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iparmq.f
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1 *> \brief \b IPARMQ
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download IPARMQ + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER IHI, ILO, ISPEC, LWORK, N
25 * CHARACTER NAME*( * ), OPTS*( * )
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> This program sets problem and machine dependent parameters
34 *> useful for xHSEQR and its subroutines. It is called whenever
35 *> ILAENV is called with 12 <= ISPEC <= 16
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] ISPEC
42 *> \verbatim
43 *> ISPEC is integer scalar
44 *> ISPEC specifies which tunable parameter IPARMQ should
45 *> return.
46 *>
47 *> ISPEC=12: (INMIN) Matrices of order nmin or less
48 *> are sent directly to xLAHQR, the implicit
49 *> double shift QR algorithm. NMIN must be
50 *> at least 11.
51 *>
52 *> ISPEC=13: (INWIN) Size of the deflation window.
53 *> This is best set greater than or equal to
54 *> the number of simultaneous shifts NS.
55 *> Larger matrices benefit from larger deflation
56 *> windows.
57 *>
58 *> ISPEC=14: (INIBL) Determines when to stop nibbling and
59 *> invest in an (expensive) multi-shift QR sweep.
60 *> If the aggressive early deflation subroutine
61 *> finds LD converged eigenvalues from an order
62 *> NW deflation window and LD.GT.(NW*NIBBLE)/100,
63 *> then the next QR sweep is skipped and early
64 *> deflation is applied immediately to the
65 *> remaining active diagonal block. Setting
66 *> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
67 *> multi-shift QR sweep whenever early deflation
68 *> finds a converged eigenvalue. Setting
69 *> IPARMQ(ISPEC=14) greater than or equal to 100
70 *> prevents TTQRE from skipping a multi-shift
71 *> QR sweep.
72 *>
73 *> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
74 *> a multi-shift QR iteration.
75 *>
76 *> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
77 *> following meanings.
78 *> 0: During the multi-shift QR sweep,
79 *> xLAQR5 does not accumulate reflections and
80 *> does not use matrix-matrix multiply to
81 *> update the far-from-diagonal matrix
82 *> entries.
83 *> 1: During the multi-shift QR sweep,
84 *> xLAQR5 and/or xLAQRaccumulates reflections and uses
85 *> matrix-matrix multiply to update the
86 *> far-from-diagonal matrix entries.
87 *> 2: During the multi-shift QR sweep.
88 *> xLAQR5 accumulates reflections and takes
89 *> advantage of 2-by-2 block structure during
90 *> matrix-matrix multiplies.
91 *> (If xTRMM is slower than xGEMM, then
92 *> IPARMQ(ISPEC=16)=1 may be more efficient than
93 *> IPARMQ(ISPEC=16)=2 despite the greater level of
94 *> arithmetic work implied by the latter choice.)
95 *> \endverbatim
96 *>
97 *> \param[in] NAME
98 *> \verbatim
99 *> NAME is character string
100 *> Name of the calling subroutine
101 *> \endverbatim
102 *>
103 *> \param[in] OPTS
104 *> \verbatim
105 *> OPTS is character string
106 *> This is a concatenation of the string arguments to
107 *> TTQRE.
108 *> \endverbatim
109 *>
110 *> \param[in] N
111 *> \verbatim
112 *> N is integer scalar
113 *> N is the order of the Hessenberg matrix H.
114 *> \endverbatim
115 *>
116 *> \param[in] ILO
117 *> \verbatim
118 *> ILO is INTEGER
119 *> \endverbatim
120 *>
121 *> \param[in] IHI
122 *> \verbatim
123 *> IHI is INTEGER
124 *> It is assumed that H is already upper triangular
125 *> in rows and columns 1:ILO-1 and IHI+1:N.
126 *> \endverbatim
127 *>
128 *> \param[in] LWORK
129 *> \verbatim
130 *> LWORK is integer scalar
131 *> The amount of workspace available.
132 *> \endverbatim
133 *
134 * Authors:
135 * ========
136 *
137 *> \author Univ. of Tennessee
138 *> \author Univ. of California Berkeley
139 *> \author Univ. of Colorado Denver
140 *> \author NAG Ltd.
141 *
142 *> \date November 2011
143 *
144 *> \ingroup auxOTHERauxiliary
145 *
146 *> \par Further Details:
147 * =====================
148 *>
149 *> \verbatim
150 *>
151 *> Little is known about how best to choose these parameters.
152 *> It is possible to use different values of the parameters
153 *> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
154 *>
155 *> It is probably best to choose different parameters for
156 *> different matrices and different parameters at different
157 *> times during the iteration, but this has not been
158 *> implemented --- yet.
159 *>
160 *>
161 *> The best choices of most of the parameters depend
162 *> in an ill-understood way on the relative execution
163 *> rate of xLAQR3 and xLAQR5 and on the nature of each
164 *> particular eigenvalue problem. Experiment may be the
165 *> only practical way to determine which choices are most
166 *> effective.
167 *>
168 *> Following is a list of default values supplied by IPARMQ.
169 *> These defaults may be adjusted in order to attain better
170 *> performance in any particular computational environment.
171 *>
172 *> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
173 *> Default: 75. (Must be at least 11.)
174 *>
175 *> IPARMQ(ISPEC=13) Recommended deflation window size.
176 *> This depends on ILO, IHI and NS, the
177 *> number of simultaneous shifts returned
178 *> by IPARMQ(ISPEC=15). The default for
179 *> (IHI-ILO+1).LE.500 is NS. The default
180 *> for (IHI-ILO+1).GT.500 is 3*NS/2.
181 *>
182 *> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
183 *>
184 *> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
185 *> a multi-shift QR iteration.
186 *>
187 *> If IHI-ILO+1 is ...
188 *>
189 *> greater than ...but less ... the
190 *> or equal to ... than default is
191 *>
192 *> 0 30 NS = 2+
193 *> 30 60 NS = 4+
194 *> 60 150 NS = 10
195 *> 150 590 NS = **
196 *> 590 3000 NS = 64
197 *> 3000 6000 NS = 128
198 *> 6000 infinity NS = 256
199 *>
200 *> (+) By default matrices of this order are
201 *> passed to the implicit double shift routine
202 *> xLAHQR. See IPARMQ(ISPEC=12) above. These
203 *> values of NS are used only in case of a rare
204 *> xLAHQR failure.
205 *>
206 *> (**) The asterisks (**) indicate an ad-hoc
207 *> function increasing from 10 to 64.
208 *>
209 *> IPARMQ(ISPEC=16) Select structured matrix multiply.
210 *> (See ISPEC=16 above for details.)
211 *> Default: 3.
212 *> \endverbatim
213 *>
214 * =====================================================================
215  INTEGER FUNCTION iparmq( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
216 *
217 * -- LAPACK auxiliary routine (version 3.4.0) --
218 * -- LAPACK is a software package provided by Univ. of Tennessee, --
219 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
220 * November 2011
221 *
222 * .. Scalar Arguments ..
223  INTEGER ihi, ilo, ispec, lwork, n
224  CHARACTER name*( * ), opts*( * )
225 *
226 * ================================================================
227 * .. Parameters ..
228  INTEGER inmin, inwin, inibl, ishfts, iacc22
229  parameter( inmin = 12, inwin = 13, inibl = 14,
230  $ ishfts = 15, iacc22 = 16 )
231  INTEGER nmin, k22min, kacmin, nibble, knwswp
232  parameter( nmin = 75, k22min = 14, kacmin = 14,
233  $ nibble = 14, knwswp = 500 )
234  REAL two
235  parameter( two = 2.0 )
236 * ..
237 * .. Local Scalars ..
238  INTEGER nh, ns
239 * ..
240 * .. Intrinsic Functions ..
241  INTRINSIC log, max, mod, nint, real
242 * ..
243 * .. Executable Statements ..
244  IF( ( ispec.EQ.ishfts ) .OR. ( ispec.EQ.inwin ) .OR.
245  $ ( ispec.EQ.iacc22 ) ) THEN
246 *
247 * ==== Set the number simultaneous shifts ====
248 *
249  nh = ihi - ilo + 1
250  ns = 2
251  IF( nh.GE.30 )
252  $ ns = 4
253  IF( nh.GE.60 )
254  $ ns = 10
255  IF( nh.GE.150 )
256  $ ns = max( 10, nh / nint( log( REAL( NH ) ) / log( two ) ) )
257  IF( nh.GE.590 )
258  $ ns = 64
259  IF( nh.GE.3000 )
260  $ ns = 128
261  IF( nh.GE.6000 )
262  $ ns = 256
263  ns = max( 2, ns-mod( ns, 2 ) )
264  END IF
265 *
266  IF( ispec.EQ.inmin ) THEN
267 *
268 *
269 * ===== Matrices of order smaller than NMIN get sent
270 * . to xLAHQR, the classic double shift algorithm.
271 * . This must be at least 11. ====
272 *
273  iparmq = nmin
274 *
275  ELSE IF( ispec.EQ.inibl ) THEN
276 *
277 * ==== INIBL: skip a multi-shift qr iteration and
278 * . whenever aggressive early deflation finds
279 * . at least (NIBBLE*(window size)/100) deflations. ====
280 *
281  iparmq = nibble
282 *
283  ELSE IF( ispec.EQ.ishfts ) THEN
284 *
285 * ==== NSHFTS: The number of simultaneous shifts =====
286 *
287  iparmq = ns
288 *
289  ELSE IF( ispec.EQ.inwin ) THEN
290 *
291 * ==== NW: deflation window size. ====
292 *
293  IF( nh.LE.knwswp ) THEN
294  iparmq = ns
295  ELSE
296  iparmq = 3*ns / 2
297  END IF
298 *
299  ELSE IF( ispec.EQ.iacc22 ) THEN
300 *
301 * ==== IACC22: Whether to accumulate reflections
302 * . before updating the far-from-diagonal elements
303 * . and whether to use 2-by-2 block structure while
304 * . doing it. A small amount of work could be saved
305 * . by making this choice dependent also upon the
306 * . NH=IHI-ILO+1.
307 *
308  iparmq = 0
309  IF( ns.GE.kacmin )
310  $ iparmq = 1
311  IF( ns.GE.k22min )
312  $ iparmq = 2
313 *
314  ELSE
315 * ===== invalid value of ispec =====
316  iparmq = -1
317 *
318  END IF
319 *
320 * ==== End of IPARMQ ====
321 *
322  END