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reduced_basis_pivoted.py
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R6746 RationalROMPy
reduced_basis_pivoted.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
.generic_pivoted_approximant
import
GenericPivotedApproximant
from
rrompy.hfengines.base
import
MarginalProxyEngine
from
rrompy.reduction_methods.trained_model
import
(
TrainedModelPivotedData
,
TrainedModelPivotedReducedBasis
as
tModel
)
from
rrompy.reduction_methods.base.reduced_basis_utils
import
\
projectAffineDecomposition
from
rrompy.utilities.base.types
import
(
Np1D
,
Np2D
,
List
,
ListAny
,
Tuple
,
DictAny
,
HFEng
,
paramVal
,
sampList
)
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
,
freepar
as
fp
from
rrompy.utilities.numerical
import
customPInv
from
rrompy.utilities.exception_manager
import
(
RROMPyWarning
,
RROMPyException
,
RROMPyAssert
)
__all__
=
[
'ReducedBasisPivoted'
]
class
ReducedBasisPivoted
(
GenericPivotedApproximant
):
"""
ROM pivoted RB approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
directionPivot(optional): Pivot components. Defaults to [0].
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'R': rank for pivot Galerkin projection; defaults to prod(S);
- 'PODTolerance': tolerance for pivot snapshots POD; defaults to
-1;
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation; allowed values include 'MONOMIAL', 'CHEBYSHEV'
and 'LEGENDRE'; defaults to 'MONOMIAL';
- 'MMarginal': degree of marginal interpolant; defaults to 0;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 0, i.e. identity;
- 'interpRcondMarginal': tolerance for marginal interpolation;
defaults to None.
Defaults to empty dict.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
directionPivot: Pivot components.
mus: Array of snapshot parameters.
approxRadius: Dummy radius of approximant (i.e. distance from mu0 to
farthest sample point).
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'R': rank for Galerkin projection;
- 'PODTolerance': tolerance for snapshots POD;
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation;
- 'MMarginal': degree of marginal interpolant;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'interpRcondMarginal': tolerance for marginal interpolation.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator.
POD: Whether to compute POD of snapshots.
S: Total number of pivot samples current approximant relies upon.
samplerPivot: Pivot sample point generator.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
R: Rank for Galerkin projection.
PODTolerance: Tolerance for pivot snapshots POD.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
MMarginal: Degree of marginal interpolant.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
interpRcondMarginal: Tolerance for marginal interpolation.
muBoundsPivot: list of bounds for pivot parameter values.
muBoundsMarginal: list of bounds for marginal parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
As: List of sparse matrices (in CSC format) representing coefficients
of linear system matrix.
bs: List of numpy vectors representing coefficients of linear system
RHS.
ARBs: List of sparse matrices (in CSC format) representing coefficients
of compressed linear system matrix.
bRBs: List of numpy vectors representing coefficients of compressed
linear system RHS.
"""
def
__init__
(
self
,
HFEngine
:
HFEng
,
mu0
:
paramVal
=
None
,
directionPivot
:
ListAny
=
[
0
],
approxParameters
:
DictAny
=
{},
verbosity
:
int
=
10
,
timestamp
:
bool
=
True
):
self
.
_preInit
()
self
.
_addParametersToList
([
"R"
,
"PODTolerance"
],
[
1
,
-
1
])
super
()
.
__init__
(
HFEngine
=
HFEngine
,
mu0
=
mu0
,
directionPivot
=
directionPivot
,
approxParameters
=
approxParameters
,
verbosity
=
verbosity
,
timestamp
=
timestamp
)
self
.
_postInit
()
@property
def
S
(
self
):
"""Value of S."""
return
self
.
_S
@S.setter
def
S
(
self
,
S
):
GenericPivotedApproximant
.
S
.
fset
(
self
,
S
)
if
not
hasattr
(
self
,
"_R"
):
self
.
_R
=
np
.
prod
(
self
.
S
)
*
np
.
prod
(
self
.
SMarginal
)
@property
def
R
(
self
):
"""Value of R. Its assignment may change S."""
return
self
.
_R
@R.setter
def
R
(
self
,
R
):
if
R
<
0
:
raise
RROMPyException
(
"R must be non-negative."
)
self
.
_R
=
R
self
.
_approxParameters
[
"R"
]
=
self
.
R
if
(
hasattr
(
self
,
"_S"
)
and
hasattr
(
self
,
"_SMarginal"
)
and
np
.
prod
(
self
.
S
)
*
np
.
prod
(
self
.
SMarginal
)
<
self
.
R
):
RROMPyWarning
((
"Prescribed S and SMarginal are too small. "
"Decreasing R."
))
self
.
R
=
np
.
prod
(
self
.
S
)
*
np
.
prod
(
self
.
SMarginal
)
@property
def
PODTolerance
(
self
):
"""Value of PODTolerance."""
return
self
.
_PODTolerance
@PODTolerance.setter
def
PODTolerance
(
self
,
PODTolerance
):
self
.
_PODTolerance
=
PODTolerance
self
.
_approxParameters
[
"PODTolerance"
]
=
self
.
PODTolerance
def
_setupProjectionMatrix
(
self
):
"""Compute projection matrix."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot setup numerator."
)
vbMng
(
self
,
"INIT"
,
"Starting computation of projection matrix."
,
7
)
if
self
.
POD
:
U
,
s
,
_
=
np
.
linalg
.
svd
(
self
.
samplingEngine
.
RPODCoalesced
)
s
=
s
**
2.
else
:
Gramian
=
self
.
HFEngine
.
innerProduct
(
self
.
samplingEngine
.
samplesCoalesced
,
self
.
samplingEngine
.
samplesCoalesced
)
U
,
s
,
_
=
np
.
linalg
.
svd
(
Gramian
)
nsamples
=
self
.
samplingEngine
.
samplesCoalesced
.
shape
[
1
]
snorm
=
np
.
cumsum
(
s
[::
-
1
])
/
np
.
sum
(
s
)
nPODTrunc
=
min
(
nsamples
-
np
.
argmax
(
snorm
>
self
.
PODTolerance
),
self
.
R
)
pMat
=
self
.
samplingEngine
.
samplesCoalesced
.
dot
(
U
[:,
:
nPODTrunc
])
vbMng
(
self
,
"MAIN"
,
"Assembling {}x{} projection matrix from {} samples."
.
format
(
*
(
pMat
.
shape
),
nsamples
),
5
)
vbMng
(
self
,
"DEL"
,
"Done computing projection matrix."
,
7
)
return
pMat
def
_setupAffineBlocks
(
self
):
"""Compute list of marginalized affine blocks of system."""
hasAs
=
hasattr
(
self
,
"AsList"
)
and
self
.
AsList
is
not
None
hasbs
=
hasattr
(
self
,
"bsList"
)
and
self
.
bsList
is
not
None
if
hasAs
and
hasbs
:
return
vbMng
(
self
,
"INIT"
,
"Computing affine blocks of system."
,
10
)
mu0Eff
=
self
.
mu0
.
data
[
0
,
self
.
directionPivot
]
if
not
hasAs
:
self
.
AsList
=
[
None
]
*
len
(
self
.
musMarginal
)
if
not
hasbs
:
self
.
bsList
=
[
None
]
*
len
(
self
.
musMarginal
)
for
k
,
muM
in
enumerate
(
self
.
musMarginal
):
muEff
=
[
fp
]
*
self
.
npar
for
jj
,
kk
in
enumerate
(
self
.
directionMarginal
):
muEff
[
kk
]
=
muM
(
0
,
jj
)
MEnginek
=
MarginalProxyEngine
(
self
.
HFEngine
,
muEff
)
if
not
hasAs
:
self
.
AsList
[
k
]
=
MEnginek
.
affineLinearSystemA
(
mu0Eff
,
self
.
scaleFactorPivot
)
if
not
hasbs
:
self
.
bsList
[
k
]
=
MEnginek
.
affineLinearSystemb
(
mu0Eff
,
self
.
scaleFactorPivot
)
vbMng
(
self
,
"DEL"
,
"Done computing affine blocks."
,
10
)
def
setupApprox
(
self
):
"""Compute RB projection matrix."""
if
self
.
checkComputedApprox
():
return
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot setup approximant."
)
vbMng
(
self
,
"INIT"
,
"Setting up {}."
.
format
(
self
.
name
()),
5
)
self
.
computeScaleFactor
()
self
.
computeSnapshots
()
self
.
_setupAffineBlocks
()
pMat
=
self
.
_setupProjectionMatrix
()
ARBsList
,
bRBsList
=
self
.
assembleReducedSystemMarginal
(
pMat
)
if
self
.
trainedModel
is
None
:
self
.
trainedModel
=
tModel
()
self
.
trainedModel
.
verbosity
=
self
.
verbosity
self
.
trainedModel
.
timestamp
=
self
.
timestamp
data
=
TrainedModelPivotedData
(
self
.
trainedModel
.
name
(),
self
.
mu0
,
pMat
,
self
.
scaleFactor
,
self
.
HFEngine
.
rescalingExp
,
self
.
directionPivot
)
data
.
musPivot
=
copy
(
self
.
musPivot
)
data
.
musMarginal
=
copy
(
self
.
musMarginal
)
self
.
trainedModel
.
data
=
data
else
:
self
.
trainedModel
=
self
.
trainedModel
self
.
trainedModel
.
data
.
projMat
=
copy
(
pMat
)
self
.
trainedModel
.
data
.
marginalInterp
=
self
.
_setupMarginalInterp
()
self
.
trainedModel
.
data
.
ARBsList
=
ARBsList
self
.
trainedModel
.
data
.
bRBsList
=
bRBsList
self
.
trainedModel
.
data
.
approxParameters
=
copy
(
self
.
approxParameters
)
vbMng
(
self
,
"DEL"
,
"Done setting up approximant."
,
5
)
def
assembleReducedSystemMarginal
(
self
,
pMat
:
sampList
=
None
)
\
->
Tuple
[
List
[
List
[
Np2D
]],
List
[
List
[
Np1D
]]]:
"""Build affine blocks of RB linear system through projections."""
if
pMat
is
None
:
self
.
setupApprox
()
ARBsList
=
self
.
trainedModel
.
data
.
ARBsList
bRBsList
=
self
.
trainedModel
.
data
.
bRBsList
else
:
vbMng
(
self
,
"INIT"
,
"Projecting affine terms of HF model."
,
10
)
ARBsList
=
[
None
]
*
len
(
self
.
musMarginal
)
bRBsList
=
[
None
]
*
len
(
self
.
musMarginal
)
for
k
,
(
As
,
bs
,
sample
)
in
enumerate
(
zip
(
self
.
AsList
,
self
.
bsList
,
self
.
samplingEngine
.
samples
)):
compLocal
=
self
.
HFEngine
.
innerProduct
(
sample
,
pMat
)
projList
=
sample
.
dot
(
customPInv
(
compLocal
))
ARBsList
[
k
],
bRBsList
[
k
]
=
projectAffineDecomposition
(
As
,
bs
,
projList
)
vbMng
(
self
,
"DEL"
,
"Done projecting affine terms."
,
10
)
return
ARBsList
,
bRBsList
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