def test_gmres_sparse(self):
# Create sparse non-Hermitian problem.
N = 100
A = self._create_sparse_nonherm_matrix(N, 5*N*(1+2j), 2)
rhs = np.ones( (N,1) )
x0 = np.zeros( (N,1) )
# Solve using GMRES.
tol = 1.0e-11
out = nm.gmres( A, rhs, x0, tol=tol )
# Make sure the method converged.
self.assertEqual(out['info'], 0)
# Check the residual.
res = rhs - A * out['xk']
self.assertAlmostEqual( np.linalg.norm(res) / np.linalg.norm(rhs),
0.0,
delta=tol )
def test_gmres_sparse(self):
# Create sparse non-Hermitian problem.
N = 100
A = self._create_sparse_nonherm_matrix(N, 5 * N * (1 + 2j), 2)
rhs = np.ones((N, 1))
x0 = np.zeros((N, 1))
# Solve using GMRES.
tol = 1.0e-11
out = nm.gmres(A, rhs, x0, tol=tol)
# Make sure the method converged.
self.assertEqual(out['info'], 0)
# Check the residual.
res = rhs - A * out['xk']
self.assertAlmostEqual(np.linalg.norm(res) / np.linalg.norm(rhs),
0.0,
delta=tol)
def test_gmres_sparse_Minner(self):
# Create sparse non-Hermitian problem.
N = 100
A = self._create_sparse_nonherm_matrix(N, 5 * N * (1 + 2j), 2)
rhs = np.ones((N, 1))
x0 = np.zeros((N, 1))
M = scipy.sparse.spdiags(range(1, N + 1), [0], N, N)
# Solve using GMRES.
tol = 1.0e-11
out = nm.gmres(A, rhs, x0, tol=tol, M=M)
# Make sure the method converged.
self.assertEqual(out['info'], 0)
# Check the residual.
res = rhs - A * out['xk']
Mres = M * res
norm_res = np.sqrt(np.dot(res.T.conj(), Mres))
self.assertAlmostEqual(norm_res / np.linalg.norm(rhs), 0.0, delta=tol)
def test_gmres_sparse_Minner(self):
# Create sparse non-Hermitian problem.
N = 100
A = self._create_sparse_nonherm_matrix(N, 5*N*(1+2j), 2)
rhs = np.ones( (N,1) )
x0 = np.zeros( (N,1) )
M = scipy.sparse.spdiags( range(1,N+1), [0], N, N)
# Solve using GMRES.
tol = 1.0e-11
out = nm.gmres( A, rhs, x0, tol=tol, M=M )
# Make sure the method converged.
self.assertEqual(out['info'], 0)
# Check the residual.
res = rhs - A * out['xk']
Mres = M*res
norm_res = np.sqrt(np.dot(res.T.conj(), Mres))
self.assertAlmostEqual( norm_res / np.linalg.norm(rhs),
0.0,
delta=tol )