def test_19(self):
V2_a2, rsi = prox.ndto2d(self.V2, axis=2)
V2_r = prox.ndfrom2d(V2_a2, rsi)
assert (metric.mse(self.V2, V2_r) < 1e-14)
V2_a1, rsi = prox.ndto2d(self.V2, axis=1)
V2_r = prox.ndfrom2d(V2_a1, rsi)
assert (metric.mse(self.V2, V2_r) < 1e-14)
V2_a0, rsi = prox.ndto2d(self.V2, axis=0)
V2_r = prox.ndfrom2d(V2_a0, rsi)
assert (metric.mse(self.V2, V2_r) < 1e-14)
def test_26(self):
B0 = np.arange(1, 7).reshape(3, 2)
C0 = np.arange(1, 5).reshape(2, 2)
A0 = np.kron(B0, C0)
B, C = linalg.nkp(A0, B0.shape, C0.shape)
assert mse(A0, np.kron(B, C)) < 1e-12
r = B0[0, 0] / B[0, 0]
B *= r
C /= r
assert mse(B0, B) < 1e-12
assert mse(C0, C) < 1e-12
def test_39(self):
B0 = np.arange(1, 7).reshape(3, 2)
C0 = np.arange(1, 5).reshape(2, 2)
A0 = np.kron(B0, C0)
B, C = util.nkp(A0, B0.shape, C0.shape)
assert (metric.mse(A0, np.kron(B, C)) < 1e-12)
r = B0[0, 0] / B[0, 0]
B *= r
C /= r
assert (metric.mse(B0, B) < 1e-12)
assert (metric.mse(C0, C) < 1e-12)
def test_28(self):
alpha = np.random.randn()
N = 7
M = 10
X0 = np.random.randn(N, M)
A = np.random.randn(N, 1)
B = np.random.randn(1, M)
C = A * X0 * B + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-14
A = A[:, 0]
B = B[0]
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-14
def test_29(self):
alpha = np.random.randn()
N = 7
M = 10
X0 = np.random.randn(N, M)
A = np.random.randn(N, 1)
Bg = np.random.randn(M, 4)
B = Bg.dot(Bg.T)
C = A * X0.dot(B) + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-12
Lambda, Q = np.linalg.eigh(B)
X1 = linalg.solve_symmetric_sylvester(A, (Lambda, Q), C, alpha)
assert mse(X0, X1) < 1e-12
def test_30(self):
alpha = np.random.randn()
N = 7
M = 10
X0 = np.random.randn(N, M)
Ag = np.random.randn(4, N)
A = Ag.T.dot(Ag)
B = np.random.randn(1, M)
C = A.dot(X0) * B + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-12
Lambda, Q = np.linalg.eigh(A)
X1 = linalg.solve_symmetric_sylvester((Lambda, Q), B, C, alpha)
assert mse(X0, X1) < 1e-12
def test_40(self):
B0 = np.random.randn(3, 5, 2)
C0 = np.random.randn(4, 6, 2)
A0 = kronsum(np.ones((2, )), B0, C0)
S, B, C = util.kpsvd(A0, B0.shape[0:2], C0.shape[0:2])
A = kronsum(S, B[..., 0:2], C[..., 0:2])
assert (metric.mse(A0, A) < 1e-12)
def test_11(self):
for beta in [0.0, 0.5, 1.0]:
for alpha in self.alpha:
pV1 = prox.prox_dl1l2(self.V1, alpha, beta=beta, axis=0)
for k in range(pV1.shape[1]):
pV1k = prox.prox_dl1l2(self.V1[:, k], alpha, beta=beta)
assert metric.mse(pV1[:, k], pV1k) < 1e-12
def test_01(self):
N = 64
L = 20
x = np.cos(np.linspace(0, np.pi, N))[np.newaxis, :]
y = np.cos(np.linspace(0, np.pi, N))[:, np.newaxis]
U = x * y
V = np.random.randn(N, N)
t = np.sort(np.abs(V).ravel())[V.size - L]
V[np.abs(V) < t] = 0
D = U + V
lmbda = 0.1
opt = spline.SplineL1.Options({
'Verbose': False,
'gEvalY': False,
'MaxMainIter': 250,
'RelStopTol': 5e-4,
'DFidWeight': V == 0,
'AutoRho': {
'Enabled': True
}
})
b = spline.SplineL1(D, lmbda, opt)
X = b.solve()
assert (np.abs(b.itstat[-1].ObjFun - 0.333606246) < 1e-6)
assert (sm.mse(U, X) < 1e-6)
def test_12(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
frc = 0.5
msk = su.rndmask(s.shape, frc, dtype=np.float32)
s *= msk
lmbda = 1e-1
mu = 1e-2
# Since cucbpdn.cbpdngrdmsk automatically ensures that the ℓ2 of
# gradient term is not applied to the AMS impulse filter, while
# cbpdn.AddMaskSim does not, we have to pass a GradWeight array
# with a zero entry corresponding to the AMS impulse filter to
# cbpdn.AddMaskSim
Wgrdi = np.hstack((np.ones(M,), np.zeros((1,))))
opt = cbpdn.ConvBPDNGradReg.Options({'Verbose': False,
'MaxMainIter': 50, 'AutoRho': {'Enabled': False}})
opt['GradWeight'] = Wgrdi
b = cbpdn.AddMaskSim(cbpdn.ConvBPDNGradReg, D, s, msk, lmbda, mu, opt)
X1 = b.solve()
opt['GradWeight'] = 1.0
X2 = cucbpdn.cbpdngrdmsk(D, s, msk, lmbda, mu, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_13(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
frc = 0.5
msk = su.rndmask(s.shape, frc, dtype=np.float32)
s *= msk
lmbda = 1e-1
mu = 1e-2
Wl1 = np.random.randn(1, 1, M).astype(np.float32)
Wl1i = np.concatenate((Wl1, np.ones(Wl1.shape[0:-1] + (1,))),
axis=-1)
Wgrdi = np.hstack((np.ones(M,), np.zeros((1,))))
opt = cbpdn.ConvBPDNGradReg.Options({'Verbose': False,
'MaxMainIter': 50, 'AutoRho': {'Enabled': False}})
opt['L1Weight'] = Wl1i
opt['GradWeight'] = Wgrdi
b = cbpdn.AddMaskSim(cbpdn.ConvBPDNGradReg, D, s, msk, lmbda, mu, opt)
X1 = b.solve()
opt['L1Weight'] = Wl1
opt['GradWeight'] = 1.0
X2 = cucbpdn.cbpdngrdmsk(D, s, msk, lmbda, mu, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_27(self):
B0 = np.random.randn(3, 5, 2)
C0 = np.random.randn(4, 6, 2)
A0 = kronsum(np.ones((2, )), B0, C0)
S, B, C = linalg.kpsvd(A0, B0.shape[0:2], C0.shape[0:2])
A = kronsum(S, B[..., 0:2], C[..., 0:2])
assert mse(A0, A) < 1e-12
def test_14(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
frc = 0.5
msk = su.rndmask(s.shape, frc, dtype=np.float32)
s *= msk
lmbda = 1e-1
mu = 1e-2
# Create a random ℓ2 of gradient term weighting array. There is no
# need to extend this array to account for the AMS impulse filter
# since this is taken care of automatically by cucbpdn.cbpdngrdmsk
Wgrd = np.random.randn(M).astype(np.float32)
# Append a zero entry to the GradWeight array, corresponding to
# the impulse filter appended to the dictionary by cbpdn.AddMaskSim,
# since this is not done automatically by cbpdn.AddMaskSim
Wgrdi = np.hstack((Wgrd, np.zeros((1,))))
opt = cbpdn.ConvBPDNGradReg.Options({'Verbose': False,
'MaxMainIter': 50, 'AutoRho': {'Enabled': False}})
opt['GradWeight'] = Wgrdi
b = cbpdn.AddMaskSim(cbpdn.ConvBPDNGradReg, D, s, msk, lmbda, mu, opt)
X1 = b.solve()
opt['GradWeight'] = Wgrd
X2 = cucbpdn.cbpdngrdmsk(D, s, msk, lmbda, mu, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_11(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
frc = 0.5
msk = su.rndmask(s.shape, frc, dtype=np.float32)
s *= msk
lmbda = 1e-1
# Create a random ℓ1 term weighting array. There is no need to
# extend this array to account for the AMS impulse filter since
# this is taken care of automatically by cucbpdn.cbpdnmsk
Wl1 = np.random.randn(1, 1, M).astype(np.float32)
# Append a zero entry to the L1Weight array, corresponding to
# the impulse filter appended to the dictionary by cbpdn.AddMaskSim,
# since this is not done automatically by cbpdn.AddMaskSim
Wl1i = np.concatenate((Wl1, np.zeros(Wl1.shape[0:-1] + (1,))),
axis=-1)
opt = cbpdn.ConvBPDN.Options({'Verbose': False, 'MaxMainIter': 50,
'AutoRho': {'Enabled': False}})
opt['L1Weight'] = Wl1i
b = cbpdn.AddMaskSim(cbpdn.ConvBPDN, D, s, msk, lmbda, opt=opt)
X1 = b.solve()
opt['L1Weight'] = Wl1
X2 = cucbpdn.cbpdnmsk(D, s, msk, lmbda, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_01(self):
lmbda = 1e-1
opt = tvl2.TVL2Denoise.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 300, 'rho': 75*lmbda})
b = tvl2.TVL2Denoise(self.D, lmbda, opt)
X = b.solve()
assert(np.abs(b.itstat[-1].ObjFun - 32.875710674129564) < 1e-3)
assert(sm.mse(self.U,X) < 1e-3)
def test_01(self):
lmbda = 3
opt = tvl1.TVL1Denoise.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250})
b = tvl1.TVL1Denoise(self.D, lmbda, opt)
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 447.78101756451662) < 1e-6
assert sm.mse(self.U, X) < 1e-6
def test_02(self):
lmbda = 3
opt = tvl1.TVL1Deconv.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250, 'rho': 10.0})
b = tvl1.TVL1Deconv(np.ones((1, 1)), self.D, lmbda, opt, axes=(0, 1))
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 12364.029061174046) < 1e-5
assert sm.mse(self.U, X) < 1e-4
def test_02(self):
lmbda = 1e-1
opt = tvl2.TVL2Deconv.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250})
b = tvl2.TVL2Deconv(np.ones((1)), self.D, lmbda, opt, axes=(0,1,2))
X = b.solve()
assert(np.abs(b.itstat[-1].ObjFun - 567.72425227) < 1e-3)
assert(sm.mse(self.U,X) < 1e-3)
def test_01(self):
lmbda = 1e-1
opt = tvl2.TVL2Denoise.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250, 'rho': 10*lmbda})
b = tvl2.TVL2Denoise(self.D, lmbda, opt, axes=(0, 1, 2))
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 366.04267554965134) < 1e-3
assert sm.mse(self.U, X) < 1e-3
def test_02(self):
lmbda = 1e-1
opt = tvl2.TVL2Deconv.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250})
b = tvl2.TVL2Deconv(np.ones((1)), self.D, lmbda, opt, axes=(0, 1, 2))
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 567.72425227) < 1e-3
assert sm.mse(self.U, X) < 1e-3
def test_02(self):
lmbda = 1e-1
opt = tvl2.TVL2Deconv.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250})
b = tvl2.TVL2Deconv(np.ones((1)), self.D, lmbda, opt)
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 45.45958573088) < 1e-3
assert sm.mse(self.U, X) < 1e-3
def test_01(self):
lmbda = 1e-1
opt = tvl2.TVL2Denoise.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 300, 'rho': 75*lmbda})
b = tvl2.TVL2Denoise(self.D, lmbda, opt)
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 32.875710674129564) < 1e-3
assert sm.mse(self.U, X) < 1e-3
def test_01(self):
lmbda = 3
opt = tvl1.TVL1Denoise.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250})
b = tvl1.TVL1Denoise(self.D, lmbda, opt, axes=(0, 1, 2))
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 6219.6209699337605) < 1e-6
assert sm.mse(self.U, X) < 1e-6
def test_02(self):
lmbda = 1e-1
opt = tvl2.TVL2Deconv.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250})
b = tvl2.TVL2Deconv(np.ones((1)), self.D, lmbda, opt)
X = b.solve()
assert(np.abs(b.itstat[-1].ObjFun - 45.45958573088) < 1e-3)
assert(sm.mse(self.U,X) < 1e-3)
def test_31(self):
alpha = np.random.randn()
N = 8
M = 11
X0 = np.random.randn(N, M)
Ag = np.random.randn(4, N)
A = Ag.T.dot(Ag)
Bg = np.random.randn(M, 4)
B = Bg.dot(Bg.T)
C = A.dot(X0).dot(B) + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-12
LambdaA, QA = np.linalg.eigh(A)
LambdaB, QB = np.linalg.eigh(B)
X1 = linalg.solve_symmetric_sylvester((LambdaA, QA), (LambdaB, QB), C,
alpha)
assert mse(X0, X1) < 1e-12
def test_01(self):
lmbda = 1e-1
opt = tvl2.TVL2Denoise.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250, 'rho': 10*lmbda})
b = tvl2.TVL2Denoise(self.D, lmbda, opt, axes=(0,1,2))
X = b.solve()
assert(np.abs(b.itstat[-1].ObjFun - 366.04267554965134) < 1e-3)
assert(sm.mse(self.U,X) < 1e-3)
def test_02(self):
lmbda = 3
opt = tvl1.TVL1Deconv.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250, 'rho': 10.0})
b = tvl1.TVL1Deconv(np.ones((1, 1)), self.D, lmbda, opt)
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 831.88219947939172) < 1e-5
assert sm.mse(self.U, X) < 1e-4
def test_01(self):
N = 64
K = 5
L = 10
u = np.random.randn(N, K)
U = np.dot(u, u.T)
V = np.random.randn(N, N)
t = np.sort(np.abs(V).ravel())[V.size-L]
V[np.abs(V) < t] = 0
D = U + V
opt = rpca.RobustPCA.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250,
'AutoRho': {'Enabled': True}})
b = rpca.RobustPCA(D, None, opt)
X, Y = b.solve()
assert(np.abs(b.itstat[-1].ObjFun - 321.493968419) < 1e-6)
assert(sm.mse(U,X) < 5e-6)
assert(sm.mse(V,Y) < 1e-8)
def test_01(self):
N = 16
x = np.random.randn(N)
y = x.copy()
y[0] = 0
xe = np.abs(x[0])
e1 = metric.mae(x, y)
e2 = metric.mse(x, y)
assert np.abs(e1 - xe / N) < 1e-12
assert np.abs(e2 - (xe**2) / N) < 1e-12
def test_01(self):
lmbda = 3
opt = tvl1.TVL1Denoise.Options({
'Verbose': False,
'gEvalY': False,
'MaxMainIter': 250
})
b = tvl1.TVL1Denoise(self.D, lmbda, opt, axes=(0, 1))
X = b.solve()
assert (np.abs(b.itstat[-1].ObjFun - 6219.3241727233126) < 1e-6)
assert (sm.mse(self.U, X) < 1e-6)
def test_01(self):
lmbda = 1e-1
opt = tvl2.TVL2Denoise.Options({
'Verbose': False,
'gEvalY': False,
'MaxMainIter': 250,
'rho': 10 * lmbda
})
b = tvl2.TVL2Denoise(self.D, lmbda, opt, axes=(0, 1))
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 363.0802047) < 1e-3
assert sm.mse(self.U, X) < 1e-3
def test_01(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
lmbda = 1e-1
opt = cbpdn.ConvBPDN.Options({'Verbose': False, 'MaxMainIter': 50,
'AutoRho': {'Enabled': False}})
b = cbpdn.ConvBPDN(D, s, lmbda, opt)
X1 = b.solve()
X2 = cucbpdn.cbpdn(D, s, lmbda, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_08(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
lmbda = 1e-1
mu = 1e-2
Wl1 = np.random.randn(Nr, Nc, M).astype(np.float32)
opt = cbpdn.ConvBPDNGradReg.Options({'Verbose': False,
'MaxMainIter': 50, 'L1Weight': Wl1,
'AutoRho': {'Enabled': False}})
b = cbpdn.ConvBPDNGradReg(D, s, lmbda, mu, opt)
X1 = b.solve()
X2 = cucbpdn.cbpdngrd(D, s, lmbda, mu, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_10(self):
Nr = 32
Nc = 31
Nd = 5
M = 4
D = np.random.randn(Nd, Nd, M).astype(np.float32)
s = np.random.randn(Nr, Nc).astype(np.float32)
frc = 0.5
msk = su.rndmask(s.shape, frc, dtype=np.float32)
s *= msk
lmbda = 1e-1
opt = cbpdn.ConvBPDN.Options({'Verbose': False, 'MaxMainIter': 50,
'AutoRho': {'Enabled': False}})
b = cbpdn.AddMaskSim(cbpdn.ConvBPDN, D, s, msk, lmbda, opt=opt)
X1 = b.solve()
X2 = cucbpdn.cbpdnmsk(D, s, msk, lmbda, opt)
assert(sm.mse(X1, X2) < 1e-10)
def test_01(self):
N = 64
L = 20
x = np.cos(np.linspace(0, np.pi, N))[np.newaxis, :]
y = np.cos(np.linspace(0, np.pi, N))[:, np.newaxis]
U = x*y
V = np.random.randn(N, N)
t = np.sort(np.abs(V).ravel())[V.size-L]
V[np.abs(V) < t] = 0
D = U + V
lmbda = 0.1
opt = spline.SplineL1.Options({'Verbose': False, 'gEvalY': False,
'MaxMainIter': 250, 'RelStopTol': 5e-4,
'DFidWeight': V == 0,
'AutoRho': {'Enabled': True}})
b = spline.SplineL1(D, lmbda, opt)
X = b.solve()
assert np.abs(b.itstat[-1].ObjFun - 0.333606246) < 1e-6
assert sm.mse(U, X) < 1e-6