NAME

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

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

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 ( 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 = 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 ( 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
 = 1 - J
O 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 >= ( k + 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.