NDLI: Rectangular full packed format for cholesky's algorithm: factorization, solution, and inversion

Content Provider	ACM Digital Library
Author	Dongarra, Jack J. Langou, Julien Waśniewski, Jerzy Gustavson, Fred G.
Copyright Year	2010
Abstract	We describe a new data format for storing triangular, symmetric, and Hermitian matrices called Rectangular Full Packed Format (RFPF). The standard two-dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full-format representation. Also, RFPF requires exactly the same minimal storage as packed the format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full-format routine and two calls to Level 3 BLAS routines. This means $\textit{no}$ new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution, and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using the standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines.
Starting Page	1
Ending Page	21
Page Count	21
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/1731022.1731028
Volume Number	37
Issue Number	2
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-04-23
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	BLAS Cholesky factorization and solution LAPACK Real symmetric matrices Rectangular Full Packed Format Complex Hermitian matrices Linear algebra libraries Novel packed matrix data structures Positive definite matrices Recursive algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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