BLAS3_D
Double Precision Real Basic Linear Algebra Subprograms - Level 3

BLAS3_D is a MATLAB library which implements the Level 3 Basic Linear Algebra Subprograms (BLAS) for matrix-matrix operations, using double precision real arithmetic.

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 primarily for use in matrix-matrix operations, such as matrix multiplication. In certain cases, they may also be used to operate on the rows or columns of a two-dimensional array.

The Level 3 BLAS were originally written in FORTRAN77. This version of the library only contains a subset of the BLAS3 library (at the moment, mainly just DGEMM). Arrays are stored according to the FORTRAN convention. Thus, an M by N mathematical array might be stored in a double precision FORTRAN array called "A" that is declared as

        double precision a(lda,sda)

where LDA is the "leading" dimension and SDA is the "second" dimension. It is natural for LDA to equal M, but it is only necessary that M <= LDA. The matrix is stored as a vector of concatenated column vectors, and the dimension statement is used to determine that columns should be LDA units long. Thus, a typical entry A(I,J) of the mathematical matrix is actually stored in the location FORTRAN vector location I+(J-1)*LDA. Of course, in C, this location would be I-1+(J-1)*LDA.

Licensing:

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

Languages:

BLAS3_D is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BLAS0, a MATLAB library which contains auxilliary functions for the Basic Linear Algebra Subprograms (BLAS).

BLAS1_C, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using single precision complex arithmetic.

BLAS1_D, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using double precision real arithmetic.

BLAS1_S, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using single precision real arithmetic.

BLAS1_Z, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using double precision complex arithmetic.

blas3_d_test

Reference:

Thomas Coleman, Charles vanLoan,
Handbook for Matrix Computations,
SIAM, 1988,
ISBN13: 978-0-898712-27-8,
LC: QA188.C65.
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979,
ISBN13: 978-0-898711-72-1,
LC: QA214.L56.
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:

dgemm.m, computes C = alpha * A * B and related operations.
dtrmm.m, performs B:=A*B or B:=B*A, A triangular, B rectangular.
dtrsm.m, solves A*X=alpha*B or X*A=alpha*B, for triangular A, rectangular B.
blas3_d_test.m a sample calling program.