def _coherency_surrogates(a):
aa_surr, aa_seas, scales, temp = a
aa_surr.construct_fourier_surrogates_spatial()
# aa_surr.construct_surrogates_with_residuals()
aa_surr.add_seasonality(aa_seas[0], aa_seas[1], aa_seas[2])
coherence = []
wvlt_coherence = []
for sc in scales:
period = sc # frequency of interest in months
s0 = period / fourier_factor # get scale
wave_temp, _, _, _ = wvlt.continous_wavelet(temp,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase_temp = np.arctan2(
np.imag(wave_temp),
np.real(wave_temp))[0, 12:-12] # get phases from oscillatory modes
wave_aa, _, _, _ = wvlt.continous_wavelet(aa_surr.surr_data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase_aa = np.arctan2(
np.imag(wave_aa),
np.real(wave_aa))[0, 12:-12] # get phases from oscillatory modes
# mutual information coherence
coherence.append(
mi.mutual_information(phase_aa,
phase_temp,
algorithm='EQQ2',
bins=8,
log2=False))
# wavelet coherence
w1 = np.complex(0, 0)
w2 = w1
w3 = w1
for i in range(12, aa.time.shape[0] - 12):
w1 += wave_aa[0, i] * np.conjugate(wave_temp[0, i])
w2 += wave_aa[0, i] * np.conjugate(wave_aa[0, i])
w3 += wave_temp[0, i] * np.conjugate(wave_temp[0, i])
w1 /= np.sqrt(np.abs(w2) * np.abs(w3))
wvlt_coherence.append(np.abs(w1))
coherence = np.array(coherence)
wvlt_coherence = np.array(wvlt_coherence)
return coherence, wvlt_coherence
def load_nino34_wavelet_phase(start_date, end_date, anom=True):
raw = np.loadtxt('/home/nikola/Work/phd/data/nino34monthly.txt')
data = []
time = []
for y in range(raw.shape[0]):
for m in range(1, 13):
dat = float(raw[y, m])
data.append(dat)
time.append(date(int(raw[y, 0]), m, 1).toordinal())
g = DataField(data=np.array(data), time=np.array(time))
g.location = "NINO3.4"
g.select_date(start_date, end_date)
if anom:
g.anomalise()
k0 = 6. # wavenumber of Morlet wavelet used in analysis
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0, 2)))
per = PERIOD * 12 # frequency of interest
s0 = per / fourier_factor # get scale
wave, _, _, _ = wvlt.continous_wavelet(g.data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=6.)
phase = np.arctan2(np.imag(wave), np.real(wave))[0, :]
return phase
def _get_amplitude(a):
"""
Gets amplitude of yearly cycle from SAT data.
"""
i, j, s0_amp, data = a
if not np.any(np.isnan(data)):
wave, _, _, _ = wvlt.continous_wavelet(data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0_amp,
j1=0,
k0=6.) # perform wavelet
amplitude = np.sqrt(
np.power(np.real(wave), 2) + np.power(np.imag(wave), 2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, data)[0]
amplitude = m * amplitude + c
else:
amplitude = np.nan
return i, j, amplitude
def load_nino34_wavelet_phase(start_date, end_date, anom = True):
raw = np.loadtxt('/home/nikola/Work/phd/data/nino34monthly.txt')
data = []
time = []
for y in range(raw.shape[0]):
for m in range(1,13):
dat = float(raw[y, m])
data.append(dat)
time.append(date(int(raw[y, 0]), m, 1).toordinal())
g = DataField(data = np.array(data), time = np.array(time))
g.location = "NINO3.4"
g.select_date(start_date, end_date)
if anom:
g.anomalise()
k0 = 6. # wavenumber of Morlet wavelet used in analysis
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0,2)))
per = PERIOD * 12 # frequency of interest
s0 = per / fourier_factor # get scale
wave, _, _, _ = wvlt.continous_wavelet(g.data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = 6.)
phase = np.arctan2(np.imag(wave), np.real(wave))[0, :]
return phase
def _cond_difference_surrogates(sg, jobq, resq):
while jobq.get() is not None:
difference = np.zeros((sg.lats.shape[0], sg.lons.shape[0]))
mean_var = np.zeros_like(difference)
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
for i in range(sg.lats.shape[0]):
for j in range(sg.lons.shape[0]):
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg.surr_data[:, i, j],
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(
np.imag(wave),
np.real(wave)) # get phases from oscillatory modes
for iota in range(
cond_means.shape[0]
): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
phase_bins = get_equidistant_bins() # equidistant bins
ndx = ((phase[0, :] >= phase_bins[iota]) &
(phase[0, :] <= phase_bins[iota + 1]))
if MEANS:
cond_means[iota] = np.mean(g.data[ndx])
else:
cond_means[iota] = np.var(g.data[ndx], ddof=1)
difference[i, j] = cond_means.max() - cond_means.min(
) # append difference to list
mean_var[i, j] = np.mean(cond_means)
resq.put((difference, mean_var))
def _cond_difference_surrogates(sg, g_temp, a, start_cut, jobq, resq):
mean, var, trend = a
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
elif SURR_TYPE == 'AR':
sg.construct_surrogates_with_residuals()
sg.add_seasonality(mean[:-1, ...], var[:-1, ...], trend[:-1, ...])
wave, _, _, _ = wavelet_analysis.continous_wavelet(sg.surr_data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
_, _, idx = g_temp.get_data_of_precise_length(WINDOW_LENGTH, start_cut, None, False)
sg.surr_data = sg.surr_data[idx[0] : idx[1]]
phase = phase[0, idx[0] : idx[1]]
phase_bins = get_equidistant_bins() # equidistant bins
for i in range(cond_means.shape[0]): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
ndx = ((phase >= phase_bins[i]) & (phase <= phase_bins[i+1]))
if MEANS:
cond_means[i] = np.mean(sg.surr_data[ndx])
else:
cond_means[i] = np.var(sg.surr_data[ndx], ddof = 1)
diff = (cond_means.max() - cond_means.min()) # append difference to list
mean_var = np.mean(cond_means)
resq.put((diff, mean_var))
def _get_oscillatory_modes(a):
"""
Gets oscillatory modes in terms of phase and amplitude from wavelet analysis for given data.
"""
i, j, s0, data = a
if not np.all(np.isnan(data)):
wave, _, _, _ = wvlt.continous_wavelet(data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = 6.)
phase = np.arctan2(np.imag(wave), np.real(wave))
else:
phase = np.nan
return i, j, phase
def _reconstruction_surrs(sg, a, jobq, resq, idx):
mean, var, trend = a
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
# sg.amplitude_adjust_surrogates(mean, var, trend)
period = AMP_PERIOD * 365.25 # frequency of interest
s0_amp = period / fourier_factor # get scale
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg.surr_data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0_amp,
j1=0,
k0=k0) # perform wavelet
amplitude2 = np.sqrt(
np.power(np.real(wave), 2) + np.power(np.imag(wave), 2))
amplitude2 = amplitude2[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
reconstruction = amplitude2 * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, sg.surr_data)[0]
amplitude2 = m * amplitude2 + c
# amp_to_plot_surr = amplitude2.copy()
# amplitude2 = m * reconstruction + c
amplitude2 = amplitude2[idx[0]:idx[1]]
# amp_to_plot_surr = amp_to_plot_surr[idx[0] : idx[1]]
phase_amp = phase_amp[idx[0]:idx[1]]
sg.surr_data = sg.surr_data[idx[0]:idx[1]]
amp_to_plot_surr = sg.surr_data.copy()
cond_temp = np.zeros((BINS, 2))
for i in range(cond_means.shape[0]):
ndx = ((phase_amp >= phase_bins[i]) &
(phase_amp <= phase_bins[i + 1]))
cond_temp[i, 0] = np.mean(amplitude2[ndx])
cond_temp[i, 1] = np.mean(sg.surr_data[ndx])
amp_diff = cond_temp[:, 0].max() - cond_temp[:, 0].min()
data_diff = cond_temp[:, 1].max() - cond_temp[:, 1].min()
resq.put([cond_temp, amp_diff, data_diff, data_diff])
def _coherency_surrogates(a):
aa_surr, aa_seas, scales, temp = a
aa_surr.construct_fourier_surrogates_spatial()
# aa_surr.construct_surrogates_with_residuals()
aa_surr.add_seasonality(aa_seas[0], aa_seas[1], aa_seas[2])
coherence = []
wvlt_coherence = []
for sc in scales:
period = sc # frequency of interest in months
s0 = period / fourier_factor # get scale
wave_temp, _, _, _ = wvlt.continous_wavelet(temp, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase_temp = np.arctan2(np.imag(wave_temp), np.real(wave_temp))[0, 12:-12] # get phases from oscillatory modes
wave_aa, _, _, _ = wvlt.continous_wavelet(aa_surr.surr_data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase_aa = np.arctan2(np.imag(wave_aa), np.real(wave_aa))[0, 12:-12] # get phases from oscillatory modes
# mutual information coherence
coherence.append(mi.mutual_information(phase_aa, phase_temp, algorithm = 'EQQ2', bins = 8, log2 = False))
# wavelet coherence
w1 = np.complex(0, 0)
w2 = w1; w3 = w1
for i in range(12,aa.time.shape[0] - 12):
w1 += wave_aa[0, i] * np.conjugate(wave_temp[0, i])
w2 += wave_aa[0, i] * np.conjugate(wave_aa[0, i])
w3 += wave_temp[0, i] * np.conjugate(wave_temp[0, i])
w1 /= np.sqrt(np.abs(w2) * np.abs(w3))
wvlt_coherence.append(np.abs(w1))
coherence = np.array(coherence)
wvlt_coherence = np.array(wvlt_coherence)
return coherence, wvlt_coherence
def _cmi_surrogates(a):
aa, aa_surr, aa_seas, temp, temp_surr, temp_seas, scales = a
aa_surr.construct_fourier_surrogates_spatial()
aa_surr.add_seasonality(aa_seas[0], aa_seas[1], aa_seas[2])
cmi1 = []
cmi2 = []
for sc in scales:
period = sc # frequency of interest in months
s0 = period / fourier_factor # get scale
wave_temp, _, _, _ = wvlt.continous_wavelet(temp.data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase_temp = np.arctan2(np.imag(wave_temp), np.real(wave_temp))[0, 12:-12] # get phases from oscillatory modes
wave_aa, _, _, _ = wvlt.continous_wavelet(aa_surr.surr_data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase_aa_surr = np.arctan2(np.imag(wave_aa), np.real(wave_aa))[0, 12:-12] # get phases from oscillatory modes
# cmi1
tmp = []
for tau in range(1,30):
x, y, z = mi.get_time_series_condition([phase_temp, phase_aa_surr], tau = tau, dim_of_condition = 1, eta = 1, phase_diff = True)
tmp.append(mi.cond_mutual_information(x, y, z, algorithm = 'EQQ2', bins = 4, log2 = False))
cmi1.append(np.mean(np.array(tmp)))
# cmi2
tmp = []
for tau in range(1,30):
x, y, z = mi.get_time_series_condition([phase_aa_surr, phase_temp], tau = tau, dim_of_condition = 1, eta = 1, phase_diff = True)
tmp.append(mi.cond_mutual_information(x, y, z, algorithm = 'EQQ2', bins = 4, log2 = False))
cmi2.append(np.mean(np.array(tmp)))
cmi1 = np.array(cmi1)
cmi2 = np.array(cmi2)
return cmi1, cmi2
def _get_oscillatory_modes(a):
"""
Gets oscillatory modes in terms of phase and amplitude from wavelet analysis for given data.
"""
i, j, s0, data = a
if not np.all(np.isnan(data)):
wave, _, _, _ = wvlt.continous_wavelet(data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=6.)
phase = np.arctan2(np.imag(wave), np.real(wave))
else:
phase = np.nan
return i, j, phase
def _reconstruction_surrs(sg, a, jobq, resq, idx):
mean, var, trend = a
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
# sg.amplitude_adjust_surrogates(mean, var, trend)
period = AMP_PERIOD * 365.25 # frequency of interest
s0_amp = period / fourier_factor # get scale
wave, _, _, _ = wavelet_analysis.continous_wavelet(sg.surr_data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0_amp, j1 = 0, k0 = k0) # perform wavelet
amplitude2 = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))
amplitude2 = amplitude2[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
reconstruction = amplitude2 * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, sg.surr_data)[0]
amplitude2 = m * amplitude2 + c
# amp_to_plot_surr = amplitude2.copy()
# amplitude2 = m * reconstruction + c
amplitude2 = amplitude2[idx[0] : idx[1]]
# amp_to_plot_surr = amp_to_plot_surr[idx[0] : idx[1]]
phase_amp = phase_amp[idx[0] : idx[1]]
sg.surr_data = sg.surr_data[idx[0] : idx[1]]
amp_to_plot_surr = sg.surr_data.copy()
cond_temp = np.zeros((BINS,2))
for i in range(cond_means.shape[0]):
ndx = ((phase_amp >= phase_bins[i]) & (phase_amp <= phase_bins[i+1]))
cond_temp[i,0] = np.mean(amplitude2[ndx])
cond_temp[i,1] = np.mean(sg.surr_data[ndx])
amp_diff = cond_temp[:, 0].max() - cond_temp[:, 0].min()
data_diff = cond_temp[:, 1].max() - cond_temp[:, 1].min()
resq.put([cond_temp, amp_diff, data_diff, data_diff])
def _get_amplitude(a):
"""
Gets amplitude of yearly cycle from SAT data.
"""
i, j, s0_amp, data = a
if not np.any(np.isnan(data)):
wave, _, _, _ = wvlt.continous_wavelet(data, 1, False, wvlt.morlet, dj = 0, s0 = s0_amp, j1 = 0, k0 = 6.) # perform wavelet
amplitude = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, data)[0]
amplitude = m * amplitude + c
else:
amplitude = np.nan
return i, j, amplitude
def _cond_difference_surrogates(sg, jobq, resq):
while jobq.get() is not None:
difference = np.zeros((sg.lats.shape[0], sg.lons.shape[0]))
mean_var = np.zeros_like(difference)
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
for i in range(sg.lats.shape[0]):
for j in range(sg.lons.shape[0]):
wave, _, _, _ = wavelet_analysis.continous_wavelet(sg.surr_data[:, i, j], 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave)) # get phases from oscillatory modes
for iota in range(cond_means.shape[0]): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
phase_bins = get_equidistant_bins() # equidistant bins
ndx = ((phase[0,:] >= phase_bins[iota]) & (phase[0,:] <= phase_bins[iota+1]))
if MEANS:
cond_means[iota] = np.mean(g.data[ndx])
else:
cond_means[iota] = np.var(g.data[ndx], ddof = 1)
difference[i, j] = cond_means.max() - cond_means.min() # append difference to list
mean_var[i, j] = np.mean(cond_means)
resq.put((difference, mean_var))
def _cond_difference_surrogates(sg, g_temp, a, start_cut, jobq, resq):
mean, var, trend = a
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
elif SURR_TYPE == 'AR':
sg.construct_surrogates_with_residuals()
sg.add_seasonality(mean[:-1, ...], var[:-1, ...], trend[:-1, ...])
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg.surr_data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
_, _, idx = g_temp.get_data_of_precise_length(WINDOW_LENGTH, start_cut,
None, False)
sg.surr_data = sg.surr_data[idx[0]:idx[1]]
phase = phase[0, idx[0]:idx[1]]
phase_bins = get_equidistant_bins() # equidistant bins
for i in range(cond_means.shape[0]
): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
ndx = ((phase >= phase_bins[i]) & (phase <= phase_bins[i + 1]))
if MEANS:
cond_means[i] = np.mean(sg.surr_data[ndx])
else:
cond_means[i] = np.var(sg.surr_data[ndx], ddof=1)
diff = (cond_means.max() - cond_means.min()
) # append difference to list
mean_var = np.mean(cond_means)
resq.put((diff, mean_var))
def _cond_difference_surrogates(sg, a, jobq, resq):
while jobq.get() is not None:
cond_means_temp = np.zeros_like(cond_means)
if MF_SURR:
sg.construct_multifractal_surrogates()
else:
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(a[0], a[1], a[2])
wave, _, _, _ = wavelet_analysis.continous_wavelet(sg.surr_data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
sg.surr_data = sg.surr_data[edge_cut_ndx]
phase = phase[0, edge_cut_ndx]
phase_bins = get_equidistant_bins()
for i in range(cond_means_surr.shape[0]):
ndx = ((phase >= phase_bins[i]) & (phase <= phase_bins[i+1]))
if MEANS:
cond_means_temp[i] = np.mean(sg.surr_data[ndx])
else:
cond_means_temp[i] = np.var(sg.surr_data[ndx], ddof = 1)
resq.put(cond_means_temp)
_, _, idx = g.get_data_of_precise_length(WINDOW_LENGTH,
date.fromordinal(g.time[4 * y]), None,
False)
first_mid_year = date.fromordinal(g.time[idx[0] + WINDOW_LENGTH / 2]).year
while end_idx < g.data.shape[0]:
# data
g_working.data = g.data[start_idx:end_idx].copy()
g_working.time = g.time[start_idx:end_idx].copy()
if np.all(np.isnan(g_working.data) == False):
wave, _, _, _ = wavelet_analysis.continous_wavelet(
g_working.data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(np.imag(wave),
np.real(wave)) # get phases from oscillatory modes
start_cut = date(start_year + cnt * WINDOW_SHIFT, sm, sd)
idx = g_working.get_data_of_precise_length(WINDOW_LENGTH, start_cut,
None, True) # 16k or 13462
print 'data ', g.get_date_from_ndx(
start_idx), ' - ', g.get_date_from_ndx(end_idx)
print 'cut from ', start_cut, ' to ', g_working.get_date_from_ndx(-1)
last_mid_year = date.fromordinal(g_working.time[WINDOW_LENGTH /
2]).year
phase = phase[0, idx[0]:idx[1]]
date(2013, 10, 1), False)
g_data = DataField()
print(
"[%s] Wavelet analysis in progress with %d year window shifted by %d year(s)..."
% (str(datetime.now()), WINDOW_LENGTH, WINDOW_SHIFT))
k0 = 6. # wavenumber of Morlet wavelet used in analysis
y = 365.25 # year in days
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0, 2)))
period = PERIOD * y # frequency of interest
s0 = period / fourier_factor # get scale
# wavelet - data
wave, _, _, _ = wavelet_analysis.continous_wavelet(g.data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(np.imag(wave),
np.real(wave)) # get phases from oscillatory modes
if AMPLITUDE:
period = 1 * 365.25 # frequency of interest
s0_amp = period / fourier_factor # get scale
wave, _, _, _ = wavelet_analysis.continous_wavelet(
g_amp.data,
1,
False,
wavelet_analysis.morlet,
dj=0,
def _cond_difference_surrogates(sg, sg_amp, g_temp, a, a_amp, start_cut, jobq,
resq, ndx_seas):
mean, var, trend = a
if AMPLITUDE:
mean2, var2, trend2 = a_amp
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_multifractal_surrogates()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_fourier_surrogates_spatial()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == 'AR':
sg.construct_surrogates_with_residuals()
sg.add_seasonality(mean[:-1, ...], var[:-1, ...], trend[:-1, ...])
if AMPLITUDE:
sg_amp.construct_surrogates_with_residuals()
sg_amp.add_seasonality(mean2[:-1, ...], var2[:-1, ...],
trend2[:-1, ...])
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg.surr_data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
if AMPLITUDE:
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg_amp.surr_data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0_amp,
j1=0,
k0=k0) # perform wavelet
amplitude = np.sqrt(
np.power(np.real(wave), 2) + np.power(np.imag(wave), 2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack(
[reconstruction,
np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, sg_amp.surr_data)[0]
amplitude = m * amplitude + c
if AA:
sg.amplitude_adjust_surrogates(mean, var, trend)
_, _, idx = g_temp.get_data_of_precise_length(WINDOW_LENGTH, start_cut,
None, False)
sg.surr_data = sg.surr_data[idx[0]:idx[1]]
phase = phase[0, idx[0]:idx[1]]
if AMPLITUDE:
amplitude = amplitude[idx[0]:idx[1]]
if SEASON != None:
sg.surr_data = sg.surr_data[ndx_seas]
phase = phase[ndx_seas]
phase_bins = get_equidistant_bins() # equidistant bins
cond_means_temp = np.zeros((8, ))
for i in range(cond_means_temp.shape[0]
): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
ndx = ((phase >= phase_bins[i]) & (phase <= phase_bins[i + 1]))
if MOMENT == 'std':
if AMPLITUDE:
cond_means_temp[i] = func(amplitude[ndx], ddof=1)
else:
cond_means_temp[i] = func(sg.surr_data[ndx], ddof=1)
else:
if AMPLITUDE:
cond_means_temp[i] = func(amplitude[ndx])
else:
cond_means_temp[i] = func(sg.surr_data[ndx])
ma = cond_means_temp.argmax()
mi = cond_means_temp.argmin()
if not SAME_BINS:
diff = (cond_means_temp[ma] - cond_means_temp[mi]
) # append difference to list
elif SAME_BINS:
diff = (cond_means_temp[max_bin] - cond_means_temp[min_bin])
mean_var = np.mean(cond_means_temp)
resq.put((diff, mean_var, cond_means_temp, np.abs(ma - mi)))
PERCENTIL = 80
g = load_station_data('../data/TG_STAID000027.txt', date(1775, 1, 1), date(2014, 1, 1), False)
g_amp = load_station_data('../data/TG_STAID000027.txt', date(1775, 1, 1), date(2014, 1, 1), False)
# g_sun = load_sunspot_data('monthssn.dat', date(1775, 1, 1), date(2014, 1, 1), False)
tg = g.copy_data()
g.anomalise()
# tg is SAT, g.data is SATA
k0 = 6. # wavenumber of Morlet wavelet used in analysis
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0,2)))
period = 8 * 365.25 # frequency of interest
s0 = period / fourier_factor # get scale
wave, _, _, _ = wvlt.continous_wavelet(g.data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave)) # get phases from oscillatory modes
period = 1 * 365.25 # frequency of interest
s0 = period / fourier_factor # get scale
wave, _, _, _ = wvlt.continous_wavelet(g_amp.data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
amplitude = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
print reconstruction.shape
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, g_amp.data)[0]
k0 = 6. # wavenumber of Morlet wavelet used in analysis
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0, 2)))
coherence = []
wvlt_coherence = []
cmi1 = []
cmi2 = []
for sc in scales:
period = sc # frequency of interest in months
s0 = period / fourier_factor # get scale
wave_temp, _, _, _ = wvlt.continous_wavelet(temp.data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase_temp = np.arctan2(
np.imag(wave_temp),
np.real(wave_temp))[0, 12:-12] # get phases from oscillatory modes
wave_aa, _, _, _ = wvlt.continous_wavelet(aa.data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
# from now only monthly -- for daily, wavelet needs polishing !!
scales = np.arange(SCALES_SPAN[0], SCALES_SPAN[-1] + 1, 1)
k0 = 6. # wavenumber of Morlet wavelet used in analysis
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0,2)))
coherence = []
wvlt_coherence = []
cmi1 = []
cmi2 = []
for sc in scales:
period = sc # frequency of interest in months
s0 = period / fourier_factor # get scale
wave_temp, _, _, _ = wvlt.continous_wavelet(temp.data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase_temp = np.arctan2(np.imag(wave_temp), np.real(wave_temp))[0, 12:-12] # get phases from oscillatory modes
wave_aa, _, _, _ = wvlt.continous_wavelet(aa.data, 1, False, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase_aa = np.arctan2(np.imag(wave_aa), np.real(wave_aa))[0, 12:-12] # get phases from oscillatory modes
# mutual information coherence
coherence.append(mi.mutual_information(phase_aa, phase_temp, algorithm = 'EQQ2', bins = 8, log2 = False))
# cmi1
# plt.figure()
tmp = []
for tau in range(1,30):
x, y, z = mi.get_time_series_condition([phase_temp, phase_aa], tau = tau, dim_of_condition = 1, eta = 0, phase_diff = True)
tmp.append(mi.cond_mutual_information(x, y, z, algorithm = 'EQQ2', bins = 4, log2 = False))
def _cond_difference_surrogates(sg, sg_amp, a, a2, jobq, resq):
mean, var, trend = a
mean2, var2, trend2 = a2
last_mid_year = first_mid_year
cond_means_out = np.zeros((8,))
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_multifractal_surrogates()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_fourier_surrogates_spatial()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == 'AR':
sg.construct_surrogates_with_residuals()
sg.add_seasonality(mean[:-1, ...], var[:-1, ...], trend[:-1, ...])
if AMPLITUDE:
sg_amp.construct_surrogates_with_residuals()
sg_amp.add_seasonality(mean2[:-1, ...], var2[:-1, ...], trend2[:-1, ...])
wave, _, _, _ = wavelet_analysis.continous_wavelet(sg.surr_data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
if AMPLITUDE:
wave, _, _, _ = wavelet_analysis.continous_wavelet(sg_amp.surr_data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0_amp, j1 = 0, k0 = k0) # perform wavelet
amplitude = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, sg_amp.surr_data)[0]
amplitude = m * amplitude + c
if SURR_TYPE == 'AR':
sg.surr_data = sg.surr_data[main_cut_ndx[:-1]]
if AMPLITUDE:
amplitude = amplitude[main_cut_ndx[:-1]]
else:
sg.surr_data = sg.surr_data[main_cut_ndx]
if AMPLITUDE:
amplitude = amplitude[main_cut_ndx]
phase = phase[0, main_cut_ndx]
phase_bins = get_equidistant_bins() # equidistant bins
cnt = 0
difference_surr = []
meanvar_surr = []
start = 0
end = WINDOW_LENGTH
while end < sg.surr_data.shape[0]:
cnt += 1
surr_temp = sg.surr_data[start : end].copy()
phase_temp = phase[start : end].copy()
if AMPLITUDE:
amp_temp = amplitude[start : end].copy()
last_mid_year += 1
for i in range(cond_means.shape[0]): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
ndx = ((phase_temp >= phase_bins[i]) & (phase_temp <= phase_bins[i+1]))
if MEANS:
if AMPLITUDE:
cond_means[i] = np.mean(amp_temp[ndx])
else:
cond_means[i] = np.mean(surr_temp[ndx])
else:
if AMPLITUDE:
cond_means[i] = np.var(amp_temp[ndx], ddof = 1)
else:
cond_means[i] = np.var(surr_temp[ndx], ddof = 1)
if PHASE_ANALYSIS_YEAR == last_mid_year:
cond_means_out = cond_means.copy()
difference_surr.append(cond_means.max() - cond_means.min()) # append difference to list
meanvar_surr.append(np.mean(cond_means))
start = g.find_date_ndx(date(y1 + cnt*WINDOW_SHIFT, 7, 28))
end = start + WINDOW_LENGTH
resq.put((np.array(difference_surr), np.array(meanvar_surr), cond_means_out))
print("[%s] Wavelet analysis in progress with %d year window shifted by %d year(s)..." % (str(datetime.now()), WINDOW_LENGTH, WINDOW_SHIFT))
k0 = 6. # wavenumber of Morlet wavelet used in analysis
y = 365.25 # year in days
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0,2)))
period = PERIOD * y # frequency of interest
s0 = period / fourier_factor # get scale
cond_means = np.zeros((8,))
def get_equidistant_bins():
return np.array(np.linspace(-np.pi, np.pi, 9))
wave, _, _, _ = wavelet_analysis.continous_wavelet(g.data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave)) # get phases from oscillatory modes
if AMPLITUDE:
s0_amp = (1 * y) / fourier_factor
wave, _, _, _ = wavelet_analysis.continous_wavelet(g_amp.data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0_amp, j1 = 0, k0 = k0) # perform wavelet
amplitude = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, g_amp.data)[0]
amplitude = m * amplitude + c
def _cond_difference_surrogates(sg, sg_amp, g_temp, a, a_amp, start_cut, jobq, resq, ndx_seas):
mean, var, trend = a
if AMPLITUDE:
mean2, var2, trend2 = a_amp
while jobq.get() is not None:
if SURR_TYPE == "MF":
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_multifractal_surrogates()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == "FT":
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_fourier_surrogates_spatial()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == "AR":
sg.construct_surrogates_with_residuals()
sg.add_seasonality(mean[:-1, ...], var[:-1, ...], trend[:-1, ...])
if AMPLITUDE:
sg_amp.construct_surrogates_with_residuals()
sg_amp.add_seasonality(mean2[:-1, ...], var2[:-1, ...], trend2[:-1, ...])
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg.surr_data, 1, False, wavelet_analysis.morlet, dj=0, s0=s0, j1=0, k0=k0
) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
if AMPLITUDE:
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg_amp.surr_data, 1, False, wavelet_analysis.morlet, dj=0, s0=s0_amp, j1=0, k0=k0
) # perform wavelet
amplitude = np.sqrt(np.power(np.real(wave), 2) + np.power(np.imag(wave), 2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, sg_amp.surr_data)[0]
amplitude = m * amplitude + c
if AA:
sg.amplitude_adjust_surrogates(mean, var, trend)
_, _, idx = g_temp.get_data_of_precise_length(WINDOW_LENGTH, start_cut, None, False)
sg.surr_data = sg.surr_data[idx[0] : idx[1]]
phase = phase[0, idx[0] : idx[1]]
if AMPLITUDE:
amplitude = amplitude[idx[0] : idx[1]]
if SEASON != None:
sg.surr_data = sg.surr_data[ndx_seas]
phase = phase[ndx_seas]
phase_bins = get_equidistant_bins() # equidistant bins
cond_means_temp = np.zeros((8,))
for i in range(cond_means_temp.shape[0]): # get conditional means for current phase range
# phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
ndx = (phase >= phase_bins[i]) & (phase <= phase_bins[i + 1])
if MOMENT == "std":
if AMPLITUDE:
cond_means_temp[i] = func(amplitude[ndx], ddof=1)
else:
cond_means_temp[i] = func(sg.surr_data[ndx], ddof=1)
else:
if AMPLITUDE:
cond_means_temp[i] = func(amplitude[ndx])
else:
cond_means_temp[i] = func(sg.surr_data[ndx])
ma = cond_means_temp.argmax()
mi = cond_means_temp.argmin()
if not SAME_BINS:
diff = cond_means_temp[ma] - cond_means_temp[mi] # append difference to list
elif SAME_BINS:
diff = cond_means_temp[max_bin] - cond_means_temp[min_bin]
mean_var = np.mean(cond_means_temp)
resq.put((diff, mean_var, cond_means_temp, np.abs(ma - mi)))
cond_means = np.zeros((8,))
def get_equidistant_bins():
return np.array(np.linspace(-np.pi, np.pi, 9))
d, m, year = g.extract_day_month_year()
difference = np.zeros((g.lats.shape[0], g.lons.shape[0]))
mean_var = np.zeros_like(difference)
for i in range(g.lats.shape[0]):
for j in range(g.lons.shape[0]):
wave, _, _, _ = wavelet_analysis.continous_wavelet(g.data[:,i,j], 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave)) # get phases from oscillatory modes
for iota in range(cond_means.shape[0]): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
phase_bins = get_equidistant_bins() # equidistant bins
ndx = ((phase[0,:] >= phase_bins[iota]) & (phase[0,:] <= phase_bins[iota+1]))
if MEANS:
cond_means[iota] = np.mean(g.data[ndx])
else:
cond_means[iota] = np.var(g.data[ndx], ddof = 1)
difference[i, j] = cond_means.max() - cond_means.min() # append difference to list
mean_var[i, j] = np.mean(cond_means)
print("[%s] Wavelet analysis done. Now computing wavelet for MF surrogates in parallel..." % str(datetime.now()))
surrogates_difference = np.zeros([num_surr] + list(difference.shape))
g.anomalise()
g_for_avg.anomalise()
g_for_avg.select_date(date(1775, 1, 1), date(PAST_UNTIL, 1, 1))
if not USE_SURR:
year = 365.25
# get average extremes
k0 = 6. # wavenumber of Morlet wavelet used in analysis
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0, 2)))
period = PERIOD * year # frequency of interest
s0 = period / fourier_factor # get scale
wave, _, _, _ = wvlt.continous_wavelet(g_for_avg.data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(np.imag(wave),
np.real(wave)) # get phases from oscillatory modes
avg_ndx = g_for_avg.select_date(date(1779, 1, 1),
date(PAST_UNTIL - 4, 1, 1))
phase = phase[0, avg_ndx]
tg_avg_sat = tg_avg_sat[avg_ndx]
# sigma
sigma = np.std(tg_avg_sat, axis=0, ddof=1)
avg_bins = np.zeros((8, 2)) # bin no. x result no. (hot / cold extremes)
g_data = DataField()
else:
for i in range(len(STATIONS)):
locals()['g' + str(i)] = load_station_data(STATIONS[i], date(1924,1,15), date(2013,10,1), True)
if AMPLITUDE:
locals()['g_amp' + str(i)] = load_station_data(STATIONS[i], date(1924,1,15), date(2013, 10, 1), False)
locals()['g_data' + str(i)] = DataField()
k0 = 6. # wavenumber of Morlet wavelet used in analysis
y = 365.25 # year in days
fourier_factor = (4 * np.pi) / (k0 + np.sqrt(2 + np.power(k0,2)))
period = PERIOD * y # frequency of interest
s0 = period / fourier_factor # get scale
# wavelet - data
if STATIONS == None:
wave, _, _, _ = wavelet_analysis.continous_wavelet(g.data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave)) # get phases from oscillatory modes
if AMPLITUDE:
period = 1 * 365.25 # frequency of interest
s0_amp = period / fourier_factor # get scale
wave, _, _, _ = wavelet_analysis.continous_wavelet(g_amp.data, 1, False, wavelet_analysis.morlet, dj = 0, s0 = s0_amp, j1 = 0, k0 = k0) # perform wavelet
amplitude = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, g_amp.data)[0]
def _cond_difference_surrogates(sg, sg_amp, a, a2, jobq, resq):
mean, var, trend = a
mean2, var2, trend2 = a2
last_mid_year = first_mid_year
cond_means_out = np.zeros((8, ))
while jobq.get() is not None:
if SURR_TYPE == 'MF':
sg.construct_multifractal_surrogates()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_multifractal_surrogates()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == 'FT':
sg.construct_fourier_surrogates_spatial()
sg.add_seasonality(mean, var, trend)
if AMPLITUDE:
sg_amp.construct_fourier_surrogates_spatial()
sg_amp.add_seasonality(mean2, var2, trend2)
elif SURR_TYPE == 'AR':
sg.construct_surrogates_with_residuals()
sg.add_seasonality(mean[:-1, ...], var[:-1, ...], trend[:-1, ...])
if AMPLITUDE:
sg_amp.construct_surrogates_with_residuals()
sg_amp.add_seasonality(mean2[:-1, ...], var2[:-1, ...],
trend2[:-1, ...])
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg.surr_data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase = np.arctan2(np.imag(wave), np.real(wave))
if AMPLITUDE:
wave, _, _, _ = wavelet_analysis.continous_wavelet(
sg_amp.surr_data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0_amp,
j1=0,
k0=k0) # perform wavelet
amplitude = np.sqrt(
np.power(np.real(wave), 2) + np.power(np.imag(wave), 2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack(
[reconstruction,
np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, sg_amp.surr_data)[0]
amplitude = m * amplitude + c
if SURR_TYPE == 'AR':
sg.surr_data = sg.surr_data[main_cut_ndx[:-1]]
if AMPLITUDE:
amplitude = amplitude[main_cut_ndx[:-1]]
else:
sg.surr_data = sg.surr_data[main_cut_ndx]
if AMPLITUDE:
amplitude = amplitude[main_cut_ndx]
phase = phase[0, main_cut_ndx]
phase_bins = get_equidistant_bins() # equidistant bins
cnt = 0
difference_surr = []
meanvar_surr = []
start = 0
end = WINDOW_LENGTH
while end < sg.surr_data.shape[0]:
cnt += 1
surr_temp = sg.surr_data[start:end].copy()
phase_temp = phase[start:end].copy()
if AMPLITUDE:
amp_temp = amplitude[start:end].copy()
last_mid_year += 1
for i in range(cond_means.shape[0]
): # get conditional means for current phase range
#phase_bins = get_equiquantal_bins(phase_temp) # equiquantal bins
ndx = ((phase_temp >= phase_bins[i]) &
(phase_temp <= phase_bins[i + 1]))
if MEANS:
if AMPLITUDE:
cond_means[i] = np.mean(amp_temp[ndx])
else:
cond_means[i] = np.mean(surr_temp[ndx])
else:
if AMPLITUDE:
cond_means[i] = np.var(amp_temp[ndx], ddof=1)
else:
cond_means[i] = np.var(surr_temp[ndx], ddof=1)
if PHASE_ANALYSIS_YEAR == last_mid_year:
cond_means_out = cond_means.copy()
difference_surr.append(
cond_means.max() -
cond_means.min()) # append difference to list
meanvar_surr.append(np.mean(cond_means))
start = g.find_date_ndx(date(y1 + cnt * WINDOW_SHIFT, 7, 28))
end = start + WINDOW_LENGTH
resq.put((np.array(difference_surr), np.array(meanvar_surr),
cond_means_out))
result = dict()
start_cut = date(1779, 1, 1)
# _, _, idx = g_amp.get_data_of_precise_length('16k', start_cut, None, False)
idx = g_amp.select_date(start_cut, date(2010, 1, 1), apply_to_data=False)
fields = [g_amp, g_amp_sata]
for i in range(len(AMP_PERIODS)):
period = AMP_PERIODS[i] * 365.25 # frequency of interest
s0_amp = period / fourier_factor # get scale
wave, _, _, _ = wavelet_analysis.continous_wavelet(
fields[i].data,
1,
False,
wavelet_analysis.morlet,
dj=0,
s0=s0_amp,
j1=0,
k0=k0) # perform wavelet
amplitude = np.sqrt(
np.power(np.real(wave), 2) + np.power(np.imag(wave), 2))
amplitude = amplitude[0, :]
phase_amp = np.arctan2(np.imag(wave), np.real(wave))
phase_amp = phase_amp[0, :]
# fitting oscillatory phase / amplitude to actual SAT
reconstruction = amplitude * np.cos(phase_amp)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, fields[i].data)[0]
amplitude = m * amplitude + c
def _cmi_surrogates(a):
aa, aa_surr, aa_seas, temp, temp_surr, temp_seas, scales = a
aa_surr.construct_fourier_surrogates_spatial()
aa_surr.add_seasonality(aa_seas[0], aa_seas[1], aa_seas[2])
cmi1 = []
cmi2 = []
for sc in scales:
period = sc # frequency of interest in months
s0 = period / fourier_factor # get scale
wave_temp, _, _, _ = wvlt.continous_wavelet(temp.data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase_temp = np.arctan2(
np.imag(wave_temp),
np.real(wave_temp))[0, 12:-12] # get phases from oscillatory modes
wave_aa, _, _, _ = wvlt.continous_wavelet(aa_surr.surr_data,
1,
False,
wvlt.morlet,
dj=0,
s0=s0,
j1=0,
k0=k0) # perform wavelet
phase_aa_surr = np.arctan2(
np.imag(wave_aa),
np.real(wave_aa))[0, 12:-12] # get phases from oscillatory modes
# cmi1
tmp = []
for tau in range(1, 30):
x, y, z = mi.get_time_series_condition([phase_temp, phase_aa_surr],
tau=tau,
dim_of_condition=1,
eta=1,
phase_diff=True)
tmp.append(
mi.cond_mutual_information(x,
y,
z,
algorithm='EQQ2',
bins=4,
log2=False))
cmi1.append(np.mean(np.array(tmp)))
# cmi2
tmp = []
for tau in range(1, 30):
x, y, z = mi.get_time_series_condition([phase_aa_surr, phase_temp],
tau=tau,
dim_of_condition=1,
eta=1,
phase_diff=True)
tmp.append(
mi.cond_mutual_information(x,
y,
z,
algorithm='EQQ2',
bins=4,
log2=False))
cmi2.append(np.mean(np.array(tmp)))
cmi1 = np.array(cmi1)
cmi2 = np.array(cmi2)
return cmi1, cmi2