dlaqr5.f(3)

NAME
dlaqr5.f -

SYNOPSIS

  Functions/Subroutines
subroutine dlaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
DLAQR5 performs a single small-bulge multi-shift QR sweep.

Function/Subroutine Documentation

  subroutine dlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, double precision, dimension( * )SR, double precision, dimension( * )SI, double precision, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldu, * )U, integerLDU, integerNV, double precision, dimension( ldwv, * )WV, integerLDWV, integerNH, double precision, dimension( ldwh, * )WH, integerLDWH)

DLAQR5 performs a single small-bulge multi-shift QR sweep.

Purpose:

        DLAQR5, called by DLAQR0, performs a
        single small-bulge multi-shift QR sweep.

Parameters:
    WANTT

              WANTT is logical scalar
                 WANTT = .true. if the quasi-triangular Schur factor
                 is being computed.  WANTT is set to .false. otherwise.

    WANTZ

              WANTZ is logical scalar
                 WANTZ = .true. if the orthogonal Schur factor is being
                 computed.  WANTZ is set to .false. otherwise.

    KACC22

              KACC22 is integer with value 0, 1, or 2.
                 Specifies the computation mode of far-from-diagonal
                 orthogonal updates.
            = 0: DLAQR5 does not accumulate reflections and does not
                 use matrix-matrix multiply to update far-from-diagonal
                 matrix entries.
            = 1: DLAQR5 accumulates reflections and uses matrix-matrix
                 multiply to update the far-from-diagonal matrix entries.
            = 2: DLAQR5 accumulates reflections, uses matrix-matrix
                 multiply to update the far-from-diagonal matrix entries,
                 and takes advantage of 2-by-2 block structure during
                 matrix multiplies.

    N

              N is integer scalar
                 N is the order of the Hessenberg matrix H upon which this
                 subroutine operates.

    KTOP

              KTOP is integer scalar

    KBOT

              KBOT is integer scalar
                 These are the first and last rows and columns of an
                 isolated diagonal block upon which the QR sweep is to be
                 applied. It is assumed without a check that
                           either KTOP = 1  or   H(KTOP,KTOP-1) = 0
                 and
                           either KBOT = N  or   H(KBOT+1,KBOT) = 0.

    NSHFTS

              NSHFTS is integer scalar
                 NSHFTS gives the number of simultaneous shifts.  NSHFTS
                 must be positive and even.

    SR

              SR is DOUBLE PRECISION array of size (NSHFTS)

    SI

              SI is DOUBLE PRECISION array of size (NSHFTS)
                 SR contains the real parts and SI contains the imaginary
                 parts of the NSHFTS shifts of origin that define the
                 multi-shift QR sweep.  On output SR and SI may be
                 reordered.

    H

              H is DOUBLE PRECISION array of size (LDH,N)
                 On input H contains a Hessenberg matrix.  On output a
                 multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
                 to the isolated diagonal block in rows and columns KTOP
                 through KBOT.

    LDH

              LDH is integer scalar
                 LDH is the leading dimension of H just as declared in the
                 calling procedure.  LDH.GE.MAX(1,N).

    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 DOUBLE PRECISION array of size (LDZ,IHI)
                 If WANTZ = .TRUE., then the QR Sweep orthogonal
                 similarity transformation is accumulated into
                 Z(ILOZ:IHIZ,ILO:IHI) from the right.
                 If WANTZ = .FALSE., then Z is unreferenced.

    LDZ

              LDZ is integer scalar
                 LDA is the leading dimension of Z just as declared in
                 the calling procedure. LDZ.GE.N.

    V

              V is DOUBLE PRECISION array of size (LDV,NSHFTS/2)

    LDV

              LDV is integer scalar
                 LDV is the leading dimension of V as declared in the
                 calling procedure.  LDV.GE.3.

    U

              U is DOUBLE PRECISION array of size
                 (LDU,3*NSHFTS-3)

    LDU

              LDU is integer scalar
                 LDU is the leading dimension of U just as declared in the
                 in the calling subroutine.  LDU.GE.3*NSHFTS-3.

    NH

              NH is integer scalar
                 NH is the number of columns in array WH available for
                 workspace. NH.GE.1.

    WH

              WH is DOUBLE PRECISION array of size (LDWH,NH)

    LDWH

              LDWH is integer scalar
                 Leading dimension of WH just as declared in the
                 calling procedure.  LDWH.GE.3*NSHFTS-3.

    NV

              NV is integer scalar
                 NV is the number of rows in WV agailable for workspace.
                 NV.GE.1.

    WV

              WV is DOUBLE PRECISION array of size
                 (LDWV,3*NSHFTS-3)

    LDWV

              LDWV is integer scalar
                 LDWV is the leading dimension of WV as declared in the
                 in the calling subroutine.  LDWV.GE.NV.

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

References:
    K. Braman, R. Byers and R. Mathias, The Multi-Shift QR Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume 23, pages 929--947, 2002.

Definition at line 258 of file dlaqr5.f.

Author

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