SYNOPSIS

INTEGER FUNCTION

IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )

    

INTEGER IHI, ILO, ISPEC, LWORK, N

    

CHARACTER NAME*( * ), OPTS*( * )

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) 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) character string

Name of the calling subroutine

OPTS (input) character string

This is a concatenation of the string arguments to TTQRE.

N (input) integer scalar

N is the order of the Hessenberg matrix H.

ILO (input) INTEGER

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

LWORK (input) 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.