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radial_basis_interpolator.py
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Mon, May 6, 17:26

radial_basis_interpolator.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 copy import deepcopy as copy
from rrompy.utilities.base.types import (List, ListAny, DictAny, Np1D, Np2D,
paramList)
from rrompy.utilities.poly_fitting.interpolator import GenericInterpolator
from rrompy.utilities.poly_fitting.custom_fit import customFit
from rrompy.utilities.poly_fitting.radial_basis.base import polyfitname
from rrompy.utilities.poly_fitting.radial_basis.val import polyval
from rrompy.utilities.poly_fitting.radial_basis.homogeneization import (
homogeneizedpolyvander as hpv)
from rrompy.utilities.poly_fitting.radial_basis.vander import polyvander as pv
from rrompy.utilities.poly_fitting.polynomial.homogeneization import (
homogeneizedToFull)
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['RadialBasisInterpolator']
class RadialBasisInterpolator(GenericInterpolator):
"""HERE"""
def __init__(self, other = None):
if other is None: return
self.support = other.support
self.coeffsGlobal = other.coeffsGlobal
self.coeffsLocal = other.coeffsLocal
self.directionalWeights = other.directionalWeights
self.npar = other.npar
self.polybasis = other.polybasis
@property
def shape(self):
sh = self.coeffsLocal.shape[1 :] if self.coeffsLocal.ndim > 1 else 1
return sh
@property
def deg(self):
return [x - 1 for x in self.coeffsGlobal.shape[: self.npar]]
def __call__(self, mu:paramList, der : List[int] = None,
scl : Np1D = None):
if der is not None and np.sum(der) > 0:
raise RROMPyException(("Cannot take derivatives of radial basis "
"function."))
return polyval(mu, self.coeffsGlobal, self.coeffsLocal, self.support,
self.directionalWeights, self.polybasis)
def __copy__(self):
return RadialBasisInterpolator(self)
def __deepcopy__(self, memo):
other = RadialBasisInterpolator()
(other.support, other.coeffsGlobal, other.coeffsLocal,
other.directionalWeights, other.npar, other.polybasis) = copy(
(self.support, self.coeffsGlobal, self.coeffsLocal,
self.directionalWeights, self.npar, self.polybasis), memo)
return other
def postmultiplyTensorize(self, A:Np2D):
RROMPyAssert(A.shape[0], self.shape[-1], "Shape of output")
self.coeffsLocal = np.tensordot(self.coeffsLocal, A, axes = (-1, 0))
self.coeffsGlobal = np.tensordot(self.coeffsGlobal, A, axes = (-1, 0))
def pad(self, nleft : List[int] = None, nright : List[int] = None):
if nleft is None: nleft = [0] * len(self.shape)
if nright is None: nright = [0] * len(self.shape)
if not hasattr(nleft, "__len__"): nleft = [nleft]
if not hasattr(nright, "__len__"): nright = [nright]
RROMPyAssert(len(self.shape), len(nleft), "Shape of output")
RROMPyAssert(len(self.shape), len(nright), "Shape of output")
padwidth = [(0, 0)] + [(l, r) for l, r in zip(nleft, nright)]
self.coeffsLocal = np.pad(self.coeffsLocal, padwidth, "constant",
constant_values = (0., 0.))
padwidth = [(0, 0)] * (self.npar - 1) + padwidth
self.coeffsGlobal = np.pad(self.coeffsGlobal, padwidth, "constant",
constant_values = (0., 0.))
def setupByInterpolation(self, support:paramList, values:ListAny,
deg:int, polybasis : str = "MONOMIAL_GAUSSIAN",
directionalWeights : Np1D = None,
verbose : bool = True, homogeneized : bool = True,
vanderCoeffs : DictAny = {},
fitCoeffs : DictAny = {}):
support = checkParameterList(support)[0]
self.support = copy(support)
if "reorder" in vanderCoeffs.keys():
self.support = self.support[vanderCoeffs["reorder"]]
self.npar = support.shape[1]
if directionalWeights is None:
directionalWeights = np.ones(self.npar)
self.directionalWeights = directionalWeights
self.polybasis = polybasis
if homogeneized:
vander, _, reorder = hpv(support, deg, basis = polybasis,
directionalWeights = self.directionalWeights,
**vanderCoeffs)
vander = vander[reorder]
vander = vander[:, reorder]
else:
if not hasattr(deg, "__len__"): deg = [deg] * self.npar
vander = pv(support, deg, basis = polybasis, **vanderCoeffs)
outDim = values.shape[1:]
values = values.reshape(values.shape[0], -1)
values = np.pad(values, ((0, len(vander) - len(values)), (0, 0)),
"constant")
fitOut = customFit(vander, values, full = True, **fitCoeffs)
P = fitOut[0][len(support) :]
if verbose:
msg = ("Fitting {}+{} samples with degree {} through {}... "
"Conditioning of LS system: {:.4e}.").format(
len(support), len(vander) - len(support),
deg, polyfitname(self.polybasis),
fitOut[1][2][0] / fitOut[1][2][-1])
else: msg = None
self.coeffsLocal = fitOut[0][: len(support)]
if homogeneized:
self.coeffsGlobal = homogeneizedToFull(
tuple([deg + 1] * self.npar) + outDim,
self.npar, P)
else:
self.coeffsGlobal = P.reshape(tuple([d + 1 for d in deg]) + outDim)
return fitOut[1][1] == vander.shape[1], msg

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