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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) 2018-2020 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.greedy import RationalInterpolantGreedy
from rrompy.reduction_methods.standard.greedy.generic_greedy_approximant \
import pruneSamples
from rrompy.reduction_methods.pivoted import (
RationalInterpolantGreedyPivotedPoleMatch)
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
from rrompy.utilities.parallel import poolRank, recv
__all__ = ['RationalInterpolantGreedyPivotedGreedyPoleMatch']
class RationalInterpolantGreedyPivotedGreedyBase(
GenericPivotedGreedyApproximantBase):
@property
def sampleBatchSize(self):
"""Value of sampleBatchSize."""
return 1
@property
def sampleBatchIdx(self):
"""Value of sampleBatchIdx."""
return self.S
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), 3)
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[j - len(mus)])):
self.samplingEngine.nextSample(mu)
if self._isLastSampleCollinear():
vbMng(self, "MAIN",
("Collinearity above tolerance detected. Starting "
"preemptive greedy loop termination."), 3)
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 _setSampleBatch(self, maxS:int):
return self.S
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()
self.samplingEngine.scaleFactor = self.scaleFactorDer
musPivot = self.samplerTrainSet.generatePoints(self.S)
while len(musPivot) > self.S: musPivot.pop()
muTestBasePivot = self.samplerPivot.generatePoints(self.nTestPoints,
False)
idxPop = pruneSamples(self.mapParameterListPivot(muTestBasePivot),
self.mapParameterListPivot(musPivot),
1e-10 * self.scaleFactorPivot[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))
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] = muTestBasePivot.data
self.muTest.data[-1, self.directionPivot] = musPivot[-1]
self.muTest.data[:, self.directionMarginal] = np.repeat(self.muMargLoc,
len(muTestBasePivot) + 1,
axis = 0)
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
self.M, self.N = ("AUTO",) * 2
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"
idx, sizes, emptyCores = self._preSetupApproxPivoted(mus)
S0 = copy(self.S)
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), 25)
self.samplingEngine.resetHistory()
self.trainedModel = None
self.verbosity -= 5
self.samplingEngine.verbosity -= 10
RationalInterpolantGreedy.setupApprox(self, self._plotEstPivot)
self.verbosity += 5
self.samplingEngine.verbosity += 10
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)]
self._S = S0
del self.muMargLoc
for r in req: r.wait()
self._postSetupApproxPivoted(musA, pMat, Ps, Qs, sizes)
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
class RationalInterpolantGreedyPivotedGreedyPoleMatch(
RationalInterpolantGreedyPivotedGreedyBase,
GenericPivotedGreedyApproximantPoleMatch,
RationalInterpolantGreedyPivotedPoleMatch):
"""
ROM greedy 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;
- 'matchingChordalRadius': radius to be used in chordal metric for
poles and residues; if <= 0, Euclidean metric is used; if
'AUTO', automatically selected; 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.
- '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';
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm; defaults to 1e-1;
- 'maxIterMarginal': maximum number of marginal greedy steps;
defaults to 1e2;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'functionalSolve': strategy for minimization of denominator
functional; allowed values include 'NORM', 'DOMINANT', 'NODAL',
'BARYCENTRIC_NORM', and 'BARYCENTRIC[_AVERAGE]' (check pdf in
main folder for meaning); 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.
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;
- 'matchingChordalRadius': radius to be used in chordal metric for
poles and residues;
- '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.
- '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;
- 'greedyTolMarginal': uniform error tolerance for marginal greedy
algorithm;
- 'maxIterMarginal': maximum number of marginal greedy steps;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- '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.
matchingChordalRadius: Radius to be used in chordal metric for poles
and residues.
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.
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.
greedyTolMarginal: Uniform error tolerance for marginal greedy
algorithm.
maxIterMarginal: Maximum number of marginal greedy steps.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
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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