ASA006
Cholesky Factor of a Positive Definite Symmetric Matrix

ASA006 is a C++ library 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 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.

Related Data and Programs:

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

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

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

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

LINPACK is a C++ library which includes routines for Cholesky factorization.

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

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

Reference:

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.
Michael Healy,
Algorithm AS 6: Triangular decomposition of a symmetric matrix,
Applied Statistics,
Volume 17, Number 2, 1968, pages 195-197.

Source Code:

asa006.C, the source code.
asa006.H, the include file.
asa006.csh, commands to compile the source code.

Examples and Tests:

asa006_prb.C, a sample calling program.
asa006_prb.csh, commands to compile and run the sample program.
asa006_prb_output.txt, the output file.

List of Routines:

CHOLESKY computes the Cholesky factorization of a PDS matrix.
SUBCHL computes the Cholesky factorization of a (subset of a) PDS matrix.
TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the C++ source codes.