def transfer_entropy(X, Y, lag = 1):
#========================================================
# TRANSFER_ENTROPY This funcion computes the transfer entropy for two given
# signals
# te =transfer_entropy(data,lag)
# INPUT:
# X: target (points of the signal)
# Y: source (points of the signal)
# lag: The number of samples to lag to obtain future series
# OUTPUT:
# te: Raw Transfer entropy
import numpy as np
from CPAC.series_mod import cond_entropy
from CPAC.series_mod import entropy
# future of i
Fi = np.roll(X, -lag)
# past of i
Pi = X
# past of j
Pj = Y
#Transfer entropy
Inf_from_Pi_to_Fi = cond_entropy(Fi, Pi)
# same as cond_entropy(Fi, Pi_Pj)
Hy = entropy(Pi,Pj)
Hyx = entropy(Fi,Pj,Pi)
Inf_from_Pi_Pj_to_Fi = Hyx - Hy
TE_from_j_to_i = Inf_from_Pi_to_Fi-Inf_from_Pi_Pj_to_Fi
return TE_from_j_to_i
def transfer_entropy(X, Y, lag=1):
#========================================================
# TRANSFER_ENTROPY This funcion computes the transfer entropy for two given
# signals
# te =transfer_entropy(data,lag)
# INPUT:
# X: target (points of the signal)
# Y: source (points of the signal)
# lag: The number of samples to lag to obtain future series
# OUTPUT:
# te: Raw Transfer entropy
import numpy as np
from CPAC.series_mod import cond_entropy
from CPAC.series_mod import entropy
# future of i
Fi = np.roll(X, -lag)
# past of i
Pi = X
# past of j
Pj = Y
#Transfer entropy
Inf_from_Pi_to_Fi = cond_entropy(Fi, Pi)
# same as cond_entropy(Fi, Pi_Pj)
Hy = entropy(Pi, Pj)
Hyx = entropy(Fi, Pj, Pi)
Inf_from_Pi_Pj_to_Fi = Hyx - Hy
TE_from_j_to_i = Inf_from_Pi_to_Fi - Inf_from_Pi_Pj_to_Fi
return TE_from_j_to_i
def mutual_information(X,Y):
from CPAC.series_mod import entropy
Hx = entropy(X)
Hy = entropy(Y)
Hxy = entropy(X,Y)
MI = Hx + Hy - Hxy
return MI
def mutual_information(X, Y):
from CPAC.series_mod import entropy
Hx = entropy(X)
Hy = entropy(Y)
Hxy = entropy(X, Y)
MI = Hx + Hy - Hxy
return MI
def cond_entropy(X, Y):
"""
Conditional entropy H(X|Y) = H(Y,X) - H(Y). X conditioned on Y
"""
from CPAC.series_mod import entropy
Hy = entropy(Y)
Hyx = entropy(Y, X)
CE = Hyx - Hy
return CE
def cond_entropy(X,Y):
"""
Conditional entropy H(X|Y) = H(Y,X) - H(Y). X conditioned on Y
"""
from CPAC.series_mod import entropy
Hy = entropy(Y)
Hyx = entropy(Y,X)
CE = Hyx - Hy
return CE
def entropy_cc(X, Y): #ENTROPY CORRELATION COEFFICIENT
"""
Entropy correlation coefficient p(H) = sqrt(I(X,Y)/0.5*(H(X)+H(Y)))
"""
import numpy as np
from CPAC.series_mod import entropy
from CPAC.series_mod import mutual_information
Hx = entropy(X)
Hy = entropy(Y)
Ixy = mutual_information(Y, X)
ECC = np.sqrt(Ixy / (0.5 * (Hx + Hy)))
return ECC
def entropy_cc(X,Y): #ENTROPY CORRELATION COEFFICIENT
"""
Entropy correlation coefficient p(H) = sqrt(I(X,Y)/0.5*(H(X)+H(Y)))
"""
import numpy as np
from CPAC.series_mod import entropy
from CPAC.series_mod import mutual_information
Hx = entropy(X)
Hy = entropy(Y)
Ixy = mutual_information(Y,X)
ECC = np.sqrt(Ixy/(0.5*(Hx+Hy)))
return ECC