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pseudo_inverse.py
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Thu, Feb 20, 11:04

pseudo_inverse.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/>.
#
from copy import deepcopy as copy
import numpy as np
from numbers import Number
from rrompy.utilities.exception_manager import RROMPyWarning
__all__ = ["pseudoInverse"]
def pseudoInverse(A, rcond=-1, full=False):
"""
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate the generalized inverse of a matrix using its
singular-value decomposition (SVD) and including all
*large* singular values.
"""
if isinstance(A, Number):
if A == 0: return np.inf
return 1. / A
u, s, vt = np.linalg.svd(A.conjugate(), full_matrices=False)
if rcond < 0: rcond = len(A) * np.finfo(A.dtype).eps
cutoff = rcond * np.amax(s)
large = s > cutoff
rank = np.sum(large)
sinv = copy(s)
sinv = np.divide(1, s, where = large, out = sinv)
sinv[large == 0] = 0
res = (vt.T * sinv).dot(u.T)
if rank != min(*A.shape) and not full:
RROMPyWarning("The pseudo-inverse is not full rank.")
if full:
return res, [rank, s, rcond]
else:
return res

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