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CHBMV(l)			 BLAS routine			      CHBMV(l)

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

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

	   COMPLEX	ALPHA, BETA

	   INTEGER	INCX, INCY, K, LDA, N

	   CHARACTER*1	UPLO

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

PURPOSE
       CHBMV  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 hermitian band matrix, with k super-diagonals.

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

       A      - COMPLEX		 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  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	refer‐
	      enced.   The  following  program segment will transfer the upper
	      triangular part of a hermitian  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 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  hermitian 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

	      Note  that the imaginary parts of the diagonal elements need not
	      be set and are assumed to be zero.  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      - COMPLEX		 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   - COMPLEX		.
	      On entry, BETA specifies the scalar beta.	 Unchanged on exit.

       Y      - COMPLEX		 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			16 October 1992			      CHBMV(l)
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