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


SYNOPSIS

       SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
                          WORK,   LWORK,  RWORK,  LRWORK,  IWORK,
                          LIWORK, INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, KD, LDAB,  LDZ,  LIWORK,  LRWORK,
                          LWORK, N

           INTEGER        IWORK( * )

           DOUBLE         PRECISION RWORK( * ), W( * )

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


PURPOSE

       ZHBEVD  computes  all  the  eigenvalues  and,  optionally,
       eigenvectors of a complex  Hermitian  band  matrix  A.  If
       eigenvectors  are  desired,  it  uses a divide and conquer
       algorithm.

       The divide and conquer algorithm makes very  mild  assump­
       tions  about  floating  point  arithmetic. It will work on
       machines with a guard digit in add/subtract, or  on  those
       binary  machines  without guard digits which subtract like
       the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.  It  could
       conceivably  fail on hexadecimal or decimal machines with­
       out guard digits, but we know of none.


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*16 array, dimension (LDAB,
               N)

               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.

       LDAB    (input) INTEGER
               The leading dimension of the array AB.  LDAB >= KD
               + 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
               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/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

       LWORK   (input) INTEGER
               The  dimension  of  the  array  WORK.   If N <= 1,
               LWORK must be at least 1.  If JOBZ = 'N' and  N  >
               1,  LWORK must be at least N.  If JOBZ = 'V' and N
               > 1, LWORK must be at least 2*N**2.

               If LWORK = -1, then a workspace query is  assumed;
               the  routine  only  calculates the optimal size of
               the WORK array, returns this value  as  the  first
               entry  of  the  WORK  array,  and no error message
               related to LWORK is issued by XERBLA.

       RWORK   (workspace/output) DOUBLE PRECISION array,
               dimension (LRWORK) On exit, if INFO = 0,  RWORK(1)
               returns the optimal LRWORK.

               The   dimension  of  array  RWORK.   If  N  <=  1,
               LRWORK must be at least 1.  If JOBZ = 'N' and N  >
               1, LRWORK must be at least N.  If JOBZ = 'V' and N
               > 1, LRWORK must be at least 1 + 5*N + 2*N**2.

               If LRWORK = -1, then a workspace query is assumed;
               the  routine  only  calculates the optimal size of
               the RWORK array, returns this value as  the  first
               entry  of  the  RWORK  array, and no error message
               related to LRWORK is issued by XERBLA.

       IWORK   (workspace/output) INTEGER array, dimension
               (LIWORK)
               On exit, if INFO = 0, IWORK(1) returns the optimal
               LIWORK.

       LIWORK  (input) INTEGER
               The dimension of array IWORK.  If JOBZ = 'N' or  N
               <=  1,  LIWORK  must be at least 1.  If JOBZ = 'V'
               and N > 1, LIWORK must be at least 3 + 5*N .

               If LIWORK = -1, then a workspace query is assumed;
               the  routine  only  calculates the optimal size of
               the IWORK array, returns this value as  the  first
               entry  of  the  IWORK  array, and no error message
               related to LIWORK is issued by XERBLA.

       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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