rayleigh_quotient_iteration.py
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	# Copyright (C) 2018 by the RROMPy authors
	#
	# This file is part of RROMPy.
	#
	# RROMPy is free software: you can redistribute it and/or modify
	# it under the terms of the GNU Lesser General Public License as published by
	# the Free Software Foundation, either version 3 of the License, or
	# (at your option) any later version.
	#
	# RROMPy is distributed in the hope that it will be useful,
	# but WITHOUT ANY WARRANTY; without even the implied warranty of
	# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	# GNU Lesser General Public License for more details.
	#
	# You should have received a copy of the GNU Lesser General Public License
	# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
	#

	import numpy as np
	from rrompy.utilities.base.types import Np1D, Np2D, DictAny
	from .tensor_la import dot, solve

	__all__ = ['rayleighQuotientIteration']

	def rayleighQuotientIteration(A:Np2D, v0:Np1D, M:Np2D, solver:callable,
	solverArgs:DictAny, sigma : float = 0.,
	nIterP : int = 10, nIterR : int = 10) -> float:
	nIterP = min(nIterP, len(v0) // 2)
	nIterR = min(nIterR, (len(v0) + 1) // 2)
	v0 /= dot(dot(M, v0).T, v0.conj()) ** .5
	for j in range(nIterP):
	v0 = solve(A - sigma * M, dot(M, v0), solver, solverArgs)
	v0 /= dot(dot(M, v0).T, v0.conj()) ** .5
	l0 = dot(A.dot(v0).T, v0.conj())
	for j in range(nIterR):
	v0 = solve(A - l0 * M, dot(M, v0), solver, solverArgs)
	v0 /= dot(dot(M, v0).T, v0.conj()) ** .5
	l0 = dot(A.dot(v0).T, v0.conj())
	if np.isnan(l0): l0 = np.finfo(float).eps
	return np.abs(l0)