public static void choleskyFactorization(double[][] A, double[][] L) {

			int n = A.length;
			for (int i = 0; i < n; i++) {
				for (int j = 0; j <= i; j++) {
					double sum = 0.0;
					for (int k = 0; k < j; k++) {
						sum += L[i][k] * L[j][k];
					}
					if (i == j)
						L[i][i] = Math.sqrt(A[i][i] - sum);
					else
						L[i][j] = 1.0 / L[j][j] * (A[i][j] - sum);
				}
			}
		}