SRC/iparmq.f(3)

NAME
SRC/iparmq.f

SYNOPSIS

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

Function/Subroutine 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.

Definition at line 229 of file iparmq.f.

Author

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