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.

BLAS routine                                     16 October 1992                                        SGEMM(3)