 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ iparmq()

 integer function iparmq ( integer ISPEC, character, dimension( * ) NAME, character, dimension( * ) OPTS, integer N, integer ILO, integer IHI, integer LWORK )

IPARMQ

Purpose:
```      This program sets problem and machine dependent parameters
useful for xHSEQR and related subroutines for eigenvalue
problems. It is called whenever
IPARMQ is called with 12 <= ISPEC <= 16```
Parameters
 [in] ISPEC ``` ISPEC is INTEGER ISPEC specifies which tunable parameter IPARMQ should return. ISPEC=12: (INMIN) Matrices of order nmin or less are sent directly to xLAHQR, the implicit double shift QR algorithm. NMIN must be at least 11. ISPEC=13: (INWIN) Size of the deflation window. This is best set greater than or equal to the number of simultaneous shifts NS. Larger matrices benefit from larger deflation windows. ISPEC=14: (INIBL) Determines when to stop nibbling and invest in an (expensive) multi-shift QR sweep. If the aggressive early deflation subroutine finds LD converged eigenvalues from an order NW deflation window and LD > (NW*NIBBLE)/100, then the next QR sweep is skipped and early deflation is applied immediately to the remaining active diagonal block. Setting IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a multi-shift QR sweep whenever early deflation finds a converged eigenvalue. Setting IPARMQ(ISPEC=14) greater than or equal to 100 prevents TTQRE from skipping a multi-shift QR sweep. ISPEC=15: (NSHFTS) The number of simultaneous shifts in a multi-shift QR iteration. ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the following meanings. 0: During the multi-shift QR/QZ sweep, blocked eigenvalue reordering, blocked Hessenberg-triangular reduction, reflections and/or rotations are not accumulated when updating the far-from-diagonal matrix entries. 1: During the multi-shift QR/QZ sweep, blocked eigenvalue reordering, blocked Hessenberg-triangular reduction, reflections and/or rotations are accumulated, and matrix-matrix multiplication is used to update the far-from-diagonal matrix entries. 2: During the multi-shift QR/QZ sweep, blocked eigenvalue reordering, blocked Hessenberg-triangular reduction, reflections and/or rotations are accumulated, and 2-by-2 block structure is exploited during matrix-matrix multiplies. (If xTRMM is slower than xGEMM, then IPARMQ(ISPEC=16)=1 may be more efficient than IPARMQ(ISPEC=16)=2 despite the greater level of arithmetic work implied by the latter choice.) ISPEC=17: (ICOST) An estimate of the relative cost of flops within the near-the-diagonal shift chase compared to flops within the BLAS calls of a QZ sweep.``` [in] NAME ``` NAME is CHARACTER string Name of the calling subroutine``` [in] OPTS ``` OPTS is CHARACTER string This is a concatenation of the string arguments to TTQRE.``` [in] N ``` N is INTEGER N is the order of the Hessenberg matrix H.``` [in] ILO ` ILO is INTEGER` [in] IHI ``` IHI is INTEGER It is assumed that H is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N.``` [in] LWORK ``` LWORK is INTEGER The amount of workspace available.```
Further Details:
```       Little is known about how best to choose these parameters.
It is possible to use different values of the parameters
for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.

It is probably best to choose different parameters for
different matrices and different parameters at different
times during the iteration, but this has not been
implemented --- yet.

The best choices of most of the parameters depend
in an ill-understood way on the relative execution
rate of xLAQR3 and xLAQR5 and on the nature of each
particular eigenvalue problem.  Experiment may be the
only practical way to determine which choices are most
effective.

Following is a list of default values supplied by IPARMQ.
These defaults may be adjusted in order to attain better
performance in any particular computational environment.

IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
Default: 75. (Must be at least 11.)

IPARMQ(ISPEC=13) Recommended deflation window size.
This depends on ILO, IHI and NS, the
number of simultaneous shifts returned
by IPARMQ(ISPEC=15).  The default for
(IHI-ILO+1) <= 500 is NS.  The default
for (IHI-ILO+1) > 500 is 3*NS/2.

IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14.

IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
a multi-shift QR iteration.

If IHI-ILO+1 is ...

greater than      ...but less    ... the
or equal to ...      than        default is

0               30       NS =   2+
30               60       NS =   4+
60              150       NS =  10
150              590       NS =  **
590             3000       NS =  64
3000             6000       NS = 128
6000             infinity   NS = 256

(+)  By default matrices of this order are
passed to the implicit double shift routine
xLAHQR.  See IPARMQ(ISPEC=12) above.   These
values of NS are used only in case of a rare
xLAHQR failure.

(**) The asterisks (**) indicate an ad-hoc
function increasing from 10 to 64.

IPARMQ(ISPEC=16) Select structured matrix multiply.
(See ISPEC=16 above for details.)
Default: 3.

IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection.
Expressed as a percentage.
Default: 10.```

Definition at line 229 of file iparmq.f.

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
396*
397 iparmq = rcost
398 ELSE
399* ===== invalid value of ispec =====
400 iparmq = -1
401*
402 END IF
403*
404* ==== End of IPARMQ ====
405*
integer function iparmq(ISPEC, NAME, OPTS, N, ILO, IHI, LWORK)
IPARMQ
Definition: iparmq.f:230
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