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@ -171,9 +171,9 @@ show()
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#! Test Gaussianity of a stochastic process
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#! Test Gaussianity of a stochastic process
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#!------------------------------------------
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#!------------------------------------------
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#! TESTGAUSSIAN simulates e(g(u)-u) = int (g(u)-u)^2 du for Gaussian processes
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#! TESTGAUSSIAN simulates e(g(u)-u) = int (g(u)-u)^2 du for Gaussian processes
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#! given the spectral density, S. The result is plotted if test0 is given.
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#! given the spectral density, S. The result is plotted if test0 is given.
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#! This is useful for testing if the process X(t) is Gaussian.
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#! This is useful for testing if the process X(t) is Gaussian.
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#! If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.
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#! If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.
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#!
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#!
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#! As we see from the figure below: none of the simulated values of test1 is
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#! As we see from the figure below: none of the simulated values of test1 is
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#! above 1.00. Thus the data significantly departs from a Gaussian distribution.
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#! above 1.00. Thus the data significantly departs from a Gaussian distribution.
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@ -182,7 +182,7 @@ test0 = glc.dist2gauss()
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#! the following test takes time
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#! the following test takes time
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N = len(xx)
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N = len(xx)
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test1 = S1.testgaussian(ns=N, cases=50, test0=test0)
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test1 = S1.testgaussian(ns=N, cases=50, test0=test0)
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is_gaussian = sum(test1 > test0) < 5
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is_gaussian = sum(test1 > test0) > 5
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print(is_gaussian)
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print(is_gaussian)
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show()
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show()
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@ -295,49 +295,31 @@ show()
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##!wafostamp('','(CR)')
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##!wafostamp('','(CR)')
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#disp('Block = 24'),pause(pstate)
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#disp('Block = 24'),pause(pstate)
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#
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#
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##!#! Estimated spectrum compared to Torsethaugen spectrum
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#! Estimated spectrum compared to Torsethaugen spectrum
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#clf
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#!-------------------------------------------------------
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#Tp = 1.1;
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#H0 = 4*sqrt(spec2mom(S1,1))
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clf()
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#St = torsethaugen([0:0.01:5],[H0 2*pi/Tp]);
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fp = 1.1;dw = 0.01
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#plotspec(S1)
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H0 = S1.characteristic('Hm0')[0]
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#hold on
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St = wsm.Torsethaugen(Hm0=H0,Tp=2*pi/fp).tospecdata(np.arange(0,5+dw/2,dw))
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#plotspec(St,'-.')
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S1.plot()
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#axis([0 6 0 0.4])
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St.plot('-.')
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##!wafostamp('','(ER)')
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axis([0, 6, 0, 0.4])
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#disp('Block = 25'),pause(pstate)
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show()
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#
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##!#!
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#clf
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#Snorm = St;
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#Snorm.S = Snorm.S/sa^2;
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#dt = spec2dt(Snorm)
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#disp('Block = 26'),pause(pstate)
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#
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##!#!
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#clf
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#[Sk Su] = spec2skew(St);
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#sa = sqrt(spec2mom(St,1));
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#gh = hermitetr([],[sa sk ku me]);
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#Snorm.tr = gh;
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#disp('Block = 27'),pause(pstate)
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#
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##!#! Transformed Gaussian model compared to Gaussian model
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#clf
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#dt = 0.5;
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#ysim_t = spec2sdat(Snorm,240,dt);
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#xsim_t = dat2gaus(ysim_t,Snorm.tr);
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#disp('Block = 28'),pause(pstate)
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#
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##!#! Compare
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##! In order to compare the Gaussian and non-Gaussian models we need to scale
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##! \verb+xsim_t+ #!{\tt xsim$_t$}
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##! to have the same first spectral moment as
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##! \verb+ysim_t+, #!{\tt ysim$_t$}, Since the process xsim_t has variance one
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##! which will be done by the following commands.
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#clf
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#xsim_t(:,2) = sa*xsim_t(:,2);
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#waveplot(xsim_t,ysim_t,5,1,sa,4.5,'r.','b')
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##!wafostamp('','(CR)')
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#disp('Block = 29, Last block'),pause(pstate)
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#! Transformed Gaussian model compared to Gaussian model
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#!--------------------------------------------------------
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dt = St.sampling_period()
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va, sk, ku = St.stats_nl(moments='vsk' )
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#sa = sqrt(va)
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gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa)
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ysim_t = St.sim(ns=240, dt=0.5)
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xsim_t = ysim_t.copy()
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xsim_t[:,1] = gh.gauss2dat(ysim_t[:,1])
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ts_y = wo.mat2timeseries(ysim_t)
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ts_x = wo.mat2timeseries(xsim_t)
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ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1)
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show()
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