NAME

zhbmv - perform the matrix-vector operation y := alpha*A*x + beta*y

SYNOPSIS

  SUBROUTINE ZHBMV( UPLO, N, NDIAG, ALPHA, A, LDA, X, INCX, BETA, Y, 
 *      INCY)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX ALPHA, BETA
  DOUBLE COMPLEX A(LDA,*), X(*), Y(*)
  INTEGER N, NDIAG, LDA, INCX, INCY

  SUBROUTINE ZHBMV_64( UPLO, N, NDIAG, ALPHA, A, LDA, X, INCX, BETA, 
 *      Y, INCY)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX ALPHA, BETA
  DOUBLE COMPLEX A(LDA,*), X(*), Y(*)
  INTEGER*8 N, NDIAG, LDA, INCX, INCY

F95 INTERFACE

  SUBROUTINE HBMV( UPLO, [N], NDIAG, ALPHA, A, [LDA], X, [INCX], BETA, 
 *       Y, [INCY])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8) :: ALPHA, BETA
  COMPLEX(8), DIMENSION(:) :: X, Y
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: N, NDIAG, LDA, INCX, INCY

  SUBROUTINE HBMV_64( UPLO, [N], NDIAG, ALPHA, A, [LDA], X, [INCX], 
 *       BETA, Y, [INCY])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8) :: ALPHA, BETA
  COMPLEX(8), DIMENSION(:) :: X, Y
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: N, NDIAG, LDA, INCX, INCY

C INTERFACE

#include <sunperf.h>

void zhbmv(char uplo, int n, int ndiag, doublecomplex alpha, doublecomplex *a, int lda, doublecomplex *x, int incx, doublecomplex beta, doublecomplex *y, int incy);

void zhbmv_64(char uplo, long n, long ndiag, doublecomplex alpha, doublecomplex *a, long lda, doublecomplex *x, long incx, doublecomplex beta, doublecomplex *y, long incy);

PURPOSE

zhbmv 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 ndiag super-diagonals.

ARGUMENTS

UPLO (input)
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 (input)
On entry, N specifies the order of the matrix A. N > = 0. Unchanged on exit.
NDIAG (input)
On entry, NDIAG specifies the number of super-diagonals of the matrix A. NDIAG must satisfy 0 .le. NDIAG. Unchanged on exit.
ALPHA (input)
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A (input)
Before entry with UPLO = 'U' or 'u', the leading ( ndiag + 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 ( ndiag + 1 ) of the array, the first super-diagonal starting at position 2 in row ndiag, and so on. The top left ndiag by ndiag 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 = NDIAG + 1 - J
      DO 10, I = MAX( 1, J - NDIAG ), J
        A( M + I, J ) = matrix( I, J )
 10   CONTINUE
 20 CONTINUE
```
Before entry with UPLO = 'L' or 'l', the leading ( ndiag + 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 ndiag by ndiag 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 + NDIAG )
        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 (input)
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA > = ( ndiag + 1 ). Unchanged on exit.
X (input)
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. Unchanged on exit.
INCX (input)
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA (input)
On entry, BETA specifies the scalar beta. Unchanged on exit.
Y (input/output)
( 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 (input)
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.