IPARMQ(3)      LAPACK routine of NEC Numeric Library Collection      IPARMQ(3)



NAME
       IPARMQ

SYNOPSIS
       INTEGER FUNCTION IPARMQ (ISPEC, NAME, OPTS, N, ILO, IHI, LWORK)



PURPOSE
                 This program sets problem and machine dependent parameters
                 useful for xHSEQR and its subroutines. It is called whenever
                 ILAENV is called with 12 <= ISPEC <= 16




ARGUMENTS
           ISPEC     (input)
                     ISPEC is integer scalar
                         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.GT.(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 sweep,
                                       xLAQR5 does not accumulate reflections and
                                       does not use matrix-matrix multiply to
                                       update the far-from-diagonal matrix
                                       entries.
                                   1:  During the multi-shift QR sweep,
                                       xLAQR5 and/or xLAQRaccumulates reflections and uses
                                       matrix-matrix multiply to update the
                                       far-from-diagonal matrix entries.
                                   2:  During the multi-shift QR sweep.
                                       xLAQR5 accumulates reflections and takes
                                       advantage of 2-by-2 block structure 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.)

           NAME      (input)
                     NAME is character string
                          Name of the calling subroutine

           OPTS      (input)
                     OPTS is character string
                          This is a concatenation of the string arguments to
                          TTQRE.

           N         (input)
                     N is integer scalar
                          N is the order of the Hessenberg matrix H.

           ILO       (input)
                     ILO is INTEGER

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

           LWORK     (input)
                     LWORK is integer scalar
                          The amount of workspace available.






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).LE.500 is NS.  The default
                                   for (IHI-ILO+1).GT.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.



LAPACK routine                  31 October 2017                      IPARMQ(3)