potential.py
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	# Copyright (C) 2018-2020 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 Tuple, Np1D
	from rrompy.utilities.exception_manager import RROMPyWarning

	__all__ = ['potential']

	def potential(x:Np1D, foci : Tuple[float, float] = [- 1., 1.]) -> Np1D:
	"""Evaluation of complex potential for ellipses or line segments."""
	mu0 = np.mean(foci)
	musig = foci[0] - mu0
	xFinite = np.isinf(x) == False
	dist = np.empty(len(x))
	dist[xFinite == False] = np.inf
	xEffR = x[xFinite] - mu0
	if np.isclose(musig, 0., atol = 1e-15):
	if foci[0] != foci[1]:
	RROMPyWarning("Collapsing different but numerically equal foci.")
	dist[xFinite] = np.abs(xEffR)
	else:
	xEffR /= musig
	bernEff = (xEffR 2. - 1) .5
	dist[xFinite] = np.max(np.vstack((np.abs(xEffR + bernEff),
	np.abs(xEffR - bernEff))), axis = 0)
	return dist