Updates

wafo/containers.py

@@ -160,6 +160,12 @@ class PlotData(object):
             return interpolate.griddata(
                 self.args, self.data, points, **options)
 
+    def to_cdf(self):
+        if isinstance(self.args, (list, tuple)):  # Multidimensional data
+            raise NotImplementedError('integration for ndim>1 not implemented')
+        cdf = np.hstack((0, integrate.cumtrapz(self.data, self.args)))
+        return PlotData(cdf, np.copy(self.args), xlab='x', ylab='F(x)')
+
     def integrate(self, a, b, **kwds):
         '''
         >>> x = np.linspace(0,5,60)
@@ -551,7 +557,7 @@ def plot2d(axis, wdata, plotflag, *args, **kwds):
         clvec = np.sort(CL)
 
         if plotflag in [1, 8, 9]:
-            h = axis.contour(*args1, levels=CL, **kwds)
+            h = axis.contour(*args1, levels=clvec, **kwds)
         # else:
         #  [cs hcs] = contour3(f.x{:},f.f,CL,sym);
 
@@ -563,9 +569,7 @@ def plot2d(axis, wdata, plotflag, *args, **kwds):
                     'Only the first 12 levels will be listed in table.')
 
             clvals = PL[:ncl] if isPL else clvec[:ncl]
-            unused_axcl = cltext(
-                clvals,
-                percent=isPL)  # print contour level text
+            unused_axcl = cltext(clvals, percent=isPL)
         elif any(plotflag == [7, 9]):
             axis.clabel(h)
         else:

wafo/doc/tutorial_scripts/chapter1.py

@@ -1,6 +1,5 @@
-from scipy import *
-from pylab import *
-
+import wafo.plotbackend.plotbackend as plt
+import numpy as np
 # pyreport -o chapter1.html chapter1.py
 
 #! CHAPTER1 demonstrates some applications of WAFO
@@ -15,16 +14,16 @@ from pylab import *
 
 #! Section 1.4 Some applications of WAFO
 #!---------------------------------------
-#! Section 1.4.1 Simulation from spectrum, estimation of spectrum 
+#! Section 1.4.1 Simulation from spectrum, estimation of spectrum
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 #! Simulation of the sea surface from spectrum
 #! The following code generates 200 seconds of data sampled with 10Hz from
 #! the Torsethaugen spectrum
 import wafo.spectrum.models as wsm
-S = wsm.Torsethaugen(Hm0=6, Tp=8);
+S = wsm.Torsethaugen(Hm0=6, Tp=8)
 S1 = S.tospecdata()
 S1.plot()
-show()
+plt.show()
 
 
 ##
@@ -32,23 +31,23 @@ import wafo.objects as wo
 xs = S1.sim(ns=2000, dt=0.1)
 ts = wo.mat2timeseries(xs)
 ts.plot_wave('-')
-show()
+plt.show()
 
 
-#! Estimation of spectrum 
+#! Estimation of spectrum
 #!~~~~~~~~~~~~~~~~~~~~~~~
 #! A common situation is that one wants to estimate the spectrum for wave
 #! measurements. The following code simulate 20 minutes signal sampled at 4Hz
 #! and compare the spectral estimate with the original Torsethaugen spectum.
-clf()
-Fs = 4;  
-xs = S1.sim(ns=fix(20 * 60 * Fs), dt=1. / Fs) 
-ts = wo.mat2timeseries(xs) 
+plt.clf()
+Fs = 4
+xs = S1.sim(ns=np.fix(20 * 60 * Fs), dt=1. / Fs)
+ts = wo.mat2timeseries(xs)
 Sest = ts.tospecdata(L=400)
 S1.plot()
 Sest.plot('--')
-axis([0, 3, 0, 5]) # This may depend on the simulation
-show()
+plt.axis([0, 3, 0, 5])
+plt.show()
 
 #! Section 1.4.2 Probability distributions of wave characteristics.
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -58,7 +57,7 @@ show()
 #! In the following example we study the trough period extracted from the
 #! time series and compared with the theoretical density computed with exact
 #! spectrum, S1, and the estimated spectrum, Sest.
-clf()
+plt.clf()
 import wafo.misc as wm
 dtyex = S1.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
 dtyest = Sest.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
@@ -69,29 +68,29 @@ wm.plot_histgrm(T, bins=bins, normed=True)
 
 dtyex.plot()
 dtyest.plot('-.')
-axis([0, 10, 0, 0.35])
-show()
+plt.axis([0, 10, 0, 0.35])
+plt.show()
 
 #! Section 1.4.3 Directional spectra
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-#! Here are a few lines of code, which produce directional spectra 
+#! Here are a few lines of code, which produce directional spectra
 #! with frequency independent and frequency dependent spreading.
-clf()
+plt.clf()
 plotflag = 1
-Nt = 101;   # number of angles
-th0 = pi / 2; # primary direction of waves
-Sp = 15;   # spreading parameter
+Nt = 101      # number of angles
+th0 = np.pi / 2  # primary direction of waves
+Sp = 15       # spreading parameter
 
-D1 = wsm.Spreading(type='cos', theta0=th0, method=None) # frequency independent
-D12 = wsm.Spreading(type='cos', theta0=0, method='mitsuyasu') # frequency dependent
+D1 = wsm.Spreading(type='cos', theta0=th0, method=None)
+D12 = wsm.Spreading(type='cos', theta0=0, method='mitsuyasu')
 
 SD1 = D1.tospecdata2d(S1)
 SD12 = D12.tospecdata2d(S1)
 SD1.plot()
-SD12.plot()#linestyle='dashdot')
-show()
+SD12.plot()  # linestyle='dashdot')
+plt.show()
 
-#! 3D Simulation of the sea surface 
+#! 3D Simulation of the sea surface
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 #! The simulations show that frequency dependent spreading leads to
 #! much more irregular surface so the orientation of waves is less
@@ -120,7 +119,7 @@ show()
 #!  The figure is not shown in the Tutorial
 #
 # Nx = 3; Ny = 2; Nt = 2 ^ 12; dx = 10; dy = 10;dt = 0.5;
-# F = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, 1, 0);  
+# F = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, 1, 0);
 # Z = permute(F.Z, [3 1 2]);
 # [X, Y] = meshgrid(F.x, F.y);
 # N = Nx * Ny;
@@ -137,16 +136,16 @@ show()
 
 #! Section 1.4.4 Fatigue, Load cycles and Markov models.
 #! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-#! Switching Markow chain of turningpoints 
+#! Switching Markow chain of turningpoints
 #! In fatigue applications the exact sample path is not important, but
 #! only the tops and bottoms of the load, called the sequence of turning
 #! points (TP). From the turning points one can extract load cycles, from
 #! which damage calculations and fatigue life predictions can be
 #! performed.
 #!
-#! The commands below computes the intensity of rainflowcycles for 
-#! the Gaussian model with spectrum S1 using the Markov approximation. 
-#! The rainflow cycles found in the simulated load signal are shown in the 
+#! The commands below computes the intensity of rainflowcycles for
+#! the Gaussian model with spectrum S1 using the Markov approximation.
+#! The rainflow cycles found in the simulated load signal are shown in the
 #! figure.
 
 #clf()
@@ -164,30 +163,30 @@ show()
 #! Section 1.4.5 Extreme value statistics
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # Plot of yura87 data
-clf()
+plt.clf()
 import wafo.data as wd
 xn = wd.yura87()
-#xn = load('yura87.dat'); 
-subplot(211) 
-plot(xn[::30, 0] / 3600, xn[::30, 1], '.')
-title('Water level')
-ylabel('(m)')
+#xn = load('yura87.dat');
+plt.subplot(211)
+plt.plot(xn[::30, 0] / 3600, xn[::30, 1], '.')
+plt.title('Water level')
+plt.ylabel('(m)')
 
 #! Formation of 5 min maxima
 yura = xn[:85500, 1]
 yura = np.reshape(yura, (285, 300)).T
 maxyura = yura.max(axis=0)
-subplot(212)
-plot(xn[299:85500:300, 0] / 3600, maxyura, '.')
-xlabel('Time (h)')
-ylabel('(m)')
-title('Maximum 5 min water level')
-show()
+plt.subplot(212)
+plt.plot(xn[299:85500:300, 0] / 3600, maxyura, '.')
+plt.xlabel('Time (h)')
+plt.ylabel('(m)')
+plt.title('Maximum 5 min water level')
+plt.show()
 
 #! Estimation of GEV for yuramax
-clf()
+plt.clf()
 import wafo.stats as ws
 phat = ws.genextreme.fit2(maxyura, method='ml')
 phat.plotfitsummary()
-show()
+plt.show()
 #disp('Block = 11, Last block')

wafo/doc/tutorial_scripts/chapter2.py

@@ -1,6 +1,5 @@
+import wafo.plotbackend.plotbackend as plt
 import numpy as np
-from scipy import *
-from pylab import *
 
 # pyreport -o chapter2.html chapter2.py
 
@@ -10,15 +9,15 @@ from pylab import *
 #! Chapter2 contains the commands used in Chapter 2 of the tutorial and
 #! present some tools for analysis of random functions with
 #! respect to their correlation, spectral and distributional properties.
-#! The presentation is divided into three examples: 
+#! The presentation is divided into three examples:
 #!
 #! Example1 is devoted to estimation of different parameters in the model.
 #! Example2 deals with spectral densities and
 #! Example3 presents the use of WAFO to simulate samples of a Gaussian
 #! process.
 #!
-#! Some of the commands are edited for fast computation. 
-#! 
+#! Some of the commands are edited for fast computation.
+#!
 #! Section 2.1 Introduction and preliminary analysis
 #!====================================================
 #! Example 1: Sea data
@@ -37,15 +36,15 @@ tp = ts.turning_points()
 cc = tp.cycle_pairs()
 lc = cc.level_crossings()
 lc.plot()
-show()
+plt.show()
 
 #! Average number of upcrossings per time unit
 #!----------------------------------------------
-#! Next we compute the mean frequency as the average number of upcrossings 
-#! per time unit of the mean level (= 0); this may require interpolation in the 
-#! crossing intensity curve, as follows.  
+#! Next we compute the mean frequency as the average number of upcrossings
+#! per time unit of the mean level (= 0); this may require interpolation in the
+#! crossing intensity curve, as follows.
 T = xx[:, 0].max() - xx[:, 0].min()
-f0 = np.interp(0, lc.args, lc.data, 0) / T  #! zero up-crossing frequency 
+f0 = np.interp(0, lc.args, lc.data, 0) / T  # zero up-crossing frequency
 print('f0 = %g' % f0)
 
 #! Turningpoints and irregularity factor
@@ -60,17 +59,17 @@ print('fm = %g, alpha = %g, ' % (fm, alfa))
 #!------------------------
 #! We finish this section with some remarks about the quality
 #! of the measured data. Especially sea surface measurements can be
-#! of poor quality. We shall now check the  quality of the dataset {\tt xx}. 
-#! It is always good practice to visually examine the data 
-#! before the analysis to get an impression of the quality, 
+#! of poor quality. We shall now check the  quality of the dataset {\tt xx}.
+#! It is always good practice to visually examine the data
+#! before the analysis to get an impression of the quality,
 #! non-linearities and narrow-bandedness of the data.
-#! First we shall plot the data and zoom in on a specific region. 
+#! First we shall plot the data and zoom in on a specific region.
 #! A part of sea data is visualized with the following commands
-clf()
+plt.clf()
 ts.plot_wave('k-', tp, '*', nfig=1, nsub=1)
 
-axis([0, 2, -2, 2])
-show()
+plt.axis([0, 2, -2, 2])
+plt.show()
 
 #! Finding possible spurious points
 #!------------------------------------
@@ -91,58 +90,59 @@ inds, indg = wm.findoutliers(ts.data, zcrit, dcrit, ddcrit, verbose=True)
 #!----------------------------------------------------
 #! Periodogram: Raw spectrum
 #!
-clf()
+plt.clf()
 Lmax = 9500
 S = ts.tospecdata(L=Lmax)
 S.plot()
-axis([0, 5, 0, 0.7])
-show()
+plt.axis([0, 5, 0, 0.7])
+plt.show()
 
-#! Calculate moments  
+#! Calculate moments
 #!-------------------
 mom, text = S.moment(nr=4)
-print('sigma = %g, m0 = %g' % (sa, sqrt(mom[0])))
+print('sigma = %g, m0 = %g' % (sa, np.sqrt(mom[0])))
 
 #! Section 2.2.1 Random functions in Spectral Domain - Gaussian processes
 #!--------------------------------------------------------------------------
-#! Smoothing of spectral estimate 
+#! Smoothing of spectral estimate
 #!----------------------------------
 #! By decreasing Lmax the spectrum estimate becomes smoother.
 
-clf()
-Lmax0 = 200; Lmax1 = 50
+plt.clf()
+Lmax0 = 200
+Lmax1 = 50
 S1 = ts.tospecdata(L=Lmax0)
 S2 = ts.tospecdata(L=Lmax1)
 S1.plot('-.')
 S2.plot()
-show()
+plt.show()
 
 #! Estimated autocovariance
 #!----------------------------
 #! Obviously knowing the spectrum one can compute the covariance
-#! function. The following code will compute the covariance for the 
-#! unimodal spectral density S1 and compare it with estimated 
+#! function. The following code will compute the covariance for the
+#! unimodal spectral density S1 and compare it with estimated
 #! covariance of the signal xx.
-clf()
+plt.clf()
 Lmax = 85
-R1 = S1.tocovdata(nr=1)   
+R1 = S1.tocovdata(nr=1)
 Rest = ts.tocovdata(lag=Lmax)
 R1.plot('.')
 Rest.plot()
-axis([0, 25, -0.1, 0.25])
-show()
+plt.axis([0, 25, -0.1, 0.25])
+plt.show()
 
-#! We can see in Figure below that the covariance function corresponding to 
-#! the spectral density S2 significantly differs from the one estimated 
-#! directly from data. 
-#! It can be seen in Figure above that the covariance corresponding to S1 
+#! We can see in Figure below that the covariance function corresponding to
+#! the spectral density S2 significantly differs from the one estimated
+#! directly from data.
+#! It can be seen in Figure above that the covariance corresponding to S1
 #! agrees much better with the estimated covariance function
 
-clf()
+plt.clf()
 R2 = S2.tocovdata(nr=1)
 R2.plot('.')
 Rest.plot()
-show()
+plt.show()
 
 #! Section 2.2.2 Transformed Gaussian models
 #!-------------------------------------------
@@ -154,68 +154,69 @@ rho3 = ws.skew(xx[:, 1])
 rho4 = ws.kurtosis(xx[:, 1])
 
 sk, ku = S1.stats_nl(moments='sk')
- 
+
 #! Comparisons of 3 transformations
-clf()
+plt.clf()
 import wafo.transform.models as wtm
 gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku).trdata()
-g = wtm.TrLinear(mean=me, sigma=sa).trdata() # Linear transformation 
+g = wtm.TrLinear(mean=me, sigma=sa).trdata()  # Linear transformation
 glc, gemp = lc.trdata(mean=me, sigma=sa)
 
-glc.plot('b-') #! Transf. estimated from level-crossings
-gh.plot('b-.') #! Hermite Transf. estimated from moments
+glc.plot('b-')  # Transf. estimated from level-crossings
+gh.plot('b-.')  # Hermite Transf. estimated from moments
 g.plot('r')
-grid('on')
-show()
- 
+plt.grid('on')
+plt.show()
+
 #! Test Gaussianity of a stochastic process
 #!------------------------------------------
-#! TESTGAUSSIAN simulates  e(g(u)-u) = int (g(u)-u)^2 du  for Gaussian processes 
+#! TESTGAUSSIAN simulates  e(g(u)-u) = int (g(u)-u)^2 du  for Gaussian processes
 #! given the spectral density, S. The result is plotted if test0 is given.
 #! This is useful for testing if the process X(t) is Gaussian.
 #! If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.
-#! 
-#! As we see from the figure below: none of the simulated values of test1 is 
-#! above 1.00. Thus the data significantly departs from a Gaussian distribution. 
-clf()
+#!
+#! As we see from the figure below: none of the simulated values of test1 is
+#! above 1.00. Thus the data significantly departs from a Gaussian distribution.
+plt.clf()
 test0 = glc.dist2gauss()
 #! the following test takes time
 N = len(xx)
 test1 = S1.testgaussian(ns=N, cases=50, test0=test0)
-is_gaussian = sum(test1 > test0) > 5 
+is_gaussian = sum(test1 > test0) > 5
 print(is_gaussian)
-show()
+plt.show()
 
 #! Normalplot of data xx
 #!------------------------
 #! indicates that the underlying distribution has a "heavy" upper tail and a
-#! "light" lower tail. 
-clf()
+#! "light" lower tail.
+plt.clf()
 import pylab
 ws.probplot(ts.data.ravel(), dist='norm', plot=pylab)
-show()
+plt.show()
 #! Section 2.2.3 Spectral densities of sea data
 #!-----------------------------------------------
 #! Example 2: Different forms of spectra
 #!
 import wafo.spectrum.models as wsm
-clf()
-Hm0 = 7; Tp = 11;
+plt.clf()
+Hm0 = 7
+Tp = 11
 spec = wsm.Jonswap(Hm0=Hm0, Tp=Tp).tospecdata()
 spec.plot()
-show()
+plt.show()
 
 #! Directional spectrum and Encountered directional spectrum
 #! Directional spectrum
-clf()
+plt.clf()
 D = wsm.Spreading('cos2s')
 Sd = D.tospecdata2d(spec)
 Sd.plot()
-show()
+plt.show()
 
 
 ##!Encountered directional spectrum
-##!--------------------------------- 
+##!---------------------------------
 #clf()
 #Se = spec2spec(Sd,'encdir',0,10);
 #plotspec(Se), hold on
@@ -254,10 +255,10 @@ show()
 #disp('Block = 20'),pause(pstate)
 #
 ##!#! Section 2.3 Simulation of transformed Gaussian process
-##!#! Example 3: Simulation of random sea    
+##!#! Example 3: Simulation of random sea
 ##! The reconstruct function replaces the spurious points of seasurface by
 ##! simulated data on the basis of the remaining data and a transformed Gaussian
-##! process. As noted previously one must be careful using the criteria 
+##! process. As noted previously one must be careful using the criteria
 ##! for finding spurious points when reconstructing a dataset, because
 ##! these criteria might remove the highest and steepest waves as we can see
 ##! in this plot where the spurious points is indicated with a '+' sign:
@@ -269,13 +270,13 @@ show()
 ##!wafostamp('','(ER)')
 #disp('Block = 21'),pause(pstate)
 #
-##! Compare transformation (grec) from reconstructed (y) 
+##! Compare transformation (grec) from reconstructed (y)
 ##! with original (glc) from (xx)
 #clf
 #trplot(g), hold on
 #plot(gemp(:,1),gemp(:,2))
 #plot(glc(:,1),glc(:,2),'-.')
-#plot(grec(:,1),grec(:,2)), hold off 
+#plot(grec(:,1),grec(:,2)), hold off
 #disp('Block = 22'),pause(pstate)
 #
 ##!#!
@@ -284,7 +285,7 @@ show()
 #x = dat2gaus(y,grec);
 #Sx = dat2spec(x,L);
 #disp('Block = 23'),pause(pstate)
-#      
+#
 ##!#!
 #clf
 #dt = spec2dt(Sx)
@@ -294,27 +295,28 @@ show()
 #waveplot(ysim,'-')
 ##!wafostamp('','(CR)')
 #disp('Block = 24'),pause(pstate)
-# 
+#
 #! Estimated spectrum compared to Torsethaugen spectrum
 #!-------------------------------------------------------
- 
-clf()
-fp = 1.1;dw = 0.01
+
+plt.clf()
+fp = 1.1
+dw = 0.01
 H0 = S1.characteristic('Hm0')[0]
-St = wsm.Torsethaugen(Hm0=H0,Tp=2*pi/fp).tospecdata(np.arange(0,5+dw/2,dw))  
+St = wsm.Torsethaugen(Hm0=H0,Tp=2*np.pi/fp).tospecdata(np.arange(0,5+dw/2,dw))
 S1.plot()
 St.plot('-.')
-axis([0, 6, 0, 0.4])
-show()
- 
+plt.axis([0, 6, 0, 0.4])
+plt.show()
+
 
 #! Transformed Gaussian model compared to Gaussian model
 #!--------------------------------------------------------
 dt = St.sampling_period()
-va, sk, ku = St.stats_nl(moments='vsk' )
+va, sk, ku = St.stats_nl(moments='vsk')
 #sa = sqrt(va)
 gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa)
- 
+
 ysim_t = St.sim(ns=240, dt=0.5)
 xsim_t = ysim_t.copy()
 xsim_t[:,1] = gh.gauss2dat(ysim_t[:,1])
@@ -322,4 +324,4 @@ xsim_t[:,1] = gh.gauss2dat(ysim_t[:,1])
 ts_y = wo.mat2timeseries(ysim_t)
 ts_x = wo.mat2timeseries(xsim_t)
 ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1)
-show()
+plt.show()

wafo/doc/tutorial_scripts/chapter4.py

@@ -1,17 +1,14 @@
-import numpy as np
-from scipy import *
-from pylab import *
 
 #! CHAPTER4 contains the commands used in Chapter 4 of the tutorial
 #!=================================================================
 #!
 #! CALL:  Chapter4
-#! 
-#! Some of the commands are edited for fast computation. 
+#!
+#! Some of the commands are edited for fast computation.
 #! Each set of commands is followed by a 'pause' command.
-#! 
-#! This routine also can print the figures; 
-#! For printing the figures on directory ../bilder/ edit the file and put  
+#!
+#! This routine also can print the figures;
+#! For printing the figures on directory ../bilder/ edit the file and put
 #!     printing=1;
 
 #! Tested on Matlab 5.3
@@ -23,76 +20,80 @@ from pylab import *
 #! Created by GL July 13, 2000
 #! from commands used in Chapter 4
 #!
- 
+
 #! Chapter 4 Fatigue load analysis and rain-flow cycles
 #!------------------------------------------------------
 
-printing=0;
+printing = 0
 
 
 #! Section 4.3.1 Crossing intensity
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+import numpy as np
+from wafo.plotbackend import plotbackend as plt
 import wafo.data as wd
 import wafo.objects as wo
 
-xx_sea = wd.sea()  
+xx_sea = wd.sea()
 ts = wo.mat2timeseries(xx_sea)
 tp = ts.turning_points()
 mM = tp.cycle_pairs(kind='min2max')
 lc = mM.level_crossings(intensity=True)
 T_sea = ts.args[-1]-ts.args[0]
 
-subplot(1,2,1)
+plt.subplot(1,2,1)
 lc.plot()
-subplot(1,2,2)
+plt.subplot(1,2,2)
 lc.setplotter(plotmethod='step')
 lc.plot()
-show() 
- 
- 
-m_sea = ts.data.mean() 
-f0_sea = interp(m_sea, lc.args,lc.data)
+plt.show()
+
+
+m_sea = ts.data.mean()
+f0_sea = np.interp(m_sea, lc.args,lc.data)
 extr_sea = len(tp.data)/(2*T_sea)
 alfa_sea = f0_sea/extr_sea
-print('alfa = %g ' % alfa_sea )
+print('alfa = %g ' % alfa_sea)
 
 #! Section 4.3.2 Extraction of rainflow cycles
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 #! Min-max and rainflow cycle plots
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 mM_rfc = tp.cycle_pairs(h=0.3)
- 
-clf()
-subplot(122), 
-mM.plot() 
-title('min-max cycle pairs')
-subplot(121), 
+
+plt.clf()
+plt.subplot(122),
+mM.plot()
+plt.title('min-max cycle pairs')
+plt.subplot(121),
 mM_rfc.plot()
-title('Rainflow filtered cycles')
-show()
+plt.title('Rainflow filtered cycles')
+plt.show()
 
 #! Min-max and rainflow cycle distributions
 #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 import wafo.misc as wm
 ampmM_sea = mM.amplitudes()
 ampRFC_sea = mM_rfc.amplitudes()
-clf()
-subplot(121) 
+plt.clf()
+plt.subplot(121)
 wm.plot_histgrm(ampmM_sea,25)
-ylim = gca().get_ylim()
-title('min-max amplitude distribution')
-subplot(122)
+ylim = plt.gca().get_ylim()
+plt.title('min-max amplitude distribution')
+plt.subplot(122)
 wm.plot_histgrm(ampRFC_sea,25)
-gca().set_ylim(ylim)
-title('Rainflow amplitude distribution')
-show()
+plt.gca().set_ylim(ylim)
+plt.title('Rainflow amplitude distribution')
+plt.show()
 
 #!#! Section 4.3.3 Simulation of rainflow cycles
 #!#! Simulation of cycles in a Markov model
-n=41; param_m=[-1, 1, n]; param_D=[1, n, n];
-u_markov=levels(param_m);
-G_markov=mktestmat(param_m,[-0.2, 0.2],0.15,1);
-T_markov=5000;
+# n = 41
+# param_m = [-1, 1, n]
+# param_D = [1, n, n]
+# u_markov=levels(param_m);
+# G_markov=mktestmat(param_m,[-0.2, 0.2],0.15,1);
+# T_markov=5000;
 #xxD_markov=mctpsim({G_markov [,]},T_markov);
 #xx_markov=[(1:T_markov)' u_markov(xxD_markov)'];
 #clf
@@ -118,7 +119,7 @@ T_markov=5000;
 #xx_herm = spec2sdat(spec_norm,[2^15 1],0.1);
 ##! ????? PJ, JR 11-Apr-2001
 ##! NOTE, in the simulation program spec2sdat
-##!the spectrum must be normalized to variance 1 
+##!the spectrum must be normalized to variance 1
 ##! ?????
 #h = 0.2;
 #[dtp,u_herm,xx_herm_1]=dat2dtp(param_h,xx_herm,h);
@@ -142,7 +143,7 @@ T_markov=5000;
 #title('h=0')
 #subplot(122), ccplot(RFC_herm_1)
 #title('h=0.2')
-#if (printing==1), print -deps ../bilder/fatigue_8.eps 
+#if (printing==1), print -deps ../bilder/fatigue_8.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 7'),pause(pstate)
@@ -157,17 +158,17 @@ T_markov=5000;
 #wafostamp([],'(ER)')
 #disp('Block 8'),pause(pstate)
 #
-##!#! 
+##!#!
 #clf
-#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},3) 
+#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},3)
 #wafostamp([],'(ER)')
-#disp('Block 9'),pause(pstate)	
+#disp('Block 9'),pause(pstate)
 #
 ##!#! Min-max-matrix and theoretical rainflow matrix for test Markov sequence.
 #cmatplot(u_markov,u_markov,{G_markov Grfc_markov},4)
 #subplot(121), axis('square'), title('min2max transition matrix')
 #subplot(122), axis('square'), title('Rainflow matrix')
-#if (printing==1), print -deps ../bilder/fatigue_9.eps 
+#if (printing==1), print -deps ../bilder/fatigue_9.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 10'),pause(pstate)
@@ -176,10 +177,10 @@ T_markov=5000;
 #n=length(u_markov);
 #Frfc_markov=dtp2rfm(xxD_markov,n);
 #clf
-#cmatplot(u_markov,u_markov,{Frfc_markov Grfc_markov*T_markov/2},3) 
+#cmatplot(u_markov,u_markov,{Frfc_markov Grfc_markov*T_markov/2},3)
 #subplot(121), axis('square'), title('Observed rainflow matrix')
 #subplot(122), axis('square'), title('Theoretical rainflow matrix')
-#if (printing==1), print -deps ../bilder/fatigue_10.eps 
+#if (printing==1), print -deps ../bilder/fatigue_10.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 11'),pause(pstate)
@@ -193,7 +194,7 @@ T_markov=5000;
 #cmatplot(u_markov,u_markov,{Frfc_markov_smooth Grfc_markov*T_markov/2},4)
 #subplot(121), axis('square'), title('Smoothed observed rainflow matrix')
 #subplot(122), axis('square'), title('Theoretical rainflow matrix')
-#if (printing==1), print -deps ../bilder/fatigue_11.eps 
+#if (printing==1), print -deps ../bilder/fatigue_11.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 12'),pause(pstate)
@@ -214,7 +215,7 @@ T_markov=5000;
 #cmatplot(u_herm,u_herm,{GmM3_herm.f Grfc_herm},4)
 #subplot(121), axis('square'), title('min-max matrix')
 #subplot(122), axis('square'), title('Theoretical rainflow matrix')
-#if (printing==1), print -deps ../bilder/fatigue_12.eps 
+#if (printing==1), print -deps ../bilder/fatigue_12.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 14'),pause(pstate)
@@ -230,7 +231,7 @@ T_markov=5000;
 #disp('Block 15'),pause(pstate)
 #
 #
-##!#! Observed smoothed and theoretical min-max matrix, 
+##!#! Observed smoothed and theoretical min-max matrix,
 ##!#! (and observed smoothed and theoretical rainflow matrix for Hermite-transformed Gaussian waves).
 #tp_herm=dat2tp(xx_herm);
 #RFC_herm=tp2rfc(tp_herm);
@@ -246,11 +247,11 @@ T_markov=5000;
 #subplot(222), axis('square'), title('Theoretical min-max matrix')
 #subplot(223), axis('square'), title('Observed smoothed rainflow matrix')
 #subplot(224), axis('square'), title('Theoretical rainflow matrix')
-#if (printing==1), print -deps ../bilder/fatigue_13.eps 
+#if (printing==1), print -deps ../bilder/fatigue_13.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 16'),pause(pstate)
-#   
+#
 ##!#! Section 4.3.5 Simulation from crossings and rainflow structure
 #
 ##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)
@@ -271,7 +272,7 @@ T_markov=5000;
 #subplot(212)
 #plot(xx_herm_sim1(:,1),xx_herm_sim1(:,2))
 #title('Simulated load, \alpha = 0.25')
-#if (printing==1), print -deps ../bilder/fatigue_14_25.eps 
+#if (printing==1), print -deps ../bilder/fatigue_14_25.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 16'),pause(pstate)
@@ -290,7 +291,7 @@ T_markov=5000;
 #subplot(212)
 #plot(xx_herm_sim2(:,1),xx_herm_sim2(:,2))
 #title('Simulated load, \alpha = 0.75')
-#if (printing==1), print -deps ../bilder/fatigue_14_75.eps 
+#if (printing==1), print -deps ../bilder/fatigue_14_75.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 17'),pause(pstate)
@@ -310,7 +311,7 @@ T_markov=5000;
 #clf
 #plot(mu_markov(:,1),mu_markov(:,2),muObs_markov(:,1),muObs_markov(:,2),'--')
 #title('Theoretical and observed crossing intensity ')
-#if (printing==1), print -deps ../bilder/fatigue_15.eps 
+#if (printing==1), print -deps ../bilder/fatigue_15.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 19'),pause(pstate)
@@ -324,13 +325,13 @@ T_markov=5000;
 #disp('Block 20'),pause(pstate)
 #
 #Dmat_markov = cmat2dmat(param_m,Grfc_markov,beta);
-#DmatObs_markov = cmat2dmat(param_m,Frfc_markov,beta)/(T_markov/2); 
+#DmatObs_markov = cmat2dmat(param_m,Frfc_markov,beta)/(T_markov/2);
 #clf
 #subplot(121), cmatplot(u_markov,u_markov,Dmat_markov,4)
-#title('Theoretical damage matrix') 
+#title('Theoretical damage matrix')
 #subplot(122), cmatplot(u_markov,u_markov,DmatObs_markov,4)
-#title('Observed damage matrix') 
-#if (printing==1), print -deps ../bilder/fatigue_16.eps 
+#title('Observed damage matrix')
+#if (printing==1), print -deps ../bilder/fatigue_16.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 21'),pause(pstate)
@@ -356,7 +357,7 @@ T_markov=5000;
 ##!#! Check of S-N-model on normal probability paper.
 #
 #normplot(reshape(log(N),8,5))
-#if (printing==1), print -deps ../bilder/fatigue_17.eps 
+#if (printing==1), print -deps ../bilder/fatigue_17.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 23'),pause(pstate)
@@ -366,7 +367,7 @@ T_markov=5000;
 #[e0,beta0,s20] = snplot(s,N,12);
 #title('S-N-data with estimated N(s)','FontSize',20)
 #set(gca,'FontSize',20)
-#if (printing==1), print -deps ../bilder/fatigue_18a.eps 
+#if (printing==1), print -deps ../bilder/fatigue_18a.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 24'),pause(pstate)
@@ -376,7 +377,7 @@ T_markov=5000;
 #[e0,beta0,s20] = snplot(s,N,14);
 #title('S-N-data with estimated N(s)','FontSize',20)
 #set(gca,'FontSize',20)
-#if (printing==1), print -deps ../bilder/fatigue_18b.eps 
+#if (printing==1), print -deps ../bilder/fatigue_18b.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 25'),pause(pstate)
@@ -388,7 +389,7 @@ T_markov=5000;
 #dRFC = DRFC/T_sea;
 #plot(beta,dRFC), axis([3 8 0 0.25])
 #title('Damage intensity as function of \beta')
-#if (printing==1), print -deps ../bilder/fatigue_19.eps 
+#if (printing==1), print -deps ../bilder/fatigue_19.eps
 #end
 #wafostamp([],'(ER)')
 #disp('Block 26'),pause(pstate)
@@ -400,7 +401,7 @@ T_markov=5000;
 #[t2,F2] = ftf(e0,dam0,s20,5,1);
 #plot(t0,F0,t1,F1,t2,F2)
 #title('Fatigue life distribution function')
-#if (printing==1), print -deps ../bilder/fatigue_20.eps 
+#if (printing==1), print -deps ../bilder/fatigue_20.eps
 #end
 #wafostamp([],'(ER)')
-#disp('Block 27, last block')
+#disp('Block 27, last block')

wafo/doc/tutorial_scripts/chapter5.py

@@ -1,195 +1,238 @@
-%% CHAPTER5 contains the commands used in Chapter 5 of the tutorial
-%
-% CALL:  Chapter5
-% 
-% Some of the commands are edited for fast computation. 
-% Each set of commands is followed by a 'pause' command.
-% 
-
-% Tested on Matlab 5.3
-% History
-% Added Return values by GL August 2008
-% Revised pab sept2005
-% Added sections -> easier to evaluate using cellmode evaluation.
-% Created by GL July 13, 2000
-% from commands used in Chapter 5
-%
- 
-%% Chapter 5 Extreme value analysis
-
-%% Section 5.1 Weibull and Gumbel papers
+## CHAPTER5 contains the commands used in Chapter 5 of the tutorial
+#
+# CALL:  Chapter5
+#
+# Some of the commands are edited for fast computation.
+# Each set of commands is followed by a 'pause' command.
+#
+
+# Tested on Matlab 5.3
+# History
+# Added Return values by GL August 2008
+# Revised pab sept2005
+# Added sections -> easier to evaluate using cellmode evaluation.
+# Created by GL July 13, 2000
+# from commands used in Chapter 5
+#
+
+## Chapter 5 Extreme value analysis
+
+## Section 5.1 Weibull and Gumbel papers
+from __future__ import division
+import numpy as np
+import scipy.interpolate as si
+from wafo.plotbackend import plotbackend as plt
+import wafo.data as wd
+import wafo.objects as wo
+import wafo.stats as ws
+import wafo.kdetools as wk
 pstate = 'off'
 
-% Significant wave-height data on Weibull paper,
-clf
-Hs = load('atlantic.dat');
-wei = plotweib(Hs)
-wafostamp([],'(ER)')
-disp('Block = 1'),pause(pstate)
-
-%%
-% Significant wave-height data on Gumbel paper,
-clf
-gum=plotgumb(Hs)
-wafostamp([],'(ER)')
-  disp('Block = 2'),pause(pstate)
-
-%%
-% Significant wave-height data on Normal probability paper,
-plotnorm(log(Hs),1,0);
-wafostamp([],'(ER)')
-disp('Block = 3'),pause(pstate)
-
-%%
-% Return values in the Gumbel distribution
-clf
-T=1:100000;
-sT=gum(2) - gum(1)*log(-log(1-1./T));
-semilogx(T,sT), hold
-N=1:length(Hs); Nmax=max(N);
-plot(Nmax./N,sort(Hs,'descend'),'.')
-title('Return values in the Gumbel model')
-xlabel('Return period')
-ylabel('Return value') 
-wafostamp([],'(ER)')
-disp('Block = 4'),pause(pstate)
-
-%% Section 5.2 Generalized Pareto and Extreme Value distributions
-%% Section 5.2.1 Generalized Extreme Value distribution
-
-% Empirical distribution of significant wave-height with estimated 
-% Generalized Extreme Value distribution,
-gev=fitgev(Hs,'plotflag',2)
-wafostamp([],'(ER)')
-disp('Block = 5a'),pause(pstate)
-
-clf
-x = linspace(0,14,200);
-plotkde(Hs,[x;pdfgev(x,gev)]')
-disp('Block = 5b'),pause(pstate)
-
-% Analysis of yura87 wave data. 
-% Wave data interpolated (spline) and organized in 5-minute intervals
-% Normalized to mean 0 and std = 1 to get stationary conditions. 
-% maximum level over each 5-minute interval analysed by GEV
-xn  = load('yura87.dat');
-XI  = 0:0.25:length(xn);
-N   = length(XI); N = N-mod(N,4*60*5); 
-YI  = interp1(xn(:,1),xn(:,2),XI(1:N),'spline');
-YI  = reshape(YI,4*60*5,N/(4*60*5)); % Each column holds 5 minutes of 
-                                     % interpolated data.
-Y5  = (YI-ones(1200,1)*mean(YI))./(ones(1200,1)*std(YI)); 
-Y5M = max(Y5);
-Y5gev = fitgev(Y5M,'method','mps','plotflag',2)
-wafostamp([],'(ER)')
-disp('Block = 6'),pause(pstate)
-
-%% Section 5.2.2 Generalized Pareto distribution
-
-% Exceedances of significant wave-height data over level 3,
-gpd3 = fitgenpar(Hs(Hs>3)-3,'plotflag',1);
-wafostamp([],'(ER)')
-
-%%
-figure
-% Exceedances of significant wave-height data over level 7,
-gpd7 = fitgenpar(Hs(Hs>7),'fixpar',[nan,nan,7],'plotflag',1);
-wafostamp([],'(ER)')
-disp('Block = 6'),pause(pstate)
-
-%% 
-%Simulates 100 values from the GEV distribution with parameters (0.3, 1, 2), then estimates the
-%parameters using two different methods and plots the estimated distribution functions together
-%with the empirical distribution.
-Rgev = rndgev(0.3,1,2,1,100);
-gp = fitgev(Rgev,'method','pwm');
-gm = fitgev(Rgev,'method','ml','start',gp.params,'plotflag',0);
-
-x=sort(Rgev);
-plotedf(Rgev,gp,{'-','r-'});
-hold on
-plot(x,cdfgev(x,gm),'--')
-hold off
-wafostamp([],'(ER)')
-disp('Block =7'),pause(pstate)
-
-%%
-% ;
-Rgpd = rndgenpar(0.4,1,0,1,100);
-plotedf(Rgpd);
-hold on
-gp = fitgenpar(Rgpd,'method','pkd','plotflag',0);
-x=sort(Rgpd);
-plot(x,cdfgenpar(x,gp))
-% gm = fitgenpar(Rgpd,'method','mom','plotflag',0);
-% plot(x,cdfgenpar(x,gm),'g--')
-gw = fitgenpar(Rgpd,'method','pwm','plotflag',0);
-plot(x,cdfgenpar(x,gw),'g:')
-gml = fitgenpar(Rgpd,'method','ml','plotflag',0);
-plot(x,cdfgenpar(x,gml),'--')
-gmps = fitgenpar(Rgpd,'method','mps','plotflag',0);
-plot(x,cdfgenpar(x,gmps),'r-.')
-hold off
-wafostamp([],'(ER)')
-disp('Block = 8'),pause(pstate)
-
-%%
-% Return values for the GEV distribution
-T = logspace(1,5,10);
-[sT, sTlo, sTup] = invgev(1./T,Y5gev,'lowertail',false,'proflog',true);
-
-%T = 2:100000;
-%k=Y5gev.params(1); mu=Y5gev.params(3); sigma=Y5gev.params(2);
-%sT1 = invgev(1./T,Y5gev,'lowertail',false);
-%sT=mu + sigma/k*(1-(-log(1-1./T)).^k);
-clf
-semilogx(T,sT,T,sTlo,'r',T,sTup,'r'), hold
-N=1:length(Y5M); Nmax=max(N);
-plot(Nmax./N,sort(Y5M,'descend'),'.')
-title('Return values in the GEV model')
-xlabel('Return priod')
-ylabel('Return value') 
-grid on 
-disp('Block = 9'),pause(pstate)
-
-%% Section 5.3 POT-analysis
-
-% Estimated expected exceedance over level u as function of u.
-clf
-plotreslife(Hs,'umin',2,'umax',10,'Nu',200);
-wafostamp([],'(ER)')
-disp('Block = 10'),pause(pstate)
-
-%%
-% Estimated distribution functions of monthly maxima 
-%with the POT method (solid),
-% fitting a GEV (dashed) and the empirical distribution.
-
-% POT- method
-gpd7 = fitgenpar(Hs(Hs>7)-7,'method','pwm','plotflag',0);
-khat = gpd7.params(1);
-sigmahat = gpd7.params(2);
-muhat = length(Hs(Hs>7))/(7*3*2);
-bhat = sigmahat/muhat^khat;
-ahat = 7-(bhat-sigmahat)/khat;
-x = linspace(5,15,200);
-plot(x,cdfgev(x,khat,bhat,ahat))
-disp('Block = 11'),pause(pstate)
-
-%%
-% Since we have data to compute the monthly maxima mm over 
-%42 months we can also try to fit a
-% GEV distribution directly:
-mm = zeros(1,41);
-for i=1:41
-  mm(i)=max(Hs(((i-1)*14+1):i*14)); 
-end
-
-gev=fitgev(mm);
-hold on
-plotedf(mm)
-plot(x,cdfgev(x,gev),'--')
-hold off
-wafostamp([],'(ER)')
-disp('Block = 12, Last block'),pause(pstate)
+# Significant wave-height data on Weibull paper,
+
+fig = plt.figure()
+ax = fig.add_subplot(111)
+Hs = wd.atlantic()
+wei = ws.weibull_min.fit(Hs)
+tmp = ws.probplot(Hs, wei, ws.weibull_min, plot=ax)
+plt.show()
+#wafostamp([],'(ER)')
+#disp('Block = 1'),pause(pstate)
+
+##
+# Significant wave-height data on Gumbel paper,
+plt.clf()
+ax = fig.add_subplot(111)
+gum = ws.gumbel_r.fit(Hs)
+tmp1 = ws.probplot(Hs, gum, ws.gumbel_r, plot=ax)
+#wafostamp([],'(ER)')
+plt.show()
+#disp('Block = 2'),pause(pstate)
+
+##
+# Significant wave-height data on Normal probability paper,
+plt.clf()
+ax = fig.add_subplot(111)
+phat = ws.norm.fit2(np.log(Hs))
+phat.plotresq()
+#tmp2 = ws.probplot(np.log(Hs), phat, ws.norm, plot=ax)
+
+#wafostamp([],'(ER)')
+plt.show()
+#disp('Block = 3'),pause(pstate)
+
+##
+# Return values in the Gumbel distribution
+plt.clf()
+T = np.r_[1:100000]
+sT = gum[0] - gum[1] * np.log(-np.log1p(-1./T))
+plt.semilogx(T, sT)
+plt.hold(True)
+# ws.edf(Hs).plot()
+Nmax = len(Hs)
+N = np.r_[1:Nmax+1]
+
+plt.plot(Nmax/N, sorted(Hs, reverse=True), '.')
+plt.title('Return values in the Gumbel model')
+plt.xlabel('Return period')
+plt.ylabel('Return value')
+#wafostamp([],'(ER)')
+plt.show()
+#disp('Block = 4'),pause(pstate)
+
+## Section 5.2 Generalized Pareto and Extreme Value distributions
+## Section 5.2.1 Generalized Extreme Value distribution
+
+# Empirical distribution of significant wave-height with estimated
+# Generalized Extreme Value distribution,
+gev = ws.genextreme.fit2(Hs)
+gev.plotfitsummary()
+# wafostamp([],'(ER)')
+# disp('Block = 5a'),pause(pstate)
+
+plt.clf()
+x = np.linspace(0,14,200)
+kde = wk.TKDE(Hs, L2=0.5)(x, output='plot')
+kde.plot()
+plt.hold(True)
+plt.plot(x, gev.pdf(x),'--')
+# disp('Block = 5b'),pause(pstate)
+
+# Analysis of yura87 wave data.
+# Wave data interpolated (spline) and organized in 5-minute intervals
+# Normalized to mean 0 and std = 1 to get stationary conditions.
+# maximum level over each 5-minute interval analysed by GEV
+xn = wd.yura87()
+XI = np.r_[1:len(xn):0.25] - .99
+N = len(XI)
+N = N - np.mod(N, 4*60*5)
+
+YI = si.interp1d(xn[:, 0],xn[:, 1], kind='linear')(XI)
+YI = YI.reshape(4*60*5, N/(4*60*5))  # Each column holds 5 minutes of
+                                     # interpolated data.
+Y5 = (YI - YI.mean(axis=0)) / YI.std(axis=0)
+Y5M = Y5.maximum(axis=0)
+Y5gev = ws.genextreme.fit2(Y5M,method='mps')
+Y5gev.plotfitsummary()
+#wafostamp([],'(ER)')
+#disp('Block = 6'),pause(pstate)
+
+## Section 5.2.2 Generalized Pareto distribution
+
+# Exceedances of significant wave-height data over level 3,
+gpd3 = ws.genpareto.fit2(Hs[Hs>3]-3, floc=0)
+gpd3.plotfitsummary()
+#wafostamp([],'(ER)')
+
+##
+plt.figure()
+# Exceedances of significant wave-height data over level 7,
+gpd7 = ws.genpareto.fit2(Hs(Hs>7), floc=7)
+gpd7.plotfitsummary()
+# wafostamp([],'(ER)')
+# disp('Block = 6'),pause(pstate)
+
+##
+#Simulates 100 values from the GEV distribution with parameters (0.3, 1, 2),
+# then estimates the parameters using two different methods and plots the
+# estimated distribution functions together with the empirical distribution.
+Rgev = ws.genextreme.rvs(0.3,1,2,size=100)
+gp = ws.genextreme.fit2(Rgev, method='mps');
+gm = ws.genextreme.fit2(Rgev, *gp.par.tolist(), method='ml')
+gm.plotfitsummary()
+
+gp.plotecdf()
+plt.hold(True)
+plt.plot(x, gm.cdf(x), '--')
+plt.hold(False)
+#wafostamp([],'(ER)')
+#disp('Block =7'),pause(pstate)
+
+##
+# ;
+Rgpd = ws.genpareto.rvs(0.4,0, 1,size=100)
+gp = ws.genpareto.fit2(Rgpd, method='mps')
+gml = ws.genpareto.fit2(Rgpd, method='ml')
+
+gp.plotecdf()
+x = sorted(Rgpd)
+plt.hold(True)
+plt.plot(x, gml.cdf(x))
+# gm = fitgenpar(Rgpd,'method','mom','plotflag',0);
+# plot(x,cdfgenpar(x,gm),'g--')
+#gw = fitgenpar(Rgpd,'method','pwm','plotflag',0);
+#plot(x,cdfgenpar(x,gw),'g:')
+#gml = fitgenpar(Rgpd,'method','ml','plotflag',0);
+#plot(x,cdfgenpar(x,gml),'--')
+#gmps = fitgenpar(Rgpd,'method','mps','plotflag',0);
+#plot(x,cdfgenpar(x,gmps),'r-.')
+plt.hold(False)
+#wafostamp([],'(ER)')
+#disp('Block = 8'),pause(pstate)
+
+##
+# Return values for the GEV distribution
+T = np.logspace(1, 5, 10);
+#[sT, sTlo, sTup] = invgev(1./T,Y5gev,'lowertail',false,'proflog',true);
+
+#T = 2:100000;
+#k=Y5gev.params(1); mu=Y5gev.params(3); sigma=Y5gev.params(2);
+#sT1 = invgev(1./T,Y5gev,'lowertail',false);
+#sT=mu + sigma/k*(1-(-log(1-1./T)).^k);
+plt.clf()
+#plt.semilogx(T,sT,T,sTlo,'r',T,sTup,'r')
+#plt.hold(True)
+#N = np.r_[1:len(Y5M)]
+#Nmax = max(N);
+#plot(Nmax./N, sorted(Y5M,reverse=True), '.')
+#plt.title('Return values in the GEV model')
+#plt.xlabel('Return priod')
+#plt.ylabel('Return value')
+#plt.grid(True)
+#disp('Block = 9'),pause(pstate)
+
+## Section 5.3 POT-analysis
+
+# Estimated expected exceedance over level u as function of u.
+plt.clf()
+
+mrl = ws.reslife(Hs,'umin',2,'umax',10,'Nu',200);
+mrl.plot()
+#wafostamp([],'(ER)')
+#disp('Block = 10'),pause(pstate)
+
+##
+# Estimated distribution functions of monthly maxima
+#with the POT method (solid),
+# fitting a GEV (dashed) and the empirical distribution.
+
+# POT- method
+gpd7 = ws.genpareto.fit2(Hs(Hs>7)-7, method='mps', floc=0)
+khat, loc, sigmahat = gpd7.par
+
+muhat = len(Hs[Hs>7])/(7*3*2)
+bhat = sigmahat/muhat**khat
+ahat = 7-(bhat-sigmahat)/khat
+x = np.linspace(5,15,200);
+plt.plot(x,ws.genextreme.cdf(x, khat,bhat,ahat))
+# disp('Block = 11'),pause(pstate)
+
+##
+# Since we have data to compute the monthly maxima mm over
+#42 months we can also try to fit a
+# GEV distribution directly:
+mm = np.zeros((1,41))
+for i in range(41):
+    mm[i] = max(Hs[((i-1)*14+1):i*14])
+
+
+gev = ws.genextreme.fit2(mm)
+
+
+plt.hold(True)
+gev.plotecdf()
+
+plt.hold(False)
+#wafostamp([],'(ER)')
+#disp('Block = 12, Last block'),pause(pstate)
 

wafo/graphutil.py

@@ -45,7 +45,10 @@ def delete_text_object(gidtxt, figure=None, axis=None, verbose=False):
 
     def _delete_gid_objects(handle, gidtxt, verbose):
         objs = handle.findobj(lmatchfun)
-        name = handle.__name__
+        try:
+            name = handle.__class__.__name__
+        except AttributeError:
+            name = 'unknown object'
         msg = "Tried to delete a non-existing {0} from {1}".format(gidtxt,
                                                                    name)
         for obj in objs:
@@ -127,7 +130,10 @@ def cltext(levels, percent=False, n=4, xs=0.036, ys=0.94, zs=0, figure=None,
     yss = yint[0] + ys * (yint[1] - yint[0])
 
     # delete cltext object if it exists
-    delete_text_object(_CLTEXT_GID, axis=axis)
+    try:
+        delete_text_object(_CLTEXT_GID, axis=axis)
+    except Exception:
+        pass
 
     charHeight = 1.0 / 33.0
     delta_y = charHeight

wafo/spectrum/core.py

@@ -3447,8 +3447,10 @@ class SpecData1D(PlotData):
         >>> S.bandwidth([0,'eps2',2,3])
         array([ 0.73062845,  0.34476034,  0.68277527,  2.90817052])
         '''
-        m, unused_mtxt = self.moment(nr=4, even=False)
 
+        m, unused_mtxt = self.moment(nr=4, even=False)
+        if isinstance(factors, str):
+            factors = [factors]
         fact_dict = dict(alpha=0, eps2=1, eps4=3, qp=3, Qp=3)
         fact = array([fact_dict.get(idx, idx)
                       for idx in list(factors)], dtype=int)