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