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updated doctests

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master
pbrod 9 years ago
parent b7ce91334e
commit 7b354864c4
4 changed files with 66 additions and 56 deletions
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10
wafo/covariance/core.py
Unescape Escape View File

@ -68,7 +68,7 @@ def rndnormnd(mean, cov, cases=1):
Example
-------
>>> mu = [0, 5]
>>> S = [[1 0.45], [0.45, 0.25]]
>>> S = [[1, 0.45], [0.45, 0.25]]
>>> r = rndnormnd(mu, S, 1)
plot(r(:,1),r(:,2),'.')
@ -211,11 +211,9 @@ class CovData1D(PlotData):
>>> abs(S1.data-S.data).max() < 1e-4
True
>>> S1.plot('r-')
>>> S.plot('b:')
>>> pylab.show()
>>> all(abs(S1.data-S.data)<1e-4)
S1.plot('r-')
S.plot('b:')
pylab.show()
See also
--------

6
wafo/gaussian.py
Unescape Escape View File

@ -109,9 +109,11 @@ class Rind(object):
>>> Bup, Blo = np.atleast_2d(Bup,Blo)
>>> Bup[0,ind] = np.minimum(Bup[0,ind] , infinity*dev[indI[ind+1]])
>>> Blo[0,ind] = np.maximum(Blo[0,ind] ,-infinity*dev[indI[ind+1]])
>>> np.allclose(rind(Sc,m,Blo,Bup,indI, xc, nt=0),
... ([0.05494076], [ 0.00083066], [ 1.00000000e-10]), rtol=1e-3)
>>> val, err, terr = rind(Sc,m,Blo,Bup,indI, xc, nt=0)
>>> np.allclose(val, 0.05494076, rtol=1e-3)
True
>>> err < 1e-3, terr< 1e-7
True, True
Compute expectation E( X1^{+}*X2^{+} ) with random
correlation coefficient,Cov(X1,X2) = rho2.

3
wafo/objects.py
Unescape Escape View File

@ -1965,7 +1965,8 @@ class TimeSeries(PlotData):
expect = 1 # reconstruct by expectation? 1=yes 0=no
tol = 0.001 # absolute tolerance of e(g_new-g_old)
cmvmax = 100 # if number of consecutive missing values (cmv) are longer they
cmvmax = 100
# if number of consecutive missing values (cmv) are longer they
# are not used in estimation of g, due to the fact that the
# conditional expectation approaches zero as the length to
# the closest known points increases, see below in the for loop

83
wafo/spectrum/core.py
Unescape Escape View File

@ -651,7 +651,6 @@ class SpecData1D(PlotData):
objects
'''
dt, rate = self._get_default_dt_and_rate(dt)
self._check_dt(dt)
@ -970,8 +969,8 @@ class SpecData1D(PlotData):
Hw1 = exp(interp1d(log(abs(S1.data / S2.data)), S2.args)(freq))
else:
# Geometric mean
Hw1 = exp((interp1d(log(abs(S1.data / S2.data)), S2.args)(freq)
+ log(Hw2)) / 2)
fun = interp1d(log(abs(S1.data / S2.data)), S2.args)
Hw1 = exp((fun(freq) + log(Hw2)) / 2)
# end
# Hw1 = (interp1q( S2.w,abs(S1.S./S2.S),freq)+Hw2)/2
# plot(freq, abs(Hw11-Hw1),'g')
@ -1549,7 +1548,7 @@ class SpecData1D(PlotData):
# semi-definitt, since the circulant spectrum are the eigenvalues of
# the circulant covariance matrix.
callFortran = 0
# callFortran = 0
# %options.method<0
# if callFortran, % call fortran
# ftmp = cov2mmtpdfexe(R,dt,u,defnr,Nstart,hg,options)
@ -1732,9 +1731,11 @@ class SpecData1D(PlotData):
between Maxima, Minima and Max to level v crossing given the Max and
the min is returned
Y=
X'(t2)..X'(ts)..X'(tn-1)||X''(t1) X''(tn) X'(ts)|| X'(t1) X'(tn) X(t1) X(tn) X(ts)
= [ Xt Xd Xc ]
Y = [Xt, Xd, Xc]
where
Xt = X'(t2)..X'(ts)..X'(tn-1)
Xd = ||X''(t1) X''(tn) X'(ts)||
Xc = X'(t1) X'(tn) X(t1) X(tn) X(ts)
Nt = tn-2, Nd = 3, Nc = 5
@ -1748,7 +1749,7 @@ class SpecData1D(PlotData):
(indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn))
(indI(4)=Nt+2); for i\in (indI(4)+1,indI(5)], Y(i)<0 (deriv. X'(ts))
'''
R0, R1, R2, R3, R4 = R[:, :5].T
R0, _R1, R2, _R3, R4 = R[:, :5].T
covinput = self._covinput_mmt_pdf
Ntime = len(R0)
Nx0 = max(1, len(hg))
@ -2110,12 +2111,14 @@ class SpecData1D(PlotData):
The order of the variables in the covariance matrix are organized as
follows:
for ts <= 1:
X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn)
= [ Xt | Xd | Xc ]
Xt = X'(t2)..X'(ts),...,X'(tn-1)
Xd = X''(t1), X''(tn), X'(t1), X'(tn)
Xc = X(t1),X(tn)
for ts > =2:
X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(ts) X'(t1),X'(tn),X(t1),X(tn) X(ts)
= [ Xt | Xd | Xc ]
Xt = X'(t2)..X'(ts),...,X'(tn-1)
Xd = X''(t1), X''(tn), X'(ts), X'(t1), X'(tn),
Xc = X(t1),X(tn) X(ts)
where
@ -2123,9 +2126,11 @@ class SpecData1D(PlotData):
Xd = derivatives
Xc = variables to condition on
Computations of all covariances follows simple rules: Cov(X(t),X(s)) = r(t,s),
Computations of all covariances follows simple rules:
Cov(X(t),X(s)) = r(t,s),
then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have
a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give
the same result).
Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|)
Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|)
@ -2141,11 +2146,11 @@ class SpecData1D(PlotData):
# for
i = np.arange(tn - 2) # 1:tn-2
# j = abs(i+1-ts)
# BIG(i,N) = -sign(R1(j+1),R1(j+1)*dble(ts-i-1)) %cov(X'(ti+1),X(ts))
# BIG(i,N) = -sign(R1(j+1),R1(j+1)*dble(ts-i-1))
j = i + 1 - ts
tau = abs(j)
# BIG(i,N) = abs(R1(tau)).*sign(R1(tau).*j.')
BIG[i, N] = R1[tau] * sign(j)
BIG[i, N] = R1[tau] * sign(j) # cov(X'(ti+1),X(ts))
# end do
# Cov(Xc)
BIG[N, N] = R0[0] # cov(X(ts),X(ts))
@ -2154,8 +2159,8 @@ class SpecData1D(PlotData):
BIG[tn + shft + 3, N] = R0[ts] # cov(X(t1),X(ts))
BIG[tn + shft + 4, N] = R0[tn - ts] # cov(X(tn),X(ts))
# Cov(Xd,Xc)
BIG[tn - 1, N] = R2[ts] # %cov(X''(t1),X(ts))
BIG[tn, N] = R2[tn - ts] # %cov(X''(tn),X(ts))
BIG[tn - 1, N] = R2[ts] # cov(X''(t1),X(ts))
BIG[tn, N] = R2[tn - ts] # cov(X''(tn),X(ts))
# ADD a level u crossing at ts
@ -2163,12 +2168,13 @@ class SpecData1D(PlotData):
# for
i = np.arange(tn - 2) # 1:tn-2
j = abs(i + 1 - ts)
BIG[i, tn + shft] = -R2[j] # %cov(X'(ti+1),X'(ts))
BIG[i, tn + shft] = -R2[j] # cov(X'(ti+1),X'(ts))
# end do
# Cov(Xd)
BIG[tn + shft, tn + shft] = -R2[0] # %cov(X'(ts),X'(ts))
BIG[tn - 1, tn + shft] = R3[ts] # %cov(X''(t1),X'(ts))
BIG[tn, tn + shft] = -R3[tn - ts] # %cov(X''(tn),X'(ts))
BIG[tn + shft, tn + shft] = -R2[0] # cov(X'(ts),X'(ts))
BIG[tn - 1, tn + shft] = R3[ts] # cov(X''(t1),X'(ts))
BIG[tn, tn + shft] = -R3[tn - ts] # cov(X''(tn),X'(ts))
# Cov(Xd,Xc)
BIG[tn + shft, N] = 0.0 # %cov(X'(ts),X(ts))
@ -2260,7 +2266,9 @@ class SpecData1D(PlotData):
# BIG(i,j) = BIG(j,i)
# end #do
# end #do
lp = np.flatnonzero(np.tril(ones(BIG.shape))) # indices to lower triangular part
# indices to lower triangular part:
lp = np.flatnonzero(np.tril(ones(BIG.shape)))
BIGT = BIG.T
BIG[lp] = BIGT[lp]
return BIG
@ -2586,7 +2594,7 @@ class SpecData1D(PlotData):
>>> import numpy as np
>>> import scipy.stats as st
>>> x2, x1 = S.sim_nl(ns=20000,cases=20)
>>> x2, x1 = S.sim_nl(ns=20000,cases=20, output='data')
>>> truth1 = [0,np.sqrt(S.moment(1)[0][0])] + S.stats_nl(moments='sk')
>>> truth1[-1] = truth1[-1]-3
>>> np.round(truth1, 3)
@ -2606,7 +2614,7 @@ class SpecData1D(PlotData):
>>> x = []
>>> for i in range(20):
... x2, x1 = S.sim_nl(ns=20000,cases=1)
... x2, x1 = S.sim_nl(ns=20000,cases=1, output='data')
... x.append(x2[:,1::])
>>> x2 = np.hstack(x)
>>> truth1 = [0,np.sqrt(S.moment(1)[0][0])] + S.stats_nl(moments='sk')
@ -2687,31 +2695,32 @@ class SpecData1D(PlotData):
# interpolate for freq. [1:(N/2)-1]*df and create 2-sided, uncentered
# spectra
f = arange(1, ns / 2.) * df
f_u = hstack((0., f_i, df * ns / 2.))
w = 2. * pi * hstack((0., f, df * ns / 2.))
ns2 = ns // 2
f = arange(1, ns2) * df
f_u = hstack((0., f_i, df * ns2))
w = 2. * pi * hstack((0., f, df * ns2))
kw = w2k(w, 0., water_depth, g)[0]
s_u = hstack((0., abs(s_i) / 2., 0.))
s_i = interp(f, f_u, s_u)
nmin = (s_i > s_max * reltol).argmax()
nmax = flatnonzero(s_i > 0).max()
s_u = hstack((0., s_i, 0, s_i[(ns / 2) - 2::-1]))
s_u = hstack((0., s_i, 0, s_i[ns2 - 2::-1]))
del(s_i, f_u)
# Generate standard normal random numbers for the simulations
randn = random.randn
z_r = randn((ns / 2) + 1, cases)
z_r = randn(ns2 + 1, cases)
z_i = vstack((zeros((1, cases)),
randn((ns / 2) - 1, cases),
randn(ns2 - 1, cases),
zeros((1, cases))))
amp = zeros((ns, cases), dtype=complex)
amp[0:(ns / 2 + 1), :] = z_r - 1j * z_i
amp[0:(ns2 + 1), :] = z_r - 1j * z_i
del(z_r, z_i)
amp[(ns / 2 + 1):ns, :] = amp[ns / 2 - 1:0:-1, :].conj()
amp[(ns2 + 1):ns, :] = amp[ns2 - 1:0:-1, :].conj()
amp[0, :] = amp[0, :] * sqrt(2.)
amp[(ns / 2), :] = amp[(ns / 2), :] * sqrt(2.)
amp[(ns2), :] = amp[(ns2), :] * sqrt(2.)
# Make simulated time series
T = (ns - 1) * d_t
@ -2719,8 +2728,8 @@ class SpecData1D(PlotData):
if method.startswith('apd'): # apdeterministic
# Deterministic amplitude and phase
amp[1:(ns / 2), :] = amp[1, 0]
amp[(ns / 2 + 1):ns, :] = amp[1, 0].conj()
amp[1:(ns2), :] = amp[1, 0]
amp[(ns2 + 1):ns, :] = amp[1, 0].conj()
amp = sqrt(2) * Ssqr[:, newaxis] * \
exp(1J * arctan2(amp.imag, amp.real))
elif method.startswith('ade'): # adeterministic
@ -3038,7 +3047,7 @@ class SpecData1D(PlotData):
>>> 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)
>>> t1 = S0.testgaussian(ns=2**13, cases=50)
>>> sum(t1 > t0) < 5
True

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