INTRO_BLAS(3S)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.
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INTRO_BLAS(3S)INTRO_BLAS(3S)
* 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)
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