BLAS3
Level 3 Basic Linear Algebra Subprograms

BLAS3 is a library of FORTRAN90 routines, using double precision arithmetic, which implement the Level 3 BLAS, or Basic Linear Algebra Subprograms.

The BLAS are a small core library of linear algebra utilities, which can be highly optimized for various architectures. Software that relies on the BLAS is thus highly portable, and will typically run very efficiently.

The Level 3 BLAS are designed to handle matrix-matrix operations.

Related Data and Programs:

BLAS1 handles vector-vector operations.

BLAS2 handles matrix-vector operations.

BLAS3 is also available in a FORTRAN77 version.

ESSL, the IBM Engineering and Scientific Subroutine Library, includes an implementation of the BLAS3 routines.

LAPACK is a linear algebra library built on top of the BLAS routines.

PETSC, is a scientific library for use in parallel computation, which includes an implementation of the BLAS3 routines.

Reference:

1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
   LAPACK User's Guide,
   Third Edition,
   SIAM, 1999,
   ISBN: 0898714478,
   LC: QA76.73.F25L36.
2. Thomas Coleman, Charles vanLoan,
   Handbook for Matrix Computations,
   SIAM, 1988,
   ISBN13: 978-0-898712-27-8,
   LC: QA188.C65.
3. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
4. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• blas3.f90, the matrix-matrix code;
• blas3.csh, commands to compile the source code;

Examples and Tests:

• blas3_prb.f90, a calling program;
• blas3_prb.csh, commands to compile, link, load and run the calling program;
• blas3_prb_output.txt, the output file.

List of Routines:

• DGEMM C:=alpha*A*B+beta*C, A, B, C rectangular.
• DSYMM C:=alpha*A*B+beta*C, A symmetric, B and C rectangular.
• DSYRK C:=alpha*A*TRANSPOSE(A)+beta*C, C symmetric.
• DSYR2K C:=alpha*A*TRANSPOSE(B)+alpha*B*TRANSPOSE(A)+beta*C, C symmetric.
• DTRMM B:=A*B or B:=B*A, A triangular, B rectangular.
• DTRSM B:=INVERSE(A)*C or B:=C*INVERSE(A), B and C rectangular, A triangular.

You can go up one level to the FORTRAN90 source codes.