ZHSEIN uses inverse iteration to find specified right and/or left
 eigenvectors of a complex upper Hessenberg matrix H.
 The right eigenvector x and the left eigenvector y of the matrix H
 corresponding to an eigenvalue w are defined by:
              H * x = w * x,     y**h * H = w * y**h
 where y**h denotes the conjugate transpose of the vector y.

SIDE

          SIDE is CHARACTER*1
          = 'R': compute right eigenvectors only;
          = 'L': compute left eigenvectors only;
          = 'B': compute both right and left eigenvectors.

EIGSRC

          EIGSRC is CHARACTER*1
          Specifies the source of eigenvalues supplied in W:
          = 'Q': the eigenvalues were found using ZHSEQR; thus, if
                 H has zero subdiagonal elements, and so is
                 block-triangular, then the j-th eigenvalue can be
                 assumed to be an eigenvalue of the block containing
                 the j-th row/column.  This property allows ZHSEIN to
                 perform inverse iteration on just one diagonal block.
          = 'N': no assumptions are made on the correspondence
                 between eigenvalues and diagonal blocks.  In this
                 case, ZHSEIN must always perform inverse iteration
                 using the whole matrix H.

INITV

          INITV is CHARACTER*1
          = 'N': no initial vectors are supplied;
          = 'U': user-supplied initial vectors are stored in the arrays
                 VL and/or VR.

SELECT

          SELECT is LOGICAL array, dimension (N)
          Specifies the eigenvectors to be computed. To select the
          eigenvector corresponding to the eigenvalue W(j),
          SELECT(j) must be set to .TRUE..

N

          N is INTEGER
          The order of the matrix H.  N >= 0.

H

          H is COMPLEX*16 array, dimension (LDH,N)
          The upper Hessenberg matrix H.
          If a NaN is detected in H, the routine will return with INFO=-6.

LDH

          LDH is INTEGER
          The leading dimension of the array H.  LDH >= max(1,N).

W

          W is COMPLEX*16 array, dimension (N)
          On entry, the eigenvalues of H.
          On exit, the real parts of W may have been altered since
          close eigenvalues are perturbed slightly in searching for
          independent eigenvectors.

VL

          VL is COMPLEX*16 array, dimension (LDVL,MM)
          On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
          contain starting vectors for the inverse iteration for the
          left eigenvectors; the starting vector for each eigenvector
          must be in the same column in which the eigenvector will be
          stored.
          On exit, if SIDE = 'L' or 'B', the left eigenvectors
          specified by SELECT will be stored consecutively in the
          columns of VL, in the same order as their eigenvalues.
          If SIDE = 'R', VL is not referenced.

LDVL

          LDVL is INTEGER
          The leading dimension of the array VL.
          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.

VR

          VR is COMPLEX*16 array, dimension (LDVR,MM)
          On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
          contain starting vectors for the inverse iteration for the
          right eigenvectors; the starting vector for each eigenvector
          must be in the same column in which the eigenvector will be
          stored.
          On exit, if SIDE = 'R' or 'B', the right eigenvectors
          specified by SELECT will be stored consecutively in the
          columns of VR, in the same order as their eigenvalues.
          If SIDE = 'L', VR is not referenced.

LDVR

          LDVR is INTEGER
          The leading dimension of the array VR.
          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.

MM

          MM is INTEGER
          The number of columns in the arrays VL and/or VR. MM >= M.

M

          M is INTEGER
          The number of columns in the arrays VL and/or VR required to
          store the eigenvectors (= the number of .TRUE. elements in
          SELECT).

WORK

          WORK is COMPLEX*16 array, dimension (N*N)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (N)

IFAILL

          IFAILL is INTEGER array, dimension (MM)
          If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left
          eigenvector in the i-th column of VL (corresponding to the
          eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
          eigenvector converged satisfactorily.
          If SIDE = 'R', IFAILL is not referenced.

IFAILR

          IFAILR is INTEGER array, dimension (MM)
          If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
          eigenvector in the i-th column of VR (corresponding to the
          eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
          eigenvector converged satisfactorily.
          If SIDE = 'L', IFAILR is not referenced.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, i is the number of eigenvectors which
                failed to converge; see IFAILL and IFAILR for further
                details.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  Each eigenvector is normalized so that the element of largest
  magnitude has magnitude 1; here the magnitude of a complex number
  (x,y) is taken to be |x|+|y|.