Implementation of the algorithm of Banachiewicz for Cholesky-Decomposition

choleskyBanachiewicz.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

def choleskyBanachiewicz(A):
    """ 
        @param A: a nested list which represents a symmetric,
				  positiv definit n x n matrix.
        @return: False if it didn't work, otherwise the matrix G
    """
    n = len(A)
    
    # Initialisation of G with A
    G = []
    for i in xrange(n):
        line = []
        for j in xrange(n):
            line.append(float(A[i][j]))
        G.append(line)
        
        
    # Computation of G
    for j in xrange(n):
        # doesn't need the diagonals
        tmp = (A[j][j] - sum([G[j][k]**2 for k in xrange(0, j)]))
        if tmp < 0:
            return False
        G[j][j] = tmp**0.5
        for i in xrange(n):
            G[i][j] = 1/G[j][j] * (A[i][j] - sum([G[i][k]*G[j][k] for k in xrange(0, j)]))
    return G
    
if __name__ == "__main__":
    print choleskyBanachiewicz([[1,2],[2,1]]) # Nicht positiv definit
    print choleskyBanachiewicz([[5,2],[1,1]]) # not Hermitian
    print choleskyBanachiewicz([[5,2],[2,1]]) # should be [[sqrt(5), 2/sqrt(5)],[0, 1/sqrt(5)]]
print choleskyBanachiewicz([[1,0,0],[0,1,0],[0,0,1]])