def test_GradientMethod(self):
n = 5
lamda = 0.1
A, x_numpy, y = self.Ax_y_setup(n, lamda)
# Compute step-size
lipschitz = np.linalg.svd(A.T @ A + lamda * np.eye(n),
compute_uv=False)[0]
alpha = 1.0 / lipschitz
for accelerate in [True, False]:
for proxg in [None, lambda alpha, x: x / (1 + lamda * alpha)]:
with self.subTest(accelerate=accelerate, proxg=proxg):
x_sigpy = np.zeros([n])
def gradf(x):
gradf_x = A.T @ (A @ x - y)
if proxg is None:
gradf_x += lamda * x
return gradf_x
alg_method = alg.GradientMethod(gradf,
x_sigpy,
alpha,
accelerate=accelerate,
proxg=proxg,
max_iter=1000)
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x_sigpy, x_numpy)
def test_GradientMethod(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) + lamda * np.eye(n),
compute_uv=False)[0]
alpha = 1.0 / lipschitz
# Gradient method
x = np.zeros([n])
alg_method = alg.GradientMethod(
lambda x: np.matmul(A.T, (np.matmul(A, x) - y)) + lamda * x,
x,
alpha,
accelerate=False)
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x, x_truth, atol=1, rtol=1e-3)
# Accelerated gradient method
x = np.zeros([n])
alg_method = alg.GradientMethod(
lambda x: np.matmul(A.T,
np.matmul(A, x) - y) + lamda * x,
x,
alpha,
accelerate=True)
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x, x_truth, atol=1, rtol=1e-3)
# Proximal gradient method
x = np.zeros([n])
alg_method = alg.GradientMethod(
lambda x: np.matmul(A.T,
np.matmul(A, x) - y),
x,
alpha,
accelerate=False,
proxg=lambda alpha, x: x / (1 + lamda * alpha))
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x, x_truth, atol=1, rtol=1e-3)
# Accelerated proximal gradient method
x = np.zeros([n])
alg_method = alg.GradientMethod(
lambda x: np.matmul(A.T,
np.matmul(A, x) - y),
x,
alpha,
proxg=lambda alpha, x: x / (1 + lamda * alpha),
accelerate=True)
while (not alg_method.done()):
alg_method.update()
npt.assert_allclose(x, x_truth, atol=1, rtol=1e-3)