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NAME
     zhbevd - compute all the eigenvalues and, optionally, eigen-
     vectors 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, * )



     #include <sunperf.h>

     void zhbevd(char jobz, char uplo, int n, int kd,  doublecom-
               plex *zab, int ldab, double *w, doublecomplex *zz,
               int ldz, int *info) ;

PURPOSE
     ZHBEVD computes all the eigenvalues and, optionally,  eigen-
     vectors  of a complex Hermitian band matrix A.  If eigenvec-
     tors are desired, it uses a divide and conquer algorithm.

     The divide and conquer algorithm makes very mild assumptions
     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  without  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)
               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.

     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
               referenced.

     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 LWORK > 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.

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

     LRWORK    (input) INTEGER
               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 + 4*N + 2*N*lg N +
               3*N**2 , where lg( N ) = smallest integer  k  such
               that 2**k >= N .

     IWORK     (workspace/output)   INTEGER   array,    dimension
               (LIWORK)
               On exit, if  LIWORK  >  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 2 + 5*N .

     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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