ZHBEVD (3lapack)

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 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 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) 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 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*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 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.