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rational_interpolant_pivoted_greedy.py
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R6746 RationalROMPy
rational_interpolant_pivoted_greedy.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_greedy_approximant
import
GenericPivotedGreedyApproximant
from
rrompy.utilities.numerical
import
dot
from
rrompy.reduction_methods.standard
import
RationalInterpolant
from
rrompy.reduction_methods.pivoted
import
(
RationalInterpolantPivoted
,
PODGlobal
)
from
rrompy.utilities.base.types
import
paramList
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.utilities.exception_manager
import
RROMPyAssert
from
rrompy.parameter
import
checkParameterList
,
emptyParameterList
__all__
=
[
'RationalInterpolantPivotedGreedy'
]
class
RationalInterpolantPivotedGreedy
(
GenericPivotedGreedyApproximant
,
RationalInterpolantPivoted
):
"""
ROM pivoted greedy rational interpolant 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;
- 'matchingWeight': weight for pole matching optimization; defaults
to 1;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
defaults to np.inf;
- 'cutOffKind': kind of cut off strategy; available values
include 'SOFT' and 'HARD'; defaults to 'HARD';
- 'matchingWeightError': weight for pole matching optimization in
error estimation; defaults to 0;
- 'cutOffToleranceError': tolerance for ignoring parasitic poles
in error estimation; defaults to 'AUTO', i.e. cutOffTolerance;
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': number of starting marginal samples;
- 'samplerMarginalGrid': marginal sample point generator via sparse
grid;
- 'polybasis': type of polynomial basis for pivot interpolation;
defaults to 'MONOMIAL';
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation; allowed values include 'MONOMIAL', 'CHEBYSHEV'
and 'LEGENDRE'; defaults to 'MONOMIAL';
- 'M': degree of rational interpolant numerator; defaults to
'AUTO', i.e. maximum allowed;
- 'N': degree of rational interpolant denominator; defaults to
'AUTO', i.e. maximum allowed;
- 'MMarginal': degree of marginal interpolant; defaults to 'AUTO',
i.e. maximum allowed;
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm; defaults to 1e-1;
- 'maxIterMarginal': maximum number of marginal greedy steps;
defaults to 1e2;
- 'polydegreetypeMarginal': type of polynomial degree for marginal;
defaults to 'TOTAL';
- 'radialDirectionalWeights': radial basis weights for pivot
numerator; defaults to 1;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'nNearestNeighbor': number of pivot nearest neighbors considered
if polybasis allows; defaults to -1;
- 'nNearestNeighborMarginal': number of marginal nearest neighbors
considered if polybasisMarginal allows; defaults to -1;
- 'interpRcond': tolerance for pivot interpolation; defaults to
None;
- 'interpRcondMarginal': tolerance for marginal interpolation;
defaults to None;
- 'robustTol': tolerance for robust rational denominator
management; defaults to 0;
- 'correctorForce': whether corrector should forcefully delete bad
poles; defaults to False;
- 'correctorTol': tolerance for corrector step; defaults to 0.,
i.e. no bad poles;
- 'correctorMaxIter': maximum number of corrector iterations;
defaults to 1.
Defaults to empty dict.
approx_state(optional): Whether to approximate state. Defaults to
False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
directionPivot: Pivot components.
mus: Array of snapshot parameters.
musPivot: Array of pivot 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': whether to compute POD of snapshots;
- 'matchingWeight': weight for pole matching optimization;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
- 'cutOffKind': kind of cut off strategy;
- 'matchingWeightError': weight for pole matching optimization in
error estimation;
- 'cutOffToleranceError': tolerance for ignoring parasitic poles
in error estimation;
- 'polybasis': type of polynomial basis for pivot interpolation;
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation;
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- 'MMarginal': degree of marginal interpolant;
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm;
- 'maxIterMarginal': maximum number of marginal greedy steps;
- 'polydegreetypeMarginal': type of polynomial degree for marginal;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'nNearestNeighbor': number of pivot nearest neighbors considered
if polybasis allows;
- 'nNearestNeighborMarginal': number of marginal nearest neighbors
considered if polybasisMarginal allows;
- 'interpRcond': tolerance for pivot interpolation;
- 'interpRcondMarginal': tolerance for marginal interpolation;
- 'robustTol': tolerance for robust rational denominator
management;
- 'correctorForce': whether corrector should forcefully delete bad
poles;
- 'correctorTol': tolerance for corrector step;
- 'correctorMaxIter': maximum number of corrector iterations.
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;
- 'samplerMarginalGrid': marginal sample point generator via sparse
grid.
approx_state: Whether to approximate state.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
matchingWeight: Weight for pole matching optimization.
cutOffTolerance: Tolerance for ignoring parasitic poles.
cutOffKind: Kind of cut off strategy.
matchingWeightError: Weight for pole matching optimization in error
estimation.
cutOffToleranceError: Tolerance for ignoring parasitic poles in error
estimation.
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.
samplerMarginalGrid: Marginal sample point generator via sparse grid.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
M: Degree of rational interpolant numerator.
N: Degree of rational interpolant denominator.
MMarginal: Degree of marginal interpolant.
greedyTolMarginal: Uniform error tolerance for marginal greedy
algorithm.
maxIterMarginal: Maximum number of marginal greedy steps.
polydegreetypeMarginal: Type of polynomial degree for marginal.
radialDirectionalWeights: Radial basis weights for pivot numerator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
nNearestNeighbor: Number of pivot nearest neighbors considered if
polybasis allows.
nNearestNeighborMarginal: Number of marginal nearest neighbors
considered if polybasisMarginal allows.
interpRcond: Tolerance for pivot interpolation.
interpRcondMarginal: Tolerance for marginal interpolation.
robustTol: Tolerance for robust rational denominator management.
correctorForce: Whether corrector should forcefully delete bad poles.
correctorTol: Tolerance for corrector step.
correctorMaxIter: Maximum number of corrector iterations.
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.
"""
def
_finalizeSnapshots
(
self
):
self
.
samplingEngine
=
self
.
_samplingEngineOld
for
muM
,
sEN
in
zip
(
self
.
musMargLoc
,
self
.
samplingEngs
):
self
.
samplingEngine
.
samples
+=
[
sEN
.
samples
]
self
.
samplingEngine
.
nsamples
+=
[
sEN
.
nsamples
]
self
.
samplingEngine
.
mus
+=
[
sEN
.
mus
]
self
.
samplingEngine
.
musMarginal
.
append
(
muM
)
self
.
samplingEngine
.
_derIdxs
+=
[[(
0
,)
*
self
.
npar
]
for
_
in
range
(
sEN
.
nsamples
)]
if
self
.
POD
:
self
.
samplingEngine
.
RPOD
+=
[
sEN
.
RPOD
]
self
.
samplingEngine
.
samples_full
+=
[
copy
(
sEN
.
samples_full
)]
if
self
.
POD
==
PODGlobal
:
self
.
samplingEngine
.
coalesceSamples
(
self
.
interpRcondMarginal
)
else
:
self
.
samplingEngine
.
coalesceSamples
()
def
computeSnapshots
(
self
):
"""Compute snapshots of solution map."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot start snapshot computation."
)
vbMng
(
self
,
"INIT"
,
"Starting computation of snapshots."
,
5
)
self
.
musPivot
=
self
.
samplerPivot
.
generatePoints
(
self
.
S
)[
list
(
range
(
self
.
S
))]
self
.
mus
=
emptyParameterList
()
self
.
mus
.
reset
((
self
.
S
,
self
.
HFEngine
.
npar
))
self
.
samplingEngine
.
resetHistory
()
for
k
in
range
(
self
.
S
):
self
.
mus
.
data
[
k
,
self
.
directionPivot
]
=
self
.
musPivot
[
k
]
.
data
self
.
mus
.
data
[
k
,
self
.
directionMarginal
]
=
self
.
musMargLoc
[
-
1
]
.
data
self
.
samplingEngine
.
iterSample
(
self
.
mus
)
vbMng
(
self
,
"DEL"
,
"Done computing snapshots."
,
5
)
self
.
_m_selfmus
=
copy
(
self
.
mus
)
self
.
_mus
=
self
.
musPivot
self
.
_m_mu0
=
copy
(
self
.
mu0
)
self
.
_m_HFErescalingExp
=
copy
(
self
.
HFEngine
.
rescalingExp
)
self
.
_mu0
=
checkParameterList
(
self
.
mu0
(
self
.
directionPivot
),
1
)[
0
]
self
.
HFEngine
.
rescalingExp
=
[
self
.
HFEngine
.
rescalingExp
[
self
.
directionPivot
[
0
]]]
def
setupApproxPivoted
(
self
,
mus
:
paramList
)
->
int
:
if
self
.
checkComputedApproxPivoted
():
return
-
1
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot setup approximant."
)
vbMng
(
self
,
"INIT"
,
"Setting up {}."
.
format
(
self
.
name
()),
10
)
self
.
computeScaleFactor
()
if
self
.
trainedModel
is
None
:
self
.
trainedModel
=
self
.
tModelType
()
self
.
trainedModel
.
verbosity
=
self
.
verbosity
self
.
trainedModel
.
timestamp
=
self
.
timestamp
datadict
=
{
"mu0"
:
self
.
mu0
,
"projMat"
:
np
.
zeros
((
0
,
0
)),
"scaleFactor"
:
self
.
scaleFactor
,
"rescalingExp"
:
self
.
HFEngine
.
rescalingExp
,
"directionPivot"
:
self
.
directionPivot
}
self
.
trainedModel
.
data
=
self
.
initializeModelData
(
datadict
)[
0
]
self
.
trainedModel
.
data
.
Qs
,
self
.
trainedModel
.
data
.
Ps
=
[],
[]
_trainedModelOld
=
copy
(
self
.
trainedModel
)
self
.
_scaleFactorOldPivot
=
copy
(
self
.
scaleFactor
)
self
.
scaleFactor
=
self
.
scaleFactorPivot
self
.
_temporaryPivot
=
1
self
.
_samplingEngineOld
=
copy
(
self
.
samplingEngine
)
self
.
musMargLoc
,
self
.
samplingEngs
=
[],
[
None
]
*
len
(
mus
)
Qs
,
Ps
=
[
None
]
*
len
(
mus
),
[
None
]
*
len
(
mus
)
self
.
verbosity
-=
15
for
j
,
mu
in
enumerate
(
mus
):
RationalInterpolant
.
setupSampling
(
self
)
self
.
trainedModel
=
None
self
.
musMargLoc
+=
[
mu
]
RationalInterpolant
.
setupApprox
(
self
)
self
.
_mu0
=
self
.
_m_mu0
self
.
_mus
=
self
.
_m_selfmus
self
.
HFEngine
.
rescalingExp
=
self
.
_m_HFErescalingExp
del
self
.
_m_mu0
,
self
.
_m_selfmus
,
self
.
_m_HFErescalingExp
self
.
samplingEngs
[
j
]
=
copy
(
self
.
samplingEngine
)
Qs
[
j
]
=
copy
(
self
.
trainedModel
.
data
.
Q
)
Ps
[
j
]
=
copy
(
self
.
trainedModel
.
data
.
P
)
self
.
scaleFactor
=
self
.
_scaleFactorOldPivot
del
self
.
_scaleFactorOldPivot
,
self
.
_temporaryPivot
self
.
_finalizeSnapshots
()
del
self
.
_samplingEngineOld
,
self
.
musMargLoc
,
self
.
samplingEngs
self
.
_mus
=
self
.
samplingEngine
.
musCoalesced
self
.
trainedModel
=
_trainedModelOld
self
.
trainedModel
.
data
.
mus
=
copy
(
self
.
mus
)
self
.
trainedModel
.
data
.
musMarginal
=
copy
(
self
.
musMarginal
)
padRight
=
(
self
.
samplingEngine
.
nsamplesTot
-
self
.
trainedModel
.
data
.
projMat
.
shape
[
1
])
nmusOld
=
len
(
self
.
trainedModel
.
data
.
Ps
)
for
j
in
range
(
nmusOld
):
nsj
=
self
.
samplingEngine
.
nsamples
[
j
]
self
.
trainedModel
.
data
.
Ps
[
j
]
.
pad
(
0
,
padRight
)
self
.
trainedModel
.
data
.
HIs
[
j
]
.
pad
(
0
,
padRight
)
padLeft
=
self
.
trainedModel
.
data
.
projMat
.
shape
[
1
]
for
j
in
range
(
len
(
mus
)):
nsj
=
self
.
samplingEngine
.
nsamples
[
nmusOld
+
j
]
if
self
.
POD
==
PODGlobal
:
rRightj
=
self
.
samplingEngine
.
RPODCPart
[:,
padLeft
:
padLeft
+
nsj
]
Ps
[
j
]
.
postmultiplyTensorize
(
rRightj
.
T
)
else
:
padRight
-=
nsj
Ps
[
j
]
.
pad
(
padLeft
,
padRight
)
padLeft
+=
nsj
pMat
=
self
.
samplingEngine
.
samplesCoalesced
.
data
pMatEff
=
dot
(
self
.
HFEngine
.
C
,
pMat
)
if
self
.
approx_state
else
pMat
self
.
trainedModel
.
data
.
projMat
=
pMatEff
self
.
trainedModel
.
data
.
Qs
+=
Qs
self
.
trainedModel
.
data
.
Ps
+=
Ps
self
.
verbosity
+=
15
vbMng
(
self
,
"DEL"
,
"Done setting up approximant."
,
10
)
return
0
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