def test_cornercase(self):
np.random.seed(1234)
# Rounding error may prevent convergence with tol=0 --- ensure
# that the return values in this case are correct, and no
# exceptions are raised
for n in [3, 5, 10, 100]:
A = 2 * eye(n)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
b = np.ones(n)
x, info = gcrotmk(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = gcrotmk(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
b = np.random.rand(n)
x, info = gcrotmk(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = gcrotmk(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
def test_arnoldi(self):
np.random.seed(1)
A = eye(2000) + rand(2000, 2000, density=5e-4)
b = np.random.rand(2000)
# The inner arnoldi should be equivalent to gmres
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag0 = gcrotmk(A,
b,
x0=zeros(A.shape[0]),
m=15,
k=0,
maxiter=1)
x1, flag1 = gmres(A,
b,
x0=zeros(A.shape[0]),
restart=15,
maxiter=1)
assert_equal(flag0, 1)
assert_equal(flag1, 1)
assert np.linalg.norm(A.dot(x0) - b) > 1e-3
assert_allclose(x0, x1)
def do_solve(**kw):
count[0] = 0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag = gcrotmk(A, b, x0=zeros(A.shape[0]), tol=1e-14, **kw)
count_0 = count[0]
assert_(allclose(A @ x0, b, rtol=1e-12, atol=1e-12), norm(A @ x0 - b))
return x0, count_0
def test_nans(self):
A = eye(3, format='lil')
A[1, 1] = np.nan
b = np.ones(3)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = gcrotmk(A, b, tol=0, maxiter=10)
assert_equal(info, 1)
def test_denormals(self):
# Check that no warnings are emitted if the matrix contains
# numbers for which 1/x has no float representation, and that
# the solver behaves properly.
A = np.array([[1, 2], [3, 4]], dtype=float)
A *= 100 * np.nextafter(0, 1)
b = np.array([1, 1])
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
xp, info = gcrotmk(A, b)
if info == 0:
assert_allclose(A.dot(xp), b)
def test_truncate(self):
np.random.seed(1234)
A = np.random.rand(30, 30) + np.eye(30)
b = np.random.rand(30)
for truncate in ['oldest', 'smallest']:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = gcrotmk(A,
b,
m=10,
k=10,
truncate=truncate,
tol=1e-4,
maxiter=200)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-3)