fmm.l

C++编写的高性能矩阵乘法的Stranssen算法

.TH fmm l "12 November 1996" "PRISM version 1.0" "PRISM routine (version 1.0)"
.TH fmm l "12 November 1996" "PRISM routine" "PRISM routine"
.SH NAME
fmm - Winograd's variant of Strassen's algorithm to perform one of the matrix-matrix operations
.br
C := alpha*op( A )*op( B ) + beta*C.
.SH SYNOPSIS
.TP 6
fmm ( char transa, char transb, int m, int n, int k,
double alpha, double *a, int lda, 
double *b, int ldb, double beta, double *c, int ldc, double *work, 
.br
int lwork )
.SH PURPOSE
fmm performs one of the matrix-matrix operations

C := alpha*op( A )*op( B ) + beta*C,

where  op( X ) is one of
.br

   op( X ) = X   or   op( X ) = X' (transpose of X),
.br

alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.

fmm calling sequence is very similar to the Level 3 BLAS routine
DGEMM except it has two extra arguments to specify work space.  It
uses Winograd's variant of Strassen's algorithm to reduce the
operations count relative to conventional matrix multiplication
(DGEMM).  It has a C calling interface but all arrays are stored in column
major format (Fortran style).

.SH PARAMETERS
.TP 8
transa  - char.
On entry, transa specifies the form of op( a ) to be used in
the matrix multiplication as follows:

transa = 'N' or 'n',  op( a ) = a.

transa = 'T' or 't',  op( a ) = a'.

transa = 'C' or 'c',  op( a ) = a'.

Unchanged on exit.
.TP 8
transb  - char
On entry, transb specifies the form of op( b ) to be used in
the matrix multiplication as follows:

transb = 'N' or 'n',  op( b ) = b.

transb = 'T' or 't',  op( b ) = b'.

transb = 'C' or 'c',  op( b ) = b'.

Unchanged on exit.
.TP 8
m       - int.
On entry,  m  specifies  the number  of rows  of the  matrix
op( a )  and of the  matrix  c.  m  must  be at least  zero.
Unchanged on exit.
.TP 8
n       - int.
On entry,  n  specifies the number  of columns of the matrix
op( b ) and the number of columns of the matrix c. n must be
at least zero.
Unchanged on exit.
.TP 8
k       - int.
On entry,  k  specifies  the number of columns of the matrix
op( a ) and the number of rows of the matrix op( b ). k must
be at least  zero.
Unchanged on exit.
.TP 8
alpha   - double.
On entry, alpha specifies the scalar alpha.
Unchanged on exit.
.TP 8
a       - double pointer.
a is logically an array of size ( LDA, ka ), 
where ka is
k  when  transa = 'N' or 'n',  and is  m  otherwise.
Before entry with  transa = 'N' or 'n',  the leading  m by k
part of the array  a  must contain the matrix  A,  otherwise
the leading  k by m  part of the array  a  must contain  the
matrix A.
Unchanged on exit.
.TP 8
lda     - int.
On entry, lda specifies the first dimension of a as "declared"
in the calling (sub) program. When  transa = 'N' or 'n' then
lda must be at least  max( 1, m ), otherwise  lda must be at
least  max( 1, k ).
Unchanged on exit.
.TP 8
b       - double pointer
b is logically an array of size  ( ldb, kb ), 
where kb is
n  when  transb = 'N' or 'n',  and is  k  otherwise.
Before entry with  transb = 'N' or 'n',  the leading  k by n
part of the array  b  must contain the matrix  B,  otherwise
the leading  n by k  part of the array  b  must contain  the
matrix B.
Unchanged on exit.
.TP 8
ldb     - int.
On entry, ldb specifies the first dimension of b as "declared"
in the calling (sub) program. When  transb = 'N' or 'n' then
ldb must be at least  max( 1, k ), otherwise  ldb must be at
least  max( 1, n ).
Unchanged on exit.
.TP 8
beta    - double.
On entry,  beta  specifies the scalar  beta.  When  beta  is
supplied as zero then c need not be set on input.
Unchanged on exit.
.TP 8
c       - double pointer.
c is logically an array of size ( ldc, n ).
Before entry, the leading  m by n  part of the array  c must
contain the matrix  C,  except when  beta  is zero, in which
case c need not be set on entry.
On exit, the array  c  is overwritten by the  m by n  matrix
( alpha*op( a )*op( b ) + beta*c ).
.TP 8
ldc     - int.
On entry, ldc specifies the first dimension of c as "declared"
in  the  calling  (sub)  program.   ldc  must  be  at  least
max( 1, m ).
Unchanged on exit.
.TP 8
work    - double pointer.
work is logically an array of size ( LWORK ) which is
temporary work space for use by the routine.  Size must be at least 
lwork double words.  Input values are ignored.
If work is NULL then fmm automatically allocates the temporary
space it needs.
On exit, the array  work will be overwritten by values that are only 
of internal use.
.TP 8
lwork   - int.
On entry, lwork specifies the size of the work space array work.
If lwork is too small for the work space needed then fmm automatically
allocates the temporary space it needs.
The size necessary can be calculated with the routine tmp_fmm.
Unchanged on exit.

.SH SEE ALSO
.BR DGEFMM (l),
.BR DGEFMM_MEM (l),
.BR TMP_DGEFMM_MEM (l),
.BR tmp_fmm (l).

.SH FURTHER INFORMATION
.LP
See the DGEFMM User's Guide provided in the doc/ directory of the distribution.

.SH BUGS
.LP
There are no known bugs.

.SH COPYRIGHT
See COPYRIGHT file provided with the software distribution.

.SH AUTHORS
.IP
Steven Huss-Lederman, University of Wisconsin
.br
Elaine M. Jacobson, Center for Computing Sciences
.br
Jeremy R. Johnson, Drexel University
.br
Anna Tsao, Center for Computing Sciences
.br
Thomas Turnbull, Center for Computing Sciences