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#!/usr/bin/python2.6
#
# Copyright (C) Christian Thurau, 2010. 
# Licensed under the GNU General Public License (GPL). 
# http://www.gnu.org/licenses/gpl.txt
"""
PyMF functions for computing matrix/simplex volumes

	cmdet(): Cayley-Menger Determinant
	simplex_volume(): Ordinary simplex volume
		
"""


import numpy as np
try:
	from scipy.misc.common import factorial
except:
	from scipy.misc import factorial

__all__ = ["cmdet", "simplex"]

def cmdet(d):
	# compute the CMD determinant of the euclidean distance matrix d
	# -> d should not be squared!
	D = np.ones((d.shape[0]+1,d.shape[0]+1))
	D[0,0] = 0.0
	D[1:,1:] = d**2
	j = np.float32(D.shape[0]-2)
	f1 = (-1.0)**(j+1) / ( (2**j) * ((factorial(j))**2))
	cmd = f1 * np.linalg.det(D)
	# sometimes, for very small values "cmd" might be negative ...
	return np.sqrt(np.abs(cmd))

def simplex(d):
	# compute the simplex volume using coordinates
	D = np.ones((d.shape[0]+1, d.shape[1]))
	D[1:,:] = d
	vol = np.abs(np.linalg.det(D)) / factorial(d.shape[1] - 1)
	return vol