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vander.py
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Sun, Apr 28, 02:45

vander.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.polynomial.vander import polyvander as pvP
from rrompy.utilities.base.types import Np1D, Np2D, List, paramList
from rrompy.parameter import checkParameterList
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from .kernel import radialGaussian, thinPlateSpline, multiQuadric
__all__ = ['rbvander', 'polyvander']
def rbvander(x:paramList, basis:str, reorder : List[int] = None,
directionalWeights : Np1D = None) -> Np2D:
"""Compute radial-basis-Vandermonde matrix."""
x = checkParameterList(x)[0]
x_un, idx_un = x.unique(return_inverse = True)
nx = len(x)
if len(x_un) < nx:
raise RROMPyException("Sample points must be distinct.")
del x_un
x = x.data
if directionalWeights is None:
directionalWeights = np.ones(x.shape[1])
RROMPyAssert(len(directionalWeights), x.shape[1],
"Number of directional weights")
try:
radialkernel = {"GAUSSIAN" : radialGaussian,
"THINPLATE" : thinPlateSpline,
"MULTIQUADRIC" : multiQuadric
}[basis.upper()]
except:
raise RROMPyException("Radial basis not recognized.")
r2 = np.zeros((nx * (nx - 1) // 2 + 1), dtype = float)
idxInv = np.zeros(nx ** 2, dtype = int)
if reorder is not None: x = x[reorder]
for j in range(nx):
idx = j * (nx - 1) - j * (j + 1) // 2
II = np.arange(j + 1, nx)
r2[idx + II] = np.sum(np.abs((x[II] - x[j])
* directionalWeights) ** 2., axis = 1)
idxInv[j * nx + II] = idx + II
idxInv[II * nx + j] = idx + II
Van = radialkernel(r2)[idxInv].reshape((nx, nx))
return Van
def polyvander(x:paramList, degs:List[int], basis:str,
derIdxs : List[List[List[int]]] = None,
reorder : List[int] = None, directionalWeights : Np1D = None,
scl : Np1D = None) -> Np2D:
"""
Compute radial-basis-inclusive Hermite-Vandermonde matrix with specified
derivative directions.
"""
if derIdxs is not None and np.sum(np.sum(derIdxs)) > 0:
raise RROMPyException(("Cannot take derivatives of radial basis "
"function."))
basisp, basisr = basis.split("_")
VanR = rbvander(x, basisr, reorder = reorder,
directionalWeights = directionalWeights)
VanP = pvP(x, degs, basisp, derIdxs = derIdxs, reorder = reorder,
scl = scl)
return np.block([[VanR, VanP],
[VanP.T.conj(), np.zeros(tuple([VanP.shape[1]] * 2))]])

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