spmv(3F)

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


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


TUNING
          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.