def test_tranproc():
import wafo.transform.models as wtm
tr = wtm.TrHermite()
x = linspace(-5, 5, 501)
g = tr(x)
y0, y1 = tranproc(x, g, range(5), ones(5))
assert_allclose(y0, [0.02659612, 1.00115284, 1.92872532, 2.81453257, 3.66292878])
assert_allclose(y1, [1.00005295, 0.9501118, 0.90589954, 0.86643821, 0.83096482])
def test_testgaussian(self):
Hs = self.Sj.Hm0
S0 = self.S
# 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, test0=None, cases=50)
assert(sum(t1 > t0) <= 5)
def test_testgaussian():
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)
assert (sum(t1 > t0) < 5)
#! Section 2.2.2 Transformed Gaussian models
#!-------------------------------------------
#! We begin with computing skewness and kurtosis
#! for the data set xx and compare it with the second order wave approximation
#! proposed by Winterstein:
import wafo.stats as ws
rho3 = ws.skew(xx[:, 1])
rho4 = ws.kurtosis(xx[:, 1])
sk, ku = S1.stats_nl(moments='sk')
#! Comparisons of 3 transformations
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
glc, gemp = lc.trdata(mean=me, sigma=sa)
glc.plot('b-') #! Transf. estimated from level-crossings
gh.plot('b-.') #! Hermite Transf. estimated from moments
g.plot('r')
grid('on')
show()
#! Test Gaussianity of a stochastic process
#!------------------------------------------
#! 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.