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CHBGV(l)					)					 CHBGV(l)

NAME
       CHBGV  - compute all the eigenvalues, and optionally, the eigenvectors of a complex gener-
       alized 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 general-
       ized 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 sub-
	       diagonals if UPLO = 'L'. KA >= 0.

       KB      (input) INTEGER
	       The number of superdiagonals of the matrix B if UPLO = 'U', or the number of  sub-
	       diagonals 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 col-
	       umn  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 col-
	       umn 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 elements of an  intermedi-
	       ate  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 factorization of B  could  not
	       be completed and no eigenvalues or eigenvectors were computed.

LAPACK version 3.0			   15 June 2000 				 CHBGV(l)
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