iparmq(3)

NAME
iparmq - iparmq: set parameters for hseqr

SYNOPSIS

  Functions

integer function iparmq (ispec, name, opts, n, ilo, ihi, lwork)
IPARMQ

Detailed Description

Function Documentation

  integer function iparmq (integer ispec, character, dimension( * ) name, character, dimension( * ) opts, integer n, integer ilo, integer ihi, integer lwork)

IPARMQ

Purpose:

    !>
    !>      This program sets problem and machine dependent parameters
    !>      useful for xHSEQR and related subroutines for eigenvalue
    !>      problems. It is called whenever
    !>      IPARMQ is called with 12 <= ISPEC <= 16
    !>

Parameters
    ISPEC

    !>          ISPEC is INTEGER
    !>              ISPEC specifies which tunable parameter IPARMQ should
    !>              return.
    !>
    !>              ISPEC=12: (INMIN)  Matrices of order nmin or less
    !>                        are sent directly to xLAHQR, the implicit
    !>                        double shift QR algorithm.  NMIN must be
    !>                        at least 11.
    !>
    !>              ISPEC=13: (INWIN)  Size of the deflation window.
    !>                        This is best set greater than or equal to
    !>                        the number of simultaneous shifts NS.
    !>                        Larger matrices benefit from larger deflation
    !>                        windows.
    !>
    !>              ISPEC=14: (INIBL) Determines when to stop nibbling and
    !>                        invest in an (expensive) multi-shift QR sweep.
    !>                        If the aggressive early deflation subroutine
    !>                        finds LD converged eigenvalues from an order
    !>                        NW deflation window and LD > (NW*NIBBLE)/100,
    !>                        then the next QR sweep is skipped and early
    !>                        deflation is applied immediately to the
    !>                        remaining active diagonal block.  Setting
    !>                        IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
    !>                        multi-shift QR sweep whenever early deflation
    !>                        finds a converged eigenvalue.  Setting
    !>                        IPARMQ(ISPEC=14) greater than or equal to 100
    !>                        prevents TTQRE from skipping a multi-shift
    !>                        QR sweep.
    !>
    !>              ISPEC=15: (NSHFTS) The number of simultaneous shifts in
    !>                        a multi-shift QR iteration.
    !>
    !>              ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
    !>                        following meanings.
    !>                        0:  During the multi-shift QR/QZ sweep,
    !>                            blocked eigenvalue reordering, blocked
    !>                            Hessenberg-triangular reduction,
    !>                            reflections and/or rotations are not
    !>                            accumulated when updating the
    !>                            far-from-diagonal matrix entries.
    !>                        1:  During the multi-shift QR/QZ sweep,
    !>                            blocked eigenvalue reordering, blocked
    !>                            Hessenberg-triangular reduction,
    !>                            reflections and/or rotations are
    !>                            accumulated, and matrix-matrix
    !>                            multiplication is used to update the
    !>                            far-from-diagonal matrix entries.
    !>                        2:  During the multi-shift QR/QZ sweep,
    !>                            blocked eigenvalue reordering, blocked
    !>                            Hessenberg-triangular reduction,
    !>                            reflections and/or rotations are
    !>                            accumulated, and 2-by-2 block structure
    !>                            is exploited during matrix-matrix
    !>                            multiplies.
    !>                        (If xTRMM is slower than xGEMM, then
    !>                        IPARMQ(ISPEC=16)=1 may be more efficient than
    !>                        IPARMQ(ISPEC=16)=2 despite the greater level of
    !>                        arithmetic work implied by the latter choice.)
    !>
    !>              ISPEC=17: (ICOST) An estimate of the relative cost of flops
    !>                        within the near-the-diagonal shift chase compared
    !>                        to flops within the BLAS calls of a QZ sweep.
    !>

    NAME

    !>          NAME is CHARACTER string
    !>               Name of the calling subroutine
    !>

    OPTS

    !>          OPTS is CHARACTER string
    !>               This is a concatenation of the string arguments to
    !>               TTQRE.
    !>

    N

    !>          N is INTEGER
    !>               N is the order of the Hessenberg matrix H.
    !>

    ILO

    !>          ILO is INTEGER
    !>

    IHI

    !>          IHI is INTEGER
    !>               It is assumed that H is already upper triangular
    !>               in rows and columns 1:ILO-1 and IHI+1:N.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>               The amount of workspace available.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>       Little is known about how best to choose these parameters.
    !>       It is possible to use different values of the parameters
    !>       for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
    !>
    !>       It is probably best to choose different parameters for
    !>       different matrices and different parameters at different
    !>       times during the iteration, but this has not been
    !>       implemented --- yet.
    !>
    !>
    !>       The best choices of most of the parameters depend
    !>       in an ill-understood way on the relative execution
    !>       rate of xLAQR3 and xLAQR5 and on the nature of each
    !>       particular eigenvalue problem.  Experiment may be the
    !>       only practical way to determine which choices are most
    !>       effective.
    !>
    !>       Following is a list of default values supplied by IPARMQ.
    !>       These defaults may be adjusted in order to attain better
    !>       performance in any particular computational environment.
    !>
    !>       IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
    !>                        Default: 75. (Must be at least 11.)
    !>
    !>       IPARMQ(ISPEC=13) Recommended deflation window size.
    !>                        This depends on ILO, IHI and NS, the
    !>                        number of simultaneous shifts returned
    !>                        by IPARMQ(ISPEC=15).  The default for
    !>                        (IHI-ILO+1) <= 500 is NS.  The default
    !>                        for (IHI-ILO+1) > 500 is 3*NS/2.
    !>
    !>       IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14.
    !>
    !>       IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
    !>                        a multi-shift QR iteration.
    !>
    !>                        If IHI-ILO+1 is ...
    !>
    !>                        greater than      ...but less    ... the
    !>                        or equal to ...      than        default is
    !>
    !>                                0               30       NS =   2+
    !>                               30               60       NS =   4+
    !>                               60              150       NS =  10
    !>                              150              590       NS =  **
    !>                              590             3000       NS =  64
    !>                             3000             6000       NS = 128
    !>                             6000             infinity   NS = 256
    !>
    !>                    (+)  By default matrices of this order are
    !>                         passed to the implicit double shift routine
    !>                         xLAHQR.  See IPARMQ(ISPEC=12) above.   These
    !>                         values of NS are used only in case of a rare
    !>                         xLAHQR failure.
    !>
    !>                    (**) The asterisks (**) indicate an ad-hoc
    !>                         function increasing from 10 to 64.
    !>
    !>       IPARMQ(ISPEC=16) Select structured matrix multiply.
    !>                        (See ISPEC=16 above for details.)
    !>                        Default: 3.
    !>
    !>       IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection.
    !>                        Expressed as a percentage.
    !>                        Default: 10.
    !>

Author

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