def _get_mutual_inf_EQQ(a):
"""
Gets mutual information using EQQ algorithm for given data.
"""
i, j, ph1, ph2 = a
return i, j, MI.mutual_information(ph1, ph2, algorithm = 'EQQ2', bins = 4, log2 = False)
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 _get_autocoherence(a):
i, j, avg, ts = a
coh = []
for tau in range(1, avg):
ts0 = ts[tau:].copy()
ts1 = ts[:-tau].copy()
coh.append(mutual_information(ts0, ts1, algorithm = 'EQQ2', bins = 4, log2 = False))
return i, j, np.mean(np.array(coh))
def _get_autocoherence(a):
i, j, avg, ts = a
coh = []
for tau in range(1, avg):
ts0 = ts[tau:].copy()
ts1 = ts[:-tau].copy()
coh.append(
mutual_information(ts0, ts1, algorithm='EQQ2', bins=4, log2=False))
return i, j, np.mean(np.array(coh))
def _get_automutual_info(a):
"""
Gets automutual information function.
"""
i, j, to, ph = a
result = []
for tau in range(1,to):
result.append(MI.mutual_information(ph[tau:], ph[:-tau], algorithm = 'EQQ2', bins = 4, log2 = False))
return i, j, np.array(result)
def _process_matrix(self, jobq, resq):
while True:
a = jobq.get() # get queued input
if a is None: # if it is None, we are finished, put poison pill to resq
break # break infinity cycle
else:
i, j, ph1, ph2, method = a # compute stuff
if method == "MPC":
# get phase diff
diff = ph1 - ph2
# compute mean phase coherence
coh = np.power(np.mean(np.cos(diff)), 2) + np.power(np.mean(np.sin(diff)), 2)
resq.put((i, j, coh))
elif method == "MIEQQ":
resq.put((i, j, MI.mutual_information(ph1, ph2, algorithm = 'EQQ2', bins = 4, log2 = False)))
elif method == "MIKNN":
resq.put((i, j, MI.knn_mutual_information(ph1, ph2, k = 32, dualtree = True)))
elif method == "MIGAU":
corr = np.corrcoef([ph1, ph2])[0, 1]
mi = -0.5 * np.log(1 - np.power(corr, 2)) if corr < 1. else 0
resq.put((i, j, mi))
elif method == "COV":
resq.put((i, j, np.cov(ph1, ph2, ddof = 1)[0,1]))
elif method == "CORR":
resq.put((i, j, st.pearsonr(ph1, ph2)[0]))
elif method == "WCOH":
# input field must be wave from wavelet!!!!
w1 = np.complex(0, 0)
w2 = w1; w3 = w1
for t in range(0, self.time.shape[0]):
w1 += ph1[t] * np.conjugate(ph2[t])
w2 += ph1[t] * np.conjugate(ph1[t])
w3 += ph2[t] * np.conjugate(ph2[t])
w1 /= np.sqrt(np.abs(w2) * np.abs(w3))
resq.put((i, j, np.abs(w1)))
elif method[0] == 'L':
p = int(method[1])
res = 0
for t in range(ph1.shape[0]):
res += np.power(np.abs(ph1[t] - ph2[t]), p)
resq.put((i, j, np.power(res, 1./p)))
def _coherency_surrogates(a):
aa_surr, aa_seas, scales, temp = a
aa_surr.construct_fourier_surrogates_spatial()
aa_surr.amplitude_adjust_surrogates(aa_seas[0], aa_seas[1], aa_seas[2])
# aa_surr.construct_surrogates_with_residuals()
# aa_surr.construct_surrogates_with_residuals()
# aa_surr.add_seasonality(aa_seas[0][:-1], aa_seas[1][:-1], aa_seas[2][:-1])
coherence = []
wvlt_coherence = []
for sc in scales:
temp.wavelet(sc, period_unit='d', save_wave=True)
phase_temp = temp.phase.copy()
wave_temp = temp.wave.copy()
phase_aa, _, wave_aa = temp.wavelet(sc,
period_unit='d',
ts=aa_surr.surr_data,
save_wave=True)
# mutual information coherence
coherence.append(
mi.mutual_information(phase_aa,
phase_temp,
algorithm='EQQ2',
bins=8,
log2=False))
# corr = np.corrcoef([phase_aa, phase_temp])[0, 1]
# coherence.append(-0.5 * np.log(1 - np.power(corr, 2)))
# wavelet coherence
w1 = np.complex(0, 0)
w2 = w1
w3 = w1
for i in range(12, aa.time.shape[0] - 12):
w1 += wave_aa[i] * np.conjugate(wave_temp[i])
w2 += wave_aa[i] * np.conjugate(wave_aa[i])
w3 += wave_temp[i] * np.conjugate(wave_temp[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 _coherency_surrogates(a):
aa_surr, aa_seas, scales, temp = a
aa_surr.construct_fourier_surrogates_spatial()
aa_surr.amplitude_adjust_surrogates(aa_seas[0], aa_seas[1], aa_seas[2])
# aa_surr.construct_surrogates_with_residuals()
# aa_surr.construct_surrogates_with_residuals()
# aa_surr.add_seasonality(aa_seas[0][:-1], aa_seas[1][:-1], aa_seas[2][:-1])
coherence = []
wvlt_coherence = []
for sc in scales:
temp.wavelet(sc, period_unit = 'd', save_wave = True)
phase_temp = temp.phase.copy()
wave_temp = temp.wave.copy()
phase_aa, _, wave_aa = temp.wavelet(sc, period_unit = 'd', ts = aa_surr.surr_data, save_wave = True)
# mutual information coherence
coherence.append(mi.mutual_information(phase_aa, phase_temp, algorithm = 'EQQ2', bins = 8, log2 = False))
# corr = np.corrcoef([phase_aa, phase_temp])[0, 1]
# coherence.append(-0.5 * np.log(1 - np.power(corr, 2)))
# wavelet coherence
w1 = np.complex(0, 0)
w2 = w1; w3 = w1
for i in range(12,aa.time.shape[0] - 12):
w1 += wave_aa[i] * np.conjugate(wave_temp[i])
w2 += wave_aa[i] * np.conjugate(wave_aa[i])
w3 += wave_temp[i] * np.conjugate(wave_temp[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 _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
cmi2 = []
for sc in scales:
temp.wavelet(sc, period_unit='d', save_wave=True)
phase_temp = temp.phase.copy()
wave_temp = temp.wave.copy()
aa.wavelet(sc, period_unit='d', save_wave=True)
phase_aa = aa.phase.copy() # get phases from oscillatory modes
wave_aa = aa.wave.copy()
# mutual information coherence
coherence.append(
mi.mutual_information(phase_aa,
phase_temp,
algorithm='EQQ2',
bins=8,
log2=False))
# corr = np.corrcoef([phase_aa, phase_temp])[0, 1]
# coherence.append(-0.5 * np.log(1 - np.power(corr, 2)))
# # 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 = 8, log2 = False))
# cmi1.append(np.mean(np.array(tmp)))
# # plt.plot(tmp, label = "1->2")
# # cmi2
from src.data_class import load_station_data
from src.mutual_information import mutual_information
import numpy as np
from datetime import date
import matplotlib.pyplot as plt
g = load_station_data('../data/TG_STAID000027.txt', date(1958,1,1), date(2015,11,1), False)
g.get_data_of_precise_length(14976, start_date = date(1958, 1, 1), apply_to_data = True)
mi = [mutual_information(g.data, g.data)]
for d in np.arange(1,401,1):
mi.append(mutual_information(g.data[d:], g.data[:-d]))
plt.plot(mi)
plt.show()
# # g.wavelet(1, period_unit = 'y')
# # reconstruction = g.amplitude * np.cos(g.phase)
# # fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
# # m, c = np.linalg.lstsq(fit_x, g.data)[0]
# # amplitude = m * g.amplitude + c
# g.wavelet(8, period_unit = 'y')
# g.anomalise()
coherence = []
wvlt_coherence = []
cmi1 = []
cmi2 = []
for sc in scales:
temp.wavelet(sc, period_unit = 'd', save_wave = True)
phase_temp = temp.phase.copy()
wave_temp = temp.wave.copy()
aa.wavelet(sc, period_unit = 'd', save_wave = True)
phase_aa = aa.phase.copy() # get phases from oscillatory modes
wave_aa = aa.wave.copy()
# mutual information coherence
coherence.append(mi.mutual_information(phase_aa, phase_temp, algorithm = 'EQQ2', bins = 8, log2 = False))
# corr = np.corrcoef([phase_aa, phase_temp])[0, 1]
# coherence.append(-0.5 * np.log(1 - np.power(corr, 2)))
# # 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 = 8, log2 = False))
# cmi1.append(np.mean(np.array(tmp)))
# # plt.plot(tmp, label = "1->2")
# # cmi2
# tmp = []
# for tau in range(1,30):
from src.data_class import load_station_data
from src.mutual_information import mutual_information
import numpy as np
from datetime import date
import matplotlib.pyplot as plt
g = load_station_data('../data/TG_STAID000027.txt', date(1958, 1, 1),
date(2015, 11, 1), False)
g.get_data_of_precise_length(14976,
start_date=date(1958, 1, 1),
apply_to_data=True)
mi = [mutual_information(g.data, g.data)]
for d in np.arange(1, 401, 1):
mi.append(mutual_information(g.data[d:], g.data[:-d]))
plt.plot(mi)
plt.show()
# # g.wavelet(1, period_unit = 'y')
# # reconstruction = g.amplitude * np.cos(g.phase)
# # fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
# # m, c = np.linalg.lstsq(fit_x, g.data)[0]
# # amplitude = m * g.amplitude + c
# g.wavelet(8, period_unit = 'y')
# g.anomalise()
# def get_equidistant_bins():
# return np.array(np.linspace(-np.pi, np.pi, 9))