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norm_utilities.py
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Fri, May 10, 17:21
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text/x-python
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Sun, May 12, 17:21 (1 d, 23 h)
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R6746 RationalROMPy
norm_utilities.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
abc
import
abstractmethod
import
numpy
as
np
from
copy
import
deepcopy
as
copy
from
rrompy.utilities.base.types
import
Np1D
,
Np2D
,
DictAny
from
rrompy.solver.linear_solver
import
setupSolver
from
rrompy.utilities.exception_manager
import
RROMPyException
__all__
=
[
'Np2DLike'
,
'Np2DLikeEye'
,
'Np2DLikeInv'
,
'Np2DLikeInvLowRank'
,
'normEngine'
]
@abstractmethod
class
Np2DLike
:
def
dot
(
self
,
u
:
Np2D
)
->
Np2D
:
pass
class
Np2DLikeEye
(
Np2DLike
):
def
dot
(
self
,
u
:
Np2D
)
->
Np2D
:
return
u
class
Np2DLikeInv
(
Np2DLike
):
def
__init__
(
self
,
K
:
Np2D
,
M
:
Np2D
,
solverType
:
str
,
solverArgs
:
DictAny
):
self
.
K
,
self
.
M
,
self
.
MH
=
K
,
M
,
M
.
T
.
conj
()
self
.
solver
,
self
.
solverArgs
=
setupSolver
(
solverType
,
solverArgs
)
def
dot
(
self
,
u
:
Np2D
)
->
Np2D
:
return
self
.
MH
.
dot
(
self
.
solver
(
self
.
K
,
self
.
M
.
dot
(
u
),
self
.
solverArgs
))
class
Np2DLikeInvLowRank
(
Np2DLike
):
def
__init__
(
self
,
K
:
Np2D
,
M
:
Np2D
,
solverType
:
str
,
solverArgs
:
DictAny
,
rank
:
int
,
oversampling
:
int
=
10
,
seed
:
int
=
420
):
if
rank
>
M
.
shape
[
1
]:
raise
RROMPyException
((
"Cannot select compressed rank larger than "
"original size."
))
if
oversampling
<
0
:
raise
RROMPyException
(
"Oversampling parameter must be positive."
)
HF
=
Np2DLikeInv
(
K
,
M
,
solverType
,
solverArgs
)
np
.
random
.
seed
(
seed
)
xs
=
np
.
random
.
randn
(
M
.
shape
[
1
],
rank
+
oversampling
)
samples
=
HF
.
dot
(
xs
)
Q
,
_
=
np
.
linalg
.
qr
(
samples
,
mode
=
"reduced"
)
R
=
HF
.
dot
(
Q
)
.
T
.
conj
()
# assuming HF (i.e. K) hermitian...
U
,
s
,
Vh
=
np
.
linalg
.
svd
(
R
)
self
.
L
=
Q
.
dot
(
U
[:,
:
rank
])
*
s
[:
rank
]
self
.
R
=
Vh
[:
rank
,
:]
def
dot
(
self
,
u
:
Np2D
)
->
Np2D
:
return
self
.
L
.
dot
(
self
.
R
.
dot
(
u
))
class
normEngine
:
def
__init__
(
self
,
energyNormMatrix
:
Np2D
):
self
.
energyNormMatrix
=
copy
(
energyNormMatrix
)
def
innerProduct
(
self
,
u
:
Np2D
,
v
:
Np2D
,
onlyDiag
:
bool
=
False
)
->
Np2D
:
if
not
isinstance
(
u
,
(
np
.
ndarray
,)):
u
=
u
.
data
if
not
isinstance
(
v
,
(
np
.
ndarray
,)):
v
=
v
.
data
if
onlyDiag
:
return
np
.
sum
(
self
.
energyNormMatrix
.
dot
(
u
)
*
v
.
conj
(),
axis
=
0
)
return
v
.
T
.
conj
()
.
dot
(
self
.
energyNormMatrix
.
dot
(
u
))
def
norm
(
self
,
u
:
Np2D
)
->
Np1D
:
return
np
.
power
(
np
.
abs
(
self
.
innerProduct
(
u
,
u
,
onlyDiag
=
True
)),
.
5
)
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