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pivoted_rational_2d.py
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Sat, Apr 27, 08:09

pivoted_rational_2d.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/>.
#
import numpy as np
from matrix_random import matrixRandom
from rrompy.reduction_methods import (
RationalInterpolantPivotedPoleMatch as RIP,
RationalInterpolantGreedyPivotedPoleMatch as RIGP)
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
ManualSampler as MS)
def test_pivoted_uniform():
mu = [5.05, 7.1]
mu0 = [5., 7.]
solver = matrixRandom()
uh = solver.solve(mu)[0]
params = {"POD": True, "S": 5, "polybasis": "CHEBYSHEV",
"samplerPivot": QS([4.75, 5.25], "CHEBYSHEV"), "SMarginal": 5,
"polybasisMarginal": "MONOMIAL", "matchingWeight": 1.,
"samplerMarginal": QS([6.75, 7.25], "UNIFORM")}
approx = RIP([0], solver, mu0, approxParameters = params, verbosity = 0)
approx.setupApprox()
uhP1 = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
myerrP = uhP1 - uh
assert np.allclose(np.abs(errP - myerrP), 0., rtol = 1e-3)
assert np.isclose(solver.norm(errP), errNP, rtol = 1e-3)
resP = approx.getRes(mu)[0]
resNP = approx.normRes(mu)
assert np.isclose(solver.norm(resP), resNP, rtol = 1e-3)
assert np.allclose(np.abs(resP - (solver.b(mu) - solver.A(mu).dot(uhP1))),
0., rtol = 1e-3)
assert np.isclose(errNP / solver.norm(uh), 6.0631706e-04, rtol = 1)
def test_pivoted_manual_grid(capsys):
mu = [5.05, 7.1]
mu0 = [5., 7.]
solver = matrixRandom()
uh = solver.solve(mu)[0]
params = {"POD": False, "S": 5, "polybasis": "MONOMIAL",
"samplerPivot": MS([4.75, 5.25], np.array([5.]),
normalFoci = [0., 0.]), "SMarginal": 5,
"polybasisMarginal": "MONOMIAL", "matchingWeight": 1.,
"samplerMarginal": MS([6.75, 7.25], np.linspace(6.75, 7.25, 5)),
"QTol": 1e-6, "interpTol": 1e-3}
approx = RIP([0], solver, mu0, approxParameters = params, verbosity = 0)
approx.setupApprox()
uhP1 = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
myerrP = uhP1 - uh
assert np.allclose(np.abs(errP - myerrP), 0., rtol = 1e-3)
assert np.isclose(solver.norm(errP), errNP, rtol = 1e-3)
resP = approx.getRes(mu)[0]
resNP = approx.normRes(mu)
assert np.isclose(solver.norm(resP), resNP, rtol = 1e-3)
assert np.allclose(np.abs(resP - (solver.b(mu) - solver.A(mu).dot(uhP1))),
0., rtol = 1e-3)
assert np.isclose(errNP / solver.norm(uh), .4763489, rtol = 1)
out, err = capsys.readouterr()
assert ("poorly conditioned" not in out)
assert len(err) == 0
def test_pivoted_greedy():
mu = [5.05, 7.1]
mu0 = [5., 7.]
solver = matrixRandom()
uh = solver.solve(mu)[0]
params = {"POD": True, "nTestPoints": 100, "greedyTol": 1e-4,
"collinearityTol": 1e8, "errorEstimatorKind": "DISCREPANCY",
"S": 5, "polybasis": "CHEBYSHEV",
"samplerPivot": QS([4.75, 5.25], "UNIFORM"),
"trainSetGenerator": QS([4.75, 5.25], "CHEBYSHEV"),
"SMarginal": 5, "polybasisMarginal": "MONOMIAL",
"samplerMarginal": QS([6.75, 7.25], "UNIFORM"),
"matchingWeight": 1.}
solver.cutOffPolesRMinRel, solver.cutOffPolesRMaxRel = -3., 3.
solver.cutOffPolesIMinRel, solver.cutOffPolesIMaxRel = -1.5, 1.5
approx = RIGP([0], solver, mu0, approxParameters = params, verbosity = 0)
approx.setupApprox()
uhP1 = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
myerrP = uhP1 - uh
assert np.allclose(np.abs(errP - myerrP), 0., rtol = 1e-3)
assert np.isclose(solver.norm(errP), errNP, rtol = 1e-3)
resP = approx.getRes(mu)[0]
resNP = approx.normRes(mu)
assert np.isclose(solver.norm(resP), resNP, rtol = 1e-3)
assert np.allclose(np.abs(resP - (solver.b(mu) - solver.A(mu).dot(uhP1))),
0., rtol = 1e-3)
assert np.isclose(errNP / solver.norm(uh), 1.181958e-02, rtol = 1)

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