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kernel.py
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kernel.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 .base import sparseMap
from rrompy.utilities.base.types import Np1D, Np2D, paramList
from rrompy.utilities.exception_manager import RROMPyException
from rrompy.parameter import checkParameterList
__all__ = ['hatFunction', 'val', 'vander']
def hatFunctionRef(x:Np1D, supp:float, depth:int, kind:str) -> Np1D:
if depth < 0: y = np.zeros_like(x)
elif depth == 0: y = np.ones_like(x)
elif depth == 1:
if not np.isclose(np.abs(supp), 1.):
raise RROMPyException(("Wrong depth. Depth 1 points must be on "
"boundary."))
y = np.array(np.sign(supp) * x)
else:
width = .5 ** (depth - 1.)
if np.abs(supp) + width > 1. + .25 * width:
raise RROMPyException(("Wrong depth or support point. Support "
"point too close to boundary."))
y = np.array(1. - np.abs(x - supp) / width)
return np.clip(y, 0., 1., y)
def hatFunction(x:paramList, supportPoints:paramList, depths:Np2D,
kind:str, lims:paramList) -> Np2D:
x = checkParameterList(x)[0]
supportPoints = checkParameterList(supportPoints, x.shape[1])[0]
lims = checkParameterList(lims, x.shape[1])[0]
res = np.ones((len(supportPoints), len(x)))
for d in range(x.shape[1]):
x0 = sparseMap(x(d), lims(d), kind, False)
for j in range(len(supportPoints)):
supp = sparseMap(supportPoints(j, d), lims(d), kind, False)
res[j] *= hatFunctionRef(x0, supp, depths[j, d], kind)
return res.T
def vander(supportPoints:paramList, depths:Np2D, kind:str,
lims:paramList) -> Np2D:
return hatFunction(supportPoints, supportPoints, depths, kind, lims)
def val(x:paramList, c:Np2D, supportPoints:paramList, depths:Np2D,
kind:str, lims:paramList) -> Np2D:
van = hatFunction(x, supportPoints, depths, kind, lims)
return np.tensordot(van, c, 1)

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