slaqr3.f(3)

NAME
slaqr3.f -

SYNOPSIS

  Functions/Subroutines
subroutine slaqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK)
SLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).

Function/Subroutine Documentation

  subroutine slaqr3 (logicalWANTT, logicalWANTZ, integerN, integerKTOP, integerKBOT, integerNW, real, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, real, dimension( ldz, * )Z, integerLDZ, integerNS, integerND, real, dimension( * )SR, real, dimension( * )SI, real, dimension( ldv, * )V, integerLDV, integerNH, real, dimension( ldt, * )T, integerLDT, integerNV, real, dimension( ldwv, * )WV, integerLDWV, real, dimension( * )WORK, integerLWORK)

SLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).

Purpose:

        Aggressive early deflation:
        SLAQR3 accepts as input an upper Hessenberg matrix
        H and performs an orthogonal similarity transformation
        designed to detect and deflate fully converged eigenvalues from
        a trailing principal submatrix.  On output H has been over-
        written by a new Hessenberg matrix that is a perturbation of
        an orthogonal similarity transformation of H.  It is to be
        hoped that the final version of H has many zero subdiagonal
        entries.

Parameters:
    WANTT

              WANTT is LOGICAL
              If .TRUE., then the Hessenberg matrix H is fully updated
              so that the quasi-triangular Schur factor may be
              computed (in cooperation with the calling subroutine).
              If .FALSE., then only enough of H is updated to preserve
              the eigenvalues.

    WANTZ

              WANTZ is LOGICAL
              If .TRUE., then the orthogonal matrix Z is updated so
              so that the orthogonal Schur factor may be computed
              (in cooperation with the calling subroutine).
              If .FALSE., then Z is not referenced.

    N

              N is INTEGER
              The order of the matrix H and (if WANTZ is .TRUE.) the
              order of the orthogonal matrix Z.

    KTOP

              KTOP is INTEGER
              It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.
              KBOT and KTOP together determine an isolated block
              along the diagonal of the Hessenberg matrix.

    KBOT

              KBOT is INTEGER
              It is assumed without a check that either
              KBOT = N or H(KBOT+1,KBOT)=0.  KBOT and KTOP together
              determine an isolated block along the diagonal of the
              Hessenberg matrix.

    NW

              NW is INTEGER
              Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).

    H

              H is REAL array, dimension (LDH,N)
              On input the initial N-by-N section of H stores the
              Hessenberg matrix undergoing aggressive early deflation.
              On output H has been transformed by an orthogonal
              similarity transformation, perturbed, and the returned
              to Hessenberg form that (it is to be hoped) has some
              zero subdiagonal entries.

    LDH

              LDH is integer
              Leading dimension of H just as declared in the calling
              subroutine.  N .LE. LDH

    ILOZ

              ILOZ is INTEGER

    IHIZ

              IHIZ is INTEGER
              Specify the rows of Z to which transformations must be
              applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.

    Z

              Z is REAL array, dimension (LDZ,N)
              IF WANTZ is .TRUE., then on output, the orthogonal
              similarity transformation mentioned above has been
              accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.
              If WANTZ is .FALSE., then Z is unreferenced.

    LDZ

              LDZ is integer
              The leading dimension of Z just as declared in the
              calling subroutine.  1 .LE. LDZ.

    NS

              NS is integer
              The number of unconverged (ie approximate) eigenvalues
              returned in SR and SI that may be used as shifts by the
              calling subroutine.

    ND

              ND is integer
              The number of converged eigenvalues uncovered by this
              subroutine.

    SR

              SR is REAL array, dimension KBOT

    SI

              SI is REAL array, dimension KBOT
              On output, the real and imaginary parts of approximate
              eigenvalues that may be used for shifts are stored in
              SR(KBOT-ND-NS+1) through SR(KBOT-ND) and
              SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.
              The real and imaginary parts of converged eigenvalues
              are stored in SR(KBOT-ND+1) through SR(KBOT) and
              SI(KBOT-ND+1) through SI(KBOT), respectively.

    V

              V is REAL array, dimension (LDV,NW)
              An NW-by-NW work array.

    LDV

              LDV is integer scalar
              The leading dimension of V just as declared in the
              calling subroutine.  NW .LE. LDV

    NH

              NH is integer scalar
              The number of columns of T.  NH.GE.NW.

    T

              T is REAL array, dimension (LDT,NW)

    LDT

              LDT is integer
              The leading dimension of T just as declared in the
              calling subroutine.  NW .LE. LDT

    NV

              NV is integer
              The number of rows of work array WV available for
              workspace.  NV.GE.NW.

    WV

              WV is REAL array, dimension (LDWV,NW)

    LDWV

              LDWV is integer
              The leading dimension of W just as declared in the
              calling subroutine.  NW .LE. LDV

    WORK

              WORK is REAL array, dimension LWORK.
              On exit, WORK(1) is set to an estimate of the optimal value
              of LWORK for the given values of N, NW, KTOP and KBOT.

    LWORK

              LWORK is integer
              The dimension of the work array WORK.  LWORK = 2*NW
              suffices, but greater efficiency may result from larger
              values of LWORK.
              If LWORK = -1, then a workspace query is assumed; SLAQR3
              only estimates the optimal workspace size for the given
              values of N, NW, KTOP and KBOT.  The estimate is returned
              in WORK(1).  No error message related to LWORK is issued
              by XERBLA.  Neither H nor Z are accessed.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Contributors:
    Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 274 of file slaqr3.f.

Author

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