C Library Functions - sgemm (3)

NAME

sgemm(3f) - [BLAS:SINGLE_BLAS_LEVEL3] C:=alpha*A*B+beta*C, A, B, C rectangular.

Synopsis
Definition
Options
C
Authors
Further Details
See Also

SYNOPSIS

subroutine sgemm(transa,transb,m,n,k,alpha,a,lda,b,ldb,beta,c,ldc)

      .. Scalar Arguments ..
      real,intent(in)      :: alpha,beta
      integer,intent(in)   :: k,lda,ldb,ldc,m,n
      character,intent(in) :: transa,transb
      ..
      .. Array Arguments ..
      real,intent(in)    :: a(lda,*),b(ldb,*)
      real,intent(inout) :: c(ldc,*)
      ..

DEFINITION

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**T,
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.

OPTIONS

TRANSA

TRANSA is 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**T.

              TRANSA = ’C’ or ’c’,  op( A ) = A**T.

TRANSB

TRANSB is 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**T.

              TRANSB = ’C’ or ’c’,  op( B ) = B**T.

M

M is 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.

N

N is 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.

K

K is 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.

ALPHA

ALPHA is REAL On entry, ALPHA specifies the scalar alpha.

A

A is REAL array, 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.

LDA

LDA is 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 ).

B

B is REAL array, 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.

LDB

LDB is 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 ).

BETA

BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.

C

C is REAL array, 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

LDC is 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 ).

AUTHORS

o Univ. of Tennessee

o Univ. of California Berkeley

o Univ. of Colorado Denver

o NAG Ltd.
 date:December 2016

FURTHER DETAILS

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.