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.

BLAS routine                                     16 October 1992                                        DSYR2(3)