def test_PrimalDualHybridGradient(self):
n = 5
lamda = 0.1
A, x_numpy, y = self.Ax_y_setup(n, lamda)
# Compute step-size
lipschitz = np.linalg.svd(np.matmul(A.T, A), compute_uv=False)[0]
tau = 1.0 / lipschitz
sigma = 1.0
x = np.zeros([n])
u = np.zeros([n])
alg_method = alg.PrimalDualHybridGradient(lambda alpha, u:
(u - alpha * y) /
(1 + alpha),
lambda alpha, x: x /
(1 + lamda * alpha),
lambda x: A @ x,
lambda x: A.T @ x,
x,
u,
tau,
sigma,
max_iter=1000)
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x, x_numpy)
def test_PrimalDualHybridGradient(self):
n = 5
A = np.random.random([n, n])
x_orig = np.random.random([n])
y = np.matmul(A, x_orig)
lamda = 1.0
x_truth = np.linalg.solve(
np.matmul(A.T, A) + lamda * np.eye(n), np.matmul(A.T, y))
# Compute step-size
lipschitz = np.linalg.svd(np.matmul(A.T, A), compute_uv=False)[0]
tau = 1.0 / lipschitz
sigma = 1.0
x = np.zeros([n])
u = np.zeros([n])
alg_method = alg.PrimalDualHybridGradient(lambda alpha, u:
(u - alpha * y) /
(1 + alpha),
lambda alpha, x: x /
(1 + lamda * alpha),
lambda x: np.matmul(A, x),
lambda x: np.matmul(A.T, x),
x,
u,
tau,
sigma,
max_iter=1000)
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x, x_truth, atol=1e-3, rtol=1e-3)