def MBBCCF(x, y, lagMax, sampFreq, Ns, width=None):
nt = x.shape[0]
nWindows = int(nt / width)
# Get CCF
ccf = atmath.ccf(x, y, lagMax=lagMax, sampFreq=sampFreq)
# Get window width (Sherman et al 1998, Mudelsee 2010)
if width is None:
eTimeSample = np.nonzero(ccf > 1. / e)[0][-1] + 1
a = np.exp(-1./eTimeSample)
width = int((6**(1./2)*a/(1-a**2))**(2./3) * nt**(1./3))
def MBBCCF(x, y, lagMax, sampFreq, Ns, width=None):
nt = x.shape[0]
nWindows = int(nt / width)
# Get CCF
ccf = atmath.ccf(x, y, lagMax=lagMax, sampFreq=sampFreq)
# Get window width (Sherman et al 1998, Mudelsee 2010)
if width is None:
eTimeSample = np.nonzero(ccf > 1. / e)[0][-1] + 1
a = np.exp(-1. / eTimeSample)
width = int((6**(1. / 2) * a / (1 - a**2))**(2. / 3) * nt**(1. / 3))
ntFull = observable.shape[0]
obsName += '_%s' % indexChoice[0]
# Get time steps array
observable = observable[spinup:]
observable = np.convolve(observable,
np.ones((sampling,))/sampling)[(sampling-1)::sampling]
nt = observable.shape[0]
time = np.arange(nt)
meanRng[k] = observable.mean()
varRng[k] = observable.var()
skewRng[k] = stats.skew(observable)
kurtRng[k] = stats.kurtosis(observable)
ccfRng[k] = atmath.ccf(observable, observable, lagMax=lagMax)[lagMax:]
np.savetxt('%s/stats/mean_yearly_%s.txt' % (dstDir, obsName),
(meanRng[k],))
np.savetxt('%s/stats/var_yearly_%s.txt' % (dstDir, obsName),
(varRng[k],))
np.savetxt('%s/stats/skew_yearly_%s.txt' % (dstDir, obsName),
(skewRng[k],))
np.savetxt('%s/stats/kurt_yearly_%s.txt' % (dstDir, obsName),
(kurtRng[k],))
np.savetxt('%s/stats/acf_yearly_%s.txt' % (dstDir, obsName),
ccfRng[k])
# fig = plt.figure()
# ax = fig.add_subplot(1,1,1)
# ax.plot(time[30:230], observable[30:230])
# ax.set_xlabel('years', fontsize=fs_latex)
print 'Reading index file %s...' % indexFile2
observable2 = np.loadtxt('%s/%s' % (indicesPath, indexFile2))
obsName += '_%s' % indexChoice[0] +'_%s' % indexChoice[1]
ntFull = observable1.shape[0]
# Get time steps array
observable1 = observable1[spinup:]
observable1Yearly = np.convolve(observable1, np.ones((sampling,)) \
/ sampling)[(sampling-1)::sampling]
nt = ntFull - spinup
observable2 = observable2[spinup:]
observable2Yearly = np.convolve(observable2, np.ones((sampling,)) \
/ sampling)[(sampling-1)::sampling]
# Get cross-correlation function
ccfRng[k] = atmath.ccf(observable1Yearly, observable2Yearly, lagMax=lagMax)
np.savetxt('%s/stats/ccf_yearly_%s.txt' % (dstDir, obsName), ccfRng[k])
# # Get cross-periodogram
# print 'Getting cross-periodogram...'
# window = np.hamming(nt)
# # Get nearest larger power of 2
# if np.log2(nt) != int(np.log2(nt)):
# nfft = 2**(int(np.log2(nt)) + 1)
# else:
# nfft = nt
# # Get frequencies and shift zero frequency to center
# freq = np.fft.fftfreq(nfft, d=1./sampFreq)
# freq = np.fft.fftshift(freq)
# freqYear = freq * daysPerYear
ntFull = observable.shape[0]
obsName += '_%s' % indexChoice[0]
# Get time steps array
observable = observable[spinup:]
observable = np.convolve(observable,
np.ones((sampling, )) / sampling)[(sampling -
1)::sampling]
nt = observable.shape[0]
time = np.arange(nt)
meanRng[k] = observable.mean()
varRng[k] = observable.var()
skewRng[k] = stats.skew(observable)
kurtRng[k] = stats.kurtosis(observable)
ccfRng[k] = atmath.ccf(observable, observable, lagMax=lagMax)[lagMax:]
np.savetxt('%s/stats/mean_yearly_%s.txt' % (dstDir, obsName),
(meanRng[k], ))
np.savetxt('%s/stats/var_yearly_%s.txt' % (dstDir, obsName), (varRng[k], ))
np.savetxt('%s/stats/skew_yearly_%s.txt' % (dstDir, obsName),
(skewRng[k], ))
np.savetxt('%s/stats/kurt_yearly_%s.txt' % (dstDir, obsName),
(kurtRng[k], ))
np.savetxt('%s/stats/acf_yearly_%s.txt' % (dstDir, obsName), ccfRng[k])
# fig = plt.figure()
# ax = fig.add_subplot(1,1,1)
# ax.plot(time[30:230], observable[30:230])
# ax.set_xlabel('years', fontsize=fs_latex)
# ax.set_ylabel(indexChoice[0], fontsize=fs_latex)
# plt.setp(ax.get_xticklabels(), fontsize=fs_xticklabels)
fig.savefig('%s/spectrum/eigvec/figs/eigvecAdjointImag_nev%d_ev03%d%s.%s' \
% (dstDir, nev, k, postfix, figFormat),
bbox_inches='tight', dpi=dpi)
# Get ccf
lagMax = 100
lags = np.arange(0, lagMax + 1, 1)
f = X.flatten()
g = X.flatten()
obsIdx0 = 0
obsIdx1 = 0
statesFileName = "%s/obs/obs%s.txt" % (dstDir, gridPostfix)
sim = np.loadtxt(statesFileName)
sim = sim.reshape(sim.shape[0] / dim, dim)
ccf = atmath.ccf(sim[:, obsIdx0], sim[:, obsIdx1], lagMax=lagMax)[lagMax:]
#ccf = atmath.ccovf(sim[:, obsIdx0], sim[:, obsIdx1], lagMax=lagMax)[lagMax:]
ccfRec = np.zeros((lags.shape[0], ), dtype=complex)
for ev in np.arange(1, nevSingle):
ccfRec += np.exp(eigvalGen[ev]*lags) \
* (f * statDen * np.conjugate(eigvecAdjoint[ev])).sum() \
* (eigvec[ev] * np.conjugate(g)).sum()
#ccfRec /= np.cov(sim[:, obsIdx0], sim[:, obsIdx1])[0, 1]
ccfRec /= ccfRec[0]
print 'Plotting'
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(lags, ccf, linewidth=2)
ax.plot(lags, ccfRec, '--', linewidth=2)
print 'Reading index file %s...' % indexFile2
observable2 = np.loadtxt('%s/%s' % (indicesPath, indexFile2))
obsName += '_%s' % indexChoice[0] + '_%s' % indexChoice[1]
ntFull = observable1.shape[0]
# Get time steps array
observable1 = observable1[spinup:]
observable1Yearly = np.convolve(observable1, np.ones((sampling,)) \
/ sampling)[(sampling-1)::sampling]
nt = ntFull - spinup
observable2 = observable2[spinup:]
observable2Yearly = np.convolve(observable2, np.ones((sampling,)) \
/ sampling)[(sampling-1)::sampling]
# Get cross-correlation function
ccfRng[k] = atmath.ccf(observable1Yearly, observable2Yearly, lagMax=lagMax)
np.savetxt('%s/stats/ccf_yearly_%s.txt' % (dstDir, obsName), ccfRng[k])
# # Get cross-periodogram
# print 'Getting cross-periodogram...'
# window = np.hamming(nt)
# # Get nearest larger power of 2
# if np.log2(nt) != int(np.log2(nt)):
# nfft = 2**(int(np.log2(nt)) + 1)
# else:
# nfft = nt
# # Get frequencies and shift zero frequency to center
# freq = np.fft.fftfreq(nfft, d=1./sampFreq)
# freq = np.fft.fftshift(freq)
# freqYear = freq * daysPerYear
fig.savefig('%s/spectrum/eigvec/figs/eigvecAdjointImag_nev%d_ev03%d%s.%s' \
% (dstDir, nev, k, postfix, figFormat),
bbox_inches='tight', dpi=dpi)
# Get ccf
lagMax = 100
lags = np.arange(0, lagMax+1, 1)
f = X.flatten()
g = X.flatten()
obsIdx0 = 0
obsIdx1 = 0
statesFileName = "%s/obs/obs%s.txt" % (dstDir, gridPostfix)
sim = np.loadtxt(statesFileName)
sim = sim.reshape(sim.shape[0] / dim, dim)
ccf = atmath.ccf(sim[:, obsIdx0], sim[:, obsIdx1], lagMax=lagMax)[lagMax:]
#ccf = atmath.ccovf(sim[:, obsIdx0], sim[:, obsIdx1], lagMax=lagMax)[lagMax:]
ccfRec = np.zeros((lags.shape[0],), dtype=complex)
for ev in np.arange(1, nevSingle):
ccfRec += np.exp(eigvalGen[ev]*lags) \
* (f * statDen * np.conjugate(eigvecAdjoint[ev])).sum() \
* (eigvec[ev] * np.conjugate(g)).sum()
#ccfRec /= np.cov(sim[:, obsIdx0], sim[:, obsIdx1])[0, 1]
ccfRec /= ccfRec[0]
print 'Plotting'
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(lags, ccf, linewidth=2)
ax.plot(lags, ccfRec, '--', linewidth=2)
obsName += '_%s' % indexChoice[0]
# Get time steps array
time = np.arange(spinup, ntFull)
nt = ntFull - spinup
observable = observable[spinup:]
seasonal = np.empty((daysPerYear,))
anom = np.empty((nt,))
for day in np.arange(daysPerYear):
seasonal[day] = observable[day::daysPerYear].mean()
anom[day::daysPerYear] = observable[day::daysPerYear] - seasonal[day]
varRng[k] = anom.var()
skewRng[k] = stats.skew(anom)
kurtRng[k] = stats.kurtosis(anom)
ccfRng[k] = atmath.ccf(anom, anom, lagMax=lagMax)
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.plot(np.arange(1, daysPerYear+1), seasonal)
ax.set_xlabel(r'days', fontsize=fs_latex)
ax.set_ylabel(indexChoice[0], fontsize=fs_latex)
plt.setp(ax.get_xticklabels(), fontsize=fs_xticklabels)
plt.setp(ax.get_yticklabels(), fontsize=fs_yticklabels)
plt.title('Seasonal cycle for case %s_%d\n\sigma = %.5f' % (restartState, S, seasonal.std()))
fig.savefig('%s/seasonal/seasonal_%s.%s' % (dstDir, obsName, figFormat),
bbox_inches='tight', dpi=dpi)
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.plot(time[200*daysPerYear:203*daysPerYear], anom[200*daysPerYear:203*daysPerYear])