SSYR  -  perform  the  symmetric  rank  1 operation   A :=
       alpha*x*x' + A,


SYNOPSIS

       SUBROUTINE SSYR ( UPLO, N, ALPHA, X, INCX, A, LDA )

           REAL        ALPHA

           INTEGER     INCX, LDA, N

           CHARACTER*1 UPLO

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


PURPOSE

       SSYR   performs the symmetric rank 1 operation

       where alpha is a real scalar, x is an n element vector 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.

              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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