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


SYNOPSIS

       SUBROUTINE SSPR ( UPLO, N, ALPHA, X, INCX, AP )

           REAL        ALPHA

           INTEGER     INCX, N

           CHARACTER*1 UPLO

           REAL        AP( * ), X( * )


PURPOSE

       SSPR    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, supplied in packed form.


PARAMETERS

       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the upper or lower
              triangular  part of the matrix A is supplied in the
              packed array AP as follows:

              UPLO = 'U' or 'u'   The upper triangular part of  A
              is supplied in AP.

              UPLO  = 'L' or 'l'   The lower triangular part of A
              is supplied in AP.

              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.

              ( ( n*( n + 1 ) )/2 ).  Before entry with   UPLO  =
              'U'  or  'u',  the  array AP must contain the upper
              triangular part  of  the  symmetric  matrix  packed
              sequentially,  column  by  column,  so that AP( 1 )
              contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain  a(
              1,  2  )  and a( 2, 2 ) respectively, and so on. On
              exit, the array AP is overwritten by the upper tri­
              angular  part  of the updated matrix.  Before entry
              with UPLO = 'L' or 'l', the array AP  must  contain
              the  lower  triangular part of the symmetric matrix
              packed sequentially, column by column, so that  AP(
              1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain
              a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On
              exit, the array AP is overwritten by the lower tri­
              angular part of the updated matrix.

              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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