expm1(-gb*xn[igm]))/gb) + + return (g-mean2)*self.ysigma/sigma2 + self.ymean + + def _gauss2dat(self,y, *yi): + if len(yi)>0: + raise ValueError('Transforming derivatives is not implemented!') + + ga, gb, sigma2, mean2 = self._get_par() + mean = self.mean + sigma = self.sigma + + yn = (atleast_1d(y)-self.ymean)/self.ysigma + xn = sigma2*yn+mean2 + + igp, = where(0 <= xn) + igm, = where(xn < 0) + + if ga!=0: + np.put(xn, igp, -log1p(-ga*xn[igp])/ga) + + if gb!=0: + np.put(xn, igm, -log1p(-gb*xn[igm])/gb) + + return sigma*xn + mean + +def main(): + import pylab + g = TrHermite(skew=0.1,kurt=3.01) + g.dist2gauss() + #g = TrOchi(skew=0.56) + x = np.linspace(-5,5) + y = g(x) + pylab.plot(np.abs(x-g.gauss2dat(y))) + #pylab.plot(x,y,x,x,':',g.gauss2dat(y),y,'r') + + pylab.show() + np.disp('finito') + +if __name__=='__main__': + if True : # False: # + import doctest + doctest.testmod() + else: + main() + + + diff --git a/wafo/wafodata.py b/wafo/wafodata.py new file mode 100755 index 0000000..987fe57 --- /dev/null +++ b/wafo/wafodata.py @@ -0,0 +1,210 @@ +import warnings +from plotbackend import plotbackend +from time import gmtime, strftime +import numpy as np + +__all__ = ['WafoData', 'AxisLabels'] + +def empty_copy(obj): + class Empty(obj.__class__): + def __init__(self): + pass + newcopy = Empty() + newcopy.__class__ = obj.__class__ + return newcopy + +def _set_seed(iseed): + if iseed != None: + try: + np.random.set_state(iseed) + except: + np.random.seed(iseed) +def now(): + ''' + Return current date and time as a string + ''' + return strftime("%a, %d %b %Y %H:%M:%S", gmtime()) + +class WafoData(object): + ''' + Container class for data objects in WAFO + + Member variables + ---------------- + data : array_like + args : vector for 1D, list of vectors for 2D, 3D, ... + labels : AxisLabels + children : list of WafoData objects + + Member methods + -------------- + plot : + copy : + + + Example + ------- + >>> import numpy as np + >>> x = np.arange(-2, 2, 0.2) + + # Plot 2 objects in one call + >>> d2 = WafoData(np.sin(x), x, xlab='x', ylab='sin', title='sinus') + >>> h = d2.plot() + + Plot with confidence interval + d3 = wdata(sin(x),x) + d3 = set(d3,'dataCI',[sin(x(:))*0.9 sin(x(:))*1.2]) + plot(d3) + + See also + -------- + wdata/plot, + specdata, + covdata + ''' + def __init__(self, data=None, args=None,**kwds): + self.data = data + self.args = args + self.date = now() + self.plotter = None + self.children = None + self.labels = AxisLabels(**kwds) + self.setplotter() + + def plot(self,*args,**kwds): + tmp = None + if self.children!=None: + plotbackend.hold('on') + tmp = [] + for child in self.children: + tmp1 = child.plot(*args, **kwds) + if tmp1 !=None: + tmp.append(tmp1) + if len(tmp)==0: + tmp = None + + tmp2 = self.plotter.plot(self,*args,**kwds) + return tmp2,tmp + + def show(self): + self.plotter.show() + + def copy(self): + newcopy = empty_copy(self) + newcopy.__dict__.update(self.__dict__) + return newcopy + + + def setplotter(self,plotmethod=None): + ''' + Set plotter based on the data type data_1d, data_2d, data_3d or data_nd + ''' + + if isinstance(self.args,(list,tuple)): # Multidimensional data + ndim = len(self.args) + if ndim<2: + warnings.warn('Unable to determine plotter-type, because len(self.args)<2.') + print('If the data is 1D, then self.args should be a vector!') + print('If the data is 2D, then length(self.args) should be 2.') + print('If the data is 3D, then length(self.args) should be 3.') + print('Unless you fix this, the plot methods will not work!') + elif ndim==2: + self.plotter = Plotter_2d(plotmethod) + else: + warnings.warn('Plotter method not implemented for ndim>2') + + else: #One dimensional data + self.plotter = Plotter_1d(plotmethod) + + +class AxisLabels: + def __init__(self,title='',xlab='',ylab='',zlab='',**kwds): + self.title = title + self.xlab = xlab + self.ylab = ylab + self.zlab = zlab + def copy(self): + newcopy = empty_copy(self) + newcopy.__dict__.update(self.__dict__) + return newcopy + #lbkwds = self.labels.__dict__.copy() + #labels = AxisLabels(**lbkwds) + #return labels + + def labelfig(self): + try: + h1 = plotbackend.title(self.title) + h2 = plotbackend.xlabel(self.xlab) + h3 = plotbackend.ylabel(self.ylab) + #h4 = plotbackend.zlabel(self.zlab) + return h1,h2,h3 + except: + pass + +class Plotter_1d(object): + """ + + Parameters + ---------- + plotmethod : string + defining type of plot. Options are: + bar : bar plot with rectangles + barh : horizontal bar plot with rectangles + loglog : plot with log scaling on the *x* and *y* axis + semilogx : plot with log scaling on the *x* axis + semilogy : plot with log scaling on the *y* axis + plot : Plot lines and/or markers (default) + stem : Stem plot + step : stair-step plot + scatter : scatter plot + """ + + def __init__(self,plotmethod='plot'): + self.plotfun = None + if plotmethod is None: + plotmethod = 'plot' + self.plotbackend = plotbackend + try: + #self.plotfun = plotbackend.__dict__[plotmethod] + self.plotfun = getattr(plotbackend, plotmethod) + except: + pass + def show(self): + plotbackend.show() + + def plot(self,wdata,*args,**kwds): + if isinstance(wdata.args,(list,tuple)): + args1 = tuple((wdata.args))+(wdata.data,)+args + else: + args1 = tuple((wdata.args,))+(wdata.data,)+args + h1 = self.plotfun(*args1,**kwds) + h2 = wdata.labels.labelfig() + return h1,h2 + +class Plotter_2d(Plotter_1d): + """ + Parameters + ---------- + plotmethod : string + defining type of plot. Options are: + contour (default) + mesh + surf + """ + + def __init__(self,plotmethod='contour'): + if plotmethod is None: + plotmethod = 'contour' + super(Plotter_2d,self).__init__(plotmethod) + #self.plotfun = plotbackend.__dict__[plotmethod] + + +def main(): + pass + +if __name__ == '__main__': + if True: #False : # + import doctest + doctest.testmod() + else: + main() \ No newline at end of file