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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 rrompy.utilities.base.types import Np1D
	from rrompy.utilities.exception_manager import RROMPyAssert

	__all__ = ['radialGaussian', 'thinPlateSpline', 'multiQuadric',
	'localWendland']

	def radialGaussian(r2:Np1D, der : int = 0) -> Np1D:
	RROMPyAssert(der, 0, "Radial basis derivative")
	return np.exp(- .5 * r2)

	def thinPlateSpline(r2:Np1D, der : int = 0) -> Np1D:
	RROMPyAssert(der, 0, "Radial basis derivative")
	return .5 * r2 * np.log(np.finfo(float).eps + r2)

	def multiQuadric(r2:Np1D, der : int = 0) -> Np1D:
	RROMPyAssert(der, 0, "Radial basis derivative")
	return np.power(r2 + 1., -.5)

	def localWendland(r2:Np1D, der : int = 0) -> Np1D:
	RROMPyAssert(der, 0, "Radial basis derivative")
	rm1 = 1. - r2 ** .5
	rm1[rm1 <= 0.] = 0.
	return rm1 ** 4. * (5. - 4. * rm1)