LAPACK_EXAMPLES
Example Programs for LAPACK

LAPACK_EXAMPLES is a FORTRAN77 program which makes example calls to 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
            

• On Apple systems running the recent El Capitan OS, vecLib is gone and you have to use Accelerate instead!

              gfortran myprog.f90 -framework Accelerate
            

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

LAPACK_EXAMPLES is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

BLAS, a FORTRAN77 library which contains the Basic Linear Algebra Subprograms (BLAS) for level 1 (vector-vector operations), level 2 (matrix-vector operations) and level 3 (matrix-matrix operations), for single precision real arithmetic, double precision real arithmetic, single precision complex arithmetic, and double precision complex arithmetic.

EISPACK, a FORTRAN77 library which is an earlier standard package of eigenvalue routines.

GEQP3, a FORTRAN77 library which contains the portion of the LAPACK library that carries out the QR factorization, with column pivoting, of an M by N rectangular matrix, with N <= M.

LAPACK_EIGEN_TEST, a FORTRAN77 program which tests some of the LAPACK eigenvalue functions.

LINPACK, a FORTRAN77 library which is an earlier standard package of linear system solvers.

LINPLUS, a FORTRAN77 library which contains simple linear solvers for a variety of matrix formats.

SVD_DEMO, a FORTRAN77 program which demonstrates the Singular Value Decomposition (SVD) for a simple example.

TEST_EIGEN, a FORTRAN77 library which defines various eigenvalue test cases.

TEST_MAT, a FORTRAN77 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

Examples and Tests:

• lapack_examples_test.f is a sample calling program.
• lapack_examples_test.sh is a shell script that compiles and runs the sample program.
• lapack_examples_test.txt contains the output from a run of the sample program.

You can go up one level to the FORTRAN77 source codes.