SRC/shsein.f(3)

NAME
SRC/shsein.f

SYNOPSIS

  Functions/Subroutines
subroutine shsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
SHSEIN

Function/Subroutine Documentation

  subroutine shsein (character side, character eigsrc, character initv, logical, dimension( * ) select, integer n, real, dimension( ldh, * ) h, integer ldh, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, real, dimension( * ) work, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)

SHSEIN

Purpose:

    !>
    !> SHSEIN uses inverse iteration to find specified right and/or left
    !> eigenvectors of a real 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 (WR,WI):
    !>          = 'Q': the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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
    !>          real eigenvector corresponding to a real eigenvalue WR(j),
    !>          SELECT(j) must be set to .TRUE.. To select the complex
    !>          eigenvector corresponding to a complex eigenvalue
    !>          (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)),
    !>          either SELECT(j) or SELECT(j+1) or both must be set to
    !>          .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is
    !>          .FALSE..
    !>

    N

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

    H

    !>          H is REAL 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).
    !>

    WR

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

    WI

    !>          WI is REAL array, dimension (N)
    !>
    !>          On entry, the real and imaginary parts of the eigenvalues of
    !>          H; a complex conjugate pair of eigenvalues must be stored in
    !>          consecutive elements of WR and WI.
    !>          On exit, WR may have been altered since close eigenvalues
    !>          are perturbed slightly in searching for independent
    !>          eigenvectors.
    !>

    VL

    !>          VL is REAL 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(s) 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. A
    !>          complex eigenvector corresponding to a complex eigenvalue is
    !>          stored in two consecutive columns, the first holding the real
    !>          part and the second the imaginary part.
    !>          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 REAL 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(s) 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. A
    !>          complex eigenvector corresponding to a complex eigenvalue is
    !>          stored in two consecutive columns, the first holding the real
    !>          part and the second the imaginary part.
    !>          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; each selected real eigenvector
    !>          occupies one column and each selected complex eigenvector
    !>          occupies two columns.
    !>

    WORK

    !>          WORK is REAL array, dimension ((N+2)*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 the i-th and (i+1)th
    !>          columns of VL hold a complex eigenvector, then IFAILL(i) and
    !>          IFAILL(i+1) are set to the same value.
    !>          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 the i-th and (i+1)th
    !>          columns of VR hold a complex eigenvector, then IFAILR(i) and
    !>          IFAILR(i+1) are set to the same value.
    !>          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.

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 260 of file shsein.f.

Author

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