The design and implementation of the parallel out-of-core ScaLAPACK LU, QR and Cholesky factorization routines

This paper describes the design and implementation of three core factorization routines--LU, QR and Cholesky--included in the out-of-core extension of ScaLAPACK. These routines allow the factorization and solution of a dense system that is too large to fit entirely in physical memory. An image of the full matrix is maintained on disk and the factorization routines transfer sub-matrices into memory. The left-looking column-oriented variant of the factorization algorithm is implemented to reduce the disk I/O traffic. The routines are implemented using a portable I/O interface and utilize high performance ScaLAPACK factorization routines as in-core computational kernels. The authors present the details of the implementation for the out-of-core ScaLAPACK factorization routines, as well as performance and scalability results on the Intel Paragon