-
Notifications
You must be signed in to change notification settings - Fork 13
/
Copy pathrunRBEF.py
230 lines (177 loc) · 7.13 KB
/
runRBEF.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
########################################################################################
# Run examples from our paper in RBEF
########################################################################################
import sys
import numpy as np
import matplotlib.pyplot as plt
import multiprocessing
import scipy
import scipy.signal
from scipy.integrate import simps
from joblib import Parallel, delayed
from ar_model import *
import pygc.pySpec
import pygc.parametric
import pygc.non_parametric
import pygc.granger
import plot_results
p = int(sys.argv[-1])
if p == 0:
# Generates figure 3 from the paper
print('Generating Figure 3 from RBEF paper...')
N = 5000 # Number of observations
Fs = 200 # Sampling frequency
dt = 1.0 / Fs # Time resolution
C = 0.25 # Coupling parameter
Trials = 5000 # Number of trials
# Covariance matrix
cov = np.array([ [1.00, 0.00],
[0.00, 1.00] ])
f = pygc.pySpec.compute_freq(N, Fs)
S = np.zeros([2,2,N//2+1]) + 1j*np.zeros([2,2,N//2+1])
print('Generating AR model time series...')
Z = ar_model_dhamala(N=N, Trials = Trials, C=C, Fs=Fs, t_start=0, t_stop=None, cov=cov)
print('Estimating spectral matrix from ' + str(Trials) + ' trials...')
for i in range(Trials):
if i%500 == 0:
print('Trial = ' + str(i))
S[0,0] += pygc.pySpec.cxy(X=Z[0,i,:], Y=[], f=f, Fs=Fs) / Trials
S[0,1] += pygc.pySpec.cxy(X=Z[0,i,:], Y=Z[1,i,:], f=f, Fs=Fs) / Trials
S[1,0] += pygc.pySpec.cxy(X=Z[1,i,:], Y=Z[0,i,:], f=f, Fs=Fs) / Trials
S[1,1] += pygc.pySpec.cxy(X=Z[1,i,:], Y=[], f=f, Fs=Fs) / Trials
print('Computing Granger Causality...')
Snew, Hnew, Znew = pygc.non_parametric.wilson_factorization(S, f, Fs, Niterations=30)
Ix2y, Iy2x, Ixy = pygc.granger.granger_causality(S, Hnew, Znew)
print('Saving data...')
np.save('data/fig3.npy', {'f': f, 'S': S, 'H': Hnew, 'Z': Znew, 'Ix2y': Ix2y, 'Iy2x': Iy2x, 'Ixy': Ixy})
print('Plotting results...')
plot_results.fig3()
if p == 1:
# Generates figure 4 from the paper
N = 900 # Number of observations
Fs = 200 # Sampling frequency
dt = 1.0 / Fs # Time resolution
C = 0.25 # Coupling parameter
Trials = 5000 # Number of trials
cov = np.array([ [1.00, 0.00],
[0.00, 1.00] ])
f = pygc.pySpec.compute_freq(N, Fs)
S = np.zeros([2,2,N,N//2+1]) + 1j*np.zeros([2,2,N,N//2+1])
print('Generating AR model time series...')
Z = ar_model_dhamala(N=N, Trials = Trials, C=C, Fs=Fs, t_start=0, t_stop=2.25, cov=cov)
print('Estimating wavelet matrix from ' + str(Trials) + ' trials...')
for i in range(Trials):
if i%500 == 0:
print('Trial = ' + str(i))
Wx = pygc.pySpec.morlet(Z[0,i,:], f, Fs)
Wy = pygc.pySpec.morlet(Z[1,i,:], f, Fs)
S[0,0] += Wx*np.conj(Wx) / Trials
S[0,1] += Wx*np.conj(Wy) / Trials
S[1,0] += Wy*np.conj(Wx) / Trials
S[1,1] += Wy*np.conj(Wy) / Trials
# S = S[:,:,idx,:]
print('Computing Granger Causality...')
def save_granger(S, idx):
Snew, Hnew, Znew = pygc.non_parametric.wilson_factorization(S[:,:,idx,:], f, Fs, Niterations=30, verbose=False)
Ix2y, Iy2x, Ixy = pygc.granger.granger_causality(S[:,:,idx,:], Hnew, Znew)
np.save('data/fig4_'+str(idx)+'.npy', {'f': f, 'Ix2y': Ix2y, 'Iy2x': Iy2x, 'Ixy': Ixy})
Parallel(n_jobs=40, backend='loky', max_nbytes=1e6)(delayed(save_granger)(S, idx) for idx in range(N))
print('Plotting results...')
plot_results.fig4()
if p == 2:
# Generates figure 7 and 8 from the paper
N = 5000 # Number of observations
Trials = 1000 # Number of trials
nvars = 5 # Number of variables
Fs = 2*np.pi
dt = 1.0 / Fs
f = pygc.pySpec.compute_freq(N, Fs)
print('Generating AR model time series...')
Y = ar_model_baccala(nvars, N, Trials)
print('Estimating spectral matrix from ' + str(Trials) + ' trials...')
S = np.zeros([nvars, nvars, N//2 + 1]) * (1 + 1j)
for trial in range(Trials):
if (trial % 100 == 0):
print('Trial = ' + str(trial))
for i in range(nvars):
for j in range(nvars):
S[i,j] += pygc.pySpec.cxy(X=Y[i,:,trial], Y=Y[j,:,trial], f=f, Fs=Fs) / Trials
print('Estimating pairwise Granger casalities')
GC = np.zeros([nvars, nvars])
for i in range(nvars):
for j in range(nvars):
if i == j:
continue
else:
S_aux = np.array([[S[i,i], S[i,j]],[S[j,i], S[j,j]]])
_, H, Z = pygc.non_parametric.wilson_factorization(S_aux, f, Fs, Niterations=10, tol=1e-12, verbose=False)
Ix2y, Iy2x, _ = pygc.granger.granger_causality(S_aux, H, Z)
GC[i,j] = simps(Ix2y, f) / 2*np.pi
GC[j,i] = simps(Iy2x, f) / 2*np.pi
print('Estimating conditional Granger casalities')
F = pygc.granger.conditional_granger_causality(S, f, Fs, Niterations = 10, verbose=False)
cGC = pygc.granger.conditional_spec_granger_causality(S, f, Fs, Niterations=100, tol=1e-12, verbose=False)
print('Saving data...')
np.save('data/fig_7_8.npy', {'f':f,'GC': GC, 'F': F, 'cGC': cGC})
print('Plotting results...')
plot_results.fig7_8()
if p == 3:
# Fits an AR model by solving YW equations as in appendix A of the paper.
Trials = 1000 # Number of trials
Fs = 200 # Sampling frequency
N = 1000 # Number of data points
X = np.zeros([1,N, Trials]) # Data matrix
tsim = N/Fs # Simulation time
# Coefficients of the ar model
c = [0.7, 0.2, -0.1, -0.3]
print('Generating AR model time series...')
for T in range(Trials):
X[0,:,T] = scipy.signal.lfilter([1], -np.array([-1]+c), np.random.randn(N))
print('Estimating AR model coefficients for ' + str(Trials) + ' trials')
for m in [2, 3, 4, 5, 6]:
print()
AR = np.zeros([1,1,m])
SIG = np.zeros([1,1])
for T in range(Trials):
aux1, aux2 = pygc.parametric.YuleWalker(X[:,:,T], m, maxlags=100)
AR += aux1.T/Trials
SIG += aux2.T/Trials
AR = np.round(AR, 2)
SIG = np.round(SIG, 2)
print('Using order = ' + str(m)+ '. Original coefficients: ' + str(c) + '. Estimated coefficients ' + str(AR[0][0]) + '. Noise variace: ' + str(SIG[0][0]))
if p == 4:
# Generates figure 3C from the paper, but using a paramtreic method
# Generates figure 3 from the paper
print('Generating Figure 3 from RBEF paper...')
N = 5000 # Number of observations
Fs = 200 # Sampling frequency
dt = 1.0 / Fs # Time resolution
C = 0.25 # Coupling parameter
Trials = 5000 # Number of trials
# Covariance matrix
cov = np.array([ [1.00, 0.00],
[0.00, 1.00] ])
print('Generating AR model time series...')
X = ar_model_dhamala(N=N, Trials = Trials, C=C, Fs=Fs, t_start=0, t_stop=None, cov=cov)
print('Estimating VAR coefficients using oreder m=2...')
m = 2
AR = np.zeros([m, 2,2])
SIG = np.zeros([2,2])
for T in range(Trials):
aux1, aux2 = pygc.parametric.YuleWalker(X[:,T,:], m, maxlags=100)
AR += aux1/Trials
SIG += aux2/Trials
print('Computing Granger Causality...')
f = pygc.pySpec.compute_freq(N, Fs)
H, S = pygc.parametric.compute_transfer_function(AR, SIG, f, Fs)
Ix2y, Iy2x, _ = pygc.granger.granger_causality(S, H, SIG)
plt.figure(figsize=(6,2))
plt.plot(f, Ix2y)
plt.plot(f, Iy2x)
plt.xlim([0, 100])
plt.ylim([-0.01, 1.2])
plt.ylabel('GC')
plt.xlabel('Frequency [Hz]')
plt.legend([r'$X_{1}\rightarrow X_{2}$', r'$X_{2}\rightarrow X_{1}$'])
plt.savefig('figures/fig9.pdf', dpi = 600)
plt.close()