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.

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 ).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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.