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rational_interpolant_pivoted_greedy.py
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rational_interpolant_pivoted_greedy.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_greedy_approximant import (
GenericPivotedGreedyApproximantBase,
GenericPivotedGreedyApproximantPoleMatch)
from rrompy.reduction_methods.standard import RationalInterpolant
from rrompy.reduction_methods.pivoted import (
RationalInterpolantPivotedPoleMatch)
from rrompy.utilities.base.types import paramList
from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.parameter import emptyParameterList
from rrompy.utilities.parallel import poolRank, recv
__all__ = ['RationalInterpolantPivotedGreedyPoleMatch']
class RationalInterpolantPivotedGreedyBase(
GenericPivotedGreedyApproximantBase):
def computeSnapshots(self):
"""Compute snapshots of solution map."""
RROMPyAssert(self._mode,
message = "Cannot start snapshot computation.")
vbMng(self, "INIT", "Starting computation of snapshots.", 5)
self.samplingEngine.scaleFactor = self.scaleFactorDer
if not hasattr(self, "musPivot") or len(self.musPivot) != self.S:
self.musPivot = self.samplerPivot.generatePoints(self.S)
while len(self.musPivot) > self.S: self.musPivot.pop()
musLoc = emptyParameterList()
musLoc.reset((self.S, self.HFEngine.npar))
self.samplingEngine.resetHistory()
musLoc.data[:, self.directionPivot] = self.musPivot.data
musLoc.data[:, self.directionMarginal] = np.repeat(self.muMargLoc,
self.S, axis = 0)
self.samplingEngine.iterSample(musLoc)
vbMng(self, "DEL", "Done computing snapshots.", 5)
self._m_selfmus = copy(musLoc)
self._mus = self.musPivot
self._m_HFEparameterMap = copy(self.HFEngine.parameterMap)
self.HFEngine.parameterMap = {
"F": [self.HFEngine.parameterMap["F"][self.directionPivot[0]]],
"B": [self.HFEngine.parameterMap["B"][self.directionPivot[0]]]}
def addMarginalSamplePoints(self, musMarginal:paramList, *args, **kwargs):
"""Add marginal sample points to reduced model."""
raise RROMPyException(("Cannot add marginal samples to marginal "
"greedy reduced model."))
def setupApproxPivoted(self, mus:paramList) -> int:
if self.checkComputedApproxPivoted(): return -1
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
vbMng(self, "INIT", "Setting up pivoted approximant.", 10)
idx, sizes, emptyCores = self._preSetupApproxPivoted(mus)
pMat, Ps, Qs, req, musA = None, [], [], [], None
if len(idx) == 0:
vbMng(self, "MAIN", "Idling.", 45)
if self.storeAllSamples: self.storeSamples()
pL, pT, mT = recv(source = 0, tag = poolRank())
pMat = np.empty((pL, 0), dtype = pT)
musA = np.empty((0, self.mu0.shape[1]), dtype = mT)
else:
for i in idx:
self.muMargLoc = mus[[i]]
vbMng(self, "MAIN", "Building marginal model no. {} at "
"{}.".format(i + 1, self.muMargLoc[0]), 25)
self.samplingEngine.resetHistory()
self.trainedModel = None
self.verbosity -= 5
self.samplingEngine.verbosity -= 5
RationalInterpolant.setupApprox(self)
self.verbosity += 5
self.samplingEngine.verbosity += 5
self._mus = self._m_selfmus
self.HFEngine.parameterMap = self._m_HFEparameterMap
del self._m_selfmus, self._m_HFEparameterMap
if self.storeAllSamples: self.storeSamples(i + self._nmusOld)
pMat, req, musA = self._localPivotedResult(pMat, req,
emptyCores, musA)
Ps += [copy(self.trainedModel.data.P)]
Qs += [copy(self.trainedModel.data.Q)]
if not self.matchState and self.autoCollapse:
Ps[-1].postmultiplyTensorize(pMat.T)
del self.muMargLoc
for r in req: r.wait()
if not self.matchState and self.autoCollapse: pMat = pMat[:, : 0]
self._postSetupApproxPivoted(musA, pMat, Ps, Qs, sizes)
vbMng(self, "DEL", "Done setting up pivoted approximant.", 10)
return 0
class RationalInterpolantPivotedGreedyPoleMatch(
RationalInterpolantPivotedGreedyBase,
GenericPivotedGreedyApproximantPoleMatch,
RationalInterpolantPivotedPoleMatch):
"""
ROM pivoted greedy rational interpolant computation for parametric
problems (with pole matching).
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';
- 'matchingWeightError': weight for pole matching optimization in
error estimation; defaults to 0;
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': number of starting marginal samples;
- 'samplerMarginal': marginal sample point generator via sparse
grid;
- 'errorEstimatorKindMarginal': kind of marginal error estimator;
available values include 'LOOK_AHEAD' and 'LOOK_AHEAD_RECOVER';
defaults to 'NONE';
- '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_*';
. '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;
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm; defaults to 1e-1;
- 'maxIterMarginal': maximum number of marginal greedy steps;
defaults to 1e2;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator; defaults to 1;
- 'radialDirectionalWeightsAdapt': bounds for adaptive rescaling of
radial basis weights; defaults to [-1, -1];
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'autoCollapse': whether to collapse trained reduced model as soon
as it is built; defaults to False;
- '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;
- '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;
- 'matchingWeightError': weight for pole matching optimization in
error estimation;
- 'errorEstimatorKindMarginal': kind of marginal error estimator;
- '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;
. '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;
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm;
- 'maxIterMarginal': maximum number of marginal greedy steps;
- 'radialDirectionalWeights': radial basis weights for pivot
numerator;
- 'radialDirectionalWeightsAdapt': bounds for adaptive rescaling of
radial basis weights;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'autoCollapse': whether to collapse trained reduced model as soon
as it is built;
- 'functionalSolve': strategy for minimization of denominator
functional;
- 'interpTol': tolerance for pivot interpolation;
- '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 via sparse
grid.
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.
matchingWeightError: Weight for pole matching optimization in error
estimation.
S: Total number of pivot samples current approximant relies upon.
samplerPivot: Pivot sample point generator.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator via sparse grid.
errorEstimatorKindMarginal: Kind of marginal error estimator.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
paramsMarginal: Dictionary of parameters for marginal interpolation.
M: Degree of rational interpolant numerator.
N: Degree of rational interpolant denominator.
greedyTolMarginal: Uniform error tolerance for marginal greedy
algorithm.
maxIterMarginal: Maximum number of marginal greedy steps.
radialDirectionalWeights: Radial basis weights for pivot numerator.
radialDirectionalWeightsAdapt: Bounds for adaptive rescaling of radial
basis weights.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
autoCollapse: Whether to collapse trained reduced model as soon as it
is built.
functionalSolve: Strategy for minimization of denominator functional.
interpTol: Tolerance for pivot interpolation.
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.
"""

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