Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  uses  inverse iteration to find specified right and/or left eigenvectors of a
       real upper Hessenberg matrix H

SYNOPSIS

       SUBROUTINE DHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL, LDVL, VR, LDVR, MM,
                          M, WORK, IFAILL, IFAILR, INFO )

           CHARACTER      EIGSRC, INITV, SIDE

           INTEGER        INFO, LDH, LDVL, LDVR, M, MM, N

           LOGICAL        SELECT( * )

           INTEGER        IFAILL( * ), IFAILR( * )

           DOUBLE         PRECISION  H(  LDH, * ), VL( LDVL, * ), VR( LDVR, * ), WI( * ), WORK( *
                          ), WR( * )

PURPOSE

       DHSEIN 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.

ARGUMENTS

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

        EIGSRC  (input) CHARACTER*1
                Specifies the source of eigenvalues supplied in (WR,WI):
                = 'Q': the eigenvalues were found using DHSEQR; 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 DHSEIN 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, DHSEIN must always perform inverse iteration
                using the whole matrix H.

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

        SELECT  (input/output) 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       (input) INTEGER
                The order of the matrix H.  N >= 0.

        H       (input) DOUBLE PRECISION array, dimension (LDH,N)
                The upper Hessenberg matrix H.

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

        WR      (input/output) DOUBLE PRECISION array, dimension (N)
                WI      (input) DOUBLE PRECISION 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      (input/output) DOUBLE PRECISION 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    (input) INTEGER
                The leading dimension of the array VL.
                LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.

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

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

        M       (output) 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    (workspace) DOUBLE PRECISION array, dimension ((N+2)*N)

        IFAILL  (output) 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  (output) 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    (output) 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.

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|.

 LAPACK routine (version 3.2)               April 2011                            DHSEIN(3lapack)