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dsymm

 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.

 ka is
      A      -
              DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where
             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 lead-
             ing m by m upper triangular part of the array  A
             must contain the upper triangular part of the  sym-
             metric 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 lead-
             ing n by n upper triangular part of the array  A
             must contain the upper triangular part of the  sym-
             metric 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.