asa006, a Python code which computes the Cholesky factor of a symmetric positive definite (SPD) matrix.
This is a version of Applied Statistics Algorithm 6.
If A is a symmetric positive definite matrix, then there is an upper triangular matrix U with the property that
A = U' * UThe matrix U is known as the Cholesky factor of A, and can be used to easily solve linear systems involving A or compute the inverse of A.
The algorithm implemented here uses a compressed storage for both the matrix A and the factor U. This saves some storage, but can make computations a little awkward.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
asa006 is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and a Python version.
asa007, a MATLAB code which computes the inverse of a symmetric positive definite (SPD) matrix, and uses a version of ASA006 for for Cholesky factorization.
asa047, a Python code which implements the Nelder-Mead minimization algorithm, and uses a version of asa006() for Cholesky factorization.
toeplitz_cholesky, a Python code which computes the Cholesky factorization of a symmetric nonnegative definite Toeplitz matrix.