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rational_interpolant_pivoted.py
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rational_interpolant_pivoted.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
from copy import deepcopy as copy
import numpy as np
from .generic_pivoted_approximant import (GenericPivotedApproximantBase,
GenericPivotedApproximantNoMatch,
GenericPivotedApproximant)
from rrompy.reduction_methods.standard.rational_interpolant import (
RationalInterpolant)
from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.numerical.hash_derivative import nextDerivativeIndices
from rrompy.utilities.exception_manager import RROMPyAssert, RROMPyWarning
from rrompy.parameter import emptyParameterList
__all__ = ['RationalInterpolantPivotedNoMatch', 'RationalInterpolantPivoted']
class RationalInterpolantPivotedBase(GenericPivotedApproximantBase,
RationalInterpolant):
def __init__(self, *args, **kwargs):
self._preInit()
self._addParametersToList(toBeExcluded = ["polydegreetype", "sampler"])
super().__init__(*args, **kwargs)
self._postInit()
@property
def scaleFactorDer(self):
"""Value of scaleFactorDer."""
if self._scaleFactorDer == "NONE": return 1.
if self._scaleFactorDer == "AUTO": return self.scaleFactorPivot
return self._scaleFactorDer
@scaleFactorDer.setter
def scaleFactorDer(self, scaleFactorDer):
if isinstance(scaleFactorDer, (str,)):
scaleFactorDer = scaleFactorDer.upper()
elif hasattr(scaleFactorDer, "__len__"):
scaleFactorDer = list(scaleFactorDer)
self._scaleFactorDer = scaleFactorDer
self._approxParameters["scaleFactorDer"] = self._scaleFactorDer
@property
def polydegreetype(self):
"""Value of polydegreetype."""
return "TOTAL"
@polydegreetype.setter
def polydegreetype(self, polydegreetype):
RROMPyWarning(("polydegreetype is used just to simplify inheritance, "
"and its value cannot be changed from 'TOTAL'."))
@property
def polybasis0(self):
if "_" in self.polybasis:
return self.polybasis.split("_")[0]
return self.polybasis
@property
def correctorTol(self):
"""Value of correctorTol."""
return self._correctorTol
@correctorTol.setter
def correctorTol(self, correctorTol):
if correctorTol < 0. or (correctorTol > 0. and self.nparPivot > 1):
RROMPyWarning(("Overriding prescribed corrector tolerance "
"to 0."))
correctorTol = 0.
self._correctorTol = correctorTol
self._approxParameters["correctorTol"] = self.correctorTol
@property
def correctorMaxIter(self):
"""Value of correctorMaxIter."""
return self._correctorMaxIter
@correctorMaxIter.setter
def correctorMaxIter(self, correctorMaxIter):
if correctorMaxIter < 1 or (correctorMaxIter > 1
and self.nparPivot > 1):
RROMPyWarning(("Overriding prescribed max number of corrector "
"iterations to 1."))
correctorMaxIter = 1
self._correctorMaxIter = correctorMaxIter
self._approxParameters["correctorMaxIter"] = self.correctorMaxIter
def _setupInterpolationIndices(self):
"""Setup parameters for polyvander."""
RROMPyAssert(self._mode,
message = "Cannot setup interpolation indices.")
if (self._musUniqueCN is None
or len(self._reorder) != len(self.musPivot)):
try:
muPC = self.trainedModel.centerNormalizePivot(self.musPivot)
except:
muPC = self.trainedModel.centerNormalize(self.musPivot)
self._musUniqueCN, musIdxsTo, musIdxs, musCount = (muPC.unique(
return_index = True, return_inverse = True,
return_counts = True))
self._musUnique = self.musPivot[musIdxsTo]
self._derIdxs = [None] * len(self._musUniqueCN)
self._reorder = np.empty(len(musIdxs), dtype = int)
filled = 0
for j, cnt in enumerate(musCount):
self._derIdxs[j] = nextDerivativeIndices([], self.nparPivot,
cnt)
jIdx = np.nonzero(musIdxs == j)[0]
self._reorder[jIdx] = np.arange(filled, filled + cnt)
filled += cnt
def setupApprox(self) -> 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.resetSamples()
self.samplingEngine.scaleFactor = self.scaleFactorDer
self.musPivot = self.samplerPivot.generatePoints(self.S)
while len(self.musPivot) > self.S: self.musPivot.pop()
self._musMarginal = self.samplerMarginal.generatePoints(self.SMarginal)
while len(self.musMarginal) > self.SMarginal: self.musMarginal.pop()
self.mus = emptyParameterList()
self.mus.reset((self.S * self.SMarginal, self.HFEngine.npar))
for j, muMarg in enumerate(self.musMarginal):
for k in range(j * self.S, (j + 1) * self.S):
self.mus.data[k, self.directionPivot] = (
self.musPivot[k - j * self.S].data)
self.mus.data[k, self.directionMarginal] = muMarg.data
if not self._noSampleMemory:
vbMng(self, "INIT", "Starting computation of snapshots.", 5)
self.samplingEngine.resetHistory(self.SMarginal)
self.samplingEngine.iterSample(self.musPivot, self.musMarginal)
vbMng(self, "DEL", "Done computing snapshots.", 5)
if self.POD:
self._RPODOldPivot = copy(self.samplingEngine.RPOD)
else:
self._samplesOldPivot = copy(self.samplingEngine.samples)
N0 = copy(self.N)
Qs, Ps = [None] * len(self.musMarginal), [None] * len(self.musMarginal)
if self._noSampleMemory:
pMat = np.zeros((0, 0))
else:
pMat = self.samplingEngine.samplesCoalesced.data
self._setupTrainedModel(pMat, forceNew = True)
_scaleFactorOldPivot = copy(self.scaleFactor)
self.scaleFactor = self.scaleFactorPivot
self._temporaryPivot = 1
for j, muMarg in enumerate(self.musMarginal):
vbMng(self, "MAIN",
"Building marginal model no. {} at {}.".format(j + 1,
muMarg), 5)
if self._noSampleMemory:
vbMng(self, "INIT", "Starting computation of snapshots.", 5)
self.samplingEngine.resetHistory()
self.samplingEngine.iterSample(
self.mus.data[self.S * j : self.S * (j + 1)])
vbMng(self, "DEL", "Done computing snapshots.", 5)
self._setupTrainedModel(self.samplingEngine.samples.data,
j > 0)
self.N = N0
if not self._noSampleMemory:
if self.POD:
self.samplingEngine.RPOD = self._RPODOldPivot[j]
else:
self.samplingEngine.samples = self._samplesOldPivot[j]
self.verbosity -= 5
self._iterCorrector()
self.verbosity += 5
Qs[j] = copy(self.trainedModel.data.Q)
Ps[j] = copy(self.trainedModel.data.P)
del self.trainedModel.data.Q, self.trainedModel.data.P
if not self._noSampleMemory:
if self.POD:
self.samplingEngine.RPOD = copy(self._RPODOldPivot)
del self._RPODOldPivot
else:
self.samplingEngine.samples = copy(self._samplesOldPivot)
del self._samplesOldPivot
Psupp = np.arange(0, len(self.musMarginal) * self.S, self.S)
self.scaleFactor = _scaleFactorOldPivot
del self._temporaryPivot
self.trainedModel.data.Qs, self.trainedModel.data.Ps = Qs, Ps
self.trainedModel.data.Psupp = list(Psupp)
self._poleMatching()
self._finalizeMarginalization()
vbMng(self, "DEL", "Done setting up approximant.", 5)
return 0
class RationalInterpolantPivotedNoMatch(RationalInterpolantPivotedBase,
GenericPivotedApproximantNoMatch):
"""
ROM pivoted rational interpolant (without 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': whether to compute POD of snapshots; defaults to True;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
defaults to np.inf;
- '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;
- 'polybasis': type of polynomial basis for pivot
interpolation; 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;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator; defaults to 1;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'interpRcond': tolerance for pivot 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;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
- 'polybasis': type of polynomial basis for pivot
interpolation;
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'interpRcond': tolerance for pivot 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;
- 'samplerMarginal': marginal sample point generator.
approx_state: Whether to approximate state.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
scaleFactorDer: Scaling factors for derivative computation.
cutOffTolerance: Tolerance for ignoring parasitic poles.
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.
polybasis: Type of polynomial basis for pivot interpolation.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
radialDirectionalWeights: Radial basis weights for pivot numerator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
interpRcond: Tolerance for pivot 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.
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 _poleMatching(self):
vbMng(self, "INIT", "Compressing poles.", 10)
self.trainedModel.initializeFromRational()
vbMng(self, "DEL", "Done compressing poles.", 10)
class RationalInterpolantPivoted(RationalInterpolantPivotedBase,
GenericPivotedApproximant):
"""
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': whether to compute POD of snapshots; defaults to True;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'matchingWeight': weight for pole matching optimization; defaults
to 1;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
defaults to np.inf;
- 'cutOffSharedRatio': required ratio of marginal points to share
resonance in cut off strategy; defaults to 1.;
- '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;
- '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' or
'PIECEWISE_LINEAR_*';
. 'polydegreetypeMarginal': type of polynomial degree for
marginal; defaults to 'TOTAL'; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'interpRcondMarginal': tolerance for marginal interpolation;
defaults to None; not for 'NEARESTNEIGHBOR'.
- '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;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator; defaults to 1;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'interpRcond': tolerance for pivot 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;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'matchingWeight': weight for pole matching optimization;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
- 'cutOffSharedRatio': required ratio of marginal points to share
resonance in cut off strategy;
- '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;
. 'interpRcondMarginal': tolerance for marginal interpolation.
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'interpRcond': tolerance for pivot 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;
- 'samplerMarginal': marginal sample point generator.
approx_state: Whether to approximate state.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
scaleFactorDer: Scaling factors for derivative computation.
matchingWeight: Weight for pole matching optimization.
cutOffTolerance: Tolerance for ignoring parasitic poles.
cutOffSharedRatio: Required ratio of marginal points to share resonance
in cut off strategy.
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.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
paramsMarginal: Dictionary of parameters for marginal interpolation.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
radialDirectionalWeights: Radial basis weights for pivot numerator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
interpRcond: Tolerance for pivot 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.
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 _poleMatching(self):
vbMng(self, "INIT", "Compressing and matching poles.", 10)
self.trainedModel.initializeFromRational(self.HFEngine,
self.matchingWeight, False)
vbMng(self, "DEL", "Done compressing and matching poles.", 10)
def setupApprox(self, *args, **kwargs) -> int:
if self.checkComputedApprox(): return -1
self.purgeparamsMarginal()
return super().setupApprox(*args, **kwargs)

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