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rational_interpolant_greedy_pivoted_greedy.py
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R6746 RationalROMPy
rational_interpolant_greedy_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.greedy
import
RationalInterpolantGreedy
from
rrompy.reduction_methods.standard.greedy.generic_greedy_approximant
\
import
pruneSamples
from
rrompy.reduction_methods.pivoted
import
RationalInterpolantGreedyPivoted
from
rrompy.reduction_methods.pivoted.generic_pivoted_approximant
import
(
PODGlobal
)
from
rrompy.utilities.base.types
import
Np1D
,
Tuple
,
paramVal
,
paramList
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.utilities.exception_manager
import
RROMPyAssert
from
rrompy.parameter
import
emptyParameterList
__all__
=
[
'RationalInterpolantGreedyPivotedGreedy'
]
class
RationalInterpolantGreedyPivotedGreedy
(
GenericPivotedGreedyApproximant
,
RationalInterpolantGreedyPivoted
):
"""
ROM greedy 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';
- '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;
- 'trainSetGenerator': training sample points generator; defaults
to sampler;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'LOOK_AHEAD',
'LOOK_AHEAD_RES', and 'NONE'; defaults to 'NONE';
- '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';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; 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.
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.
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;
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- '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;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- '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.
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.
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.
trainSetGenerator: training sample points generator.
errorEstimatorKind: kind of error estimator.
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.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
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.
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.
"""
@property
def
sampleBatchSize
(
self
):
"""Value of sampleBatchSize."""
return
1
@property
def
sampleBatchIdx
(
self
):
"""Value of sampleBatchIdx."""
return
self
.
S
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
greedyNextSample
(
self
,
muidx
:
int
,
plotEst
:
str
=
"NONE"
)
\
->
Tuple
[
Np1D
,
int
,
float
,
paramVal
]:
"""Compute next greedy snapshot of solution map."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot add greedy sample."
)
mus
=
copy
(
self
.
muTest
[
muidx
])
self
.
muTest
.
pop
(
muidx
)
for
j
,
mu
in
enumerate
(
mus
):
vbMng
(
self
,
"MAIN"
,
(
"Adding sample point no. {} at {} to training "
"set."
)
.
format
(
len
(
self
.
mus
)
+
1
,
mu
),
3
)
self
.
mus
.
append
(
mu
)
self
.
_S
=
len
(
self
.
mus
)
self
.
_approxParameters
[
"S"
]
=
self
.
S
if
(
self
.
samplingEngine
.
nsamples
<=
len
(
mus
)
-
j
-
1
or
not
np
.
allclose
(
mu
,
self
.
samplingEngine
.
mus
.
data
[
j
-
len
(
mus
)])):
self
.
samplingEngine
.
nextSample
(
mu
)
if
self
.
_isLastSampleCollinear
():
vbMng
(
self
,
"MAIN"
,
(
"Collinearity above tolerance detected. Starting "
"preemptive greedy loop termination."
),
3
)
self
.
_collinearityFlag
=
1
errorEstTest
=
np
.
empty
(
len
(
self
.
muTest
))
errorEstTest
[:]
=
np
.
nan
return
errorEstTest
,
[
-
1
],
np
.
nan
,
np
.
nan
errorEstTest
,
muidx
,
maxErrorEst
=
self
.
errorEstimator
(
self
.
muTest
,
True
)
if
plotEst
==
"ALL"
:
self
.
plotEstimator
(
errorEstTest
,
muidx
,
maxErrorEst
)
return
errorEstTest
,
muidx
,
maxErrorEst
,
self
.
muTest
[
muidx
]
def
_preliminaryTraining
(
self
):
"""Initialize starting snapshots of solution map."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot start greedy algorithm."
)
if
self
.
samplingEngine
.
nsamples
>
0
:
return
self
.
resetSamples
()
self
.
samplingEngine
.
scaleFactor
=
self
.
_scaleFactorOldPivot
musPivot
=
self
.
trainSetGenerator
.
generatePoints
(
self
.
S
)
while
len
(
musPivot
)
>
self
.
S
:
musPivot
.
pop
()
muTestBasePivot
=
self
.
samplerPivot
.
generatePoints
(
self
.
nTestPoints
,
False
)
idxPop
=
pruneSamples
(
muTestBasePivot
**
self
.
HFEngine
.
rescalingExp
[
self
.
directionPivot
[
0
]],
musPivot
**
self
.
HFEngine
.
rescalingExp
[
self
.
directionPivot
[
0
]],
1e-10
*
self
.
scaleFactor
[
0
])
muTestBasePivot
.
pop
(
idxPop
)
self
.
mus
=
emptyParameterList
()
self
.
mus
.
reset
((
self
.
S
-
1
,
self
.
HFEngine
.
npar
))
self
.
muTest
=
emptyParameterList
()
self
.
muTest
.
reset
((
len
(
muTestBasePivot
)
+
1
,
self
.
HFEngine
.
npar
))
for
k
in
range
(
self
.
S
-
1
):
self
.
mus
.
data
[
k
,
self
.
directionPivot
]
=
musPivot
[
k
]
.
data
self
.
mus
.
data
[
k
,
self
.
directionMarginal
]
=
self
.
musMargLoc
[
-
1
]
.
data
for
k
in
range
(
len
(
muTestBasePivot
)):
self
.
muTest
.
data
[
k
,
self
.
directionPivot
]
=
muTestBasePivot
[
k
]
.
data
self
.
muTest
.
data
[
k
,
self
.
directionMarginal
]
=
(
self
.
musMargLoc
[
-
1
]
.
data
)
self
.
muTest
.
data
[
-
1
,
self
.
directionPivot
]
=
musPivot
[
-
1
]
.
data
self
.
muTest
.
data
[
-
1
,
self
.
directionMarginal
]
=
self
.
musMargLoc
[
-
1
]
.
data
if
len
(
self
.
mus
)
>
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
.
_S
=
len
(
self
.
mus
)
self
.
_approxParameters
[
"S"
]
=
self
.
S
self
.
M
,
self
.
N
=
(
"AUTO"
,)
*
2
def
setupApproxPivoted
(
self
,
mus
:
paramList
)
->
int
:
if
self
.
checkComputedApproxPivoted
():
return
-
1
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot setup approximant."
)
vbMng
(
self
,
"INIT"
,
"Setting up pivoted approximant."
,
10
)
if
not
hasattr
(
self
,
"_plotEstPivot"
):
self
.
_plotEstPivot
=
"NONE"
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
S0
=
copy
(
self
.
S
)
for
j
,
mu
in
enumerate
(
mus
):
RationalInterpolantGreedy
.
setupSampling
(
self
)
self
.
trainedModel
=
None
self
.
musMargLoc
+=
[
mu
]
RationalInterpolantGreedy
.
setupApprox
(
self
,
self
.
_plotEstPivot
)
self
.
samplingEngs
[
j
]
=
copy
(
self
.
samplingEngine
)
Qs
[
j
]
=
copy
(
self
.
trainedModel
.
data
.
Q
)
Ps
[
j
]
=
copy
(
self
.
trainedModel
.
data
.
P
)
self
.
_S
=
S0
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
.
trainedModel
.
data
.
approxParameters
=
copy
(
self
.
approxParameters
)
self
.
verbosity
+=
15
vbMng
(
self
,
"DEL"
,
"Done setting up pivoted approximant."
,
10
)
return
0
def
setupApprox
(
self
,
plotEst
:
str
=
"NONE"
)
->
int
:
if
self
.
checkComputedApprox
():
return
-
1
if
'_'
not
in
plotEst
:
plotEst
=
plotEst
+
"_NONE"
plotEstM
,
self
.
_plotEstPivot
=
plotEst
.
split
(
"_"
)
val
=
super
()
.
setupApprox
(
plotEstM
)
return
val
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