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zhsein.f(3) LAPACK zhsein.f(3)

zhsein.f -


subroutine zhsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
 
ZHSEIN

ZHSEIN
Purpose:
 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.
Parameters:
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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
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|.
Definition at line 244 of file zhsein.f.

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