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rational_interpolant_greedy_pivoted.py
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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.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 _marginalizeMiscellanea(self, forward:bool):
if forward:
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]]]}
else:
self._mus = self._m_selfmus
self.HFEngine.parameterMap = self._m_HFEparameterMap
del self._m_selfmus, self._m_HFEparameterMap
def _marginalizeTrainedModel(self, forward:bool):
if forward:
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 hasattr(self.HFEngine.A, "is_affine"):
self._A_is_affine = self.HFEngine.A.is_affine
else:
self._A_is_affine = 0
if hasattr(self.HFEngine.b, "is_affine"):
self._b_is_affine = self.HFEngine.b.is_affine
else:
self._b_is_affine = 0
if self._A_is_affine >= 1 / 2 and self._b_is_affine >= 1 / 2:
self._affine_lvl += [1 / 2]
else:
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._A_is_affine >= 1 / 2 and self._b_is_affine >= 1 / 2:
self._affine_lvl.pop()
del self._A_is_affine, self._b_is_affine
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(True)
errRes = super().errorEstimator(mus, return_max)
self._marginalizeTrainedModel(False)
return errRes
def _preliminaryTraining(self):
"""Initialize starting snapshots of solution map."""
RROMPyAssert(self._mode, message = "Cannot start greedy algorithm.")
self.resetSamples()
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._S = len(self.mus)
self._approxParameters["S"] = self.S
def setupApproxLocal(self) -> int:
"""Compute rational interpolant."""
self._marginalizeMiscellanea(True)
setupOK = super().setupApproxLocal()
self._marginalizeMiscellanea(False)
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 self.POD == 1 and not (
hasattr(self.HFEngine.C, "is_mu_independent")
and self.HFEngine.C.is_mu_independent in self._output_lvl):
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;
- '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', 'DOMINANT',
'BARYCENTRIC[_NORM]', and 'BARYCENTRIC_AVERAGE' (check pdf in
main folder for explanation); 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;
- '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.
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;
- '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', 'DOMINANT',
'BARYCENTRIC[_NORM]', and 'BARYCENTRIC_AVERAGE' (check pdf in
main folder for explanation); 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;
- '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.
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;
- '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', 'DOMINANT',
'BARYCENTRIC[_NORM]', and 'BARYCENTRIC_AVERAGE' (check pdf in
main folder for explanation); 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;
- '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.
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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