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generic_greedy_approximant.py
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R6746 RationalROMPy
generic_greedy_approximant.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
rrompy.reduction_methods.standard.generic_standard_approximant
\
import
GenericStandardApproximant
from
rrompy.utilities.base.types
import
(
Np1D
,
Np2D
,
DictAny
,
HFEng
,
Tuple
,
List
,
normEng
,
paramVal
,
paramList
,
sampList
)
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.utilities.numerical
import
dot
from
rrompy.utilities.expression
import
expressionEvaluator
from
rrompy.solver
import
normEngine
from
rrompy.utilities.exception_manager
import
(
RROMPyException
,
RROMPyAssert
,
RROMPyWarning
)
from
rrompy.parameter
import
checkParameterList
,
emptyParameterList
__all__
=
[
'GenericGreedyApproximant'
]
def
localL2Distance
(
mus
:
Np2D
,
badmus
:
Np2D
)
->
Np2D
:
return
np
.
linalg
.
norm
(
np
.
tile
(
mus
[
...
,
np
.
newaxis
],
[
1
,
1
,
len
(
badmus
)])
-
badmus
[
...
,
np
.
newaxis
]
.
T
,
axis
=
1
)
def
pruneSamples
(
mus
:
paramList
,
badmus
:
paramList
,
tol
:
float
=
1e-8
)
->
Np1D
:
"""Remove from mus all the elements which are too close to badmus."""
if
len
(
badmus
)
==
0
:
return
mus
proximity
=
np
.
min
(
localL2Distance
(
mus
.
data
,
badmus
.
data
),
axis
=
1
)
return
np
.
arange
(
len
(
mus
))[
proximity
<=
tol
]
class
GenericGreedyApproximant
(
GenericStandardApproximant
):
"""
ROM greedy interpolant computation for parametric problems
(ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. 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': number of starting training points;
- 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
defaults to 0.;
- 'interactive': whether to interactively terminate greedy
algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement; defaults to 0.2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to sampler.
Defaults to empty dict.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of 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.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'interactive': whether to interactively terminate greedy
algorithm;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
POD: whether to compute POD of snapshots.
S: number of test points.
sampler: Sample point generator.
greedyTol: Uniform error tolerance for greedy algorithm.
collinearityTol: Collinearity tolerance for greedy algorithm.
interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
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.
"""
TOL_INSTABILITY
=
1e-6
def
__init__
(
self
,
HFEngine
:
HFEng
,
mu0
:
paramVal
=
None
,
approxParameters
:
DictAny
=
{},
verbosity
:
int
=
10
,
timestamp
:
bool
=
True
):
self
.
_preInit
()
self
.
_addParametersToList
([
"greedyTol"
,
"collinearityTol"
,
"interactive"
,
"maxIter"
,
"refinementRatio"
,
"nTestPoints"
],
[
1e-2
,
0.
,
False
,
1e2
,
.
2
,
5e2
],
[
"trainSetGenerator"
],
[
"AUTO"
])
super
()
.
__init__
(
HFEngine
=
HFEngine
,
mu0
=
mu0
,
approxParameters
=
approxParameters
,
verbosity
=
verbosity
,
timestamp
=
timestamp
)
self
.
_postInit
()
@property
def
greedyTol
(
self
):
"""Value of greedyTol."""
return
self
.
_greedyTol
@greedyTol.setter
def
greedyTol
(
self
,
greedyTol
):
if
greedyTol
<
0
:
raise
RROMPyException
(
"greedyTol must be non-negative."
)
if
hasattr
(
self
,
"_greedyTol"
)
and
self
.
greedyTol
is
not
None
:
greedyTolold
=
self
.
greedyTol
else
:
greedyTolold
=
-
1
self
.
_greedyTol
=
greedyTol
self
.
_approxParameters
[
"greedyTol"
]
=
self
.
greedyTol
if
greedyTolold
!=
self
.
greedyTol
:
self
.
resetSamples
()
@property
def
collinearityTol
(
self
):
"""Value of collinearityTol."""
return
self
.
_collinearityTol
@collinearityTol.setter
def
collinearityTol
(
self
,
collinearityTol
):
if
collinearityTol
<
0
:
raise
RROMPyException
(
"collinearityTol must be non-negative."
)
if
(
hasattr
(
self
,
"_collinearityTol"
)
and
self
.
collinearityTol
is
not
None
):
collinearityTolold
=
self
.
collinearityTol
else
:
collinearityTolold
=
-
1
self
.
_collinearityTol
=
collinearityTol
self
.
_approxParameters
[
"collinearityTol"
]
=
self
.
collinearityTol
if
collinearityTolold
!=
self
.
collinearityTol
:
self
.
resetSamples
()
@property
def
interactive
(
self
):
"""Value of interactive."""
return
self
.
_interactive
@interactive.setter
def
interactive
(
self
,
interactive
):
self
.
_interactive
=
interactive
@property
def
maxIter
(
self
):
"""Value of maxIter."""
return
self
.
_maxIter
@maxIter.setter
def
maxIter
(
self
,
maxIter
):
if
maxIter
<=
0
:
raise
RROMPyException
(
"maxIter must be positive."
)
if
hasattr
(
self
,
"_maxIter"
)
and
self
.
maxIter
is
not
None
:
maxIterold
=
self
.
maxIter
else
:
maxIterold
=
-
1
self
.
_maxIter
=
maxIter
self
.
_approxParameters
[
"maxIter"
]
=
self
.
maxIter
if
maxIterold
!=
self
.
maxIter
:
self
.
resetSamples
()
@property
def
refinementRatio
(
self
):
"""Value of refinementRatio."""
return
self
.
_refinementRatio
@refinementRatio.setter
def
refinementRatio
(
self
,
refinementRatio
):
if
refinementRatio
<=
0.
or
refinementRatio
>
1.
:
raise
RROMPyException
((
"refinementRatio must be between 0 "
"(excluded) and 1."
))
if
(
hasattr
(
self
,
"_refinementRatio"
)
and
self
.
refinementRatio
is
not
None
):
refinementRatioold
=
self
.
refinementRatio
else
:
refinementRatioold
=
-
1
self
.
_refinementRatio
=
refinementRatio
self
.
_approxParameters
[
"refinementRatio"
]
=
self
.
refinementRatio
if
refinementRatioold
!=
self
.
refinementRatio
:
self
.
resetSamples
()
@property
def
nTestPoints
(
self
):
"""Value of nTestPoints."""
return
self
.
_nTestPoints
@nTestPoints.setter
def
nTestPoints
(
self
,
nTestPoints
):
if
nTestPoints
<=
0
:
raise
RROMPyException
(
"nTestPoints must be positive."
)
if
not
np
.
isclose
(
nTestPoints
,
np
.
int
(
nTestPoints
)):
raise
RROMPyException
(
"nTestPoints must be an integer."
)
nTestPoints
=
np
.
int
(
nTestPoints
)
if
hasattr
(
self
,
"_nTestPoints"
)
and
self
.
nTestPoints
is
not
None
:
nTestPointsold
=
self
.
nTestPoints
else
:
nTestPointsold
=
-
1
self
.
_nTestPoints
=
nTestPoints
self
.
_approxParameters
[
"nTestPoints"
]
=
self
.
nTestPoints
if
nTestPointsold
!=
self
.
nTestPoints
:
self
.
resetSamples
()
@property
def
trainSetGenerator
(
self
):
"""Value of trainSetGenerator."""
return
self
.
_trainSetGenerator
@trainSetGenerator.setter
def
trainSetGenerator
(
self
,
trainSetGenerator
):
if
(
isinstance
(
trainSetGenerator
,
(
str
,))
and
trainSetGenerator
.
upper
()
==
"AUTO"
):
trainSetGenerator
=
self
.
sampler
if
'generatePoints'
not
in
dir
(
trainSetGenerator
):
raise
RROMPyException
(
"trainSetGenerator type not recognized."
)
if
(
hasattr
(
self
,
'_trainSetGenerator'
)
and
self
.
trainSetGenerator
not
in
[
None
,
"AUTO"
]):
trainSetGeneratorOld
=
self
.
trainSetGenerator
self
.
_trainSetGenerator
=
trainSetGenerator
self
.
_approxParameters
[
"trainSetGenerator"
]
=
self
.
trainSetGenerator
if
(
not
'trainSetGeneratorOld'
in
locals
()
or
trainSetGeneratorOld
!=
self
.
trainSetGenerator
):
self
.
resetSamples
()
def
resetSamples
(
self
):
"""Reset samples."""
super
()
.
resetSamples
()
self
.
_mus
=
emptyParameterList
()
def
initEstimatorNormEngine
(
self
,
normEngn
:
normEng
=
None
):
"""Initialize estimator norm engine."""
if
(
normEngn
is
not
None
or
not
hasattr
(
self
,
"estimatorNormEngine"
)
or
self
.
estimatorNormEngine
is
None
):
if
normEngn
is
None
:
if
not
hasattr
(
self
.
HFEngine
,
"energyNormPartialDualMatrix"
):
self
.
HFEngine
.
buildEnergyNormPartialDualForm
()
estimatorEnergyMatrix
=
(
self
.
HFEngine
.
energyNormPartialDualMatrix
)
else
:
if
hasattr
(
normEngn
,
"buildEnergyNormPartialDualForm"
):
if
not
hasattr
(
normEngn
,
"energyNormPartialDualMatrix"
):
normEngn
.
buildEnergyNormPartialDualForm
()
estimatorEnergyMatrix
=
(
normEngn
.
energyNormPartialDualMatrix
)
else
:
estimatorEnergyMatrix
=
normEngn
self
.
estimatorNormEngine
=
normEngine
(
estimatorEnergyMatrix
)
def
_affineResidualMatricesContraction
(
self
,
rb
:
Np2D
,
rA
:
Np2D
=
None
)
\
->
Tuple
[
Np1D
,
Np1D
,
Np1D
]:
self
.
assembleReducedResidualBlocks
(
full
=
True
)
# 'ij,jk,ik->k', resbb, radiusb, radiusb.conj()
ff
=
np
.
sum
(
self
.
trainedModel
.
data
.
resbb
.
dot
(
rb
)
*
rb
.
conj
(),
axis
=
0
)
if
rA
is
None
:
return
ff
# 'ijk,jkl,il->l', resAb, radiusA, radiusb.conj()
Lf
=
np
.
sum
(
np
.
tensordot
(
self
.
trainedModel
.
data
.
resAb
,
rA
,
2
)
*
rb
.
conj
(),
axis
=
0
)
# 'ijkl,klt,ijt->t', resAA, radiusA, radiusA.conj()
LL
=
np
.
sum
(
np
.
tensordot
(
self
.
trainedModel
.
data
.
resAA
,
rA
,
2
)
*
rA
.
conj
(),
axis
=
(
0
,
1
))
return
ff
,
Lf
,
LL
def
errorEstimator
(
self
,
mus
:
Np1D
)
->
Np1D
:
"""Standard residual-based error estimator."""
self
.
setupApprox
()
mus
=
checkParameterList
(
mus
,
self
.
npar
)[
0
]
vbMng
(
self
.
trainedModel
,
"INIT"
,
"Evaluating error estimator at mu = {}."
.
format
(
mus
),
10
)
verb
=
self
.
trainedModel
.
verbosity
self
.
trainedModel
.
verbosity
=
0
uApproxRs
=
self
.
getApproxReduced
(
mus
)
muTestEff
=
mus
**
self
.
HFEngine
.
rescalingExp
radiusA
=
np
.
empty
((
len
(
self
.
HFEngine
.
thAs
),
len
(
mus
)),
dtype
=
np
.
complex
)
radiusb
=
np
.
empty
((
len
(
self
.
HFEngine
.
thbs
),
len
(
mus
)),
dtype
=
np
.
complex
)
for
j
,
thA
in
enumerate
(
self
.
HFEngine
.
thAs
):
radiusA
[
j
]
=
expressionEvaluator
(
thA
[
0
],
muTestEff
)
for
j
,
thb
in
enumerate
(
self
.
HFEngine
.
thbs
):
radiusb
[
j
]
=
expressionEvaluator
(
thb
[
0
],
muTestEff
)
radiusA
=
np
.
expand_dims
(
uApproxRs
.
data
,
1
)
*
radiusA
ff
,
Lf
,
LL
=
self
.
_affineResidualMatricesContraction
(
radiusb
,
radiusA
)
err
=
np
.
abs
((
LL
-
2.
*
np
.
real
(
Lf
)
+
ff
)
/
ff
)
**
.
5
self
.
trainedModel
.
verbosity
=
verb
vbMng
(
self
.
trainedModel
,
"DEL"
,
"Done evaluating error estimator"
,
10
)
return
err
def
getMaxErrorEstimator
(
self
,
mus
:
paramList
)
->
Tuple
[
Np1D
,
int
,
float
]:
"""
Compute maximum of (and index of maximum of) error estimator over given
parameters.
"""
errorEstTest
=
self
.
errorEstimator
(
mus
)
idxMaxEst
=
[
np
.
argmax
(
errorEstTest
)]
return
errorEstTest
,
idxMaxEst
,
errorEstTest
[
idxMaxEst
]
def
_isLastSampleCollinear
(
self
)
->
bool
:
"""Check collinearity of last sample."""
if
self
.
collinearityTol
<=
0.
:
return
False
if
self
.
POD
:
reff
=
self
.
samplingEngine
.
RPOD
[:,
-
1
]
else
:
RROMPyWarning
((
"Repeated orthogonalization of the samples for "
"collinearity check. Consider setting POD to "
"True."
))
if
not
hasattr
(
self
,
"_PODEngine"
):
from
rrompy.sampling.base.pod_engine
import
PODEngine
self
.
_PODEngine
=
PODEngine
(
self
.
HFEngine
)
reff
=
self
.
_PODEngine
.
generalizedQR
(
self
.
samplingEngine
.
samples
,
only_R
=
True
)[:,
-
1
]
cLevel
=
np
.
abs
(
reff
[
-
1
])
/
np
.
linalg
.
norm
(
reff
)
vbMng
(
self
,
"MAIN"
,
"Collinearity indicator {:.4e}."
.
format
(
cLevel
),
5
)
return
cLevel
<
self
.
collinearityTol
def
greedyNextSample
(
self
,
muidx
:
int
,
plotEst
:
bool
=
False
)
\
->
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
mu
in
mus
:
vbMng
(
self
,
"MAIN"
,
(
"Adding sample point no. {} at {} to training "
"set."
)
.
format
(
self
.
samplingEngine
.
nsamples
+
1
,
mu
),
2
)
self
.
mus
.
append
(
mu
)
self
.
samplingEngine
.
nextSample
(
mu
)
if
self
.
_isLastSampleCollinear
():
RROMPyWarning
(
"Collinearity above tolerance detected."
)
errorEstTest
=
np
.
empty
(
len
(
self
.
muTest
))
errorEstTest
[:]
=
np
.
nan
return
errorEstTest
,
[
-
1
],
np
.
nan
,
np
.
nan
errorEstTest
,
muidx
,
maxErrorEst
=
self
.
getMaxErrorEstimator
(
self
.
muTest
)
if
(
plotEst
and
not
np
.
any
(
np
.
isnan
(
errorEstTest
))
and
not
np
.
any
(
np
.
isinf
(
errorEstTest
))):
musre
=
copy
(
self
.
muTest
.
re
.
data
)
from
matplotlib
import
pyplot
as
plt
plt
.
figure
()
errCP
=
copy
(
errorEstTest
)
while
len
(
musre
)
>
0
:
if
self
.
npar
==
1
:
currIdx
=
np
.
arange
(
len
(
musre
))
else
:
currIdx
=
np
.
where
(
np
.
isclose
(
np
.
sum
(
np
.
abs
(
musre
[:,
1
:]
-
musre
[
0
,
1
:]),
1
),
0.
))[
0
]
plt
.
semilogy
(
musre
[
currIdx
,
0
],
errCP
[
currIdx
],
'k'
,
linewidth
=
1
)
musre
=
np
.
delete
(
musre
,
currIdx
,
0
)
errCP
=
np
.
delete
(
errCP
,
currIdx
)
plt
.
semilogy
([
self
.
muTest
.
re
(
0
,
0
),
self
.
muTest
.
re
(
-
1
,
0
)],
[
self
.
greedyTol
]
*
2
,
'r--'
)
plt
.
semilogy
(
self
.
mus
.
re
(
0
),
2.
*
self
.
greedyTol
*
np
.
ones
(
len
(
self
.
mus
)),
'*m'
)
plt
.
semilogy
(
self
.
muTest
.
re
(
muidx
,
0
),
maxErrorEst
,
'xr'
)
plt
.
grid
()
plt
.
show
()
plt
.
close
()
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
.
computeScaleFactor
()
self
.
resetSamples
()
self
.
mus
=
self
.
trainSetGenerator
.
generatePoints
(
self
.
S
)[
list
(
range
(
self
.
S
))]
muTestBase
=
self
.
sampler
.
generatePoints
(
self
.
nTestPoints
)
idxPop
=
pruneSamples
(
muTestBase
**
self
.
HFEngine
.
rescalingExp
,
self
.
mus
**
self
.
HFEngine
.
rescalingExp
,
1e-10
*
self
.
scaleFactor
[
0
])
muTestBase
.
pop
(
idxPop
)
muTestBase
=
muTestBase
.
sort
()
muLast
=
copy
(
self
.
mus
[
-
1
])
self
.
mus
.
pop
()
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
),
2
)
self
.
samplingEngine
.
iterSample
(
self
.
mus
)
self
.
muTest
=
emptyParameterList
()
self
.
muTest
.
reset
((
len
(
muTestBase
)
+
1
,
self
.
mus
.
shape
[
1
]))
self
.
muTest
[:
-
1
]
=
muTestBase
.
data
self
.
muTest
[
-
1
]
=
muLast
.
data
def
_enrichTestSet
(
self
,
nTest
:
int
):
"""Add extra elements to test set."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot enrich test set."
)
muTestExtra
=
self
.
sampler
.
generatePoints
(
2
*
nTest
)
muTotal
=
copy
(
self
.
mus
)
muTotal
.
append
(
self
.
muTest
)
idxPop
=
pruneSamples
(
muTestExtra
**
self
.
HFEngine
.
rescalingExp
,
muTotal
**
self
.
HFEngine
.
rescalingExp
,
1e-10
*
self
.
scaleFactor
[
0
])
muTestExtra
.
pop
(
idxPop
)
muTestNew
=
np
.
empty
((
len
(
self
.
muTest
)
+
len
(
muTestExtra
),
self
.
muTest
.
shape
[
1
]),
dtype
=
np
.
complex
)
muTestNew
[:
len
(
self
.
muTest
)]
=
self
.
muTest
.
data
muTestNew
[
len
(
self
.
muTest
)
:]
=
muTestExtra
.
data
self
.
muTest
=
checkParameterList
(
muTestNew
,
self
.
npar
)[
0
]
.
sort
()
vbMng
(
self
,
"MAIN"
,
"Enriching test set by {} elements."
.
format
(
len
(
muTestExtra
)),
5
)
def
greedy
(
self
,
plotEst
:
bool
=
False
):
"""Compute greedy snapshots of solution map."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot start greedy algorithm."
)
if
self
.
samplingEngine
.
nsamples
>
0
:
return
vbMng
(
self
,
"INIT"
,
"Starting computation of snapshots."
,
2
)
self
.
_preliminaryTraining
()
nTest
=
self
.
nTestPoints
muT0
=
copy
(
self
.
muTest
[
-
1
])
errorEstTest
,
muidx
,
maxErrorEst
,
mu
=
self
.
greedyNextSample
(
[
len
(
self
.
muTest
)
-
1
],
plotEst
)
if
np
.
any
(
np
.
isnan
(
maxErrorEst
)):
RROMPyWarning
((
"Instability in a posteriori estimator. "
"Starting preemptive greedy loop termination."
))
self
.
muTest
.
append
(
muT0
)
self
.
mus
.
pop
(
-
1
)
self
.
samplingEngine
.
popSample
()
self
.
setupApprox
()
else
:
vbMng
(
self
,
"MAIN"
,
(
"Uniform testing error estimate "
"{:.4e}."
)
.
format
(
np
.
max
(
maxErrorEst
)),
2
)
trainedModelOld
=
copy
(
self
.
trainedModel
)
while
(
self
.
samplingEngine
.
nsamples
<
self
.
maxIter
and
np
.
max
(
maxErrorEst
)
>
self
.
greedyTol
):
if
(
1.
-
self
.
refinementRatio
)
*
nTest
>
len
(
self
.
muTest
):
self
.
_enrichTestSet
(
nTest
)
nTest
=
len
(
self
.
muTest
)
muTestOld
,
maxErrorEstOld
=
self
.
muTest
,
np
.
max
(
maxErrorEst
)
errorEstTest
,
muidx
,
maxErrorEst
,
mu
=
self
.
greedyNextSample
(
muidx
,
plotEst
)
vbMng
(
self
,
"MAIN"
,
(
"Uniform testing error estimate "
"{:.4e}."
)
.
format
(
np
.
max
(
maxErrorEst
)),
2
)
if
(
np
.
any
(
np
.
isnan
(
maxErrorEst
))
or
np
.
any
(
np
.
isinf
(
maxErrorEst
))
or
maxErrorEstOld
<
(
np
.
max
(
maxErrorEst
)
*
self
.
TOL_INSTABILITY
)):
RROMPyWarning
((
"Instability in a posteriori estimator. "
"Starting preemptive greedy loop "
"termination."
))
self
.
muTest
=
muTestOld
self
.
mus
.
pop
(
-
1
)
self
.
samplingEngine
.
popSample
()
self
.
trainedModel
.
data
=
copy
(
trainedModelOld
.
data
)
break
trainedModelOld
.
data
=
copy
(
self
.
trainedModel
.
data
)
if
(
self
.
interactive
and
np
.
max
(
maxErrorEst
)
<=
self
.
greedyTol
):
vbMng
(
self
,
"MAIN"
,
(
"Required tolerance {} achieved. Want to decrease "
"greedyTol and continue? "
"Y/N"
)
.
format
(
self
.
greedyTol
),
0
,
end
=
""
)
increasemaxIter
=
input
()
if
increasemaxIter
.
upper
()
==
"Y"
:
vbMng
(
self
,
"MAIN"
,
"Reducing value of greedyTol..."
,
0
)
while
np
.
max
(
maxErrorEst
)
<=
self
.
_greedyTol
:
self
.
_greedyTol
*=
.
5
if
(
self
.
interactive
and
self
.
samplingEngine
.
nsamples
>=
self
.
maxIter
):
vbMng
(
self
,
"MAIN"
,
(
"Maximum number of iterations {} reached. Want to "
"increase maxIter and continue? "
"Y/N"
)
.
format
(
self
.
maxIter
),
0
,
end
=
""
)
increasemaxIter
=
input
()
if
increasemaxIter
.
upper
()
==
"Y"
:
vbMng
(
self
,
"MAIN"
,
"Doubling value of maxIter..."
,
0
)
self
.
_maxIter
*=
2
vbMng
(
self
,
"DEL"
,
(
"Done computing snapshots (final snapshot count: "
"{})."
)
.
format
(
self
.
samplingEngine
.
nsamples
),
2
)
def
checkComputedApprox
(
self
)
->
bool
:
"""
Check if setup of new approximant is not needed.
Returns:
True if new setup is not needed. False otherwise.
"""
return
(
super
()
.
checkComputedApprox
()
and
len
(
self
.
mus
)
==
self
.
trainedModel
.
data
.
projMat
.
shape
[
1
])
def
assembleReducedResidualGramian
(
self
,
pMat
:
sampList
):
"""
Build residual gramian of reduced linear system through projections.
"""
self
.
initEstimatorNormEngine
()
if
(
not
hasattr
(
self
.
trainedModel
.
data
,
"gramian"
)
or
self
.
trainedModel
.
data
.
gramian
is
None
):
gramian
=
self
.
estimatorNormEngine
.
innerProduct
(
pMat
,
pMat
)
else
:
Sold
=
self
.
trainedModel
.
data
.
gramian
.
shape
[
0
]
S
=
len
(
self
.
mus
)
if
Sold
>
S
:
gramian
=
self
.
trainedModel
.
data
.
gramian
[:
S
,
:
S
]
else
:
idxOld
=
list
(
range
(
Sold
))
idxNew
=
list
(
range
(
Sold
,
S
))
gramian
=
np
.
empty
((
S
,
S
),
dtype
=
np
.
complex
)
gramian
[:
Sold
,
:
Sold
]
=
self
.
trainedModel
.
data
.
gramian
gramian
[:
Sold
,
Sold
:]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
pMat
(
idxNew
),
pMat
(
idxOld
)))
gramian
[
Sold
:,
:
Sold
]
=
gramian
[:
Sold
,
Sold
:]
.
T
.
conj
()
gramian
[
Sold
:,
Sold
:]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
pMat
(
idxNew
),
pMat
(
idxNew
)))
self
.
trainedModel
.
data
.
gramian
=
gramian
def
assembleReducedResidualBlocksbb
(
self
,
bs
:
List
[
Np1D
]):
"""
Build blocks (of type bb) of reduced linear system through projections.
"""
self
.
initEstimatorNormEngine
()
nbs
=
len
(
bs
)
if
(
not
hasattr
(
self
.
trainedModel
.
data
,
"resbb"
)
or
self
.
trainedModel
.
data
.
resbb
is
None
):
resbb
=
np
.
empty
((
nbs
,
nbs
),
dtype
=
np
.
complex
)
for
i
in
range
(
nbs
):
Mbi
=
bs
[
i
]
resbb
[
i
,
i
]
=
self
.
estimatorNormEngine
.
innerProduct
(
Mbi
,
Mbi
)
for
j
in
range
(
i
):
Mbj
=
bs
[
j
]
resbb
[
i
,
j
]
=
self
.
estimatorNormEngine
.
innerProduct
(
Mbj
,
Mbi
)
for
i
in
range
(
nbs
):
for
j
in
range
(
i
+
1
,
nbs
):
resbb
[
i
,
j
]
=
resbb
[
j
,
i
]
.
conj
()
self
.
trainedModel
.
data
.
resbb
=
resbb
def
assembleReducedResidualBlocksAb
(
self
,
As
:
List
[
Np2D
],
bs
:
List
[
Np1D
],
pMat
:
sampList
):
"""
Build blocks (of type Ab) of reduced linear system through projections.
"""
self
.
initEstimatorNormEngine
()
nAs
=
len
(
As
)
nbs
=
len
(
bs
)
S
=
len
(
self
.
mus
)
if
(
not
hasattr
(
self
.
trainedModel
.
data
,
"resAb"
)
or
self
.
trainedModel
.
data
.
resAb
is
None
):
if
not
isinstance
(
pMat
,
(
np
.
ndarray
,)):
pMat
=
pMat
.
data
resAb
=
np
.
empty
((
nbs
,
S
,
nAs
),
dtype
=
np
.
complex
)
for
j
in
range
(
nAs
):
MAj
=
dot
(
As
[
j
],
pMat
)
for
i
in
range
(
nbs
):
Mbi
=
bs
[
i
]
resAb
[
i
,
:,
j
]
=
self
.
estimatorNormEngine
.
innerProduct
(
MAj
,
Mbi
)
else
:
Sold
=
self
.
trainedModel
.
data
.
resAb
.
shape
[
1
]
if
Sold
==
S
:
return
if
Sold
>
S
:
resAb
=
self
.
trainedModel
.
data
.
resAb
[:,
:
S
,
:]
else
:
if
not
isinstance
(
pMat
,
(
np
.
ndarray
,)):
pMat
=
pMat
.
data
resAb
=
np
.
empty
((
nbs
,
S
,
nAs
),
dtype
=
np
.
complex
)
resAb
[:,
:
Sold
,
:]
=
self
.
trainedModel
.
data
.
resAb
for
j
in
range
(
nAs
):
MAj
=
dot
(
As
[
j
],
pMat
[:,
Sold
:])
for
i
in
range
(
nbs
):
Mbi
=
bs
[
i
]
resAb
[
i
,
Sold
:,
j
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAj
,
Mbi
))
self
.
trainedModel
.
data
.
resAb
=
resAb
def
assembleReducedResidualBlocksAA
(
self
,
As
:
List
[
Np2D
],
pMat
:
sampList
):
"""
Build blocks (of type AA) of reduced linear system through projections.
"""
self
.
initEstimatorNormEngine
()
nAs
=
len
(
As
)
S
=
len
(
self
.
mus
)
if
(
not
hasattr
(
self
.
trainedModel
.
data
,
"resAA"
)
or
self
.
trainedModel
.
data
.
resAA
is
None
):
if
not
isinstance
(
pMat
,
(
np
.
ndarray
,)):
pMat
=
pMat
.
data
resAA
=
np
.
empty
((
S
,
nAs
,
S
,
nAs
),
dtype
=
np
.
complex
)
for
i
in
range
(
nAs
):
MAi
=
dot
(
As
[
i
],
pMat
)
resAA
[:,
i
,
:,
i
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAi
,
MAi
))
for
j
in
range
(
i
):
MAj
=
dot
(
As
[
j
],
pMat
)
resAA
[:,
i
,
:,
j
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAj
,
MAi
))
for
i
in
range
(
nAs
):
for
j
in
range
(
i
+
1
,
nAs
):
resAA
[:,
i
,
:,
j
]
=
resAA
[:,
j
,
:,
i
]
.
T
.
conj
()
else
:
Sold
=
self
.
trainedModel
.
data
.
resAA
.
shape
[
0
]
if
Sold
==
S
:
return
if
Sold
>
S
:
resAA
=
self
.
trainedModel
.
data
.
resAA
[:
S
,
:,
:
S
,
:]
else
:
if
not
isinstance
(
pMat
,
(
np
.
ndarray
,)):
pMat
=
pMat
.
data
resAA
=
np
.
empty
((
S
,
nAs
,
S
,
nAs
),
dtype
=
np
.
complex
)
resAA
[:
Sold
,
:,
:
Sold
,
:]
=
self
.
trainedModel
.
data
.
resAA
for
i
in
range
(
nAs
):
MAi
=
dot
(
As
[
i
],
pMat
)
resAA
[:
Sold
,
i
,
Sold
:,
i
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAi
[:,
Sold
:],
MAi
[:,
:
Sold
]))
resAA
[
Sold
:,
i
,
:
Sold
,
i
]
=
resAA
[:
Sold
,
i
,
Sold
:,
i
]
.
T
.
conj
()
resAA
[
Sold
:,
i
,
Sold
:,
i
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAi
[:,
Sold
:],
MAi
[:,
Sold
:]))
for
j
in
range
(
i
):
MAj
=
dot
(
As
[
j
],
pMat
)
resAA
[:
Sold
,
i
,
Sold
:,
j
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAj
[:,
Sold
:],
MAi
[:,
:
Sold
]))
resAA
[
Sold
:,
i
,
:
Sold
,
j
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAj
[:,
:
Sold
],
MAi
[:,
Sold
:]))
resAA
[
Sold
:,
i
,
Sold
:,
j
]
=
(
self
.
estimatorNormEngine
.
innerProduct
(
MAj
[:,
Sold
:],
MAi
[:,
Sold
:]))
for
i
in
range
(
nAs
):
for
j
in
range
(
i
+
1
,
nAs
):
resAA
[:
Sold
,
i
,
Sold
:,
j
]
=
(
resAA
[
Sold
:,
j
,
:
Sold
,
i
]
.
T
.
conj
())
resAA
[
Sold
:,
i
,
:
Sold
,
j
]
=
(
resAA
[:
Sold
,
j
,
Sold
:,
i
]
.
T
.
conj
())
resAA
[
Sold
:,
i
,
Sold
:,
j
]
=
(
resAA
[
Sold
:,
j
,
Sold
:,
i
]
.
T
.
conj
())
self
.
trainedModel
.
data
.
resAA
=
resAA
def
assembleReducedResidualBlocks
(
self
,
full
:
bool
=
False
):
"""Build affine blocks of affine decomposition of residual."""
self
.
assembleReducedResidualBlocksbb
(
self
.
HFEngine
.
bs
)
if
full
:
pMat
=
self
.
trainedModel
.
data
.
projMat
self
.
assembleReducedResidualBlocksAb
(
self
.
HFEngine
.
As
,
self
.
HFEngine
.
bs
,
pMat
)
self
.
assembleReducedResidualBlocksAA
(
self
.
HFEngine
.
As
,
pMat
)
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