NAME

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

SYNOPSIS

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

           CHARACTER*1  SIDE, UPLO

           INTEGER      M, N, LDA, LDB, LDC

           COMPLEX      ALPHA, BETA

           COMPLEX      A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE

       CSYMM  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  - COMPLEX         .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - COMPLEX          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      - COMPLEX          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   - COMPLEX         .
              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      - COMPLEX          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.

BLAS routine                                     16 October 1992                                        CSYMM(3)