def test_expectA(self): M = 51 K = 2 J = 25 N = 325 D = 3 TR = 1. Thrf = 25. dt = .5 data = self.data_simu Y = data.bold Onsets = data.get_joined_onsets() Gamma = np.identity(N) XX = np.zeros((M, N, D), dtype=np.int32) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) y_tilde = Y - np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) m_h = m_h[:D] sigma_epsilone = np.ones(J) m_H = np.array(m_h) Sigma_H = np.ones((D, D), dtype=float) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.zeros((M, M, J), np.float64) for j in xrange(0, J): Sigma_A[:, :, j] = 0.01 * np.identity(M) mu_M = np.zeros((M, K), dtype=np.float64) sigma_M = np.ones((M, K), dtype=np.float64) q_Z = np.zeros((M, K, J), dtype=np.float64) UtilsC.expectation_A(q_Z, mu_M, sigma_M, PL, sigma_epsilone, Gamma, Sigma_H, Y, y_tilde, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N, K)
def test_polyFit(self): N = 325 TR = 1. data = self.data_simu Y = data.bold P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P)
def test_expectH(self): M = 51 J = 25 N = 325 D = 3 TR = 1. Thrf = 25. dt = .5 data = self.data_simu Gamma = np.identity(N) Q_barnCond = np.zeros((M, M, D, D), dtype=np.float64) XGamma = np.zeros((M, D, N), dtype=np.float64) XX = np.zeros((M, N, D), dtype=np.int32) Y = data.bold P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) y_tilde = Y - np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) m_h = m_h[:D] m_H = np.array(m_h) sigma_epsilone = np.ones(J) Sigma_H = np.ones((D, D), dtype=float) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.zeros((M, M, J), np.float64) scale = 1 order = 2 D2 = vt.buildFiniteDiffMatrix(order, D) R = np.dot(D2, D2) / pow(dt, 2 * order) sigmaH = 0.1 UtilsC.expectation_H(XGamma, Q_barnCond, sigma_epsilone, Gamma, R, Sigma_H, Y, y_tilde, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N, scale, sigmaH)
def test_max_sigma_noise(self): M = 51 N = 325 J = 25 TR = 1. Thrf = 25. dt = .5 data = self.data_simu X = OrderedDict([]) Y = data.bold onsets = data.get_joined_onsets() durations = data.paradigm.stimDurations P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) sigma_epsilone = np.ones(J) Gamma = np.identity(N) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.zeros((M, M, J), np.float64) m_H = np.array(m_h).astype(np.float64) D = len(m_H) Sigma_H = np.ones((D, D), dtype=np.float64) zerosMM = np.zeros((M, M), dtype=np.float64) _, occurence_matrix, _ = vt.create_conditions(onsets, durations, M, N, D, TR, dt) sigma_eps = vt.maximization_noise_var(occurence_matrix, m_H, Sigma_H, m_A, Sigma_A, Gamma, Y, N)
def test_free_energy(self): """ Test of vem tool to compute free energy """ M = 51 D = 3 N = 325 J = 25 K = 2 TR = 1. Thrf = 25. dt = .5 gamma_h = 1000 data = self.data_simu Y = data.bold graph = data.get_graph() onsets = data.paradigm.get_joined_onsets() durations = data.paradigm.stimDurations P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) y_tilde = Y - np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) order = 2 D2 = vt.buildFiniteDiffMatrix(order, D) R = np.dot(D2, D2) / pow(dt, 2*order) invR = np.linalg.inv(R) Det_invR = np.linalg.det(invR) q_Z = 0.5 * np.ones((M, K, J), dtype=np.float64) neighbours_indexes = vt.create_neighbours(graph) Beta = np.ones((M), dtype=np.float64) sigma_epsilone = np.ones(J) _, occurence_matrix, _ = vt.create_conditions(onsets, durations, M, N, D, TR, dt) Gamma = np.identity(N) Det_Gamma = np.linalg.det(Gamma) XGamma = np.zeros((M, D, N), dtype=np.float64) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.zeros((M, M, J), np.float64) mu_M = np.zeros((M, K), dtype=np.float64) sigma_M = np.ones((M, K), dtype=np.float64) m_H = np.array(m_h[:D]).astype(np.float64) Sigma_H = np.ones((D, D), dtype=np.float64) free_energy = vt.free_energy_computation(m_A, Sigma_A, m_H, Sigma_H, D, q_Z, y_tilde, occurence_matrix, sigma_epsilone, Gamma, M, J, N, K, mu_M, sigma_M, neighbours_indexes, Beta, Sigma_H, np.linalg.inv(R), R, Det_Gamma, gamma_h)
def test_max_L(self): M = 51 N = 325 J = 25 D = 3 TR = 1. Thrf = 25. dt = .5 TT, m_h = getCanoHRF(Thrf, dt) m_A = np.zeros((J, M), dtype=np.float64) m_H = np.array(m_h).astype(np.float64) data = self.data_simu Y = data.bold XX = np.zeros((M, N, D), dtype=np.int32) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) Ndrift = L.shape[0] zerosP = np.zeros((P.shape[0]), dtype=np.float64) UtilsC.maximization_L(Y, m_A, m_H, L, P, XX.astype(np.int32), J, D, M, Ndrift, N)
def test_max_L(self): M = 51 N = 325 J = 25 TR = 1. Thrf = 25. dt = .5 TT, m_h = getCanoHRF(Thrf, dt) m_A = np.zeros((J, M), dtype=np.float64) m_H = np.array(m_h).astype(np.float64) data = self.data_simu onsets = data.paradigm.get_joined_onsets() durations = data.paradigm.get_joined_durations() Y = data.bold X = OrderedDict([]) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) zerosP = np.zeros((P.shape[0]), dtype=np.float64) _, occurence_matrix, _ = vt.create_conditions(onsets, durations, M, N, len(m_H), TR, dt) L = vt.maximization_drift_coeffs(Y, m_A, occurence_matrix, m_H, np.identity(N), P)
def test_expectA(self): M = 51 K = 2 J = 25 N = 325 D = 3 TR = 1. Thrf = 25. dt = .5 data = self.data_simu Y = data.bold Onsets = data.get_joined_onsets() durations = data.paradigm.stimDurations Gamma = np.identity(N) X = OrderedDict([]) for condition, Ons in Onsets.iteritems(): X[condition] = vt.compute_mat_X_2(N, TR, D, dt, Ons) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) y_tilde = Y - np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) m_h = m_h[:D] sigma_epsilone = np.ones(J) m_H = np.array(m_h) Sigma_H = np.ones((D, D), dtype=float) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.ones((M, M, J), np.float64) for j in xrange(0, J): Sigma_A[:, :, j] = 0.01*np.identity(M) mu_M = np.zeros((M, K), dtype=np.float64) sigma_M = np.ones((M, K), dtype=np.float64) q_Z = 0.5 * np.ones((M, K, J), dtype=np.float64) zerosJMD = np.zeros((J, M, D), dtype=np.float64) _, occurence_matrix, _ = vt.create_conditions(Onsets, durations, M, N, D, TR, dt) m_A, Sigma_A = vt.nrls_expectation(m_H, m_A, occurence_matrix, Gamma, q_Z, mu_M, sigma_M, M, y_tilde, Sigma_A, Sigma_H, sigma_epsilone)
def test_expectH(self): M = 51 K = 2 J = 25 N = 325 D = 3 TR = 1. Thrf = 25. dt = .5 data = self.data_simu Gamma = np.identity(N) X = OrderedDict([]) Y = data.bold onsets = data.get_joined_onsets() durations = data.paradigm.stimDurations P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) y_tilde = Y - np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) m_h = m_h[:D] m_H = np.array(m_h) sigma_epsilone = np.ones(J) Sigma_H = np.ones((D, D), dtype=float) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.zeros((M, M, J), np.float64) scale = 1 zerosDD = np.zeros((D, D), dtype=np.float64) zerosD = np.zeros((D), dtype=np.float64) zerosND = np.zeros((N, D), dtype=np.float64) order = 2 D2 = vt.buildFiniteDiffMatrix(order, D) R = np.dot(D2, D2) / pow(dt, 2*order) sigmaH = 0.1 _, occurence_matrix, _ = vt.create_conditions(onsets, durations, M, N, D, TR, dt) m_H, Sigma_H = vt.hrf_expectation(Sigma_A, m_A, occurence_matrix, Gamma, R, sigmaH, J, y_tilde, sigma_epsilone)
def test_max_sigma_noise(self): M = 51 D = 3 N = 325 J = 25 TR = 1. Thrf = 25. dt = .5 Gamma = np.identity(N) data = self.data_simu XX = np.zeros((M, N, D), dtype=np.int32) Y = data.bold P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) TT, m_h = getCanoHRF(Thrf, dt) sigma_epsilone = np.ones(J) m_A = np.zeros((J, M), dtype=np.float64) Sigma_A = np.zeros((M, M, J), np.float64) m_H = np.array(m_h).astype(np.float64) Sigma_H = np.ones((D, D), dtype=np.float64) UtilsC.maximization_sigma_noise(Gamma, PL, sigma_epsilone, Sigma_H, Y, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N)
def Main_vbjde_physio(graph, Y, Onsets, durations, Thrf, K, TR, beta, dt, scale=1, estimateSigmaH=True, estimateSigmaG=True, sigmaH=0.05, sigmaG=0.05, gamma_h=0, gamma_g=0, NitMax=-1, NitMin=1, estimateBeta=True, PLOT=False, contrasts=[], computeContrast=False, idx_first_tag=0, simulation=None, sigmaMu=None, estimateH=True, estimateG=True, estimateA=True, estimateC=True, estimateZ=True, estimateNoise=True, estimateMP=True, estimateLA=True, use_hyperprior=False, positivity=False, constraint=False, phy_params=PHY_PARAMS_KHALIDOV11, prior='omega', zc=False): logger.info("EM for ASL!") np.random.seed(6537540) logger.info("data shape: ") logger.info(Y.shape) Thresh = 1e-5 D, M = np.int(np.ceil(Thrf / dt)) + 1, len(Onsets) #D, M = np.int(np.ceil(Thrf / dt)), len(Onsets) N, J = Y.shape[0], Y.shape[1] Crit_AH, Crit_CG, cTime, rerror, FE = 1, 1, [], [], [] EP, EPlh, Ent = [],[],[] Crit_H, Crit_G, Crit_Z, Crit_A, Crit_C = 1, 1, 1, 1, 1 cAH, cCG, AH1, CG1 = [], [], [], [] cA, cC, cH, cG, cZ = [], [], [], [], [] h_norm, g_norm = [], [] SUM_q_Z = [[] for m in xrange(M)] mua1 = [[] for m in xrange(M)] muc1 = [[] for m in xrange(M)] # Beta data MaxItGrad = 200 gradientStep = 0.005 gamma = 7.5 maxNeighbours, neighboursIndexes = vt.create_neighbours(graph, J) # Control-tag w = np.ones((N)) w[idx_first_tag + 1::2] = -1 W = np.diag(w) # Conditions X, XX, condition_names = vt.create_conditions_block(Onsets, durations, M, N, D, TR, dt) #X, XX, condition_names = vt.create_conditions(Onsets, M, N, D, TR, dt) if zc: XX = XX[:, :, 1:-1] # XX shape (S, M, N, D) D = D - 2 AH1, CG1 = np.zeros((J, M, D)), np.zeros((J, M, D)) # Covariance matrix #R = vt.covariance_matrix(2, D, dt) _, R_inv = genGaussianSmoothHRF(False, D, dt, 1., 2) R = np.linalg.inv(R_inv) # Noise matrix Gamma = np.identity(N) # Noise initialization sigma_eps = np.ones(J) # Labels logger.info("Labels are initialized by setting active probabilities " "to ones ...") q_Z = np.ones((M, K, J), dtype=np.float64) / 2. #q_Z = np.zeros((M, K, J), dtype=np.float64) #q_Z[:, 1, :] = 1 q_Z1 = copy.deepcopy(q_Z) Z_tilde = copy.deepcopy(q_Z) # H and G TT, m_h = getCanoHRF(Thrf, dt) H = np.array(m_h[1:D+1]).astype(np.float64) H /= np.linalg.norm(H) G = copy.deepcopy(H) Hb = create_physio_brf(phy_params, response_dt=dt, response_duration=Thrf) Hb /= np.linalg.norm(Hb) Gb = create_physio_prf(phy_params, response_dt=dt, response_duration=Thrf) Gb /= np.linalg.norm(Gb) if prior=='balloon': H = Hb.copy() G = Gb.copy() Mu = Hb.copy() H1 = copy.deepcopy(H) Sigma_H = np.zeros((D, D), dtype=np.float64) G1 = copy.deepcopy(G) Sigma_G = copy.deepcopy(Sigma_H) normOh = False normg = False if prior=='hierarchical' or prior=='omega': Omega = linear_rf_operator(len(H), phy_params, dt, calculating_brf=False) if prior=='omega': Omega0 = Omega.copy() OmegaH = np.dot(Omega, H) G = np.dot(Omega, H) if normOh or normg: Omega /= np.linalg.norm(OmegaH) OmegaH /=np.linalg.norm(OmegaH) G /= np.linalg.norm(G) # Initialize model parameters Beta = beta * np.ones((M), dtype=np.float64) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) alpha = np.zeros((J), dtype=np.float64) WP = np.append(w[:, np.newaxis], P, axis=1) AL = np.append(alpha[np.newaxis, :], L, axis=0) y_tilde = Y - WP.dot(AL) # Parameters Gaussian mixtures mu_Ma = np.append(np.zeros((M, 1)), np.ones((M, 1)), axis=1).astype(np.float64) mu_Mc = mu_Ma.copy() sigma_Ma = np.ones((M, K), dtype=np.float64) * 0.3 sigma_Mc = sigma_Ma.copy() # Params RLs m_A = np.zeros((J, M), dtype=np.float64) for j in xrange(0, J): m_A[j, :] = (np.random.normal(mu_Ma, np.sqrt(sigma_Ma)) * q_Z[:, :, j]).sum(axis=1).T m_A1 = m_A.copy() Sigma_A = np.ones((M, M, J)) * np.identity(M)[:, :, np.newaxis] m_C = m_A.copy() m_C1 = m_C.copy() Sigma_C = Sigma_A.copy() # Precomputations WX = W.dot(XX).transpose(1, 0, 2) Gamma_X = np.tensordot(Gamma, XX, axes=(1, 1)) X_Gamma_X = np.tensordot(XX.T, Gamma_X, axes=(1, 0)) # shape (D, M, M, D) Gamma_WX = np.tensordot(Gamma, WX, axes=(1, 1)) XW_Gamma_WX = np.tensordot(WX.T, Gamma_WX, axes=(1, 0)) # shape (D, M, M, D) Gamma_WP = Gamma.dot(WP) WP_Gamma_WP = WP.T.dot(Gamma_WP) sigma_eps_m = np.maximum(sigma_eps, eps) cov_noise = sigma_eps_m[:, np.newaxis, np.newaxis] ########################################################################### ############################################# VBJDE t1 = time.time() ni = 0 #while ((ni < NitMin + 1) or (((Crit_AH > Thresh) or (Crit_CG > Thresh)) \ # and (ni < NitMax))): #while ((ni < NitMin + 1) or (((Crit_AH > Thresh)) \ # and (ni < NitMax))): while ((ni < NitMin + 1) or (((Crit_FE > Thresh * np.ones_like(Crit_FE)).any()) \ and (ni < NitMax))): logger.info("-------- Iteration n° " + str(ni + 1) + " --------") if PLOT and ni >= 0: # Plotting HRF and PRF logger.info("Plotting HRF and PRF for current iteration") vt.plot_response_functions_it(ni, NitMin, M, H, G, Mu, prior) # Managing types of prior priorH_cov_term = np.zeros_like(R_inv) priorG_cov_term = np.zeros_like(R_inv) matrix_covH = R_inv.copy() matrix_covG = R_inv.copy() if prior=='balloon': logger.info(" prior balloon") #matrix_covH = np.eye(R_inv.shape[0], R_inv.shape[1]) #matrix_covG = np.eye(R_inv.shape[0], R_inv.shape[1]) priorH_mean_term = np.dot(matrix_covH / sigmaH, Hb) priorG_mean_term = np.dot(matrix_covG / sigmaG, Gb) elif prior=='omega': logger.info(" prior omega") #matrix_covG = np.eye(R_inv.shape[0], R_inv.shape[1]) priorH_mean_term = np.dot(np.dot(Omega.T, matrix_covG / sigmaG), G) priorH_cov_term = np.dot(np.dot(Omega.T, matrix_covG / sigmaG), Omega) priorG_mean_term = np.dot(matrix_covG / sigmaG, OmegaH) elif prior=='hierarchical': logger.info(" prior hierarchical") matrix_covH = np.eye(R_inv.shape[0], R_inv.shape[1]) matrix_covG = np.eye(R_inv.shape[0], R_inv.shape[1]) priorH_mean_term = Mu / sigmaH priorG_mean_term = np.dot(Omega, Mu / sigmaG) else: logger.info(" NO prior") priorH_mean_term = np.zeros_like(H) priorG_mean_term = np.zeros_like(G) ##################### # EXPECTATION ##################### # HRF H if estimateH: logger.info("E H step ...") Ht, Sigma_H = vt.expectation_H_asl(Sigma_A, m_A, m_C, G, XX, W, Gamma, Gamma_X, X_Gamma_X, J, y_tilde, cov_noise, matrix_covH, sigmaH, priorH_mean_term, priorH_cov_term) if constraint: if not np.linalg.norm(Ht)==1: logger.info(" constraint l2-norm = 1") H = vt.constraint_norm1_b(Ht, Sigma_H) #H = Ht / np.linalg.norm(Ht) else: logger.info(" l2-norm already 1!!!!!") H = Ht.copy() Sigma_H = np.zeros_like(Sigma_H) else: H = Ht.copy() h_norm = np.append(h_norm, np.linalg.norm(H)) print 'h_norm = ', h_norm Crit_H = (np.linalg.norm(H - H1) / np.linalg.norm(H1)) ** 2 cH += [Crit_H] H1[:] = H[:] if prior=='omega': OmegaH = np.dot(Omega0, H) Omega = Omega0 if normOh: Omega /= np.linalg.norm(OmegaH) OmegaH /= np.linalg.norm(OmegaH) if ni > 0: free_energyH = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyH < free_energy: logger.info("free energy has decreased after E-H step from %f to %f", free_energy, free_energyH) # A if estimateA: logger.info("E A step ...") m_A, Sigma_A = vt.expectation_A_asl(H, G, m_C, W, XX, Gamma, Gamma_X, q_Z, mu_Ma, sigma_Ma, J, y_tilde, Sigma_H, sigma_eps_m) cA += [(np.linalg.norm(m_A - m_A1) / np.linalg.norm(m_A1)) ** 2] m_A1[:, :] = m_A[:, :] if ni > 0: free_energyA = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyA < free_energyH: logger.info("free energy has decreased after E-A step from %f to %f", free_energyH, free_energyA) # PRF G if estimateG: logger.info("E G step ...") Gt, Sigma_G = vt.expectation_G_asl(Sigma_C, m_C, m_A, H, XX, W, WX, Gamma, Gamma_WX, XW_Gamma_WX, J, y_tilde, cov_noise, matrix_covG, sigmaG, priorG_mean_term, priorG_cov_term) if constraint and normg: if not np.linalg.norm(Gt)==1: logger.info(" constraint l2-norm = 1") G = vt.constraint_norm1_b(Gt, Sigma_G, positivity=positivity) #G = Gt / np.linalg.norm(Gt) else: logger.info(" l2-norm already 1!!!!!") G = Gt.copy() Sigma_G = np.zeros_like(Sigma_G) else: G = Gt.copy() g_norm = np.append(g_norm, np.linalg.norm(G)) print 'g_norm = ', g_norm cG += [(np.linalg.norm(G - G1) / np.linalg.norm(G1)) ** 2] G1[:] = G[:] if ni > 0: free_energyG = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyG < free_energyA: logger.info("free energy has decreased after E-G step from %f to %f", free_energyA, free_energyG) # C if estimateC: logger.info("E C step ...") m_C, Sigma_C = vt.expectation_C_asl(G, H, m_A, W, XX, Gamma, Gamma_X, q_Z, mu_Mc, sigma_Mc, J, y_tilde, Sigma_G, sigma_eps_m) cC += [(np.linalg.norm(m_C - m_C1) / np.linalg.norm(m_C1)) ** 2] m_C1[:, :] = m_C[:, :] if ni > 0: free_energyC = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyC < free_energyG: logger.info("free energy has decreased after E-C step from %f to %f", free_energyG, free_energyC) # Q labels if estimateZ: logger.info("E Q step ...") q_Z, Z_tilde = vt.expectation_Q_asl(Sigma_A, m_A, Sigma_C, m_C, sigma_Ma, mu_Ma, sigma_Mc, mu_Mc, Beta, Z_tilde, q_Z, neighboursIndexes, graph, M, J, K) #q_Z0, Z_tilde0 = vt.expectation_Q_async(Sigma_A, m_A, Sigma_C, m_C, # sigma_Ma, mu_Ma, sigma_Mc, mu_Mc, # Beta, Z_tilde, q_Z, neighboursIndexes, graph, M, J, K) #print 'synchronous vs asynchronous: ', np.abs(q_Z - q_Z0).sum() cZ += [(np.linalg.norm(q_Z - q_Z1) / (np.linalg.norm(q_Z1) + eps)) ** 2] q_Z1 = q_Z if ni > 0: free_energyQ = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyQ < free_energyC: logger.info("free energy has decreased after E-Q step from %f to %f", free_energyC, free_energyQ) # crit. AH and CG logger.info("crit. AH and CG") AH = m_A[:, :, np.newaxis] * H[np.newaxis, np.newaxis, :] CG = m_C[:, :, np.newaxis] * G[np.newaxis, np.newaxis, :] Crit_AH = (np.linalg.norm(AH - AH1) / (np.linalg.norm(AH1) + eps)) ** 2 cAH += [Crit_AH] AH1 = AH.copy() Crit_CG = (np.linalg.norm(CG - CG1) / (np.linalg.norm(CG1) + eps)) ** 2 cCG += [Crit_CG] CG1 = CG.copy() logger.info("Crit_AH = " + str(Crit_AH)) logger.info("Crit_CG = " + str(Crit_CG)) ##################### # MAXIMIZATION ##################### if prior=='balloon': logger.info(" prior balloon") AuxH = H - Hb AuxG = G - Gb elif prior=='omega': logger.info(" prior omega") AuxH = H.copy() AuxG = G - np.dot(Omega, H) #/np.linalg.norm(np.dot(Omega, H)) elif prior=='hierarchical': logger.info(" prior hierarchical") AuxH = H - Mu AuxG = G - np.dot(Omega, Mu) else: logger.info(" NO prior") AuxH = H.copy() AuxG = G.copy() # Variance HRF: sigmaH if estimateSigmaH: logger.info("M sigma_H step ...") sigmaH = vt.maximization_sigma_asl(D, Sigma_H, matrix_covH, AuxH, use_hyperprior, gamma_h) logger.info('sigmaH = ' + str(sigmaH)) if ni > 0: free_energyVh = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyVh < free_energyQ: logger.info("free energy has decreased after v_h computation from %f to %f", free_energyQ, free_energyVh) # Variance PRF: sigmaG if estimateSigmaG: logger.info("M sigma_G step ...") sigmaG = vt.maximization_sigma_asl(D, Sigma_G, matrix_covG, AuxG, use_hyperprior, gamma_g) logger.info('sigmaG = ' + str(sigmaG)) if ni > 0: free_energyVg = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyVg < free_energyVh: logger.info("free energy has decreased after v_g computation from %f to %f", free_energyVh, free_energyVg) # Mu: True HRF in the hierarchical prior case if prior=='hierarchical': logger.info("M sigma_G step ...") Mu = vt.maximization_Mu_asl(H, G, matrix_covH, matrix_covG, sigmaH, sigmaG, sigmaMu, Omega, R_inv) logger.info('sigmaG = ' + str(sigmaG)) if ni > 0: free_energyMu = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyMu < free_energyVg: logger.info("free energy has decreased after v_g computation from %f to %f", free_energyVg, free_energyMu) # (mu,sigma) if estimateMP: logger.info("M (mu,sigma) a and c step ...") mu_Ma, sigma_Ma = vt.maximization_mu_sigma_asl(q_Z, m_A, Sigma_A) mu_Mc, sigma_Mc = vt.maximization_mu_sigma_asl(q_Z, m_C, Sigma_C) if ni > 0: free_energyMP = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyMP < free_energyVg: logger.info("free energy has decreased after GMM parameters computation from %f to %f", free_energyVg, free_energyMP) # Drift L, alpha if estimateLA: logger.info("M L, alpha step ...") AL = vt.maximization_LA_asl(Y, m_A, m_C, XX, WP, W, WP_Gamma_WP, H, G, Gamma) y_tilde = Y - WP.dot(AL) if ni > 0: free_energyLA = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyLA < free_energyMP: logger.info("free energy has decreased after drifts computation from %f to %f", free_energyMP, free_energyLA) # Beta if estimateBeta: logger.info("M beta step ...") """ Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2) Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3) Beta = vt.maximization_beta_m2(Beta.copy(), q_Z, Qtilde_sumneighbour, Qtilde, neighboursIndexes, maxNeighbours, gamma, MaxItGrad, gradientStep) """ Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2) Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3) for m in xrange(0, M): Beta[m] = vt.maximization_beta_m2_scipy_asl(Beta[m].copy(), q_Z[m, :, :], Qtilde_sumneighbour[m, :, :], Qtilde[m, :, :], neighboursIndexes, maxNeighbours, gamma, MaxItGrad, gradientStep) logger.info(Beta) if ni > 0: free_energyB = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX) if free_energyB < free_energyLA: logger.info("free energy has decreased after Beta computation from %f to %f", \ free_energyLA, free_energyB) if 0: plt.close('all') for m in xrange(0, M): range_b = np.arange(-10., 20., 0.1) beta_plotting = np.zeros_like(range_b) for ib, b in enumerate(range_b): beta_plotting[ib] = vt.beta_function(b, q_Z[m, :, :], Qtilde_sumneighbour[m, :, :], neighboursIndexes, gamma) #print beta_plotting plt.figure(1) plt.hold('on') plt.plot(range_b, beta_plotting) plt.show() # Sigma noise if estimateNoise: logger.info("M sigma noise step ...") sigma_eps = vt.maximization_sigma_noise_asl(XX, m_A, Sigma_A, H, m_C, Sigma_C, \ G, Sigma_H, Sigma_G, W, y_tilde, Gamma, \ Gamma_X, Gamma_WX, N) if PLOT: for m in xrange(M): SUM_q_Z[m] += [q_Z[m, 1, :].sum()] mua1[m] += [mu_Ma[m, 1]] muc1[m] += [mu_Mc[m, 1]] free_energy = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps, XX, W, J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX, plot=True) if ni > 0: if free_energy < free_energyB: logger.info("free energy has decreased after Noise computation from %f to %f", free_energyB, free_energy) if ni > 0: if free_energy < FE[-1]: logger.info("WARNING! free energy has decreased in this iteration from %f to %f", FE[-1], free_energy) FE += [free_energy] #EP += [EPt] #EPlh += [EPt_lh] #Ent += [Entropy] if ni > NitMin: #Crit_FE = np.abs((FE[-1] - FE[-2]) / FE[-2]) FE0 = np.array(FE) Crit_FE = np.abs((FE0[-5:] - FE0[-6:-1]) / FE0[-6:-1]) print Crit_FE print (Crit_FE > Thresh * np.ones_like(Crit_FE)).any() else: Crit_FE = 100 ni += 1 cTime += [time.time() - t1] logger.info("Computing reconstruction error") StimulusInducedSignal = vt.computeFit_asl(H, m_A, G, m_C, W, XX) rerror = np.append(rerror, \ np.mean(((Y - StimulusInducedSignal) ** 2).sum(axis=0)) \ / np.mean((Y ** 2).sum(axis=0))) CompTime = time.time() - t1 # Normalize if not done already if not constraint or not normg: logger.info("l2-norm of H and G to 1 if not constraint") Hnorm = np.linalg.norm(H) H /= Hnorm Sigma_H /= Hnorm**2 m_A *= Hnorm Gnorm = np.linalg.norm(G) G /= Gnorm Sigma_G /= Gnorm**2 m_C *= Gnorm if zc: H = np.concatenate(([0], H, [0])) G = np.concatenate(([0], G, [0])) ## Compute contrast maps and variance if computeContrast and len(contrasts) > 0: logger.info("Computing contrasts ... ") CONTRAST_A, CONTRASTVAR_A, \ CONTRAST_C, CONTRASTVAR_C = vt.compute_contrasts(condition_names, contrasts, m_A, m_C, Sigma_A, Sigma_C, M, J) else: CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C = 0, 0, 0, 0 ########################################################################### ########################################## PLOTS and SNR computation if PLOT: logger.info("plotting...") print 'FE = ', FE vt.plot_convergence(ni, M, cA, cC, cH, cG, cAH, cCG, SUM_q_Z, mua1, muc1, FE) logger.info("Nb iterations to reach criterion: %d", ni) logger.info("Computational time = %s min %s s", str(np.int(CompTime // 60)), str(np.int(CompTime % 60))) logger.info("Iteration time = %s min %s s", str(np.int((CompTime // ni) // 60)), str(np.int((CompTime / ni) % 60))) logger.info("perfusion baseline mean = %f", np.mean(AL[0, :])) logger.info("perfusion baseline var = %f", np.var(AL[0, :])) logger.info("drifts mean = %f", np.mean(AL[1:, :])) logger.info("drifts var = %f", np.var(AL[1:, :])) logger.info("noise mean = %f", np.mean(sigma_eps)) logger.info("noise var = %f", np.var(sigma_eps)) SNR10 = 20 * (np.log10(np.linalg.norm(Y) / \ np.linalg.norm(Y - StimulusInducedSignal - WP.dot(AL)))) logger.info("SNR = %d", SNR10) return ni, m_A, H, m_C, G, Z_tilde, sigma_eps, \ mu_Ma, sigma_Ma, mu_Mc, sigma_Mc, Beta, AL[1:, :], np.dot(P, AL[1:, :]), \ AL[0, :], Sigma_A, Sigma_C, Sigma_H, Sigma_G, rerror, \ CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C, \ cA[:], cH[2:], cC[2:], cG[2:], cZ[2:], cAH[2:], cCG[2:], \ cTime, FE #, EP, EPlh, Ent
def Main_vbjde_physio(graph, Y, Onsets, durations, Thrf, K, TR, beta, dt, scale=1, estimateSigmaH=True, estimateSigmaG=True, sigmaH=0.05, sigmaG=0.05, gamma_h=0, gamma_g=0, NitMax=-1, NitMin=1, estimateBeta=True, PLOT=False, contrasts=[], computeContrast=False, idx_first_tag=0, simulation=None, sigmaMu=None, estimateH=True, estimateG=True, estimateA=True, estimateC=True, estimateZ=True, estimateNoise=True, estimateMP=True, estimateLA=True, use_hyperprior=False, positivity=False, constraint=False, phy_params=PHY_PARAMS_KHALIDOV11, prior='omega', zc=False): logger.info("EM for ASL!") np.random.seed(6537540) logger.info("data shape: ") logger.info(Y.shape) Thresh = 1e-5 D, M = np.int(np.ceil(Thrf / dt)) + 1, len(Onsets) #D, M = np.int(np.ceil(Thrf / dt)), len(Onsets) n_sess, N, J = Y.shape[0], Y.shape[1], Y.shape[2] Crit_AH, Crit_CG, cTime, rerror, FE = 1, 1, [], [], [] EP, EPlh, Ent = [],[],[] Crit_H, Crit_G, Crit_Z, Crit_A, Crit_C = 1, 1, 1, 1, 1 cAH, cCG, AH1, CG1 = [], [], [], [] cA, cC, cH, cG, cZ = [], [], [], [], [] h_norm, g_norm = [], [] SUM_q_Z = [[] for m in xrange(M)] mua1 = [[] for m in xrange(M)] muc1 = [[] for m in xrange(M)] sigmaH = sigmaH * J / 100 print sigmaH gamma_h = gamma_h * 100 / J print gamma_h # Beta data MaxItGrad = 200 gradientStep = 0.005 gamma = 7.5 print 'gamma = ', gamma print 'voxels = ', J maxNeighbours, neighboursIndexes = vt.create_neighbours(graph, J) print 'graph.shape = ', graph.shape # Conditions print 'Onsets: ', Onsets print 'durations = ', durations print 'creating conditions...' X, XX, condition_names = vt.create_conditions_block_ms(Onsets, durations, M, N, D, n_sess, TR, dt) # Covariance matrix #R = vt.covariance_matrix(2, D, dt) _, R_inv = genGaussianSmoothHRF(zc, D, dt, 1., 2) R = np.linalg.inv(R_inv) if zc: XX = XX[:, :, :, 1:-1] # XX shape (S, M, N, D) D = D - 2 AH1, CG1 = np.zeros((J, M, D)), np.zeros((J, M, D)) print 'HRF length = ', D print 'Condition number = ', M print 'Number of scans = ', N print 'Number of voxels = ', J print 'Number of sessions = ', n_sess print 'XX.shape = ', XX.shape # Noise matrix Gamma = np.identity(N) # Noise initialization sigma_eps = np.ones((n_sess, J)) # Labels logger.info("Labels are initialized by setting active probabilities " "to ones ...") q_Z = np.ones((M, K, J), dtype=np.float64) / 2. #q_Z = np.zeros((M, K, J), dtype=np.float64) #q_Z[:, 1, :] = 1 q_Z1 = copy.deepcopy(q_Z) Z_tilde = copy.deepcopy(q_Z) # H and G TT, m_h = getCanoHRF(Thrf, dt) H = np.array(m_h[:D]).astype(np.float64) H /= np.linalg.norm(H) Hb = create_physio_brf(phy_params, response_dt=dt, response_duration=Thrf) Hb /= np.linalg.norm(Hb) if prior=='balloon': H = Hb.copy() H1 = copy.deepcopy(H) Sigma_H = np.zeros((D, D), dtype=np.float64) # Initialize model parameters Beta = beta * np.ones((M), dtype=np.float64) n_drift = 4 P = np.zeros((n_sess, N, n_drift+1), dtype=np.float64) L = np.zeros((n_drift+1, J, n_sess), dtype=np.float64) for s in xrange(0, n_sess): P[s, :, :] = vt.PolyMat(N, n_drift, TR) L[:, :, s] = vt.polyFit(Y[s, :, :], TR, n_drift, P[s, :, :]) print 'P shape = ', P.shape print 'L shape = ', L.shape WP = P.copy() AL = L.copy() PL = np.einsum('ijk,kli->ijl', P, L) y_tilde = Y - PL # Parameters Gaussian mixtures mu_Ma = np.append(np.zeros((M, 1)), np.ones((M, 1)), axis=1).astype(np.float64) sigma_Ma = np.ones((M, K), dtype=np.float64) * 0.3 # Params RLs m_A = np.zeros((n_sess, J, M), dtype=np.float64) for s in xrange(0, n_sess): for j in xrange(0, J): m_A[s, j, :] = (np.random.normal(mu_Ma, np.sqrt(sigma_Ma)) * q_Z[:, :, j]).sum(axis=1).T m_A1 = m_A.copy() Sigma_A = np.ones((M, M, J, n_sess)) * np.identity(M)[:, :, np.newaxis, np.newaxis] G = np.zeros_like(H) m_C = np.zeros_like(m_A) Sigma_G = np.zeros_like(Sigma_H) Sigma_C = np.zeros_like(Sigma_A) mu_Mc = np.zeros_like(mu_Ma) sigma_Mc = np.ones_like(sigma_Ma) W = np.zeros_like(Gamma) # (N, N) # Precomputations print 'W shape is ', W.shape WX = W.dot(XX).transpose(1, 2, 0, 3) # shape (S, M, N, D) Gamma_X = np.zeros((N, n_sess, M, D), dtype=np.float64) # shape (N, S, M, D) X_Gamma_X = np.zeros((D, M, n_sess, M, D), dtype=np.float64) # shape (D, M, S, M, D) Gamma_WX = np.zeros((N, n_sess, M, D), dtype=np.float64) # shape (N, S, M, D) XW_Gamma_WX = np.zeros((D, M, n_sess, M, D), dtype=np.float64) # shape (D, M, S, M, D) Gamma_WP = np.zeros((N, n_sess, n_drift+1), dtype=np.float64) # shape (N, S, M, D) WP_Gamma_WP = np.zeros((n_sess, n_drift+1, n_drift+1), dtype=np.float64) # shape (D, M, S, M, D) for s in xrange(0, n_sess): Gamma_X[:, s, :, :] = np.tensordot(Gamma, XX[s, :, :, :], axes=(1, 1)) X_Gamma_X[:, :, s, :, :] = np.tensordot(XX[s, :, :, :].T, Gamma_X[:, s, :, :], axes=(1, 0)) Gamma_WX[:, s, :, :] = np.tensordot(Gamma, WX[s, :, :, :], axes=(1, 1)) XW_Gamma_WX[:, :, s, :, :] = np.tensordot(WX[s, :, :, :].T, Gamma_WX[:, s, :, :], axes=(1, 0)) Gamma_WP[:, s, :] = Gamma.dot(WP[s, :, :]) # (N, n_drift) WP_Gamma_WP[s, :, :] = WP[s, :, :].T.dot(Gamma_WP[:, s, :]) # (n_drift, n_drift) sigma_eps_m = np.maximum(sigma_eps, eps) # (n_sess, J) cov_noise = sigma_eps_m[:, :, np.newaxis, np.newaxis] # (n_sess, J, 1, 1) ########################################################################### ############################################# VBJDE t1 = time.time() ni = 0 #while ((ni < NitMin + 1) or (((Crit_AH > Thresh) or (Crit_CG > Thresh)) \ # and (ni < NitMax))): #while ((ni < NitMin + 1) or (((Crit_AH > Thresh)) \ # and (ni < NitMax))): while ((ni < NitMin + 1) or (((Crit_FE > Thresh * np.ones_like(Crit_FE)).any()) \ and (ni < NitMax))): logger.info("-------- Iteration n° " + str(ni + 1) + " --------") if PLOT and ni >= 0: # Plotting HRF and PRF logger.info("Plotting HRF and PRF for current iteration") vt.plot_response_functions_it(ni, NitMin, M, H, G) # Managing types of prior priorH_cov_term = np.zeros_like(R_inv) matrix_covH = R_inv.copy() if prior=='balloon': logger.info(" prior balloon") #matrix_covH = np.eye(R_inv.shape[0], R_inv.shape[1]) priorH_mean_term = np.dot(matrix_covH / sigmaH, Hb) else: logger.info(" NO prior") priorH_mean_term = np.zeros_like(H) priorG_mean_term = np.zeros_like(G) ##################### # EXPECTATION ##################### # HRF H if estimateH: logger.info("E H step ...") Ht, Sigma_H = vt.expectation_H_ms(Sigma_A, m_A, m_C, G, XX, W, Gamma, Gamma_X, X_Gamma_X, J, y_tilde, cov_noise, matrix_covH, sigmaH, priorH_mean_term, priorH_cov_term, N, M, D, n_sess) if constraint: if not np.linalg.norm(Ht)==1: logger.info(" constraint l2-norm = 1") H = vt.constraint_norm1_b(Ht, Sigma_H) #H = Ht / np.linalg.norm(Ht) else: logger.info(" l2-norm already 1!!!!!") H = Ht.copy() Sigma_H = np.zeros_like(Sigma_H) else: H = Ht.copy() h_norm = np.append(h_norm, np.linalg.norm(H)) print 'h_norm = ', h_norm Crit_H = (np.linalg.norm(H - H1) / np.linalg.norm(H1)) ** 2 cH += [Crit_H] H1[:] = H[:] # A if estimateA: logger.info("E A step ...") m_A, Sigma_A = vt.expectation_A_ms(m_A, Sigma_A, H, G, m_C, W, XX, Gamma, Gamma_X, q_Z, mu_Ma, sigma_Ma, J, y_tilde, Sigma_H, sigma_eps_m, N, M, D, n_sess) cA += [(np.linalg.norm(m_A - m_A1) / np.linalg.norm(m_A1)) ** 2] m_A1[:, :, :] = m_A[:, :, :] # Q labels if estimateZ: logger.info("E Q step ...") q_Z, Z_tilde = vt.expectation_Q_ms(Sigma_A, m_A, Sigma_C, m_C, sigma_Ma, mu_Ma, sigma_Mc, mu_Mc, Beta, Z_tilde, q_Z, neighboursIndexes, graph, M, J, K, n_sess) if 0: import matplotlib.pyplot as plt plt.close('all') fig = plt.figure(1) for m in xrange(M): ax = fig.add_subplot(2, M, m + 1) im = ax.matshow(m_A[:, :, m].mean(0).reshape(20, 20)) plt.colorbar(im, ax=ax) ax = fig.add_subplot(2, M, m + 3) im = ax.matshow(q_Z[m, 1, :].reshape(20, 20)) plt.colorbar(im, ax=ax) fig = plt.figure(2) for m in xrange(M): for s in xrange(n_sess): ax = fig.add_subplot(M, n_sess, n_sess * m + s + 1) im = ax.matshow(m_A[s, :, m].reshape(20, 20)) plt.colorbar(im, ax=ax) plt.show() cZ += [(np.linalg.norm(q_Z - q_Z1) / (np.linalg.norm(q_Z1) + eps)) ** 2] q_Z1 = q_Z if ni > 0: free_energyE = 0 for s in xrange(n_sess): free_energyE += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess) if free_energyE < free_energy: logger.info("free energy has decreased after E step from %f to %f", free_energy, free_energyE) # crit. AH and CG logger.info("crit. AH and CG") AH = m_A[:, :, :, np.newaxis] * H[np.newaxis, np.newaxis, :] Crit_AH = (np.linalg.norm(AH - AH1) / (np.linalg.norm(AH1) + eps)) ** 2 cAH += [Crit_AH] AH1 = AH.copy() logger.info("Crit_AH = " + str(Crit_AH)) ##################### # MAXIMIZATION ##################### if prior=='balloon': logger.info(" prior balloon") AuxH = H - Hb AuxG = G - Gb else: logger.info(" NO prior") AuxH = H.copy() AuxG = G.copy() # Variance HRF: sigmaH if estimateSigmaH: logger.info("M sigma_H step ...") sigmaH = vt.maximization_sigma_asl(D, Sigma_H, matrix_covH, AuxH, use_hyperprior, gamma_h) logger.info('sigmaH = ' + str(sigmaH)) if ni > 0: free_energyVh = 0 for s in xrange(n_sess): free_energyVh += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess) if free_energyVh < free_energyE: logger.info("free energy has decreased after v_h computation from %f to %f", free_energyE, free_energyVh) # (mu,sigma) if estimateMP: logger.info("M (mu,sigma) a and c step ...") #print 'q_Z = ', q_Z #print q_Z.shape mu_Ma, sigma_Ma = vt.maximization_mu_sigma_ms(q_Z, m_A, Sigma_A, M, J, n_sess, K) print 'mu_Ma = ', mu_Ma print 'sigma_Ma = ', sigma_Ma if ni > 0: free_energyMP = 0 for s in xrange(n_sess): free_energyMP += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess) if free_energyMP < free_energyVh: logger.info("free energy has decreased after GMM parameters computation from %f to %f", free_energyVh, free_energyMP) # Drift L, alpha if estimateLA: logger.info("M L, alpha step ...") for s in xrange(n_sess): AL[:, :, s] = vt.maximization_LA_asl(Y[s, :, :], m_A[s, :, :], m_C[s, :, :], XX[s, :, :, :], WP[s, :, :], W, WP_Gamma_WP[s, :, :], H, G, Gamma) PL = np.einsum('ijk,kli->ijl', WP, AL) y_tilde = Y - PL if ni > 0: free_energyLA = 0 for s in xrange(n_sess): free_energyLA += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess) if free_energyLA < free_energyMP: logger.info("free energy has decreased after drifts computation from %f to %f", free_energyMP, free_energyLA) # Beta if estimateBeta: logger.info("M beta step ...") """Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2) Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3) Beta = vt.maximization_beta_m2(Beta.copy(), q_Z, Qtilde_sumneighbour, Qtilde, neighboursIndexes, maxNeighbours, gamma, MaxItGrad, gradientStep) logger.info(Beta) """ logger.info("M beta step ...") Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2) Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3) for m in xrange(0, M): Beta[m] = vt.maximization_beta_m2_scipy_asl(Beta[m].copy(), q_Z[m, :, :], Qtilde_sumneighbour[m, :, :], Qtilde[m, :, :], neighboursIndexes, maxNeighbours, gamma, MaxItGrad, gradientStep) logger.info(Beta) if ni > 0: free_energyB = 0 for s in xrange(n_sess): free_energyB += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess) if free_energyB < free_energyLA: logger.info("free energy has decreased after Beta computation from %f to %f", \ free_energyLA, free_energyB) if 0 and ni < 5: plt.close('all') for m in xrange(0, M): range_b = np.arange(-10., 20., 0.1) beta_plotting = np.zeros_like(range_b) grad_plotting = np.zeros_like(range_b) for ib, b in enumerate(range_b): beta_plotting[ib] = vt.fun(b, q_Z[m, :, :], Qtilde_sumneighbour[m, :, :], neighboursIndexes, gamma) grad_plotting[ib] = vt.grad_fun(b, q_Z[m, :, :], Qtilde_sumneighbour[m, :, :], neighboursIndexes, gamma) #print beta_plotting plt.figure(1) plt.hold('on') plt.plot(range_b, beta_plotting) plt.figure(2) plt.hold('on') plt.plot(range_b, grad_plotting) plt.show() # Sigma noise if estimateNoise: logger.info("M sigma noise step ...") for s in xrange(n_sess): sigma_eps[s, :] = vt.maximization_sigma_noise_asl(XX[s, :, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], H, m_C[s, :, :], Sigma_C[:, :, :, s], \ G, Sigma_H, Sigma_G, W, y_tilde[s, :, :], Gamma, \ Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], N) if PLOT: for m in xrange(M): SUM_q_Z[m] += [q_Z[m, 1, :].sum()] mua1[m] += [mu_Ma[m, 1]] free_energy = 0 for s in xrange(n_sess): if s==n_sess-1: plotFE = True else: plotFE = False free_energy += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG, m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G, AuxG, q_Z, neighboursIndexes, Beta, Gamma, gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], plot=plotFE, bold=True, S=n_sess) if ni > 0: if free_energy < free_energyB: logger.info("free energy has decreased after Noise computation from %f to %f", free_energyB, free_energy) if ni > 0: if free_energy < FE[-1]: logger.info("WARNING! free energy has decreased in this iteration from %f to %f", FE[-1], free_energy) FE += [free_energy] if ni > 5: #Crit_FE = np.abs((FE[-1] - FE[-2]) / FE[-2]) FE0 = np.array(FE) Crit_FE = np.abs((FE0[-5:] - FE0[-6:-1]) / FE0[-6:-1]) print Crit_FE print (Crit_FE > Thresh * np.ones_like(Crit_FE)).any() else: Crit_FE = 100 ni += 1 cTime += [time.time() - t1] logger.info("Computing reconstruction error") StimulusInducedSignal = vt.computeFit_asl(H, m_A[s, :, :], G, m_C[s, :, :], W, XX[s, :, :, :]) rerror = np.append(rerror, \ np.mean(((Y[s, :, :] - StimulusInducedSignal) ** 2).sum(axis=0)) \ / np.mean((Y[s, :, :] ** 2).sum(axis=0))) CompTime = time.time() - t1 # Normalize if not done already if not constraint: # or not normg: logger.info("l2-norm of H and G to 1 if not constraint") Hnorm = np.linalg.norm(H) H /= Hnorm Sigma_H /= Hnorm**2 m_A *= Hnorm if zc: H = np.concatenate(([0], H, [0])) ## Compute contrast maps and variance if computeContrast and len(contrasts) > 0: logger.info("Computing contrasts ... ") CONTRAST_A, CONTRASTVAR_A, \ CONTRAST_C, CONTRASTVAR_C = vt.compute_contrasts(condition_names, contrasts, m_A[s, :, :], m_C[s, :, :], Sigma_A[:, :, :, s], Sigma_C[:, :, :, s], M, J) else: CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C = 0, 0, 0, 0 ########################################################################### ########################################## PLOTS and SNR computation logger.info("Nb iterations to reach criterion: %d", ni) logger.info("Computational time = %s min %s s", str(np.int(CompTime // 60)), str(np.int(CompTime % 60))) logger.info("Iteration time = %s min %s s", str(np.int((CompTime // ni) // 60)), str(np.int((CompTime / ni) % 60))) logger.info("perfusion baseline mean = %f", np.mean(AL[0, :, s])) logger.info("perfusion baseline var = %f", np.var(AL[0, :, s])) logger.info("drifts mean = %f", np.mean(AL[1:, :, s])) logger.info("drifts var = %f", np.var(AL[1:, :, s])) logger.info("noise mean = %f", np.mean(sigma_eps[s, :])) logger.info("noise var = %f", np.var(sigma_eps[s, :])) SNR10 = 20 * (np.log10(np.linalg.norm(Y[s, :, :]) / \ np.linalg.norm(Y[s, :, :] - StimulusInducedSignal - PL[s, :, :]))) logger.info("SNR = %d", SNR10) return ni, m_A.mean(0), H, m_C.mean(0), G, Z_tilde, sigma_eps[s, :], \ mu_Ma, sigma_Ma, mu_Mc, sigma_Mc, Beta, AL[:, :, s], PL[s, :, :], \ np.zeros_like(AL[0, :, s]), Sigma_A[:, :, :, s], Sigma_C[:, :, :, s], Sigma_H, Sigma_G, rerror, \ CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C, \ cA[:], cH[2:], cC[2:], cG[2:], cZ[2:], cAH[2:], cCG[2:], \ cTime, FE
def test_PolyMat(self): N = 325 TR = 1. P = vt.PolyMat(N, 4, TR)
def Main_vbjde_Extension_constrained_stable(graph, Y, Onsets, Thrf, K, TR, beta, dt, scale=1, estimateSigmaH=True, sigmaH=0.05, NitMax=-1, NitMin=1, estimateBeta=True, PLOT=False, contrasts=[], computeContrast=False, gamma_h=0): """ Version modified by Lofti from Christine's version """ logger.info( "Fast EM with C extension started ... Here is the stable version !") np.random.seed(6537546) # Initialize parameters S = 100 if NitMax < 0: NitMax = 100 gamma = 7.5 # 7.5 gradientStep = 0.003 MaxItGrad = 200 Thresh = 1e-5 # Initialize sizes vectors D = np.int(np.ceil(Thrf / dt)) + 1 M = len(Onsets) N = Y.shape[0] J = Y.shape[1] l = np.int(np.sqrt(J)) condition_names = [] # 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) condition_names += [condition] XX = np.zeros((M, N, D), dtype=np.int32) nc = 0 for condition, Ons in Onsets.iteritems(): XX[nc, :, :] = X[condition] nc += 1 # Covariance matrix order = 2 D2 = vt.buildFiniteDiffMatrix(order, D) R = np.dot(D2, D2) / pow(dt, 2 * order) invR = np.linalg.inv(R) Det_invR = np.linalg.det(invR) Gamma = np.identity(N) Det_Gamma = np.linalg.det(Gamma) Crit_H = 1 Crit_Z = 1 Crit_A = 1 Crit_AH = 1 AH = np.zeros((J, M, D), dtype=np.float64) AH1 = np.zeros((J, M, D), dtype=np.float64) Crit_FreeEnergy = 1 cTime = [] cA = [] cH = [] cZ = [] cAH = [] CONTRAST = np.zeros((J, len(contrasts)), dtype=np.float64) CONTRASTVAR = np.zeros((J, len(contrasts)), dtype=np.float64) Q_barnCond = np.zeros((M, M, D, D), dtype=np.float64) XGamma = np.zeros((M, D, N), dtype=np.float64) m1 = 0 for k1 in X: # Loop over the M conditions m2 = 0 for k2 in X: Q_barnCond[m1, m2, :, :] = np.dot( np.dot(X[k1].transpose(), Gamma), X[k2]) m2 += 1 XGamma[m1, :, :] = np.dot(X[k1].transpose(), Gamma) m1 += 1 sigma_epsilone = np.ones(J) logger.info( "Labels are initialized by setting active probabilities to ones ...") q_Z = np.zeros((M, K, J), dtype=np.float64) q_Z[:, 1, :] = 1 q_Z1 = np.zeros((M, K, J), dtype=np.float64) Z_tilde = q_Z.copy() TT, m_h = getCanoHRF(Thrf, dt) # TODO: check m_h = m_h[:D] m_H = np.array(m_h).astype(np.float64) m_H1 = np.array(m_h) sigmaH1 = sigmaH Sigma_H = np.ones((D, D), dtype=np.float64) Beta = beta * np.ones((M), dtype=np.float64) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) y_tilde = Y - PL Ndrift = L.shape[0] sigma_M = np.ones((M, K), dtype=np.float64) sigma_M[:, 0] = 0.5 sigma_M[:, 1] = 0.6 mu_M = np.zeros((M, K), dtype=np.float64) for k in xrange(1, K): mu_M[:, k] = 1 # InitMean Sigma_A = np.zeros((M, M, J), np.float64) for j in xrange(0, J): Sigma_A[:, :, j] = 0.01 * np.identity(M) m_A = np.zeros((J, M), dtype=np.float64) m_A1 = np.zeros((J, M), dtype=np.float64) for j in xrange(0, J): 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])) * q_Z[m, k, j] m_A1 = m_A t1 = time.time() ########################################################################## # VBJDE num. iter. minimum ni = 0 while ((ni < NitMin + 1) or ((Crit_AH > Thresh) and (ni < NitMax))): logger.info("------------------------------ Iteration n° " + str(ni + 1) + " ------------------------------") ##################### # EXPECTATION ##################### # A logger.info("E A step ...") UtilsC.expectation_A(q_Z, mu_M, sigma_M, PL, sigma_epsilone, Gamma, Sigma_H, Y, y_tilde, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N, K) # crit. A DIFF = np.reshape(m_A - m_A1, (M * J)) Crit_A = ( np.linalg.norm(DIFF) / np.linalg.norm(np.reshape(m_A1, (M * J)))) ** 2 cA += [Crit_A] m_A1[:, :] = m_A[:, :] # HRF h UtilsC.expectation_H(XGamma, Q_barnCond, sigma_epsilone, Gamma, R, Sigma_H, Y, y_tilde, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N, scale, sigmaH) #m_H[0] = 0 #m_H[-1] = 0 # Constrain with optimization strategy import cvxpy as cvx m, n = Sigma_H.shape Sigma_H_inv = np.linalg.inv(Sigma_H) zeros_H = np.zeros_like(m_H[:, np.newaxis]) # Construct the problem. PRIMAL h = cvx.Variable(n) expression = cvx.quad_form(h - m_H[:, np.newaxis], Sigma_H_inv) objective = cvx.Minimize(expression) #constraints = [h[0] == 0, h[-1]==0, h >= zeros_H, cvx.square(cvx.norm(h,2))<=1] constraints = [h[0] == 0, h[-1] == 0, cvx.square(cvx.norm(h, 2)) <= 1] prob = cvx.Problem(objective, constraints) result = prob.solve(verbose=0, solver=cvx.CVXOPT) # Now we update the mean of h m_H_old = m_H Sigma_H_old = Sigma_H m_H = np.squeeze(np.array((h.value))) Sigma_H = np.zeros_like(Sigma_H) # and the norm h_norm += [np.linalg.norm(m_H)] # crit. h Crit_H = (np.linalg.norm(m_H - m_H1) / np.linalg.norm(m_H1)) ** 2 cH += [Crit_H] m_H1[:] = m_H[:] # crit. AH for d in xrange(0, D): AH[:, :, d] = m_A[:, :] * m_H[d] DIFF = np.reshape(AH - AH1, (M * J * D)) Crit_AH = (np.linalg.norm( DIFF) / (np.linalg.norm(np.reshape(AH1, (M * J * D))) + eps)) ** 2 cAH += [Crit_AH] AH1[:, :, :] = AH[:, :, :] # Z labels logger.info("E Z step ...") UtilsC.expectation_Z(Sigma_A, m_A, sigma_M, Beta, Z_tilde, mu_M, q_Z, neighboursIndexes.astype(np.int32), M, J, K, maxNeighbours) # crit. Z DIFF = np.reshape(q_Z - q_Z1, (M * K * J)) Crit_Z = (np.linalg.norm(DIFF) / (np.linalg.norm(np.reshape(q_Z1, (M * K * J))) + eps)) ** 2 cZ += [Crit_Z] q_Z1[:, :, :] = q_Z[:, :, :] ##################### # MAXIMIZATION ##################### # HRF: Sigma_h if estimateSigmaH: logger.info("M sigma_H step ...") if gamma_h > 0: sigmaH = vt.maximization_sigmaH_prior( D, Sigma_H, R, m_H, gamma_h) else: sigmaH = vt.maximization_sigmaH(D, Sigma_H, R, m_H) logger.info('sigmaH = %s', str(sigmaH)) # (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 UtilsC.maximization_L( Y, m_A, m_H, L, P, XX.astype(np.int32), J, D, M, Ndrift, N) PL = np.dot(P, L) y_tilde = Y - PL # Beta if estimateBeta: logger.info("estimating beta") for m in xrange(0, M): Beta[m] = UtilsC.maximization_beta(beta, q_Z[m, :, :].astype(np.float64), Z_tilde[m, :, :].astype( np.float64), J, K, neighboursIndexes.astype(np.int32), gamma, maxNeighbours, MaxItGrad, gradientStep) logger.info("End estimating beta") logger.info(Beta) # Sigma noise logger.info("M sigma noise step ...") UtilsC.maximization_sigma_noise( Gamma, PL, sigma_epsilone, Sigma_H, Y, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N) t02 = time.time() cTime += [t02 - t1] t2 = time.time() ########################################################################## # PLOTS and SNR computation if PLOT and 0: font = {'size': 15} matplotlib.rc('font', **font) savefig('./HRF_Iter_CompMod.png') hold(False) figure(2) plot(cAH[1:-1], 'lightblue') hold(True) plot(cFE[1:-1], 'm') hold(False) legend(('CAH', 'CFE')) grid(True) savefig('./Crit_CompMod.png') figure(3) plot(FreeEnergyArray) grid(True) savefig('./FreeEnergy_CompMod.png') figure(4) for m in xrange(M): plot(SUM_q_Z_array[m]) hold(True) hold(False) savefig('./Sum_q_Z_Iter_CompMod.png') figure(5) for m in xrange(M): plot(mu1_array[m]) hold(True) hold(False) savefig('./mu1_Iter_CompMod.png') figure(6) plot(h_norm_array) 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 """ Norm = np.linalg.norm(m_H) m_H /= Norm Sigma_H /= Norm**2 sigmaH /= Norm**2 m_A *= Norm Sigma_A *= Norm**2 mu_M *= Norm sigma_M *= Norm**2 sigma_M = np.sqrt(np.sqrt(sigma_M)) """ logger.info("Nb iterations to reach criterion: %d", ni) logger.info("Computational time = %s min %s s", str( np.int(CompTime // 60)), str(np.int(CompTime % 60))) 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 ni, m_A, m_H, q_Z, sigma_epsilone, mu_M, sigma_M, Beta, L, PL, CONTRAST, CONTRASTVAR, cA[2:], cH[2:], cZ[2:], cAH[2:], cTime[2:], cTimeMean, Sigma_A, StimulusInducedSignal
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
def Main_vbjde_Extension_constrained(graph, Y, Onsets, Thrf, K, TR, beta, dt, scale=1, estimateSigmaH=True, sigmaH=0.05, NitMax=-1, NitMin=1, estimateBeta=True, PLOT=False, contrasts=[], computeContrast=False, gamma_h=0, estimateHRF=True, TrueHrfFlag=False, HrfFilename='hrf.nii', estimateLabels=True, LabelsFilename='labels.nii', MFapprox=False, InitVar=0.5, InitMean=2.0, MiniVEMFlag=False, NbItMiniVem=5): # VBJDE Function for BOLD with contraints logger.info("Fast EM with C extension started ...") np.random.seed(6537546) ########################################################################## # INITIALIZATIONS # Initialize parameters tau1 = 0.0 tau2 = 0.0 S = 100 Init_sigmaH = sigmaH Nb2Norm = 1 NormFlag = False if NitMax < 0: NitMax = 100 gamma = 7.5 #gamma_h = 1000 gradientStep = 0.003 MaxItGrad = 200 Thresh = 1e-5 Thresh_FreeEnergy = 1e-5 estimateLabels = True # WARNING!! They should be estimated # Initialize sizes vectors D = int(np.ceil(Thrf / dt)) + 1 # D = int(np.ceil(Thrf/dt)) M = len(Onsets) N = Y.shape[0] J = Y.shape[1] l = int(np.sqrt(J)) condition_names = [] # 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) condition_names += [condition] XX = np.zeros((M, N, D), dtype=np.int32) nc = 0 for condition, Ons in Onsets.iteritems(): XX[nc, :, :] = X[condition] nc += 1 # Covariance matrix order = 2 D2 = vt.buildFiniteDiffMatrix(order, D) R = np.dot(D2, D2) / pow(dt, 2 * order) invR = np.linalg.inv(R) Det_invR = np.linalg.det(invR) Gamma = np.identity(N) Det_Gamma = np.linalg.det(Gamma) p_Wtilde = np.zeros((M, K), dtype=np.float64) p_Wtilde1 = np.zeros((M, K), dtype=np.float64) p_Wtilde[:, 1] = 1 Crit_H = 1 Crit_Z = 1 Crit_A = 1 Crit_AH = 1 AH = np.zeros((J, M, D), dtype=np.float64) AH1 = np.zeros((J, M, D), dtype=np.float64) Crit_FreeEnergy = 1 cA = [] cH = [] cZ = [] cAH = [] FreeEnergy_Iter = [] cTime = [] cFE = [] SUM_q_Z = [[] for m in xrange(M)] mu1 = [[] for m in xrange(M)] h_norm = [] h_norm2 = [] CONTRAST = np.zeros((J, len(contrasts)), dtype=np.float64) CONTRASTVAR = np.zeros((J, len(contrasts)), dtype=np.float64) Q_barnCond = np.zeros((M, M, D, D), dtype=np.float64) XGamma = np.zeros((M, D, N), dtype=np.float64) m1 = 0 for k1 in X: # Loop over the M conditions m2 = 0 for k2 in X: Q_barnCond[m1, m2, :, :] = np.dot( np.dot(X[k1].transpose(), Gamma), X[k2]) m2 += 1 XGamma[m1, :, :] = np.dot(X[k1].transpose(), Gamma) m1 += 1 if MiniVEMFlag: logger.info("MiniVEM to choose the best initialisation...") """InitVar, InitMean, gamma_h = MiniVEM_CompMod(Thrf,TR,dt,beta,Y,K, gamma,gradientStep, MaxItGrad,D,M,N,J,S, maxNeighbours, neighboursIndexes, XX,X,R,Det_invR,Gamma, Det_Gamma, scale,Q_barnCond,XGamma, NbItMiniVem, sigmaH,estimateHRF)""" InitVar, InitMean, gamma_h = vt.MiniVEM_CompMod(Thrf, TR, dt, beta, Y, K, gamma, gradientStep, MaxItGrad, D, M, N, J, S, maxNeighbours, neighboursIndexes, XX, X, R, Det_invR, Gamma, Det_Gamma, p_Wtilde, scale, Q_barnCond, XGamma, tau1, tau2, NbItMiniVem, sigmaH, estimateHRF) sigmaH = Init_sigmaH sigma_epsilone = np.ones(J) logger.info( "Labels are initialized by setting active probabilities to ones ...") q_Z = np.zeros((M, K, J), dtype=np.float64) q_Z[:, 1, :] = 1 q_Z1 = np.zeros((M, K, J), dtype=np.float64) Z_tilde = q_Z.copy() # TT,m_h = getCanoHRF(Thrf-dt,dt) #TODO: check TT, m_h = getCanoHRF(Thrf, dt) # TODO: check m_h = m_h[:D] m_H = np.array(m_h).astype(np.float64) m_H1 = np.array(m_h) sigmaH1 = sigmaH if estimateHRF: Sigma_H = np.ones((D, D), dtype=np.float64) else: Sigma_H = np.zeros((D, D), dtype=np.float64) Beta = beta * np.ones((M), dtype=np.float64) P = vt.PolyMat(N, 4, TR) L = vt.polyFit(Y, TR, 4, P) PL = np.dot(P, L) y_tilde = Y - PL Ndrift = L.shape[0] sigma_M = np.ones((M, K), dtype=np.float64) sigma_M[:, 0] = 0.5 sigma_M[:, 1] = 0.6 mu_M = np.zeros((M, K), dtype=np.float64) for k in xrange(1, K): mu_M[:, k] = InitMean Sigma_A = np.zeros((M, M, J), np.float64) for j in xrange(0, J): Sigma_A[:, :, j] = 0.01 * np.identity(M) m_A = np.zeros((J, M), dtype=np.float64) m_A1 = np.zeros((J, M), dtype=np.float64) for j in xrange(0, J): 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])) * q_Z[m, k, j] m_A1 = m_A t1 = time.time() ########################################################################## # VBJDE num. iter. minimum ni = 0 while ((ni < NitMin) or (((Crit_FreeEnergy > Thresh_FreeEnergy) or (Crit_AH > Thresh)) and (ni < NitMax))): logger.info("------------------------------ Iteration n° " + str(ni + 1) + " ------------------------------") ##################### # EXPECTATION ##################### # A logger.info("E A step ...") UtilsC.expectation_A(q_Z, mu_M, sigma_M, PL, sigma_epsilone, Gamma, Sigma_H, Y, y_tilde, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N, K) val = np.reshape(m_A, (M * J)) val[np.where((val <= 1e-50) & (val > 0.0))] = 0.0 val[np.where((val >= -1e-50) & (val < 0.0))] = 0.0 # crit. A DIFF = np.reshape(m_A - m_A1, (M * J)) # To avoid numerical problems DIFF[np.where((DIFF < 1e-50) & (DIFF > 0.0))] = 0.0 # To avoid numerical problems DIFF[np.where((DIFF > -1e-50) & (DIFF < 0.0))] = 0.0 Crit_A = ( np.linalg.norm(DIFF) / np.linalg.norm(np.reshape(m_A1, (M * J)))) ** 2 cA += [Crit_A] m_A1[:, :] = m_A[:, :] # HRF h if estimateHRF: ################################ # HRF ESTIMATION ################################ UtilsC.expectation_H(XGamma, Q_barnCond, sigma_epsilone, Gamma, R, Sigma_H, Y, y_tilde, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N, scale, sigmaH) import cvxpy as cvx m, n = Sigma_H.shape Sigma_H_inv = np.linalg.inv(Sigma_H) zeros_H = np.zeros_like(m_H[:, np.newaxis]) # Construct the problem. PRIMAL h = cvx.Variable(n) expression = cvx.quad_form(h - m_H[:, np.newaxis], Sigma_H_inv) objective = cvx.Minimize(expression) #constraints = [h[0] == 0, h[-1]==0, h >= zeros_H, cvx.square(cvx.norm(h,2))<=1] constraints = [ h[0] == 0, h[-1] == 0, cvx.square(cvx.norm(h, 2)) <= 1] prob = cvx.Problem(objective, constraints) result = prob.solve(verbose=0, solver=cvx.CVXOPT) # Now we update the mean of h m_H_old = m_H Sigma_H_old = Sigma_H m_H = np.squeeze(np.array((h.value))) Sigma_H = np.zeros_like(Sigma_H) h_norm += [np.linalg.norm(m_H)] # print 'h_norm = ', h_norm # Plotting HRF if PLOT and ni >= 0: import matplotlib.pyplot as plt plt.figure(M + 1) plt.plot(m_H) plt.hold(True) else: if TrueHrfFlag: #TrueVal, head = read_volume(HrfFilename) TrueVal, head = read_volume(HrfFilename)[:, 0, 0, 0] print TrueVal print TrueVal.shape m_H = TrueVal # crit. h Crit_H = (np.linalg.norm(m_H - m_H1) / np.linalg.norm(m_H1)) ** 2 cH += [Crit_H] m_H1[:] = m_H[:] # crit. AH for d in xrange(0, D): AH[:, :, d] = m_A[:, :] * m_H[d] DIFF = np.reshape(AH - AH1, (M * J * D)) # To avoid numerical problems DIFF[np.where((DIFF < 1e-50) & (DIFF > 0.0))] = 0.0 # To avoid numerical problems DIFF[np.where((DIFF > -1e-50) & (DIFF < 0.0))] = 0.0 if np.linalg.norm(np.reshape(AH1, (M * J * D))) == 0: Crit_AH = 1000000000. else: Crit_AH = ( np.linalg.norm(DIFF) / np.linalg.norm(np.reshape(AH1, (M * J * D)))) ** 2 cAH += [Crit_AH] AH1[:, :, :] = AH[:, :, :] # Z labels if estimateLabels: logger.info("E Z step ...") # WARNING!!! ParsiMod gives better results, but we need the other # one. if MFapprox: UtilsC.expectation_Z(Sigma_A, m_A, sigma_M, Beta, Z_tilde, mu_M, q_Z, neighboursIndexes.astype( np.int32), M, J, K, maxNeighbours) if not MFapprox: UtilsC.expectation_Z_ParsiMod_RVM_and_CompMod( Sigma_A, m_A, sigma_M, Beta, mu_M, q_Z, neighboursIndexes.astype(np.int32), M, J, K, maxNeighbours) else: logger.info("Using True Z ...") TrueZ = read_volume(LabelsFilename) for m in xrange(M): q_Z[m, 1, :] = np.reshape(TrueZ[0][:, :, :, m], J) q_Z[m, 0, :] = 1 - q_Z[m, 1, :] # crit. Z val = np.reshape(q_Z, (M * K * J)) val[np.where((val <= 1e-50) & (val > 0.0))] = 0.0 DIFF = np.reshape(q_Z - q_Z1, (M * K * J)) # To avoid numerical problems DIFF[np.where((DIFF < 1e-50) & (DIFF > 0.0))] = 0.0 # To avoid numerical problems DIFF[np.where((DIFF > -1e-50) & (DIFF < 0.0))] = 0.0 if np.linalg.norm(np.reshape(q_Z1, (M * K * J))) == 0: Crit_Z = 1000000000. else: Crit_Z = ( np.linalg.norm(DIFF) / np.linalg.norm(np.reshape(q_Z1, (M * K * J)))) ** 2 cZ += [Crit_Z] q_Z1 = q_Z ##################### # MAXIMIZATION ##################### # HRF: Sigma_h if estimateHRF: if estimateSigmaH: logger.info("M sigma_H step ...") if gamma_h > 0: sigmaH = vt.maximization_sigmaH_prior( D, Sigma_H_old, R, m_H_old, gamma_h) else: sigmaH = vt.maximization_sigmaH(D, Sigma_H, R, m_H) logger.info('sigmaH = %s', str(sigmaH)) # (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) for m in xrange(M): SUM_q_Z[m] += [sum(q_Z[m, 1, :])] mu1[m] += [mu_M[m, 1]] # Drift L UtilsC.maximization_L( Y, m_A, m_H, L, P, XX.astype(np.int32), J, D, M, Ndrift, N) PL = np.dot(P, L) y_tilde = Y - PL # Beta if estimateBeta: logger.info("estimating beta") for m in xrange(0, M): if MFapprox: Beta[m] = UtilsC.maximization_beta(beta, q_Z[m, :, :].astype(np.float64), Z_tilde[m, :, :].astype( np.float64), J, K, neighboursIndexes.astype(np.int32), gamma, maxNeighbours, MaxItGrad, gradientStep) if not MFapprox: #Beta[m] = UtilsC.maximization_beta(beta,q_Z[m,:,:].astype(np.float64),q_Z[m,:,:].astype(np.float64),J,K,neighboursIndexes.astype(int32),gamma,maxNeighbours,MaxItGrad,gradientStep) Beta[m] = UtilsC.maximization_beta_CB(beta, q_Z[m, :, :].astype( np.float64), J, K, neighboursIndexes.astype(np.int32), gamma, maxNeighbours, MaxItGrad, gradientStep) logger.info("End estimating beta") logger.info(Beta) # Sigma noise logger.info("M sigma noise step ...") UtilsC.maximization_sigma_noise( Gamma, PL, sigma_epsilone, Sigma_H, Y, m_A, m_H, Sigma_A, XX.astype(np.int32), J, D, M, N) #### Computing Free Energy #### if ni > 0: FreeEnergy1 = FreeEnergy """FreeEnergy = vt.Compute_FreeEnergy(y_tilde,m_A,Sigma_A,mu_M,sigma_M, m_H,Sigma_H,R,Det_invR,sigmaH, p_Wtilde,q_Z,neighboursIndexes, maxNeighbours,Beta,sigma_epsilone, XX,Gamma,Det_Gamma,XGamma,J,D,M, N,K,S,"CompMod")""" FreeEnergy = vt.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 t02 = time.time() cTime += [t02 - t1] 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] 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.legend( ('m=0','m=1', 'm=2', 'm=3') ) #plt.legend( ('m=0','m=1') ) 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 sigma_M = np.sqrt(np.sqrt(sigma_M)) 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" # print "sigma_H = " + str(sigmaH) 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 = %d", SNR) return ni, m_A, m_H, q_Z, sigma_epsilone, mu_M, sigma_M, Beta, L, PL, CONTRAST, CONTRASTVAR, cA[2:], cH[2:], cZ[2:], cAH[2:], cTime[2:], cTimeMean, Sigma_A, StimulusInducedSignal, FreeEnergyArray