NAME

       DSYMM - perform one of the matrix-matrix operations   C := alpha*A*B + beta*C,

SYNOPSIS

       SUBROUTINE DSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC )

           CHARACTER*1  SIDE, UPLO

           INTEGER      M, N, LDA, LDB, LDC

           DOUBLE       PRECISION ALPHA, BETA

           DOUBLE       PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE

       DSYMM  performs one of the matrix-matrix operations

       or

          C := alpha*B*A + beta*C,

       where  alpha  and  beta  are  scalars,   A  is a symmetric matrix and  B and C are  m by n
       matrices.

PARAMETERS

       SIDE   - CHARACTER*1.
              On entry,  SIDE  specifies whether  the  symmetric matrix  A appears on  the   left
              or right  in the  operation as follows:

              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

              Unchanged on exit.

       UPLO   - CHARACTER*1.
              On   entry,    UPLO  specifies  whether  the  upper  or  lower triangular  part  of
              the  symmetric  matrix   A  is  to  be referenced as follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of the symmetric matrix is to be
              referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of the symmetric matrix is to be
              referenced.

              Unchanged on exit.

       M      - INTEGER.
              On entry,  M  specifies the number of rows 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 C.  N  must be at least
              zero.  Unchanged on exit.

       ALPHA  - DOUBLE PRECISION.
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
              m  when  SIDE = 'L' or 'l'  and is  n otherwise.  Before entry  with  SIDE = 'L' or
              'l',   the  m by m  part of the array  A  must contain the  symmetric matrix,  such
              that when  UPLO = 'U' or 'u', the leading m by m upper triangular part of the array
              A   must  contain  the  upper  triangular  part  of  the   symmetric matrix and the
              strictly  lower triangular part of  A  is not referenced,  and when  UPLO = 'L'  or
              'l',  the  leading   m  by m  lower triangular part  of the  array  A must  contain
              the  lower triangular part  of  the   symmetric  matrix  and  the   strictly  upper
              triangular  part  of  A  is not referenced.  Before entry  with  SIDE = 'R' or 'r',
              the  n by n  part of the array  A  must contain the  symmetric matrix,   such  that
              when   UPLO  = 'U' or 'u', the leading n by n upper triangular part of the array  A
              must contain the upper triangular part of the  symmetric matrix and  the   strictly
              lower  triangular  part of  A  is not referenced,  and when  UPLO = 'L' or 'l', the
              leading  n by n  lower triangular part  of the  array  A must  contain  the   lower
              triangular  part   of the  symmetric matrix and the  strictly upper triangular part
              of  A  is not referenced.  Unchanged on exit.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as declared in the  calling  (sub)
              program.   When   SIDE  =  'L'  or  'l'   then  LDA  must be at least  max( 1, m ),
              otherwise  LDA must be at least  max( 1, n ).  Unchanged on exit.

       B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
              Before entry, the leading  m by n 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.   LDB  must  be  at  least max( 1, m ).  Unchanged on exit.

       BETA   - DOUBLE PRECISION.
              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      - DOUBLE PRECISION 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 updated matrix.

       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.