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enable multiple vector rayleigh_quotient_iteration

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Jan Petykiewicz 2019-11-24 22:50:03 -08:00
parent 3b57619c2f
commit f0ef31c25d
1 changed files with 20 additions and 14 deletions
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34
meanas/eigensolvers.py
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@ -34,7 +34,7 @@ def power_iteration(operator: sparse.spmatrix,
def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperator, def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperator,
guess_vector: numpy.ndarray, guess_vectors: numpy.ndarray,
iterations: int = 40, iterations: int = 40,
tolerance: float = 1e-13, tolerance: float = 1e-13,
solver=None, solver=None,
@ -42,15 +42,21 @@ def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperato
""" """
Use Rayleigh quotient iteration to refine an eigenvector guess. Use Rayleigh quotient iteration to refine an eigenvector guess.
:param operator: Matrix to analyze. TODO:
:param guess_vector: Eigenvector to refine. Need to test this for more than one guess_vectors.
:param iterations: Maximum number of iterations to perform. Default 40.
:param tolerance: Stop iteration if (A - I*eigenvalue) @ v < tolerance. Args:
Default 1e-13. operator: Matrix to analyze.
:param solver: Solver function of the form x = solver(A, b). guess_vectors: Eigenvectors to refine.
By default, use scipy.sparse.spsolve for sparse matrices and iterations: Maximum number of iterations to perform. Default 40.
scipy.sparse.bicgstab for general LinearOperator instances. tolerance: Stop iteration if `(A - I*eigenvalue) @ v < num_vectors * tolerance`,
:return: (eigenvalue, eigenvector) Default 1e-13.
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.
Returns:
(eigenvalues, eigenvectors)
""" """
try: try:
_test = operator - sparse.eye(operator.shape[0]) _test = operator - sparse.eye(operator.shape[0])
@ -64,16 +70,16 @@ def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperato
if solver is None: if solver is None:
solver = lambda A, b: spalg.bicgstab(A, b)[0] solver = lambda A, b: spalg.bicgstab(A, b)[0]
v = guess_vector v = numpy.atleast_2d(guess_vectors)
v /= norm(v) 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) < v.shape[1] * tolerance:
break break
shifted_operator = operator - shift(eigval) shifted_operator = operator - shift(eigval)
v = solver(shifted_operator, v) v = solver(shifted_operator, v)
v /= norm(v) v /= norm(v, axis=0)
return eigval, v return eigval, v
@ -99,7 +105,7 @@ def signed_eigensolve(operator: sparse.spmatrix or spalg.LinearOperator,
Shift by the absolute value of the largest eigenvalue, then find a few of the Shift by the absolute value of the largest eigenvalue, then find a few of the
largest-magnitude (shifted) eigenvalues. A positive shift ensures that we find the largest-magnitude (shifted) eigenvalues. A positive shift ensures that we find the
largest _positive_ eigenvalues, since any negative eigenvalues will be shifted to the largest _positive_ eigenvalues, since any negative eigenvalues will be shifted to the
range 0 >= neg_eigval + abs(lm_eigval) > abs(lm_eigval) range `0 >= neg_eigval + abs(lm_eigval) > abs(lm_eigval)`
''' '''
shift = numpy.abs(lm_eigval) shift = numpy.abs(lm_eigval)
if negative: if negative: