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INTEGER FUNCTION <a name="IPARMQ.1"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER IHI, ILO, ISPEC, LWORK, N
CHARACTER NAME*( * ), OPTS*( * )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This program sets problem and machine dependent parameters
</span><span class="comment">*</span><span class="comment"> useful for xHSEQR and its subroutines. It is called whenever
</span><span class="comment">*</span><span class="comment"> <a name="ILAENV.16"></a><a href="hfy-index.html#ILAENV">ILAENV</a> is called with 12 <= ISPEC <= 16
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISPEC (input) integer scalar
</span><span class="comment">*</span><span class="comment"> ISPEC specifies which tunable parameter <a name="IPARMQ.22"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a> should
</span><span class="comment">*</span><span class="comment"> return.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISPEC=12: (INMIN) Matrices of order nmin or less
</span><span class="comment">*</span><span class="comment"> are sent directly to xLAHQR, the implicit
</span><span class="comment">*</span><span class="comment"> double shift QR algorithm. NMIN must be
</span><span class="comment">*</span><span class="comment"> at least 11.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISPEC=13: (INWIN) Size of the deflation window.
</span><span class="comment">*</span><span class="comment"> This is best set greater than or equal to
</span><span class="comment">*</span><span class="comment"> the number of simultaneous shifts NS.
</span><span class="comment">*</span><span class="comment"> Larger matrices benefit from larger deflation
</span><span class="comment">*</span><span class="comment"> windows.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISPEC=14: (INIBL) Determines when to stop nibbling and
</span><span class="comment">*</span><span class="comment"> invest in an (expensive) multi-shift QR sweep.
</span><span class="comment">*</span><span class="comment"> If the aggressive early deflation subroutine
</span><span class="comment">*</span><span class="comment"> finds LD converged eigenvalues from an order
</span><span class="comment">*</span><span class="comment"> NW deflation window and LD.GT.(NW*NIBBLE)/100,
</span><span class="comment">*</span><span class="comment"> then the next QR sweep is skipped and early
</span><span class="comment">*</span><span class="comment"> deflation is applied immediately to the
</span><span class="comment">*</span><span class="comment"> remaining active diagonal block. Setting
</span><span class="comment">*</span><span class="comment"> <a name="IPARMQ.44"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>(ISPEC=14) = 0 causes TTQRE to skip a
</span><span class="comment">*</span><span class="comment"> multi-shift QR sweep whenever early deflation
</span><span class="comment">*</span><span class="comment"> finds a converged eigenvalue. Setting
</span><span class="comment">*</span><span class="comment"> <a name="IPARMQ.47"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>(ISPEC=14) greater than or equal to 100
</span><span class="comment">*</span><span class="comment"> prevents TTQRE from skipping a multi-shift
</span><span class="comment">*</span><span class="comment"> QR sweep.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
</span><span class="comment">*</span><span class="comment"> a multi-shift QR iteration.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISPEC=16: (IACC22) <a name="IPARMQ.54"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a> is set to 0, 1 or 2 with the
</span><span class="comment">*</span><span class="comment"> following meanings.
</span><span class="comment">*</span><span class="comment"> 0: During the multi-shift QR sweep,
</span><span class="comment">*</span><span class="comment"> xLAQR5 does not accumulate reflections and
</span><span class="comment">*</span><span class="comment"> does not use matrix-matrix multiply to
</span><span class="comment">*</span><span class="comment"> update the far-from-diagonal matrix
</span><span class="comment">*</span><span class="comment"> entries.
</span><span class="comment">*</span><span class="comment"> 1: During the multi-shift QR sweep,
</span><span class="comment">*</span><span class="comment"> xLAQR5 and/or xLAQRaccumulates reflections and uses
</span><span class="comment">*</span><span class="comment"> matrix-matrix multiply to update the
</span><span class="comment">*</span><span class="comment"> far-from-diagonal matrix entries.
</span><span class="comment">*</span><span class="comment"> 2: During the multi-shift QR sweep.
</span><span class="comment">*</span><span class="comment"> xLAQR5 accumulates reflections and takes
</span><span class="comment">*</span><span class="comment"> advantage of 2-by-2 block structure during
</span><span class="comment">*</span><span class="comment"> matrix-matrix multiplies.
</span><span class="comment">*</span><span class="comment"> (If xTRMM is slower than xGEMM, then
</span><span class="comment">*</span><span class="comment"> <a name="IPARMQ.70"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>(ISPEC=16)=1 may be more efficient than
</span><span class="comment">*</span><span class="comment"> <a name="IPARMQ.71"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>(ISPEC=16)=2 despite the greater level of
</span><span class="comment">*</span><span class="comment"> arithmetic work implied by the latter choice.)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NAME (input) character string
</span><span class="comment">*</span><span class="comment"> Name of the calling subroutine
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> OPTS (input) character string
</span><span class="comment">*</span><span class="comment"> This is a concatenation of the string arguments to
</span><span class="comment">*</span><span class="comment"> TTQRE.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) integer scalar
</span><span class="comment">*</span><span class="comment"> N is the order of the Hessenberg matrix H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ILO (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IHI (input) INTEGER
</span><span class="comment">*</span><span class="comment"> It is assumed that H is already upper triangular
</span><span class="comment">*</span><span class="comment"> in rows and columns 1:ILO-1 and IHI+1:N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) integer scalar
</span><span class="comment">*</span><span class="comment"> The amount of workspace available.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Little is known about how best to choose these parameters.
</span><span class="comment">*</span><span class="comment"> It is possible to use different values of the parameters
</span><span class="comment">*</span><span class="comment"> for each of <a name="CHSEQR.97"></a><a href="chseqr.f.html#CHSEQR.1">CHSEQR</a>, <a name="DHSEQR.97"></a><a href="dhseqr.f.html#DHSEQR.1">DHSEQR</a>, <a name="SHSEQR.97"></a><a href="shseqr.f.html#SHSEQR.1">SHSEQR</a> and <a name="ZHSEQR.97"></a><a href="zhseqr.f.html#ZHSEQR.1">ZHSEQR</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> It is probably best to choose different parameters for
</span><span class="comment">*</span><span class="comment"> different matrices and different parameters at different
</span><span class="comment">*</span><span class="comment"> times during the iteration, but this has not been
</span><span class="comment">*</span><span class="comment"> implemented --- yet.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The best choices of most of the parameters depend
</span><span class="comment">*</span><span class="comment"> in an ill-understood way on the relative execution
</span><span class="comment">*</span><span class="comment"> rate of xLAQR3 and xLAQR5 and on the nature of each
</span><span class="comment">*</span><span class="comment"> particular eigenvalue problem. Experiment may be the
</span><span class="comment">*</span><span class="comment"> only practical way to determine which choices are most
</span><span class="comment">*</span><span class="comment"> effective.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Following is a list of default values supplied by <a name="IPARMQ.112"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>.
</span><span class="comment">*</span><span class="comment"> These defaults may be adjusted in order to attain better
</span><span class="comment">*</span><span class="comment"> performance in any particular computational environment.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="IPARMQ.116"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
</span><span class="comment">*</span><span class="comment"> Default: 75. (Must be at least 11.)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="IPARMQ.119"></a><a href="iparmq.f.html#IPARMQ.1">IPARMQ</a>(ISPEC=13) Recommended deflation window size.
</span><span class="comment">*</span><span class="comment"> This depends on ILO, IHI and NS, the
</span><span class="comment">*</span><span class="comment"> number of simultaneous shifts returned
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