def test_complex_prec_solve_2D(arpack_eigs, interface, x, num_evs, tol, atol, interactive=False):
from fvm import JadaHYMLSInterface
from jadapy import ComplexEpetraInterface
from jadapy import jdqz
numpy.random.seed(1234)
jac_op = ComplexEpetraInterface.CrsMatrix(interface.jacobian(x))
mass_op = ComplexEpetraInterface.CrsMatrix(interface.mass_matrix())
jada_interface = JadaHYMLSInterface.ComplexJadaHYMLSInterface(interface.map, interface, preconditioned_solve=True)
alpha, beta = jdqz.jdqz(jac_op, mass_op, num_evs, tol=tol, subspace_dimensions=[20, 40],
interface=jada_interface)
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 solve(self, op, rhs, tol, maxit):
solver_parameters = self.parameters.sublist('Solver')
iterative_solver_parameters = solver_parameters.sublist(
'Iterative Solver')
iterative_solver_parameters.set('Convergence Tolerance',
tol if maxit > 1 else 1e-3)
# iterative_solver_parameters.set('Maximum Iterations', maxit)
solver_parameters.set('Complex', True)
x = EpetraInterface.Vector(rhs.real.Map(), 2)
y = EpetraInterface.Vector(rhs.real.Map(), 2)
x[:, 0] = rhs.real
x[:, 1] = rhs.imag
epetra_op = ComplexEpetraInterface.Operator(op)
if self.preconditioned_solve:
epetra_precop = ComplexJadaHYMLSPrecOp(
op, self.interface.preconditioner)
solver = HYMLS.Solver(epetra_op, epetra_precop, self.parameters)
else:
solver = HYMLS.Solver(epetra_op, epetra_op, self.parameters)
solver.ApplyInverse(x, y)
out = ComplexEpetraInterface.ComplexVector(y[:, 0], y[:, 1])
return out
def test_Complex_Epetra():
try:
from PyTrilinos import Epetra
from jadapy import ComplexEpetraInterface
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_Complex_Epetra_test_matrix(map, [n, n], dtype)
b1, b2 = generate_Complex_Epetra_test_matrix(map, [n, n], dtype)
interface = ComplexEpetraInterface.ComplexEpetraInterface(map)
alpha, beta = jdqz.jdqz(a2, b2, k, tol=tol, interface=interface)
jdqz_eigs = numpy.array(sorted(alpha / beta, key=lambda x: abs(x)))
eigs = scipy.linalg.eigvals(a1, b1)
eigs = numpy.array(sorted(eigs, key=lambda x: abs(x)))
eigs = eigs[:k]
assert_allclose(jdqz_eigs.real, eigs.real, rtol=0, atol=atol)
assert_allclose(abs(jdqz_eigs.imag), abs(eigs.imag), rtol=0, atol=atol)
def prec(self, x, *args):
y = EpetraInterface.Vector(x.real.Map(), 2)
z = EpetraInterface.Vector(x.real.Map(), 2)
y[:, 0] = x.real
y[:, 1] = x.imag
self.interface.preconditioner.ApplyInverse(y, z)
out = ComplexEpetraInterface.ComplexVector(z[:, 0], z[:, 1])
return out
def ApplyInverse(self, x, y):
self.prec.ApplyInverse(x, y)
assert x.NumVectors() == 2
# Create a view here because this is an Epetra.MultiVector.
y = EpetraInterface.Vector(Epetra.View, y, 0, y.NumVectors())
y = ComplexEpetraInterface.ComplexVector(y[:, 0], y[:, 1])
z = self.op.proj(y)
y *= 0.0
y += z
return 0
def solve(self, op, rhs, tol, maxit):
solver_parameters = self.parameters.sublist('Solver')
iterative_solver_parameters = solver_parameters.sublist(
'Iterative Solver')
iterative_solver_parameters.set('Convergence Tolerance',
tol if maxit > 1 else 1e-3)
# iterative_solver_parameters.set('Maximum Iterations', maxit)
solver_parameters.set('Complex', True)
solver_parameters.set('Use Bordering', True)
x = EpetraInterface.Vector(rhs.real.Map(), 2)
y = EpetraInterface.Vector(rhs.real.Map(), 2)
x[:, 0] = rhs.real
x[:, 1] = rhs.imag
m = op.Q.real.NumVectors()
Q = EpetraInterface.Vector(rhs.real.Map(), m * 2)
Q[:, 0:m] = op.Q.real
Q[:, m:2 * m] = op.Q.imag
Z = EpetraInterface.Vector(rhs.real.Map(), m * 2)
Z[:, 0:m] = op.Z.real
Z[:, m:2 * m] = op.Z.imag
epetra_op = ComplexEpetraInterface.Operator(ShiftedOperator(op))
if self.preconditioned_solve:
solver = HYMLS.Solver(epetra_op, self.interface.preconditioner,
self.parameters)
solver.SetBorder(Z, Q)
self.interface.preconditioner.Compute()
solver.ApplyInverse(x, y)
solver.UnsetBorder()
else:
raise Exception('Not implemented')
out = ComplexEpetraInterface.ComplexVector(y[:, 0], y[:, 1])
return out
def generate_Complex_Epetra_test_matrix(map, shape, dtype):
try:
from PyTrilinos import Epetra
from jadapy import ComplexEpetraInterface
except ImportError:
pytest.skip("Trilinos not found")
a1 = generate_test_matrix(shape, dtype)
a2 = ComplexEpetraInterface.CrsMatrix(Epetra.Copy, map, shape[1])
for i in range(shape[0]):
for j in range(shape[1]):
a2[i, j] = a1[i, j]
a2.FillComplete()
return a1, a2