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CGBMV(l)			 BLAS routine			      CGBMV(l)

NAME
       CGBMV  - 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,

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

	   COMPLEX	ALPHA, BETA

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

	   CHARACTER*1	TRANS

	   COMPLEX	A( LDA, * ), X( * ), Y( * )

PURPOSE
       CGBMV  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.

PARAMETERS
       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*conjg( 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  - COMPLEX		.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - COMPLEX		 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      - COMPLEX		 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   - COMPLEX		.
	      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      - COMPLEX		 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.

	      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			16 October 1992			      CGBMV(l)
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