compress_matrix.py
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	# Copyright (C) 2018-2020 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.numerical.tensor_la import dot
	from rrompy.utilities.base.types import Np2D, Tuple, HFEng

	__all__ = ["compressMatrix"]

	def compressMatrix(A:Np2D, tol : float = 0., HFEngine : HFEng = None,
	is_state : bool = True) -> Tuple[Np2D, Np2D, float]:
	"""Compress matrix by SVD."""
	if HFEngine is None:
	_, s, U = np.linalg.svd(A)
	s, U = s ** 2., U.T.conj()
	else:
	s, U = np.linalg.eigh(HFEngine.innerProduct(A, A, is_state = is_state))
	s, U = s[::-1], U[:, ::-1]
	remove = np.where(s < tol * s[0])[0]
	ncut = len(s) if len(remove) == 0 else remove[0]
	sums = np.sum(s)
	s = s[: ncut] ** .5
	R = (U[:, : ncut].conj() * s).T
	U = dot(A, U[:, : ncut] * s ** -1.)
	return U, R, 1. - np.linalg.norm(s) / sums