hash_derivative.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/>.
	#

	from scipy.special import binom
	from rrompy.utilities.base.types import List

	__all__ = ['hashDerivativeToIdx', 'hashIdxToDerivative']

	def shellCount(shell:int, dim:int) -> int:
	return int(binom(shell + dim, dim))

	def hashDerivativeToIdx(derIdx:List[int]) -> int:
	dim = len(derIdx)
	if dim == 0: return 0
	derMag = sum(derIdx)
	base = shellCount(derMag - 1, dim)
	if derMag == derIdx[0]: return base
	return base + hashDerivativeToIdx(derIdx[1:])

	def hashIdxToDerivative(n:int, dim:int) -> List[int]:
	if n == 0: return [0] * dim
	shell = 0
	shellOld = -1
	shellNew = 1
	while shellNew <= n:
	shell += 1
	shellOld = shellNew
	shellNew = shellCount(shell, dim)
	rest = hashIdxToDerivative(n - shellOld, dim - 1)
	return [shell - sum(rest)] + rest