NAME

       DSYR2 - perform the symmetric rank 2 operation   A := alpha*x*y' + alpha*y*x' + A,

SYNOPSIS

       SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )

           DOUBLE       PRECISION ALPHA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

           DOUBLE       PRECISION A( LDA, * ), X( * ), Y( * )

PURPOSE

       DSYR2  performs the symmetric rank 2 operation

       where  alpha  is  a  scalar,  x  and  y are n element vectors and A is an n by n symmetric
       matrix.

PARAMETERS

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

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

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

              Unchanged on exit.

       N      - INTEGER.
              On  entry,  N  specifies  the  order  of  the  matrix  A.  N must be at least zero.
              Unchanged on exit.

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

       X      - DOUBLE PRECISION array of dimension at least
              ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must  contain
              the n element vector x.  Unchanged on exit.

       INCX   - INTEGER.
              On  entry,  INCX  specifies  the  increment for the elements of X. INCX must not be
              zero.  Unchanged on exit.

       Y      - DOUBLE PRECISION array of dimension at least
              ( 1 + ( n - 1 )*abs( INCY ) ).  Before entry, the incremented array Y must  contain
              the n element vector y.  Unchanged on exit.

       INCY   - INTEGER.
              On  entry,  INCY  specifies  the  increment for the elements of Y. INCY must not be
              zero.  Unchanged on exit.

       A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
              Before entry with  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.  On  exit,  the  upper
              triangular  part  of the array A is overwritten by the upper triangular part of the
              updated matrix.  Before entry with 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.  On
              exit,  the  lower  triangular  part  of  the  array  A  is overwritten by the lower
              triangular part of the updated matrix.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as declared in the  calling  (sub)
              program. LDA must be at least max( 1, n ).  Unchanged on exit.

              Level 2 Blas routine.

              --  Written  on  22-October-1986.   Jack Dongarra, Argonne National Lab.  Jeremy Du
              Croz, Nag Central Office.  Sven Hammarling, Nag Central  Office.   Richard  Hanson,
              Sandia National Labs.