Guide

• Essentials
  • LAPACK
  • Problems that LAPACK can Solve
  • Computers for which LAPACK is Suitable
  • LAPACK Compared with LINPACK and EISPACK
  • LAPACK and the BLAS
  • Documentation for LAPACK
  • Availability of LAPACK
  • Installation of LAPACK
  • Support for LAPACK
  • Known Problems in LAPACK
  • Other Related Software
    • LAPACK++
    • CLAPACK
    • ScaLAPACK
    • LAPACK routines exploiting IEEE arithmetic
• Contents of LAPACK
  • Structure of LAPACK
    • Levels of Routines
    • Data Types and Precision
    • Naming Scheme
  • Driver Routines
    • Linear Equations
    • Linear Least Squares (LLS) Problems
    • Generalized Linear Least Squares (LSE and GLM) Problems
    • Standard Eigenvalue and Singular Value Problems
      • Symmetric Eigenproblems (SEP)
      • Nonsymmetric Eigenproblems (NEP)
      • Singular Value Decomposition (SVD)
    • Generalized Eigenvalue and Singular Value Problems
      • Generalized Symmetric Definite Eigenproblems (GSEP)
      • Generalized Nonsymmetric Eigenproblems (GNEP)
      • Generalized Singular Value Decomposition (GSVD)
  • 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 and Linear Least Squares Problems
      • Generalized QR Factorization
      • Generalized RQ factorization
    • Symmetric Eigenproblems
    • Nonsymmetric Eigenproblems
      • Eigenvalues, Eigenvectors and Schur Factorization
      • Balancing
      • Invariant Subspaces and Condition Numbers
    • Singular Value Decomposition
    • Generalized Symmetric Definite Eigenproblems
    • Generalized Nonsymmetric Eigenproblems
    • Generalized (or Quotient) Singular Value Decomposition
• Performance of LAPACK
  • Factors that Affect Performance
    • Vectorization
    • Data Movement
    • Parallelism
  • The BLAS as the Key to Portability
  • Block Algorithms and their Derivation
  • Examples of Block Algorithms in LAPACK
    • Factorizations for Solving Linear Equations
    • QR Factorization
    • Eigenvalue Problems
  • LAPACK Benchmark
• Accuracy and Stability
  • Sources of Error in Numerical Calculations
    • Further Details: Floating point arithmetic
  • How to Measure Errors
    • Further Details: How to Measure Errors
  • Further Details: How Error Bounds Are Derived
    • Standard Error Analysis
    • Improved Error Bounds
  • Error Bounds for Linear Equation Solving
    • Further Details: Error Bounds for Linear Equation Solving
  • Error Bounds for Linear Least Squares Problems
    • Further Details: Error Bounds for Linear Least Squares Problems
  • Error Bounds for Generalized Least Squares Problems
  • Error Bounds for the Symmetric Eigenproblem
    • Further Details: Error Bounds for the Symmetric Eigenproblem
  • Error Bounds for the Nonsymmetric Eigenproblem
    • Further Details: Error Bounds for the Nonsymmetric Eigenproblem
      • Overview
      • Balancing and Conditioning
      • Computing s and sep
  • Error Bounds for the Singular Value Decomposition
    • Further Details: Error Bounds for the Singular Value Decomposition
  • Error Bounds for the Generalized Symmetric Definite Eigenproblem
    • Further Details: Error Bounds for the Generalized Symmetric Definite Eigenproblem
  • Error Bounds for the Generalized Nonsymmetric Eigenproblem
  • Error Bounds for the Generalized Singular Value Decomposition
    • Further Details: Error Bounds for the Generalized Singular Value Decomposition
  • Error Bounds for Fast Level 3 BLAS
• Documentation and Software Conventions
  • Design and Documentation of Argument Lists
    • Structure of the Documentation
    • Order of Arguments
    • Argument Descriptions
    • Option Arguments
    • Problem Dimensions
    • Array Arguments
    • Work Arrays
    • Error Handling and the Diagnostic Argument INFO
  • Determining the Block Size for Block Algorithms
  • Matrix Storage Schemes
    • Conventional Storage
    • Packed Storage
    • Band Storage
    • Tridiagonal and Bidiagonal Matrices
    • Unit Triangular Matrices
    • Real Diagonal Elements of Complex Matrices
  • Representation of Orthogonal or Unitary Matrices
• Installing LAPACK Routines
  • Points to Note
  • Installing ILAENV
• Troubleshooting
  • Common Errors in Calling LAPACK Routines
  • Failures Detected by LAPACK Routines
    • Invalid Arguments and XERBLA
    • Computational Failures and INFO > 0
  • Wrong Results
  • Poor Performance
• Index of Driver and Computational Routines
  • Notes
• Index of Auxiliary Routines
  • Notes
• Quick Reference  Guide to the BLAS
• Converting from LINPACK or EISPACK
  • Notes
• LAPACK Working Notes