LAPACK
Example Programs for LAPACK

LAPACK is a FORTRAN90 program which shows some examples of calling the LAPACK library, which can solve linear systems and compute eigevalues.

Many vendors supply a compiled copy of LAPACK, optimized for their hardware, and easily available as a library.

• On Apple systems running OSX, a compiled copy of LAPACK is available by adding the clause "-framework vecLib" to your link/load statement:

              gfortran myprog.f90 -framework vecLib
            

LAPACK includes routines to

• Solve a linear system;
• Solve an under- or over-determined linear system;
• Compute the determinant;
• Compute the inverse matrix;
• Compute the condition number;
• Compute the singular value decomposition;
• Compute the QR decomposition;
• Compute the eigenvalues and eigenvectors of a matrix;

The source code and documentation for LAPACK is available through the NETLIB web site.

Related Data and Programs:

BLAS1 is a FORTRAN90 library of vector-vector routines needed by LAPACK.

BLAS2 is a FORTRAN90 library of matrix-vector routines needed by LAPACK.

BLAS3 is a FORTRAN90 library of matrix-matrix routines needed by LAPACK.

EISPACK is a FORTRAN90 library which is an earlier standard package of eigenvalue routines.

LAPACK is a FORTRAN90 library which is a modern general-purpose package of linear algebra routines including the ability to handle a variety of single or double precision, real or complex arithmetic models.

LAPACK_D is also available in a FORTRAN77 version.

LAPACK_S is a FORTRAN90 library which is the single precision real version of the LAPACK library.

LINPACK is a FORTRAN90 library which is an earlier standard package of linear system solvers.

LINPLUS is a FORTRAN90 library of simple linear solvers for a variety of matrix formats.

TEST_EIGEN is a FORTRAN90 library of routines which defines various eigenvalue test cases.

TEST_MAT is a FORTRAN90 library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses, and so on.

Reference:

1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy DuCroz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
   LAPACK User's Guide,
   Third Edition,
   SIAM, 1999,
   ISBN: 0898714478,
   LC: QA76.73.F25L36
2. Vincent Barker, Susan Blackford, Jack Dongarra, Jeremy Du Croz, Sven Hammarling, Minka Marinova, Jerzy Wasniewski, Plamen Yalamov,
   LAPACK95 User's Guide,
   SIAM, 2001,
   ISBN13: 978-0-898715-04-0,
   LC: QA76.73.F25.L36.

Examples and Tests:

• lapack_prb.f90, a sample calling program.
• lapack_prb.csh, commands to compile, link and run the calling program;
• lapack_prb_output.txt, output from the calling program;

On the Macintosh, an optimized version of LAPACK is available as vecLib.

• lapack_OSX_prb.csh is a shell script that compiles and runs the sample program with vecLib
• lapack_OSX_prb_output.txt contains the output from a run of the sample program.