tol = 1e-8

maxIter = 1e6

d, n = X.shape

m = A.shape[1]

rho = 1.1

max_mu = 1e10

mu = 1e-6

atx = A.T.dot(X)

inv_a = np.linalg.inv(A.T.dot(A) + np.eye(m))

# Initializing optimization variables

# intialize

J = np.zeros((m, n))

Z = np.zeros((m, n))

E = np.zeros((d, n)) # sparse

Y1 = np.zeros((d, n))

Y2 = np.zeros((m, n))

# Start main loop

iter = 0

if display:

print "initial,rank=%f" % np.linalg.matrix_rank(Z)

while iter < maxIter:

iter += 1

# update J

temp = Z + Y2 / mu

U, sigma, V = np.linalg.svd(temp, 'econ')

V = V.T

svp = len(np.flatnonzero(sigma > 1.0 / mu))

if svp >= 1:

sigma = sigma[0:svp] - 1.0 / mu

else:

svp = 1

sigma = np.array([0])

J = U[:, 0:svp].dot(np.diag(sigma).dot(V[:, 0:svp].T))

# udpate Z

Z = inv_a.dot(atx - A.T.dot(E) + J + (A.T.dot(Y1) - Y2) / mu)

# update E

xmaz = X - A.dot(Z)

temp = xmaz + Y1 / mu

E = solve_l1l2(temp, lamb / mu)

leq1 = xmaz - E

leq2 = Z - J

stopC = max(np.max(np.abs(leq1)), np.max(np.abs(leq2)))

if display and (iter == 1 or np.mod(iter, 50) == 0 or stopC < tol):

print "iter", iter, ",mu=", mu, ",rank=", \

np.linalg.matrix_rank(Z, tol=1e-3*np.linalg.norm(Z, 2)), \

",stopALM=", stopC

if stopC < tol:

break

else:

Y1 += mu * leq1

Y2 += mu * leq2

mu = min(max_mu, mu * rho)