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rational_interpolant_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/>.
#
import numpy as np
from collections.abc import Iterable
from copy import deepcopy as copy
from .generic_pivoted_approximant import (GenericPivotedApproximantBase,
GenericPivotedApproximantNoMatch,
GenericPivotedApproximantPolyMatch,
GenericPivotedApproximantPoleMatch)
from .gather_pivoted_approximant import gatherPivotedApproximant
from rrompy.reduction_methods.standard.rational_interpolant import (
RationalInterpolant)
from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.base.types import paramList
from rrompy.utilities.numerical.hash_derivative import nextDerivativeIndices
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__ = ['RationalInterpolantPivotedNoMatch',
'RationalInterpolantPivotedPolyMatch',
'RationalInterpolantPivotedPoleMatch']
class RationalInterpolantPivotedBase(GenericPivotedApproximantBase,
RationalInterpolant):
def __init__(self, *args, **kwargs):
self._preInit()
self._addParametersToList(toBeExcluded = ["polydegreetype",
"MAuxiliary", "NAuxiliary"])
super().__init__(*args, **kwargs)
if self.nparPivot > 1: self.HFEngine._ignoreResidues = 1
self._postInit()
@property
def MAuxiliary(self): return 0
@property
def NAuxiliary(self): return 0
@property
def polydegreetype(self): return "TENSOR_TOTAL"
@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 isinstance(scaleFactorDer, Iterable):
scaleFactorDer = list(scaleFactorDer)
self._scaleFactorDer = scaleFactorDer
self._approxParameters["scaleFactorDer"] = self._scaleFactorDer
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 addMarginalSamplePoints(self, musMarginal:paramList) -> 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."))
mus = np.empty((self.S * len(musMarginal), self.HFEngine.npar),
dtype = np.complex)
mus[:, self.directionPivot] = np.tile(self.musPivot.data,
(len(musMarginal), 1))
mus[:, self.directionMarginal] = np.repeat(musMarginal.data, self.S,
axis = 0)
self._mus.append(mus)
self._musMarginal.append(musMarginal)
N0 = copy(self.N)
req, is_master = [], masterCore()
idx, sizes = indicesScatter(len(musMarginal), return_sizes = True)
_collapsed = self.trainedModel.data._collapsed
pMat, Ps, Qs = None, [], []
emptyCores = np.where(np.array(sizes) == 0)[0] if is_master else []
if len(idx) == 0:
vbMng(self, "MAIN", "Idling.", 30)
if self.storeAllSamples: self.storeSamples()
pL = recv(source = 0, tag = poolRank())
pMat = np.empty((pL, 0), dtype = np.complex)
else:
_scaleFactorOldPivot = copy(self.scaleFactor)
self.scaleFactor = self.scaleFactorPivot
self._temporaryPivot = 1
for i in idx:
musi = self.mus[self.S * (i + self.SMarginal)
: self.S * (i + self.SMarginal + 1)]
vbMng(self, "MAIN",
"Building marginal model no. {} at {}.".format(
i + self.SMarginal + 1,
self.musMarginal[i + self.SMarginal]), 5)
vbMng(self, "INIT", "Starting computation of snapshots.", 10)
self.samplingEngine.resetHistory()
self.samplingEngine.iterSample(musi)
vbMng(self, "DEL", "Done computing snapshots.", 10)
self.verbosity -= 5
self.samplingEngine.verbosity -= 5
if self.rationalMode[-6:] == "OUTPUT":
vbMng(self, "INIT", "Extracting system output from state.",
35)
self.samplingEngine.samples_output = self.HFEngine.applyC(
self.samplingEngine.samples, self.mus)
_POD, self._POD = self.POD, 1
vbMng(self, "DEL", "Done extracting system output.", 35)
self._setupRational(self._setupDenominator())
if self.rationalMode[-6:] == "OUTPUT":
self._POD = _POD
pMati = np.empty((1, 0), dtype = np.complex)
else:
pMati = self.samplingEngine.projectionMatrix
self.verbosity += 5
self.samplingEngine.verbosity += 5
if self.storeAllSamples: self.storeSamples(i + self.SMarginal)
if self.rationalMode[-6:] != "OUTPUT" and 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:
for dest in emptyCores:
req += [isend(len(pMati), dest = dest, tag = dest)]
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 and self.rationalMode[-6:] != "OUTPUT":
Ps[-1].postmultiplyTensorize(pMati.T) # collapse by hand
del self.trainedModel.data.Q, self.trainedModel.data.P
self.N = N0
del self._temporaryPivot
self.scaleFactor = _scaleFactorOldPivot
if _collapsed: pMat = pMati[:, : 0]
for r in req: r.wait()
pMat, Ps, Qs, _, _ = gatherPivotedApproximant(pMat, Ps, Qs,
self.mus.data, sizes,
self.polybasis, False)
if _collapsed:
self._setupTrainedModel(1.)
Psupp = [0] * len(musMarginal)
else:
self._setupTrainedModel(pMat,
len(self.trainedModel.data.projMat) > 0)
Psupp = (self.SMarginal + np.arange(0, len(musMarginal))) * self.S
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) -> 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._mus = emptyParameterList()
self._musMarginal = emptyParameterList()
self.musPivot = self.samplerPivot.generatePoints(self.S)
while len(self.musPivot) > self.S: self.musPivot.pop()
musMarginal = self.samplerMarginal.generatePoints(self.SMarginal)
while len(musMarginal) > self.SMarginal: musMarginal.pop()
self._setupTrainedModel(np.zeros((0, 0)), forceNew = True,
collapsed = self.rationalMode[-6:] == "OUTPUT")
self.trainedModel.data.Qs, self.trainedModel.data.Ps = [], []
self.trainedModel.data.Psupp = []
self._SMarginal = 0
val = self.addMarginalSamplePoints(musMarginal)
vbMng(self, "DEL", "Done setting up approximant.", 5)
return val
class RationalInterpolantPivotedNoMatch(RationalInterpolantPivotedBase,
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;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'rationalMode': mode of rational approximation; allowed values
include 'MINIMAL[_STATE]', 'MINIMAL_OUTPUT',
'STANDARD[_STATE]', and 'STANDARD_OUTPUT'; defaults to
'MINIMAL';
- '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;
- '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.
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': kind of snapshots orthogonalization;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'rationalMode': mode of rational approximation;
- 'polybasis': type of polynomial basis for pivot
interpolation;
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- '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.
samplerPivot: Pivot sample point generator.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
rationalMode: Mode of rational approximation.
polybasis: Type of polynomial basis for pivot interpolation.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
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 RationalInterpolantPivotedPolyMatch(RationalInterpolantPivotedBase,
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;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'rationalMode': mode of rational approximation; allowed values
include 'MINIMAL[_STATE]', 'MINIMAL_OUTPUT',
'STANDARD[_STATE]', and 'STANDARD_OUTPUT'; defaults to
'MINIMAL';
- '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.
- '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;
- '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.
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': 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;
- 'rationalMode': mode of rational approximation;
- '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.
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- '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.
samplerPivot: Pivot sample point generator.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
rationalMode: Mode of rational approximation.
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.
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
if self.rationalMode[-6:] == "OUTPUT": self.matchState = False
self.purgeparamsMarginal()
setupOK = super().setupApprox(*args, **kwargs)
if self.matchState: self._postApplyC()
return setupOK
class RationalInterpolantPivotedPoleMatch(RationalInterpolantPivotedBase,
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;
- 'rationalMode': mode of rational approximation; allowed values
include 'MINIMAL[_STATE]', 'MINIMAL_OUTPUT',
'STANDARD[_STATE]', and 'STANDARD_OUTPUT'; defaults to
'MINIMAL';
- '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.
- '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;
- '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.
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': 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;
- 'rationalMode': mode of rational approximation;
- '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.
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- '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.
rationalMode: Mode of rational approximation.
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.
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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