Ⅰ GENERAL INFORMATION

1 Essentials

1.1 LAPACK95

1.2 Problems that LAPACK95 can Solve

1.3 Computers for which LAPACK95 is Suitable

1.4 LAPACK and the BLAS

1.5 Availability and Installation of Software

1.5.1 LAPACK95

1.5.1.1 Incorporating Machine Dependencies

1.5.2 LAPACK

1.5.3 BLAS

1.5.4 Installation Debugging Hints

1.5.5 Mirror Repositories of netlib

1.5.6 Availability of Software via CD-ROM

1.6 Support

1.7 Commercial Use

2 Contents of LAPACK95

2.1 Structure of LAPACK95

2.1.1 Levels of Routines

2.1.2 Data Types and Precision

2.1.3 Naming Scheme

2.2 Driver Routines

2.2.1 Linear Equations

2.2.2 Linear Least Squares(LLS)Problems

2.2.3 Generalized Linear Least Squares(LSE and GLM)Problems

2.2.4 Standard Eigenvalue and Singular Value Problems

2.2.4.1 Symmetric Eigenproblems(SEP)

2.2.4.2 Nonsymmetric Eigenproblems(NEP)

2.2.4.3 Singular Value Decomposition(SVD)

2.2.5 Generalized Eigenvalue and Singular Value Problems

2.2.5.1 Generalized Symmetric Definite Eigenproblems(GSEP)

2.2.5.2 Generalized Nonsymmetric Eigenproblems(GNEP)

2.2.5.3 Generalized Singular Value Decomposition(GSVD)

3 Documentation Design and Program Examples

3.1 Design of the LAPACK95 Driver Interface

3.2 Design and Documentation of Driver Argument Lists

3.2.1 Structure of the Documentation

3.2.2 Order of Arguments

3.2.3 Argument Descriptions

3.2.4 Optional Arguments

3.2.5 Array Arguments

3.3 Error Handling

3.4 Matrix Storage Schemes

3.5 Design of Interfaces for Computational Routines

3.6 How to call an LAPACK95 Routine

3.7 Code for One Version of LA_SYEV

3.8 LAPACK and LAPACK95 Interface Module Blocks

3.8.1 F77_LAPACK Generic Interface Blocks

3.8.1.1 LA_SYEV/LA_HEEV

3.8.1.2 LA_GESV Multiple RHS Case

3.8.1.3 LA_GESV Single RHS Case

3.8.2 F95_LAPACK Generic Interface Blocks

3.8.2.1 LA_SYEV/LA_HEEV

3.8.2.2 LA_GESV

3.8.3 LA_LAMCH Interfaces

4 Performance and Troubleshooting

4.1 Performance of LAPACK95

4.1.1 Performance Issues

4.1.2 Performance Tables

4.2 Accuracy and Stability

4.3 Errors and Poor Performance

Ⅱ DRIVER ROUTINES

5 Driver Routines for Linear Systems

5.1 General Linear Systems

5.1.1 LA_GESV

5.1.2 LA_GESVX

5.1.3 LA_GBSV

5.1.4 LA_GBSVX

5.1.5 LA_GTSV

5.1.6 LA_GTSVX

5.2 Symmetric/Hermitian Positive Definite Linear Systems

5.2.1 LA_POSV

5.2.2 LA_POSVX

5.2.3 LA_PPSV

5.2.4 LA_PPSVX

5.2.5 LA_PBSV

5.2.6 LA_PBSVX

5.2.7 LA_PTSV

5.2.8 LA_PTSVX

5.3 Symmetric Indefinite Linear Systems

5.3.1 LA_SYSV/LA_HESV

5.3.2 LA_SYSVX/LA_HESVX

5.3.3 LA_SPSV/LA_HPSV

5.3.4 LA_SPSVX/LA_HPSVX

6 Driver Routines for Least Squares Problems

6.1 Linear Least Squares Problems

6.1.1 LA_GELS

6.1.2 LA_GELSY

6.1.3 LA_GELSS/LA_GELSD

6.2 Generalized Linear Least Squares Problems

6.2.1 LA_GGLSE

6.2.2 LA_GGGLM

7 Driver Routines for Standard Eigenvalue Problems

7.1 Standard Symmetric Eigenvalue Problems

7.1.1 LA_SYEV/LA_HEEV/LA_SYEVD/LA_HEEVD

7.1.2 LA_SYEVX/LA_HEEVX

7.1.3 LA_SYEVR/LA_HEEVR

7.1.4 LA_SPEV/LA_HPEV/LA_SPEVD/LA_HPEVD

7.1.5 LA_SPEVX/LA_HPEVX

7.1.6 LA_SBEV/LA_HBEV/LA_SBEVD/LA_HBEVD

7.1.7 LA_SBEVX/LA_HBEVX

7.1.8 LA_STEV/LA_STEVD

7.1.9 LA_STEVX

7.1.10 LA_STEVR

7.2 Standard Nonsymmetric Eigenvalue Problems

7.2.1 LA_GEES

7.2.2 LA_GEESX

7.2.3 LA_GEEV

7.2.4 LA_GEEVX

8 Driver Routines for Generalized Eigenvalue Problems

8.1 Generalized Symmetric Eigenvalue Problems

8.1.1 LA_SYGV/LA_SYGVD/LA_HEGV/LA_HEGVD

8.1.2 LA_SYGVX/LA_HEGVX

8.1.3 LA_SPGV/LA_SPGVD/LA_HPGV/LA_HPGVD

8.1.4 LA_SPGVX/LA_HPGVX

8.1.5 LA_SBGV/LA_SBGVD/LA_HBGV/LA_HBGVD

8.1.6 LA_SBGVX/LA_HBGVX

8.2 Generalized Nonsymmetric Eigenvalue Problems

8.2.1 LA_GGES

8.2.2 LA_GGESX

8.2.3 LA_GGEV

8.2.4 LA_GGEVX

9 Driver Routines for Singular Value Problems

9.1 Standard Singular Value Problems

9.1.1 LA_GESVD/LA_GESDD

9.2 Generalized Singular Value Problems

9.2.1 LA_GGSVD

Ⅲ COMPUTATIONAL ROUTINES

10 Computational Routines

10.1 Computational Routines for Linear Equations

10.1.1 General Linear Systems

10.1.2 Symmetric/Hermitian Positive Definite Linear Systems

10.1.3 Symmetric Indefinite Linear Systems

10.1.4 Triangular Linear Systems

10.2 Computational Routines for Orthogonal Factorizations

10.3 Computational Routines for the Symmetric Eigenproblem

10.4 Computational Routines for the Nonsymmetric eigenproblem

10.5 Computational Routines for the Singular Value Decomposition

10.6 Computational Routines for the Generalized Symmetric Definite Eigenproblem

10.7 Computational Routines for the Generalized Nonsymmetric Eigenproblem

10.8 Computational Routines for the Generalized Singular Value Decomposition

Bibliography

Index by Keyword

Index by Routine Name

List of Tables

1.1 Machine constants returned by LA_LAMCH

2.1 Matrix types in the LAPACK naming scheme

2.2 Driver routines for linear equations

2.3 Driver routines for linear least squares problems

2.4 Driver routines for generalized linear least squares problems

2.5 Driver routines for standard eigenvalue and singular value problems

2.6 Driver routines for generalized eigenvalue and singular value problems

4.1 Computer used for running the performance timing

4.2 Floating point coefficient of operation counts for LAPACK drivers for n×n matrices(see also Table 3.13 of[1]).The number of operations is α×n3

4.3 Performance of LA_GESV in megaflops;n=100 and 1000

4.4 Performance of LA_GEEV in megaflops(eigenvalues only);n=100 and 1000

4.5 Performance of LA_GEEV in megaflops(eigenvalues and right eigenvectors);n=100 and 1000

4.6 Performance of LA_GESVD in megaflops(singular values and left and right singular vectors);n=100 and 1000

4.7 Performance of LA_GESDD in megaflops(singular values only);n=100 and 1000

4.8 Performance of LA_GESDD in megaflops(singular values and left and right singular vectors);n=100 and 1000

List of Figures

3.1 Example program calling an LAPACK95 driver routine

3.2 Example program calling an LAPACK95 computational routine