ASA006
Cholesky Factor of a Positive Definite Symmetric Matrix

ASA006 is a MATLAB program which computes the Cholesky factor of a positive definite symmetric matrix.

ASA006 is Applied Statistics Algorithm 6. Source code for many Applied Statistics Algorithms is available through STATLIB.

If A is a positive definite symmetric matrix, then there is an upper triangular matrix U with the property that

A = U' * U

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ASA006 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ASA007, a MATLAB library which computes the inverse of a symmetric positive definite matrix, and uses a version of ASA006 for for Cholesky factorization.

ASA047, a MATLAB library which implements the Nelder-Mead minimization algorithm, and uses a version of ASA006 for Cholesky factorization.

LAPACK, a FORTRAN90 library which includes routines for Cholesky factorization.

LINPACK, a MATLAB library which includes routines for Cholesky factorization.

NL2SOL, a FORTRAN77 library which solves nonlinear least squares problems, and includes routines for Cholesky factorization.

PPPACK, a FORTRAN77 library which carries out piecewise polynomial interpolation and includes routines for Cholesky factorization.

TOEPLITZ_CHOLESKY, a MATLAB library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

Reference:

1. PR Freeman,
   Remark AS R44: A Remark on AS 6 and AS7: Triangular decomposition of a symmetric matrix and Inversion of a positive semi-definite symmetric matrix,
   Applied Statistics,
   Volume 31, Number 3, 1982, pages 336-339.
2. Michael Healy,
   Algorithm AS 6: Triangular decomposition of a symmetric matrix,
   Applied Statistics,
   Volume 17, Number 2, 1968, pages 195-197.

Source Code:

• cholesky.m computes the Cholesky factorization of a PDS matrix.
• subchl.m computes the Cholesky factorization of a (subset of a) PDS matrix.
• timestamp.m prints out the current YMDHMS date as a timestamp.

Examples and Tests:

• asa006_test.m, a sample calling program.
• asa006_test01.m, tests CHOLESKY on a simple matrix.
• asa006_test02.m, tests CHOLESKY on the Hilbert matrix.
• asa006_test03.m, tests SUBCHL on the Hilbert matrix.
• asa006_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.