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_GEMV(3F)							     _GEMV(3F)


NAME    [Toc]    [Back]

     dgemv, sgemv, zgemv, cgemv	- BLAS Level Two Matrix-Vector Product


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

     subroutine	sgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy	)
	   character*1	      trans
	   integer	      n, m, lda, incx, incy
	   real		      alpha, beta
	   real		      a( lda,*), x(*), y(*)

     subroutine	zgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy	)
	   character*1	      trans
	   integer	      n, m, lda, incx, incy
	   double complex     alpha, beta
	   double complex     a( lda,*), x(*), y(*)

     subroutine	cgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy	)
	   character*1	      trans
	   integer	      n, m, lda, incx, incy
	   complex	      alpha, beta
	   complex	      a( lda,*), x(*), y(*)

C SYNOPSIS    [Toc]    [Back]

     void dgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
	   MatrixTranspose    trans;
	   Integer	      n, m, lda, incx, incy;
	   double	      alpha, beta;
	   double	     (*a)[lda*n], (*x)[	n ], (*y)[ n ];

     void sgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
	   MatrixTranspose    trans;
	   Integer	      n, m, lda, incx, incy;
	   float	      alpha, beta;
	   float	     (*a)[lda*n], (*x)[	n ], (*y)[ n ];

     void zgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
	   MatrixTranspose    trans;
	   Integer	      n, m, lda, incx, incy;
	   Zomplex	      alpha, beta;
	   Zomplex	     (*a)[lda*n], (*x)[	n ], (*y)[ n ];

     void cgemv( trans,m,n,alpha,a,lda,x,incx,beta,y,incy )
	   MatrixTranspose    trans;
	   Integer	      n, m, lda, incx, incy;



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_GEMV(3F)							     _GEMV(3F)



	   Complex	      alpha, beta;
	   Complex	     (*a)[lda*n], (*x)[	n ], (*y)[ n ];

DESCRIPTION    [Toc]    [Back]

     dgemv , sgemv , dgemv and cgemv perform one of the	matrix-vector
     operations:

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

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

     where alpha and beta are scalars, x and y are vectors and A is an m by n
     matrix.

PARAMETERS    [Toc]    [Back]

     trans   On	entry, trans specifies the operation to	be performed as
	     follows:

	     FORTRAN
	     trans = 'N' or 'n'		   y :=	alpha*A*x + beta*y.
	     trans = 'T' or 't'		   y :=	alpha*A'*x + beta*y.
	     trans = 'C' or 'c'		   y :=	alpha*conjg( A'	)*x + beta*y.

	     C
	     trans = NoTranspose	   y :=	alpha*A*x + beta*y.
	     trans = Transpose		   y :=	alpha*A'*x + beta*y.
	     trans = ConjugateTranspose	   y :=	alpha*conjg( A'	)*x + beta**y.

	     Unchanged on exit.

     m	     On	entry, m specifies the number of rows of the matrix A.	m must
	     be	at least zero.
	     Unchanged on exit.

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

     alpha   On	entry, 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.




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_GEMV(3F)							     _GEMV(3F)



	     Before entry, the leading m by n part of the array	A must contain
	     the matrix	of coefficients.
	     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 )	) when trans =
	     'N' or 'n'	or NoTranspose and at least ( 1	+ ( m -	1 )*abs( incx
	     ) ) otherwise. 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	+ ( m -	1 )*abs( incy )	) when trans =
	     'N' or 'n'	or NoTranspose and at least ( 1	+ ( n -	1 )*abs( incy
	     ) ) otherwise.

	     Before entry with beta non-zero, the incremented array y must
	     contain the 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    [Toc]    [Back]

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





									Page 3






_GEMV(3F)							     _GEMV(3F)


TUNING    [Toc]    [Back]

	  Optimized and	parallelized for SGI R3000, R4x00 and R8000 platforms.


									PPPPaaaaggggeeee 4444
[ Back ]
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