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Avoid using "non-Pythonic" variable names

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master
Per A Brodtkorb 8 years ago
parent e26325dfc3
commit 9930a88572
1 changed files with 84 additions and 82 deletions
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166
wafo/covariance/core.py
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@ -176,7 +176,7 @@ class CovData1D(PlotData):
nugget effect to ensure that round off errors do not result in
negative spectral estimates. Good choice might be 10^-12.
trunc : scalar, real
truncates all spectral values where S/max(S) < trunc
truncates all spectral values where spec/max(spec) < trunc
0 <= trunc <1 This is to ensure that high frequency
noise is not added to the spectrum. (default 1e-5)
fast : bool
@ -185,7 +185,7 @@ class CovData1D(PlotData):
Returns
--------
S : SpecData1D object
spec : SpecData1D object
spectral density
NB! This routine requires that the covariance is evenly spaced
@ -205,14 +205,14 @@ class CovData1D(PlotData):
>>> S0 = R0.tospecdata()
>>> Sj = sm.Jonswap()
>>> S = Sj.tospecdata()
>>> R2 = S.tocovdata()
>>> spec = Sj.tospecdata()
>>> R2 = spec.tocovdata()
>>> S1 = R2.tospecdata()
>>> abs(S1.data-S.data).max() < 1e-4
>>> abs(S1.data-spec.data).max() < 1e-4
True
S1.plot('r-')
S.plot('b:')
spec.plot('b:')
pylab.show()
See also
@ -252,26 +252,26 @@ class CovData1D(PlotData):
nf = int(nfft // 2) # number of frequencies
acf = r_[acf, zeros(nfft - 2 * n + 2), acf[n - 2:0:-1]]
Rper = (fft(acf, nfft).real).clip(0) # periodogram
RperMax = Rper.max()
Rper = where(Rper < trunc * RperMax, 0, Rper)
r_per = (fft(acf, nfft).real).clip(0) # periodogram
r_per_max = r_per.max()
r_per = where(r_per < trunc * r_per_max, 0, r_per)
S = abs(Rper[0:(nf + 1)]) * dt / pi
spec = abs(r_per[0:(nf + 1)]) * dt / pi
w = linspace(0, pi / dt, nf + 1)
So = _wafospec.SpecData1D(S, w, type=spectype, freqtype=ftype)
So.tr = self.tr
So.h = self.h
So.norm = self.norm
spec_out = _wafospec.SpecData1D(spec, w, type=spectype, freqtype=ftype)
spec_out.tr = self.tr
spec_out.h = self.h
spec_out.norm = self.norm
if method != 'fft' and rate > 1:
So.args = linspace(0, pi / dt, nf * rate)
spec_out.args = linspace(0, pi / dt, nf * rate)
if method == 'stineman':
So.data = stineman_interp(So.args, w, S)
spec_out.data = stineman_interp(spec_out.args, w, spec)
else:
intfun = interpolate.interp1d(w, S, kind=method)
So.data = intfun(So.args)
So.data = So.data.clip(0) # clip negative values to 0
return So
intfun = interpolate.interp1d(w, spec, kind=method)
spec_out.data = intfun(spec_out.args)
spec_out.data = spec_out.data.clip(0) # clip negative values to 0
return spec_out
def sampling_period(self):
'''
@ -303,7 +303,7 @@ class CovData1D(PlotData):
Parameters
----------
ns : scalar
number of simulated points. (default length(S)-1=n-1).
number of simulated points. (default length(spec)-1=n-1).
If ns>n-1 it is assummed that R(k)=0 for all k>n-1
cases : scalar
number of replicates (default=1)
@ -336,8 +336,8 @@ class CovData1D(PlotData):
Example:
>>> import wafo.spectrum.models as sm
>>> Sj = sm.Jonswap()
>>> S = Sj.tospecdata() #Make spec
>>> R = S.tocovdata()
>>> spec = Sj.tospecdata() #Make spec
>>> R = spec.tocovdata()
>>> x = R.sim(ns=1000,dt=0.2)
See also
@ -365,7 +365,7 @@ class CovData1D(PlotData):
n = acf.size
acf.shape = (n, 1)
dT = self.sampling_period()
dt = self.sampling_period()
x = zeros((ns, cases + 1))
@ -391,10 +391,10 @@ class CovData1D(PlotData):
acf = r_[acf, zeros((nfft - m2, 1)), acf[n - 1:1:-1, :]]
# m2=2*n-2
S = fft(acf, nfft, axis=0).real # periodogram
spec = fft(acf, nfft, axis=0).real # periodogram
I = S.argmax()
k = flatnonzero(S < 0)
I = spec.argmax()
k = flatnonzero(spec < 0)
if k.size > 0:
_msg = '''
Not able to construct a nonnegative circulant vector from ACF.
@ -404,7 +404,7 @@ class CovData1D(PlotData):
# truncating negative values to zero to ensure that
# that this noise is not added to the simulated timeseries
S[k] = 0.
spec[k] = 0.
ix = flatnonzero(k > 2 * I)
if ix.size > 0:
@ -413,13 +413,13 @@ class CovData1D(PlotData):
# that high frequency noise is not added to
# the simulated timeseries.
ix0 = k[ix[0]]
S[ix0:-ix0] = 0.0
spec[ix0:-ix0] = 0.0
trunc = 1e-5
maxS = S[I]
k = flatnonzero(S[I:-I] < maxS * trunc)
max_spec = spec[I]
k = flatnonzero(spec[I:-I] < max_spec * trunc)
if k.size > 0:
S[k + I] = 0.
spec[k + I] = 0.
# truncating small values to zero to ensure that
# that high frequency noise is not added to
# the simulated timeseries
@ -430,18 +430,18 @@ class CovData1D(PlotData):
# randn = np.random.randn
epsi = randn(nfft, cases2) + 1j * randn(nfft, cases2)
Ssqr = sqrt(S / (nfft)) # sqrt(S(wn)*dw )
ephat = epsi * Ssqr # [:,np.newaxis]
sqrt_spec = sqrt(spec / (nfft)) # sqrt(spec(wn)*dw )
ephat = epsi * sqrt_spec # [:,np.newaxis]
y = fft(ephat, nfft, axis=0)
x[:, 1:cases + 1] = hstack((y[2:ns + 2, 0:cases2].real,
y[2:ns + 2, 0:cases1].imag))
x[:, 0] = linspace(0, (ns - 1) * dT, ns) # (0:dT:(dT*(np-1)))'
x[:, 0] = linspace(0, (ns - 1) * dt, ns) # (0:dt:(dt*(np-1)))'
if derivative:
Ssqr = Ssqr * \
r_[0:(nfft / 2 + 1), -(nfft / 2 - 1):0] * 2 * pi / nfft / dT
ephat = epsi * Ssqr # [:,newaxis]
sqrt_spec = sqrt_spec * \
r_[0:(nfft / 2 + 1), -(nfft / 2 - 1):0] * 2 * pi / nfft / dt
ephat = epsi * sqrt_spec # [:,newaxis]
y = fft(ephat, nfft, axis=0)
xder[:, 1:(cases + 1)] = hstack((y[2:ns + 2, 0:cases2].imag -
y[2:ns + 2, 0:cases1].real))
@ -486,24 +486,26 @@ class CovData1D(PlotData):
else:
return acf[:n]
def _split_cov(self, sigma, i_known, i_unknown):
@staticmethod
def _split_cov(sigma, i_known, i_unknown):
'''
Split covariance matrix between known/unknown observations
Returns
-------
Soo covariance between known observations
S11 = covariance between unknown observations
S1o = covariance between known and unknown obs
soo covariance between known observations
s1o = covariance between known and unknown obs
s11 = covariance between unknown observations
'''
Soo, So1 = sigma[i_known][:, i_known], sigma[i_known][:, i_unknown]
S11 = sigma[i_unknown][:, i_unknown]
return Soo, So1, S11
soo, so1 = sigma[i_known][:, i_known], sigma[i_known][:, i_unknown]
s11 = sigma[i_unknown][:, i_unknown]
return soo, so1, s11
def _update_window(self, idx, i_unknown, num_x, num_acf,
@staticmethod
def _update_window(idx, i_unknown, num_x, num_acf,
overlap, nw, num_restored):
Nsig = len(idx)
start_max = num_x - Nsig
num_sig = len(idx)
start_max = num_x - num_sig
if (nw == 0) and (num_restored < len(i_unknown)):
# move to the next missing data
start_ix = min(i_unknown[num_restored + 1] - overlap, start_max)
@ -594,38 +596,38 @@ class CovData1D(PlotData):
if method.startswith('exac'):
# exact but slow. It also may not return any result
if num_acf > 0.3 * num_x:
Sigma = toeplitz(hstack((acf, zeros(num_x - num_acf))))
sigma = toeplitz(hstack((acf, zeros(num_x - num_acf))))
else:
acf[0] = acf[0] * 1.00001
Sigma = sptoeplitz(hstack((acf, zeros(num_x - num_acf))))
Soo, So1, S11 = self._split_cov(Sigma, i_known, i_unknown)
sigma = sptoeplitz(hstack((acf, zeros(num_x - num_acf))))
soo, so1, s11 = self._split_cov(sigma, i_known, i_unknown)
if issparse(Sigma):
So1 = So1.todense()
S11 = S11.todense()
S1o_Sooinv = spsolve(Soo + Soo.T, 2 * So1).T
if issparse(sigma):
so1 = so1.todense()
s11 = s11.todense()
s1o_sooinv = spsolve(soo + soo.T, 2 * so1).T
else:
Sooinv_So1, _res, _rank, _s = lstsq(Soo + Soo.T, 2 * So1,
sooinv_so1, _res, _rank, _s = lstsq(soo + soo.T, 2 * so1,
cond=1e-4)
S1o_Sooinv = Sooinv_So1.T
mu1o = S1o_Sooinv.dot(x[i_known])
Sigma1o = S11 - S1o_Sooinv.dot(So1)
if (diag(Sigma1o) < 0).any():
s1o_sooinv = sooinv_so1.T
mu1o = s1o_sooinv.dot(x[i_known])
sigma1o = s11 - s1o_sooinv.dot(so1)
if (diag(sigma1o) < 0).any():
raise ValueError('Failed to converge to a solution')
mu1o_std = sqrt(diag(Sigma1o))
sample[:] = rndnormnd(mu1o, Sigma1o, cases=1).ravel()
mu1o_std = sqrt(diag(sigma1o))
sample[:] = rndnormnd(mu1o, sigma1o, cases=1).ravel()
elif method.startswith('appr'):
# approximating by only condition on the closest points
Nsig = min(2 * num_acf, num_x)
num_sig = min(2 * num_acf, num_x)
Sigma = toeplitz(hstack((acf, zeros(Nsig - num_acf))))
overlap = int(Nsig / 4)
sigma = toeplitz(hstack((acf, zeros(num_sig - num_acf))))
overlap = int(num_sig / 4)
# indices to the points used
idx = r_[0:Nsig] + max(0, min(i_unknown[0] - overlap,
num_x - Nsig))
idx = r_[0:num_sig] + max(0, min(i_unknown[0] - overlap,
num_x - num_sig))
mask_unknown = zeros(num_x, dtype=bool)
# temporary storage of indices to missing points
mask_unknown[i_unknown] = True
@ -637,29 +639,29 @@ class CovData1D(PlotData):
x2 = x.copy()
while ns > 0:
Soo, So1, S11 = self._split_cov(Sigma, t_known, t_unknown)
if issparse(Soo):
So1 = So1.todense()
S11 = S11.todense()
S1o_Sooinv = spsolve(Soo + Soo.T, 2 * So1).T
soo, so1, s11 = self._split_cov(sigma, t_known, t_unknown)
if issparse(soo):
so1 = so1.todense()
s11 = s11.todense()
s1o_sooinv = spsolve(soo + soo.T, 2 * so1).T
else:
Sooinv_So1, _res, _rank, _s = lstsq(Soo + Soo.T, 2 * So1,
sooinv_so1, _res, _rank, _s = lstsq(soo + soo.T, 2 * so1,
cond=1e-4)
S1o_Sooinv = Sooinv_So1.T
Sigma1o = S11 - S1o_Sooinv.dot(So1)
if (diag(Sigma1o) < 0).any():
s1o_sooinv = sooinv_so1.T
sigma1o = s11 - s1o_sooinv.dot(so1)
if (diag(sigma1o) < 0).any():
raise ValueError('Failed to converge to a solution')
ix = slice((num_restored), (num_restored + ns))
# standard deviation of the expected surface
mu1o_std[ix] = np.maximum(mu1o_std[ix], sqrt(diag(Sigma1o)))
mu1o_std[ix] = np.maximum(mu1o_std[ix], sqrt(diag(sigma1o)))
# expected surface conditioned on the closest known
# observations from x
mu1o[ix] = S1o_Sooinv.dot(x2[idx[t_known]])
mu1o[ix] = s1o_sooinv.dot(x2[idx[t_known]])
# sample conditioned on the known observations from x
mu1os = S1o_Sooinv.dot(x[idx[t_known]])
sample[ix] = rndnormnd(mu1os, Sigma1o, cases=1)
mu1os = s1o_sooinv.dot(x[idx[t_known]])
sample[ix] = rndnormnd(mu1os, sigma1o, cases=1)
if idx[-1] == num_x - 1:
ns = 0 # no more points to simulate
else:
@ -732,7 +734,7 @@ def main():
if __name__ == '__main__':
if False: # True: #
import doctest
doctest.testmod()
from wafo.testing import test_docstrings
test_docstrings(__file__)
else:
main()

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