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vander.py
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Wed, May 1, 19:04

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,
polyvanderTotal as pvTP)
from rrompy.utilities.base.types import Np1D, Np2D, Tuple, List, paramList
from rrompy.parameter import checkParameterList
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['heavisidevander', 'polyvander', 'polyvanderTotal']
def heavisidevander(x:paramList, poles:Np1D,
reorder : List[int] = None) -> Np2D:
"""Compute Heaviside-Vandermonde matrix."""
x = checkParameterList(x, 1)[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.flatten()
if reorder is not None: x = x[reorder]
poles = poles.flatten()
Van = np.empty((len(x), len(poles)), dtype = np.complex)
for j in range(len(x)):
Van[j, :] = 1. / (x[j] - poles)
return Van
def polyvander(x:paramList, poles:Np1D, degs : List[int] = None,
basis : str = "MONOMIAL_HEAVISIDE",
derIdxs : List[List[List[int]]] = None,
reorder : List[int] = None, scl : Np1D = None) -> Np2D:
"""
Compute full 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 heaviside "
"function."))
basisp = basis.split("_")[0]
VanH = heavisidevander(x, poles, reorder = reorder)
if degs is None or np.sum(degs) < 0:
VanP = np.empty((len(x), 0))
else:
VanP = pvP(x, degs, basisp, derIdxs = derIdxs, reorder = reorder,
scl = scl)
return np.block([[VanH, VanP]])
def polyvanderTotal(x:paramList, poles:Np1D, deg : int = None,
basis : str = "MONOMIAL_HEAVISIDE",
derIdxs : List[List[List[int]]] = None,
reorder : List[int] = None, scl : Np1D = None)\
-> Tuple[Np2D, List[List[int]], List[int]]:
"""
Compute full total degree 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 = basis.split("_")[0]
VanR = heavisidevander(x, poles, reorder = reorder)
if deg is None or deg < 0:
VanP = np.empty((len(x), 0))
derIdxs, ordIdxs = np.zeros(0, dtype = int), np.zeros(0, dtype = int)
else:
VanP, derIdxs, ordIdxs = pvTP(x, deg, basisp, derIdxs = derIdxs,
reorder = reorder, scl = scl)
ordIdxsEff = np.concatenate((np.arange(len(VanR)), ordIdxs + len(VanR)))
return (np.block([[VanR, VanP],
[VanP.T.conj(), np.zeros(tuple([VanP.shape[1]] * 2))]]),
derIdxs, ordIdxsEff)

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