NAME

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

SYNOPSIS

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

           DOUBLE      PRECISION ALPHA

           INTEGER     INCX, N

           CHARACTER*1 UPLO

           DOUBLE      PRECISION AP( * ), X( * )

PURPOSE

       DSPR    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  - DOUBLE PRECISION.
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - DOUBLE PRECISION 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     - DOUBLE PRECISION 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.