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NAME

       DSPR2  -  perform  the  symmetric  rank 2 operation   A := alpha*x*y’ +
       alpha*y*x’ + A,

SYNOPSIS

       SUBROUTINE DSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )

           DOUBLE       PRECISION ALPHA

           INTEGER      INCX, INCY, N

           CHARACTER*1  UPLO

           DOUBLE       PRECISION AP( * ), X( * ), Y( * )

PURPOSE

       DSPR2  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, 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.

       Y      - DOUBLE PRECISION array of dimension at least
              ( 1 + ( n - 1 )*abs( INCY ) ).  Before  entry,  the  incremented
              array Y must contain the n element vector y.  Unchanged on exit.

       INCY   - INTEGER.
              On entry, INCY specifies the increment for the  elements  of  Y.
              INCY 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.