intro_blas(3S)

NAME
     INTRO_BLAS - Introduction to SCSL Basic Linear Algebra Subprograms

IMPLEMENTATION
     See individual man pages for operating system and hardware availability.

DESCRIPTION
     The Basic Linear Algebra Subprograms comprise a library of routines that
     perform basic operations involving matrices and vectors. They were
     designed as a way of achieving efficiency in the solution of linear
     algebra problems. The BLAS, as they are now commonly called, have been
     very successful and have been used in a wide range of software, including
     LINPACK, LAPACK and many of the algorithms published by the ACM
     Transactions on Mathematical Software. They are an aid to clarity,
     portability, modularity and maintenance of software, and have become the
     de facto standard for elementary vector and matrix operations.

     The BLAS promote modularity by identifying frequently occurring
     operations of linear algebra and by specifying a standard interface to
     these operations.  Efficiency is achieved through optimization within the
     BLAS without altering the higher-level code that references them.

     There are three levels of BLAS:

     *   Level 1: The original set of BLAS, commonly referred as the Level 1
         BLAS, perform low-level operations such as dot-product and the adding
         of a multiple of one vector to another.

         Typically these operations involve O(n) floating point operations and
         O(n) data items moved (loaded or stored), where n is the length of
         the vectors. The Level 1 BLAS permit efficient implementation on
         scalar machines, but the ratio of floating-point operations to data
         movement is too low to be effective on most vector or parallel
         hardware.

         For more details on Level 1 BLAS routines available in SCSL, please
         refer to the INTRO_BLAS1(3S) man page.

     *   Level 2: The Level 2 BLAS perform matrix-vector operations that occur
         frequently in the implementation of many of the most common linear
         algebra algorithms.

         These routines involve O(n2) floating point operations. Algorithms
         that use Level 2 BLAS can be very efficient on vector computers, but
         are not well suited to computers with a hierarchy of memory (such as
         cache memory).

         For more details on Level 2 BLAS routines available in SCSL, please
         refer to the INTRO_BLAS2(3S) man page.
     *   Level 3:  The Level 3 BLAS are targeted at matrix-matrix operations.

         They involve O(n3) floating point operations, but only create O(n2)
         data movement. These operations permit efficient reuse of data that
         reside in cache and create what is often called the surface-to-volume
         effect for the ratio of computations to data movement. In addition,
         matrices can be partitioned into blocks, and operations on distinct
         blocks can be performed in parallel, and within the operations on
         each block, scalar or vector operations may be performed in parallel.

         For more details on Level 3 BLAS routines available in SCSL, please
         refer to the INTRO_BLAS3(3S) man page.

     BLAS2 and BLAS3 modules in SCSL are optimized and parallelized to take
     advantage of SGI's chip-level and system-level architectures. The best
     performance is achieved with BLAS3 routines (for example, DGEMM) where
     outer-loop unrolling and blocking techniques have been applied to take
     advantage of the memory cache. The performance of BLAS2 routines (for
     example, DGEMV) is sensitive to the size of the problem; for large sizes
     the high cache miss rate slows down the algorithms.

     SCSL's LAPACK algorithms make extensive use of BLAS3 modules and are more
     efficient than the older, BLAS1-based LINPACK algorithms.

NOTES
     SCSL does not currently support reshaped arrays.

SEE ALSO
     S.P. Datardina, J.J. Du Croz, S.J. Hammarling and M.W. Pont, "A Proposed
     Specification of BLAS Routines in C", NAG Technical Report TR6/90.

     C. Lawson, R. Hanson, D. Kincaid, and F. Krogh, "Basic Linear Algebra
     Subprograms for Fortran Usage", ACM Transactions on Mathematical
     Software, 5 (1979), pp. 308-325.

     J. Dongarra, J. DuCroz, S. Hammarling, and R. Hanson, "An extended set of
     Fortran Basic Linear Algebra Subprograms", ACM Trans. on Math. Soft. 14,
     1 (1988), pp. 1-32.

     J. Dongarra, J. DuCroz, I. Duff, and S. Hammarling, "An set of level 3
     Basic Algebra Subprograms", ACM Trans. on Math. Soft. (Dec 1989).

     INTRO_SCSL(3S), INTRO_BLAS1(3S), INTRO_BLAS2(3S), INTRO_BLAS3(3S),
     INTRO_CBLAS(3S), INTRO_LAPACK(3S)