# BLAS3_D Double Precision Real Basic Linear Algebra Subprograms - Level 3

BLAS3_D, a C library which implements the Level 3 BLAS, or Basic Linear Algebra Subprograms, 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 and SGEMM). 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.

### 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 C library which contains auxilliary functions for the Basic Linear Algebra Subprograms (BLAS).

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

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

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

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

### Reference:

1. Thomas Coleman, Charles vanLoan,
Handbook for Matrix Computations,
SIAM, 1988,
ISBN13: 978-0-898712-27-8,
LC: QA188.C65.
2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979,
ISBN13: 978-0-898711-72-1,
LC: QA214.L56.
3. 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:

Last revised on 10 June 2019.