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_SPMV,_HPMV(3F)						       _SPMV,_HPMV(3F)


NAME    [Toc]    [Back]

     dspmv, sspmv, zhpmv, chpmv	- BLAS Level Two   (Symmetric/Hermitian)
     Packed Matrix - Vector Product


FORTRAN	77 SYNOPSIS
     subroutine	dspmv( uplo,n,alpha,ap,x,incx,beta,y,incy )
	   character*1	      uplo
	   integer	      n, incx, incy
	   double precision   alpha, beta
	   double precision   ap(*), x(*), y(*)

     subroutine	sspmv( uplo,n,alpha,ap,x,incx,beta,y,incy )
	   character*1	      uplo
	   integer	      n, incx, incy
	   real		      alpha, beta
	   real		      ap(*), x(*), y(*)

     subroutine	zhpmv( uplo,n,alpha,ap,x,incx,beta,y,incy )
	   character*1	      uplo
	   integer	      n, incx, incy
	   double complex     alpha, beta
	   double complex     ap(*), x(*), y(*)

     subroutine	chpmv( uplo,n,alpha,ap,x,incx,beta,y,incy )
	   character*1	      uplo
	   integer	      n, incx, incy
	   complex	      alpha, beta
	   complex	      ap(*), x(*), y(*)

C SYNOPSIS    [Toc]    [Back]

     void dspmv( uplo,n,alpha,ap,x,incx,beta,y,incy )
	   MatrixTriangle     uplo;
	   Integer	      n, incx, incy;
	   double	      alpha, beta;
	   double	      (*ap)[ n*( n + 1 ) )/2 ],	(*x)[ n	], (*y)[ n ];

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

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

     void chpmv( uplo,n,alpha,ap,x,incx,beta,y,incy )
	   MatrixTriangle     uplo;



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_SPMV,_HPMV(3F)						       _SPMV,_HPMV(3F)



	   Integer	      n, incx, incy;
	   Complex	      alpha, beta;
	   Complex	      (*ap)[ n*( n + 1 ) )/2 ],	(*x)[ n	], (*y)[ n ];

DESCRIPTION    [Toc]    [Back]

     dspmv , sspmv , dhpmv and chpmv perform matrix-vector operation

	  y := alpha*A*x + beta*y,

     where alpha and beta are scalars, x and y are n element vectors and A is
     an	n by n symmetric/hermitian matrix, supplied in packed form.

PARAMETERS    [Toc]    [Back]

     uplo    On	entry, uplo specifies whether the upper	or lower triangular
	     part of the matrix	A is being supplied as follows:



	     FORTRAN
	     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.

	     C
	     uplo = UpperTriangle     The upper	triangular part	of A is
				      supplied in AP.
	     uplo = LowerTriangle     The lower	triangular part	of A is
				      supplied in AP.

	     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.

     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(



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_SPMV,_HPMV(3F)						       _SPMV,_HPMV(3F)



	     3,	1 ) respectively, and so on.

	     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.

     beta    On	entry, beta specifies the scalar beta. When beta is supplied
	     as	zero then y need not be	set on input.
	     Unchanged on exit.

     y	     Array of size at least ( 1	+ ( n -	1 )*abs( INCY )	). Before
	     entry, the	incremented array y must contain the n element vector
	     y.	On exit, y is overwritten by the updated vector	y.

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

AUTHORS    [Toc]    [Back]

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

TUNING    [Toc]    [Back]

	  DSPMV	and SSPMV are optimized	and parallelized for SGI R3000 and
	  R4x00	platforms.
	  ZHPMV	and CHPMV are optimized	and parallelized for SGI R3000,	R4x00
	  and R8000 platforms.


									PPPPaaaaggggeeee 3333
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