Contents

 
• List of Figures
• List of Tables
• Guide
  • Essentials
    • ScaLAPACK
    • Structure and Functionality
    • Software Components
      • LAPACK
      • BLAS
      • PBLAS
      • BLACS
    • Efficiency and Portability
    • Availability
    • Commercial Use
    • Installation
    • Documentation
    • Support
    • Errata
    • Related Projects
    • Contents of the CD-ROM
  • Getting Started with ScaLAPACK
    • How to Run an Example Program Using MPI
    • Source Code for Example Program #1
    • Details of Example Program #1
      • Simplifying Assumptions Used in Example Program
      • Notation Used in Example Program
      • Output of Example Program #1 Using MPI
      • Output of Example Program #1 Using PVM
    • Four Basic Steps Required to Call a ScaLAPACK Routine
      • Initialize the Process Grid
      • Distribute the Matrix on the Process Grid
      • Call the ScaLAPACK Routine
      • Release the Process Grid
  • Contents of ScaLAPACK
    • Structure of ScaLAPACK
      • Levels of Routines
      • Data Types and Precision
      • Naming Scheme
    • Driver Routines
      • Linear Equations
      • Linear Least Squares Problems
      • Standard Eigenvalue and Singular Value Problems
        • Symmetric Eigenproblems
        • Singular Value Decomposition
      • Generalized Symmetric Definite Eigenproblems (GSEP)
    • Computational Routines
      • Linear Equations
      • Orthogonal Factorizations and Linear Least Squares Problems
        • QR Factorization
        • LQ Factorization
        • QR Factorization with Column Pivoting
        • Complete Orthogonal Factorization
        • Other Factorizations
      • Generalized Orthogonal Factorizations
        • Generalized QR Factorization
        • Generalized RQ factorization
      • Symmetric Eigenproblems
      • Nonsymmetric Eigenproblems
        • Eigenvalues, Eigenvectors, and Schur Factorization
      • Singular Value Decomposition
      • Generalized Symmetric Definite Eigenproblems
    • Orthogonal or Unitary Matrices
    • Algorithmic Differences between LAPACK and ScaLAPACK
  • Data Distributions and Software Conventions
    • Basics
      • Process Grid
      • Contexts
      • Scoped Operations
    • Array Descriptors
    • In-core Dense Matrices
      • The Two-dimensional Block-Cyclic Distribution
      • Local Storage Scheme and Block-Cyclic Mapping
      • Array Descriptor for In-core Dense Matrices
      • Example
      • Submatrix Argument Descriptions
      • Matrix and Vector Storage Conventions
    • 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
      • Array Descriptor for Out-core Dense Matrices
    • Design and Documentation of Argument Lists
      • Structure of the Documentation
      • Order of Arguments
      • Option Arguments
      • Problem Dimensions
      • Workspace Issues
        • WORK Arrays
        • LWORK Query
        • LWORK WORK(1)
      • Error Handling and the Diagnostic Argument INFO
      • Alignment Restrictions
    • Extensions
  • Performance of ScaLAPACK
    • Achieving High Performance with ScaLAPACK
      • Achieving High Performance on a Distributed Memory Computer
      • Achieving High Performance on a Network of Workstations
    • 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
        • Parallel Efficiency
      • ScaLAPACK Performance
      • Performance of Selected BLACS and Level 3 BLAS Routines
        • Performance of Selected PBLAS routines
        • Solution of Common Numerical Linear Algebra Problems
      • Solving Linear Systems of Equations
        • Solving Linear Least Squares Problems
        • Eigenvalue Problems
    • Performance Evaluation
      • Obtaining High Performance with ScaLAPACK Codes
      • Checking the BLAS and BLACS Libraries
      • Estimate Execution Time
      • Determine Whether Reasonable Performance Is Achieved
      • Identify Performance Bottlenecks
      • Performance Bottlenecks in the Expert Symmetric Eigenproblem Drivers
    • Performance Improvement
      • Choosing a Faster BLACS Library
      • Choosing a Faster BLAS Library
      • Tuning the Distribution Parameters for Better Performance
    • 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
      • Standard Error Analysis
      • Improved Error Bounds
    • 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
      • Further Details: Error Bounds for the Singular Value Decomposition
    • Error Bounds for the Generalized Symmetric Definite Eigenproblem
  • Troubleshooting
    • Installation Debugging Hints
    • Application Debugging Hints
    • Common Errors in Calling ScaLAPACK Routines
    • Failures Detected by ScaLAPACK Routines
      • Invalid Arguments and PXERBLA
      • Computational Failures and INFO > 0
    • Wrong Results
    • Error Handling in the PBLAS
    • Error Handling in the BLACS
      • BLACS Warning and Error Messages
    • System Error Messages
    • Poor Performance
  • Index of ScaLAPACK Routines
    • Index of Driver and Computational Routines
    • Index of Auxiliary Routines
    • Matrix Redistribution/Copy Routines
      • Fortran Interface
      • C Interface
      • Code Fragment Calling C Interface Cpdgemr2d
  • Call Conversion: LAPACK to ScaLAPACK and BLAS to PBLAS
    • Translating BLAS-based programs to the PBLAS
    • Translating LAPACK-based programs to ScaLAPACK
      • Sequential LU Factorization
      • Parallel LU Factorization
  • Example Programs
    • Example Program #2
    • HPF Interface to ScaLAPACK
  • Quick Reference Guides
    • ScaLAPACK Quick Reference Guide
    • Quick Reference Guide to the PBLAS
    • Quick Reference Guide to the BLACS
• Specifications of Routines
• References
• Index
• About this document ...