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 vec­
              tor x.  Unchanged on exit.

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

              ( 1 + ( n - 1 )*abs( INCY ) ).  Before  entry,  the
              incremented array Y must contain the n element vec­
              tor y.  Unchanged on exit.

       INCY   - INTEGER.
              On entry, INCY specifies the increment for the ele­
              ments  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 con­
              tain 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.


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