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ASA006\ Cholesky Factor of a Positive Definite Symmetric Matrix {#asa006-cholesky-factor-of-a-positive-definite-symmetric-matrix align=”center”} =======================================================

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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.

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

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: {#related-data-and-programs align=”center”}

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

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

LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK_D, a C++ 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 C++ library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

Reference: {#reference align=”center”}

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: {#source-code align=”center”}

• asa006.cpp, the source code.
• asa006.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• asa006_prb.cpp, a sample calling program.
• asa006_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• 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.

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Last revised on 14 December 2011.