mi@0: #!/usr/bin/python2.6
mi@0: #
mi@0: # Copyright (C) Christian Thurau, 2010. 
mi@0: # Licensed under the GNU General Public License (GPL). 
mi@0: # http://www.gnu.org/licenses/gpl.txt
mi@0: """
mi@0: PyMF functions for computing matrix/simplex volumes
mi@0: 
mi@0: 	cmdet(): Cayley-Menger Determinant
mi@0: 	simplex_volume(): Ordinary simplex volume
mi@0: 		
mi@0: """
mi@0: 
mi@0: 
mi@0: import numpy as np
mi@0: try:
mi@0: 	from scipy.misc.common import factorial
mi@0: except:
mi@0: 	from scipy.misc import factorial
mi@0: 
mi@0: __all__ = ["cmdet", "simplex"]
mi@0: 
mi@0: def cmdet(d):
mi@0: 	# compute the CMD determinant of the euclidean distance matrix d
mi@0: 	# -> d should not be squared!
mi@0: 	D = np.ones((d.shape[0]+1,d.shape[0]+1))
mi@0: 	D[0,0] = 0.0
mi@0: 	D[1:,1:] = d**2
mi@0: 	j = np.float32(D.shape[0]-2)
mi@0: 	f1 = (-1.0)**(j+1) / ( (2**j) * ((factorial(j))**2))
mi@0: 	cmd = f1 * np.linalg.det(D)
mi@0: 	# sometimes, for very small values "cmd" might be negative ...
mi@0: 	return np.sqrt(np.abs(cmd))
mi@0: 
mi@0: def simplex(d):
mi@0: 	# compute the simplex volume using coordinates
mi@0: 	D = np.ones((d.shape[0]+1, d.shape[1]))
mi@0: 	D[1:,:] = d
mi@0: 	vol = np.abs(np.linalg.det(D)) / factorial(d.shape[1] - 1)
mi@0: 	return vol