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Update Rayleigh quotient iteration to allow arbitrary linear operators

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jan 2017-12-17 20:51:34 -08:00
parent 4aa2d07cef
commit d09eff990f
1 changed files with 22 additions and 4 deletions
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26
fdfd_tools/eigensolvers.py
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@ -33,10 +33,11 @@ def power_iteration(operator: sparse.spmatrix,
return lm_eigval, v return lm_eigval, v
def rayleigh_quotient_iteration(operator: sparse.spmatrix, def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperator,
guess_vector: numpy.ndarray, guess_vector: numpy.ndarray,
iterations: int = 40, iterations: int = 40,
tolerance: float = 1e-13, tolerance: float = 1e-13,
solver=None,
) -> Tuple[complex, numpy.ndarray]: ) -> Tuple[complex, numpy.ndarray]:
""" """
Use Rayleigh quotient iteration to refine an eigenvector guess. Use Rayleigh quotient iteration to refine an eigenvector guess.
@ -46,16 +47,33 @@ def rayleigh_quotient_iteration(operator: sparse.spmatrix,
:param iterations: Maximum number of iterations to perform. Default 40. :param iterations: Maximum number of iterations to perform. Default 40.
:param tolerance: Stop iteration if (A - I*eigenvalue) @ v < tolerance. :param tolerance: Stop iteration if (A - I*eigenvalue) @ v < tolerance.
Default 1e-13. Default 1e-13.
:param solver: Solver function of the form x = solver(A, b).
By default, use scipy.sparse.spsolve for sparse matrices and
scipy.sparse.bicgstab for general LinearOperator instances.
:return: (eigenvalue, eigenvector) :return: (eigenvalue, eigenvector)
""" """
try:
_test = operator - sparse.eye(operator.shape)
shift = lambda eigval: eigval * sparse.eye(operator.shape[0])
if solver is None:
solver = spalg.spsolve
except TypeError:
shift = lambda eigval: spalg.LinearOperator(shape=operator.shape,
dtype=operator.dtype,
matvec=lambda v: eigval * v)
if solver is None:
solver = lambda A, b: spalg.bicgstab(A, b)[0]
v = guess_vector v = guess_vector
v /= norm(v)
for _ in range(iterations): for _ in range(iterations):
eigval = v.conj() @ operator @ v eigval = v.conj() @ (operator @ v)
if norm(operator @ v - eigval * v) < tolerance: if norm(operator @ v - eigval * v) < tolerance:
break break
v = spalg.spsolve(operator - eigval * sparse.eye(operator.shape[0]), v)
v /= norm(v)
shifted_operator = operator - shift(eigval)
v = solver(shifted_operator, v)
v /= norm(v)
return eigval, v return eigval, v