spr(3F)

NAME
     dspr, sspr, zhpr, chpr - BLAS Level Two   Symmetric Packed Matrix Rank 1
     Update


FORTRAN 77 SYNOPSIS
     subroutine dspr( uplo, n, alpha, x, incx, ap )
           character*1        uplo
           integer            n, incx
           double precision   alpha
           double precision   ap(*), x(*)

     subroutine sspr( uplo, n, alpha, x, incx, ap )
           character*1        uplo
           integer            n, incx
           real               alpha
           real               ap(*), x(*)

     subroutine zhpr( uplo, n, alpha, x, incx, ap )
           character*1        uplo
           integer            n, incx
           complex*16         alpha
           complex*16         ap(*), x(*)

     subroutine chpr( uplo, n, alpha, x, incx, ap )
           character*1        uplo
           integer            n, incx
           complex            alpha
           complex            ap(*), x(*)


C SYNOPSIS
     void dspr( uplo, n, alpha, x, incx, ap )
           MatrixTriangle     uplo;
           Integer            n, incx;
           double             alpha;
           double             (*ap)[ n*( n + 1 ) )/2 ], (*x)[ n ];

     void sspr( uplo, n, alpha, x, incx, ap )
           MatrixTriangle     uplo;
           Integer            n, incx;
           float              alpha;
           float              (*ap)[ n*( n + 1 ) )/2 ], (*x)[ n ];

     void zhpr( uplo, n, alpha, x, incx, ap )
           MatrixTriangle     uplo;
           Integer            n, incx;
           Zomplex            alpha;
           Zomplex            (*ap)[ n*( n + 1 ) )/2 ], (*x)[ n ];

     void chpr( uplo, n, alpha, x, incx, ap )
           MatrixTriangle     uplo;
           Integer            n, incx;
           Complex            alpha;
           Complex            (*ap)[ n*( n + 1 ) )/2 ], (*x)[ n ];


DESCRIPTION
     dspr and sspr perform the symmetric rank 1 operation

           A := alpha*x*x' + A,

     zhpr and chpr perform the hermitian rank 1 operation

           A := alpha*x*conjg( x' ) + A,

     where alpha is a real/complex scalar, x is an n element vector and A is
     an n by n symmetric/hermitian matrix, supplied in packed form.


PARAMETERS
     uplo    On entry, uplo specifies whether the upper or lower triangular
             part of the array A is to be referenced a follows:



             FORTRAN
             uplo = 'U' or 'u'   Only the upper triangular part of A
                                 is to be referenced.
             uplo = 'L' or 'l'   Only the lower triangular part of A
                                 is to be referenced.

             C
             uplo = UpperTriangle     Only the lower triangular part of A
                                      is to be referenced.
             uplo = LowerTriangle     Only the lower triangular part of A
                                      is to be referenced.

             Unchanged on exit.

     n       On entry, n specifies the the order of the matrix A.  n must be
             at least zero.
             Unchanged on exit.

     alpha   specifies the scalar alpha.
             Unchanged on exit.

     x       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
             entry, the incremented array x must contain the n element vector
             x.
             Unchanged on exit.

     incx    On entry, incx specifies the increment for the elements of x.
             incx must not be zero.
             Unchanged on exit.

     ap      Array of size at least ( ( n*( n + 1 ) )/2 ).
             Before entry with uplo = 'U' or 'u' or the array ap must contain
             the upper triangular part of the symmetric/hermitian 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.

             Before entry with UPLO = 'L' or 'l' or , the array ap must
             contain the lower triangular part of the symmetric/hermitian
             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.

             Note that for the hermitian matrix the imaginary parts of the
             diagonal elements need not be set, they are assumed to be zero,
             and on exit they are set to zero.

             Unchanged on exit.


AUTHORS
          Jack Dongarra, Argonne National Laboratory.
          Iain Duff, AERE Harwell.
          Jeremy Du Croz, Numerical Algorithms Group Ltd.
          Sven Hammarling, Numerical Algorithms Group Ltd.