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rational_interpolant_greedy_pivoted.py
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R6746 RationalROMPy
rational_interpolant_greedy_pivoted.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
.generic_pivoted_approximant
import
(
GenericPivotedApproximantBase
,
GenericPivotedApproximantNoMatch
,
GenericPivotedApproximantPolyMatch
,
GenericPivotedApproximantPoleMatch
)
from
.gather_pivoted_approximant
import
gatherPivotedApproximant
from
rrompy.reduction_methods.standard.greedy.rational_interpolant_greedy
\
import
RationalInterpolantGreedy
from
rrompy.reduction_methods.standard.greedy.generic_greedy_approximant
\
import
pruneSamples
from
rrompy.utilities.base.types
import
Np1D
,
paramList
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.utilities.base.decorators
import
(
get_is_affine
,
get_is_mu_independent
)
from
rrompy.utilities.poly_fitting.polynomial
import
polyvander
as
pv
from
rrompy.utilities.poly_fitting.piecewise_linear
import
sparsekinds
as
sk
from
rrompy.utilities.exception_manager
import
(
RROMPyException
,
RROMPyAssert
,
RROMPyWarning
)
from
rrompy.parameter
import
emptyParameterList
from
rrompy.utilities.parallel
import
(
masterCore
,
poolRank
,
indicesScatter
,
isend
,
recv
)
__all__
=
[
'RationalInterpolantGreedyPivotedNoMatch'
,
'RationalInterpolantGreedyPivotedPolyMatch'
,
'RationalInterpolantGreedyPivotedPoleMatch'
]
class
RationalInterpolantGreedyPivotedBase
(
GenericPivotedApproximantBase
,
RationalInterpolantGreedy
):
def
__init__
(
self
,
*
args
,
**
kwargs
):
self
.
_preInit
()
self
.
_addParametersToList
(
toBeExcluded
=
[
"MAuxiliary"
,
"NAuxiliary"
])
super
()
.
__init__
(
*
args
,
**
kwargs
)
if
self
.
nparPivot
>
1
:
self
.
HFEngine
.
_ignoreResidues
=
1
self
.
_postInit
()
@property
def
tModelType
(
self
):
if
hasattr
(
self
,
"_temporaryPivot"
):
return
RationalInterpolantGreedy
.
tModelType
.
fget
(
self
)
return
super
()
.
tModelType
@property
def
MAuxiliary
(
self
):
return
0
@property
def
NAuxiliary
(
self
):
return
0
def
_polyvanderAuxiliary
(
self
,
mus
,
deg
,
*
args
,
**
kwargs
):
degEff
=
[
0
]
*
self
.
npar
degEff
[
self
.
directionPivot
[
0
]]
=
deg
[
0
]
return
pv
(
mus
,
degEff
,
*
args
,
**
kwargs
)
def
_marginalizeTrainedModel
(
self
):
del
self
.
_temporaryPivot
self
.
trainedModel
.
data
.
mu0
=
self
.
mu0
self
.
trainedModel
.
data
.
scaleFactor
=
[
1.
]
*
self
.
npar
self
.
trainedModel
.
data
.
scaleFactor
[
self
.
directionPivot
[
0
]]
=
(
self
.
scaleFactor
[
0
])
self
.
trainedModel
.
data
.
parameterMap
=
self
.
HFEngine
.
parameterMap
self
.
_m_musUniqueCN
=
copy
(
self
.
_musUniqueCN
)
musUniqueCNAux
=
np
.
zeros
((
self
.
S
,
self
.
npar
),
dtype
=
np
.
complex
)
musUniqueCNAux
[:,
self
.
directionPivot
[
0
]]
=
self
.
_musUniqueCN
(
0
)
self
.
_musUniqueCN
=
self
.
checkParameterList
(
musUniqueCNAux
)
self
.
_m_derIdxs
=
copy
(
self
.
_derIdxs
)
for
j
in
range
(
len
(
self
.
_derIdxs
)):
for
l
in
range
(
len
(
self
.
_derIdxs
[
j
])):
derjl
=
self
.
_derIdxs
[
j
][
l
][
0
]
self
.
_derIdxs
[
j
][
l
]
=
[
0
]
*
self
.
npar
self
.
_derIdxs
[
j
][
l
][
self
.
directionPivot
[
0
]]
=
derjl
self
.
trainedModel
.
data
.
Q
.
_dirPivot
=
self
.
directionPivot
[
0
]
self
.
trainedModel
.
data
.
P
.
_dirPivot
=
self
.
directionPivot
[
0
]
# tell greedy error estimator that operator / RHS is pivot-affine
if
(
get_is_affine
(
self
.
HFEngine
.
A
)
>=
1
/
2
and
get_is_affine
(
self
.
HFEngine
.
b
)
>=
1
/
2
):
self
.
_affine_lvl
+=
[
1
/
2
]
self
.
_affine_lvl_extra
=
1
else
:
self
.
_affine_lvl_extra
=
0
self
.
trainedModel
.
data
.
npar
=
self
.
npar
def
_demarginalizeTrainedModel
(
self
):
self
.
_temporaryPivot
=
1
self
.
trainedModel
.
data
.
mu0
=
self
.
checkParameterListPivot
(
self
.
mu0
(
self
.
directionPivot
))
self
.
trainedModel
.
data
.
scaleFactor
=
self
.
scaleFactor
self
.
trainedModel
.
data
.
parameterMap
=
{
"F"
:
[
self
.
HFEngine
.
parameterMap
[
"F"
][
self
.
directionPivot
[
0
]]],
"B"
:
[
self
.
HFEngine
.
parameterMap
[
"B"
][
self
.
directionPivot
[
0
]]]}
self
.
_musUniqueCN
=
copy
(
self
.
_m_musUniqueCN
)
self
.
_derIdxs
=
copy
(
self
.
_m_derIdxs
)
del
self
.
_m_musUniqueCN
,
self
.
_m_derIdxs
del
self
.
trainedModel
.
data
.
Q
.
_dirPivot
del
self
.
trainedModel
.
data
.
P
.
_dirPivot
if
self
.
_affine_lvl_extra
:
self
.
_affine_lvl
.
pop
()
del
self
.
_affine_lvl_extra
self
.
trainedModel
.
data
.
npar
=
self
.
npar
def
errorEstimator
(
self
,
mus
:
Np1D
,
return_max
:
bool
=
False
)
->
Np1D
:
"""Standard residual-based error estimator."""
setupOK
=
self
.
setupApproxLocal
()
if
setupOK
>
0
:
err
=
np
.
empty
(
len
(
mus
))
err
[:]
=
np
.
nan
if
not
return_max
:
return
err
return
err
,
[
-
setupOK
],
np
.
nan
self
.
_marginalizeTrainedModel
()
errRes
=
super
()
.
errorEstimator
(
mus
,
return_max
)
self
.
_demarginalizeTrainedModel
()
return
errRes
def
_preliminaryTraining
(
self
):
"""Initialize starting snapshots of solution map."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot start greedy algorithm."
)
self
.
resetSamples
(
1
)
self
.
samplingEngine
.
scaleFactor
=
self
.
scaleFactorDer
musPivot
=
self
.
samplerTrainSet
.
generatePoints
(
self
.
S
)
while
len
(
musPivot
)
>
self
.
S
:
musPivot
.
pop
()
muTestPivot
=
self
.
samplerPivot
.
generatePoints
(
self
.
nTestPoints
,
False
)
idxPop
=
pruneSamples
(
self
.
mapParameterListPivot
(
muTestPivot
),
self
.
mapParameterListPivot
(
musPivot
),
1e-10
*
self
.
scaleFactorPivot
[
0
])
muTestPivot
.
pop
(
idxPop
)
self
.
_mus
=
emptyParameterList
()
self
.
mus
.
reset
((
self
.
S
-
1
,
self
.
HFEngine
.
npar
))
self
.
muTest
=
emptyParameterList
()
self
.
muTest
.
reset
((
len
(
muTestPivot
)
+
1
,
self
.
HFEngine
.
npar
))
self
.
mus
.
data
[:,
self
.
directionPivot
]
=
musPivot
[:
-
1
]
self
.
mus
.
data
[:,
self
.
directionMarginal
]
=
np
.
repeat
(
self
.
muMargLoc
,
self
.
S
-
1
,
axis
=
0
)
self
.
muTest
.
data
[:
-
1
,
self
.
directionPivot
]
=
muTestPivot
.
data
self
.
muTest
.
data
[
-
1
,
self
.
directionPivot
]
=
musPivot
[
-
1
]
self
.
muTest
.
data
[:,
self
.
directionMarginal
]
=
np
.
repeat
(
self
.
muMargLoc
,
len
(
muTestPivot
)
+
1
,
axis
=
0
)
vbMng
(
self
,
"MAIN"
,
(
"Adding first {} sample point{} at {} to training "
"set."
)
.
format
(
self
.
S
-
1
,
""
+
"s"
*
(
self
.
S
>
2
),
self
.
mus
),
3
)
self
.
samplingEngine
.
iterSample
(
self
.
mus
)
self
.
_approxParameters
[
"S"
]
=
self
.
_S
=
len
(
self
.
mus
)
def
setupApproxLocal
(
self
)
->
int
:
"""Compute rational interpolant."""
self
.
_m_selfmus
=
copy
(
self
.
mus
)
self
.
_m_HFEparameterMap
=
copy
(
self
.
HFEngine
.
parameterMap
)
self
.
_mus
=
self
.
checkParameterListPivot
(
self
.
mus
(
self
.
directionPivot
))
self
.
HFEngine
.
parameterMap
=
{
"F"
:
[
self
.
HFEngine
.
parameterMap
[
"F"
][
self
.
directionPivot
[
0
]]],
"B"
:
[
self
.
HFEngine
.
parameterMap
[
"B"
][
self
.
directionPivot
[
0
]]]}
setupOK
=
super
()
.
setupApproxLocal
()
self
.
_mus
=
self
.
_m_selfmus
self
.
HFEngine
.
parameterMap
=
self
.
_m_HFEparameterMap
del
self
.
_m_selfmus
,
self
.
_m_HFEparameterMap
return
setupOK
def
addMarginalSamplePoints
(
self
,
musMarginal
:
paramList
,
*
args
,
**
kwargs
)
->
int
:
"""Add marginal sample points to reduced model."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot add sample points."
)
musMarginal
=
self
.
checkParameterListMarginal
(
musMarginal
)
vbMng
(
self
,
"INIT"
,
"Adding marginal sample point{} at {}."
.
format
(
"s"
*
(
len
(
musMarginal
)
>
1
),
musMarginal
),
5
)
if
(
self
.
SMarginal
>
0
and
hasattr
(
self
,
"polybasisMarginal"
)
and
self
.
polybasisMarginal
in
sk
):
RROMPyWarning
((
"Manually adding new samples with piecewise linear "
"marginal interpolation is dangerous. Sample depth "
"in samplerMarginal must be managed correctly."
))
_musOld
=
self
.
mus
self
.
_musMarginal
.
append
(
musMarginal
)
S0
=
copy
(
self
.
S
)
req
,
is_master
=
[],
masterCore
()
idx
,
sizes
=
indicesScatter
(
len
(
musMarginal
),
return_sizes
=
True
)
_trainedModelOld
=
copy
(
self
.
trainedModel
)
_collapsed
=
(
_trainedModelOld
is
not
None
and
_trainedModelOld
.
data
.
_collapsed
)
pMat
,
Ps
,
Qs
,
mus
=
None
,
[],
[],
None
emptyCores
=
np
.
where
(
np
.
array
(
sizes
)
==
0
)[
0
]
if
is_master
else
[]
if
len
(
idx
)
==
0
:
vbMng
(
self
,
"MAIN"
,
"Idling."
,
25
)
if
self
.
storeAllSamples
:
self
.
storeSamples
()
pL
=
recv
(
source
=
0
,
tag
=
poolRank
())
pMat
=
np
.
empty
((
pL
,
0
),
dtype
=
np
.
complex
)
mus
=
np
.
empty
((
0
,
self
.
mu0
.
shape
[
1
]),
dtype
=
np
.
complex
)
else
:
_scaleFactorOldPivot
=
copy
(
self
.
scaleFactor
)
self
.
scaleFactor
=
self
.
scaleFactorPivot
self
.
_temporaryPivot
=
1
for
i
in
idx
:
self
.
muMargLoc
=
self
.
musMarginal
[[
i
+
self
.
SMarginal
]]
vbMng
(
self
,
"MAIN"
,
"Building marginal model no. {} at {}."
.
format
(
i
+
self
.
SMarginal
+
1
,
self
.
musMarginal
[
i
+
self
.
SMarginal
]),
5
)
self
.
samplingEngine
.
resetHistory
()
self
.
trainedModel
=
None
self
.
verbosity
-=
5
self
.
samplingEngine
.
verbosity
-=
5
RationalInterpolantGreedy
.
setupApprox
(
self
,
*
args
,
**
kwargs
)
self
.
verbosity
+=
5
self
.
samplingEngine
.
verbosity
+=
5
musi
=
self
.
samplingEngine
.
mus
pMati
=
self
.
samplingEngine
.
projectionMatrix
if
self
.
storeAllSamples
:
self
.
storeSamples
(
i
+
self
.
SMarginal
)
if
not
self
.
matchState
:
if
(
get_is_mu_independent
(
self
.
HFEngine
.
C
)
not
in
self
.
_output_lvl
and
self
.
POD
==
1
):
raise
RROMPyException
((
"Cannot apply mu-dependent C "
"to orthonormalized samples."
))
vbMng
(
self
,
"INIT"
,
"Extracting system output from state."
,
35
)
pMatiEff
=
None
for
j
,
mu
in
enumerate
(
musi
):
pMij
=
np
.
expand_dims
(
self
.
HFEngine
.
applyC
(
pMati
[:,
j
],
mu
),
-
1
)
if
pMatiEff
is
None
:
pMatiEff
=
np
.
array
(
pMij
)
else
:
pMatiEff
=
np
.
append
(
pMatiEff
,
pMij
,
axis
=
1
)
pMati
=
pMatiEff
vbMng
(
self
,
"DEL"
,
"Done extracting system output."
,
35
)
if
i
==
0
:
mus
=
copy
(
musi
.
data
)
for
dest
in
emptyCores
:
req
+=
[
isend
(
len
(
pMati
),
dest
=
dest
,
tag
=
dest
)]
else
:
mus
=
np
.
vstack
((
mus
,
musi
.
data
))
if
not
_collapsed
:
if
pMat
is
None
:
pMat
=
copy
(
pMati
)
else
:
pMat
=
np
.
hstack
((
pMat
,
pMati
))
Ps
+=
[
copy
(
self
.
trainedModel
.
data
.
P
)]
Qs
+=
[
copy
(
self
.
trainedModel
.
data
.
Q
)]
if
_collapsed
:
# collapse by hand
Ps
[
-
1
]
.
postmultiplyTensorize
(
pMati
.
T
)
self
.
_S
=
S0
del
self
.
_temporaryPivot
,
self
.
muMargLoc
self
.
scaleFactor
=
_scaleFactorOldPivot
for
r
in
req
:
r
.
wait
()
if
_collapsed
:
pMat
=
pMati
[:,
:
0
]
pMat
,
Ps
,
Qs
,
mus
,
nsamples
=
gatherPivotedApproximant
(
pMat
,
Ps
,
Qs
,
mus
,
sizes
,
self
.
polybasis
)
self
.
_mus
=
_musOld
self
.
mus
.
append
(
mus
)
Psupp
=
np
.
append
(
0
,
np
.
cumsum
(
nsamples
[:
-
1
])
.
astype
(
int
))
if
_trainedModelOld
is
None
:
self
.
_setupTrainedModel
(
pMat
,
forceNew
=
True
)
self
.
trainedModel
.
data
.
Qs
,
self
.
trainedModel
.
data
.
Ps
=
[],
[]
self
.
trainedModel
.
data
.
Psupp
=
[]
else
:
self
.
_trainedModel
=
_trainedModelOld
if
_collapsed
:
self
.
_setupTrainedModel
(
1.
)
Psupp
=
[
0
]
*
len
(
musMarginal
)
else
:
Psupp
=
Psupp
+
self
.
trainedModel
.
data
.
projMat
.
shape
[
1
]
self
.
_setupTrainedModel
(
pMat
,
1
)
self
.
_SMarginal
+=
len
(
musMarginal
)
self
.
trainedModel
.
data
.
Qs
+=
Qs
self
.
trainedModel
.
data
.
Ps
+=
Ps
self
.
trainedModel
.
data
.
Psupp
+=
list
(
Psupp
)
self
.
_preliminaryMarginalFinalization
()
self
.
_finalizeMarginalization
()
vbMng
(
self
,
"DEL"
,
"Done adding marginal sample points."
,
5
)
return
0
def
setupApprox
(
self
,
*
args
,
**
kwargs
)
->
int
:
"""Compute rational interpolant."""
if
self
.
checkComputedApprox
():
return
-
1
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot setup approximant."
)
vbMng
(
self
,
"INIT"
,
"Setting up {}."
.
format
(
self
.
name
()),
5
)
self
.
computeScaleFactor
()
self
.
_mus
=
emptyParameterList
()
self
.
_musMarginal
=
emptyParameterList
()
musMarginal
=
self
.
samplerMarginal
.
generatePoints
(
self
.
SMarginal
)
while
len
(
musMarginal
)
>
self
.
SMarginal
:
musMarginal
.
pop
()
self
.
_SMarginal
=
0
val
=
self
.
addMarginalSamplePoints
(
musMarginal
,
*
args
,
**
kwargs
)
vbMng
(
self
,
"DEL"
,
"Done setting up approximant."
,
5
)
return
val
class
RationalInterpolantGreedyPivotedNoMatch
(
RationalInterpolantGreedyPivotedBase
,
GenericPivotedApproximantNoMatch
):
"""
ROM pivoted rational interpolant (without matching) 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': kind of snapshots orthogonalization; allowed values
include 0, 1/2, and 1; defaults to 1, i.e. POD;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'S': total number of pivot samples current approximant relies
upon;
- 'N': degree of rational interpolant denominator; defaults to
'AUTO', i.e. maximum allowed;
- 'samplerPivot': pivot sample point generator;
- 'rationalMode': mode of rational approximation; allowed values
include 'MINIMAL[_STATE]' and 'BARYCENTRIC[_STATE]'; defaults
to 'MINIMAL';
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'polybasis': type of polynomial basis for pivot
interpolation; defaults to 'MONOMIAL';
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
defaults to 0.;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'samplerTrainSet': training sample points generator; defaults to
samplerPivot;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'LOOK_AHEAD',
'LOOK_AHEAD_RES', and 'NONE'; defaults to 'NONE';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'functionalSolve': strategy for minimization of denominator
functional; allowed values include 'NORM' and 'DOMINANT';
defaults to 'NORM';
- 'interpTol': tolerance for pivot interpolation; defaults to
None;
- 'forceQReal': force denominator to have real coefficients;
defaults to False;
- 'polyTruncateTol': tolerance for truncation of rational terms;
defaults to 0;
- 'QTol': tolerance for robust rational denominator management;
defaults to 0.
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.
musMarginal: Array of marginal snapshot parameters.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': kind of snapshots orthogonalization;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'N': degree of rational interpolant denominator;
- 'rationalMode': mode of rational approximation;
- 'polybasis': type of polynomial basis for pivot interpolation;
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'nTestPoints': number of test points;
- 'samplerTrainSet': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'functionalSolve': strategy for minimization of denominator
functional;
- 'interpTol': tolerance for pivot interpolation;
- 'forceQReal': force denominator to have real coefficients;
- 'polyTruncateTol': tolerance for truncation of rational terms;
- 'QTol': tolerance for robust rational denominator management.
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.
verbosity: Verbosity level.
POD: Kind of snapshots orthogonalization.
scaleFactorDer: Scaling factors for derivative computation.
S: Total number of pivot samples current approximant relies upon.
N: Denominator degree of approximant.
samplerPivot: Pivot sample point generator.
rationalMode: Mode of rational approximation.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
polybasis: Type of polynomial basis for pivot interpolation.
greedyTol: uniform error tolerance for greedy algorithm.
collinearityTol: Collinearity tolerance for greedy algorithm.
maxIter: maximum number of greedy steps.
nTestPoints: number of starting training points.
samplerTrainSet: training sample points generator.
errorEstimatorKind: kind of error estimator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
functionalSolve: Strategy for minimization of denominator functional.
interpTol: Tolerance for pivot interpolation.
forceQReal: Force denominator to have real coefficients.
polyTruncateTol: Tolerance for truncation of rational terms.
QTol: Tolerance for robust rational denominator management.
muBounds: 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.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
class
RationalInterpolantGreedyPivotedPolyMatch
(
RationalInterpolantGreedyPivotedBase
,
GenericPivotedApproximantPolyMatch
):
"""
ROM pivoted rational interpolant (with polynomial matching) 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': kind of snapshots orthogonalization; allowed values
include 0, 1/2, and 1; defaults to 1, i.e. POD;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'matchState': whether to match the system state rather than the
system output; defaults to False;
- 'matchingWeight': weight for matching; defaults to 1;
- 'matchingKind': kind of matching; allowed values include 'ROTATE'
and 'PROJECT'; defaults to 'ROTATE';
- 'S': total number of pivot samples current approximant relies
upon;
- 'N': degree of rational interpolant denominator; defaults to
'AUTO', i.e. maximum allowed;
- 'samplerPivot': pivot sample point generator;
- 'rationalMode': mode of rational approximation; allowed values
include 'MINIMAL[_STATE]' and 'BARYCENTRIC[_STATE]'; defaults
to 'MINIMAL';
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'polybasis': type of polynomial basis for pivot
interpolation; defaults to 'MONOMIAL';
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation; allowed values include 'MONOMIAL_*',
'CHEBYSHEV_*', 'LEGENDRE_*', 'NEARESTNEIGHBOR', and
'PIECEWISE_LINEAR_*'; defaults to 'MONOMIAL';
- 'paramsMarginal': dictionary of parameters for marginal
interpolation; include:
. 'MMarginal': degree of marginal interpolant; defaults to
'AUTO', i.e. maximum allowed; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'nNeighborsMarginal': number of marginal nearest neighbors;
defaults to 1; only for 'NEARESTNEIGHBOR';
. 'polydegreetypeMarginal': type of polynomial degree for
marginal; defaults to 'TOTAL'; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'polyTruncateTolMarginal': tolerance for truncation of
marginal interpolator; defaults to 0;
. 'interpTolMarginal': tolerance for marginal interpolation;
defaults to None; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'radialDirectionalWeightsMarginalAdapt': bounds for adaptive
rescaling of marginal radial basis weights; only for
radial basis.
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
defaults to 0.;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'samplerTrainSet': training sample points generator; defaults to
samplerPivot;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'LOOK_AHEAD',
'LOOK_AHEAD_RES', and 'NONE'; defaults to 'NONE';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'functionalSolve': strategy for minimization of denominator
functional; allowed values include 'NORM' and 'DOMINANT';
defaults to 'NORM';
- 'interpTol': tolerance for pivot interpolation; defaults to None;
- 'forceQReal': force denominator to have real coefficients;
defaults to False;
- 'polyTruncateTol': tolerance for truncation of rational terms;
defaults to 0;
- 'QTol': tolerance for robust rational denominator management;
defaults to 0.
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.
musMarginal: Array of marginal snapshot parameters.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': kind of snapshots orthogonalization;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'matchState': whether to match the system state rather than the
system output;
- 'matchingWeight': weight for matching;
- 'matchingKind': kind of matching;
- 'N': degree of rational interpolant denominator;
- 'rationalMode': mode of rational approximation;
- 'polybasis': type of polynomial basis for pivot interpolation;
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation;
- 'paramsMarginal': dictionary of parameters for marginal
interpolation; include:
. 'MMarginal': degree of marginal interpolant;
. 'nNeighborsMarginal': number of marginal nearest neighbors;
. 'polydegreetypeMarginal': type of polynomial degree for
marginal;
. 'polyTruncateTolMarginal': tolerance for truncation of
marginal interpolator;
. 'interpTolMarginal': tolerance for marginal interpolation;
. 'radialDirectionalWeightsMarginalAdapt': bounds for adaptive
rescaling of marginal radial basis weights.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'nTestPoints': number of test points;
- 'samplerTrainSet': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'functionalSolve': strategy for minimization of denominator
functional;
- 'interpTol': tolerance for pivot interpolation;
- 'forceQReal': force denominator to have real coefficients;
- 'polyTruncateTol': tolerance for truncation of rational terms;
- 'QTol': tolerance for robust rational denominator management.
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.
verbosity: Verbosity level.
POD: Kind of snapshots orthogonalization.
scaleFactorDer: Scaling factors for derivative computation.
matchState: Whether to match the system state rather than the system
output.
matchingWeight: Weight for matching.
matchingKind: Kind of matching.
S: Total number of pivot samples current approximant relies upon.
N: Denominator degree of approximant.
samplerPivot: Pivot sample point generator.
rationalMode: Mode of rational approximation.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
paramsMarginal: Dictionary of parameters for marginal interpolation.
greedyTol: uniform error tolerance for greedy algorithm.
collinearityTol: Collinearity tolerance for greedy algorithm.
maxIter: maximum number of greedy steps.
nTestPoints: number of starting training points.
samplerTrainSet: training sample points generator.
errorEstimatorKind: kind of error estimator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
functionalSolve: Strategy for minimization of denominator functional.
interpTol: Tolerance for pivot interpolation.
forceQReal: Force denominator to have real coefficients.
polyTruncateTol: Tolerance for truncation of rational terms.
QTol: Tolerance for robust rational denominator management.
muBounds: 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.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
def
setupApprox
(
self
,
*
args
,
**
kwargs
)
->
int
:
if
self
.
checkComputedApprox
():
return
-
1
self
.
purgeparamsMarginal
()
setupOK
=
super
()
.
setupApprox
(
*
args
,
**
kwargs
)
if
self
.
matchState
:
self
.
_postApplyC
()
return
setupOK
class
RationalInterpolantGreedyPivotedPoleMatch
(
RationalInterpolantGreedyPivotedBase
,
GenericPivotedApproximantPoleMatch
):
"""
ROM pivoted rational interpolant (with pole matching) 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': kind of snapshots orthogonalization; allowed values
include 0, 1/2, and 1; defaults to 1, i.e. POD;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'matchState': whether to match the system state rather than the
system output; defaults to False;
- 'matchingWeight': weight for pole matching optimization; defaults
to 1;
- 'matchingShared': required ratio of marginal points to share
resonance; defaults to 1.;
- 'badPoleCorrection': strategy for correction of bad poles;
available values include 'ERASE', 'RATIONAL', and 'POLYNOMIAL';
defaults to 'ERASE';
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'rationalMode': mode of rational approximation; allowed values
include 'MINIMAL[_STATE]' and 'BARYCENTRIC[_STATE]'; defaults
to 'MINIMAL';
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'polybasis': type of polynomial basis for pivot
interpolation; defaults to 'MONOMIAL';
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation; allowed values include 'MONOMIAL_*',
'CHEBYSHEV_*', 'LEGENDRE_*', 'NEARESTNEIGHBOR', and
'PIECEWISE_LINEAR_*'; defaults to 'MONOMIAL';
- 'paramsMarginal': dictionary of parameters for marginal
interpolation; include:
. 'MMarginal': degree of marginal interpolant; defaults to
'AUTO', i.e. maximum allowed; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'nNeighborsMarginal': number of marginal nearest neighbors;
defaults to 1; only for 'NEARESTNEIGHBOR';
. 'polydegreetypeMarginal': type of polynomial degree for
marginal; defaults to 'TOTAL'; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'polyTruncateTolMarginal': tolerance for truncation of
marginal interpolator; defaults to 0;
. 'interpTolMarginal': tolerance for marginal interpolation;
defaults to None; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'radialDirectionalWeightsMarginalAdapt': bounds for adaptive
rescaling of marginal radial basis weights; only for
radial basis.
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
defaults to 0.;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'samplerTrainSet': training sample points generator; defaults to
samplerPivot;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'LOOK_AHEAD',
'LOOK_AHEAD_RES', and 'NONE'; defaults to 'NONE';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'functionalSolve': strategy for minimization of denominator
functional; allowed values include 'NORM' and 'DOMINANT';
defaults to 'NORM';
- 'interpTol': tolerance for pivot interpolation; defaults to None;
- 'forceQReal': force denominator to have real coefficients;
defaults to False;
- 'polyTruncateTol': tolerance for truncation of rational terms;
defaults to 0;
- 'QTol': tolerance for robust rational denominator management;
defaults to 0.
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.
musMarginal: Array of marginal snapshot parameters.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': kind of snapshots orthogonalization;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'matchState': whether to match the system state rather than the
system output;
- 'matchingWeight': weight for pole matching optimization;
- 'matchingShared': required ratio of marginal points to share
resonance;
- 'badPoleCorrection': strategy for correction of bad poles;
- 'rationalMode': mode of rational approximation;
- 'polybasis': type of polynomial basis for pivot
interpolation;
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation;
- 'paramsMarginal': dictionary of parameters for marginal
interpolation; include:
. 'MMarginal': degree of marginal interpolant;
. 'nNeighborsMarginal': number of marginal nearest neighbors;
. 'polydegreetypeMarginal': type of polynomial degree for
marginal;
. 'polyTruncateTolMarginal': tolerance for truncation of
marginal interpolator;
. 'interpTolMarginal': tolerance for marginal interpolation;
. 'radialDirectionalWeightsMarginalAdapt': bounds for adaptive
rescaling of marginal radial basis weights.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'nTestPoints': number of test points;
- 'samplerTrainSet': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'functionalSolve': strategy for minimization of denominator
functional;
- 'interpTol': tolerance for pivot interpolation;
- 'forceQReal': force denominator to have real coefficients;
- 'polyTruncateTol': tolerance for truncation of rational terms;
- 'QTol': tolerance for robust rational denominator management.
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.
verbosity: Verbosity level.
POD: Kind of snapshots orthogonalization.
scaleFactorDer: Scaling factors for derivative computation.
matchState: Whether to match the system state rather than the system
output.
matchingWeight: Weight for pole matching optimization.
matchingShared: Required ratio of marginal points to share resonance.
badPoleCorrection: Strategy for correction of bad poles.
S: Total number of pivot samples current approximant relies upon.
samplerPivot: Pivot sample point generator.
rationalMode: Mode of rational approximation.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
paramsMarginal: Dictionary of parameters for marginal interpolation.
greedyTol: uniform error tolerance for greedy algorithm.
collinearityTol: Collinearity tolerance for greedy algorithm.
maxIter: maximum number of greedy steps.
nTestPoints: number of starting training points.
samplerTrainSet: training sample points generator.
errorEstimatorKind: kind of error estimator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
functionalSolve: Strategy for minimization of denominator functional.
interpTol: Tolerance for pivot interpolation.
forceQReal: Force denominator to have real coefficients.
polyTruncateTol: Tolerance for truncation of rational terms.
QTol: Tolerance for robust rational denominator management.
muBounds: 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.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
def
setupApprox
(
self
,
*
args
,
**
kwargs
)
->
int
:
if
self
.
checkComputedApprox
():
return
-
1
self
.
purgeparamsMarginal
()
setupOK
=
super
()
.
setupApprox
(
*
args
,
**
kwargs
)
if
self
.
matchState
:
self
.
_postApplyC
()
return
setupOK
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