Example #1
0
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))
Example #2
0
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)
Example #4
0
    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
Example #5
0
    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)
Example #7
0
    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)
Example #9
0
    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])