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NAME

       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 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.

       AP     - REAL             array of DIMENSION at least
              (  (  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  triangular  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 triangular 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.