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rational_moving_least_squares.py
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rational_moving_least_squares.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 .rational_interpolant import RationalInterpolant
from rrompy.utilities.poly_fitting.polynomial import (polybases as ppb,
polyvander as pvP,
polyvanderTotal as pvTP)
from rrompy.reduction_methods.trained_model import (
TrainedModelRationalMLS as tModel)
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import Np2D, HFEng, DictAny, paramVal
from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.numerical import (fullDegreeMaxMask, totalDegreeMaxMask,
dot)
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
__all__ = ['RationalMovingLeastSquares']
class RationalMovingLeastSquares(RationalInterpolant):
"""
ROM rational moving LS interpolant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. 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;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- 'polybasis': type of polynomial basis for interpolation; defaults
to 'MONOMIAL';
- 'M': degree of rational interpolant numerator; defaults to 0;
- 'N': degree of rational interpolant denominator; defaults to 0;
- 'polydegreetype': type of polynomial degree; defaults to 'TOTAL';
- 'radialBasis': numerator radial basis type; defaults to
'GAUSSIAN';
- 'radialDirectionalWeights': radial basis weights for interpolant
numerator; defaults to 0, i.e. identity;
- 'nNearestNeighbor': number of nearest neighbors considered in
numerator if radialBasis allows; defaults to -1;
- 'radialBasisDen': denominator radial basis type; defaults to
'GAUSSIAN';
- 'radialDirectionalWeightsDen': radial basis weights for
interpolant denominator; defaults to 0, i.e. identity;
- 'nNearestNeighborDen': number of nearest neighbors considered in
denominator if radialBasisDen allows; defaults to -1;
- 'interpRcond': tolerance for interpolation; defaults to None;
- 'robustTol': 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.
mus: Array of 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;
- 'polybasis': type of polynomial basis for interpolation;
- 'M': degree of rational interpolant numerator;
- 'N': degree of rational interpolant denominator;
- 'polydegreetype': type of polynomial degree;
- 'radialBasis': numerator radial basis type;
- 'radialDirectionalWeights': radial basis weights for interpolant
numerator;
- 'nNearestNeighbor': number of nearest neighbors considered in
numerator if radialBasis allows;
- 'radialBasisDen': denominator radial basis type;
- 'radialDirectionalWeightsDen': radial basis weights for
interpolant denominator;
- 'nNearestNeighborDen': number of nearest neighbors considered in
denominator if radialBasisDen allows;
- 'interpRcond': tolerance for interpolation via numpy.polyfit;
- 'robustTol': tolerance for robust rational denominator
management.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
POD: Whether to compute POD of snapshots.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
polybasis: type of polynomial basis for interpolation.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
polydegreetype: Type of polynomial degree.
radialBasis: Numerator radial basis type.
radialDirectionalWeights: Radial basis weights for interpolant
numerator.
nNearestNeighbor: Number of nearest neighbors considered in numerator
if radialBasis allows.
radialBasisDen: Denominator radial basis type.
radialDirectionalWeightsDen: Radial basis weights for interpolant
denominator.
nNearestNeighborDen: Number of nearest neighbors considered in
denominator if radialBasisDen allows.
interpRcond: Tolerance for interpolation via numpy.polyfit.
robustTol: Tolerance for robust rational denominator management.
muBounds: list of bounds for 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 __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, verbosity : int = 10,
timestamp : bool = True):
self._preInit()
self._addParametersToList(["radialBasis", "radialBasisDen",
"radialDirectionalWeightsDen",
"nNearestNeighborDen"],
["GAUSSIAN", "GAUSSIAN", 1, -1])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
verbosity = verbosity, timestamp = timestamp)
self.catchInstability = False
self._postInit()
@property
def polybasis(self):
"""Value of polybasis."""
return self._polybasis
@polybasis.setter
def polybasis(self, polybasis):
try:
polybasis = polybasis.upper().strip().replace(" ","")
if polybasis not in ppb:
raise RROMPyException("Prescribed polybasis not recognized.")
self._polybasis = polybasis
except:
RROMPyWarning(("Prescribed polybasis not recognized. Overriding "
"to 'MONOMIAL'."))
self._polybasis = "MONOMIAL"
self._approxParameters["polybasis"] = self.polybasis
@property
def radialBasis(self):
"""Value of radialBasis."""
return self._radialBasis
@radialBasis.setter
def radialBasis(self, radialBasis):
self._radialBasis = radialBasis
self._approxParameters["radialBasis"] = self.radialBasis
@property
def radialBasisDen(self):
"""Value of radialBasisDen."""
return self._radialBasisDen
@radialBasisDen.setter
def radialBasisDen(self, radialBasisDen):
self._radialBasisDen = radialBasisDen
self._approxParameters["radialBasisDen"] = self.radialBasisDen
@property
def radialDirectionalWeightsDen(self):
"""Value of radialDirectionalWeightsDen."""
return self._radialDirectionalWeightsDen
@radialDirectionalWeightsDen.setter
def radialDirectionalWeightsDen(self, radialDirectionalWeightsDen):
self._radialDirectionalWeightsDen = radialDirectionalWeightsDen
self._approxParameters["radialDirectionalWeightsDen"] = (
self.radialDirectionalWeightsDen)
@property
def nNearestNeighborDen(self):
"""Value of nNearestNeighborDen."""
return self._nNearestNeighborDen
@nNearestNeighborDen.setter
def nNearestNeighborDen(self, nNearestNeighborDen):
self._nNearestNeighborDen = nNearestNeighborDen
self._approxParameters["nNearestNeighborDen"] = (
self.nNearestNeighborDen)
def _setupDenominator(self) -> Np2D:
"""Compute rational denominator."""
RROMPyAssert(self._mode, message = "Cannot setup denominator.")
vbMng(self, "INIT",
"Starting computation of denominator-related blocks.", 7)
self._setupInterpolationIndices()
if self.polydegreetype == "TOTAL":
TN, _, argIdxs = pvTP(self._musUniqueCN, self.N, self.polybasis0,
self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TN = TN[:, argIdxs]
else: #if self.polydegreetype == "FULL":
TN = pvP(self._musUniqueCN, [self.N] * self.npar,
self.polybasis0, self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TNTen = np.zeros((self.S, self.S, TN.shape[1]), dtype = TN.dtype)
TNTen[np.arange(self.S), np.arange(self.S)] = TN
if self.POD: TNTen = dot(self.samplingEngine.RPOD, TNTen)
vbMng(self, "DEL", "Done computing denominator-related blocks.", 7)
return TN, TNTen
def _setupNumerator(self) -> Np2D:
"""Compute rational numerator."""
RROMPyAssert(self._mode, message = "Cannot setup numerator.")
vbMng(self, "INIT",
"Starting computation of denominator-related blocks.", 7)
self._setupInterpolationIndices()
if self.polydegreetype == "TOTAL":
TM, _, argIdxs = pvTP(self._musUniqueCN, self.M, self.polybasis0,
self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TM = TM[:, argIdxs]
else: #if self.polydegreetype == "FULL":
TM = pvP(self._musUniqueCN, [self.M] * self.npar,
self.polybasis0, self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
vbMng(self, "DEL", "Done computing denominator-related blocks.", 7)
return TM
def setupApprox(self):
"""
Compute rational interpolant.
SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.computeSnapshots()
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
self.samplingEngine.samples,
self.scaleFactor,
self.HFEngine.rescalingExp)
data.POD = self.POD
data.polybasis = self.polybasis
data.polydegreetype = self.polydegreetype
data.radialBasis = self.radialBasis
data.radialWeights = self.radialDirectionalWeights
data.nNearestNeighbor = self.nNearestNeighbor
data.radialBasisDen = self.radialBasisDen
data.radialWeightsDen = self.radialDirectionalWeightsDen
data.nNearestNeighborDen = self.nNearestNeighborDen
data.interpRcond = self.interpRcond
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(self.samplingEngine.samples)
if not self.POD:
self.trainedModel.data.gramian = self.HFEngine.innerProduct(
self.samplingEngine.samples,
self.samplingEngine.samples)
self.trainedModel.data.mus = copy(self.mus)
self.trainedModel.data.M = self.M
self.trainedModel.data.N = self.N
QVan, self.trainedModel.data.QBlocks = self._setupDenominator()
self.trainedModel.data.PVan = self._setupNumerator()
if self.polydegreetype == "TOTAL":
degreeMaxMask = totalDegreeMaxMask
else: #if self.polydegreetype == "FULL":
degreeMaxMask = fullDegreeMaxMask
if self.N > self.M:
self.trainedModel.data.QVan = QVan
self.trainedModel.data.domQIdxs = degreeMaxMask(self.N, self.npar)
else:
self.trainedModel.data.domQIdxs = degreeMaxMask(self.M, self.npar)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
vbMng(self, "DEL", "Done setting up approximant.", 5)

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