LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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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 related subroutines for eigenvalue
35*> problems. It is called whenever
36*> IPARMQ is called with 12 <= ISPEC <= 16
37*> \endverbatim
38*
39* Arguments:
40* ==========
41*
42*> \param[in] ISPEC
43*> \verbatim
44*> ISPEC is INTEGER
45*> ISPEC specifies which tunable parameter IPARMQ should
46*> return.
47*>
48*> ISPEC=12: (INMIN) Matrices of order nmin or less
49*> are sent directly to xLAHQR, the implicit
50*> double shift QR algorithm. NMIN must be
51*> at least 11.
52*>
53*> ISPEC=13: (INWIN) Size of the deflation window.
54*> This is best set greater than or equal to
55*> the number of simultaneous shifts NS.
56*> Larger matrices benefit from larger deflation
57*> windows.
58*>
59*> ISPEC=14: (INIBL) Determines when to stop nibbling and
60*> invest in an (expensive) multi-shift QR sweep.
61*> If the aggressive early deflation subroutine
62*> finds LD converged eigenvalues from an order
63*> NW deflation window and LD > (NW*NIBBLE)/100,
64*> then the next QR sweep is skipped and early
65*> deflation is applied immediately to the
66*> remaining active diagonal block. Setting
67*> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
68*> multi-shift QR sweep whenever early deflation
69*> finds a converged eigenvalue. Setting
70*> IPARMQ(ISPEC=14) greater than or equal to 100
71*> prevents TTQRE from skipping a multi-shift
72*> QR sweep.
73*>
74*> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
75*> a multi-shift QR iteration.
76*>
77*> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
78*> following meanings.
79*> 0: During the multi-shift QR/QZ sweep,
80*> blocked eigenvalue reordering, blocked
81*> Hessenberg-triangular reduction,
82*> reflections and/or rotations are not
83*> accumulated when updating the
84*> far-from-diagonal matrix entries.
85*> 1: During the multi-shift QR/QZ sweep,
86*> blocked eigenvalue reordering, blocked
87*> Hessenberg-triangular reduction,
88*> reflections and/or rotations are
89*> accumulated, and matrix-matrix
90*> multiplication is used to update the
91*> far-from-diagonal matrix entries.
92*> 2: During the multi-shift QR/QZ sweep,
93*> blocked eigenvalue reordering, blocked
94*> Hessenberg-triangular reduction,
95*> reflections and/or rotations are
96*> accumulated, and 2-by-2 block structure
97*> is exploited during matrix-matrix
98*> multiplies.
99*> (If xTRMM is slower than xGEMM, then
100*> IPARMQ(ISPEC=16)=1 may be more efficient than
101*> IPARMQ(ISPEC=16)=2 despite the greater level of
102*> arithmetic work implied by the latter choice.)
103*>
104*> ISPEC=17: (ICOST) An estimate of the relative cost of flops
105*> within the near-the-diagonal shift chase compared
106*> to flops within the BLAS calls of a QZ sweep.
107*> \endverbatim
108*>
109*> \param[in] NAME
110*> \verbatim
111*> NAME is CHARACTER string
112*> Name of the calling subroutine
113*> \endverbatim
114*>
115*> \param[in] OPTS
116*> \verbatim
117*> OPTS is CHARACTER string
118*> This is a concatenation of the string arguments to
119*> TTQRE.
120*> \endverbatim
121*>
122*> \param[in] N
123*> \verbatim
124*> N is INTEGER
125*> N is the order of the Hessenberg matrix H.
126*> \endverbatim
127*>
128*> \param[in] ILO
129*> \verbatim
130*> ILO is INTEGER
131*> \endverbatim
132*>
133*> \param[in] IHI
134*> \verbatim
135*> IHI is INTEGER
136*> It is assumed that H is already upper triangular
137*> in rows and columns 1:ILO-1 and IHI+1:N.
138*> \endverbatim
139*>
140*> \param[in] LWORK
141*> \verbatim
142*> LWORK is INTEGER
143*> The amount of workspace available.
144*> \endverbatim
145*
146* Authors:
147* ========
148*
149*> \author Univ. of Tennessee
150*> \author Univ. of California Berkeley
151*> \author Univ. of Colorado Denver
152*> \author NAG Ltd.
153*
154*> \ingroup iparmq
155*
156*> \par Further Details:
157* =====================
158*>
159*> \verbatim
160*>
161*> Little is known about how best to choose these parameters.
162*> It is possible to use different values of the parameters
163*> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
164*>
165*> It is probably best to choose different parameters for
166*> different matrices and different parameters at different
167*> times during the iteration, but this has not been
168*> implemented --- yet.
169*>
170*>
171*> The best choices of most of the parameters depend
172*> in an ill-understood way on the relative execution
173*> rate of xLAQR3 and xLAQR5 and on the nature of each
174*> particular eigenvalue problem. Experiment may be the
175*> only practical way to determine which choices are most
176*> effective.
177*>
178*> Following is a list of default values supplied by IPARMQ.
179*> These defaults may be adjusted in order to attain better
180*> performance in any particular computational environment.
181*>
182*> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
183*> Default: 75. (Must be at least 11.)
184*>
185*> IPARMQ(ISPEC=13) Recommended deflation window size.
186*> This depends on ILO, IHI and NS, the
187*> number of simultaneous shifts returned
188*> by IPARMQ(ISPEC=15). The default for
189*> (IHI-ILO+1) <= 500 is NS. The default
190*> for (IHI-ILO+1) > 500 is 3*NS/2.
191*>
192*> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
193*>
194*> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
195*> a multi-shift QR iteration.
196*>
197*> If IHI-ILO+1 is ...
198*>
199*> greater than ...but less ... the
200*> or equal to ... than default is
201*>
202*> 0 30 NS = 2+
203*> 30 60 NS = 4+
204*> 60 150 NS = 10
205*> 150 590 NS = **
206*> 590 3000 NS = 64
207*> 3000 6000 NS = 128
208*> 6000 infinity NS = 256
209*>
210*> (+) By default matrices of this order are
211*> passed to the implicit double shift routine
212*> xLAHQR. See IPARMQ(ISPEC=12) above. These
213*> values of NS are used only in case of a rare
214*> xLAHQR failure.
215*>
216*> (**) The asterisks (**) indicate an ad-hoc
217*> function increasing from 10 to 64.
218*>
219*> IPARMQ(ISPEC=16) Select structured matrix multiply.
220*> (See ISPEC=16 above for details.)
221*> Default: 3.
222*>
223*> IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection.
224*> Expressed as a percentage.
225*> Default: 10.
226*> \endverbatim
227*>
228* =====================================================================
229 INTEGER FUNCTION iparmq( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
230*
231* -- LAPACK auxiliary routine --
232* -- LAPACK is a software package provided by Univ. of Tennessee, --
233* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
234*
235* .. Scalar Arguments ..
236 INTEGER ihi, ilo, ispec, lwork, n
237 CHARACTER name*( * ), opts*( * )
238*
239* ================================================================
240* .. Parameters ..
241 INTEGER inmin, inwin, inibl, ishfts, iacc22, icost
242 parameter( inmin = 12, inwin = 13, inibl = 14,
243 $ ishfts = 15, iacc22 = 16, icost = 17 )
244 INTEGER nmin, k22min, kacmin, nibble, knwswp, rcost
245 parameter( nmin = 75, k22min = 14, kacmin = 14,
246 $ nibble = 14, knwswp = 500, rcost = 10 )
247 REAL two
248 parameter( two = 2.0 )
249* ..
250* .. Local Scalars ..
251 INTEGER nh, ns
252 INTEGER i, ic, iz
253 CHARACTER subnam*6
254* ..
255* .. Intrinsic Functions ..
256 INTRINSIC log, max, mod, nint, real
257* ..
258* .. Executable Statements ..
259 IF( ( ispec.EQ.ishfts ) .OR. ( ispec.EQ.inwin ) .OR.
260 $ ( ispec.EQ.iacc22 ) ) THEN
261*
262* ==== Set the number simultaneous shifts ====
263*
264 nh = ihi - ilo + 1
265 ns = 2
266 IF( nh.GE.30 )
267 $ ns = 4
268 IF( nh.GE.60 )
269 $ ns = 10
270 IF( nh.GE.150 )
271 $ ns = max( 10, nh / nint( log( real( nh ) ) / log( two ) ) )
272 IF( nh.GE.590 )
273 $ ns = 64
274 IF( nh.GE.3000 )
275 $ ns = 128
276 IF( nh.GE.6000 )
277 $ ns = 256
278 ns = max( 2, ns-mod( ns, 2 ) )
279 END IF
280*
281 IF( ispec.EQ.inmin ) THEN
282*
283*
284* ===== Matrices of order smaller than NMIN get sent
285* . to xLAHQR, the classic double shift algorithm.
286* . This must be at least 11. ====
287*
288 iparmq = nmin
289*
290 ELSE IF( ispec.EQ.inibl ) THEN
291*
292* ==== INIBL: skip a multi-shift qr iteration and
293* . whenever aggressive early deflation finds
294* . at least (NIBBLE*(window size)/100) deflations. ====
295*
296 iparmq = nibble
297*
298 ELSE IF( ispec.EQ.ishfts ) THEN
299*
300* ==== NSHFTS: The number of simultaneous shifts =====
301*
302 iparmq = ns
303*
304 ELSE IF( ispec.EQ.inwin ) THEN
305*
306* ==== NW: deflation window size. ====
307*
308 IF( nh.LE.knwswp ) THEN
309 iparmq = ns
310 ELSE
311 iparmq = 3*ns / 2
312 END IF
313*
314 ELSE IF( ispec.EQ.iacc22 ) THEN
315*
316* ==== IACC22: Whether to accumulate reflections
317* . before updating the far-from-diagonal elements
318* . and whether to use 2-by-2 block structure while
319* . doing it. A small amount of work could be saved
320* . by making this choice dependent also upon the
321* . NH=IHI-ILO+1.
322*
323*
324* Convert NAME to upper case if the first character is lower case.
325*
326 iparmq = 0
327 subnam = name
328 ic = ichar( subnam( 1: 1 ) )
329 iz = ichar( 'Z' )
330 IF( iz.EQ.90 .OR. iz.EQ.122 ) THEN
331*
332* ASCII character set
333*
334 IF( ic.GE.97 .AND. ic.LE.122 ) THEN
335 subnam( 1: 1 ) = char( ic-32 )
336 DO i = 2, 6
337 ic = ichar( subnam( i: i ) )
338 IF( ic.GE.97 .AND. ic.LE.122 )
339 $ subnam( i: i ) = char( ic-32 )
340 END DO
341 END IF
342*
343 ELSE IF( iz.EQ.233 .OR. iz.EQ.169 ) THEN
344*
345* EBCDIC character set
346*
347 IF( ( ic.GE.129 .AND. ic.LE.137 ) .OR.
348 $ ( ic.GE.145 .AND. ic.LE.153 ) .OR.
349 $ ( ic.GE.162 .AND. ic.LE.169 ) ) THEN
350 subnam( 1: 1 ) = char( ic+64 )
351 DO i = 2, 6
352 ic = ichar( subnam( i: i ) )
353 IF( ( ic.GE.129 .AND. ic.LE.137 ) .OR.
354 $ ( ic.GE.145 .AND. ic.LE.153 ) .OR.
355 $ ( ic.GE.162 .AND. ic.LE.169 ) )subnam( i:
356 $ i ) = char( ic+64 )
357 END DO
358 END IF
359*
360 ELSE IF( iz.EQ.218 .OR. iz.EQ.250 ) THEN
361*
362* Prime machines: ASCII+128
363*
364 IF( ic.GE.225 .AND. ic.LE.250 ) THEN
365 subnam( 1: 1 ) = char( ic-32 )
366 DO i = 2, 6
367 ic = ichar( subnam( i: i ) )
368 IF( ic.GE.225 .AND. ic.LE.250 )
369 $ subnam( i: i ) = char( ic-32 )
370 END DO
371 END IF
372 END IF
373*
374 IF( subnam( 2:6 ).EQ.'GGHRD' .OR.
375 $ subnam( 2:6 ).EQ.'GGHD3' ) THEN
376 iparmq = 1
377 IF( nh.GE.k22min )
378 $ iparmq = 2
379 ELSE IF ( subnam( 4:6 ).EQ.'EXC' ) THEN
380 IF( nh.GE.kacmin )
381 $ iparmq = 1
382 IF( nh.GE.k22min )
383 $ iparmq = 2
384 ELSE IF ( subnam( 2:6 ).EQ.'HSEQR' .OR.
385 $ subnam( 2:5 ).EQ.'LAQR' ) THEN
386 IF( ns.GE.kacmin )
387 $ iparmq = 1
388 IF( ns.GE.k22min )
389 $ iparmq = 2
390 END IF
391*
392 ELSE IF( ispec.EQ.icost ) THEN
393*
394* === Relative cost of near-the-diagonal chase vs
395* BLAS updates ===
396*
397 iparmq = rcost
398 ELSE
399* ===== invalid value of ispec =====
400 iparmq = -1
401*
402 END IF
403*
404* ==== End of IPARMQ ====
405*
406 END
iparmq
integer function iparmq(ispec, name, opts, n, ilo, ihi, lwork)
IPARMQ
Definition iparmq.f:230