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

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

       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.