chbmv()

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

CHBMV

Purpose:

!>
!> CHBMV  performs 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 hermitian band matrix, with k super-diagonals.
!> 

Parameters

[in]	UPLO	!> UPLO is 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 supplied. !> !> UPLO = 'L' or 'l' The lower triangular part of A is !> being supplied. !>
[in]	N	!> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !>
[in]	K	!> K is INTEGER !> On entry, K specifies the number of super-diagonals of the !> matrix A. K must satisfy 0 .le. K. !>
[in]	ALPHA	!> ALPHA is COMPLEX !> On entry, ALPHA specifies the scalar alpha. !>
[in]	A	!> A is COMPLEX array, 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 referenced. !> 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. !>
[in]	LDA	!> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> ( k + 1 ). !>
[in]	X	!> X is COMPLEX array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the !> vector x. !>
[in]	INCX	!> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !>
[in]	BETA	!> BETA is COMPLEX !> On entry, BETA specifies the scalar beta. !>
[in,out]	Y	!> Y is COMPLEX array, 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. !>
[in]	INCY	!> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 2 Blas routine.
!>  The vector and matrix arguments are not referenced when N = 0, or M = 0
!>
!>  -- 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.
!>