Name
Title | ||
|---|---|---|
Level-3 Cholesky Factorization Routines Improve Performance of Many Cholesky Algorithms |
Abstract | ||
|---|---|---|
Four routines called DPOTF3i, i = a,b,c,d, are presented. DPOTF3i are a novel type of level-3 BLAS for use by BPF (Blocked Packed Format) Cholesky factorization and LAPACK routine DPOTRF. Performance of routines DPOTF3i are still increasing when the performance of Level-2 routine DPOTF2 of LAPACK starts decreasing. This is our main result and it implies, due to the use of larger block size nb, that DGEMM, DSYRK, and DTRSM performance also increases! The four DPOTF3i routines use simple register blocking. Different platforms have different numbers of registers. Thus, our four routines have different register blocking sizes. BPF is introduced. LAPACK routines for POTRF and PPTRF using BPF instead of full and packed format are shown to be trivial modifications of LAPACK POTRF source codes. We call these codes BPTRF. There are two variants of BPF: lower and upper. Upper BPF is “identical” to Square Block Packed Format (SBPF). “LAPACK” implementations on multicore processors use SBPF. Lower BPF is less efficient than upper BPF. Vector inplace transposition converts lower BPF to upper BPF very efficiently. Corroborating performance results for DPOTF3i versus DPOTF2 on a variety of common platforms are given for n ≈ nb as well as results for large n comparing DBPTRF versus DPOTRF. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1145/2427023.2427026 | ACM Trans. Math. Softw. |
Keywords | Field | DocType |
upper bpf,improve performance,lapack routine,dtrsm performance,corroborating performance result,cholesky algorithms,lapack potrf source code,different number,lower bpf,routines dpotf3i,dpotf3i routine,level-3 cholesky factorization routines,different platform,mathematics,cache blocking,blas,computer science | Block size,Computer software,Loop nest optimization,Data structure,Computer science,Source code,Parallel computing,Algorithm,Theoretical computer science,Multi-core processor,Cholesky decomposition,Basic Linear Algebra Subprograms | Journal |
Volume | Issue | ISSN |
39 | 2 | 0098-3500 |
Citations | PageRank | References |
2 | 0.45 | 21 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fred G. Gustavson | 1 | 1185 | 223.40 |
| Jerzy Waśniewski | 2 | 239 | 36.64 |
| Jack J. Dongarra | 3 | 17625 | 2615.79 |
| José R. Herrero | 4 | 94 | 16.90 |
| Julien Langou | 5 | 1028 | 71.98 |