# sgemm

```SGEMM(1)                         BLAS routine                         SGEMM(1)

NAME
SGEMM - performs 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)

REAL                                                           ALPHA,BETA

INTEGER                                                        K,LDA,LDB,LDC,M,N

CHARACTER                                                      TRANSA,TRANSB

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.

ARGUMENTS
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.

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.

BLAS routine                     November 2008                        SGEMM(1)```