symv(3F)

NAME
     dsymv, ssymv, zhemv, chemv - BLAS Level Two   (Symmetric/Hermitian)Matrix
     - Vector Product


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

     subroutine ssymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           character*1        uplo
           integer            n, lda, incx, incy
           real               alpha, beta
           real               a( lda,*), x(*), y(*)

     subroutine zhemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           character*1        uplo
           integer            n, lda, incx, incy
           double complex     alpha, beta
           double complex     a( lda,*), x(*), y(*)

     subroutine chemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           character*1        uplo
           integer            n, lda, incx, incy
           complex            alpha, beta
           complex            a( lda,*), x(*), y(*)


C SYNOPSIS
     void dsymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           MatrixTriangle        uplo;
           Integer            n, lda, incx, incy;
           double             alpha, beta;
           double             (*a)[lda*n], (*x)[ n ], (*y)[ n ];

     void ssymv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           MatrixTriangle        uplo;
           Integer            n, lda, incx, incy;
           float              alpha, beta;
           float              (*a)[lda*n], (*x)[ n ], (*y)[ n ];

     void zhemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           MatrixTriangle        uplo;
           Integer            n, lda, incx, incy;
           Zomplex            alpha, beta;
           Zomplex           (*a)[lda*n], (*x)[ n ], (*y)[ n ];

     void chemv( uplo,n,alpha,a,lda,x,incx,beta,y,incy )
           MatrixTriangle        uplo;
           Integer            n, lda, incx, incy;
           Complex            alpha, beta;
           Complex           (*a)[lda*n], (*x)[ n ], (*y)[ n ];





DESCRIPTION
     dsymv , ssymv , dhemv and chemv perform the 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.


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
                                 being supplied.
             uplo = 'L' or 'l'   The lower triangular part of A is
                                 being supplied.

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

             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.

     a       An array containing the matrix A.

             FORTRAN
             Array of dimension ( lda, n ).

             C
             A pointer to an array of size lda*n.
             See note below about array storage convention for C.
             Before entry with uplo = 'U' or 'u' or , the array elements
             corresponding to the leading n by n upper triangular part of the
             matrix A must contain the corresponding upper triangular part of
             the symmetric/hermitian matrix and the strictly lower triangular
             part of A is not referenced.

             Before entry with uplo = 'L' or 'l' or , the array elements
             corresponding to the leading n by n lower triangular part of the
             array A must contain the corresponding lower triangular part of
             the symmetric/hermitian matrix and the strictly upper triangular
             part of A is not referenced.

             Note that the imaginary parts of the diagonal elements need not
             be set and are assumed to be zero.

             Unchanged on exit.

     lda     On entry, lda specifies the first dimension of A as declared in
             the calling (sub) program. lda must be at least ( k + 1 ).
             Unchanged on exit.

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


C ARRAY STORAGE CONVENTION
       The matrices  are assumed  to be stored in a  one dimensional C array
       in an analogous fashion as a Fortran array (column major). Therefore,
       the element  A(i+1,j)  of matrix A  is stored  immediately  after the
       element  A(i,j), while  A(i,j+1) is lda  elements apart from  A(i,j).
       The element A(i,j) of the matrix can be accessed directly by reference
       to  a[ (j-1)*lda + (i-1) ].

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


TUNING
          DSYMV and SSYMV are optimized and parallelized for SGI R3000 and
          R4x00 platforms. For the R8000 it is optimized an parallelized
          for the case when INCX = 1.
          ZHEMV and CHEMV are optimized and parallelized for SGI R3000, R4x00
          and R8000 platforms.