!>
!>      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.
!> 

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!>
!>       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.
!>