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)