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pseudo_inverse.py
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Created
Wed, May 29, 11:41
Size
1 KB
Mime Type
text/x-python
Expires
Fri, May 31, 11:41 (1 d, 23 h)
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blob
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Handle
17958995
Attached To
R6746 RationalROMPy
pseudo_inverse.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/>.
#
from
copy
import
deepcopy
as
copy
import
numpy
as
np
from
numbers
import
Number
from
rrompy.utilities.exception_manager
import
RROMPyException
__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
np
.
isclose
(
A
,
0.
):
return
np
.
inf
return
1.
/
A
A
=
A
.
conjugate
()
try
:
u
,
s
,
vt
=
np
.
linalg
.
svd
(
A
,
full_matrices
=
False
)
except
np
.
linalg
.
LinAlgError
as
e
:
raise
RROMPyException
(
e
)
if
rcond
<
0
:
rcond
=
len
(
A
)
*
np
.
finfo
(
A
.
dtype
)
.
eps
cutoff
=
rcond
*
np
.
amax
(
s
)
large
=
s
>
cutoff
sinv
=
copy
(
s
)
sinv
=
np
.
divide
(
1
,
s
,
where
=
large
,
out
=
sinv
)
sinv
[
~
large
]
=
0
res
=
(
vt
.
T
*
sinv
)
@
u
.
T
if
full
:
return
res
,
[
np
.
sum
(
large
),
s
,
rcond
]
else
:
return
res
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