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NAME

       SSYR2  -  perform  the  symmetric  rank 2 operation   A := alpha*x*y’ +
       alpha*y*x’ + A,

SYNOPSIS

       SUBROUTINE SSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )

           REAL         ALPHA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

           REAL         A( LDA, * ), X( * ), Y( * )

PURPOSE

       SSYR2  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  - REAL            .
              On  entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - REAL             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      - REAL             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      - REAL             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.