def test_gmres(self):
# Ensure repeatability
random.seed(0)
# For these small matrices, Householder and MGS GMRES should give the same result,
# and for symmetric (but possibly indefinite) matrices CR and GMRES should give same result
for maxiter in [1,2,3]:
for case, symm_case in zip(self.cases, self.symm_cases):
A = case['A']
b = case['b']
x0 = case['x0']
A_symm = symm_case['A']
b_symm = symm_case['b']
x0_symm = symm_case['x0']
# Test agreement between Householder and GMRES
(x, flag) = gmres_householder(A,b,x0=x0,maxiter=min(A.shape[0],maxiter))
(x2, flag2) = gmres_mgs(A,b,x0=x0,maxiter=min(A.shape[0],maxiter))
assert_array_almost_equal(x/norm(x), x2/norm(x2),
err_msg='Householder GMRES and MGS GMRES gave different results for small matrix')
assert_equal(flag, flag2,
err_msg='Householder GMRES and MGS GMRES returned different convergence flags for small matrix')
# Test agreement between GMRES and CR
if A_symm.shape[0] > 1:
residuals2 = []
(x2, flag2) = gmres_mgs(A_symm, b_symm, x0=x0_symm, maxiter=min(A.shape[0],maxiter),residuals=residuals2)
residuals3 = []
(x3, flag2) = cr(A_symm, b_symm, x0=x0_symm, maxiter=min(A.shape[0],maxiter),residuals=residuals3)
residuals2 = array(residuals2)
residuals3 = array(residuals3)
assert_array_almost_equal(residuals3/norm(residuals3), residuals2/norm(residuals2),
err_msg='CR and GMRES yield different residual vectors')
assert_array_almost_equal(x2/norm(x2), x3/norm(x3), err_msg='CR and GMRES yield different answers')
def test_gmres(self):
# Ensure repeatability
random.seed(0)
# For these small matrices, Householder and MGS GMRES should give the
# same result, and for symmetric (but possibly indefinite) matrices CR
# and GMRES should give same result
for maxiter in [1, 2, 3]:
for case, symm_case in zip(self.cases, self.symm_cases):
A = case['A']
b = case['b']
x0 = case['x0']
A_symm = symm_case['A']
b_symm = symm_case['b']
x0_symm = symm_case['x0']
# Test agreement between Householder and GMRES
(x, flag) = gmres_householder(A, b, x0=x0,
maxiter=min(A.shape[0], maxiter))
(x2, flag2) = gmres_mgs(A, b, x0=x0, maxiter=min(A.shape[0],
maxiter))
err_msg = ('Householder GMRES and MGS GMRES gave '
'different results for small matrix')
assert_array_almost_equal(x/norm(x), x2/norm(x2),
err_msg=err_msg)
err_msg = ('Householder GMRES and MGS GMRES returned '
'different convergence flags for small matrix')
assert_equal(flag, flag2, err_msg=err_msg)
# Test agreement between GMRES and CR
if A_symm.shape[0] > 1:
residuals2 = []
(x2, flag2) = gmres_mgs(A_symm, b_symm, x0=x0_symm,
maxiter=min(A.shape[0], maxiter),
residuals=residuals2)
residuals3 = []
(x3, flag2) = cr(A_symm, b_symm, x0=x0_symm,
maxiter=min(A.shape[0], maxiter),
residuals=residuals3)
residuals2 = array(residuals2)
residuals3 = array(residuals3)
err_msg = 'CR and GMRES yield different residual vectors'
assert_array_almost_equal(residuals3/norm(residuals3),
residuals2/norm(residuals2),
err_msg=err_msg)
err_msg = 'CR and GMRES yield different answers'
assert_array_almost_equal(x2/norm(x2), x3/norm(x3),
err_msg=err_msg)
def test_gmres(self):
for case in self.cases:
A = case['A']
b = case['b']
x0 = case['x0']
tol = case['tol']
mgsres = []
_ = gmres_mgs(A,
b,
x0,
residuals=mgsres,
tol=tol,
restrt=3,
maxiter=2)
hhres = []
_ = gmres_householder(A,
b,
x0,
residuals=hhres,
tol=tol,
restrt=3,
maxiter=2)
scipyres = []
normb = np.linalg.norm(b)
def cb(x):
scipyres.append(x * normb)
_ = sla.isolve.iterative.gmres(A,
b,
x0,
callback=cb,
callback_type='pr_norm',
tol=tol,
atol=0,
restrt=3,
maxiter=2)
assert_array_almost_equal(mgsres[1:], scipyres)
assert_array_almost_equal(hhres[1:], scipyres)