Cholesky-Zerlegung in Wikipedia oldid=104368978

choleskyWikiWrong.py

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

def choleskyDecomposition(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 i in xrange(0,n):
        for j in xrange(0, i):
            sum = G[i][j]
            for k in xrange(0, j-1):
                sum -= G[i][k] * G[j][k]
            G[j][i] = sum / G[j][j]

        sum = G[i][i]
        
        for k in xrange(0, i):
            sum -= G[k][i]**2

        if sum > 0:
            G[i][i] = sum**0.5
        else:
            return False
    return G

print choleskyDecomposition([[1,2],[2,1]]) # Nicht positiv definit
print choleskyDecomposition([[5,2],[1,1]]) # not Hermitian
print choleskyDecomposition([[5,2],[2,1]]) # should be [[sqrt(5), 2/sqrt(5)],[0, 1/sqrt(5)]]