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Small enhancements

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-Added trdata method to TimeSeries class
-Added TrLinear class to transform/models.py
-Added more doctest examples to spectrum/core.py
master
Per.Andreas.Brodtkorb 15 years ago
parent da96ab184a
commit acab68c0a1
8 changed files with 464 additions and 194 deletions
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17
pywafo/src/wafo/misc.py
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@ -672,6 +672,13 @@ def findtp(x, h=0.0, kind=None):
>>> tph = x1[itph,:]
>>> a = pylab.plot(x1[:,0],x1[:,1],tp[:,0],tp[:,1],'ro',tph[:,1],tph[:,1],'k.')
>>> pylab.close('all')
>>> itp
array([ 11, 21, 22, 24, 26, 28, 31, 39, 43, 45, 47, 51, 56,
64, 70, 78, 82, 84, 89, 94, 101, 108, 119, 131, 141, 148,
149, 150, 159, 173, 184, 190, 199])
>>> itph
array([ 11, 64, 28, 31, 47, 51, 39, 56, 70, 94, 78, 89, 101,
108, 119, 148, 131, 141, 0, 159, 173, 184, 190])
See also
---------
@ -1748,15 +1755,15 @@ def tranproc(x, f, x0, *xi):
#% Transform X with the derivatives of f.
fxder = zeros((N, x0.size))
fder = vstack((xo, fo)).T
fder = vstack((xo, fo))
for k in range(N): #% Derivation of f(x) using a difference method.
n = fder.shape[0]
n = fder.shape[-1]
#%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])
fder = vstack([(fder[0, 0:n - 1] + fder[0, 1:n]) / 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
# 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)

207
pywafo/src/wafo/objects.py
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@ -14,14 +14,15 @@
from __future__ import division
from wafo.transform.core import TrData
from wafo.transform.models import TrHermite, TrOchi, TrLinear
from wafo.interpolate import SmoothSpline
from scipy.interpolate.interpolate import interp1d
from scipy.integrate.quadrature import cumtrapz
from wafo.interpolate import SmoothSpline
import warnings
import numpy as np
from numpy import (inf, pi, zeros, ones, sqrt, where, log, exp, sin, arcsin, mod, finfo, interp, #@UnresolvedImport
newaxis, linspace, arange, sort, all, abs, linspace, vstack, hstack, atleast_1d, #@UnresolvedImport
newaxis, linspace, arange, sort, all, abs, 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
@ -603,8 +604,6 @@ class TurningPoints(WafoData):
----------------
data : array_like
args : vector for 1D
'''
def __init__(self, *args, **kwds):
super(TurningPoints, self).__init__(*args, **kwds)
@ -857,6 +856,206 @@ class TimeSeries(WafoData):
fact = 2.0 * pi
w = fact * f
return _wafospec.SpecData1D(S / fact, w)
def trdata(self, method='nonlinear', **options):
'''
Estimate transformation, g, from data.
CALL: [g test cmax irr g2] = dat2tr(x,def,options);
g,g2 = the smoothed and empirical transformation, respectively.
A two column matrix if multip=0.
If multip=1 it is a 2*(m-1) column matrix where the
first and second column is the transform
for values in column 2 and third and fourth column is the
transform for values in column 3 ......
test = int (g(u)-u)^2 du where int. limits is given by param. This
is a measure of departure of the data from the Gaussian model.
Parameters
----------
method : string
'nonlinear' : transform based on smoothed crossing intensity (default)
'mnonlinear': transform based on smoothed marginal distribution
'hermite' : transform based on cubic Hermite polynomial
'ochi' : transform based on exponential function
'linear' : identity.
options = options structure with the following fields:
csm,gsm - defines the smoothing of the logarithm of crossing intensity
and the transformation g, respectively. 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 see lc2tr).
plotflag - 0 no plotting (Default)
1 plots empirical and smoothed g(u) and the theoretical for
a Gaussian model.
2 monitor the development of the 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)
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 or CDF.
The empirical crossing intensity or CDF is interpolated
linearly before smoothing if their lengths 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)
multip - 0 the data in columns belong to the same seastate (default).
1 the data in columns are from separate seastates.
DAT2TR estimates the transformation in a transformed Gaussian model.
Assumption: a Gaussian process, Y, is related to the
non-Gaussian process, X, by Y = g(X).
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 CSM. In order to check the effect
of smoothing it is recomended to also plot g and g2 in the same plot or
plot the smoothed g against an interpolated version of g (when CSM=GSM=1).
If x is likely to cross levels higher than 5 standard deviations
then the vector param has to be modified. For example if x is
unlikely to cross a level of 7 standard deviations one can use
PARAM=[-7 7 513].
Example
-------
>>> import wafo.spectrum.models as sm
>>> import wafo.transform.models as tm
>>> from wafo.objects import mat2timeseries
>>> Hs = 7.0
>>> Sj = sm.Jonswap(Hm0=Hs)
>>> S = Sj.tospecdata() #Make spectrum object from numerical values
>>> S.tr = tm.TrOchi(mean=0, skew=0.16, kurt=0, sigma=Hs/4, ysigma=Hs/4)
>>> xs = S.sim(ns=2**16)
>>> ts = mat2timeseries(xs)
>>> g0, gemp = ts.trdata(monitor=True) # Monitor the development
>>> g1, gemp = ts.trdata(method='m', gvar=0.5 ) # Equal weight on all points
>>> g2, gemp = ts.trdata(method='n', gvar=[3.5, 0.5, 3.5]) # Less weight on the ends
>>> S.tr.dist2gauss()
5.9322684525265501
>>> np.round(gemp.dist2gauss())
6.0
>>> np.round(g0.dist2gauss())
4.0
>>> np.round(g1.dist2gauss())
4.0
>>> np.round(g2.dist2gauss())
4.0
Hm0 = 7;
S = jonswap([],Hm0); g=ochitr([],[Hm0/4]);
S.tr=g;S.tr(:,2)=g(:,2)*Hm0/4;
xs = spec2sdat(S,2^13);
g0 = dat2tr(xs,[],'plot','iter'); % Monitor the development
g1 = dat2tr(xs,'mnon','gvar', .5 ); % More weight on all points
g2 = dat2tr(xs,'nonl','gvar', [3.5 .5 3.5]); % Less weight on the ends
hold on, trplot(g1,g) % Check the fit
trplot(g2)
See also
--------
troptset, lc2tr, cdf2tr, trplot
References
----------
Rychlik, I. , Johannesson, P and Leadbetter, M. R. (1997)
"Modelling and statistical analysis of ocean wavedata using
transformed Gaussian process."
Marine structures, Design, Construction and Safety, Vol. 10, No. 1, pp 13--47
Brodtkorb, P, Myrhaug, D, and Rue, H (1999)
"Joint distribution of wave height and crest velocity from
reconstructed data"
in Proceedings of 9th ISOPE Conference, Vol III, pp 66-73
'''
# Tested on: Matlab 5.3, 5.2, 5.1
# History:
# revised pab Dec2004
# -Fixed bug: string comparison for def at fault.
# revised pab Nov2004
# -Fixed bug: linextrap was not accounted for
# revised pab july 2004
# revised pab 3 april 2004
# -fixed a bug in hermite estimation: excess changed to kurtosis
# revised pab 29.12.2000
# - added example, hermite and ochi options
# - replaced optional arguments with a options struct
# - default param is now [-5 5 513] -> better to have the discretization
# represented with exact numbers, especially when calculating
# derivatives of the transformation numerically.
# revised pab 19.12.2000
# - updated call edf(X,-inf,[],monitor) to edf(X,[],monitor)
# due to new calling syntax for edf
# modifed pab 24.09.2000
# - changed call from norminv to wnorminv
# - also removed the 7 lowest and 7 highest points from
# the estimation using def='mnonlinear'
# (This is similar to what lc2tr does. lc2tr removes
# the 9 highest and 9 lowest TP from the estimation)
# modified pab 09.06.2000
# - made all the *empirical options secret.
# - Added 'mnonlinear' and 'mempirical'
# - Fixed the problem of multip==1 and def=='empirical' by interpolating
# with spline to ensure that the length of g is fixed
# - Replaced the test statistic for def=='empirical' with the one
# obtained when csm1=csm2=1. (Previously only the smoothed test
# statistic where returned)
# modified pab 12.10.1999
# fixed a bug
# added secret output of empirical estimate g2
# modified by svi 29.09.1999
# changed input def by adding new options.
# revised by pab 11.08.99
# changed name from dat2tran to dat2tr
# modified by Per A. Brodtkorb 12.05.1999,15.08.98
# added secret option: to accept multiple data, to monitor the steps
# of estimation of the transformation
# also removed some code and replaced it with a call to lc2tr (cross2tr)
# making the maintainance easier
#
#opt = troptset('plotflag','off','csm',.95,'gsm',.05,....
# 'param',[-5 5 513],'delay',2,'linextrap','on','ne',7,...
# 'cvar',1,'gvar',1,'multip',0);
opt = DotDict(chkder=True, plotflag=True, csm=.95, gsm=.05,
param=[-5, 5, 513], delay=2, ntr=inf, linextrap=True, ne=7, cvar=1, gvar=1,
multip=False, crossdef='uM')
opt.update(**options)
ma = self.data.mean()
sa = self.data.std()
if method.startswith('lin'):
return TrLinear(mean=ma, sigma=sa)
if method[0] == 'n':
tp = self.turning_points()
mM = tp.cycle_pairs()
lc = mM.level_crossings(opt.crossdef)
return lc.trdata()
elif method[0] == 'm':
return cdftr()
elif method[0] == 'h':
ga1 = np.skew(self.data)
ga2 = np.kurtosis(self.data, fisher=True) #kurt(xx(n+1:end))-3;
up = min(4 * (4 * ga1 / 3) ** 2, 13)
lo = (ga1 ** 2) * 3 / 2;
kurt1 = min(up, max(ga2, lo)) + 3
return TrHermite(mean=ma, var=sa ** 2, skew=ga1, kurt=kurt1)
elif method[0] == 'o':
ga1 = np.skew(self.data)
return TrOchi(mean=ma, var=sa ** 2, skew=ga1)
def turning_points(self, h=0.0, wavetype=None):
'''

135
pywafo/src/wafo/spectrum/core.py
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@ -1,5 +1,6 @@
from __future__ import division
from scipy.misc.ppimport import ppimport
from wafo.objects import mat2timeseries, TimeSeries
import warnings
import numpy as np
from numpy import (pi, inf, meshgrid, zeros, ones, where, nonzero, #@UnresolvedImport
@ -17,7 +18,8 @@ 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, tranproc
from wafo.misc import sub_dict_select, nextpow2, discretize, JITImport #, tranproc
try:
from wafo.gaussian import Rind
except ImportError:
@ -28,7 +30,8 @@ except ImportError:
warnings.warn('Compile the c_library.pyd again!')
c_library = None
from wafo.transform import TrData
#from wafo.transform import TrData
from wafo.transform.models import TrLinear
from wafo.plotbackend import plotbackend
@ -190,7 +193,7 @@ class SpecData1D(WafoData):
self.freqtype = 'w'
self.angletype = ''
self.h = inf
self.tr = None
self.tr = None #TrLinear()
self.phi = 0.0
self.v = 0.0
self.norm = False
@ -572,7 +575,9 @@ class SpecData1D(WafoData):
#Fs = 2*freq(end)+eps; % sampling frequency
for ix in xrange(max_sim):
[x2, x1] = spec2nlsdat(SL, [np, cases], [], iseed, method, fnLimit)
#[x2, x1] = spec2nlsdat(SL, [np, cases], [], iseed, method, fnLimit)
[x2, x1] = self.sim_nl(ns=np, cases=cases, dt=None, iseed=iseed, method=method,
fnlimit=fn_limit)
#%x2(:,2:end) = x2(:,2:end) -x1(:,2:end);
S2 = dat2spec(x2, L)
S1 = dat2spec(x1, L)
@ -727,9 +732,10 @@ class SpecData1D(WafoData):
if self.tr is None:
y = linspace(-5, 5, 513)
g = TrLinear(var=m[0])
#y = linspace(-5, 5, 513)
#g = _wafotransform.
g = TrData(y, sqrt(m[0]) * y)
#g = TrData(y, sqrt(m[0]) * y)
else:
g = self.tr
@ -1053,7 +1059,7 @@ class SpecData1D(WafoData):
xder[:, 0] = x[:, 0]
if spec.tr is not None:
print(' Transforming data.')
#print(' Transforming data.')
g = spec.tr
if derivative:
for i in range(cases):
@ -1079,7 +1085,7 @@ class SpecData1D(WafoData):
# 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):
fnlimit=1.4142, reltol=1e-3, g=9.81, verbose=False):
"""
Simulates a Randomized 2nd order non-linear wave X(t)
@ -1142,6 +1148,21 @@ class SpecData1D(WafoData):
Example
--------
>>> import wafo.spectrum.models as sm
>>> Sj = sm.Jonswap();S = Sj.tospecdata()
>>> ns =100; dt = .2
>>> x1 = S.sim_nl(ns,dt=dt)
>>> import numpy as np
>>> import scipy.stats as st
>>> x2 = S.sim_nl(ns=20000,cases=20)
>>> truth1 = [0,np.sqrt(S.moment(1)[0])] + S.stats_nl(moments='sk')
>>> 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)<sa)
np =100; dt = .2
[x1, x2] = spec2nlsdat(jonswap,np,dt)
waveplot(x1,'r',x2,'g',1,1)
@ -1281,7 +1302,7 @@ class SpecData1D(WafoData):
#if isempty(nmin),nmin = 2end % Must always be greater than 1
f_limit_up = df * nmax
f_limit_lo = df * nmin
if verbose:
print('2nd order frequency Limits = %g,%g' % (f_limit_lo, f_limit_up))
@ -1298,7 +1319,7 @@ class SpecData1D(WafoData):
## % 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
amp = np.array(amp.T).ravel()
rvec, ivec = c_library.disufq(amp.real, amp.imag, w, kw, water_depth, g, nmin, nmax, cases, ns)
svec = rvec + 1J * ivec
@ -1325,8 +1346,8 @@ class SpecData1D(WafoData):
composed of letters ['mvsk'] specifying which moments to compute:
'm' = mean,
'v' = variance,
's' = (Fisher's) skew,
'k' = (Fisher's) kurtosis.
's' = skewness,
'k' = (Pearson's) kurtosis.
method : string
'approximate' method due to Marthinsen & Winterstein (default)
'eigenvalue' method due to Kac and Siegert
@ -1358,17 +1379,16 @@ class SpecData1D(WafoData):
--------
#Simulate a Transformed Gaussian process:
>>> import wafo.spectrum.models as sm
>>> Sj = sm.Jonswap()
>>> import wafo.transform.models as wtm
>>> Hs = 7.
>>> Sj = sm.Jonswap(Hm0=Hs, Tp=11)
>>> S = Sj.tospecdata()
>>> me, va, sk, ku = S.stats_nl(moments='mvsk')
>>> g = wtm.TrHermite(mean=me, sigma=Hs/4, skew=sk, kurt=ku, ysigma=Hs/4)
>>> ys = S.sim(15000) # Simulated in the Gaussian world
>>> xs = g.gauss2dat(ys[:,1]) # Transformed to the real world
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
@ -1483,7 +1503,7 @@ class SpecData1D(WafoData):
## skew = sum((6*C2+8*E2).*E)/sa^3 % skewness
## kurt = 3+48*sum((C2+E2).*E2)/sa^4 % kurtosis
return output
def testgaussian(ns,test0=None, cases=100, method='nonlinear',**opt):
def testgaussian(self, ns,test0=None, cases=100, method='nonlinear',**opt):
'''
TESTGAUSSIAN Test if a stochastic process is Gaussian.
@ -1508,12 +1528,23 @@ class SpecData1D(WafoData):
If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.
Example:
Hm0 = 7;
S0 = jonswap([],Hm0); g=ochitr([],[Hm0/4]); S=S0;
S.tr=g;S.tr(:,2)=g(:,2)*Hm0/4;
xs = spec2sdat(S,2^13);
[g0 t0] = dat2tr(xs);
t1 = testgaussian(S0,[2^13 50],t0);
-------
>>> import wafo.spectrum.models as sm
>>> import wafo.transform.models as wtm
>>> import wafo.objects as wo
>>> Hs = 7
>>> Sj = sm.Jonswap(Hm0=Hs)
>>> S0 = Sj.tospecdata()
>>> ns =100; dt = .2
>>> x1 = S0.sim(ns, dt=dt)
>>> S = S0.copy()
>>> me, va, sk, ku = S.stats_nl(moments='mvsk')
>>> S.tr = wtm.TrHermite(mean=me, sigma=Hs/4, skew=sk, kurt=ku, ysigma=Hs/4)
>>> ys = wo.mat2timeseries(S.sim(ns=2**13))
>>> g0, gemp = ys.trdata()
>>> t0 = g0.dist2gauss()
>>> t1 = S0.testgaussian(ns=2**13, t0=t0, cases=50)
See also cov2sdat, dat2tr, troptset
'''
@ -1542,49 +1573,43 @@ class SpecData1D(WafoData):
#
# opt = troptset(opt,'multip',1)
if test0 is None:
plotflag=0
else:
plotflag=1
plotflag=0 if test0 is None else 1
if cases>50:
print(' ... be patient this may take a while')
test1 = []
rep = floor(ns*cases/maxsize)+1
Nstep = floor(cases/rep);
rep = int(np.floor(ns*cases/maxsize)+1)
Nstep = np.floor(cases/rep);
acf = self.tocovdata()
#R = spec2cov(S);
test1 = []
for ix in range(rep):
xs = acf.sim(ns=ns, cases=Nstep)
for iy in range(1, xs.shape[-1]):
ts = TimeSeries(xs[:, iy], xs[:, 0].ravel())
g, tmp = ts.trdata(method, **opt)
test1.append(g.dist2gauss())
#xs = cov2sdat(R,[ns Nstep]);
[g, tmp] = dat2tr(xs,method, **opt);
#[g, tmp] = dat2tr(xs,method, **opt);
#test1 = [test1; tmp(:)]
print('finished %d of %d ' % (ix,rep) )
print('finished %d of %d ' % (ix+1,rep) )
if rep>1:
xs = acf.sim(ns=ns, cases=rem(cases,rep))
[g, tmp] = dat2tr(xs,method,**opt);
#test1 = [test1; tmp(:)];
xs = acf.sim(ns=ns, cases=np.remainder(cases,rep))
for iy in range(1, xs.shape[-1]):
ts = TimeSeries(xs[:, iy], xs[:, 0].ravel())
g, tmp = ts.trdata(method, **opt)
test1.append(g.dist2gauss())
if plotflag:
plotbackend.plot(test1,'o')
plotbackend.plot([1, cases], [test0, test0],'--')
# if (nargout>0 || plotflag==0),
# test2=test1;
# end
#
#
# if plotflag
# plot(test1,'o'),hold on
# if 1
# plot([1 cases],test0*[1 1],'--'),
# end
# hold off
# ylabel('e(g(u)-u)')
# xlabel('Simulation number')
# end
plotbackend.ylabel('e(g(u)-u)')
plotbackend.xlabel('Simulation number')
return test1
def moment(self, nr=2, even=True, j=0):
''' Calculates spectral moments from spectrum
@ -2326,7 +2351,7 @@ class SpecData2D(WafoData):
##% 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!')

6
pywafo/src/wafo/spectrum/models.py
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@ -55,7 +55,7 @@ from numpy import (inf, atleast_1d, newaxis, any, minimum, maximum, array, #@Unr
from dispersion_relation import w2k
#ppimport.enable()
#_wafospectrum = ppimport.ppimport('wafo.spectrum')
from core import SpecData1D
from wafo.spectrum import SpecData1D
sech = lambda x: 1.0 / cosh(x)
eps = finfo(float).eps
@ -542,9 +542,9 @@ class Jonswap(ModelSpectrum):
outsideJonswapRange = Tp > 5 * sqrt(Hm0) or Tp < 3.6 * sqrt(Hm0)
if outsideJonswapRange:
txt0 = '''
Hm0,Tp is outside the JONSWAP range.
Hm0=%g,Tp=%g is outside the JONSWAP range.
The validity of the spectral density is questionable.
'''
''' % (Hm0, Tp)
warnings.warn(txt0)
if gam < 1 or 7 < gam:

4
pywafo/src/wafo/stats/core.py
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@ -8,7 +8,7 @@ __all__ = ['edf']
def edf(x, method=2):
'''
Returns EDF Empirical Distribution Function.
Returns Empirical Distribution Function (EDF).
Parameters
----------
@ -48,7 +48,7 @@ def edf(x, method=2):
def edfcnd(x, c=None, method=2):
'''
EDFCND Empirical Distribution Function CoNDitioned that X>=c.
Returns empirical Distribution Function CoNDitioned that X>=c (EDFCND).
Parameters
----------

2
pywafo/src/wafo/stats/estimation.py
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@ -92,7 +92,7 @@ class rv_frozen(object):
def __init__(self, dist, *args, **kwds):
self.dist = dist
loc0, scale0 = map(kwds.get, ['loc', 'scale'])
if hasattr(dist, 'fix_loc_scale'): #isinstance(dist, _WAFODIST.rv_continuous):
if hasattr(dist, 'fix_loc_scale'): #isinstance(dist, rv_continuous):
args, loc0, scale0 = dist.fix_loc_scale(args, loc0, scale0)
self.par = args + (loc0, scale0)
else: # rv_discrete

5
pywafo/src/wafo/transform/core.py
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@ -48,8 +48,8 @@ class TrCommon(object):
self.ymean = kwds.get('ymean', 0e0)
self.ysigma = kwds.get('ysigma', 1e0)
def __call__(self, x):
return self._dat2gauss(x)
def __call__(self, x, *xi):
return self._dat2gauss(x, *xi)
def dist2gauss(self, x=None, xnmin=-5, xnmax=5, n=513):
"""
@ -158,6 +158,7 @@ class TrData(WafoData, TrCommon):
1
>>> g.sigma
5
>>> g.dat2gauss(1,2,3)
Check that the departure from a Gaussian model is zero

48
pywafo/src/wafo/transform/models.py
Unescape Escape View File

@ -15,20 +15,18 @@ TrOchi
# Licence: <your licence>
#-------------------------------------------------------------------------------
#!/usr/bin/env python
from __future__ import division
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']
__all__ = ['TrHermite', 'TrLinear', 'TrOchi']
_example = '''
>>> std = 7./4
>>> g = <generic>(sigma=std, ysigma=std)
>>> g.dist2gauss()
3.9858776379926808
Simulate a Transformed Gaussian process:
>>> import numpy as np
@ -43,6 +41,7 @@ _example = '''
>>> xs = g2.gauss2dat(ys[:,1:]) # Transformed to the real world
'''
class TrHermite(TrCommon):
__doc__ = TrCommon.__doc__.replace('<generic>', 'Hermite') + """
pardef : scalar, integer
@ -80,6 +79,8 @@ class TrHermite(TrCommon):
Example:
--------
""" + _example.replace('<generic>', 'TrHermite') + """
>>> g.dist2gauss()
3.9858776379926808
See also
--------
@ -214,7 +215,7 @@ class TrHermite(TrCommon):
def _gauss2dat(self, y, *yi):
if len(yi) > 0:
raise ValueError('Transforming derivatives is not implemented!')
yn = (atleast_1d(y)-self.mean)/self.ysigma
yn = (atleast_1d(y) - self.ymean) / self.ysigma
#self.check_forward(y)
if self._backward is None:
@ -288,6 +289,41 @@ class TrHermite(TrCommon):
#%x=-(A0+B0)/2+(A0-B0)*sqrt(-3)/2-x0
class TrLinear(TrCommon):
__doc__ = TrCommon.__doc__.replace('<generic>', 'Linear') + """
Description
-----------
The linear transformation model is monotonic linear polynomial, calibrated
such that the first 2 moments of the transformed model G(y)=g^-1(y) match
the moments of the true process.
Example:
--------
""" + _example.replace('<generic>', 'TrLinear') + """
>>> g.dist2gauss()
0.0
See also
--------
spec2skew, ochitr, lc2tr, dat2tr
"""
def _dat2gauss(self, x, *xi):
sratio = atleast_1d(self.ysigma / self.sigma)
y = (atleast_1d(x) - self.mean) * sratio + self.ymean
if len(xi) > 0:
y = [y, ] + [ ix * sratio for ix in xi]
return y
def _gauss2dat(self, y, *yi):
sratio = atleast_1d(self.sigma / self.ysigma)
x = (atleast_1d(y) - self.ymean) * sratio + self.mean
if len(yi) > 0:
x = [x, ] + [iy * sratio for iy in yi]
return x
class TrOchi(TrCommon):
__doc__ = TrCommon.__doc__.replace('<generic>', 'Ochi') + """
@ -323,6 +359,8 @@ class TrOchi(TrCommon):
Example
-------
""" + _example.replace('<generic>', 'TrOchi') + """
>>> g.dist2gauss()
5.9322684525265501
See also
--------

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