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NAME

       zhsein.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine zhsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( *
       )SELECT, integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16, dimension( *
       )W, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR,
       integerLDVR, integerMM, integerM, complex*16, dimension( * )WORK, double precision,
       dimension( * )RWORK, integer, dimension( * )IFAILL, integer, dimension( * )IFAILR,
       integerINFO)
       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.

Author

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