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generic_approximant_taylor.py
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Fri, May 3, 15:51

generic_approximant_taylor.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/>.
#
import numpy as np
from rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
from rrompy.utilities.base.types import DictAny, HFEng
from rrompy.utilities.base import purgeDict, verbosityDepth
from rrompy.utilities.exception_manager import (RROMPyException, modeAssert,
RROMPyWarning)
__all__ = ['GenericApproximantTaylor']
class GenericApproximantTaylor(GenericApproximant):
"""
ROM single-point approximant computation for parametric problems
(ABSTRACT).
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;
- 'E': total number of derivatives current approximant relies upon;
defaults to 1;
- 'sampleType': label of sampling type; available values are:
- 'ARNOLDI': orthogonalization of solution derivatives through
Arnoldi algorithm;
- 'KRYLOV': standard computation of solution derivatives.
Defaults to 'KRYLOV'.
Defaults to empty dict.
homogeneized: Whether to homogeneize Dirichlet BCs. Defaults to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'E': total number of derivatives current approximant relies upon;
- 'sampleType': label of sampling type.
POD: Whether to compute QR factorization of derivatives.
E: Number of solution derivatives over which current approximant is
based upon.
sampleType: Label of sampling type.
initialHFData: HF problem initial data.
samplingEngine: Sampling engine.
uHF: High fidelity solution with wavenumber lastSolvedHF as numpy
complex vector.
lastSolvedHF: Wavenumber corresponding to last computed high fidelity
solution.
uApp: Last evaluated approximant as numpy complex vector.
"""
def __init__(self, HFEngine:HFEng, mu0 : complex = 0,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["E", "sampleType"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
def setupSampling(self):
"""Setup sampling engine."""
modeAssert(self._mode, message = "Cannot setup sampling engine.")
if not hasattr(self, "_sampleType"): return
if self.sampleType == "ARNOLDI":
from rrompy.sampling.linear_problem.sampling_engine_arnoldi \
import SamplingEngineArnoldi
super().setupSampling(SamplingEngineArnoldi)
elif self.sampleType == "KRYLOV":
from rrompy.sampling.linear_problem.sampling_engine_krylov \
import SamplingEngineKrylov
super().setupSampling(SamplingEngineKrylov)
else:
raise RROMPyException("Sample type not recognized.")
@property
def approxParameters(self):
"""Value of approximant parameters. Its assignment may change E."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters, ["E", "sampleType"],
True, True, baselevel = 1)
GenericApproximant.approxParameters.fset(self, approxParametersCopy)
keyList = list(approxParameters.keys())
if "E" in keyList:
self.E = approxParameters["E"]
elif hasattr(self, "_E") and self._E is not None:
self.E = self.E
else:
self.E = 1
if "sampleType" in keyList:
self.sampleType = approxParameters["sampleType"]
elif not hasattr(self, "_sampleType") or self._sampleType is None:
self.sampleType = "KRYLOV"
@property
def E(self):
"""Value of E."""
return self._E
@E.setter
def E(self, E):
if E < 0: raise RROMPyException("E must be non-negative.")
self._E = E
self._approxParameters["E"] = self.E
@property
def sampleType(self):
"""Value of sampleType."""
return self._sampleType
@sampleType.setter
def sampleType(self, sampleType):
if hasattr(self, "_sampleType") and self._sampleType is not None:
sampleTypeOld = self.sampleType
else: sampleTypeOld = -1
try:
sampleType = sampleType.upper().strip().replace(" ","")
if sampleType not in ["ARNOLDI", "KRYLOV"]:
raise RROMPyException("Sample type not recognized.")
self._sampleType = sampleType
except:
RROMPyWarning(("Prescribed sampleType not recognized. Overriding "
"to 'KRYLOV'."))
self._sampleType = "KRYLOV"
self._approxParameters["sampleType"] = self.sampleType
if sampleTypeOld != self.sampleType:
self.resetSamples()
def computeDerivatives(self):
"""Compute derivatives of solution map starting from order 0."""
modeAssert(self._mode,
message = "Cannot start derivative computation.")
if self.samplingEngine.samples is None:
if self.verbosity >= 5:
verbosityDepth("INIT", "Starting computation of derivatives.",
timestamp = self.timestamp)
self.samplingEngine.iterSample(self.mu0, self.E + 1,
homogeneized = self.homogeneized)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done computing derivatives.",
timestamp = self.timestamp)
def normApprox(self, mu:complex, homogeneized : bool = False) -> float:
"""
Compute norm of approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of approximant.
"""
if self.sampleType != "ARNOLDI" or self.homogeneized != homogeneized:
return super().normApprox(mu, homogeneized)
return np.linalg.norm(self.getApproxReduced(mu, homogeneized))

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