def test_2D(arpack_eigs, interface, x, num_evs, tol, atol, interactive=False):
from fvm import JadaInterface
from jadapy import jdqz
numpy.random.seed(1234)
jac_op = JadaInterface.JadaOp(interface.jacobian(x))
mass_op = JadaInterface.JadaOp(interface.mass_matrix())
alpha, beta = jdqz.jdqz(jac_op,
mass_op,
num_evs,
tol=tol,
subspace_dimensions=[20, 40],
target=0.1)
jdqz_eigs = numpy.array(sorted(alpha / beta, key=lambda x: abs(x)))
jdqz_eigs = jdqz_eigs[:num_evs]
assert_allclose(jdqz_eigs.real, arpack_eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqz_eigs.imag),
abs(arpack_eigs.imag),
rtol=0,
atol=atol)
if not interactive:
return x
fig, ax = plt.subplots()
ax.scatter(jdqz_eigs.real, jdqz_eigs.imag, marker='+')
plt.show()
def test_complex_shifted_prec_solve_2D(arpack_eigs,
interface,
x,
num_evs,
tol,
atol,
interactive=False):
from fvm import JadaInterface
from jadapy import jdqz
numpy.random.seed(1234)
jac_op = JadaInterface.JadaOp(interface.jacobian(x))
mass_op = JadaInterface.JadaOp(interface.mass_matrix())
jada_interface = JadaInterface.JadaInterface(interface,
jac_op,
mass_op,
len(x),
numpy.complex128,
preconditioned_solve=True,
shifted=True)
assert jada_interface.preconditioned_solve
assert jada_interface.shifted
alpha, beta, v = jdqz.jdqz(jac_op,
mass_op,
num_evs,
tol=tol,
subspace_dimensions=[20, 40],
arithmetic='complex',
return_eigenvectors=True,
interface=jada_interface)
check_eigenvalues(jac_op, mass_op, alpha / beta, v, num_evs, atol)
jdqz_eigs = numpy.array(sorted(alpha / beta, key=lambda x: abs(x)))
assert_allclose(jdqz_eigs.real, arpack_eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqz_eigs.imag),
abs(arpack_eigs.imag),
rtol=0,
atol=atol)
if not interactive:
return x
fig, ax = plt.subplots()
ax.scatter(jdqz_eigs.real, jdqz_eigs.imag, marker='+')
plt.show()
def arpack_eigs(numpy_interface, numpy_x, num_evs, tol, atol):
from fvm import JadaInterface
A_op = JadaInterface.JadaOp(numpy_interface.jacobian(numpy_x))
B_op = JadaInterface.JadaOp(numpy_interface.mass_matrix())
# A_mat = A_op.mat.todense()
# B_mat = B_op.mat.todense()
# eigs, v = scipy.linalg.eig(A_mat, B_mat, left=False, right=True)
eigs, v = sparse.linalg.eigs(A_op, num_evs, B_op, sigma=0.1, tol=tol)
check_eigenvalues(A_op, B_op, eigs, v, num_evs, atol)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
return eigs[:num_evs]