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_SBMV,_HBMV(3F)						       _SBMV,_HBMV(3F)

NAME
     dsbmv, ssbmv, zhbmv, chbmv - BLAS Level Two   (Symmetric/Hermitian)
     Banded Matrix - Vector Product

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

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

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

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

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

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

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

     void chbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy )
	   MatrixTriangle     uplo;

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_SBMV,_HBMV(3F)						       _SBMV,_HBMV(3F)

	   Integer	      n, k, lda, incx, incy;
	   Complex	      alpha, beta;
	   Complex	      (*a)[lda*n], (*x)[ n ], (*y)[ n ];

DESCRIPTION
     dsbmv , ssbmv , dhbmv and chbmv 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 band matrix, with k super-diagonals.

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 leading ( k + 1 ) by

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_SBMV,_HBMV(3F)						       _SBMV,_HBMV(3F)

	     n part of the array A must contain the upper triangular band part
	     of the symmetric/hermitian matrix, supplied column by column,
	     with the leading diagonal of the matrix in row ( k + 1 ) of the
	     array, the first super-diagonal starting at position 2 in row k,
	     and so on. The top left k by k triangle of the array A is not
	     referenced.  The following program segment will transfer the
	     upper triangular part of a symmetric/hermitian band matrix from
	     conventional full matrix storage to band storage:

	     FORTRAN
			    DO 20, J = 1, N
			       M = K + 1 - J
			       DO 10, I = MAX( 1, J - K ), J
				  A( M + I, J ) = matrix( I, J )
			 10    CONTINUE
			 20 CONTINUE
	     C
			 for ( j = 0; j < n; j++ )
			 {
			       m = k - j;
			       for ( i = MAX(0, j-k); i < j )
				     a( j*lda + m+i ) = Matrix( j*ldm + i );
			 }

	     Before entry with UPLO = 'L' or 'l' or , the leading ( k + 1 ) by
	     n part of the array A must contain the lower triangular band part
	     of the symmetric/hermitian matrix, supplied column by column,
	     with the leading diagonal of the matrix in row 1 of the array,
	     the first sub-diagonal starting at position 1 in row 2, and so
	     on. The bottom right k by k triangle of the array A is not
	     referenced.  The following program segment will transfer the
	     lower triangular part of a symmetric/hermitian band matrix from
	     conventional full matrix storage to band storage:

	     FORTRAN
			    DO 20, J = 1, N
			       M = 1 - J
			       DO 10, I = J, MIN( N, J + K )
				  A( M + I, J ) = matrix( I, J )
			 10    CONTINUE
			 20 CONTINUE

	     C
			 for ( j = 0; j < n; j++ )
			 {
			       m = 1 - j;
			       for ( i = j; i < MIN( n, j+k ); i++ )
				     a( j*lda + m+i ) = Matrix( j*ldm + i );

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_SBMV,_HBMV(3F)						       _SBMV,_HBMV(3F)

			 }

	     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 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.

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
	  DSBMV and SSBMV are optimized and parallelized for SGI R3000 and
	  R4x00 platforms.
	  ZHBMV and CHBMV are optimized and parallelized for SGI R3000, R4x00
	  and R8000 platforms.

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