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DSBMV(1)			 BLAS routine			      DSBMV(1)

NAME
       DSBMV - performs the matrix-vector operation   y := alpha*A*x + beta*y,

SYNOPSIS
       SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)

	   DOUBLE						 PRECISION
								 ALPHA,BETA

	   INTEGER						 INCX,INCY,K,LDA,N

	   CHARACTER						 UPLO

	   DOUBLE						 PRECISION
								 A(LDA,*),X(*),Y(*)

PURPOSE
       DSBMV  performs the matrix-vector  operation

       where  alpha  and beta are scalars, x and y are n element vectors and A
       is an n by n symmetric band matrix, with k super-diagonals.

ARGUMENTS
       UPLO   - CHARACTER*1.
	      On entry, UPLO specifies whether the upper or  lower  triangular
	      part of the band matrix A is being supplied as follows:

	      UPLO = 'U' or 'u'	  The upper triangular part of A is being sup‐
	      plied.

	      UPLO = 'L' or 'l'	  The lower triangular part of A is being sup‐
	      plied.

	      Unchanged on exit.

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

       K      - INTEGER.
	      On entry, K specifies  the  number  of  super-diagonals  of  the
	      matrix A. K must satisfy	0 .le. K.  Unchanged on exit.

       ALPHA  - DOUBLE PRECISION.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
	      Before  entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n
	      part of the array A must contain the upper triangular band  part
	      of  the  symmetric  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	refer‐
	      enced.   The  following  program segment will transfer the upper
	      triangular part of a symmetric  band  matrix  from  conventional
	      full matrix storage to band storage:

	      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

	      Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by  n
	      part  of the array A must contain the lower triangular band part
	      of the symmetric 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 band matrix from conventional full matrix
	      storage to band storage:

	      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

	      Unchanged on exit.

       LDA    - INTEGER.
	      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      - DOUBLE PRECISION array of DIMENSION at least
	      (	 1  +  ( n - 1 )*abs( INCX ) ).	 Before entry, the incremented
	      array X must contain the vector x.  Unchanged on exit.

       INCX   - INTEGER.
	      On entry, INCX specifies the increment for the  elements	of  X.
	      INCX must not be zero.  Unchanged on exit.

       BETA   - DOUBLE PRECISION.
	      On entry, BETA specifies the scalar beta.	 Unchanged on exit.

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

       INCY   - INTEGER.
	      On  entry,  INCY	specifies the increment for the elements of Y.
	      INCY must not be zero.  Unchanged on exit.

	      Level 2 Blas routine.

	      -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
	      Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
	      Central Office.  Richard Hanson, Sandia National Labs.

BLAS routine			 November 2008			      DSBMV(1)
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