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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( * )



     #include <sunperf.h>

     void dspr2(char uplo, int n, double alpha, double  *dx,  int
               incx, double *dy, int incy, double *ap) ;

PURPOSE
     DSPR2   performs  the  symmetric  rank  2  operation  A   :=
     alpha*x*y' + alpha*y*x' + A 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.

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