ZHBMV(3f)

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

SYNOPSIS

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

COMPLEX*16
    ALPHA, BETA

INTEGER
    INCX, INCY, K, LDA, N

CHARACTER*1
    UPLO

COMPLEX*16
    A( LDA, * ), X( * ), Y( * )

PURPOSE
ZHBMV 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 supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied. 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*16      .
    On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A      - COMPLEX*16       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 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. 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*16       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*16      .
    On entry, BETA specifies the scalar beta. Unchanged on exit.

Y      - COMPLEX*16       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.