LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dhsein()

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

DHSEIN

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

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.
!>
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 (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.
!>
[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,out]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..
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix H.  N >= 0.
!>
[in]H
!>          H is DOUBLE PRECISION 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]WR
!>          WR is DOUBLE PRECISION array, dimension (N)
!>
[in]WI
!>          WI is 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.
!>
[in,out]VL
!>          VL is 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.
!>
[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 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.
!>
[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; each selected real eigenvector
!>          occupies one column and each selected complex eigenvector
!>          occupies two columns.
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array, dimension ((N+2)*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 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.
!>
[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 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.
!>
[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|.
!>