CXML
        	    
LAPACK version 3.0
zhbgv(3)

PURPOSE
  ZHBGV - compute all the eigenvalues, and optionally, the eigenvectors of a
  complex generalized Hermitian-definite banded eigenproblem, of the form
  A*x=(lambda)*B*x

SYNTAX
  SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
		    WORK, RWORK, INFO )

      CHARACTER	    JOBZ, UPLO

      INTEGER	    INFO, KA, KB, LDAB, LDBB, LDZ, N

      DOUBLE	    PRECISION RWORK( * ), W( * )

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

DESCRIPTION
  ZHBGV computes all the eigenvalues, and optionally, the eigenvectors of a
  complex generalized Hermitian-definite banded eigenproblem, of the form
  A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and
  B is also positive definite.

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

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangles of A and B are stored;
	  = 'L':  Lower triangles of A and B are stored.

  N	  (input) INTEGER
	  The order of the matrices A and B.  N >= 0.

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

  KB	  (input) INTEGER
	  The number of superdiagonals of the matrix B if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO =
	  'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

	  On exit, the contents of AB are destroyed.

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

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

	  On exit, the factor S from the split Cholesky factorization B =
	  S**H*S, as returned by ZPBSTF.

  LDBB	  (input) INTEGER
	  The leading dimension of the array BB.  LDBB >= KB+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 matrix Z of
	  eigenvectors, with the i-th column of Z holding the eigenvector
	  associated with W(i). The eigenvectors are normalized so that
	  Z**H*B*Z = 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 >= N.

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

  RWORK	  (workspace) DOUBLE PRECISION array, dimension (3*N)

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value
	  > 0:	if INFO = i, and i is:
	  <= N:	 the algorithm failed to converge: i off-diagonal elements of
	  an intermediate tridiagonal form did not converge to zero; > N:
	  if INFO = N + i, for 1 <= i <= N, then ZPBSTF
	  returned INFO = i: B is not positive definite.  The factorization
	  of B could not be completed and no eigenvalues or eigenvectors were
	  computed.