BLAS3
Level 3 Basic Linear Algebra Subprograms

BLAS3 is a library of FORTRAN77 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 is a FORTRAN77 library which handles vector-vector operations.

BLAS2 is a FORTRAN77 library which handles matrix-vector operations.

BLAS3 is also available in a FORTRAN90 version.

LAPACK is a FORTRAN77 library which is a linear algebra library built on top of the BLAS routines.

LINPACK is a FORTRAN77 library which is a linear algebra library built on top of the BLAS routines.

Reference:

1. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
2. 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.
3. Thomas Coleman, Charles Van Loan,
   Handbook for Matrix Computations,
   Society for Industrial and Applied Mathematics,
   3600 University City Science Center,
   Philadelphia, PA 19104-2688.

Source Code:

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

Examples and Tests:

• blas3_prb.f, a calling program;
• blas3_prb.csh, commands to compile, link, load and run the calling program;
• blas3_prb.out, the sample output.

List of Routines:

• CGEMM C:=alpha*A*B+beta*C, A, B, C rectangular complex matrices.
• CSYMM C:=alpha*A*B+beta*C, A symmetric, B and C rectangular complex matrices.
• CHEMM C:=alpha*A*B+beta*C, A Hermitian, B and C rectangular complex matrices.
• CHERK C:=alpha*A*Hermitian(A)+beta*C, A, B rectangular, C square complex matrices.
• CHER2K C:=alpha*A*Hermitian(B)+conjugate(alpha)*B*Hermitian(A)+beta*C, A, B rectangular, C square complex matrices.
• CSYRK C:=alpha*A*TRANSPOSE(A)+beta*C, A general, C square complex matrices.
• CSYR2K C:=alpha*A*TRANSPOSE(B)+alpha*B*TRANSPOSE(A)+beta*C, A, B rectangular, C square complex matrices.
• CTRMM B:=A*B or B:=B*A, A triangular, B rectangular complex matrices.
• CTRSM B:=INVERSE(A)*C or B:=C*INVERSE(A), A triangular, B and C rectangular complex matrices.
• DGEMM C:=alpha*A*B+beta*C, A, B, C rectangular double precision matrices.
• DSYMM C:=alpha*A*B+beta*C, A symmetric, B and C rectangular double precision matrices.
• DSYRK C:=alpha*A*TRANSPOSE(A)+beta*C, A general, C symmetric double precision matrices.
• DSYR2K C:=alpha*A*TRANSPOSE(B)+alpha*B*TRANSPOSE(A)+beta*C, A, B rectangular, C symmetric double precision matrices.
• DTRMM B:=A*B or B:=B*A, A triangular, B rectangular double precision matrices.
• DTRSM B:=INVERSE(A)*C or B:=C*INVERSE(A), A triangular, B and C rectangular double precision matrices.
• SGEMM C:=alpha*A*B+beta*C, A, B, C rectangular real matrices.
• SSYMM C:=alpha*A*B+beta*C, A symmetric, B and C rectangular real matrices.
• SSYRK C:=alpha*A*TRANSPOSE(A)+beta*C, A general, C symmetric real matrices.
• SSYR2K C:=alpha*A*TRANSPOSE(B)+alpha*B*TRANSPOSE(A)+beta*C, A, B rectangular, C symmetric real matrices.
• STRMM B:=A*B or B:=B*A, A triangular, B rectangular real matrices.
• STRSM B:=INVERSE(A)*C or B:=C*INVERSE(A), A triangular, B and C rectangular real matrices.
• ZGEMM C:=alpha*A*B+beta*C, A, B, C rectangular double complex matrices.
• ZSYMM C:=alpha*A*B+beta*C, A symmetric, B and C rectangular double complex matrices.
• ZHEMM C:=alpha*A*B+beta*C, A Hermitian, B and C rectangular double complex matrices.
• ZHERK C:=alpha*A*Hermitian(A)+beta*C, A, B rectangular, C square double complex matrices.
• ZHER2K C:=alpha*A*Hermitian(B)+conjugate(alpha)*B*Hermitian(A)+beta*C, A, B rectangular, C square double complex matrices.
• ZSYRK C:=alpha*A*TRANSPOSE(A)+beta*C, A general, C square double complex matrices.
• ZSYR2K C:=alpha*A*TRANSPOSE(B)+alpha*B*TRANSPOSE(A)+beta*C, A, B rectangular, C square double complex matrices.
• ZTRMM B:=A*B or B:=B*A, A triangular, B rectangular double complex matrices.
• ZTRSM B:=INVERSE(A)*C or B:=C*INVERSE(A), A triangular, B and C rectangular double complex matrices.

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