Abdelrahman Said
346 lines
12 KiB
C
346 lines
12 KiB
C
/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* > \brief \b IPARMQ
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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> \htmlonly
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> Download IPARMQ + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.
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f">
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> [TGZ]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.
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f">
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> [ZIP]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.
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f">
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> [TXT]</a>
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> \endhtmlonly
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Definition:
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===========
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INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
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INTEGER IHI, ILO, ISPEC, LWORK, N
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CHARACTER NAME*( * ), OPTS*( * )
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> \par Purpose:
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=============
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>
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> \verbatim
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>
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> This program sets problem and machine dependent parameters
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> useful for xHSEQR and its subroutines. It is called whenever
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> ILAENV is called with 12 <= ISPEC <= 16
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> \endverbatim
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Arguments:
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==========
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> \param[in] ISPEC
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> \verbatim
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> ISPEC is integer scalar
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> ISPEC specifies which tunable parameter IPARMQ should
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> return.
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>
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> ISPEC=12: (INMIN) Matrices of order nmin or less
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> are sent directly to xLAHQR, the implicit
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> double shift QR algorithm. NMIN must be
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> at least 11.
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>
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> ISPEC=13: (INWIN) Size of the deflation window.
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> This is best set greater than or equal to
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> the number of simultaneous shifts NS.
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> Larger matrices benefit from larger deflation
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> windows.
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>
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> ISPEC=14: (INIBL) Determines when to stop nibbling and
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> invest in an (expensive) multi-shift QR sweep.
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> If the aggressive early deflation subroutine
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> finds LD converged eigenvalues from an order
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> NW deflation window and LD.GT.(NW*NIBBLE)/100,
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> then the next QR sweep is skipped and early
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> deflation is applied immediately to the
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> remaining active diagonal block. Setting
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> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
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> multi-shift QR sweep whenever early deflation
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> finds a converged eigenvalue. Setting
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> IPARMQ(ISPEC=14) greater than or equal to 100
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> prevents TTQRE from skipping a multi-shift
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> QR sweep.
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>
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> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
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> a multi-shift QR iteration.
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>
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> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
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> following meanings.
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> 0: During the multi-shift QR sweep,
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> xLAQR5 does not accumulate reflections and
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> does not use matrix-matrix multiply to
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> update the far-from-diagonal matrix
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> entries.
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> 1: During the multi-shift QR sweep,
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> xLAQR5 and/or xLAQRaccumulates reflections and uses
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> matrix-matrix multiply to update the
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> far-from-diagonal matrix entries.
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> 2: During the multi-shift QR sweep.
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> xLAQR5 accumulates reflections and takes
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> advantage of 2-by-2 block structure during
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> matrix-matrix multiplies.
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> (If xTRMM is slower than xGEMM, then
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> IPARMQ(ISPEC=16)=1 may be more efficient than
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> IPARMQ(ISPEC=16)=2 despite the greater level of
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> arithmetic work implied by the latter choice.)
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> \endverbatim
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>
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> \param[in] NAME
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> \verbatim
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> NAME is character string
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> Name of the calling subroutine
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> \endverbatim
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>
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> \param[in] OPTS
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> \verbatim
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> OPTS is character string
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> This is a concatenation of the string arguments to
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> TTQRE.
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> \endverbatim
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>
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> \param[in] N
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> \verbatim
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> N is integer scalar
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> N is the order of the Hessenberg matrix H.
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> \endverbatim
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>
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> \param[in] ILO
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> \verbatim
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> ILO is INTEGER
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> \endverbatim
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>
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> \param[in] IHI
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> \verbatim
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> IHI is INTEGER
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> It is assumed that H is already upper triangular
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> in rows and columns 1:ILO-1 and IHI+1:N.
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> \endverbatim
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>
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> \param[in] LWORK
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> \verbatim
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> LWORK is integer scalar
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> The amount of workspace available.
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> \endverbatim
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Authors:
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========
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> \author Univ. of Tennessee
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> \author Univ. of California Berkeley
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> \author Univ. of Colorado Denver
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> \author NAG Ltd.
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> \date November 2011
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> \ingroup auxOTHERauxiliary
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> \par Further Details:
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=====================
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>
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> \verbatim
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>
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> Little is known about how best to choose these parameters.
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> It is possible to use different values of the parameters
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> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
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>
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> It is probably best to choose different parameters for
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> different matrices and different parameters at different
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> times during the iteration, but this has not been
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> implemented --- yet.
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>
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>
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> The best choices of most of the parameters depend
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> in an ill-understood way on the relative execution
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> rate of xLAQR3 and xLAQR5 and on the nature of each
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> particular eigenvalue problem. Experiment may be the
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> only practical way to determine which choices are most
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> effective.
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>
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> Following is a list of default values supplied by IPARMQ.
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> These defaults may be adjusted in order to attain better
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> performance in any particular computational environment.
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>
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> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
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> Default: 75. (Must be at least 11.)
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>
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> IPARMQ(ISPEC=13) Recommended deflation window size.
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> This depends on ILO, IHI and NS, the
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> number of simultaneous shifts returned
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> by IPARMQ(ISPEC=15). The default for
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> (IHI-ILO+1).LE.500 is NS. The default
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> for (IHI-ILO+1).GT.500 is 3*NS/2.
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>
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> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
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>
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> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
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> a multi-shift QR iteration.
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>
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> If IHI-ILO+1 is ...
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>
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> greater than ...but less ... the
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> or equal to ... than default is
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>
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> 0 30 NS = 2+
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> 30 60 NS = 4+
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> 60 150 NS = 10
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> 150 590 NS = **
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> 590 3000 NS = 64
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> 3000 6000 NS = 128
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> 6000 infinity NS = 256
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>
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> (+) By default matrices of this order are
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> passed to the implicit double shift routine
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> xLAHQR. See IPARMQ(ISPEC=12) above. These
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> values of NS are used only in case of a rare
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> xLAHQR failure.
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>
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> (**) The asterisks (**) indicate an ad-hoc
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> function increasing from 10 to 64.
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>
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> IPARMQ(ISPEC=16) Select structured matrix multiply.
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> (See ISPEC=16 above for details.)
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> Default: 3.
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> \endverbatim
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>
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===================================================================== */
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integer igraphiparmq_(integer *ispec, char *name__, char *opts, integer *n, integer
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*ilo, integer *ihi, integer *lwork)
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{
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/* System generated locals */
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integer ret_val, i__1, i__2;
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real r__1;
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/* Builtin functions */
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double log(doublereal);
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integer i_nint(real *);
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/* Local variables */
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integer nh, ns;
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/* -- LAPACK auxiliary routine (version 3.4.0) --
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-- LAPACK is a software package provided by Univ. of Tennessee, --
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-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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November 2011
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================================================================ */
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if (*ispec == 15 || *ispec == 13 || *ispec == 16) {
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/* ==== Set the number simultaneous shifts ==== */
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nh = *ihi - *ilo + 1;
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ns = 2;
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if (nh >= 30) {
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ns = 4;
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}
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if (nh >= 60) {
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ns = 10;
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}
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if (nh >= 150) {
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/* Computing MAX */
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r__1 = log((real) nh) / log(2.f);
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i__1 = 10, i__2 = nh / i_nint(&r__1);
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ns = max(i__1,i__2);
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}
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if (nh >= 590) {
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ns = 64;
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}
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if (nh >= 3000) {
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ns = 128;
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}
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if (nh >= 6000) {
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ns = 256;
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}
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/* Computing MAX */
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i__1 = 2, i__2 = ns - ns % 2;
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ns = max(i__1,i__2);
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}
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if (*ispec == 12) {
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/* ===== Matrices of order smaller than NMIN get sent
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. to xLAHQR, the classic double shift algorithm.
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. This must be at least 11. ==== */
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ret_val = 75;
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} else if (*ispec == 14) {
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/* ==== INIBL: skip a multi-shift qr iteration and
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. whenever aggressive early deflation finds
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. at least (NIBBLE*(window size)/100) deflations. ==== */
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ret_val = 14;
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} else if (*ispec == 15) {
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/* ==== NSHFTS: The number of simultaneous shifts ===== */
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ret_val = ns;
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} else if (*ispec == 13) {
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/* ==== NW: deflation window size. ==== */
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if (nh <= 500) {
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ret_val = ns;
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} else {
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ret_val = ns * 3 / 2;
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}
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} else if (*ispec == 16) {
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/* ==== IACC22: Whether to accumulate reflections
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. before updating the far-from-diagonal elements
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. and whether to use 2-by-2 block structure while
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. doing it. A small amount of work could be saved
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. by making this choice dependent also upon the
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. NH=IHI-ILO+1. */
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ret_val = 0;
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if (ns >= 14) {
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ret_val = 1;
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}
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if (ns >= 14) {
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ret_val = 2;
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}
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} else {
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/* ===== invalid value of ispec ===== */
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ret_val = -1;
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}
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/* ==== End of IPARMQ ==== */
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return ret_val;
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} /* igraphiparmq_ */
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