ZHBEV (3lapack)

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

SYNOPSIS

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

      CHARACTER     JOBZ, UPLO

      INTEGER       INFO, KD, LDAB, LDZ, N

      DOUBLE        PRECISION RWORK( * ), W( * )

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

PURPOSE

  ZHBEV computes all the eigenvalues and, optionally, eigenvectors 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*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) COMPLEX*16 array, dimension (N)

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

  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.