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radial_fitting.py
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radial_fitting.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.utilities.poly_fitting import customFit
from rrompy.utilities.poly_fitting.radial_basis import (radialGaussian,
thinPlateSpline,
multiQuadric,
polybases, polyfitname,
polydomcoeff,
polyval, polyvander,
homogeneizedpolyvander)
from rrompy.utilities.poly_fitting.polynomial import homogeneizedToFull
from rrompy.parameter import checkParameterList
def test_monomial_gaussian():
polyrbname = "MONOMIAL_GAUSSIAN"
assert polyrbname in polybases
fitname = polyfitname(polyrbname)
domcoeff = polydomcoeff(5, polyrbname)
assert fitname == "polyfit_gaussian"
assert np.isclose(domcoeff, 1., rtol = 1e-5)
directionalWeights = np.array([5.])
xSupp = checkParameterList(np.arange(-1, 3), 1)[0]
cRBCoeffs = np.array([-1., 3., -3., 1., 1., 2., -.5])
globalCoeffs = cRBCoeffs[4 :]
localCoeffs = cRBCoeffs[: 4]
ySupp = 1 + 2. * xSupp.data - .5 * xSupp.data ** 2.
xx = np.linspace(-2., 3., 100)
yy = polyval(checkParameterList(xx, 1)[0], globalCoeffs, localCoeffs,
xSupp, directionalWeights, polyrbname)
yyman = 1. + 2. * xx - .5 * xx ** 2.
for j, xc in enumerate(np.arange(-1, 3)):
r2j = (5. * (xx - xc)) ** 2.
rbj = radialGaussian(r2j)
assert np.allclose(rbj, np.exp(-.5 * r2j))
yyman += localCoeffs[j] * rbj
ySupp += localCoeffs[j] * radialGaussian((directionalWeights[0]
* (xSupp.data - xc)) ** 2.)
assert np.allclose(yy, yyman, atol = 1e-5)
VanT = polyvander(xSupp, [2], polyrbname,
directionalWeights = directionalWeights)
ySupp = np.pad(ySupp.flatten(), (0, len(VanT) - len(xSupp)), "constant")
out = customFit(VanT, ySupp)
assert np.allclose(out, cRBCoeffs, atol = 1e-8)
def test_legendre_thinplate():
polyrbname = "LEGENDRE_THINPLATE"
assert polyrbname in polybases
fitname = polyfitname(polyrbname)
domcoeff = polydomcoeff(5, polyrbname)
assert fitname == "legfit_thinplate"
assert np.isclose(domcoeff, 63. / 8, rtol = 1e-5)
directionalWeights = np.array([.5])
xSupp = checkParameterList(np.arange(-1, 3), 1)[0]
cRBCoeffs = np.array([-1., 3., -3., 1., 1., 2., -.5])
localCoeffs = cRBCoeffs[: 4]
globalCoeffs = cRBCoeffs[4 :]
ySupp = 1 + 2. * xSupp.data - .5 * (.5 * (3. * xSupp.data ** 2. - 1.))
xx = np.linspace(-2., 3., 100)
yy = polyval(checkParameterList(xx, 1)[0], globalCoeffs, localCoeffs,
xSupp, directionalWeights, polyrbname)
yyman = 1. + 2. * xx - .5 * (.5 * (3. * xx ** 2. - 1.))
for j, xc in enumerate(np.arange(-1, 3)):
r2j = (directionalWeights[0] * (xx - xc)) ** 2.
rbj = thinPlateSpline(r2j)
assert np.allclose(rbj, .5 * r2j * np.log(np.finfo(float).eps + r2j))
yyman += localCoeffs[j] * rbj
ySupp += localCoeffs[j] * thinPlateSpline((directionalWeights[0]
* (xSupp.data - xc)) ** 2.)
assert np.allclose(yy, yyman, atol = 1e-5)
VanT = polyvander(xSupp, [2], polyrbname,
directionalWeights = directionalWeights)
ySupp = np.pad(ySupp.flatten(), (0, len(VanT) - len(xSupp)), "constant")
out = customFit(VanT, ySupp)
assert np.allclose(out, cRBCoeffs, atol = 1e-8)
def test_chebyshev_multiquadric():
polyrbname = "CHEBYSHEV_MULTIQUADRIC"
assert polyrbname in polybases
fitname = polyfitname(polyrbname)
domcoeff = polydomcoeff(5, polyrbname)
assert fitname == "chebfit_multiquadric"
assert np.isclose(domcoeff, 16, rtol = 1e-5)
directionalWeights = np.array([1.])
xSupp = checkParameterList(np.arange(-1, 3), 1)[0]
cRBCoeffs = np.array([-1., 3., -3., 1., 1., 2., -.5])
localCoeffs = cRBCoeffs[: 4]
globalCoeffs = cRBCoeffs[4 :]
ySupp = 1 + 2. * xSupp.data - .5 * (2. * xSupp.data ** 2. - 1.)
xx = np.linspace(-2., 3., 100)
yy = polyval(checkParameterList(xx, 1)[0], globalCoeffs, localCoeffs,
xSupp, directionalWeights, polyrbname)
yyman = 1. + 2. * xx - .5 * (2. * xx ** 2. - 1.)
for j, xc in enumerate(np.arange(-1, 3)):
r2j = (directionalWeights[0] * (xx - xc)) ** 2.
rbj = multiQuadric(r2j)
assert np.allclose(rbj, np.power(r2j + 1, -.5))
yyman += localCoeffs[j] * rbj
ySupp += localCoeffs[j] * multiQuadric((directionalWeights[0]
* (xSupp.data - xc)) ** 2.)
assert np.allclose(yy, yyman, atol = 1e-5)
VanT = polyvander(xSupp, [2], polyrbname,
directionalWeights = directionalWeights)
ySupp = np.pad(ySupp.flatten(), (0, len(VanT) - len(xSupp)), "constant")
out = customFit(VanT, ySupp)
assert np.allclose(out, cRBCoeffs, atol = 1e-8)
def test_total_degree_2d():
values = lambda x, y: (x - 3.) ** 2. * y - (x + 1.) * y ** 2.
polyrbname = "CHEBYSHEV_GAUSSIAN"
xs, ys = np.meshgrid(np.linspace(0., 4., 5), np.linspace(0., 4., 4))
xySupp = np.concatenate((xs.reshape(-1, 1), ys.reshape(-1, 1)), axis = 1)
zs = values(xs, ys)
zSupp = zs.flatten()
deg = 3
directionalWeights = [2., 1.]
VanT, _, reidxs = homogeneizedpolyvander(xySupp, deg, polyrbname,
directionalWeights = directionalWeights)
VanT = VanT[reidxs]
VanT = VanT[:, reidxs]
cFit = np.linalg.solve(VanT, np.pad(zSupp, (0, len(VanT) - len(zSupp)),
'constant'))
globCoeff = homogeneizedToFull([deg + 1] * 2, 2, cFit[len(zSupp) :])
localCoeffs = cFit[: len(zSupp)]
globalCoeffs = globCoeff
xx, yy = np.meshgrid(np.linspace(0., 4., 100), np.linspace(0., 4., 100))
xxyy = np.concatenate((xx.reshape(-1, 1), yy.reshape(-1, 1)), axis = 1)
zz = polyval(xxyy, globalCoeffs, localCoeffs, xySupp, directionalWeights,
polyrbname).reshape(xx.shape)
zzex = values(xx, yy)
error = np.abs(zz - zzex)
print(np.max(error))
assert np.max(error) < 1e-10

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