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@ -6,7 +6,8 @@ from __future__ import division
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import sys
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import fractions
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import numpy as np
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from numpy import (abs, amax, any, logical_and, arange, linspace, atleast_1d, #atleast_2d,
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from numpy import (
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abs, amax, any, logical_and, arange, linspace, atleast_1d, # atleast_2d,
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array, asarray, broadcast_arrays, ceil, floor, frexp, hypot,
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sqrt, arctan2, sin, cos, exp, log, mod, diff, empty_like,
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finfo, inf, pi, interp, isnan, isscalar, zeros, ones, linalg,
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@ -25,7 +26,8 @@ except:
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floatinfo = finfo(float)
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__all__ = ['is_numlike', 'JITImport', 'DotDict', 'Bunch', 'printf', 'sub_dict_select',
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__all__ = [
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'is_numlike', 'JITImport', 'DotDict', 'Bunch', 'printf', 'sub_dict_select',
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'parse_kwargs', 'detrendma', 'ecross', 'findcross',
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'findextrema', 'findpeaks', 'findrfc', 'rfcfilter', 'findtp', 'findtc',
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'findoutliers', 'common_shape', 'argsreduce',
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@ -43,7 +45,9 @@ def is_numlike(obj):
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else:
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return True
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class JITImport(object):
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'''
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Just In Time Import of module
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@ -53,9 +57,11 @@ class JITImport(object):
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>>> np.exp(0)==1.0
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True
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'''
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def __init__(self, module_name):
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self._module_name = module_name
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self._module = None
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def __getattr__(self, attr):
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try:
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return getattr(self._module, attr)
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@ -67,7 +73,9 @@ class JITImport(object):
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else:
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raise
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class DotDict(dict):
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''' Implement dot access to dict values
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Example
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@ -78,7 +86,9 @@ class DotDict(dict):
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'''
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__getattr__ = dict.__getitem__
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class Bunch(object):
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''' Implement keyword argument initialization of class
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Example
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@ -87,13 +97,17 @@ class Bunch(object):
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>>> d.test1
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1
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'''
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def __init__(self, **kwargs):
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self.__dict__.update(kwargs)
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def keys(self):
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return self.__dict__.keys()
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def update(self, ** kwargs):
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self.__dict__.update(kwargs)
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def printf(format, *args): # @ReservedAssignment
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sys.stdout.write(format % args)
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@ -122,7 +136,7 @@ def sub_dict_select(somedict, somekeys):
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def parse_kwargs(options, **kwargs):
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''' Update options dict from keyword arguments if the keyword exists in options
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''' Update options dict from keyword arguments if it exists in options
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Example
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>>> opt = dict(arg1=2, arg2=3)
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@ -140,13 +154,16 @@ def parse_kwargs(options, **kwargs):
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options.update(newopts)
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return options
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def testfun(*args, **kwargs):
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opts = dict(opt1=1, opt2=2)
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if len(args) == 1 and len(kwargs) == 0 and type(args[0]) is str and args[0].startswith('default'):
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if (len(args) == 1 and len(kwargs) == 0 and type(args[0]) is str and
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args[0].startswith('default')):
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return opts
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opts = parse_kwargs(opts, **kwargs)
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return opts
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def detrendma(x, L):
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"""
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Removes a trend from data using a moving average
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@ -194,7 +211,6 @@ def detrendma(x, L):
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if n < 2 * L + 1: # only able to remove the mean
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return x1 - x1.mean(axis=0)
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mn = x1[0:2 * L + 1].mean(axis=0)
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y = empty_like(x1)
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y[0:L] = x1[0:L] - mn
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@ -205,6 +221,7 @@ def detrendma(x, L):
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y[n - L::] = x1[n - L::] - trend[-1]
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return y
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def ecross(t, f, ind, v=0):
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'''
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Extracts exact level v crossings
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@ -252,7 +269,9 @@ def ecross(t, f, ind, v=0):
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# Tested on: Python 2.5
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# revised pab Feb2004
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# By pab 18.06.2001
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return t[ind] + (v - f[ind]) * (t[ind + 1] - t[ind]) / (f[ind + 1] - f[ind])
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return (t[ind] + (v - f[ind]) * (t[ind + 1] - t[ind]) /
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(f[ind + 1] - f[ind]))
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def _findcross(xn):
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'''Return indices to zero up and downcrossings of a vector
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@ -288,6 +307,7 @@ def _findcross(xn):
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ind, = (xn[:n - 1] * xn[1:] < 0).nonzero()
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return ind
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def findcross(x, v=0.0, kind=None):
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'''
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Return indices to level v up and/or downcrossings of a vector
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@ -352,10 +372,11 @@ def findcross(x, v=0.0, kind=None):
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t_0 = int(xn[ind[0] + 1] < 0)
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ind = ind[t_0::2]
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elif kind in ('dw', 'uw', 'tw', 'cw'):
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#make sure that the first is a level v down-crossing if wdef=='dw'
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#or make sure that the first is a level v up-crossing if wdef=='uw'
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#make sure that the first is a level v down-crossing if wdef=='tw'
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#or make sure that the first is a level v up-crossing if wdef=='cw'
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# make sure the first is a level v down-crossing if wdef=='dw'
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# or make sure the first is a level v up-crossing if wdef=='uw'
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# make sure the first is a level v down-crossing if wdef=='tw'
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# or make sure the first is a level v up-crossing if
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# wdef=='cw'
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xor = lambda a, b: a ^ b
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first_is_down_crossing = int(xn[ind[0]] > xn[ind[0] + 1])
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if xor(first_is_down_crossing, kind in ('dw', 'tw')):
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@ -372,6 +393,7 @@ def findcross(x, v=0.0, kind=None):
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raise ValueError('Unknown wave/crossing definition!')
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return ind
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def findextrema(x):
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'''
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Return indices to minima and maxima of a vector
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@ -402,6 +424,8 @@ def findextrema(x):
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'''
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xn = atleast_1d(x).ravel()
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return findcross(diff(xn), 0.0) + 1
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def findpeaks(data, n=2, min_h=None, min_p=0.0):
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'''
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Find peaks of vector or matrix possibly rainflow filtered
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@ -461,7 +485,8 @@ def findpeaks(data, n=2, min_h=None, min_p=0.0):
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elif iy == nrows - 1:
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ind2 = np.flatnonzero(S[iy, ind] > S[iy - 1, ind])
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else:
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ind2 = np.flatnonzero((S[iy, ind] > S[iy - 1, ind]) & (S[iy, ind] > S[iy + 1, ind]))
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ind2 = np.flatnonzero((S[iy, ind] > S[iy - 1, ind]) &
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(S[iy, ind] > S[iy + 1, ind]))
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if len(ind2):
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indP.append((ind[ind2] + iy * mcols))
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@ -474,16 +499,17 @@ def findpeaks(data, n=2, min_h=None, min_p=0.0):
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peaks = S.take(ind)
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ind2 = peaks.argsort()[::-1]
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# keeping only the Np most significant peak frequencies.
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nmax = min(n, len(ind))
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ind = ind[ind2[:nmax]]
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if (min_p > 0):
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# Keeping only peaks larger than min_p percent relative to the maximum peak
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# Keeping only peaks larger than min_p percent relative to the maximum
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# peak
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ind = ind[(S.take(ind) > min_p * smax)]
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return ind
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def findrfc_astm(tp):
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"""
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Return rainflow counted cycles
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@ -514,6 +540,7 @@ def findrfc_astm(tp):
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# sig_rfc holds the actual rainflow counted cycles, not the indices
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return sig_rfc
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def findrfc(tp, h=0.0, method='clib'):
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'''
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Return indices to rainflow cycles of a sequence of TP.
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@ -624,7 +651,6 @@ def findrfc(tp, h=0.0, method='clib'):
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#iy = i
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continue
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# goto L180
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# L170:
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if (xplus <= xminus):
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@ -646,9 +672,11 @@ def findrfc(tp, h=0.0, method='clib'):
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ind, ix = clib.findrfc(y, h)
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return np.sort(ind[:ix])
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def mctp2rfc(fmM, fMm=None):
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'''
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Return Rainflow matrix given a Markov matrix of a Markov chain of turning points
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Return Rainflow matrix given a Markov matrix of a Markov chain
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of turning points
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computes f_rfc = f_mM + F_mct(f_mM).
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@ -707,7 +735,8 @@ def mctp2rfc(fmM, fMm=None):
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SRA = RAA.sum()
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DRFC = SA - SRA
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NT = min(mA[0] - sum(RAA[:, 0]), MA[0] - sum(RAA[0, :])) # ?? check
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# ?? check
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NT = min(mA[0] - sum(RAA[:, 0]), MA[0] - sum(RAA[0, :]))
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NT = max(NT, 0) # ??check
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if NT > 1e-6 * max(MA[0], mA[0]):
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@ -722,13 +751,14 @@ def mctp2rfc(fmM, fMm=None):
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e[j] = e[j] / norm
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# end
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# end
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fx = 0.0;
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if max(abs(e)) > 1e-6 and max(abs(NN)) > 1e-6 * max(MA[0], mA[0]):
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fx = 0.0
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if (max(abs(e)) > 1e-6 and
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max(abs(NN)) > 1e-6 * max(MA[0], mA[0])):
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PMm = AA1.copy()
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for j in range(nA):
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norm = MA[j]
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if norm != 0:
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PMm[j, :] = PMm[j, :] / norm;
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PMm[j, :] = PMm[j, :] / norm
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# end
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# end
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PMm = np.fliplr(PMm)
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@ -740,7 +770,8 @@ def mctp2rfc(fmM, fMm=None):
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fx = NN * (A / (1 - B * A) * e)
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else:
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rh = np.eye(A.shape[0]) - np.dot(B, A)
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fx = np.dot(NN, np.dot(A, linalg.solve(rh, e))) #least squares
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#least squares
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fx = np.dot(NN, np.dot(A, linalg.solve(rh, e)))
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# end
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# end
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f_rfc[N - 1 - k, k - i] = fx + DRFC
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@ -758,8 +789,8 @@ def mctp2rfc(fmM, fMm=None):
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# end
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for k in range(1, N):
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M0 = max(0, f_max[0] - np.sum(f_rfc[0, N - k:N]));
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m0 = max(0, f_min[N - 1 - k] - np.sum(f_rfc[1:k+1, N - 1 - k]));
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M0 = max(0, f_max[0] - np.sum(f_rfc[0, N - k:N]))
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m0 = max(0, f_min[N - 1 - k] - np.sum(f_rfc[1:k + 1, N - 1 - k]))
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f_rfc[0, N - 1 - k] = min(m0, M0)
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# end
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@ -781,7 +812,6 @@ def mctp2rfc(fmM, fMm=None):
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return f_rfc
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def rfcfilter(x, h, method=0):
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"""
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Rainflow filter a signal.
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@ -866,9 +896,11 @@ def rfcfilter(x, h, method=0):
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z1 = 0
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t1, y1 = (t0, y0) if z1 == 0 else (ti, yi)
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else:
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if (((z0 == +1) & cmpfun1(yi, fmi)) | ((z0 == -1) & cmpfun2(yi, fpi))):
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if (((z0 == +1) & cmpfun1(yi, fmi)) |
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((z0 == -1) & cmpfun2(yi, fpi))):
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z1 = -1
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elif (((z0 == +1) & cmpfun2(fmi, yi)) | ((z0 == -1) & cmpfun1(fpi, yi))):
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elif (((z0 == +1) & cmpfun2(fmi, yi)) |
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((z0 == -1) & cmpfun1(fpi, yi))):
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|
z1 = +1
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|
else:
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|
|
warnings.warn('Something wrong, i=%d' % tim1)
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|
@ -898,6 +930,7 @@ def rfcfilter(x, h, method=0):
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|
t[j] = t0
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|
return y[t[:j + 1]]
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def findtp(x, h=0.0, kind=None):
|
|
|
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|
'''
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|
|
Return indices to turning points (tp) of data, optionally rainflowfiltered.
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|
|
|
@ -936,7 +969,9 @@ def findtp(x, h=0.0, kind=None):
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|
>>> itph = wm.findtp(x1[:,1],0.3,'Mw')
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|
>>> tp = x1[itp,:]
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|
>>> tph = x1[itph,:]
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|
>>> a = plb.plot(x1[:,0],x1[:,1],tp[:,0],tp[:,1],'ro',tph[:,1],tph[:,1],'k.')
|
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|
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|
>>> a = plb.plot(x1[:,0],x1[:,1],
|
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|
|
|
... tp[:,0],tp[:,1],'ro',
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|
|
|
... tph[:,1],tph[:,1],'k.')
|
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|
|
>>> plb.close('all')
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|
>>> itp
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|
|
array([ 11, 21, 22, 24, 26, 28, 31, 39, 43, 45, 47, 51, 56,
|
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|
|
@ -970,7 +1005,8 @@ def findtp(x, h=0.0, kind=None):
|
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|
|
|
if kind == 'astm':
|
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|
|
|
# the Nieslony approach always put the first loading point as the first
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|
# turning point.
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|
if x[ind[0]] != x[0]: # add the first turning point is the first of the signal
|
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|
# add the first turning point is the first of the signal
|
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|
|
if x[ind[0]] != x[0]:
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|
ind = np.r_[0, ind, n - 1]
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else: # only add the last point of the signal
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|
ind = np.r_[ind, n - 1]
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|
@ -1000,6 +1036,7 @@ def findtp(x, h=0.0, kind=None):
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|
ind = ind[:-1]
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|
return ind
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|
def findtc(x_in, v=None, kind=None):
|
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|
"""
|
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|
Return indices to troughs and crests of data.
|
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|
@ -1092,6 +1129,7 @@ def findtc(x_in, v=None, kind=None):
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|
return v_ind[:n_c - 1] + ind + 1, v_ind
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def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
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|
"""
|
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|
Return indices to spurious points of data
|
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|
@ -1120,7 +1158,8 @@ def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
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|
-----
|
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|
|
|
Consecutive points less than zcrit apart are considered as spurious.
|
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|
The point immediately after and before are also removed. Jumps greater than
|
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|
|
dcrit in Dxn and greater than ddcrit in D^2xn are also considered as spurious.
|
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|
|
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:
|
|
|
|
|
|
|
|
|
|
@ -1153,7 +1192,6 @@ def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
|
|
|
|
waveplot, reconstruct
|
|
|
|
|
"""
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# finding outliers
|
|
|
|
|
findjumpsDx = True # find jumps in Dx
|
|
|
|
|
# two point spikes and Spikes dcrit above/under the
|
|
|
|
|
@ -1168,7 +1206,6 @@ def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
|
|
|
|
if xn.size < 2:
|
|
|
|
|
raise ValueError('The vector must have more than 2 elements!')
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ind = zeros(0, dtype=int)
|
|
|
|
|
# indg=[]
|
|
|
|
|
indmiss = isnan(xn)
|
|
|
|
|
@ -1249,7 +1286,8 @@ def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
|
|
|
|
indtr, = nonzero((diff(indzeros)))
|
|
|
|
|
indtr = indtr + 1
|
|
|
|
|
#%indices to consecutive equal points
|
|
|
|
|
if True: # removing the point before + all equal points + the point after
|
|
|
|
|
# removing the point before + all equal points + the point after
|
|
|
|
|
if True:
|
|
|
|
|
ind = hstack((ind, indtr - 1, indz, indtr, indtr + 1))
|
|
|
|
|
else: # % removing all points + the point after
|
|
|
|
|
ind = hstack((ind, indz, indtr, indtr + 1))
|
|
|
|
|
@ -1258,7 +1296,8 @@ def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
|
|
|
|
if zcrit == 0.:
|
|
|
|
|
print('Found %d consecutive equal values' % indz.size)
|
|
|
|
|
else:
|
|
|
|
|
print('Found %d consecutive values less than %g apart.' % (indz.size, zcrit))
|
|
|
|
|
print('Found %d consecutive values less than %g apart.' %
|
|
|
|
|
(indz.size, zcrit))
|
|
|
|
|
indg = ones(xn.size, dtype=bool)
|
|
|
|
|
|
|
|
|
|
if ind.size > 1:
|
|
|
|
|
@ -1271,6 +1310,7 @@ def findoutliers(x, zcrit=0.0, dcrit=None, ddcrit=None, verbose=False):
|
|
|
|
|
|
|
|
|
|
return ind, indg
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def common_shape(*args, ** kwds):
|
|
|
|
|
'''
|
|
|
|
|
Return the common shape of a sequence of arrays
|
|
|
|
|
@ -1339,8 +1379,8 @@ def common_shape(*args, ** kwds):
|
|
|
|
|
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.
|
|
|
|
|
# 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)
|
|
|
|
|
@ -1351,6 +1391,7 @@ def common_shape(*args, ** kwds):
|
|
|
|
|
|
|
|
|
|
return tuple(c_shape)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def argsreduce(condition, * args):
|
|
|
|
|
""" Return the elements of each input array that satisfy some condition.
|
|
|
|
|
|
|
|
|
|
@ -1399,7 +1440,8 @@ def argsreduce(condition, * args):
|
|
|
|
|
|
|
|
|
|
def stirlerr(n):
|
|
|
|
|
'''
|
|
|
|
|
Return error of Stirling approximation, i.e., log(n!) - log( sqrt(2*pi*n)*(n/exp(1))**n )
|
|
|
|
|
Return error of Stirling approximation,
|
|
|
|
|
i.e., log(n!) - log( sqrt(2*pi*n)*(n/exp(1))**n )
|
|
|
|
|
|
|
|
|
|
Example
|
|
|
|
|
-------
|
|
|
|
|
@ -1430,7 +1472,6 @@ def stirlerr(n):
|
|
|
|
|
|
|
|
|
|
y = gammaln(n1 + 1) - log(sqrt(2 * pi * n1) * (n1 / exp(1)) ** n1)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
nn = n1 * n1
|
|
|
|
|
|
|
|
|
|
n500 = 500 < n1
|
|
|
|
|
@ -1446,11 +1487,16 @@ def stirlerr(n):
|
|
|
|
|
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]
|
|
|
|
|
y[n15] = (
|
|
|
|
|
S0 - (S1 - (S2 - (S3 - S4 / nn15) / nn15) / nn15) / nn15) / n1[n15]
|
|
|
|
|
|
|
|
|
|
return y
|
|
|
|
|
|
|
|
|
|
def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssignment
|
|
|
|
|
#@ReservedAssignment
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def getshipchar(value=None, property="max_deadweight", # @ReservedAssignment
|
|
|
|
|
**kwds):
|
|
|
|
|
'''
|
|
|
|
|
Return ship characteristics from value of one ship-property
|
|
|
|
|
|
|
|
|
|
@ -1464,15 +1510,16 @@ def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssign
|
|
|
|
|
'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]_.
|
|
|
|
|
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:
|
|
|
|
|
containing estimated mean values and standard-deviations of ship
|
|
|
|
|
characteristics:
|
|
|
|
|
max_deadweight [kkg], (weight of cargo, fuel etc.)
|
|
|
|
|
length [m]
|
|
|
|
|
beam [m]
|
|
|
|
|
@ -1504,8 +1551,8 @@ def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssign
|
|
|
|
|
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.
|
|
|
|
|
"Source level model for propeller blade rate radiation for the world's
|
|
|
|
|
merchant fleet", Bolt Beranek and Newman Technical Memorandum No. 458.
|
|
|
|
|
'''
|
|
|
|
|
if value is None:
|
|
|
|
|
names = kwds.keys()
|
|
|
|
|
@ -1522,7 +1569,8 @@ def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssign
|
|
|
|
|
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)))
|
|
|
|
|
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'
|
|
|
|
|
@ -1540,7 +1588,6 @@ def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssign
|
|
|
|
|
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)
|
|
|
|
|
|
|
|
|
|
@ -1550,13 +1597,16 @@ def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssign
|
|
|
|
|
shipchar = OrderedDict(beam=beam, beamSTD=beam_err,
|
|
|
|
|
draught=draught, draughtSTD=draught_err,
|
|
|
|
|
length=length, lengthSTD=length_err,
|
|
|
|
|
max_deadweight=max_deadweight, max_deadweightSTD=max_deadweightSTD,
|
|
|
|
|
propeller_diameter=p_diam, propeller_diameterSTD=p_diam_err,
|
|
|
|
|
max_deadweight=max_deadweight,
|
|
|
|
|
max_deadweightSTD=max_deadweightSTD,
|
|
|
|
|
propeller_diameter=p_diam,
|
|
|
|
|
propeller_diameterSTD=p_diam_err,
|
|
|
|
|
service_speed=speed, service_speedSTD=speed_err)
|
|
|
|
|
|
|
|
|
|
shipchar[propertySTD] = 0
|
|
|
|
|
return shipchar
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def betaloge(z, w):
|
|
|
|
|
'''
|
|
|
|
|
Natural Logarithm of beta function.
|
|
|
|
|
@ -1595,6 +1645,7 @@ def betaloge(z, w):
|
|
|
|
|
# (-(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
|
|
|
|
|
|
|
|
|
|
@ -1638,7 +1689,9 @@ def gravity(phi=45):
|
|
|
|
|
'''
|
|
|
|
|
|
|
|
|
|
phir = phi * pi / 180. # change from degrees to radians
|
|
|
|
|
return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2. - 0.0000059 * sin(2 * phir) ** 2.)
|
|
|
|
|
return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2. -
|
|
|
|
|
0.0000059 * sin(2 * phir) ** 2.)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def nextpow2(x):
|
|
|
|
|
'''
|
|
|
|
|
@ -1662,6 +1715,7 @@ def nextpow2(x):
|
|
|
|
|
n = n - 1
|
|
|
|
|
return n
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def discretize(fun, a, b, tol=0.005, n=5, method='linear'):
|
|
|
|
|
'''
|
|
|
|
|
Automatic discretization of function
|
|
|
|
|
@ -1702,13 +1756,13 @@ def discretize(fun, a, b, tol=0.005, n=5, method='linear'):
|
|
|
|
|
else:
|
|
|
|
|
return _discretize_linear(fun, a, b, tol, n)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _discretize_linear(fun, a, b, tol=0.005, n=5):
|
|
|
|
|
'''
|
|
|
|
|
Automatic discretization of function, linear gridding
|
|
|
|
|
'''
|
|
|
|
|
tiny = floatinfo.tiny
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
x = linspace(a, b, n)
|
|
|
|
|
y = fun(x)
|
|
|
|
|
|
|
|
|
|
@ -1726,6 +1780,7 @@ def _discretize_linear(fun, a, b, tol=0.005, n=5):
|
|
|
|
|
err = 0.5 * amax(abs((y00 - y) / (abs(y00 + y) + tiny)))
|
|
|
|
|
return x, y
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _discretize_adaptive(fun, a, b, tol=0.005, n=5):
|
|
|
|
|
'''
|
|
|
|
|
Automatic discretization of function, adaptive gridding.
|
|
|
|
|
@ -1747,7 +1802,8 @@ def _discretize_adaptive(fun, a, b, tol=0.005, n=5):
|
|
|
|
|
|
|
|
|
|
I, = where(erri > tol)
|
|
|
|
|
# double the sample rate in intervals with the most error
|
|
|
|
|
y = (vstack(((x[I] + x[I - 1]) / 2, (x[I + 1] + x[I]) / 2)).T).ravel()
|
|
|
|
|
y = (vstack(((x[I] + x[I - 1]) / 2,
|
|
|
|
|
(x[I + 1] + x[I]) / 2)).T).ravel()
|
|
|
|
|
fy = fun(y)
|
|
|
|
|
|
|
|
|
|
fy0 = interp(y, x, fx)
|
|
|
|
|
@ -1903,10 +1959,10 @@ def meshgrid(*xi, **kwargs):
|
|
|
|
|
sparse = kwargs.get('sparse', False)
|
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indexing = kwargs.get('indexing', 'xy') # 'ij'
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ndim = len(args)
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s0 = (1,) * ndim
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output = [x.reshape(s0[:i] + (-1,) + s0[i + 1::]) for i, x in enumerate(args)]
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output = [x.reshape(s0[:i] + (-1,) + s0[i + 1::])
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for i, x in enumerate(args)]
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shape = [x.size for x in output]
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@ -1938,6 +1994,7 @@ def ndgrid(*args, **kwargs):
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kwargs['indexing'] = 'ij'
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return meshgrid(*args, ** kwargs)
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def trangood(x, f, min_n=None, min_x=None, max_x=None, max_n=inf):
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"""
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Make sure transformation is efficient.
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@ -2004,10 +2061,10 @@ def trangood(x, f, min_n=None, min_x=None, max_x=None, max_n=inf):
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L = float(xn - x0)
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eps = floatinfo.eps
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if ((nf < min_n) or (max_n < nf) or any(abs(ddx) > 10 * eps * (L))):
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## % pab 07.01.2001: Always choose the stepsize df so that
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## % it is an exactly representable number.
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## % This is important when calculating numerical derivatives and is
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## % accomplished by the following.
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# % pab 07.01.2001: Always choose the stepsize df so that
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# % it is an exactly representable number.
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# % This is important when calculating numerical derivatives and is
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# % accomplished by the following.
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dx = L / (min(min_n, max_n) - 1)
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dx = (dx + 2.) - 2.
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xi = arange(x0, xn + dx / 2., dx)
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@ -2033,6 +2090,7 @@ def trangood(x, f, min_n=None, min_x=None, max_x=None, max_n=inf):
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return xo, fo
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def tranproc(x, f, x0, *xi):
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"""
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Transforms process X and up to four derivatives
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@ -2108,16 +2166,17 @@ def tranproc(x, f, x0, *xi):
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y = [y0]
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hn = xo[1] - xo[0]
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if hn ** N < sqrt(eps):
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print('Numerical problems may occur for the derivatives in tranproc.')
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warnings.warn('The sampling of the transformation may be too small.')
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msg = ('Numerical problems may occur for the derivatives in ' +
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'tranproc.\nThe sampling of the transformation may be too small.')
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warnings.warn(msg)
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#% Transform X with the derivatives of f.
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# Transform X with the derivatives of f.
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fxder = zeros((N, x0.size))
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fder = vstack((xo, fo))
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for k in range(N): #% Derivation of f(x) using a difference method.
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for k in range(N): # Derivation of f(x) using a difference method.
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n = fder.shape[-1]
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#%fder = [(fder(1:n-1,1)+fder(2:n,1))/2 diff(fder(:,2))./diff(fder(:,1))]
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fder = vstack([(fder[0, 0:n - 1] + fder[0, 1:n]) / 2, diff(fder[1, :]) / hn])
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fder = vstack([(fder[0, 0:n - 1] + fder[0, 1:n]) / 2,
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diff(fder[1, :]) / hn])
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fxder[k] = tranproc(fder[0], fder[1], x0)
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|
# Calculate the transforms of the derivatives of X.
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@ -2141,14 +2200,18 @@ def tranproc(x, f, x0, *xi):
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# Fourth time derivative of y:
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# y4 = f''''(x)*x1.^4+f'(x)*x4
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# +6*f'''(x)*x1^2*x2+f''(x)*(3*x2^2+4x1*x3)
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y4 = (fxder[3] * xi[0] ** 4. + fxder[0] * xi[3] + \
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6. * fxder[2] * xi[0] ** 2. * xi[1] + \
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y4 = (fxder[3] * xi[0] ** 4. + fxder[0] * xi[3] +
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6. * fxder[2] * xi[0] ** 2. * xi[1] +
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|
fxder[1] * (3. * xi[1] ** 2. + 4. * xi[0] * xi[1]))
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|
|
y.append(y4)
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|
|
if N > 4:
|
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|
|
warnings.warn('Transformation of derivatives of order>4 not supported.')
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|
|
warnings.warn('Transformation of derivatives of ' +
|
|
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|
|
'order>4 not supported.')
|
|
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|
|
return y # y0,y1,y2,y3,y4
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|
def good_bins(data=None, range=None, num_bins=None, num_data=None, odd=False, loose=True): #@ReservedAssignment
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|
def good_bins(data=None, range=None, num_bins=None, # @ReservedAssignment
|
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|
|
num_data=None, odd=False, loose=True):
|
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|
|
''' Return good bins for histogram
|
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|
|
Parameters
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|
|
@ -2158,7 +2221,8 @@ def good_bins(data=None, range=None, num_bins=None, num_data=None, odd=False, lo
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|
|
range : (float, float)
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|
|
minimum and maximum range of bins (default data.min(), data.max())
|
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|
|
num_bins : scalar integer
|
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|
|
approximate number of bins wanted (default depending on num_data=len(data))
|
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|
|
approximate number of bins wanted
|
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|
|
(default depending on num_data=len(data))
|
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|
|
odd : bool
|
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|
|
placement of bins (0 or 1) (default 0)
|
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|
|
loose : bool
|
|
|
|
|
@ -2188,7 +2252,7 @@ def good_bins(data=None, range=None, num_bins=None, num_data=None, odd=False, lo
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|
|
num_bins = np.ceil(4 * np.sqrt(np.sqrt(num_data)))
|
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|
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|
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|
|
d = float(mx - mn) / num_bins * 2
|
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|
|
e = np.floor(np.log(d) / np.log(10));
|
|
|
|
|
e = np.floor(np.log(d) / np.log(10))
|
|
|
|
|
m = np.floor(d / 10 ** e)
|
|
|
|
|
if m > 5:
|
|
|
|
|
m = 5
|
|
|
|
|
@ -2201,7 +2265,9 @@ def good_bins(data=None, range=None, num_bins=None, num_data=None, odd=False, lo
|
|
|
|
|
limits = np.arange(mn, mx + d / 2, d)
|
|
|
|
|
return limits
|
|
|
|
|
|
|
|
|
|
def plot_histgrm(data, bins=None, range=None, normed=False, weights=None, lintype='b-'): #@ReservedAssignment
|
|
|
|
|
|
|
|
|
|
def plot_histgrm(data, bins=None, range=None, # @ReservedAssignment
|
|
|
|
|
normed=False, weights=None, lintype='b-'):
|
|
|
|
|
'''
|
|
|
|
|
Plot histogram
|
|
|
|
|
|
|
|
|
|
@ -2254,7 +2320,9 @@ def plot_histgrm(data, bins=None, range=None, normed=False, weights=None, lintyp
|
|
|
|
|
if bins is None:
|
|
|
|
|
bins = np.ceil(4 * np.sqrt(np.sqrt(len(x))))
|
|
|
|
|
|
|
|
|
|
bin_, limits = np.histogram(data, bins=bins, normed=normed, weights=weights) #, new=True)
|
|
|
|
|
#, new=True)
|
|
|
|
|
bin_, limits = np.histogram(
|
|
|
|
|
data, bins=bins, normed=normed, weights=weights)
|
|
|
|
|
limits.shape = (-1, 1)
|
|
|
|
|
xx = limits.repeat(3, axis=1)
|
|
|
|
|
xx.shape = (-1,)
|
|
|
|
|
@ -2267,6 +2335,7 @@ def plot_histgrm(data, bins=None, range=None, normed=False, weights=None, lintyp
|
|
|
|
|
yy = np.hstack((yy, 0.0))
|
|
|
|
|
return plotbackend.plot(xx, yy, lintype, limits, limits * 0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def num2pistr(x, n=3):
|
|
|
|
|
'''
|
|
|
|
|
Convert a scalar to a text string in fractions of pi
|
|
|
|
|
@ -2303,6 +2372,7 @@ def num2pistr(x, n=3):
|
|
|
|
|
xtxt = format % x
|
|
|
|
|
return xtxt
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def fourier(data, t=None, T=None, m=None, n=None, method='trapz'):
|
|
|
|
|
'''
|
|
|
|
|
Returns Fourier coefficients.
|
|
|
|
|
@ -2314,7 +2384,8 @@ def fourier(data, t=None, T=None, m=None, n=None, method='trapz'):
|
|
|
|
|
t : array-like
|
|
|
|
|
vector with n values indexed from 1 to N.
|
|
|
|
|
T : real scalar
|
|
|
|
|
primitive period of signal, i.e., smallest period. (default T = t[-1]-t[0]
|
|
|
|
|
primitive period of signal, i.e., smallest period.
|
|
|
|
|
(default T = t[-1]-t[0]
|
|
|
|
|
m : scalar integer
|
|
|
|
|
defines no of harmonics desired (default M = N)
|
|
|
|
|
n : scalar integer
|
|
|
|
|
@ -2398,7 +2469,7 @@ def fourier(data, t=None, T=None, m=None, n=None, method='trapz'):
|
|
|
|
|
#
|
|
|
|
|
#
|
|
|
|
|
#
|
|
|
|
|
# # Fourier coefficients by fft
|
|
|
|
|
# Fourier coefficients by fft
|
|
|
|
|
# Fcof1 = 2*ifft(x(1:N1,:),[],1);
|
|
|
|
|
# Pcor = [1; exp(sqrt(-1)*(1:M-1).'*t(1))]; % correction term to get
|
|
|
|
|
# % the correct integration limits
|
|
|
|
|
@ -2409,10 +2480,10 @@ def fourier(data, t=None, T=None, m=None, n=None, method='trapz'):
|
|
|
|
|
return a, b
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _test_find_cross():
|
|
|
|
|
t = findcross([0, 0, 1, -1, 1], 0) # @UnusedVariable
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _test_common_shape():
|
|
|
|
|
|
|
|
|
|
A = ones((4, 1))
|
|
|
|
|
@ -2443,18 +2514,20 @@ def _test_meshgrid():
|
|
|
|
|
yv[0, 0] = 10
|
|
|
|
|
print(xv)
|
|
|
|
|
print(yv)
|
|
|
|
|
## >>> xv
|
|
|
|
|
# >>> xv
|
|
|
|
|
## array([[ 0. , 0.5, 1. ]])
|
|
|
|
|
## >>> yv
|
|
|
|
|
## array([[ 0.],
|
|
|
|
|
## [ 1.]])
|
|
|
|
|
## array([[-1. , -0.5, 1. , 4. , 5. ],
|
|
|
|
|
# >>> 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.],
|
|
|
|
|
# [-1. , -0.5, 1. , 4. , 5. ]])
|
|
|
|
|
#
|
|
|
|
|
# array([[ 0., 0., 0., 0., 0.],
|
|
|
|
|
## [-2., -2., -2., -2., -2.],
|
|
|
|
|
## [-5., -5., -5., -5., -5.]])
|
|
|
|
|
# [-5., -5., -5., -5., -5.]])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _test_tranproc():
|
|
|
|
|
import wafo.transform.models as wtm
|
|
|
|
|
tr = wtm.TrHermite()
|
|
|
|
|
@ -2466,14 +2539,19 @@ def _test_tranproc():
|
|
|
|
|
#>>> 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
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
@ -2485,7 +2563,6 @@ def _test_extrema():
|
|
|
|
|
_ind1 = findrfc(tp, 0.3)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _test_discretize():
|
|
|
|
|
import pylab as plb
|
|
|
|
|
x, y = discretize(cos, 0, pi)
|
|
|
|
|
@ -2501,6 +2578,7 @@ def _test_stirlerr():
|
|
|
|
|
print getshipchar(1000)
|
|
|
|
|
print betaloge(3, 2)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _test_parse_kwargs():
|
|
|
|
|
opt = dict(arg1=1, arg2=3)
|
|
|
|
|
print opt
|
|
|
|
|
@ -2519,6 +2597,7 @@ def _test_parse_kwargs():
|
|
|
|
|
out1 = testfun(opt0['opt1'], **opt0)
|
|
|
|
|
print out1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def test_docstrings():
|
|
|
|
|
import doctest
|
|
|
|
|
doctest.testmod()
|
|
|
|
|
|
Per.Andreas.Brodtkorb
11 years ago