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 OTHERauxiliary
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
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