cholesky-decomposition
Simple octave program to compute the Cholesky factor of an n-by-n symmetric, positive-definite matrix.
Usage
Obtain the n-by-n symmetric, positive-definite matrix that you want to compute the Cholesky factor of. Let's say you define it as the matrix A. Run the program as follows:
cholesky(A, n)where A is your matrix and n is its order.
What will be returned is the upper-triangular Cholesky factor.
Example Use
% Creating a random 5x5 matrix, A
M = rand(5);
A = M'*M
A =
1.41147 0.50368 0.72197 0.90387 0.65699
0.50368 0.23568 0.32488 0.27783 0.30763
0.72197 0.32488 0.78400 0.50235 0.83792
0.90387 0.27783 0.50235 1.14882 0.53843
0.65699 0.30763 0.83792 0.53843 0.96092
% Set the Cholesky factor to a matrix called R
R = cholesky(A, 5)
R =
1.18805 0.42395 0.60769 0.76080 0.55300
0.00000 0.23652 0.28434 -0.18905 0.30942
0.00000 0.00000 0.57781 0.16230 0.71630
0.00000 0.00000 0.00000 0.71269 0.08412
0.00000 0.00000 0.00000 0.00000 0.19803