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kommt nochScaLAPACK Users' Guide
ScaLAPACK is a library of high-performance linear algebra routines for distributed-memory message-passing MIMD computers and networks of workstations supporting PVM and/or MPI. It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared-memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems.
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ScaLAPACK Users' Guide
- L. S. Blackford,
- J. Choi,
- A. Cleary,
- E. D'Azevedo,
- J. Demmel,
- I. Dhillon,
- J. Dongarra,
- S. Hammarling,
- G. Henry,
- A. Petitet,
- K. Stanley,
- D. Walker,
- R. C. Whaley
1 May 1997
Dedication
This work is dedicated to the pioneers of high-performance computing who blazed a trail, set standards, and made our job easier.
Acknowledgment
We give credit to and thank all of the LAPACK authors for allowing us to reuse large portions of the LAPACK Users' Guide in creating this users guide for ScaLAPACK.
1997 by the Society for
Industrial and Applied Mathematics. Certain derivative work portions have
been copyrighted by the Numerical Algorithms Group Ltd.
The printed version of the ScaLAPACK Users' Guide will be available from SIAM in July 1997. The list price for SIAM members is $39.60; the cost for nonmembers is $49.50. Contact SIAM for additional information.
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- fax: 215-386-7999
- phone: (USA) 800-447-SIAM
- (outside USA) 215-386-7999
- mail: SIAM, 3600 University City Science Center, Philadelphia, PA 19104-2688.
The royalties from the sales of this book are being placed in a fund to help students attend SIAM meetings and other SIAM related activities. This fund is administered by SIAM and qualified individuals are encouraged to write directly to SIAM for guidelines.
- Contents
- List of Figures
- List of Tables
-
Guide
- Essentials
- Getting Started with ScaLAPACK
- Contents of ScaLAPACK
-
Data
Distributions and Software Conventions
- Basics
- Array Descriptors
- In-core Dense Matrices
-
In-Core Narrow Band and Tridiagonal
Matrices
- The Block Column and Row Distributions
- The Block Mapping
- Local Storage Scheme for Narrow Band Matrices
- Local Storage Schemes for Tridiagonal Matrices
- Array Descriptor for Narrow Band and Tridiagonal Matrices
- Array Descriptor for the Matrix of Right-Hand-Side Vectors
- Argument Descriptions for Band and Tridiagonal Routines
- Matrix Storage Conventions for Band and Tridiagonal Matrices
- Out-of-Core Matrices
- Design and Documentation of Argument Lists
- Extensions
-
Performance of ScaLAPACK
- Achieving High Performance with ScaLAPACK
-
Performance, Portability and Scalability
- The BLAS as the Key to (Trans)portable Efficiency
- Two-Dimensional Block Cyclic Data Distribution as a Key to Load Balancing and Software Reuse
- BLACS as an Efficient, Portable and Adequate Message-Passing Interface
- ScaLAPACK Performance
- Performance of Selected BLACS and Level 3 BLAS Routines
- Solving Linear Systems of Equations
- Performance Evaluation
- Performance Improvement
- Performance of Banded and Out-of-Core Drivers
-
Accuracy and Stability
- Sources of Error in Numerical Calculations
- New Sources of Error in Parallel Numerical Computations
- How to Measure Errors
- Further Details: How Error Bounds Are Derived
- Error Bounds for Linear Equation Solving
- Error Bounds for Linear Least Squares Problems
- Error Bounds for the Symmetric Eigenproblem
- Error Bounds for the Singular Value Decomposition
- Error Bounds for the Generalized Symmetric Definite Eigenproblem
- Troubleshooting
- Index of ScaLAPACK Routines
- Call Conversion: LAPACK to ScaLAPACK and BLAS to PBLAS
- Example Programs
- Quick Reference Guides
- Specifications of Routines
- References
- Index
- About this document ...
Susan Blackford
Tue May 13 09:21:01 EDT 1997