Update Rayleigh quotient iteration to allow arbitrary linear operators
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@ -33,10 +33,11 @@ def power_iteration(operator: sparse.spmatrix,
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return lm_eigval, v
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def rayleigh_quotient_iteration(operator: sparse.spmatrix,
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def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperator,
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guess_vector: numpy.ndarray,
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iterations: int = 40,
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tolerance: float = 1e-13,
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solver=None,
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) -> Tuple[complex, numpy.ndarray]:
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"""
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Use Rayleigh quotient iteration to refine an eigenvector guess.
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@ -46,16 +47,33 @@ def rayleigh_quotient_iteration(operator: sparse.spmatrix,
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:param iterations: Maximum number of iterations to perform. Default 40.
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:param tolerance: Stop iteration if (A - I*eigenvalue) @ v < tolerance.
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Default 1e-13.
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:param solver: Solver function of the form x = solver(A, b).
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By default, use scipy.sparse.spsolve for sparse matrices and
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scipy.sparse.bicgstab for general LinearOperator instances.
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:return: (eigenvalue, eigenvector)
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"""
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try:
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_test = operator - sparse.eye(operator.shape)
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shift = lambda eigval: eigval * sparse.eye(operator.shape[0])
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if solver is None:
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solver = spalg.spsolve
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except TypeError:
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shift = lambda eigval: spalg.LinearOperator(shape=operator.shape,
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dtype=operator.dtype,
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matvec=lambda v: eigval * v)
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if solver is None:
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solver = lambda A, b: spalg.bicgstab(A, b)[0]
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v = guess_vector
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v /= norm(v)
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for _ in range(iterations):
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eigval = v.conj() @ operator @ v
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eigval = v.conj() @ (operator @ v)
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if norm(operator @ v - eigval * v) < tolerance:
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break
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v = spalg.spsolve(operator - eigval * sparse.eye(operator.shape[0]), v)
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v /= norm(v)
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shifted_operator = operator - shift(eigval)
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v = solver(shifted_operator, v)
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v /= norm(v)
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return eigval, v
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