def test_minimal_residual(self):
# Ensure repeatability
random.seed(0)
self.definite_cases.extend(self.spd_cases)
for case in self.definite_cases:
A = case['A']
maxiter = case['maxiter']
x0 = rand(A.shape[0], )
b = zeros_like(x0)
reduction_factor = case['reduction_factor']
if A.dtype != complex:
# This function should always decrease (assuming zero RHS)
fvals = []
def callback(x):
fvals.append(
sqrt(dot(ravel(x), ravel(A * x.reshape(-1, 1)))))
#
(x, flag) = minimal_residual(A,
b,
x0=x0,
tol=1e-16,
maxiter=maxiter,
callback=callback)
actual_factor = (norm(ravel(b) - ravel(A * x.reshape(-1, 1))) /
norm(ravel(b) - ravel(A * x0.reshape(-1, 1))))
assert (actual_factor < reduction_factor)
if A.dtype != complex:
for i in range(len(fvals) - 1):
assert (fvals[i + 1] <= fvals[i])
# Test preconditioning
A = pyamg.gallery.poisson((10, 10), format='csr')
x0 = rand(A.shape[0], 1)
b = zeros_like(x0)
fvals = []
def callback(x):
fvals.append(sqrt(dot(ravel(x), ravel(A * x.reshape(-1, 1)))))
#
resvec = []
sa = pyamg.smoothed_aggregation_solver(A)
(x, flag) = minimal_residual(A,
b,
x0,
tol=1e-8,
maxiter=20,
residuals=resvec,
M=sa.aspreconditioner(),
callback=callback)
assert (resvec[-1] < 1e-8)
for i in range(len(fvals) - 1):
assert (fvals[i + 1] <= fvals[i])
def test_minimal_residual(self):
# Ensure repeatability
np.random.seed(0)
self.definite_cases.extend(self.spd_cases)
for case in self.definite_cases:
A = case['A']
maxiter = case['maxiter']
x0 = np.random.rand(A.shape[0],)
b = np.zeros_like(x0)
reduction_factor = case['reduction_factor']
if A.dtype != complex:
# This function should always decrease (assuming zero RHS)
fvals = []
def callback(x):
fvals.append(np.sqrt(np.dot(np.ravel(x),
np.ravel(A*x.reshape(-1, 1)))))
#
(x, flag) = minimal_residual(A, b, x0=x0,
tol=1e-16, maxiter=maxiter,
callback=callback)
actual_factor = (norm(np.ravel(b) -
np.ravel(A * x.reshape(-1, 1))) /
norm(np.ravel(b) -
np.ravel(A * x0.reshape(-1, 1))))
assert(actual_factor < reduction_factor)
if A.dtype != complex:
for i in range(len(fvals)-1):
assert(fvals[i+1] <= fvals[i])
# Test preconditioning
A = pyamg.gallery.poisson((10, 10), format='csr')
x0 = np.random.rand(A.shape[0], 1)
b = np.zeros_like(x0)
fvals = []
def callback(x):
fvals.append(np.sqrt(np.dot(np.ravel(x),
np.ravel(A*x.reshape(-1, 1)))))
#
resvec = []
sa = pyamg.smoothed_aggregation_solver(A)
(x, flag) = minimal_residual(A, b, x0, tol=1e-8, maxiter=20,
residuals=resvec, M=sa.aspreconditioner(),
callback=callback)
assert(resvec[-1]/resvec[0] < 1e-8)
for i in range(len(fvals)-1):
assert(fvals[i+1] <= fvals[i])