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rational_interpolant_greedy_pivoted_greedy.py
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rational_interpolant_greedy_pivoted_greedy.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_greedy_approximant import GenericPivotedGreedyApproximant
from rrompy.utilities.numerical import dot
from rrompy.reduction_methods.standard.greedy import RationalInterpolantGreedy
from rrompy.reduction_methods.standard.greedy.generic_greedy_approximant \
import pruneSamples
from rrompy.reduction_methods.pivoted import RationalInterpolantGreedyPivoted
from rrompy.reduction_methods.pivoted.generic_pivoted_approximant import (
PODGlobal)
from rrompy.utilities.base.types import Np1D, Tuple, paramVal, paramList
from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.parameter import emptyParameterList
__all__ = ['RationalInterpolantGreedyPivotedGreedy']
class RationalInterpolantGreedyPivotedGreedy(GenericPivotedGreedyApproximant,
RationalInterpolantGreedyPivoted):
"""
ROM greedy pivoted greedy rational interpolant 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;
- 'matchingWeight': weight for pole matching optimization; defaults
to 1;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
defaults to np.inf;
- 'cutOffKind': kind of cut off strategy; available values
include 'SOFT' and 'HARD'; defaults to 'HARD';
- 'matchingWeightError': weight for pole matching optimization in
error estimation; defaults to 0;
- 'cutOffToleranceError': tolerance for ignoring parasitic poles
in error estimation; defaults to 'AUTO', i.e. cutOffTolerance;
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': number of starting marginal samples;
- 'samplerMarginalGrid': marginal sample point generator via sparse
grid;
- 'polybasis': type of polynomial basis for pivot interpolation;
defaults to 'MONOMIAL';
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation; allowed values include 'MONOMIAL', 'CHEBYSHEV'
and 'LEGENDRE'; 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;
- 'trainSetGenerator': training sample points generator; defaults
to sampler;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'INTERPOLATORY',
'LOOK_AHEAD', and 'NONE'; defaults to 'NONE';
- 'MMarginal': degree of marginal interpolant; 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;
- 'polydegreetypeMarginal': type of polynomial degree for marginal;
defaults to 'TOTAL';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'nNearestNeighborMarginal': number of marginal nearest neighbors
considered if polybasisMarginal allows; defaults to -1;
- 'interpRcond': tolerance for pivot interpolation; defaults to
None;
- 'interpRcondMarginal': tolerance for marginal interpolation;
defaults to None;
- 'robustTol': tolerance for robust rational denominator
management; defaults to 0.
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.
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;
- 'matchingWeight': weight for pole matching optimization;
- 'cutOffTolerance': tolerance for ignoring parasitic poles;
- 'cutOffKind': kind of cut off strategy;
- 'matchingWeightError': weight for pole matching optimization in
error estimation;
- 'cutOffToleranceError': tolerance for ignoring parasitic poles
in error estimation;
- 'polybasis': type of polynomial basis for pivot interpolation;
- 'polybasisMarginal': type of polynomial basis 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 test points;
- 'trainSetGenerator': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- 'MMarginal': degree of marginal interpolant;
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm;
- 'maxIterMarginal': maximum number of marginal greedy steps;
- 'polydegreetypeMarginal': type of polynomial degree for marginal;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'nNearestNeighborMarginal': number of marginal nearest neighbors
considered if polybasisMarginal allows;
- 'interpRcond': tolerance for pivot interpolation;
- 'interpRcondMarginal': tolerance for marginal interpolation;
- 'robustTol': 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;
- 'samplerMarginalGrid': marginal sample point generator via sparse
grid.
approx_state: Whether to approximate state.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
matchingWeight: Weight for pole matching optimization.
cutOffTolerance: Tolerance for ignoring parasitic poles.
cutOffKind: Kind of cut off strategy.
matchingWeightError: Weight for pole matching optimization in error
estimation.
cutOffToleranceError: Tolerance for ignoring parasitic poles 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.
samplerMarginalGrid: Marginal sample point generator via sparse grid.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis 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.
trainSetGenerator: training sample points generator.
errorEstimatorKind: kind of error estimator.
MMarginal: Degree of marginal interpolant.
greedyTolMarginal: Uniform error tolerance for marginal greedy
algorithm.
maxIterMarginal: Maximum number of marginal greedy steps.
polydegreetypeMarginal: Type of polynomial degree for marginal.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
nNearestNeighborMarginal: Number of marginal nearest neighbors
considered if polybasisMarginal allows.
interpRcond: Tolerance for pivot interpolation.
interpRcondMarginal: Tolerance for marginal interpolation.
robustTol: 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.
"""
@property
def sampleBatchSize(self):
"""Value of sampleBatchSize."""
return 1
@property
def sampleBatchIdx(self):
"""Value of sampleBatchIdx."""
return self.S
def _finalizeSnapshots(self):
self.samplingEngine = self._samplingEngineOld
for muM, sEN in zip(self.musMargLoc, self.samplingEngs):
self.samplingEngine.samples += [sEN.samples]
self.samplingEngine.nsamples += [sEN.nsamples]
self.samplingEngine.mus += [sEN.mus]
self.samplingEngine.musMarginal.append(muM)
self.samplingEngine._derIdxs += [[(0,) * self.npar]
for _ in range(sEN.nsamples)]
if self.POD:
self.samplingEngine.RPOD += [sEN.RPOD]
self.samplingEngine.samples_full += [copy(sEN.samples_full)]
if self.POD == PODGlobal:
self.samplingEngine.coalesceSamples(self.interpRcondMarginal)
else:
self.samplingEngine.coalesceSamples()
def greedyNextSample(self, muidx:int, plotEst : str = "NONE")\
-> Tuple[Np1D, int, float, paramVal]:
"""Compute next greedy snapshot of solution map."""
RROMPyAssert(self._mode, message = "Cannot add greedy sample.")
mus = copy(self.muTest[muidx])
self.muTest.pop(muidx)
for j, mu in enumerate(mus):
vbMng(self, "MAIN",
("Adding sample point no. {} at {} to training "
"set.").format(len(self.mus) + 1, mu), 2)
self.mus.append(mu)
self._S = len(self.mus)
self._approxParameters["S"] = self.S
if (self.samplingEngine.nsamples <= len(mus) - j - 1
or not np.allclose(mu,
self.samplingEngine.mus.data[j - len(mus)])):
self.samplingEngine.nextSample(mu)
if self._isLastSampleCollinear():
vbMng(self, "MAIN",
("Collinearity above tolerance detected. Starting "
"preemptive greedy loop termination."), 2)
self._collinearityFlag = 1
errorEstTest = np.empty(len(self.muTest))
errorEstTest[:] = np.nan
return errorEstTest, [-1], np.nan, np.nan
errorEstTest, muidx, maxErrorEst = self.errorEstimator(self.muTest,
True)
if plotEst == "ALL":
self.plotEstimator(errorEstTest, muidx, maxErrorEst)
return errorEstTest, muidx, maxErrorEst, self.muTest[muidx]
def _preliminaryTraining(self):
"""Initialize starting snapshots of solution map."""
RROMPyAssert(self._mode, message = "Cannot start greedy algorithm.")
if self.samplingEngine.nsamples > 0: return
self.resetSamples()
musPivot = self.trainSetGenerator.generatePoints(self.S)
while len(musPivot) > self.S: musPivot.pop()
muTestBasePivot = self.samplerPivot.generatePoints(self.nTestPoints,
False)
idxPop = pruneSamples(
muTestBasePivot ** self.HFEngine.rescalingExp[self.directionPivot[0]],
musPivot ** self.HFEngine.rescalingExp[self.directionPivot[0]],
1e-10 * self.scaleFactor[0])
muTestBasePivot.pop(idxPop)
self.mus = emptyParameterList()
self.mus.reset((self.S - 1, self.HFEngine.npar))
self.muTest = emptyParameterList()
self.muTest.reset((len(muTestBasePivot) + 1, self.HFEngine.npar))
for k in range(self.S - 1):
self.mus.data[k, self.directionPivot] = musPivot[k].data
self.mus.data[k, self.directionMarginal] = self.musMargLoc[-1].data
for k in range(len(muTestBasePivot)):
self.muTest.data[k, self.directionPivot] = muTestBasePivot[k].data
self.muTest.data[k, self.directionMarginal] = (
self.musMargLoc[-1].data)
self.muTest.data[-1, self.directionPivot] = musPivot[-1].data
self.muTest.data[-1, self.directionMarginal] = self.musMargLoc[-1].data
if len(self.mus) > 0:
vbMng(self, "MAIN",
("Adding first {} sample point{} at {} to training "
"set.").format(self.S - 1, "" + "s" * (self.S > 2),
self.mus), 3)
self.samplingEngine.iterSample(self.mus)
self._S = len(self.mus)
self._approxParameters["S"] = self.S
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)
if not hasattr(self, "_plotEstPivot"): self._plotEstPivot = "NONE"
self.computeScaleFactor()
if self.trainedModel is None:
self.trainedModel = self.tModelType()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
datadict = {"mu0": self.mu0, "projMat": np.zeros((0, 0)),
"scaleFactor": self.scaleFactor,
"rescalingExp": self.HFEngine.rescalingExp,
"directionPivot": self.directionPivot}
self.trainedModel.data = self.initializeModelData(datadict)[0]
self.trainedModel.data.Qs, self.trainedModel.data.Ps = [], []
_trainedModelOld = copy(self.trainedModel)
self._scaleFactorOldPivot = copy(self.scaleFactor)
self.scaleFactor = self.scaleFactorPivot
self._temporaryPivot = 1
self._samplingEngineOld = copy(self.samplingEngine)
self.musMargLoc, self.samplingEngs = [], [None] * len(mus)
Qs, Ps = [None] * len(mus), [None] * len(mus)
self.verbosity -= 15
S0 = copy(self.S)
for j, mu in enumerate(mus):
RationalInterpolantGreedy.setupSampling(self)
self.trainedModel = None
self.musMargLoc += [mu]
RationalInterpolantGreedy.setupApprox(self, self._plotEstPivot)
self.samplingEngs[j] = copy(self.samplingEngine)
Qs[j] = copy(self.trainedModel.data.Q)
Ps[j] = copy(self.trainedModel.data.P)
self._S = S0
self.scaleFactor = self._scaleFactorOldPivot
del self._scaleFactorOldPivot, self._temporaryPivot
self._finalizeSnapshots()
del self._samplingEngineOld, self.musMargLoc, self.samplingEngs
self._mus = self.samplingEngine.musCoalesced
self.trainedModel = _trainedModelOld
self.trainedModel.data.mus = copy(self.mus)
self.trainedModel.data.musMarginal = copy(self.musMarginal)
padRight = (self.samplingEngine.nsamplesTot
- self.trainedModel.data.projMat.shape[1])
nmusOld = len(self.trainedModel.data.Ps)
for j in range(nmusOld):
nsj = self.samplingEngine.nsamples[j]
self.trainedModel.data.Ps[j].pad(0, padRight)
self.trainedModel.data.HIs[j].pad(0, padRight)
padLeft = self.trainedModel.data.projMat.shape[1]
for j in range(len(mus)):
nsj = self.samplingEngine.nsamples[nmusOld + j]
if self.POD == PODGlobal:
rRightj = self.samplingEngine.RPODCPart[:,
padLeft : padLeft + nsj]
Ps[j].postmultiplyTensorize(rRightj.T)
else:
padRight -= nsj
Ps[j].pad(padLeft, padRight)
padLeft += nsj
pMat = self.samplingEngine.samplesCoalesced.data
pMatEff = dot(self.HFEngine.C, pMat) if self.approx_state else pMat
self.trainedModel.data.projMat = pMatEff
self.trainedModel.data.Qs += Qs
self.trainedModel.data.Ps += Ps
self.trainedModel.data.approxParameters = copy(self.approxParameters)
self.verbosity += 15
vbMng(self, "DEL", "Done setting up pivoted approximant.", 10)
return 0
def setupApprox(self, plotEst : str = "NONE") -> int:
if self.checkComputedApprox(): return -1
if '_' not in plotEst: plotEst = plotEst + "_NONE"
plotEstM, self._plotEstPivot = plotEst.split("_")
val = super().setupApprox(plotEstM)
return val

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