def test_proximal_method():
X = np.random.standard_normal((100, 50))
X[:,:7] *= 5
qX = identity_quadratic(1,X,0,0)
P = FM.nuclear_norm(X.shape, lagrange=1)
RP = todense(P.proximal(qX))
B = FM.nuclear_norm(X.shape, bound=1)
RB = todense(B.proximal(qX))
BO = FM.operator_norm(X.shape, bound=1)
PO = FM.operator_norm(X.shape, lagrange=1)
RPO = todense(PO.proximal(qX))
RBO = todense(BO.proximal(qX))
D = np.linalg.svd(X, full_matrices=0)[1]
lD = np.linalg.svd(RP, full_matrices=0)[1]
lagrange_rank = (lD > 1.e-10).sum()
all_close(lD[:lagrange_rank] + P.lagrange, D[:lagrange_rank], 'proximal method lagrange', None)
bD = np.linalg.svd(RB, full_matrices=0)[1]
bound_rank = (bD > 1.e-10).sum()
all_close(bD[:bound_rank], projl1(D, B.bound)[:bound_rank], 'proximal method bound', None)
nt.assert_true(np.linalg.norm(RPO+RB-X) / np.linalg.norm(X) < 0.01)
nt.assert_true(np.linalg.norm(RBO+RP-X) / np.linalg.norm(X) < 0.01)
def test_proximal_maps():
X = np.random.standard_normal((100, 50))
X[:, :7] *= 5
P = FM.nuclear_norm(X.shape, lagrange=1)
RP = todense(P.lagrange_prox(X))
B = FM.nuclear_norm(X.shape, bound=1)
RB = todense(B.bound_prox(X))
BO = FM.operator_norm(X.shape, bound=1)
PO = FM.operator_norm(X.shape, lagrange=1)
RPO = todense(PO.lagrange_prox(X))
RBO = todense(BO.bound_prox(X))
D = np.linalg.svd(X, full_matrices=0)[1]
lD = np.linalg.svd(RP, full_matrices=0)[1]
lagrange_rank = (lD > 1.e-10).sum()
all_close(lD[:lagrange_rank] + P.lagrange, D[:lagrange_rank],
'proximal lagrange', None)
bD = np.linalg.svd(RB, full_matrices=0)[1]
bound_rank = (bD > 1.e-10).sum()
all_close(bD[:bound_rank],
projl1(D, B.bound)[:bound_rank], 'proximal bound', None)
nt.assert_true(np.linalg.norm(RPO + RB - X) / np.linalg.norm(X) < 0.01)
nt.assert_true(np.linalg.norm(RBO + RP - X) / np.linalg.norm(X) < 0.01)
# running code to ensure it is tested
P.conjugate
P.quadratic = identity_quadratic(1, 0, 0, 0)
P.conjugate
BO.conjugate
BO.quadratic = identity_quadratic(1, 0, 0, 0)
BO.conjugate
B.conjugate
B.quadratic = identity_quadratic(1, 0, 0, 0)
B.conjugate
PO.conjugate
PO.quadratic = identity_quadratic(1, 0, 0, 0)
PO.conjugate
def test_proximal_maps():
X = np.random.standard_normal((100, 50))
X[:,:7] *= 5
P = FM.nuclear_norm(X.shape, lagrange=1)
RP = todense(P.lagrange_prox(X))
B = FM.nuclear_norm(X.shape, bound=1)
RB = todense(B.bound_prox(X))
BO = FM.operator_norm(X.shape, bound=1)
PO = FM.operator_norm(X.shape, lagrange=1)
RPO = todense(PO.lagrange_prox(X))
RBO = todense(BO.bound_prox(X))
D = np.linalg.svd(X, full_matrices=0)[1]
lD = np.linalg.svd(RP, full_matrices=0)[1]
lagrange_rank = (lD > 1.e-10).sum()
all_close(lD[:lagrange_rank] + P.lagrange, D[:lagrange_rank], 'proximal lagrange', None)
bD = np.linalg.svd(RB, full_matrices=0)[1]
bound_rank = (bD > 1.e-10).sum()
all_close(bD[:bound_rank], projl1(D, B.bound)[:bound_rank], 'proximal bound', None)
nt.assert_true(np.linalg.norm(RPO+RB-X) / np.linalg.norm(X) < 0.01)
nt.assert_true(np.linalg.norm(RBO+RP-X) / np.linalg.norm(X) < 0.01)
# running code to ensure it is tested
P.conjugate
P.quadratic = identity_quadratic(1, 0, 0, 0)
P.conjugate
BO.conjugate
BO.quadratic = identity_quadratic(1, 0, 0, 0)
BO.conjugate
B.conjugate
B.quadratic = identity_quadratic(1, 0, 0, 0)
B.conjugate
PO.conjugate
PO.quadratic = identity_quadratic(1, 0, 0, 0)
PO.conjugate
def test_stopping_rule():
'''
use a stopping rule in compute_iterative_svd
'''
def soft_threshold_rule(L):
return lambda D: np.fabs(D).min() <= L
L = 30
svt_rule = soft_threshold_rule(L)
U, D, VT = FM.compute_iterative_svd(X, initial_rank=3, stopping_rule=svt_rule, tol=1.e-12, debug=True)
D2 = (D - L) * (D > L)
D1 = np.linalg.svd(X)[1]
D1 = (D1 - L) * (D1 > L)
rank = (D2 > 0).sum()
all_close(D1[:rank], D2[:rank], 'stopping_rule', None)
def test_stopping_rule():
'''
use a stopping rule in compute_iterative_svd
'''
def soft_threshold_rule(L):
return lambda D: np.fabs(D).min() <= L
L = 30
svt_rule = soft_threshold_rule(L)
U, D, VT = FM.compute_iterative_svd(X,
initial_rank=3,
stopping_rule=svt_rule,
tol=1.e-12,
debug=True)
D2 = (D - L) * (D > L)
D1 = np.linalg.svd(X)[1]
D1 = (D1 - L) * (D1 > L)
rank = (D2 > 0).sum()
all_close(D1[:rank], D2[:rank], 'stopping_rule', None)
