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


SYNOPSIS

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

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, KD, LDAB, LDZ, N

           REAL          RWORK( * ), W( * )

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


PURPOSE

       CHBEV computes all the eigenvalues and, optionally, eigen­
       vectors 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 array, dimension (LDAB, N)
               On entry, the upper or lower triangle of the  Her­
               mitian  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.

               The leading dimension of the array AB.  LDAB >= KD
               + 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
               orthonormal eigenvectors of the matrix A, with the
               i-th  column  of Z holding the eigenvector associ­
               ated with W(i).  If JOBZ = 'N', then Z is not ref­
               erenced.

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

       WORK    (workspace) COMPLEX array, dimension (N)

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

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


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