def nuc_al(I, X, turn, epsilon=.1, quiet=False): m,K = np.shape(X) if not turn: V = cp.variable(m,K, name='V') U = X else: V = X U = cp.variable(m,K, name='U') f_cost = cp.parameter(name='f_cost') f_cost.value = 0 J = cp.parameter(K,K, name='J') J.value = cp.zeros((K,K)) # define the cost parameter for k in range(K): # create a list of interferer indeces Ik # from the interference set I Ik = np.arange(1,K+1)*I[k,:] # careful about zero indexing... Ik = Ik[Ik>0] - 1 #print 'I_%d = ' % k, Ik if len(Ik) > 0: for l in Ik: l = int(l) J[k,l] = U[:,k].T*V[:,l] # interference terms f_cost = f_cost + cp.nuclear_norm(J[k,:]) #f_cost = f_cost + cp.norm1(J[k,:]) # create constraints constraints = [] for k in range(K): c = cp.geq(U[:,k].T*V[:,k], epsilon) #c = cp.geq(cp.lambda_min(U[:,k].T*V[:,k]), epsilon) constraints.append(c) p = cp.program(cp.minimize(f_cost), constraints) print 'minimize: ', p.objective print 'subject to:' print p.constraints p.solve(quiet) if not turn: return V.value else: return U.value
def nuc_al(I, X, turn, epsilon=.1, quiet=False):
m, K = np.shape(X)
if not turn:
V = cp.variable(m, K, name='V')
U = X
else:
V = X
U = cp.variable(m, K, name='U')
f_cost = cp.parameter(name='f_cost')
f_cost.value = 0
J = cp.parameter(K, K, name='J')
J.value = cp.zeros((K, K))
# define the cost parameter
for k in range(K):
# create a list of interferer indeces Ik
# from the interference set I
Ik = np.arange(1, K + 1) * I[k, :] # careful about zero indexing...
Ik = Ik[Ik > 0] - 1
#print 'I_%d = ' % k, Ik
if len(Ik) > 0:
for l in Ik:
l = int(l)
J[k, l] = U[:, k].T * V[:, l] # interference terms
f_cost = f_cost + cp.nuclear_norm(J[k, :])
#f_cost = f_cost + cp.norm1(J[k,:])
# create constraints
constraints = []
for k in range(K):
c = cp.geq(U[:, k].T * V[:, k], epsilon)
#c = cp.geq(cp.lambda_min(U[:,k].T*V[:,k]), epsilon)
constraints.append(c)
p = cp.program(cp.minimize(f_cost), constraints)
print 'minimize: ', p.objective
print 'subject to:'
print p.constraints
p.solve(quiet)
if not turn:
return V.value
else:
return U.value
import cvxpy as cp import numpy as np I = np.random.randn(10,10) > .4 I[np.diag_indices_from(I)] = 0 K = np.shape(I)[0] X = cp.variable(K,K, name='X') const = [] for i in range(K): for j in range(K): if I[i,j] > 0: c = cp.equals(X[i,j],0) const.append(c) c = cp.equals(cp.diag(X),1) const.append(c) p = cp.program(cp.minimize(cp.nuclear_norm(X)), const) p.solve(quiet=False) print X.value
import cvxpy as cp
import numpy as np
I = np.random.randn(10, 10) > .4
I[np.diag_indices_from(I)] = 0
K = np.shape(I)[0]
X = cp.variable(K, K, name='X')
const = []
for i in range(K):
for j in range(K):
if I[i, j] > 0:
c = cp.equals(X[i, j], 0)
const.append(c)
c = cp.equals(cp.diag(X), 1)
const.append(c)
p = cp.program(cp.minimize(cp.nuclear_norm(X)), const)
p.solve(quiet=False)
print X.value
