SGEMM(3)

SYNOPSIS
SUBROUTINE SGEMM (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, $ BETA, C, LDC)

NAME
sgemm - Multiply a real general matrix by a real general matrix.

LIBRARY
SLATEC (BLAS)

CATEGORY
D1B6

TYPE
SINGLE PRECISION (SGEMM-S, DGEMM-D, CGEMM-C)

KEYWORDS
LEVEL 3 BLAS, LINEAR ALGEBRA

AUTHOR
Dongarra, J., (ANL) Duff, I., (AERE) Du Croz, J., (NAG) Hammarling, S. (NAG)

DESCRIPTION
SGEMM performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, 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.

REFERENCES
Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S. A set of level 3 basic linear algebra subprograms. ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.

ROUTINES CALLED
LSAME, XERBLA

REVISION HISTORY (YYMMDD)
890208 DATE WRITTEN
910605 Modified to meet SLATEC prologue standards. Only comment lines were modified. (BKS)