def test_jdqr_smallest_magnitude_eigenvectors_with_mass(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
a = generate_test_matrix([n, n], dtype)
m = generate_mass_matrix([n, n], dtype)
alpha, v = jdqr.jdqr(a, num=k, tol=tol, M=m, return_eigenvectors=True)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: abs(x)))
jdqr_eigs = jdqr_eigs[:k]
eigs = scipy.linalg.eigvals(a, m)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
i = 0
while i < k:
ctype = numpy.dtype(numpy.dtype(dtype).char.upper())
if dtype != ctype and alpha[i].imag:
assert norm(a @ v[:, i] - alpha[i].real * m @ v[:, i] + alpha[i].imag * m @ v[:, i+1]) < atol
assert norm(a @ v[:, i+1] - alpha[i].imag * m @ v[:, i] - alpha[i].real * m @ v[:, i+1]) < atol
i += 2
else:
assert norm(a @ v[:, i] - alpha[i] * m @ v[:, i]) < atol
i += 1
def test_Epetra_lowdim():
try:
from PyTrilinos import Epetra
from jadapy import EpetraInterface
except ImportError:
pytest.skip("Trilinos not found")
dtype = numpy.float64
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 2
comm = Epetra.PyComm()
map = Epetra.Map(n, 0, comm)
a1, a2 = generate_Epetra_test_matrix(map, [n, n], dtype)
interface = EpetraInterface.EpetraInterface(map)
alpha = jdqr.jdqr(a2, k, Target.LargestMagnitude, tol=tol, subspace_dimensions=[10, 18], interface=interface)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: -abs(x)))
eigs = scipy.linalg.eigvals(a1)
eigs = numpy.array(sorted(eigs, key=lambda x: -abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_jdqr_smallest_magnitude_initial_subspace(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
a = generate_test_matrix([n, n], dtype)
alpha, q = jdqr.jdqr(a, num=k, tol=tol, return_subspace=True)
alpha = jdqr.jdqr(a, num=k, tol=tol, initial_subspace=q)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: abs(x)))
jdqr_eigs = jdqr_eigs[:k]
eigs = scipy.linalg.eigvals(a)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_jdqr_largest_magnitude(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
a = generate_test_matrix([n, n], dtype)
alpha = jdqr.jdqr(a, k, Target.LargestMagnitude, tol=tol)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: -abs(x)))
eigs = scipy.linalg.eigvals(a)
eigs = numpy.array(sorted(eigs, key=lambda x: -abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_jdqr_smallest_imag(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
a = generate_test_matrix([n, n], dtype)
alpha = jdqr.jdqr(a, k, Target.SmallestImaginaryPart, tol=tol, arithmetic='complex')
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: x.imag))
eigs = scipy.linalg.eigvals(a)
eigs = numpy.array(sorted(eigs, key=lambda x: x.imag))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_jdqr_smallest_magnitude_with_mass(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
a = generate_test_matrix([n, n], dtype)
m = generate_mass_matrix([n, n], dtype)
alpha = jdqr.jdqr(a, num=k, tol=tol, M=m)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: abs(x)))
eigs = scipy.linalg.eigvals(a, m)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_jdqr_largest_magnitude_lowdim_with_mass(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 2
a = generate_test_matrix([n, n], dtype)
m = generate_mass_matrix([n, n], dtype)
alpha = jdqr.jdqr(a, k, Target.LargestMagnitude, tol=tol, subspace_dimensions=[10, 18], M=m)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: -abs(x)))
eigs = scipy.linalg.eigvals(a, m)
eigs = numpy.array(sorted(eigs, key=lambda x: -abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_Epetra_eigenvectors():
try:
from PyTrilinos import Epetra
from jadapy import EpetraInterface
except ImportError:
pytest.skip("Trilinos not found")
dtype = numpy.float64
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
comm = Epetra.PyComm()
map = Epetra.Map(n, 0, comm)
a1, a2 = generate_Epetra_test_matrix(map, [n, n], dtype)
interface = EpetraInterface.EpetraInterface(map)
alpha, v = jdqr.jdqr(a2, num=k, tol=tol, return_eigenvectors=True, interface=interface)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: abs(x)))
jdqr_eigs = jdqr_eigs[:k]
eigs = scipy.linalg.eigvals(a1)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
i = 0
while i < k:
if alpha[i].imag:
assert norm(a2 @ v[:, i] - v[:, i] * alpha[i].real + v[:, i+1] * alpha[i].imag) < atol
assert norm(a2 @ v[:, i+1] - v[:, i] * alpha[i].imag - v[:, i+1] * alpha[i].real) < atol
i += 2
else:
assert norm(a2 @ v[:, i] - v[:, i] * alpha[i].real) < atol
i += 1
def test_jdqr_prec(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 5
a = generate_test_matrix([n, n], dtype)
inv = scipy.sparse.linalg.spilu(scipy.sparse.csc_matrix(a))
def _prec(x, *args):
return inv.solve(x)
alpha = jdqr.jdqr(a, num=k, tol=tol, prec=_prec)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: abs(x)))
eigs = scipy.linalg.eigvals(a)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
eigs = eigs[:k]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def test_jdqr_largest_imag_real(dtype):
numpy.random.seed(1234)
tol = numpy.finfo(dtype).eps * 1e3
atol = tol * 10
n = 20
k = 6
a = generate_test_matrix([n, n], dtype)
alpha = jdqr.jdqr(a, k, Target.LargestImaginaryPart, tol=tol)
jdqr_eigs = numpy.array(sorted(alpha, key=lambda x: -x.imag))
eigs = scipy.linalg.eigvals(a)
eigs = numpy.array(sorted(eigs, key=lambda x: -x.imag))
eigs = eigs[:k]
# In the real case, we store complex conjugate eigenpairs, so only
# at least half of the eigenvalues are correct
eigs = eigs[:k // 2]
jdqr_eigs = jdqr_eigs[:k // 2]
assert_allclose(jdqr_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqr_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)