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
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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*> \endverbatim
104*>
105*> \param[in] NAME
106*> \verbatim
107*>          NAME is CHARACTER string
108*>               Name of the calling subroutine
109*> \endverbatim
110*>
111*> \param[in] OPTS
112*> \verbatim
113*>          OPTS is CHARACTER string
114*>               This is a concatenation of the string arguments to
115*>               TTQRE.
116*> \endverbatim
117*>
118*> \param[in] N
119*> \verbatim
120*>          N is INTEGER
121*>               N is the order of the Hessenberg matrix H.
122*> \endverbatim
123*>
124*> \param[in] ILO
125*> \verbatim
126*>          ILO is INTEGER
127*> \endverbatim
128*>
129*> \param[in] IHI
130*> \verbatim
131*>          IHI is INTEGER
132*>               It is assumed that H is already upper triangular
133*>               in rows and columns 1:ILO-1 and IHI+1:N.
134*> \endverbatim
135*>
136*> \param[in] LWORK
137*> \verbatim
138*>          LWORK is INTEGER
139*>               The amount of workspace available.
140*> \endverbatim
141*
142*  Authors:
143*  ========
144*
145*> \author Univ. of Tennessee
146*> \author Univ. of California Berkeley
147*> \author Univ. of Colorado Denver
148*> \author NAG Ltd.
149*
150*> \date June 2017
151*
152*> \ingroup OTHERauxiliary
153*
154*> \par Further Details:
155*  =====================
156*>
157*> \verbatim
158*>
159*>       Little is known about how best to choose these parameters.
160*>       It is possible to use different values of the parameters
161*>       for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
162*>
163*>       It is probably best to choose different parameters for
164*>       different matrices and different parameters at different
165*>       times during the iteration, but this has not been
166*>       implemented --- yet.
167*>
168*>
169*>       The best choices of most of the parameters depend
170*>       in an ill-understood way on the relative execution
171*>       rate of xLAQR3 and xLAQR5 and on the nature of each
172*>       particular eigenvalue problem.  Experiment may be the
173*>       only practical way to determine which choices are most
174*>       effective.
175*>
176*>       Following is a list of default values supplied by IPARMQ.
177*>       These defaults may be adjusted in order to attain better
178*>       performance in any particular computational environment.
179*>
180*>       IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
181*>                        Default: 75. (Must be at least 11.)
182*>
183*>       IPARMQ(ISPEC=13) Recommended deflation window size.
184*>                        This depends on ILO, IHI and NS, the
185*>                        number of simultaneous shifts returned
186*>                        by IPARMQ(ISPEC=15).  The default for
187*>                        (IHI-ILO+1) <= 500 is NS.  The default
188*>                        for (IHI-ILO+1) > 500 is 3*NS/2.
189*>
190*>       IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14.
191*>
192*>       IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
193*>                        a multi-shift QR iteration.
194*>
195*>                        If IHI-ILO+1 is ...
196*>
197*>                        greater than      ...but less    ... the
198*>                        or equal to ...      than        default is
199*>
200*>                                0               30       NS =   2+
201*>                               30               60       NS =   4+
202*>                               60              150       NS =  10
203*>                              150              590       NS =  **
204*>                              590             3000       NS =  64
205*>                             3000             6000       NS = 128
206*>                             6000             infinity   NS = 256
207*>
208*>                    (+)  By default matrices of this order are
209*>                         passed to the implicit double shift routine
210*>                         xLAHQR.  See IPARMQ(ISPEC=12) above.   These
211*>                         values of NS are used only in case of a rare
212*>                         xLAHQR failure.
213*>
214*>                    (**) The asterisks (**) indicate an ad-hoc
215*>                         function increasing from 10 to 64.
216*>
217*>       IPARMQ(ISPEC=16) Select structured matrix multiply.
218*>                        (See ISPEC=16 above for details.)
219*>                        Default: 3.
220*> \endverbatim
221*>
222*  =====================================================================
223      INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
224*
225*  -- LAPACK auxiliary routine (version 3.7.1) --
226*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
227*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
228*     June 2017
229*
230*     .. Scalar Arguments ..
231      INTEGER            IHI, ILO, ISPEC, LWORK, N
232      CHARACTER          NAME*( * ), OPTS*( * )
233*
234*  ================================================================
235*     .. Parameters ..
236      INTEGER            INMIN, INWIN, INIBL, ISHFTS, IACC22
237      PARAMETER          ( INMIN = 12, INWIN = 13, INIBL = 14,
238     $                   ISHFTS = 15, IACC22 = 16 )
239      INTEGER            NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
240      PARAMETER          ( NMIN = 75, K22MIN = 14, KACMIN = 14,
241     $                   NIBBLE = 14, KNWSWP = 500 )
242      REAL               TWO
243      PARAMETER          ( TWO = 2.0 )
244*     ..
245*     .. Local Scalars ..
246      INTEGER            NH, NS
247      INTEGER            I, IC, IZ
248      CHARACTER          SUBNAM*6
249*     ..
250*     .. Intrinsic Functions ..
251      INTRINSIC          LOG, MAX, MOD, NINT, REAL
252*     ..
253*     .. Executable Statements ..
254      IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
255     $    ( ISPEC.EQ.IACC22 ) ) THEN
256*
257*        ==== Set the number simultaneous shifts ====
258*
259         NH = IHI - ILO + 1
260         NS = 2
261         IF( NH.GE.30 )
262     $      NS = 4
263         IF( NH.GE.60 )
264     $      NS = 10
265         IF( NH.GE.150 )
266     $      NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
267         IF( NH.GE.590 )
268     $      NS = 64
269         IF( NH.GE.3000 )
270     $      NS = 128
271         IF( NH.GE.6000 )
272     $      NS = 256
273         NS = MAX( 2, NS-MOD( NS, 2 ) )
274      END IF
275*
276      IF( ISPEC.EQ.INMIN ) THEN
277*
278*
279*        ===== Matrices of order smaller than NMIN get sent
280*        .     to xLAHQR, the classic double shift algorithm.
281*        .     This must be at least 11. ====
282*
283         IPARMQ = NMIN
284*
285      ELSE IF( ISPEC.EQ.INIBL ) THEN
286*
287*        ==== INIBL: skip a multi-shift qr iteration and
288*        .    whenever aggressive early deflation finds
289*        .    at least (NIBBLE*(window size)/100) deflations. ====
290*
291         IPARMQ = NIBBLE
292*
293      ELSE IF( ISPEC.EQ.ISHFTS ) THEN
294*
295*        ==== NSHFTS: The number of simultaneous shifts =====
296*
297         IPARMQ = NS
298*
299      ELSE IF( ISPEC.EQ.INWIN ) THEN
300*
301*        ==== NW: deflation window size.  ====
302*
303         IF( NH.LE.KNWSWP ) THEN
304            IPARMQ = NS
305         ELSE
306            IPARMQ = 3*NS / 2
307         END IF
308*
309      ELSE IF( ISPEC.EQ.IACC22 ) THEN
310*
311*        ==== IACC22: Whether to accumulate reflections
312*        .     before updating the far-from-diagonal elements
313*        .     and whether to use 2-by-2 block structure while
314*        .     doing it.  A small amount of work could be saved
315*        .     by making this choice dependent also upon the
316*        .     NH=IHI-ILO+1.
317*
318*
319*        Convert NAME to upper case if the first character is lower case.
320*
321         IPARMQ = 0
322         SUBNAM = NAME
323         IC = ICHAR( SUBNAM( 1: 1 ) )
324         IZ = ICHAR( 'Z' )
325         IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN
326*
327*           ASCII character set
328*
329            IF( IC.GE.97 .AND. IC.LE.122 ) THEN
330               SUBNAM( 1: 1 ) = CHAR( IC-32 )
331               DO I = 2, 6
332                  IC = ICHAR( SUBNAM( I: I ) )
333                  IF( IC.GE.97 .AND. IC.LE.122 )
334     $               SUBNAM( I: I ) = CHAR( IC-32 )
335               END DO
336            END IF
337*
338         ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN
339*
340*           EBCDIC character set
341*
342            IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
343     $          ( IC.GE.145 .AND. IC.LE.153 ) .OR.
344     $          ( IC.GE.162 .AND. IC.LE.169 ) ) THEN
345               SUBNAM( 1: 1 ) = CHAR( IC+64 )
346               DO I = 2, 6
347                  IC = ICHAR( SUBNAM( I: I ) )
348                  IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
349     $                ( IC.GE.145 .AND. IC.LE.153 ) .OR.
350     $                ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I:
351     $                I ) = CHAR( IC+64 )
352               END DO
353            END IF
354*
355         ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN
356*
357*           Prime machines:  ASCII+128
358*
359            IF( IC.GE.225 .AND. IC.LE.250 ) THEN
360               SUBNAM( 1: 1 ) = CHAR( IC-32 )
361               DO I = 2, 6
362                  IC = ICHAR( SUBNAM( I: I ) )
363                  IF( IC.GE.225 .AND. IC.LE.250 )
364     $               SUBNAM( I: I ) = CHAR( IC-32 )
365               END DO
366            END IF
367         END IF
368*
369         IF( SUBNAM( 2:6 ).EQ.'GGHRD' .OR.
370     $       SUBNAM( 2:6 ).EQ.'GGHD3' ) THEN
371            IPARMQ = 1
372            IF( NH.GE.K22MIN )
373     $         IPARMQ = 2
374         ELSE IF ( SUBNAM( 4:6 ).EQ.'EXC' ) THEN
375            IF( NH.GE.KACMIN )
376     $         IPARMQ = 1
377            IF( NH.GE.K22MIN )
378     $         IPARMQ = 2
379         ELSE IF ( SUBNAM( 2:6 ).EQ.'HSEQR' .OR.
380     $             SUBNAM( 2:5 ).EQ.'LAQR' ) THEN
381            IF( NS.GE.KACMIN )
382     $         IPARMQ = 1
383            IF( NS.GE.K22MIN )
384     $         IPARMQ = 2
385         END IF
386*
387      ELSE
388*        ===== invalid value of ispec =====
389         IPARMQ = -1
390*
391      END IF
392*
393*     ==== End of IPARMQ ====
394*
395      END
396