1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id: weight.cc,v 1.9 1998-06-13 14:20:07 Singular Exp $ */ |
---|
5 | |
---|
6 | /* |
---|
7 | * ABSTRACT: |
---|
8 | */ |
---|
9 | |
---|
10 | #include <math.h> |
---|
11 | #include "mod2.h" |
---|
12 | #include "tok.h" |
---|
13 | #include "mmemory.h" |
---|
14 | #include "polys.h" |
---|
15 | #include "intvec.h" |
---|
16 | #include "febase.h" |
---|
17 | #include "ipid.h" |
---|
18 | #include "ipshell.h" |
---|
19 | #include "subexpr.h" |
---|
20 | #include "ideals.h" |
---|
21 | #include "weight.h" |
---|
22 | |
---|
23 | /*0 implementation*/ |
---|
24 | |
---|
25 | pFDegProc pFDegOld; |
---|
26 | pLDegProc pLDegOld; |
---|
27 | #ifdef ALIGN_8 |
---|
28 | #define wDouble(A) ((double *)A) |
---|
29 | #else |
---|
30 | extern "C" double * wDouble(void *adr); |
---|
31 | #endif |
---|
32 | |
---|
33 | #ifndef __MWERKS__ |
---|
34 | extern "C" double (*wFunctional)(int *degw, int *lpol, int npol, |
---|
35 | double *rel, double wx); |
---|
36 | extern "C" double wFunctionalMora(int *degw, int *lpol, int npol, |
---|
37 | double *rel, double wx); |
---|
38 | extern "C" double wFunctionalBuch(int *degw, int *lpol, int npol, |
---|
39 | double *rel, double wx); |
---|
40 | extern "C" void wAdd(int *A, int mons, int kn, int xx); |
---|
41 | extern "C" void wNorm(int *degw, int *lpol, int npol, double *rel); |
---|
42 | extern "C" void wFirstSearch(int *A, int *x, int mons, |
---|
43 | int *lpol, int npol, double *rel, double *fopt); |
---|
44 | extern "C" void wSecondSearch(int *A, int *x, int *lpol, |
---|
45 | int npol, int mons, double *rel, double *fk); |
---|
46 | extern "C" void wGcd(int *x, int n); |
---|
47 | extern double wNsqr; |
---|
48 | #else |
---|
49 | short * ecartWeights=NULL; |
---|
50 | |
---|
51 | double wNsqr; |
---|
52 | double (*wFunctional)(int *degw, int *lpol, int npol, |
---|
53 | double *rel, double wx); |
---|
54 | |
---|
55 | |
---|
56 | static double wFunctionalMora(int *degw, int *lpol, int npol, |
---|
57 | double *rel, double wx) |
---|
58 | { |
---|
59 | int i, j, e1, ecu, ecl, ec; |
---|
60 | int *ex; |
---|
61 | double gfmax, gecart, ghom, pfmax; |
---|
62 | double *r; |
---|
63 | |
---|
64 | ex = degw; |
---|
65 | r = rel; |
---|
66 | gfmax = (double)0.0; |
---|
67 | gecart = (double)0.4 + (double)npol; |
---|
68 | ghom = (double)1.0; |
---|
69 | for (i = 0; i < npol; i++) |
---|
70 | { |
---|
71 | ecl = ecu = e1 = *ex++; |
---|
72 | for (j = lpol[i] - 1; j!=0; j--) |
---|
73 | { |
---|
74 | ec = *ex++; |
---|
75 | if (ec > ecu) |
---|
76 | ecu = ec; |
---|
77 | else if (ec < ecl) |
---|
78 | ecl = ec; |
---|
79 | } |
---|
80 | pfmax = (double)ecl / (double)ecu; |
---|
81 | if (pfmax < ghom) |
---|
82 | ghom = pfmax; |
---|
83 | pfmax = (double)e1 / (double)ecu; |
---|
84 | if (pfmax > (double)0.5) |
---|
85 | gecart -= (pfmax * pfmax); |
---|
86 | else |
---|
87 | gecart -= (double)0.25; |
---|
88 | ecu = 2 * ecu - ecl; |
---|
89 | gfmax += (double)(ecu * ecu) * (*r++); |
---|
90 | } |
---|
91 | if (ghom > (double)0.8) |
---|
92 | { |
---|
93 | ghom *= (double)5.0; |
---|
94 | gecart *= ((double)5.0 - ghom); |
---|
95 | } |
---|
96 | return (gfmax * gecart) / pow(wx, wNsqr); |
---|
97 | } |
---|
98 | |
---|
99 | |
---|
100 | static double wFunctionalBuch(int *degw, int *lpol, int npol, |
---|
101 | double *rel, double wx) |
---|
102 | { |
---|
103 | int i, j, ecl, ecu, ec; |
---|
104 | int *ex; |
---|
105 | double gfmax, ghom, pfmax; |
---|
106 | double *r; |
---|
107 | |
---|
108 | ex = degw; |
---|
109 | r = rel; |
---|
110 | gfmax = (double)0.0; |
---|
111 | ghom = (double)1.0; |
---|
112 | for (i = 0; i < npol; i++) |
---|
113 | { |
---|
114 | ecu = ecl = *ex++; |
---|
115 | for (j = lpol[i] - 1; j!=0; j--) |
---|
116 | { |
---|
117 | ec = *ex++; |
---|
118 | if (ec < ecl) |
---|
119 | ecl = ec; |
---|
120 | else if (ec > ecu) |
---|
121 | ecu = ec; |
---|
122 | } |
---|
123 | pfmax = (double)ecl / (double)ecu; |
---|
124 | if (pfmax < ghom) |
---|
125 | ghom = pfmax; |
---|
126 | gfmax += (double)(ecu * ecu) * (*r++); |
---|
127 | } |
---|
128 | if (ghom > (double)0.5) |
---|
129 | gfmax *= ((double)1.0 - (ghom * ghom)) / (double)0.75; |
---|
130 | return gfmax / pow(wx, wNsqr); |
---|
131 | } |
---|
132 | |
---|
133 | |
---|
134 | static void wSub(int *A, int mons, int kn, int xx) |
---|
135 | { |
---|
136 | int i, *B, *ex; |
---|
137 | |
---|
138 | B = A + ((kn - 1) * mons); |
---|
139 | ex = A + (pVariables * mons); |
---|
140 | if (xx == 1) |
---|
141 | { |
---|
142 | for (i = mons; i!=0; i--) |
---|
143 | *ex++ -= *B++; |
---|
144 | } |
---|
145 | else |
---|
146 | { |
---|
147 | for (i = mons; i!=0; i--) |
---|
148 | *ex++ -= (*B++) * xx; |
---|
149 | } |
---|
150 | } |
---|
151 | |
---|
152 | |
---|
153 | static void wAdd(int *A, int mons, int kn, int xx) |
---|
154 | { |
---|
155 | int i, *B, *ex; |
---|
156 | |
---|
157 | B = A + ((kn - 1) * mons); |
---|
158 | ex = A + (pVariables * mons); |
---|
159 | if (xx == 1) |
---|
160 | { |
---|
161 | for (i = mons; i!=0; i--) |
---|
162 | *ex++ += *B++; |
---|
163 | } |
---|
164 | else |
---|
165 | { |
---|
166 | for (i = mons; i!=0; i--) |
---|
167 | *ex++ += (*B++) * xx; |
---|
168 | } |
---|
169 | } |
---|
170 | |
---|
171 | |
---|
172 | static void wFirstSearch(int *A, int *x, int mons, |
---|
173 | int *lpol, int npol, double *rel, double *fopt) |
---|
174 | { |
---|
175 | int a0, a, n, xn, t, xx, y1; |
---|
176 | int *y, *degw, *xopt; |
---|
177 | double fy, fmax, wx; |
---|
178 | double *pr; |
---|
179 | void *adr; |
---|
180 | |
---|
181 | fy = *fopt; |
---|
182 | n = pVariables; |
---|
183 | xn = n + 6 + (21 / n); |
---|
184 | a0 = n * sizeof(double) + 8; |
---|
185 | a = n * sizeof(int); |
---|
186 | y = (int * )Alloc(a); |
---|
187 | adr = (void * )Alloc(a0); |
---|
188 | pr = wDouble(adr); |
---|
189 | *pr = (double)1.0; |
---|
190 | *y = 0; |
---|
191 | degw = A + (n * mons); |
---|
192 | xopt = x + (n + 2); |
---|
193 | t = 1; |
---|
194 | loop |
---|
195 | { |
---|
196 | while (t < n) |
---|
197 | { |
---|
198 | xx = x[t] + 1; |
---|
199 | wx = pr[t-1] * (double)xx; |
---|
200 | y1 = y[t-1] + xx; |
---|
201 | if ((y1 + n - t) <= xn) |
---|
202 | { |
---|
203 | pr[t] = wx; |
---|
204 | y[t] = y1; |
---|
205 | x[t] = xx; |
---|
206 | if (xx > 1) |
---|
207 | wAdd(A, mons, t, 1); |
---|
208 | t++; |
---|
209 | } |
---|
210 | else |
---|
211 | { |
---|
212 | xx = x[t] - 1; |
---|
213 | x[t] = 0; |
---|
214 | if (xx!=0) |
---|
215 | wSub(A, mons, t, xx); |
---|
216 | t--; |
---|
217 | if (t==0) |
---|
218 | { |
---|
219 | *fopt = fy; |
---|
220 | Free((ADDRESS)y, a); |
---|
221 | Free((ADDRESS)adr, a0); |
---|
222 | return; |
---|
223 | } |
---|
224 | } |
---|
225 | } |
---|
226 | xx = xn - y[t-1]; |
---|
227 | wx = pr[t-1] * (double)xx; |
---|
228 | x[t] = xx; |
---|
229 | xx--; |
---|
230 | if (xx!=0) |
---|
231 | wAdd(A, mons, t, xx); |
---|
232 | fmax = (*wFunctional)(degw, lpol, npol, rel, wx); |
---|
233 | if (xx!=0) |
---|
234 | wSub(A, mons, t, xx); |
---|
235 | if (fmax < fy) |
---|
236 | { |
---|
237 | fy = fmax; |
---|
238 | memcpy(xopt, x + 1, a); |
---|
239 | } |
---|
240 | t--; |
---|
241 | } /* end loop */ |
---|
242 | } |
---|
243 | |
---|
244 | |
---|
245 | static double wPrWeight(int *x, int n) |
---|
246 | { |
---|
247 | int i; |
---|
248 | double y; |
---|
249 | |
---|
250 | y = (double)x[n]; |
---|
251 | for (i = n - 1; i!=0; i--) |
---|
252 | y *= (double)x[i]; |
---|
253 | return y; |
---|
254 | } |
---|
255 | |
---|
256 | |
---|
257 | static void wEstimate(int *A, int *x, int *lpol, int npol, int mons, |
---|
258 | double wx, double *rel, double *fopt, int *s0, int *s1, int *s2) |
---|
259 | { |
---|
260 | int n, i1, i2, k0 = 0, k1 = 0, k2 = 0; |
---|
261 | int *degw; |
---|
262 | double fo1, fo2, fmax, wx1, wx2; |
---|
263 | |
---|
264 | n = pVariables; |
---|
265 | degw = A + (n * mons); |
---|
266 | fo2 = fo1 = (double)1.0e10; |
---|
267 | for (i1 = n; i1!=0; i1--) |
---|
268 | { |
---|
269 | if (x[i1] > 1) |
---|
270 | { |
---|
271 | wSub(A, mons, i1, 1); |
---|
272 | wx1 = wx - wx / (double)x[i1]; |
---|
273 | x[i1]--; |
---|
274 | fmax = (*wFunctional)(degw, lpol, npol, rel, wx1); |
---|
275 | if (fmax < fo1) |
---|
276 | { |
---|
277 | fo1 = fmax; |
---|
278 | k0 = i1; |
---|
279 | } |
---|
280 | for (i2 = i1; i2!=0; i2--) |
---|
281 | { |
---|
282 | if (x[i2] > 1) |
---|
283 | { |
---|
284 | wSub(A, mons, i2, 1); |
---|
285 | wx2 = wx1 - wx1 / (double)x[i2]; |
---|
286 | fmax = (*wFunctional)(degw, lpol, npol, rel, wx2); |
---|
287 | if (fmax < fo2) |
---|
288 | { |
---|
289 | fo2 = fmax; |
---|
290 | k1 = i1; |
---|
291 | k2 = i2; |
---|
292 | } |
---|
293 | wAdd(A, mons, i2, 1); |
---|
294 | } |
---|
295 | } |
---|
296 | wAdd(A, mons, i1, 1); |
---|
297 | x[i1]++; |
---|
298 | } |
---|
299 | } |
---|
300 | if (fo1 < fo2) |
---|
301 | { |
---|
302 | *fopt = fo1; |
---|
303 | *s0 = k0; |
---|
304 | } |
---|
305 | else |
---|
306 | { |
---|
307 | *fopt = fo2; |
---|
308 | *s0 = 0; |
---|
309 | } |
---|
310 | *s1 = k1; |
---|
311 | *s2 = k2; |
---|
312 | } |
---|
313 | |
---|
314 | |
---|
315 | static void wSecondSearch(int *A, int *x, int *lpol, |
---|
316 | int npol, int mons, double *rel, double *fk) |
---|
317 | { |
---|
318 | int n, s0, s1, s2, *xopt; |
---|
319 | double one, fx, fopt, wx; |
---|
320 | |
---|
321 | n = pVariables; |
---|
322 | xopt = x + (n + 2); |
---|
323 | fopt = *fk * (double)0.999999999999; |
---|
324 | wx = wPrWeight(x, n); |
---|
325 | one = (double)1.0; |
---|
326 | loop |
---|
327 | { |
---|
328 | wEstimate(A, x, lpol, npol, mons, wx, rel, &fx, &s0, &s1, &s2); |
---|
329 | if (fx > fopt) |
---|
330 | { |
---|
331 | if (s0!=0) |
---|
332 | x[s0]--; |
---|
333 | else if (s1!=0) |
---|
334 | { |
---|
335 | x[s1]--; |
---|
336 | x[s2]--; |
---|
337 | } |
---|
338 | else |
---|
339 | break; |
---|
340 | } |
---|
341 | else |
---|
342 | { |
---|
343 | fopt = fx; |
---|
344 | if (s0!=0) |
---|
345 | { |
---|
346 | x[s0]--; |
---|
347 | memcpy(xopt, x + 1, n * sizeof(int)); |
---|
348 | if (s1==0) |
---|
349 | break; |
---|
350 | } |
---|
351 | else if (s1!=0) |
---|
352 | { |
---|
353 | x[s1]--; |
---|
354 | x[s2]--; |
---|
355 | memcpy(xopt, x + 1, n * sizeof(int)); |
---|
356 | } |
---|
357 | else |
---|
358 | break; |
---|
359 | } |
---|
360 | if (s0!=0) |
---|
361 | wSub(A, mons, s0, 1); |
---|
362 | else |
---|
363 | { |
---|
364 | wSub(A, mons, s1, 1); |
---|
365 | wSub(A, mons, s2, 1); |
---|
366 | } |
---|
367 | wx = wPrWeight(x, n); |
---|
368 | } |
---|
369 | *fk = fopt; |
---|
370 | } |
---|
371 | |
---|
372 | |
---|
373 | static void wGcd(int *x, int n) |
---|
374 | { |
---|
375 | int i, b, a, h; |
---|
376 | |
---|
377 | i = n; |
---|
378 | b = x[i]; |
---|
379 | loop |
---|
380 | { |
---|
381 | i--; |
---|
382 | if (i==0) |
---|
383 | break; |
---|
384 | a = x[i]; |
---|
385 | if (a < b) |
---|
386 | { |
---|
387 | h = a; |
---|
388 | a = b; |
---|
389 | b = h; |
---|
390 | } |
---|
391 | do |
---|
392 | { |
---|
393 | h = a % b; |
---|
394 | a = b; |
---|
395 | b = h; |
---|
396 | } |
---|
397 | while (b!=0); |
---|
398 | b = a; |
---|
399 | if (b == 1) |
---|
400 | return; |
---|
401 | } |
---|
402 | for (i = n; i; i--) |
---|
403 | x[i] /= b; |
---|
404 | } |
---|
405 | |
---|
406 | |
---|
407 | static void wSimple(int *x, int n) |
---|
408 | { |
---|
409 | int g, min, c, d, f, kopt, k, i; |
---|
410 | int *xopt; |
---|
411 | double sopt, s1, s2; |
---|
412 | |
---|
413 | xopt = x + (n + 1); |
---|
414 | kopt = k = g = 0; |
---|
415 | min = 1000000; |
---|
416 | for (i = n; i!=0; i--) |
---|
417 | { |
---|
418 | c = xopt[i]; |
---|
419 | if (c > 1) |
---|
420 | { |
---|
421 | if (c < min) |
---|
422 | min = c; |
---|
423 | if (c > k) |
---|
424 | k = c; |
---|
425 | } |
---|
426 | else |
---|
427 | g = 1; |
---|
428 | } |
---|
429 | k -= min; |
---|
430 | if ((g==0) && (k < 4)) |
---|
431 | return; |
---|
432 | if (k < min) |
---|
433 | min = k+1; |
---|
434 | sopt = (double)1.0e10; |
---|
435 | for (k = min; k > 1; k--) |
---|
436 | { |
---|
437 | s2 = s1 = (double)0.0; |
---|
438 | for(i = n; i!=0; i--) |
---|
439 | { |
---|
440 | c = xopt[i]; |
---|
441 | if (c > 1) |
---|
442 | { |
---|
443 | d = c / k; |
---|
444 | d *= k; |
---|
445 | f = d = c - d; |
---|
446 | if (f!=0) |
---|
447 | { |
---|
448 | f = k - f; |
---|
449 | if (f < d) |
---|
450 | s2 += (double)f / (double)c; |
---|
451 | else |
---|
452 | s1 += (double)d / (double)c; |
---|
453 | } |
---|
454 | } |
---|
455 | } |
---|
456 | s1 += s2 + sqrt(s1 * s2); |
---|
457 | s1 -= (double)0.01 * sqrt((double)k); |
---|
458 | if (s1 < sopt) |
---|
459 | { |
---|
460 | sopt = s1; |
---|
461 | kopt = k; |
---|
462 | } |
---|
463 | } |
---|
464 | for(i = n; i!=0; i--) |
---|
465 | { |
---|
466 | x[i] = 1; |
---|
467 | c = xopt[i]; |
---|
468 | if (c > 1) |
---|
469 | { |
---|
470 | d = c / kopt; |
---|
471 | d *= kopt; |
---|
472 | x[i] = d; |
---|
473 | d = c - d; |
---|
474 | if ((d!=0) && (kopt < 2 * d)) |
---|
475 | x[i] += kopt; |
---|
476 | } |
---|
477 | } |
---|
478 | if (g==0) |
---|
479 | wGcd(x, n); |
---|
480 | } |
---|
481 | |
---|
482 | |
---|
483 | static void wNorm(int *degw, int *lpol, int npol, double *rel) |
---|
484 | { |
---|
485 | int i, j, ecu, ec; |
---|
486 | int *ex; |
---|
487 | double *r; |
---|
488 | |
---|
489 | ex = degw; |
---|
490 | r = rel; |
---|
491 | for (i = 0; i < npol; i++) |
---|
492 | { |
---|
493 | ecu = *ex++; |
---|
494 | for (j = lpol[i] - 1; j!=0; j--) |
---|
495 | { |
---|
496 | ec = *ex++; |
---|
497 | if (ec > ecu) |
---|
498 | ecu = ec; |
---|
499 | } |
---|
500 | *r = (double)1.0 / (double)(ecu * ecu); |
---|
501 | r++; |
---|
502 | } |
---|
503 | } |
---|
504 | #endif /* __MWERKS */ |
---|
505 | |
---|
506 | |
---|
507 | static void wDimensions(polyset s, int sl, int *lpol, int *npol, int *mons) |
---|
508 | { |
---|
509 | int i, i1, j, k; |
---|
510 | poly p, q; |
---|
511 | |
---|
512 | i1 = j = 0; |
---|
513 | for (i = 0; i <= sl; i++) |
---|
514 | { |
---|
515 | p = s[i]; |
---|
516 | if (p!=NULL) |
---|
517 | { |
---|
518 | k = 1; |
---|
519 | q = pNext(p); |
---|
520 | while (q!=NULL) |
---|
521 | { |
---|
522 | k++; |
---|
523 | q = pNext(q); |
---|
524 | } |
---|
525 | if (k > 1) |
---|
526 | { |
---|
527 | lpol[i1++] = k; |
---|
528 | j += k; |
---|
529 | } |
---|
530 | } |
---|
531 | } |
---|
532 | *npol = i1; |
---|
533 | *mons = j; |
---|
534 | } |
---|
535 | |
---|
536 | |
---|
537 | static void wInit(polyset s, int sl, int mons, int *A) |
---|
538 | { |
---|
539 | int n, a, i, j, *B, *C; |
---|
540 | poly p, q; |
---|
541 | Exponent_t *pl; |
---|
542 | |
---|
543 | B = A; |
---|
544 | n = pVariables; |
---|
545 | a = (n + 1) * sizeof(Exponent_t); |
---|
546 | pl = (Exponent_t * )Alloc(a); |
---|
547 | for (i = 0; i <= sl; i++) |
---|
548 | { |
---|
549 | p = s[i]; |
---|
550 | if (p!=NULL) |
---|
551 | { |
---|
552 | q = pNext(p); |
---|
553 | if (q!=NULL) |
---|
554 | { |
---|
555 | C = B; |
---|
556 | B++; |
---|
557 | pGetExpV(p, pl); |
---|
558 | for (j = 0; j < n; j++) |
---|
559 | { |
---|
560 | *C = pl[j+1]; |
---|
561 | C += mons; |
---|
562 | } |
---|
563 | } |
---|
564 | while (q!=NULL) |
---|
565 | { |
---|
566 | C = B; |
---|
567 | B++; |
---|
568 | pGetExpV(q, pl); |
---|
569 | for (j = 0; j < n; j++) |
---|
570 | { |
---|
571 | *C = pl[j+1]; |
---|
572 | C += mons; |
---|
573 | } |
---|
574 | pIter(q); |
---|
575 | } |
---|
576 | } |
---|
577 | } |
---|
578 | Free((ADDRESS)pl, a); |
---|
579 | } |
---|
580 | |
---|
581 | static void wCall(polyset s, int sl, int *x) |
---|
582 | { |
---|
583 | int n, q, npol, mons, i; |
---|
584 | int *A, *xopt, *lpol, *degw; |
---|
585 | double f1, fx, eps, *rel; |
---|
586 | void *adr; |
---|
587 | |
---|
588 | n = pVariables; |
---|
589 | lpol = (int * )Alloc((sl + 1) * sizeof(int)); |
---|
590 | wDimensions(s, sl, lpol, &npol, &mons); |
---|
591 | xopt = x + (n + 1); |
---|
592 | for (i = n; i!=0; i--) |
---|
593 | xopt[i] = 1; |
---|
594 | if (mons==0) |
---|
595 | { |
---|
596 | Free((ADDRESS)lpol, (sl + 1) * sizeof(int)); |
---|
597 | return; |
---|
598 | } |
---|
599 | adr = (void * )Alloc(npol * sizeof(double) + 8); |
---|
600 | rel = wDouble(adr); |
---|
601 | q = (n + 1) * mons * sizeof(int); |
---|
602 | A = (int * )Alloc(q); |
---|
603 | wInit(s, sl, mons, A); |
---|
604 | degw = A + (n * mons); |
---|
605 | memset(degw, 0, mons * sizeof(int)); |
---|
606 | for (i = n; i!=0; i--) |
---|
607 | wAdd(A, mons, i, 1); |
---|
608 | wNorm(degw, lpol, npol, rel); |
---|
609 | f1 = (*wFunctional)(degw, lpol, npol, rel, (double)1.0); |
---|
610 | if (TEST_OPT_PROT) Print("// %e\n",f1); |
---|
611 | eps = f1; |
---|
612 | fx = (double)2.0 * eps; |
---|
613 | memset(x, 0, (n + 1) * sizeof(int)); |
---|
614 | wFirstSearch(A, x, mons, lpol, npol, rel, &fx); |
---|
615 | if (TEST_OPT_PROT) Print("// %e\n",fx); |
---|
616 | memcpy(x + 1, xopt + 1, n * sizeof(int)); |
---|
617 | memset(degw, 0, mons * sizeof(int)); |
---|
618 | for (i = n; i!=0; i--) |
---|
619 | { |
---|
620 | x[i] *= 16; |
---|
621 | wAdd(A, mons, i, x[i]); |
---|
622 | } |
---|
623 | wSecondSearch(A, x, lpol, npol, mons, rel, &fx); |
---|
624 | if (TEST_OPT_PROT) Print("// %e\n",fx); |
---|
625 | if (fx >= eps) |
---|
626 | { |
---|
627 | for (i = n; i!=0; i--) |
---|
628 | xopt[i] = 1; |
---|
629 | } |
---|
630 | else |
---|
631 | { |
---|
632 | wGcd(xopt, n); |
---|
633 | // if (BTEST1(22)) |
---|
634 | // { |
---|
635 | // f1 = fx + (double)0.1 * (f1 - fx); |
---|
636 | // wSimple(x, n); |
---|
637 | // memset(degw, 0, mons * sizeof(int)); |
---|
638 | // for (i = n; i!=0; i--) |
---|
639 | // wAdd(A, mons, i, x[i]); |
---|
640 | // eps = wPrWeight(x, n); |
---|
641 | // fx = (*wFunctional)(degw, lpol, npol, rel, eps); |
---|
642 | // if (fx < f1) |
---|
643 | // { |
---|
644 | // if (TEST_OPT_PROT) Print("// %e\n",fx); |
---|
645 | // memcpy(xopt + 1, x + 1, n * sizeof(int)); |
---|
646 | // } |
---|
647 | // } |
---|
648 | } |
---|
649 | Free((ADDRESS)A, q); |
---|
650 | Free((ADDRESS)lpol, (sl + 1) * sizeof(int)); |
---|
651 | Free((ADDRESS)adr, npol * sizeof(double) + 8); |
---|
652 | } |
---|
653 | |
---|
654 | |
---|
655 | void kEcartWeights(polyset s, int sl, short *eweight) |
---|
656 | { |
---|
657 | int n, i; |
---|
658 | int *x; |
---|
659 | |
---|
660 | *eweight = 0; |
---|
661 | n = pVariables; |
---|
662 | wNsqr = (double)2.0 / (double)n; |
---|
663 | if (pOrdSgn == -1) |
---|
664 | wFunctional = wFunctionalMora; |
---|
665 | else |
---|
666 | wFunctional = wFunctionalBuch; |
---|
667 | x = (int * )Alloc(2 * (n + 1) * sizeof(int)); |
---|
668 | wCall(s, sl, x); |
---|
669 | for (i = n; i!=0; i--) |
---|
670 | eweight[i] = x[i + n + 1]; |
---|
671 | Free((ADDRESS)x, 2 * (n + 1) * sizeof(int)); |
---|
672 | } |
---|
673 | |
---|
674 | |
---|
675 | BOOLEAN kWeight(leftv res,leftv id) |
---|
676 | { |
---|
677 | ideal F=(ideal)id->Data(); |
---|
678 | intvec * iv = new intvec(pVariables); |
---|
679 | polyset s; |
---|
680 | int sl, n, i; |
---|
681 | int *x; |
---|
682 | |
---|
683 | res->data=(char *)iv; |
---|
684 | s = F->m; |
---|
685 | sl = IDELEMS(F) - 1; |
---|
686 | n = pVariables; |
---|
687 | wNsqr = (double)2.0 / (double)n; |
---|
688 | wFunctional = wFunctionalBuch; |
---|
689 | x = (int * )Alloc(2 * (n + 1) * sizeof(int)); |
---|
690 | wCall(s, sl, x); |
---|
691 | for (i = n; i!=0; i--) |
---|
692 | (*iv)[i-1] = x[i + n + 1]; |
---|
693 | Free((ADDRESS)x, 2 * (n + 1) * sizeof(int)); |
---|
694 | return FALSE; |
---|
695 | } |
---|
696 | |
---|
697 | BOOLEAN kQHWeight(leftv res,leftv v) |
---|
698 | { |
---|
699 | res->data=(char *)idQHomWeights((ideal)v->Data()); |
---|
700 | if (res->data==NULL) |
---|
701 | res->data=(char *)new intvec(pVariables); |
---|
702 | return FALSE; |
---|
703 | } |
---|
704 | |
---|
705 | short * iv2array(intvec * iv) |
---|
706 | { |
---|
707 | short *s=(short *)Alloc((pVariables+1)*sizeof(short)); |
---|
708 | int len=iv->length(); |
---|
709 | int i; |
---|
710 | |
---|
711 | for (i=pVariables;i>len;i--) |
---|
712 | s[i]= 1; |
---|
713 | for (;i>0;i--) |
---|
714 | s[i]= (*iv)[i-1]; |
---|
715 | return s; |
---|
716 | } |
---|
717 | |
---|
718 | /*2 |
---|
719 | *computes the degree of the leading term of the polynomial |
---|
720 | *with respect to given ecartWeights |
---|
721 | *used for Graebes method if BTEST1(31) is set |
---|
722 | */ |
---|
723 | int totaldegreeWecart(poly p) |
---|
724 | { |
---|
725 | int i; |
---|
726 | int j =0; |
---|
727 | |
---|
728 | for (i=pVariables; i; i--) |
---|
729 | j += (int)(pGetExp(p,i) * ecartWeights[i]); |
---|
730 | return j; |
---|
731 | } |
---|
732 | |
---|
733 | /*2 |
---|
734 | *computes the maximal degree of all terms of the polynomial |
---|
735 | *with respect to given ecartWeights and |
---|
736 | *computes the length of the polynomial |
---|
737 | *used for Graebes method if BTEST1(31) is set |
---|
738 | */ |
---|
739 | int maxdegreeWecart(poly p,int *l) |
---|
740 | { |
---|
741 | short k=pGetComp(p); |
---|
742 | int ll=1; |
---|
743 | int t,max; |
---|
744 | |
---|
745 | max=totaldegreeWecart(p); |
---|
746 | pIter(p); |
---|
747 | while ((p!=NULL) && (pGetComp(p)==k)) |
---|
748 | { |
---|
749 | t=totaldegreeWecart(p); |
---|
750 | if (t>max) max=t; |
---|
751 | ll++; |
---|
752 | pIter(p); |
---|
753 | } |
---|
754 | *l=ll; |
---|
755 | return max; |
---|
756 | } |
---|