iparmq - Man Page

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

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.