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