Loading...
Searching...
No Matches

## chsein()

subroutine chsein | ( | character | side,
|  | character | eigsrc,
|  | character | initv,
|  | logical, dimension( * ) | select,
|  | integer | n,
|  | complex, dimension( ldh, * ) | h,
|  | integer | ldh,
|  | complex, dimension( * ) | w,
|  | complex, dimension( ldvl, * ) | vl,
|  | integer | ldvl,
|  | complex, dimension( ldvr, * ) | vr,
|  | integer | ldvr,
|  | integer | mm,
|  | integer | m,
|  | complex, dimension( * ) | work,
|  | real, dimension( * ) | rwork,
|  | integer, dimension( * ) | ifaill,
|  | integer, dimension( * ) | ifailr,
|  | integer | info )

CHSEIN

Download CHSEIN + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CHSEIN 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.
      !>

Parameters

  [in]

  SIDE

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

  [in]

  EIGSRC

      !>          EIGSRC is CHARACTER*1
      !>          Specifies the source of eigenvalues supplied in W:
      !>          = 'Q': the eigenvalues were found using CHSEQR; 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 CHSEIN 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, CHSEIN must always perform inverse iteration
      !>                 using the whole matrix H.
      !>

  [in]

  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.
      !>

  [in]

  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..
      !>

  [in]

  N

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

  [in]

  H

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

  [in]

  LDH

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

  [in,out]

  W

      !>          W is COMPLEX 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.
      !>

  [in,out]

  VL

      !>          VL is COMPLEX 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.
      !>

  [in]

  LDVL

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

  [in,out]

  VR

      !>          VR is COMPLEX 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.
      !>

  [in]

  LDVR

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

  [in]

  MM

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

  [out]

  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).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension (N*N)
      !>

  [out]

  RWORK

      !>          RWORK is REAL array, dimension (N)
      !>

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  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.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  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|.
      !>