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sgemm

 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 fol-
      lows:

      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 fol-
      lows:

      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.

 ka is
      A      -
              REAL             array of DIMENSION ( LDA, ka ), where
             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.

 kb is
      B      -
              REAL             array of DIMENSION ( LDB, kb ), where
             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.