asa006

asa006, a FORTRAN90 code which computes the Cholesky factor of a symmetric positive definite (SPD) matrix.

The code is 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' * 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:

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

Languages:

asa006 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

asa006_test

asa007, a FORTRAN90 code which computes the inverse of a symmetric positive definite matrix, and uses a version of ASA006 for for Cholesky factorization.

asa047, a FORTRAN90 code which implements the Nelder-Mead minimization algorithm, and uses a version of ASA006 for Cholesky factorization.

LAPACK_EXAMPLES, a FORTRAN90 code which demonstrates the use of the LAPACK linear algebra library.

LINPACK, a FORTRAN90 code which includes routines for Cholesky factorization.

PPPACK, a FORTRAN90 code which computes piecewise polynomial functions, including cubic splines.

TOEPLITZ_CHOLESKY, a FORTRAN90 code 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:

Last revised on 26 August 2021.