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DGBMV(1)			 BLAS routine			      DGBMV(1)

NAME
       DGBMV - performs one of the matrix-vector operations   y := alpha*A*x +
       beta*y, or y := alpha*A'*x + beta*y,

SYNOPSIS
       SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)

	   DOUBLE							PRECI‐
									SION
									ALPHA,BETA

	   INTEGER							INCX,INCY,KL,KU,LDA,M,N

	   CHARACTER							TRANS

	   DOUBLE							PRECI‐
									SION
									A(LDA,*),X(*),Y(*)

PURPOSE
       DGBMV  performs one of the matrix-vector operations

       where  alpha and beta are scalars, x and y are vectors and A is an m by
       n band matrix, with kl sub-diagonals and ku super-diagonals.

ARGUMENTS
       TRANS  - CHARACTER*1.
	      On entry, TRANS specifies the operation to be performed as  fol‐
	      lows:

	      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*A'*x + beta*y.

	      Unchanged on exit.

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

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

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

       KU     - INTEGER.
	      On entry, KU specifies the  number  of  super-diagonals  of  the
	      matrix A. KU must satisfy	 0 .le. KU.  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, the leading ( kl + ku + 1 ) by n part of the array
	      A must contain the matrix of coefficients,  supplied  column  by
	      column,  with the leading diagonal of the matrix in row ( ku + 1
	      ) of the array, the first super-diagonal starting at position  2
	      in  row ku, the first sub-diagonal starting at position 1 in row
	      ( ku + 2 ), and so on.  Elements in the array A that do not cor‐
	      respond  to elements in the band matrix (such as the top left ku
	      by ku triangle) are not referenced.  The following program  seg‐
	      ment  will  transfer a band matrix from conventional full matrix
	      storage to band storage:

	      DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN(
	      M,  J  +	KL  ) A( K + 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 ( kl + ku + 1 ).
	      Unchanged on exit.

       X      - DOUBLE PRECISION array of DIMENSION at least
	      ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N'  or  'n'  and  at
	      least  (	1  + ( m - 1 )*abs( INCX ) ) otherwise.	 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. When BETA is  supplied
	      as zero then Y need not be set on input.	Unchanged on exit.

       Y      - DOUBLE PRECISION array of DIMENSION at least
	      (	 1  +  (  m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at
	      least ( 1 + ( n - 1 )*abs( INCY ) )  otherwise.	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.

FURTHER DETAILS
       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			      DGBMV(1)
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