def soft_scal_nodiag(Y, lam):
p = Y.shape[1]
X = matrix(zeros((p,p)))
xtilde = matrix(zeros((p-1,p-1)))
ytilde = nodiag_construction(Y)
xtilde = soft_scal(ytilde, lam)
return diag_construction(xtilde, diag(Y))
def ADM_CNJGL(S1, S2, lam1, lam2, n1, n2):
# Begin algorithm
p = S1.shape[0]
# Initialize variables
Theta1old = eye(p)
Theta2old = eye(p)
Theta1 = eye(p)
Theta2 = eye(p)
V1 = Theta1old/2
V2 = Theta2old/2
W1 = V1.transpose()
W2 = V2.transpose()
Z1 = Theta1
Z2 = Theta2
Gamma1 = matrix(zeros((p,p)))
Gamma2 = matrix(zeros((p,p)))
Lambda1 = matrix(zeros((p,p)))
Lambda2 = matrix(zeros((p,p)))
Q1 = matrix(zeros((p,p)))
Q2 = Q1
# Load parameters
rho = ADM_parameters.opts['rho_init']
iter_adm = matrix(zeros((ADM_parameters.opts['homotopy_size'], 1)))
relError = matrix(zeros((ADM_parameters.opts['maxiter'] + ADM_parameters.opts['homotopy_size']*ADM_parameters.opts['maxiter'], 1)))
print "homotopy_size", int(ADM_parameters.opts['homotopy_size'])
print "maxiter", int(ADM_parameters.opts['maxiter'])
# Begin outer loop for homotopy parameter
for r in range(0, int(ADM_parameters.opts['homotopy_size'])): # 5
# Begin ADM
for i in range(0, ADM_parameters.opts['maxiter']): # 500
# Update of Theta1 and Theta2
Theta1 = expand_ni(1.0/(2.0*rho)*(rho*(V1 + W1 + Z1) - (Gamma1 + Lambda1)), S1, rho, n1)
Theta2 = expand_ni(1.0/(2.0*rho)*(rho*(V2 + W2 + Z2) - (Gamma2 + Lambda2)), S2, rho, n2)
# print "Theta1\n", Theta1
# Update of Z1 and Z2
Z1 = soft_thresh(Theta1 + Lambda1/(rho+0.0), lam1/(rho+0.0))
Z2 = soft_thresh(Theta2 + Lambda2/(rho+0.0), lam1/(rho+0.0))
# Update of V1 and V2
C1 = 1/(2.0*rho)*(rho*(W1.transpose() + Theta1 - W1) - (Q1 - Gamma1))
C2 = 1/(2.0*rho)*(rho*(W2.transpose() + Theta2 - W2) - (Q2 - Gamma2));
# print "C1", C1.shape
d1 = diag(C1)
d2 = diag(C2)
N1 = nodiag_construction(C1)
N2 = nodiag_construction(C2)
# print "N1", N1.shape
N = concatenate((N1,N2))
# print "N", N.shape
H = soft_scal(N,lam2/(2.0*rho))
d = concatenate((d1,d2))
# print "d1", d1.shape
# print "H", H.shape
# print "diagcon H", H[0:p-1,:].shape
V1 = diag_construction(H[0:p-1,:],d1);
# print "diagcon2 H", H[p-1:,:].shape
V2 = diag_construction(H[p-1:,:],d2); # err?
# Update of W1 and W2
W1 = 1/(2.0*rho)*(rho*(V1.transpose() + Theta1 - V1) + Gamma1 + Q1.transpose());
W2 = 1/(2.0*rho)*(rho*(V2.transpose() + Theta2 - V2) + Gamma2 + Q2.transpose());
# Update of dual variables
Gamma1 = Gamma1 + rho*(Theta1 - V1 - W1);
Gamma2 = Gamma2 + rho*(Theta2 - V2 - W2);
Lambda1 = Lambda1 + rho*(Theta1 - Z1);
Lambda2 = Lambda2 + rho*(Theta2 - Z2);
Q1 = Q1 + rho*(V1 - W1.transpose());
Q2 = Q2 + rho*(V2 - W2.transpose());
norm1 = norm(Theta1 - Theta1old, 'fro') / norm(Theta1, 'fro')
norm2 = norm(Theta2 - Theta2old, 'fro') / norm(Theta2, 'fro')
relError[i + r*ADM_parameters.opts['maxiter'], 0] = \
max(norm(Theta1 - Theta1old, 'fro') / norm(Theta1, 'fro'), \
norm(Theta2 - Theta2old, 'fro') / norm(Theta2, 'fro'))
# print i, r, relError[i + r*ADM_parameters.opts['maxiter'], 0]
if relError[i + (r*ADM_parameters.opts['maxiter']), 0] <= ADM_parameters.opts['eps']:
break
Theta1old = Theta1
Theta2old = Theta2
# End ADM
rho = rho * ADM_parameters.opts['homotopy']
iter_adm[r,0] = i
return (Theta1, Theta2, V1, V2, iter_adm, relError)
