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iparmq.f(3)				      LAPACK				      iparmq.f(3)

       iparmq.f -

       INTEGER function iparmq (ISPEC, NAME, OPTS, N, ILO, IHI, LWORK)

Function/Subroutine Documentation
   INTEGER function iparmq (integerISPEC, character, dimension( * )NAME, character, dimension( *
       )OPTS, integerN, integerILO, integerIHI, integerLWORK)


		 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


		     ISPEC is integer scalar
			 ISPEC specifies which tunable parameter IPARMQ should

			 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

			 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
				   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 is character string
			  Name of the calling subroutine


		     OPTS is character string
			  This is a concatenation of the string arguments to


		     N is integer scalar
			  N is the order of the Hessenberg matrix H.


		     ILO is INTEGER


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


		     LWORK is integer scalar
			  The amount of workspace available.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       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

		  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.

       Definition at line 215 of file iparmq.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      iparmq.f(3)
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