2013-05-31 23:35:54 +08:00
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*> \brief \b IPARMQ
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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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.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.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.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
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*
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* .. Scalar Arguments ..
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* INTEGER IHI, ILO, ISPEC, LWORK, N
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* CHARACTER NAME*( * ), OPTS*( * )
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*
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*
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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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*
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* Arguments:
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* ==========
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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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*
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* Authors:
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* ========
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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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*
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*> \date November 2011
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*
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*> \ingroup auxOTHERauxiliary
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*
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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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2012-01-07 01:41:26 +08:00
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INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
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*
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2013-05-31 23:35:54 +08:00
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* -- LAPACK auxiliary routine (version 3.4.0) --
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2012-01-07 01:41:26 +08:00
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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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2013-05-31 23:35:54 +08:00
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* November 2011
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*
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2012-01-07 01:41:26 +08:00
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* .. Scalar Arguments ..
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INTEGER IHI, ILO, ISPEC, LWORK, N
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CHARACTER NAME*( * ), OPTS*( * )
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*
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2013-05-31 23:35:54 +08:00
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* ================================================================
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2012-01-07 01:41:26 +08:00
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* .. Parameters ..
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INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22
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PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14,
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$ ISHFTS = 15, IACC22 = 16 )
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INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
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PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14,
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$ NIBBLE = 14, KNWSWP = 500 )
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REAL TWO
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PARAMETER ( TWO = 2.0 )
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* ..
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* .. Local Scalars ..
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INTEGER NH, NS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC LOG, MAX, MOD, NINT, REAL
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* ..
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* .. Executable Statements ..
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IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
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$ ( ISPEC.EQ.IACC22 ) ) THEN
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*
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* ==== Set the number simultaneous shifts ====
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*
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NH = IHI - ILO + 1
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NS = 2
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IF( NH.GE.30 )
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$ NS = 4
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IF( NH.GE.60 )
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$ NS = 10
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IF( NH.GE.150 )
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$ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
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IF( NH.GE.590 )
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$ NS = 64
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IF( NH.GE.3000 )
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$ NS = 128
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IF( NH.GE.6000 )
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$ NS = 256
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NS = MAX( 2, NS-MOD( NS, 2 ) )
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END IF
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*
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IF( ISPEC.EQ.INMIN ) THEN
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*
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*
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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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*
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IPARMQ = NMIN
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*
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ELSE IF( ISPEC.EQ.INIBL ) THEN
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*
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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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*
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IPARMQ = NIBBLE
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*
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ELSE IF( ISPEC.EQ.ISHFTS ) THEN
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*
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* ==== NSHFTS: The number of simultaneous shifts =====
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*
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IPARMQ = NS
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*
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ELSE IF( ISPEC.EQ.INWIN ) THEN
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*
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* ==== NW: deflation window size. ====
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*
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IF( NH.LE.KNWSWP ) THEN
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IPARMQ = NS
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ELSE
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IPARMQ = 3*NS / 2
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END IF
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*
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ELSE IF( ISPEC.EQ.IACC22 ) THEN
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*
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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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*
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IPARMQ = 0
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IF( NS.GE.KACMIN )
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$ IPARMQ = 1
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IF( NS.GE.K22MIN )
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$ IPARMQ = 2
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*
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ELSE
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* ===== invalid value of ispec =====
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IPARMQ = -1
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*
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END IF
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*
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* ==== End of IPARMQ ====
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*
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END
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