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


SYNOPSIS

       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, * )


PURPOSE

       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  Her­
               mitian  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

               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  Her­
               mitian  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 fac­
               torization 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 ille­
               gal 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

               returned INFO = i: B  is  not  positive  definite.
               The  factorization of B could not be completed and
               no eigenvalues or eigenvectors were computed.


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