ScaLAPACK Users' Guide
Published on 31. July 1997
Book
Paperback/Softback
341 pages
978-0-89871-397-8 (ISBN)
Description
ScaLAPACK is an acronym for Scalable Linear Algebra Package or Scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (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. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use.
ScaLAPACK includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite/ Hermitian-definite generalized eigenproblem to standard form, the symmetric/Hermitian, generalized symmetric/Hermitian, and nonsymmetric eigenproblem, and the singular value decomposition. Prototype codes are provided for out-of-core linear solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems, an HPF interface to a subset of ScaLAPACK routines, and SuperLU.
Software is available in single-precision real, double-precision real, single-precision complex, and double-precision complex. The software has been written to be portable across a wide range of distributed-memory environments such as the Cray T3, IBM SP, Intel series, TM CM-5, networks of workstations, and any system for which PVM or MPI is available.
Each Users' Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users' Guide, the source code for ScaLAPACK and LAPACK, testing and timing programs, prebuilt versions of the library for a number of computers, example programs, and the full set of LAPACK Working Notes.
ScaLAPACK includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite/ Hermitian-definite generalized eigenproblem to standard form, the symmetric/Hermitian, generalized symmetric/Hermitian, and nonsymmetric eigenproblem, and the singular value decomposition. Prototype codes are provided for out-of-core linear solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems, an HPF interface to a subset of ScaLAPACK routines, and SuperLU.
Software is available in single-precision real, double-precision real, single-precision complex, and double-precision complex. The software has been written to be portable across a wide range of distributed-memory environments such as the Cray T3, IBM SP, Intel series, TM CM-5, networks of workstations, and any system for which PVM or MPI is available.
Each Users' Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users' Guide, the source code for ScaLAPACK and LAPACK, testing and timing programs, prebuilt versions of the library for a number of computers, example programs, and the full set of LAPACK Working Notes.
More details
Series
Language
English
Place of publication
New York
United States
Target group
College/higher education
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 28 mm
Weight
903 gr
ISBN-13
978-0-89871-397-8 (9780898713978)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
List of Figures
List of Tables
Preface
Suggestions for Reading
List of Notation
Part I: Guide. Chapter 1: Essentials. ScaLAPACK
Structure and Functionality
Software Components
Efficiency and Portability
Availability
Commercial Use
Installation
Documentation
Support
Errata
Related Projects
Contents of the CD-ROM
Chapter 2: Getting Started with ScaLAPACK. How to Run an Example Program Using MPI
Source Code for Example Program #1
Details of Example Program #1
Four Basic Steps Required to Call a ScaLAPACK Routine
Chapter 3: Contents of ScaLAPACK. Structure of ScaLAPACK
Driver Routines
Computational Routines
Orthogonal or Unitary Matrices
Algorithmic Differences between LAPACK and ScaLAPACK
Chapter 4: Data Distribution and Software Conventions. Basics
Array Descriptors
In-Core Dense Matrices
In-Core Narrow Band and Tridiagonal Matrices
Out-of-Core Matrices
Design and Documentation of Argument Lists
Extensions
Chapter 5: Performance of ScaLAPACK. Achieving High Performance with ScaLAPACK
Performance, Portability and Scalability
Performance Evaluation
Performance Improvement
Performance of Banded and Out-of-Core Drivers
Chapter 6: 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
Chapter 7: Troubleshooting. Installation Debugging Hints
Application Debugging Hints
Common Errors in Calling ScaLAPACK Routines
Failures Detected by ScaLAPACK Routines
Wrong Results
Error Handling in the PBLAS
Error Handling in the BLACS
System Error Messages
Poor Performance
Appendix A: Index of ScaLAPACK Routines. Index of Driver and Computational Routines
Index of Auxiliary Routines
Matrix Redistribution/Copy Routines
Appendix B: Call Conversion: LAPACK to ScaLAPACK and BLAS to PBLAS. Translating BLAS-based programs to the PBLAS
Translating LAPACK-based programs to ScaLAPACK
Appendix C: Example Programs. Example Program #2
HPF Interface to ScaLAPACK
Appendix D: Quick Reference Guides. ScaLAPACK Quick Reference Guide
Quick Reference Guide to the PBLAS
Quick Reference Guide to the BLACS
Glossary
Part II: Specifications of Routines. Bibliography
Index by Keyword
Index by Routine Name.
List of Tables
Preface
Suggestions for Reading
List of Notation
Part I: Guide. Chapter 1: Essentials. ScaLAPACK
Structure and Functionality
Software Components
Efficiency and Portability
Availability
Commercial Use
Installation
Documentation
Support
Errata
Related Projects
Contents of the CD-ROM
Chapter 2: Getting Started with ScaLAPACK. How to Run an Example Program Using MPI
Source Code for Example Program #1
Details of Example Program #1
Four Basic Steps Required to Call a ScaLAPACK Routine
Chapter 3: Contents of ScaLAPACK. Structure of ScaLAPACK
Driver Routines
Computational Routines
Orthogonal or Unitary Matrices
Algorithmic Differences between LAPACK and ScaLAPACK
Chapter 4: Data Distribution and Software Conventions. Basics
Array Descriptors
In-Core Dense Matrices
In-Core Narrow Band and Tridiagonal Matrices
Out-of-Core Matrices
Design and Documentation of Argument Lists
Extensions
Chapter 5: Performance of ScaLAPACK. Achieving High Performance with ScaLAPACK
Performance, Portability and Scalability
Performance Evaluation
Performance Improvement
Performance of Banded and Out-of-Core Drivers
Chapter 6: 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
Chapter 7: Troubleshooting. Installation Debugging Hints
Application Debugging Hints
Common Errors in Calling ScaLAPACK Routines
Failures Detected by ScaLAPACK Routines
Wrong Results
Error Handling in the PBLAS
Error Handling in the BLACS
System Error Messages
Poor Performance
Appendix A: Index of ScaLAPACK Routines. Index of Driver and Computational Routines
Index of Auxiliary Routines
Matrix Redistribution/Copy Routines
Appendix B: Call Conversion: LAPACK to ScaLAPACK and BLAS to PBLAS. Translating BLAS-based programs to the PBLAS
Translating LAPACK-based programs to ScaLAPACK
Appendix C: Example Programs. Example Program #2
HPF Interface to ScaLAPACK
Appendix D: Quick Reference Guides. ScaLAPACK Quick Reference Guide
Quick Reference Guide to the PBLAS
Quick Reference Guide to the BLACS
Glossary
Part II: Specifications of Routines. Bibliography
Index by Keyword
Index by Routine Name.