def test_matrix(self):
Thrf = 25.
dt = .5
TT, m_h = getCanoHRF(Thrf, dt)
m_H = np.array(m_h)
m = vt.mult(m_H, m_H)
def Main_vbjde_Python_constrained(graph, Y, Onsets, Thrf, K, TR, beta, dt, scale=1, estimateSigmaH=True, sigmaH=0.1, NitMax=-1, NitMin=1, estimateBeta=False, PLOT=False):
logger.info("EM started ...")
np.random.seed(6537546)
##########################################################################
# INITIALIZATIONS
# Initialize parameters
if NitMax < 0:
NitMax = 100
gamma = 7.5
gradientStep = 0.005
MaxItGrad = 120
#Thresh = 1e-5
Thresh_FreeEnergy = 1e-5
# Initialize sizes vectors
D = int(np.ceil(Thrf / dt))
M = len(Onsets)
N = Y.shape[0]
J = Y.shape[1]
l = int(np.sqrt(J))
sigma_epsilone = np.ones(J)
# Neighbours
maxNeighbours = max([len(nl) for nl in graph])
neighboursIndexes = np.zeros((J, maxNeighbours), dtype=np.int32)
neighboursIndexes -= 1
for i in xrange(J):
neighboursIndexes[i, :len(graph[i])] = graph[i]
# Conditions
X = OrderedDict([])
for condition, Ons in Onsets.iteritems():
X[condition] = vt.compute_mat_X_2(N, TR, D, dt, Ons)
XX = np.zeros((M, N, D), dtype=np.int32)
nc = 0
for condition, Ons in Onsets.iteritems():
XX[nc, :, :] = X[condition]
nc += 1
# Sigma and mu
mu_M = np.zeros((M, K), dtype=np.float64)
sigma_M = 0.5 * np.ones((M, K), dtype=np.float64)
sigma_M0 = 0.5 * np.ones((M, K), dtype=np.float64)
for k in xrange(1, K):
mu_M[:, k] = 2.0
# Covariance matrix
order = 2
D2 = vt.buildFiniteDiffMatrix(order, D)
R = np.dot(D2, D2) / pow(dt, 2 * order)
Gamma = np.identity(N)
q_Z = np.zeros((M, K, J), dtype=np.float64)
# for k in xrange(0,K):
q_Z[:, 1, :] = 1
q_Z1 = np.zeros((M, K, J), dtype=np.float64)
Z_tilde = q_Z.copy()
Sigma_A = np.zeros((M, M, J), np.float64)
m_A = np.zeros((J, M), dtype=np.float64)
TT, m_h = getCanoHRF(Thrf - dt, dt) # TODO: check
for j in xrange(0, J):
Sigma_A[:, :, j] = 0.01 * np.identity(M)
for m in xrange(0, M):
for k in xrange(0, K):
m_A[j, m] += np.random.normal(mu_M[m, k],
np.sqrt(sigma_M[m, k])) * Z_tilde[m, k, j]
m_H = np.array(m_h).astype(np.float64)
m_H1 = np.array(m_h)
Sigma_H = np.ones((D, D), dtype=np.float64)
Beta = beta * np.ones((M), dtype=np.float64)
zerosDD = np.zeros((D, D), dtype=np.float64)
zerosD = np.zeros((D), dtype=np.float64)
zerosND = np.zeros((N, D), dtype=np.float64)
zerosMM = np.zeros((M, M), dtype=np.float64)
zerosJMD = np.zeros((J, M, D), dtype=np.float64)
zerosK = np.zeros(K)
P = vt.PolyMat(N, 4, TR)
zerosP = np.zeros((P.shape[0]), dtype=np.float64)
L = vt.polyFit(Y, TR, 4, P)
PL = np.dot(P, L)
y_tilde = Y - PL
sigmaH1 = sigmaH
Crit_H = 1
Crit_Z = 1
Crit_A = 1
cA = []
cH = []
cZ = []
Ndrift = L.shape[0]
Crit_FreeEnergy = 1
t1 = time.time()
##########################################################################
# VBJDE num. iter. minimum
ni = 0
while ((ni < NitMin) or (((Crit_FreeEnergy > Thresh_FreeEnergy) or ((Crit_H > Thresh) and (Crit_Z > Thresh) and (Crit_A > Thresh))) and (ni < NitMax))):
logger.info("------------------------------ Iteration n° " +
str(ni + 1) + " ------------------------------")
#####################
# EXPECTATION
#####################
# A
logger.info("E A step ...")
Sigma_A, m_A = vt.expectation_A(
Y, Sigma_H, m_H, m_A, X, Gamma, PL, sigma_M, q_Z, mu_M, D, N, J, M, K, y_tilde, Sigma_A, sigma_epsilone, zerosJMD)
m_A1 = m_A
# crit A
DIFF = np.abs(np.reshape(m_A, (M * J)) - np.reshape(m_A1, (M * J)))
Crit_A = sum(DIFF) / len(np.where(DIFF != 0))
cA += [Crit_A]
# H
logger.info("E H step ...")
Sigma_H, m_H = vt.expectation_H(
Y, Sigma_A, m_A, X, Gamma, PL, D, R, sigmaH, J, N, y_tilde, zerosND, sigma_epsilone, scale, zerosDD, zerosD)
m_H[0] = 0
m_H[-1] = 0
m_H1 = m_H
# crit H
Crit_H = np.abs(np.mean(m_H - m_H1) / np.mean(m_H))
cH += [Crit_H]
# Z
logger.info("E Z step ...")
q_Z, Z_tilde = vt.expectation_Z(
Sigma_A, m_A, sigma_M, Beta, Z_tilde, mu_M, q_Z, graph, M, J, K, zerosK)
# crit Z
DIFF = np.abs(
np.reshape(q_Z, (M * K * J)) - np.reshape(q_Z1, (M * K * J)))
Crit_Z = sum(DIFF) / len(np.where(DIFF != 0))
cZ += [Crit_Z]
q_Z1 = q_Z
# Plotting HRF
if PLOT and ni >= 0:
import matplotlib.pyplot as plt
plt.figure(M + 1)
plt.plot(m_H)
plt.hold(True)
####################
# MAXIMIZATION
#####################
# HRF: Sigma_h
if estimateSigmaH:
logger.info("M sigma_H step ...")
sigmaH = (np.dot(vt.mult(m_H, m_H) + Sigma_H, R)).trace()
sigmaH /= D
# (mu,sigma)
logger.info("M (mu,sigma) step ...")
mu_M, sigma_M = vt.maximization_mu_sigma(
mu_M, sigma_M, q_Z, m_A, K, M, Sigma_A)
# Drift L
L = vt.maximization_L(Y, m_A, X, m_H, L, P, zerosP)
PL = np.dot(P, L)
y_tilde = Y - PL
# Beta
if estimateBeta:
logger.info("estimating beta")
for m in xrange(0, M):
Beta[m] = vt.maximization_beta(
Beta[m], q_Z, Z_tilde, J, K, m, graph, gamma, neighboursIndexes, maxNeighbours)
logger.info("End estimating beta")
# logger.info(Beta)
# Sigma noise
logger.info("M sigma noise step ...")
sigma_epsilone = vt.maximization_sigma_noise(
Y, X, m_A, m_H, Sigma_H, Sigma_A, PL, sigma_epsilone, M, zerosMM)
#### Computing Free Energy ####
"""
if ni > 0:
FreeEnergy1 = FreeEnergy
FreeEnergy = Compute_FreeEnergy(y_tilde,m_A,Sigma_A,mu_M,sigma_M,m_H,Sigma_H,R,Det_invR,sigmaH,p_Wtilde,tau1,tau2,q_Z,neighboursIndexes,maxNeighbours,Beta,sigma_epsilone,XX,Gamma,Det_Gamma,XGamma,J,D,M,N,K,S,"CompMod")
if ni > 0:
Crit_FreeEnergy = (FreeEnergy1 - FreeEnergy) / FreeEnergy1
FreeEnergy_Iter += [FreeEnergy]
cFE += [Crit_FreeEnergy]
"""
# Update index
ni += 1
t2 = time.time()
##########################################################################
# PLOTS and SNR computation
"""FreeEnergyArray = np.zeros((ni),dtype=np.float64)
for i in xrange(ni):
FreeEnergyArray[i] = FreeEnergy_Iter[i]
SUM_q_Z_array = np.zeros((M,ni),dtype=np.float64)
mu1_array = np.zeros((M,ni),dtype=np.float64)
h_norm_array = np.zeros((ni),dtype=np.float64)
for m in xrange(M):
for i in xrange(ni):
SUM_q_Z_array[m,i] = SUM_q_Z[m][i]
mu1_array[m,i] = mu1[m][i]
h_norm_array[i] = h_norm[i]
sigma_M = np.sqrt(np.sqrt(sigma_M))
"""
Norm = np.linalg.norm(m_H)
m_H /= Norm
m_A *= Norm
mu_M *= Norm
sigma_M *= Norm
sigma_M = np.sqrt(sigma_M)
if PLOT and 0:
import matplotlib.pyplot as plt
import matplotlib
font = {'size': 15}
matplotlib.rc('font', **font)
plt.savefig('./HRF_Iter_CompMod.png')
plt.hold(False)
plt.figure(2)
plt.plot(cAH[1:-1], 'lightblue')
plt.hold(True)
plt.plot(cFE[1:-1], 'm')
plt.hold(False)
#plt.legend( ('CA','CH', 'CZ', 'CAH', 'CFE') )
plt.legend(('CAH', 'CFE'))
plt.grid(True)
plt.savefig('./Crit_CompMod.png')
plt.figure(3)
plt.plot(FreeEnergyArray)
plt.grid(True)
plt.savefig('./FreeEnergy_CompMod.png')
plt.figure(4)
for m in xrange(M):
plt.plot(SUM_q_Z_array[m])
plt.hold(True)
plt.hold(False)
plt.savefig('./Sum_q_Z_Iter_CompMod.png')
plt.figure(5)
for m in xrange(M):
plt.plot(mu1_array[m])
plt.hold(True)
plt.hold(False)
plt.savefig('./mu1_Iter_CompMod.png')
plt.figure(6)
plt.plot(h_norm_array)
plt.savefig('./HRF_Norm_CompMod.png')
Data_save = xndarray(h_norm_array, ['Iteration'])
Data_save.save('./HRF_Norm_Comp.nii')
CompTime = t2 - t1
cTimeMean = CompTime / ni
logger.info("Nb iterations to reach criterion: %d", ni)
logger.info("Computational time = %s min %s s", str(
int(CompTime // 60)), str(int(CompTime % 60)))
# print "Computational time = " + str(int( CompTime//60 ) ) + " min " +
# str(int(CompTime%60)) + " s"
logger.info('mu_M: %f', mu_M)
logger.info('sigma_M: %f', sigma_M)
logger.info("sigma_H = %s" + str(sigmaH))
logger.info("Beta = %s" + str(Beta))
StimulusInducedSignal = vt.computeFit(m_H, m_A, X, J, N)
SNR = 20 * \
np.log(
np.linalg.norm(Y) / np.linalg.norm(Y - StimulusInducedSignal - PL))
SNR /= np.log(10.)
print 'SNR comp =', SNR
return m_A, m_H, q_Z, sigma_epsilone, mu_M, sigma_M, Beta, L, PL
def Main_vbjde_Python_constrained(graph, Y, Onsets, Thrf, K, TR, beta, dt, scale=1, estimateSigmaH=True, sigmaH=0.1, NitMax=-1, NitMin=1, estimateBeta=False, PLOT=False):
logger.info("EM started ...")
np.random.seed(6537546)
##########################################################################
# INITIALIZATIONS
# Initialize parameters
if NitMax < 0:
NitMax = 100
gamma = 7.5
gradientStep = 0.005
MaxItGrad = 120
#Thresh = 1e-5
Thresh_FreeEnergy = 1e-5
# Initialize sizes vectors
D = int(np.ceil(Thrf / dt))
M = len(Onsets)
N = Y.shape[0]
J = Y.shape[1]
l = int(np.sqrt(J))
sigma_epsilone = np.ones(J)
# Neighbours
maxNeighbours = max([len(nl) for nl in graph])
neighboursIndexes = np.zeros((J, maxNeighbours), dtype=np.int32)
neighboursIndexes -= 1
for i in xrange(J):
neighboursIndexes[i, :len(graph[i])] = graph[i]
# Conditions
X = OrderedDict([])
for condition, Ons in Onsets.iteritems():
X[condition] = vt.compute_mat_X_2(N, TR, D, dt, Ons)
XX = np.zeros((M, N, D), dtype=np.int32)
nc = 0
for condition, Ons in Onsets.iteritems():
XX[nc, :, :] = X[condition]
nc += 1
# Sigma and mu
mu_M = np.zeros((M, K), dtype=np.float64)
sigma_M = 0.5 * np.ones((M, K), dtype=np.float64)
sigma_M0 = 0.5 * np.ones((M, K), dtype=np.float64)
for k in xrange(1, K):
mu_M[:, k] = 2.0
# Covariance matrix
order = 2
D2 = vt.buildFiniteDiffMatrix(order, D)
R = np.dot(D2, D2) / pow(dt, 2 * order)
Gamma = np.identity(N)
q_Z = np.zeros((M, K, J), dtype=np.float64)
# for k in xrange(0,K):
q_Z[:, 1, :] = 1
q_Z1 = np.zeros((M, K, J), dtype=np.float64)
Z_tilde = q_Z.copy()
Sigma_A = np.zeros((M, M, J), np.float64)
m_A = np.zeros((J, M), dtype=np.float64)
TT, m_h = getCanoHRF(Thrf - dt, dt) # TODO: check
for j in xrange(0, J):
Sigma_A[:, :, j] = 0.01 * np.identity(M)
for m in xrange(0, M):
for k in xrange(0, K):
m_A[j, m] += np.random.normal(mu_M[m, k],
np.sqrt(sigma_M[m, k])) * Z_tilde[m, k, j]
m_H = np.array(m_h).astype(np.float64)
m_H1 = np.array(m_h)
Sigma_H = np.ones((D, D), dtype=np.float64)
Beta = beta * np.ones((M), dtype=np.float64)
zerosDD = np.zeros((D, D), dtype=np.float64)
zerosD = np.zeros((D), dtype=np.float64)
zerosND = np.zeros((N, D), dtype=np.float64)
zerosMM = np.zeros((M, M), dtype=np.float64)
zerosJMD = np.zeros((J, M, D), dtype=np.float64)
zerosK = np.zeros(K)
P = vt.PolyMat(N, 4, TR)
zerosP = np.zeros((P.shape[0]), dtype=np.float64)
L = vt.polyFit(Y, TR, 4, P)
PL = np.dot(P, L)
y_tilde = Y - PL
sigmaH1 = sigmaH
Crit_H = 1
Crit_Z = 1
Crit_A = 1
cA = []
cH = []
cZ = []
Ndrift = L.shape[0]
Crit_FreeEnergy = 1
t1 = time.time()
##########################################################################
# VBJDE num. iter. minimum
ni = 0
while ((ni < NitMin) or (((Crit_FreeEnergy > Thresh_FreeEnergy) or ((Crit_H > Thresh) and (Crit_Z > Thresh) and (Crit_A > Thresh))) and (ni < NitMax))):
logger.info("------------------------------ Iteration n° " +
str(ni + 1) + " ------------------------------")
#####################
# EXPECTATION
#####################
# A
logger.info("E A step ...")
Sigma_A, m_A = vt.expectation_A(
Y, Sigma_H, m_H, m_A, X, Gamma, PL, sigma_M, q_Z, mu_M, D, N, J, M, K, y_tilde, Sigma_A, sigma_epsilone, zerosJMD)
m_A1 = m_A
# crit A
DIFF = np.abs(np.reshape(m_A, (M * J)) - np.reshape(m_A1, (M * J)))
Crit_A = sum(DIFF) / len(np.where(DIFF != 0))
cA += [Crit_A]
# H
logger.info("E H step ...")
Sigma_H, m_H = vt.expectation_H(
Y, Sigma_A, m_A, X, Gamma, PL, D, R, sigmaH, J, N, y_tilde, zerosND, sigma_epsilone, scale, zerosDD, zerosD)
m_H[0] = 0
m_H[-1] = 0
m_H1 = m_H
# crit H
Crit_H = np.abs(np.mean(m_H - m_H1) / np.mean(m_H))
cH += [Crit_H]
# Z
logger.info("E Z step ...")
q_Z, Z_tilde = vt.expectation_Z(
Sigma_A, m_A, sigma_M, Beta, Z_tilde, mu_M, q_Z, graph, M, J, K, zerosK)
# crit Z
DIFF = np.abs(
np.reshape(q_Z, (M * K * J)) - np.reshape(q_Z1, (M * K * J)))
Crit_Z = sum(DIFF) / len(np.where(DIFF != 0))
cZ += [Crit_Z]
q_Z1 = q_Z
# Plotting HRF
if PLOT and ni >= 0:
import matplotlib.pyplot as plt
plt.figure(M + 1)
plt.plot(m_H)
plt.hold(True)
####################
# MAXIMIZATION
#####################
# HRF: Sigma_h
if estimateSigmaH:
logger.info("M sigma_H step ...")
sigmaH = (np.dot(vt.mult(m_H, m_H) + Sigma_H, R)).trace()
sigmaH /= D
# (mu,sigma)
logger.info("M (mu,sigma) step ...")
mu_M, sigma_M = vt.maximization_mu_sigma(
mu_M, sigma_M, q_Z, m_A, K, M, Sigma_A)
# Drift L
L = vt.maximization_L(Y, m_A, X, m_H, L, P, zerosP)
PL = np.dot(P, L)
y_tilde = Y - PL
# Beta
if estimateBeta:
logger.info("estimating beta")
for m in xrange(0, M):
Beta[m] = vt.maximization_beta(
Beta[m], q_Z, Z_tilde, J, K, m, graph, gamma, neighboursIndexes, maxNeighbours)
logger.info("End estimating beta")
# logger.info(Beta)
# Sigma noise
logger.info("M sigma noise step ...")
sigma_epsilone = vt.maximization_sigma_noise(
Y, X, m_A, m_H, Sigma_H, Sigma_A, PL, sigma_epsilone, M, zerosMM)
#### Computing Free Energy ####
"""
if ni > 0:
FreeEnergy1 = FreeEnergy
FreeEnergy = Compute_FreeEnergy(y_tilde,m_A,Sigma_A,mu_M,sigma_M,m_H,Sigma_H,R,Det_invR,sigmaH,p_Wtilde,tau1,tau2,q_Z,neighboursIndexes,maxNeighbours,Beta,sigma_epsilone,XX,Gamma,Det_Gamma,XGamma,J,D,M,N,K,S,"CompMod")
if ni > 0:
Crit_FreeEnergy = (FreeEnergy1 - FreeEnergy) / FreeEnergy1
FreeEnergy_Iter += [FreeEnergy]
cFE += [Crit_FreeEnergy]
"""
# Update index
ni += 1
t2 = time.time()
##########################################################################
# PLOTS and SNR computation
"""FreeEnergyArray = np.zeros((ni),dtype=np.float64)
for i in xrange(ni):
FreeEnergyArray[i] = FreeEnergy_Iter[i]
SUM_q_Z_array = np.zeros((M,ni),dtype=np.float64)
mu1_array = np.zeros((M,ni),dtype=np.float64)
h_norm_array = np.zeros((ni),dtype=np.float64)
for m in xrange(M):
for i in xrange(ni):
SUM_q_Z_array[m,i] = SUM_q_Z[m][i]
mu1_array[m,i] = mu1[m][i]
h_norm_array[i] = h_norm[i]
sigma_M = np.sqrt(np.sqrt(sigma_M))
"""
Norm = np.linalg.norm(m_H)
m_H /= Norm
m_A *= Norm
mu_M *= Norm
sigma_M *= Norm
sigma_M = np.sqrt(sigma_M)
if PLOT and 0:
import matplotlib.pyplot as plt
import matplotlib
font = {'size': 15}
matplotlib.rc('font', **font)
plt.savefig('./HRF_Iter_CompMod.png')
plt.hold(False)
plt.figure(2)
plt.plot(cAH[1:-1], 'lightblue')
plt.hold(True)
plt.plot(cFE[1:-1], 'm')
plt.hold(False)
#plt.legend( ('CA','CH', 'CZ', 'CAH', 'CFE') )
plt.legend(('CAH', 'CFE'))
plt.grid(True)
plt.savefig('./Crit_CompMod.png')
plt.figure(3)
plt.plot(FreeEnergyArray)
plt.grid(True)
plt.savefig('./FreeEnergy_CompMod.png')
plt.figure(4)
for m in xrange(M):
plt.plot(SUM_q_Z_array[m])
plt.hold(True)
plt.hold(False)
plt.savefig('./Sum_q_Z_Iter_CompMod.png')
plt.figure(5)
for m in xrange(M):
plt.plot(mu1_array[m])
plt.hold(True)
plt.hold(False)
plt.savefig('./mu1_Iter_CompMod.png')
plt.figure(6)
plt.plot(h_norm_array)
plt.savefig('./HRF_Norm_CompMod.png')
Data_save = xndarray(h_norm_array, ['Iteration'])
Data_save.save('./HRF_Norm_Comp.nii')
CompTime = t2 - t1
cTimeMean = CompTime / ni
logger.info("Nb iterations to reach criterion: %d", ni)
logger.info("Computational time = %s min %s s", str(
int(CompTime // 60)), str(int(CompTime % 60)))
# print "Computational time = " + str(int( CompTime//60 ) ) + " min " +
# str(int(CompTime%60)) + " s"
logger.info('mu_M: %f', mu_M)
logger.info('sigma_M: %f', sigma_M)
logger.info("sigma_H = %s" + str(sigmaH))
logger.info("Beta = %s" + str(Beta))
StimulusInducedSignal = vt.computeFit(m_H, m_A, X, J, N)
SNR = 20 * \
np.log(
np.linalg.norm(Y) / np.linalg.norm(Y - StimulusInducedSignal - PL))
SNR /= np.log(10.)
logger.info('SNR comp = %f', SNR)
return m_A, m_H, q_Z, sigma_epsilone, mu_M, sigma_M, Beta, L, PL
