Small enhancements

-Added trdata method to TimeSeries class
-Added TrLinear class to transform/models.py
-Added more doctest examples to spectrum/core.py

pywafo/src/wafo/misc.py

@@ -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.
+        # Calculate the transforms of the derivatives of X.
-        #% First time derivative of y: y1 = f'(x)*x1
+        # First time derivative of y: y1 = f'(x)*x1
         
         y1 = fxder[0] * xi[0]
         y.append(y1)

pywafo/src/wafo/objects.py

@@ -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):
         ''' 

pywafo/src/wafo/spectrum/core.py

@@ -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,
+                   's' = skewness,
-                   'k' = (Fisher's) kurtosis.
+                   '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;
+        >>> import wafo.spectrum.models as sm
-         S.tr=g;S.tr(:,2)=g(:,2)*Hm0/4;
+        >>> import wafo.transform.models as wtm
-         xs = spec2sdat(S,2^13);
+        >>> import wafo.objects as wo
-         [g0 t0] = dat2tr(xs);
+        >>> Hs = 7
-         t1 = testgaussian(S0,[2^13 50],t0); 
+        >>> 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 if test0 is None else 1
-            plotflag=0
-        else: 
-            plotflag=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))
+            xs = acf.sim(ns=ns, cases=np.remainder(cases,rep))
-            [g, tmp] = dat2tr(xs,method,**opt);
+            for iy in range(1, xs.shape[-1]):
-            #test1 = [test1; tmp(:)];
+                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),
+            plotbackend.ylabel('e(g(u)-u)')
-#          test2=test1;
+            plotbackend.xlabel('Simulation number')
-#        end
+        return test1
-#        
-#        
-#        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
         
     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!')

pywafo/src/wafo/spectrum/models.py

@@ -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:

pywafo/src/wafo/stats/core.py

@@ -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
     ----------

pywafo/src/wafo/stats/estimation.py

@@ -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

pywafo/src/wafo/transform/core.py

@@ -48,8 +48,8 @@ class TrCommon(object):
         self.ymean = kwds.get('ymean', 0e0)
         self.ysigma = kwds.get('ysigma', 1e0)
 
-    def __call__(self, x):
+    def __call__(self, x, *xi):
-        return self._dat2gauss(x)
+        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

pywafo/src/wafo/transform/models.py

@@ -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
     --------