Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format

Abstract

We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion article. The matrix is packed into n(n + 1)/2 real variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage (n2 variables). Included are subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel subroutine that is used for the Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric matrix that is small enough to be held in cache. We provide a comprehensive test program and simple example programs. © 2007 ACM.