CXML
        	    
LAPACK version 3.0
zhbev(3)

PURPOSE
  ZHBEV - compute all the eigenvalues and, optionally, eigenvectors of a
  complex Hermitian band matrix A

SYNTAX
  SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO
		    )

      CHARACTER	    JOBZ, UPLO

      INTEGER	    INFO, KD, LDAB, LDZ, N

      DOUBLE	    PRECISION RWORK( * ), W( * )

      COMPLEX*16    AB( LDAB, * ), WORK( * ), Z( LDZ, * )

DESCRIPTION
  ZHBEV computes all the eigenvalues and, optionally, eigenvectors of a
  complex Hermitian band matrix A.

ARGUMENTS
  JOBZ	  (input) CHARACTER*1
	  = 'N':  Compute eigenvalues only;
	  = 'V':  Compute eigenvalues and eigenvectors.

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangle of A is stored;
	  = 'L':  Lower triangle of A is stored.

  N	  (input) INTEGER
	  The order of the matrix A.  N >= 0.

  KD	  (input) INTEGER
	  The number of superdiagonals of the matrix A if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'.	 KD >= 0.

  AB	  (input/output) COMPLEX*16 array, dimension (LDAB, N)
	  On entry, the upper or lower triangle of the Hermitian band matrix
	  A, stored in the first KD+1 rows of the array.  The j-th column of
	  A is stored in the j-th column of the array AB as follows: if UPLO
	  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO =
	  'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

	  On exit, AB is overwritten by values generated during the reduction
	  to tridiagonal form.	If UPLO = 'U', the first superdiagonal and
	  the diagonal of the tridiagonal matrix T are returned in rows KD
	  and KD+1 of AB, and if UPLO = 'L', the diagonal and first
	  subdiagonal of T are returned in the first two rows of AB.

  LDAB	  (input) INTEGER
	  The leading dimension of the array AB.  LDAB >= KD + 1.

  W	  (output) DOUBLE PRECISION array, dimension (N)
	  If INFO = 0, the eigenvalues in ascending order.

  Z	  (output) COMPLEX*16 array, dimension (LDZ, N)
	  If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
	  eigenvectors of the matrix A, with the i-th column of Z holding the
	  eigenvector associated with W(i).  If JOBZ = 'N', then Z is not
	  referenced.

  LDZ	  (input) INTEGER
	  The leading dimension of the array Z.	 LDZ >= 1, and if JOBZ = 'V',
	  LDZ >= max(1,N).

  WORK	  (workspace) COMPLEX*16 array, dimension (N)

  RWORK	  (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))

  INFO	  (output) INTEGER
	  = 0:	successful exit.
	  < 0:	if INFO = -i, the i-th argument had an illegal value.
	  > 0:	if INFO = i, the algorithm failed to converge; i off-diagonal
	  elements of an intermediate tridiagonal form did not converge to
	  zero.