NAME
SGEMM - perform one of the matrix-matrix operations C := alpha*op( A
)*op( B ) + beta*C,
SYNOPSIS
SUBROUTINE SGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
BETA, C, LDC )
CHARACTER*1 TRANSA, TRANSB
INTEGER M, N, K, LDA, LDB, LDC
REAL ALPHA, BETA
REAL A( LDA, * ), B( LDB, * ), C( LDC, * )
PURPOSE
SGEMM performs one of the matrix-matrix operations
where op( X ) is one of
op( X ) = X or op( X ) = X’,
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.
PARAMETERS
TRANSA - CHARACTER*1. 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.
TRANSB - CHARACTER*1. 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.
M - INTEGER.
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.
N - INTEGER.
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.
K - INTEGER.
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.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A - REAL array of DIMENSION ( 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.
LDA - INTEGER.
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.
B - REAL array of DIMENSION ( 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.
LDB - INTEGER.
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.
BETA - REAL .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input. Unchanged on
exit.
C - REAL array of DIMENSION ( 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 ).
LDC - INTEGER.
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.
Level 3 Blas routine.
-- Written on 8-February-1989. Jack Dongarra, Argonne National
Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical
Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms
Group Ltd.