chbevd(3F)

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

SYNOPSIS
     SUBROUTINE CHBEVD( 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( * )

         REAL           RWORK( * ), W( * )

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

PURPOSE
     CHBEVD 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 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 array, dimension (LDAB, N)
             On entry, the upper or lower triangle of the Hermitian 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) 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 associated 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 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) REAL 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 illegal value.
             > 0:  if INFO = i, the algorithm failed to converge; i off-
             diagonal elements of an intermediate tridiagonal form did not
             converge to zero.