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CHBGV(l)			       )			      CHBGV(l)

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

SYNOPSIS
       SUBROUTINE CHBGV( 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

	   REAL		 RWORK( * ), W( * )

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

PURPOSE
       CHBGV 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 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 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 CPBSTF.

       LDBB    (input) INTEGER
	       The leading dimension of the array BB.  LDBB >= KB+1.

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

       Z       (output) COMPLEX 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 array, dimension (N)

       RWORK   (workspace) REAL 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  ele‐
	       ments  of  an intermediate tridiagonal form did not converge to
	       zero; > N:   if INFO = N + i, for 1 <= i <= N, then CPBSTF
	       returned INFO = i: B is not positive definite.  The  factoriza‐
	       tion  of	 B could not be completed and no eigenvalues or eigen‐
	       vectors were computed.

LAPACK version 3.0		 15 June 2000			      CHBGV(l)
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