1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id: sparsmat.cc,v 1.31 2000-08-14 12:56:51 obachman Exp $ */ |
---|
5 | |
---|
6 | /* |
---|
7 | * ABSTRACT: operations with sparse matrices (bareiss, ...) |
---|
8 | */ |
---|
9 | |
---|
10 | #include "mod2.h" |
---|
11 | #include "structs.h" |
---|
12 | #include "tok.h" |
---|
13 | #include "febase.h" |
---|
14 | #include "structs.h" |
---|
15 | #include "intvec.h" |
---|
16 | #include "lists.h" |
---|
17 | #include "ring.h" |
---|
18 | #include "polys.h" |
---|
19 | #include "ipid.h" |
---|
20 | #include "ideals.h" |
---|
21 | #include "numbers.h" |
---|
22 | #include "sparsmat.h" |
---|
23 | #include "prCopy.h" |
---|
24 | |
---|
25 | /* ----------------- general definitions ------------------ */ |
---|
26 | /* in structs.h |
---|
27 | typedef struct smprec sm_prec; |
---|
28 | typedef sm_prec * smpoly; |
---|
29 | struct smprec{ |
---|
30 | smpoly n; // the next element |
---|
31 | int pos; // position |
---|
32 | int e; // level |
---|
33 | poly m; // the element |
---|
34 | float f; // complexity of the element |
---|
35 | }; |
---|
36 | */ |
---|
37 | /* declare internal 'C' stuff */ |
---|
38 | static void smExactPolyDiv(poly, poly); |
---|
39 | static BOOLEAN smIsNegQuot(poly, const poly, const poly); |
---|
40 | static poly smEMult(poly, const poly); |
---|
41 | static BOOLEAN smCheckLead(const poly, const poly); |
---|
42 | static poly smDMult(poly, const poly); |
---|
43 | static void smComplete(poly, const poly, const poly); |
---|
44 | static void smPolyDivN(poly, const number); |
---|
45 | static BOOLEAN smSmaller(poly, poly); |
---|
46 | static void smCombineChain(poly *, poly); |
---|
47 | static void smFindRef(poly *, poly *, poly); |
---|
48 | |
---|
49 | static void smElemDelete(smpoly *); |
---|
50 | static smpoly smElemCopy(smpoly); |
---|
51 | static float smPolyWeight(smpoly); |
---|
52 | static smpoly smPoly2Smpoly(poly); |
---|
53 | static poly smSmpoly2Poly(smpoly); |
---|
54 | static BOOLEAN smHaveDenom(poly); |
---|
55 | static number smCleardenom(ideal); |
---|
56 | |
---|
57 | /* class for sparse matrix: |
---|
58 | * 3 parts of matrix during the algorithm |
---|
59 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
60 | * input pivotcols as rows result |
---|
61 | * pivot like a stack from pivot and pivotcols |
---|
62 | * elimination rows reordered according |
---|
63 | * to pivot choise |
---|
64 | * stored in perm |
---|
65 | * a step is as follows |
---|
66 | * - search of pivot (smPivot) |
---|
67 | * - swap pivot column and last column (smSwapC) |
---|
68 | * select pivotrow to piv and red (smSelectPR) |
---|
69 | * consider sign |
---|
70 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
---|
71 | * clear zero column as result of elimination (smZeroElim) |
---|
72 | * - tranfer from |
---|
73 | * piv and m_row to m_res (smRowToCol) |
---|
74 | * m_act to m_row (smColToRow) |
---|
75 | */ |
---|
76 | class sparse_mat{ |
---|
77 | private: |
---|
78 | int nrows, ncols; // dimension of the problem |
---|
79 | int sign; // for determinant (start: 1) |
---|
80 | int act; // number of unreduced columns (start: ncols) |
---|
81 | int crd; // number of reduced columns (start: 0) |
---|
82 | int tored; // border for rows to reduce |
---|
83 | int inred; // unreducable part |
---|
84 | int rpiv, cpiv; // position of the pivot |
---|
85 | int normalize; // Normalization flag |
---|
86 | int *perm; // permutation of rows |
---|
87 | float wpoints; // weight of all points |
---|
88 | float *wrw, *wcl; // weights of rows and columns |
---|
89 | smpoly * m_act; // unreduced columns |
---|
90 | smpoly * m_res; // reduced columns (result) |
---|
91 | smpoly * m_row; // reduced part of rows |
---|
92 | smpoly red; // row to reduce |
---|
93 | smpoly piv, oldpiv; // pivot and previous pivot |
---|
94 | smpoly dumm; // allocated dummy |
---|
95 | void smColToRow(); |
---|
96 | void smRowToCol(); |
---|
97 | void smFinalMult(); |
---|
98 | void smSparseHomog(); |
---|
99 | void smWeights(); |
---|
100 | void smPivot(); |
---|
101 | void smNewWeights(); |
---|
102 | void smNewPivot(); |
---|
103 | void smZeroElim(); |
---|
104 | void smToredElim(); |
---|
105 | void smCopToRes(); |
---|
106 | void smSelectPR(); |
---|
107 | void smElim(); |
---|
108 | void sm1Elim(); |
---|
109 | void smHElim(); |
---|
110 | void smMultCol(); |
---|
111 | poly smMultPoly(smpoly); |
---|
112 | void smActDel(); |
---|
113 | void smColDel(); |
---|
114 | void smPivDel(); |
---|
115 | void smSign(); |
---|
116 | void smInitPerm(); |
---|
117 | int smCheckNormalize(); |
---|
118 | void smNormalize(); |
---|
119 | public: |
---|
120 | sparse_mat(ideal); |
---|
121 | ~sparse_mat(); |
---|
122 | int smGetSign() { return sign; } |
---|
123 | smpoly * smGetAct() { return m_act; } |
---|
124 | int smGetRed() { return tored; } |
---|
125 | ideal smRes2Mod(); |
---|
126 | poly smDet(); |
---|
127 | void smBareiss(int, int); |
---|
128 | void smNewBareiss(int, int); |
---|
129 | void smToIntvec(intvec *); |
---|
130 | }; |
---|
131 | |
---|
132 | /* ----------------- ops with rings ------------------ */ |
---|
133 | ideal smRingCopy(ideal I, ring *ri, sip_sring &tmpR) |
---|
134 | { |
---|
135 | ring origR =NULL; |
---|
136 | ideal II; |
---|
137 | if (currRing->order[0]!=ringorder_c) |
---|
138 | { |
---|
139 | origR =currRing; |
---|
140 | tmpR=*origR; |
---|
141 | int *ord=(int*)omAlloc0(3*sizeof(int)); |
---|
142 | int *block0=(int*)omAlloc(3*sizeof(int)); |
---|
143 | int *block1=(int*)omAlloc(3*sizeof(int)); |
---|
144 | ord[0]=ringorder_c; |
---|
145 | ord[1]=ringorder_dp; |
---|
146 | tmpR.order=ord; |
---|
147 | block0[1]=1; |
---|
148 | tmpR.block0=block0; |
---|
149 | block1[1]=tmpR.N; |
---|
150 | tmpR.block1=block1; |
---|
151 | rComplete(&tmpR,1); |
---|
152 | rChangeCurrRing(&tmpR,TRUE); |
---|
153 | // fetch data from the old ring |
---|
154 | II=idInit(IDELEMS(I),I->rank); |
---|
155 | int k; |
---|
156 | for (k=0;k<IDELEMS(I);k++) II->m[k] = prCopyR( I->m[k], origR); |
---|
157 | } |
---|
158 | else |
---|
159 | { |
---|
160 | II=idCopy(I); |
---|
161 | } |
---|
162 | *ri = origR; |
---|
163 | return II; |
---|
164 | } |
---|
165 | |
---|
166 | void smRingClean(ring origR, ip_sring &tmpR) |
---|
167 | { |
---|
168 | rChangeCurrRing(origR,TRUE); |
---|
169 | rUnComplete(&tmpR); |
---|
170 | omFreeSize((ADDRESS)tmpR.order,3*sizeof(int)); |
---|
171 | omFreeSize((ADDRESS)tmpR.block0,3*sizeof(int)); |
---|
172 | omFreeSize((ADDRESS)tmpR.block1,3*sizeof(int)); |
---|
173 | } |
---|
174 | |
---|
175 | /* ----------------- basics (used from 'C') ------------------ */ |
---|
176 | /*2 |
---|
177 | *returns the determinant of the module I; |
---|
178 | *uses Bareiss algorithm |
---|
179 | */ |
---|
180 | poly smCallDet(ideal I) |
---|
181 | { |
---|
182 | if (I->ncols != I->rank) |
---|
183 | { |
---|
184 | Werror("det of %d x %d module (matrix)",I->rank,I->ncols); |
---|
185 | return NULL; |
---|
186 | } |
---|
187 | int r=idRankFreeModule(I); |
---|
188 | if (I->ncols != r) // some 0-lines at the end |
---|
189 | { |
---|
190 | return NULL; |
---|
191 | } |
---|
192 | number diag,h=nInit(1); |
---|
193 | poly res,save; |
---|
194 | ring origR; |
---|
195 | sip_sring tmpR; |
---|
196 | sparse_mat *det; |
---|
197 | ideal II=smRingCopy(I,&origR,tmpR); |
---|
198 | |
---|
199 | diag = smCleardenom(II); |
---|
200 | det = new sparse_mat(II); |
---|
201 | idDelete(&II); |
---|
202 | if (det->smGetAct() == NULL) |
---|
203 | { |
---|
204 | delete det; |
---|
205 | if (origR!=NULL) smRingClean(origR,tmpR); |
---|
206 | return NULL; |
---|
207 | } |
---|
208 | res=det->smDet(); |
---|
209 | if(det->smGetSign()<0) res=pNeg(res); |
---|
210 | delete det; |
---|
211 | if (origR!=NULL) |
---|
212 | { |
---|
213 | rChangeCurrRing(origR,TRUE); |
---|
214 | save = res; |
---|
215 | res = prCopyR( save, &tmpR); |
---|
216 | rChangeCurrRing(&tmpR,FALSE); |
---|
217 | pDelete(&save); |
---|
218 | smRingClean(origR,tmpR); |
---|
219 | } |
---|
220 | if (nEqual(diag,h) == FALSE) |
---|
221 | { |
---|
222 | pMultN(res,diag); |
---|
223 | pNormalize(res); |
---|
224 | } |
---|
225 | nDelete(&diag); |
---|
226 | nDelete(&h); |
---|
227 | return res; |
---|
228 | } |
---|
229 | |
---|
230 | lists smCallBareiss(ideal I, int x, int y) |
---|
231 | { |
---|
232 | ring origR; |
---|
233 | sip_sring tmpR; |
---|
234 | lists res=(lists)omAllocBin(slists_bin); |
---|
235 | ideal II = smRingCopy(I,&origR,tmpR); |
---|
236 | sparse_mat *bareiss = new sparse_mat(II); |
---|
237 | ideal mm=II; |
---|
238 | intvec *v; |
---|
239 | ideal m; |
---|
240 | |
---|
241 | if (bareiss->smGetAct() == NULL) |
---|
242 | { |
---|
243 | delete bareiss; |
---|
244 | if (origR!=NULL) smRingClean(origR,tmpR); |
---|
245 | v=new intvec(1,pVariables); |
---|
246 | } |
---|
247 | else |
---|
248 | { |
---|
249 | idDelete(&II); |
---|
250 | bareiss->smBareiss(x, y); |
---|
251 | m = bareiss->smRes2Mod(); |
---|
252 | v = new intvec(bareiss->smGetRed()); |
---|
253 | bareiss->smToIntvec(v); |
---|
254 | delete bareiss; |
---|
255 | if (origR!=NULL) |
---|
256 | { |
---|
257 | rChangeCurrRing(origR,TRUE); |
---|
258 | mm=idInit(IDELEMS(m),m->rank); |
---|
259 | int k; |
---|
260 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
---|
261 | rChangeCurrRing(&tmpR,FALSE); |
---|
262 | idDelete(&m); |
---|
263 | smRingClean(origR,tmpR); |
---|
264 | } |
---|
265 | else |
---|
266 | { |
---|
267 | mm=m; |
---|
268 | } |
---|
269 | } |
---|
270 | res->Init(2); |
---|
271 | res->m[0].rtyp=MODUL_CMD; |
---|
272 | res->m[0].data=(void *)mm; |
---|
273 | res->m[1].rtyp=INTVEC_CMD; |
---|
274 | res->m[1].data=(void *)v; |
---|
275 | return res; |
---|
276 | } |
---|
277 | |
---|
278 | lists smCallNewBareiss(ideal I, int x, int y) |
---|
279 | { |
---|
280 | ring origR; |
---|
281 | sip_sring tmpR; |
---|
282 | lists res=(lists)omAllocBin(slists_bin); |
---|
283 | ideal II=smRingCopy(I,&origR,tmpR); |
---|
284 | sparse_mat *bareiss = new sparse_mat(II); |
---|
285 | ideal mm=II; |
---|
286 | intvec *v; |
---|
287 | ideal m; |
---|
288 | |
---|
289 | if (bareiss->smGetAct() == NULL) |
---|
290 | { |
---|
291 | delete bareiss; |
---|
292 | if (origR!=NULL) smRingClean(origR,tmpR); |
---|
293 | v=new intvec(1,pVariables); |
---|
294 | } |
---|
295 | else |
---|
296 | { |
---|
297 | idDelete(&II); |
---|
298 | bareiss->smNewBareiss(x, y); |
---|
299 | m = bareiss->smRes2Mod(); |
---|
300 | v = new intvec(bareiss->smGetRed()); |
---|
301 | bareiss->smToIntvec(v); |
---|
302 | delete bareiss; |
---|
303 | if (origR!=NULL) |
---|
304 | { |
---|
305 | rChangeCurrRing(origR,TRUE); |
---|
306 | mm=idInit(IDELEMS(m),m->rank); |
---|
307 | int k; |
---|
308 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
---|
309 | rChangeCurrRing(&tmpR,FALSE); |
---|
310 | idDelete(&m); |
---|
311 | smRingClean(origR,tmpR); |
---|
312 | } |
---|
313 | else |
---|
314 | { |
---|
315 | mm=m; |
---|
316 | } |
---|
317 | } |
---|
318 | res->Init(2); |
---|
319 | res->m[0].rtyp=MODUL_CMD; |
---|
320 | res->m[0].data=(void *)mm; |
---|
321 | res->m[1].rtyp=INTVEC_CMD; |
---|
322 | res->m[1].data=(void *)v; |
---|
323 | return res; |
---|
324 | } |
---|
325 | |
---|
326 | /* |
---|
327 | * constructor |
---|
328 | */ |
---|
329 | sparse_mat::sparse_mat(ideal smat) |
---|
330 | { |
---|
331 | int i; |
---|
332 | polyset pmat; |
---|
333 | |
---|
334 | ncols = smat->ncols; |
---|
335 | nrows = idRankFreeModule(smat); |
---|
336 | if (nrows <= 0) |
---|
337 | { |
---|
338 | m_act = NULL; |
---|
339 | return; |
---|
340 | } |
---|
341 | sign = 1; |
---|
342 | inred = act = ncols; |
---|
343 | crd = 0; |
---|
344 | tored = nrows; // without border |
---|
345 | i = tored+1; |
---|
346 | perm = (int *)omAlloc(sizeof(int)*(i+1)); |
---|
347 | perm[i] = 0; |
---|
348 | m_row = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
---|
349 | wrw = (float *)omAlloc(sizeof(float)*i); |
---|
350 | i = ncols+1; |
---|
351 | wcl = (float *)omAlloc(sizeof(float)*i); |
---|
352 | m_act = (smpoly *)omAlloc(sizeof(smpoly)*i); |
---|
353 | m_res = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
---|
354 | dumm = (smpoly)omAllocBin(smprec_bin); |
---|
355 | m_res[0] = (smpoly)omAllocBin(smprec_bin); |
---|
356 | m_res[0]->m = NULL; |
---|
357 | pmat = smat->m; |
---|
358 | for(i=ncols; i; i--) |
---|
359 | { |
---|
360 | m_act[i] = smPoly2Smpoly(pmat[i-1]); |
---|
361 | pmat[i-1] = NULL; |
---|
362 | } |
---|
363 | this->smZeroElim(); |
---|
364 | oldpiv = NULL; |
---|
365 | } |
---|
366 | |
---|
367 | /* |
---|
368 | * destructor |
---|
369 | */ |
---|
370 | sparse_mat::~sparse_mat() |
---|
371 | { |
---|
372 | int i; |
---|
373 | if (m_act == NULL) return; |
---|
374 | omFreeBin((ADDRESS)m_res[0], smprec_bin); |
---|
375 | omFreeBin((ADDRESS)dumm, smprec_bin); |
---|
376 | i = ncols+1; |
---|
377 | omFreeSize((ADDRESS)m_res, sizeof(smpoly)*i); |
---|
378 | omFreeSize((ADDRESS)m_act, sizeof(smpoly)*i); |
---|
379 | omFreeSize((ADDRESS)wcl, sizeof(float)*i); |
---|
380 | i = nrows+1; |
---|
381 | omFreeSize((ADDRESS)wrw, sizeof(float)*i); |
---|
382 | omFreeSize((ADDRESS)m_row, sizeof(smpoly)*i); |
---|
383 | omFreeSize((ADDRESS)perm, sizeof(int)*(i+1)); |
---|
384 | } |
---|
385 | |
---|
386 | /* |
---|
387 | * transform the result to a module |
---|
388 | */ |
---|
389 | ideal sparse_mat::smRes2Mod() |
---|
390 | { |
---|
391 | ideal res = idInit(crd, crd); |
---|
392 | int i; |
---|
393 | |
---|
394 | for (i=crd; i; i--) res->m[i-1] = smSmpoly2Poly(m_res[i]); |
---|
395 | res->rank = idRankFreeModule(res); |
---|
396 | return res; |
---|
397 | } |
---|
398 | |
---|
399 | /* |
---|
400 | * permutation of rows |
---|
401 | */ |
---|
402 | void sparse_mat::smToIntvec(intvec *v) |
---|
403 | { |
---|
404 | int i; |
---|
405 | |
---|
406 | for (i=v->rows()-1; i>=0; i--) |
---|
407 | (*v)[i] = perm[i+1]; |
---|
408 | } |
---|
409 | /* ---------------- the algorithm's ------------------ */ |
---|
410 | /* |
---|
411 | * the determinant (up to sign), uses new Bareiss elimination |
---|
412 | */ |
---|
413 | poly sparse_mat::smDet() |
---|
414 | { |
---|
415 | int y; |
---|
416 | poly res = NULL; |
---|
417 | |
---|
418 | if (sign == 0) |
---|
419 | { |
---|
420 | this->smActDel(); |
---|
421 | return NULL; |
---|
422 | } |
---|
423 | if (act < 2) |
---|
424 | { |
---|
425 | if (act != 0) res = m_act[1]->m; |
---|
426 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
427 | return res; |
---|
428 | } |
---|
429 | normalize = 0; |
---|
430 | this->smInitPerm(); |
---|
431 | this->smPivot(); |
---|
432 | this->smSign(); |
---|
433 | this->smSelectPR(); |
---|
434 | this->sm1Elim(); |
---|
435 | crd++; |
---|
436 | m_res[crd] = piv; |
---|
437 | this->smColDel(); |
---|
438 | act--; |
---|
439 | this->smZeroElim(); |
---|
440 | if (sign == 0) |
---|
441 | { |
---|
442 | this->smActDel(); |
---|
443 | return NULL; |
---|
444 | } |
---|
445 | if (act < 2) |
---|
446 | { |
---|
447 | this->smFinalMult(); |
---|
448 | this->smPivDel(); |
---|
449 | if (act != 0) res = m_act[1]->m; |
---|
450 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
451 | return res; |
---|
452 | } |
---|
453 | loop |
---|
454 | { |
---|
455 | this->smNewPivot(); |
---|
456 | this->smSign(); |
---|
457 | this->smSelectPR(); |
---|
458 | this->smMultCol(); |
---|
459 | this->smHElim(); |
---|
460 | crd++; |
---|
461 | m_res[crd] = piv; |
---|
462 | this->smColDel(); |
---|
463 | act--; |
---|
464 | this->smZeroElim(); |
---|
465 | if (sign == 0) |
---|
466 | { |
---|
467 | this->smPivDel(); |
---|
468 | this->smActDel(); |
---|
469 | return NULL; |
---|
470 | } |
---|
471 | if (act < 2) |
---|
472 | { |
---|
473 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
474 | this->smFinalMult(); |
---|
475 | this->smPivDel(); |
---|
476 | if (act != 0) res = m_act[1]->m; |
---|
477 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
478 | return res; |
---|
479 | } |
---|
480 | } |
---|
481 | } |
---|
482 | |
---|
483 | /* |
---|
484 | * the Bareiss elimination: |
---|
485 | * - with x unreduced last rows, pivots from here are not allowed |
---|
486 | * - the method will finish for number of unreduced columns < y |
---|
487 | */ |
---|
488 | void sparse_mat::smBareiss(int x, int y) |
---|
489 | { |
---|
490 | if ((x > 0) && (x < nrows)) |
---|
491 | { |
---|
492 | tored -= x; |
---|
493 | this->smToredElim(); |
---|
494 | } |
---|
495 | if (y < 1) y = 1; |
---|
496 | if (act <= y) |
---|
497 | { |
---|
498 | this->smCopToRes(); |
---|
499 | return; |
---|
500 | } |
---|
501 | normalize = this->smCheckNormalize(); |
---|
502 | if (normalize) this->smNormalize(); |
---|
503 | this->smPivot(); |
---|
504 | this->smSelectPR(); |
---|
505 | this->smElim(); |
---|
506 | crd++; |
---|
507 | this->smColToRow(); |
---|
508 | act--; |
---|
509 | this->smRowToCol(); |
---|
510 | this->smZeroElim(); |
---|
511 | if (tored != nrows) |
---|
512 | this->smToredElim(); |
---|
513 | if (act < y) |
---|
514 | { |
---|
515 | this->smCopToRes(); |
---|
516 | return; |
---|
517 | } |
---|
518 | loop |
---|
519 | { |
---|
520 | if (normalize) this->smNormalize(); |
---|
521 | this->smPivot(); |
---|
522 | oldpiv = piv; |
---|
523 | this->smSelectPR(); |
---|
524 | this->smElim(); |
---|
525 | crd++; |
---|
526 | this->smColToRow(); |
---|
527 | act--; |
---|
528 | this->smRowToCol(); |
---|
529 | this->smZeroElim(); |
---|
530 | if (tored != nrows) |
---|
531 | this->smToredElim(); |
---|
532 | if (act < y) |
---|
533 | { |
---|
534 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
535 | this->smCopToRes(); |
---|
536 | return; |
---|
537 | } |
---|
538 | } |
---|
539 | } |
---|
540 | |
---|
541 | /* |
---|
542 | * the new Bareiss elimination: |
---|
543 | * - with x unreduced last rows, pivots from here are not allowed |
---|
544 | * - the method will finish for number of unreduced columns < y |
---|
545 | */ |
---|
546 | void sparse_mat::smNewBareiss(int x, int y) |
---|
547 | { |
---|
548 | if ((x > 0) && (x < nrows)) |
---|
549 | { |
---|
550 | tored -= x; |
---|
551 | this->smToredElim(); |
---|
552 | } |
---|
553 | if (y < 1) y = 1; |
---|
554 | if (act <= y) |
---|
555 | { |
---|
556 | this->smCopToRes(); |
---|
557 | return; |
---|
558 | } |
---|
559 | normalize = this->smCheckNormalize(); |
---|
560 | if (normalize) this->smNormalize(); |
---|
561 | this->smPivot(); |
---|
562 | this->smSelectPR(); |
---|
563 | this->sm1Elim(); |
---|
564 | crd++; |
---|
565 | this->smColToRow(); |
---|
566 | act--; |
---|
567 | this->smRowToCol(); |
---|
568 | this->smZeroElim(); |
---|
569 | if (tored != nrows) |
---|
570 | this->smToredElim(); |
---|
571 | if (act <= y) |
---|
572 | { |
---|
573 | this->smFinalMult(); |
---|
574 | this->smCopToRes(); |
---|
575 | return; |
---|
576 | } |
---|
577 | loop |
---|
578 | { |
---|
579 | if (normalize) this->smNormalize(); |
---|
580 | this->smNewPivot(); |
---|
581 | this->smSelectPR(); |
---|
582 | this->smMultCol(); |
---|
583 | this->smHElim(); |
---|
584 | crd++; |
---|
585 | this->smColToRow(); |
---|
586 | act--; |
---|
587 | this->smRowToCol(); |
---|
588 | this->smZeroElim(); |
---|
589 | if (tored != nrows) |
---|
590 | this->smToredElim(); |
---|
591 | if (act <= y) |
---|
592 | { |
---|
593 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
594 | this->smFinalMult(); |
---|
595 | this->smCopToRes(); |
---|
596 | return; |
---|
597 | } |
---|
598 | } |
---|
599 | } |
---|
600 | |
---|
601 | /* ----------------- pivot method ------------------ */ |
---|
602 | |
---|
603 | /* |
---|
604 | * prepare smPivot, compute weights for rows and columns |
---|
605 | * and the weight for all points |
---|
606 | */ |
---|
607 | void sparse_mat::smWeights() |
---|
608 | { |
---|
609 | float wc, wp, w; |
---|
610 | smpoly a; |
---|
611 | int i; |
---|
612 | |
---|
613 | wp = 0.0; |
---|
614 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
615 | for (i=act; i; i--) |
---|
616 | { |
---|
617 | wc = 0.0; |
---|
618 | a = m_act[i]; |
---|
619 | loop |
---|
620 | { |
---|
621 | if (a->pos > tored) |
---|
622 | break; |
---|
623 | w = a->f = smPolyWeight(a); |
---|
624 | wc += w; |
---|
625 | wrw[a->pos] += w; |
---|
626 | a = a->n; |
---|
627 | if (a == NULL) |
---|
628 | break; |
---|
629 | } |
---|
630 | wp += wc; |
---|
631 | wcl[i] = wc; |
---|
632 | } |
---|
633 | wpoints = wp; |
---|
634 | } |
---|
635 | |
---|
636 | /* |
---|
637 | * compute pivot |
---|
638 | */ |
---|
639 | void sparse_mat::smPivot() |
---|
640 | { |
---|
641 | float wopt = 1.0e30; |
---|
642 | float wc, wr, wp, w; |
---|
643 | smpoly a; |
---|
644 | int i, copt, ropt; |
---|
645 | |
---|
646 | this->smWeights(); |
---|
647 | for (i=act; i; i--) |
---|
648 | { |
---|
649 | a = m_act[i]; |
---|
650 | loop |
---|
651 | { |
---|
652 | if (a->pos > tored) |
---|
653 | break; |
---|
654 | w = a->f; |
---|
655 | wc = wcl[i]-w; |
---|
656 | wr = wrw[a->pos]-w; |
---|
657 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
658 | { |
---|
659 | if (w<wopt) |
---|
660 | { |
---|
661 | wopt = w; |
---|
662 | copt = i; |
---|
663 | ropt = a->pos; |
---|
664 | } |
---|
665 | } |
---|
666 | else // elimination |
---|
667 | { |
---|
668 | wp = w*(wpoints-wcl[i]-wr); |
---|
669 | wp += wr*wc; |
---|
670 | if (wp < wopt) |
---|
671 | { |
---|
672 | wopt = wp; |
---|
673 | copt = i; |
---|
674 | ropt = a->pos; |
---|
675 | } |
---|
676 | } |
---|
677 | a = a->n; |
---|
678 | if (a == NULL) |
---|
679 | break; |
---|
680 | } |
---|
681 | } |
---|
682 | rpiv = ropt; |
---|
683 | cpiv = copt; |
---|
684 | if (cpiv != act) |
---|
685 | { |
---|
686 | a = m_act[act]; |
---|
687 | m_act[act] = m_act[cpiv]; |
---|
688 | m_act[cpiv] = a; |
---|
689 | } |
---|
690 | } |
---|
691 | |
---|
692 | /* |
---|
693 | * prepare smPivot, compute weights for rows and columns |
---|
694 | * and the weight for all points |
---|
695 | */ |
---|
696 | void sparse_mat::smNewWeights() |
---|
697 | { |
---|
698 | float wc, wp, w, hp = piv->f; |
---|
699 | smpoly a; |
---|
700 | int i, f, e = crd; |
---|
701 | |
---|
702 | wp = 0.0; |
---|
703 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
704 | for (i=act; i; i--) |
---|
705 | { |
---|
706 | wc = 0.0; |
---|
707 | a = m_act[i]; |
---|
708 | loop |
---|
709 | { |
---|
710 | if (a->pos > tored) |
---|
711 | break; |
---|
712 | w = a->f; |
---|
713 | f = a->e; |
---|
714 | if (f < e) |
---|
715 | { |
---|
716 | w *= hp; |
---|
717 | if (f) w /= m_res[f]->f; |
---|
718 | } |
---|
719 | wc += w; |
---|
720 | wrw[a->pos] += w; |
---|
721 | a = a->n; |
---|
722 | if (a == NULL) |
---|
723 | break; |
---|
724 | } |
---|
725 | wp += wc; |
---|
726 | wcl[i] = wc; |
---|
727 | } |
---|
728 | wpoints = wp; |
---|
729 | } |
---|
730 | |
---|
731 | /* |
---|
732 | * compute pivot |
---|
733 | */ |
---|
734 | void sparse_mat::smNewPivot() |
---|
735 | { |
---|
736 | float wopt = 1.0e30, hp = piv->f; |
---|
737 | float wc, wr, wp, w; |
---|
738 | smpoly a; |
---|
739 | int i, copt, ropt, f, e = crd; |
---|
740 | |
---|
741 | this->smNewWeights(); |
---|
742 | for (i=act; i; i--) |
---|
743 | { |
---|
744 | a = m_act[i]; |
---|
745 | loop |
---|
746 | { |
---|
747 | if (a->pos > tored) |
---|
748 | break; |
---|
749 | w = a->f; |
---|
750 | f = a->e; |
---|
751 | if (f < e) |
---|
752 | { |
---|
753 | w *= hp; |
---|
754 | if (f) w /= m_res[f]->f; |
---|
755 | } |
---|
756 | wc = wcl[i]-w; |
---|
757 | wr = wrw[a->pos]-w; |
---|
758 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
759 | { |
---|
760 | if (w<wopt) |
---|
761 | { |
---|
762 | wopt = w; |
---|
763 | copt = i; |
---|
764 | ropt = a->pos; |
---|
765 | } |
---|
766 | } |
---|
767 | else // elimination |
---|
768 | { |
---|
769 | wp = w*(wpoints-wcl[i]-wr); |
---|
770 | wp += wr*wc; |
---|
771 | if (wp < wopt) |
---|
772 | { |
---|
773 | wopt = wp; |
---|
774 | copt = i; |
---|
775 | ropt = a->pos; |
---|
776 | } |
---|
777 | } |
---|
778 | a = a->n; |
---|
779 | if (a == NULL) |
---|
780 | break; |
---|
781 | } |
---|
782 | } |
---|
783 | rpiv = ropt; |
---|
784 | cpiv = copt; |
---|
785 | if (cpiv != act) |
---|
786 | { |
---|
787 | a = m_act[act]; |
---|
788 | m_act[act] = m_act[cpiv]; |
---|
789 | m_act[cpiv] = a; |
---|
790 | } |
---|
791 | } |
---|
792 | |
---|
793 | /* ----------------- elimination ------------------ */ |
---|
794 | |
---|
795 | /* steps of elimination */ |
---|
796 | void sparse_mat::smElim() |
---|
797 | { |
---|
798 | poly p = piv->m; // pivotelement |
---|
799 | smpoly c = m_act[act]; // pivotcolumn |
---|
800 | smpoly r = red; // row to reduce |
---|
801 | poly q; |
---|
802 | smpoly res, a, b; |
---|
803 | poly w, ha, hb; |
---|
804 | int i; |
---|
805 | |
---|
806 | if (oldpiv != NULL) q = oldpiv->m; // previous pivot |
---|
807 | else q = NULL; |
---|
808 | if ((c == NULL) || (r == NULL)) |
---|
809 | { |
---|
810 | while (r) smElemDelete(&r); |
---|
811 | for (i=1; i<act; i++) |
---|
812 | { |
---|
813 | a = m_act[i]; |
---|
814 | while (a != NULL) |
---|
815 | { |
---|
816 | ha = SM_MULT(a->m, p, q); |
---|
817 | pDelete(&a->m); |
---|
818 | if (q) SM_DIV(ha, q); |
---|
819 | a->m = ha; |
---|
820 | a = a->n; |
---|
821 | } |
---|
822 | } |
---|
823 | return; |
---|
824 | } |
---|
825 | for (i=1; i<act; i++) |
---|
826 | { |
---|
827 | a = m_act[i]; |
---|
828 | if ((r == NULL) || (i != r->pos)) // cols without elimination |
---|
829 | { |
---|
830 | while (a != NULL) |
---|
831 | { |
---|
832 | ha = SM_MULT(a->m, p, q); |
---|
833 | pDelete(&a->m); |
---|
834 | if (q) SM_DIV(ha, q); |
---|
835 | a->m = ha; |
---|
836 | a = a->n; |
---|
837 | } |
---|
838 | } |
---|
839 | else // cols with elimination |
---|
840 | { |
---|
841 | res = dumm; |
---|
842 | res->n = NULL; |
---|
843 | b = c; |
---|
844 | w = r->m; |
---|
845 | loop // combine the chains a and b: p*a + w*b |
---|
846 | { |
---|
847 | if (a == NULL) |
---|
848 | { |
---|
849 | if (b != NULL) |
---|
850 | { |
---|
851 | do |
---|
852 | { |
---|
853 | res = res->n = smElemCopy(b); |
---|
854 | hb = SM_MULT(b->m, w, q); |
---|
855 | if (q) SM_DIV(hb, q); |
---|
856 | res->m = hb; |
---|
857 | b = b->n; |
---|
858 | } while (b != NULL); |
---|
859 | } |
---|
860 | else |
---|
861 | res->n = NULL; |
---|
862 | break; |
---|
863 | } |
---|
864 | if (b == NULL) |
---|
865 | { |
---|
866 | do |
---|
867 | { |
---|
868 | ha = SM_MULT(a->m, p, q); |
---|
869 | pDelete(&a->m); |
---|
870 | if (q) SM_DIV(ha, q); |
---|
871 | a->m = ha; |
---|
872 | res = res->n = a; |
---|
873 | a = a->n; |
---|
874 | } while (a != NULL); |
---|
875 | break; |
---|
876 | } |
---|
877 | if (a->pos < b->pos) |
---|
878 | { |
---|
879 | ha = SM_MULT(a->m, p, q); |
---|
880 | pDelete(&a->m); |
---|
881 | if (q) SM_DIV(ha, q); |
---|
882 | a->m = ha; |
---|
883 | res = res->n = a; |
---|
884 | a = a->n; |
---|
885 | } |
---|
886 | else if (a->pos > b->pos) |
---|
887 | { |
---|
888 | res = res->n = smElemCopy(b); |
---|
889 | hb = SM_MULT(b->m, w, q); |
---|
890 | b = b->n; |
---|
891 | if (q) SM_DIV(hb, q); |
---|
892 | res->m = hb; |
---|
893 | } |
---|
894 | else |
---|
895 | { |
---|
896 | ha = SM_MULT(a->m, p, q); |
---|
897 | pDelete(&a->m); |
---|
898 | hb = SM_MULT(b->m, w, q); |
---|
899 | ha = pAdd(ha, hb); |
---|
900 | if (ha != NULL) |
---|
901 | { |
---|
902 | if (q) SM_DIV(ha, q); |
---|
903 | a->m = ha; |
---|
904 | res = res->n = a; |
---|
905 | a = a->n; |
---|
906 | } |
---|
907 | else |
---|
908 | { |
---|
909 | smElemDelete(&a); |
---|
910 | } |
---|
911 | b = b->n; |
---|
912 | } |
---|
913 | } |
---|
914 | m_act[i] = dumm->n; |
---|
915 | if (r) smElemDelete(&r); |
---|
916 | } |
---|
917 | } |
---|
918 | } |
---|
919 | |
---|
920 | /* first step of elimination */ |
---|
921 | void sparse_mat::sm1Elim() |
---|
922 | { |
---|
923 | poly p = piv->m; // pivotelement |
---|
924 | smpoly c = m_act[act]; // pivotcolumn |
---|
925 | smpoly r = red; // row to reduce |
---|
926 | smpoly res, a, b; |
---|
927 | poly w, ha, hb; |
---|
928 | |
---|
929 | if ((c == NULL) || (r == NULL)) |
---|
930 | { |
---|
931 | while (r!=NULL) smElemDelete(&r); |
---|
932 | return; |
---|
933 | } |
---|
934 | do |
---|
935 | { |
---|
936 | a = m_act[r->pos]; |
---|
937 | res = dumm; |
---|
938 | res->n = NULL; |
---|
939 | b = c; |
---|
940 | w = r->m; |
---|
941 | loop // combine the chains a and b: p*a + w*b |
---|
942 | { |
---|
943 | if (a == NULL) |
---|
944 | { |
---|
945 | do |
---|
946 | { |
---|
947 | res = res->n = smElemCopy(b); |
---|
948 | res->m = smMult(b->m, w); |
---|
949 | res->e = 1; |
---|
950 | res->f = smPolyWeight(res); |
---|
951 | b = b->n; |
---|
952 | } while (b != NULL); |
---|
953 | break; |
---|
954 | } |
---|
955 | if (a->pos < b->pos) |
---|
956 | { |
---|
957 | res = res->n = a; |
---|
958 | a = a->n; |
---|
959 | } |
---|
960 | else if (a->pos > b->pos) |
---|
961 | { |
---|
962 | res = res->n = smElemCopy(b); |
---|
963 | res->m = smMult(b->m, w); |
---|
964 | res->e = 1; |
---|
965 | res->f = smPolyWeight(res); |
---|
966 | b = b->n; |
---|
967 | } |
---|
968 | else |
---|
969 | { |
---|
970 | ha = smMult(a->m, p); |
---|
971 | pDelete(&a->m); |
---|
972 | hb = smMult(b->m, w); |
---|
973 | ha = pAdd(ha, hb); |
---|
974 | if (ha != NULL) |
---|
975 | { |
---|
976 | a->m = ha; |
---|
977 | a->e = 1; |
---|
978 | a->f = smPolyWeight(a); |
---|
979 | res = res->n = a; |
---|
980 | a = a->n; |
---|
981 | } |
---|
982 | else |
---|
983 | { |
---|
984 | smElemDelete(&a); |
---|
985 | } |
---|
986 | b = b->n; |
---|
987 | } |
---|
988 | if (b == NULL) |
---|
989 | { |
---|
990 | res->n = a; |
---|
991 | break; |
---|
992 | } |
---|
993 | } |
---|
994 | m_act[r->pos] = dumm->n; |
---|
995 | smElemDelete(&r); |
---|
996 | } while (r != NULL); |
---|
997 | } |
---|
998 | |
---|
999 | /* higher steps of elimination */ |
---|
1000 | void sparse_mat::smHElim() |
---|
1001 | { |
---|
1002 | poly hp = this->smMultPoly(piv); |
---|
1003 | poly gp = piv->m; // pivotelement |
---|
1004 | smpoly c = m_act[act]; // pivotcolumn |
---|
1005 | smpoly r = red; // row to reduce |
---|
1006 | smpoly res, a, b; |
---|
1007 | poly ha, hr, x, y; |
---|
1008 | int e, ip, ir, ia, lev; |
---|
1009 | |
---|
1010 | if ((c == NULL) || (r == NULL)) |
---|
1011 | { |
---|
1012 | while(r!=NULL) smElemDelete(&r); |
---|
1013 | pDelete(&hp); |
---|
1014 | return; |
---|
1015 | } |
---|
1016 | e = crd+1; |
---|
1017 | ip = piv->e; |
---|
1018 | do |
---|
1019 | { |
---|
1020 | a = m_act[r->pos]; |
---|
1021 | res = dumm; |
---|
1022 | res->n = NULL; |
---|
1023 | b = c; |
---|
1024 | hr = r->m; |
---|
1025 | ir = r->e; |
---|
1026 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
1027 | { |
---|
1028 | if (a == NULL) |
---|
1029 | { |
---|
1030 | do |
---|
1031 | { |
---|
1032 | res = res->n = smElemCopy(b); |
---|
1033 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1034 | b = b->n; |
---|
1035 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1036 | res->m = x; |
---|
1037 | res->e = e; |
---|
1038 | res->f = smPolyWeight(res); |
---|
1039 | } while (b != NULL); |
---|
1040 | break; |
---|
1041 | } |
---|
1042 | if (a->pos < b->pos) |
---|
1043 | { |
---|
1044 | res = res->n = a; |
---|
1045 | a = a->n; |
---|
1046 | } |
---|
1047 | else if (a->pos > b->pos) |
---|
1048 | { |
---|
1049 | res = res->n = smElemCopy(b); |
---|
1050 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1051 | b = b->n; |
---|
1052 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1053 | res->m = x; |
---|
1054 | res->e = e; |
---|
1055 | res->f = smPolyWeight(res); |
---|
1056 | } |
---|
1057 | else |
---|
1058 | { |
---|
1059 | ha = a->m; |
---|
1060 | ia = a->e; |
---|
1061 | if (ir >= ia) |
---|
1062 | { |
---|
1063 | if (ir > ia) |
---|
1064 | { |
---|
1065 | x = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m); |
---|
1066 | pDelete(&ha); |
---|
1067 | ha = x; |
---|
1068 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1069 | ia = ir; |
---|
1070 | } |
---|
1071 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1072 | pDelete(&ha); |
---|
1073 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1074 | } |
---|
1075 | else if (ir >= ip) |
---|
1076 | { |
---|
1077 | if (ia < crd) |
---|
1078 | { |
---|
1079 | x = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m); |
---|
1080 | pDelete(&ha); |
---|
1081 | ha = x; |
---|
1082 | SM_DIV(ha, m_res[ia]->m); |
---|
1083 | } |
---|
1084 | y = hp; |
---|
1085 | if(ir > ip) |
---|
1086 | { |
---|
1087 | y = SM_MULT(y, m_res[ir]->m, m_res[ip]->m); |
---|
1088 | if (ip) SM_DIV(y, m_res[ip]->m); |
---|
1089 | } |
---|
1090 | ia = ir; |
---|
1091 | x = SM_MULT(ha, y, m_res[ia]->m); |
---|
1092 | if (y != hp) pDelete(&y); |
---|
1093 | pDelete(&ha); |
---|
1094 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1095 | } |
---|
1096 | else |
---|
1097 | { |
---|
1098 | x = SM_MULT(hr, m_res[ia]->m, m_res[ir]->m); |
---|
1099 | if (ir) SM_DIV(x, m_res[ir]->m); |
---|
1100 | y = SM_MULT(b->m, x, m_res[ia]->m); |
---|
1101 | pDelete(&x); |
---|
1102 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1103 | pDelete(&ha); |
---|
1104 | } |
---|
1105 | ha = pAdd(x, y); |
---|
1106 | if (ha != NULL) |
---|
1107 | { |
---|
1108 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1109 | a->m = ha; |
---|
1110 | a->e = e; |
---|
1111 | a->f = smPolyWeight(a); |
---|
1112 | res = res->n = a; |
---|
1113 | a = a->n; |
---|
1114 | } |
---|
1115 | else |
---|
1116 | { |
---|
1117 | a->m = NULL; |
---|
1118 | smElemDelete(&a); |
---|
1119 | } |
---|
1120 | b = b->n; |
---|
1121 | } |
---|
1122 | if (b == NULL) |
---|
1123 | { |
---|
1124 | res->n = a; |
---|
1125 | break; |
---|
1126 | } |
---|
1127 | } |
---|
1128 | m_act[r->pos] = dumm->n; |
---|
1129 | smElemDelete(&r); |
---|
1130 | } while (r != NULL); |
---|
1131 | pDelete(&hp); |
---|
1132 | } |
---|
1133 | |
---|
1134 | /* ----------------- transfer ------------------ */ |
---|
1135 | |
---|
1136 | /* |
---|
1137 | * select the pivotrow and store it to red and piv |
---|
1138 | */ |
---|
1139 | void sparse_mat::smSelectPR() |
---|
1140 | { |
---|
1141 | smpoly b = dumm; |
---|
1142 | smpoly a, ap; |
---|
1143 | int i; |
---|
1144 | |
---|
1145 | if (TEST_OPT_PROT) |
---|
1146 | { |
---|
1147 | if ((crd+1)%10) |
---|
1148 | PrintS("."); |
---|
1149 | else |
---|
1150 | PrintS(".\n"); |
---|
1151 | } |
---|
1152 | a = m_act[act]; |
---|
1153 | if (a->pos < rpiv) |
---|
1154 | { |
---|
1155 | do |
---|
1156 | { |
---|
1157 | ap = a; |
---|
1158 | a = a->n; |
---|
1159 | } while (a->pos < rpiv); |
---|
1160 | ap->n = a->n; |
---|
1161 | } |
---|
1162 | else |
---|
1163 | m_act[act] = a->n; |
---|
1164 | piv = a; |
---|
1165 | a->n = NULL; |
---|
1166 | for (i=1; i<act; i++) |
---|
1167 | { |
---|
1168 | a = m_act[i]; |
---|
1169 | if (a->pos < rpiv) |
---|
1170 | { |
---|
1171 | loop |
---|
1172 | { |
---|
1173 | ap = a; |
---|
1174 | a = a->n; |
---|
1175 | if ((a == NULL) || (a->pos > rpiv)) |
---|
1176 | break; |
---|
1177 | if (a->pos == rpiv) |
---|
1178 | { |
---|
1179 | ap->n = a->n; |
---|
1180 | a->m = pNeg(a->m); |
---|
1181 | b = b->n = a; |
---|
1182 | b->pos = i; |
---|
1183 | break; |
---|
1184 | } |
---|
1185 | } |
---|
1186 | } |
---|
1187 | else if (a->pos == rpiv) |
---|
1188 | { |
---|
1189 | m_act[i] = a->n; |
---|
1190 | a->m = pNeg(a->m); |
---|
1191 | b = b->n = a; |
---|
1192 | b->pos = i; |
---|
1193 | } |
---|
1194 | } |
---|
1195 | b->n = NULL; |
---|
1196 | red = dumm->n; |
---|
1197 | } |
---|
1198 | |
---|
1199 | /* |
---|
1200 | * store the pivotcol in m_row |
---|
1201 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
1202 | */ |
---|
1203 | void sparse_mat::smColToRow() |
---|
1204 | { |
---|
1205 | smpoly c = m_act[act]; |
---|
1206 | smpoly h; |
---|
1207 | |
---|
1208 | while (c != NULL) |
---|
1209 | { |
---|
1210 | h = c; |
---|
1211 | c = c->n; |
---|
1212 | h->n = m_row[h->pos]; |
---|
1213 | m_row[h->pos] = h; |
---|
1214 | h->pos = crd; |
---|
1215 | } |
---|
1216 | } |
---|
1217 | |
---|
1218 | /* |
---|
1219 | * store the pivot and the assosiated row in m_row |
---|
1220 | * to m_res (result): |
---|
1221 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
1222 | */ |
---|
1223 | void sparse_mat::smRowToCol() |
---|
1224 | { |
---|
1225 | smpoly r = m_row[rpiv]; |
---|
1226 | smpoly a, ap, h; |
---|
1227 | |
---|
1228 | m_row[rpiv] = NULL; |
---|
1229 | perm[crd] = rpiv; |
---|
1230 | piv->pos = crd; |
---|
1231 | m_res[crd] = piv; |
---|
1232 | while (r != NULL) |
---|
1233 | { |
---|
1234 | ap = m_res[r->pos]; |
---|
1235 | loop |
---|
1236 | { |
---|
1237 | a = ap->n; |
---|
1238 | if (a == NULL) |
---|
1239 | { |
---|
1240 | ap->n = h = r; |
---|
1241 | r = r->n; |
---|
1242 | h->n = a; |
---|
1243 | h->pos = crd; |
---|
1244 | break; |
---|
1245 | } |
---|
1246 | ap = a; |
---|
1247 | } |
---|
1248 | } |
---|
1249 | } |
---|
1250 | |
---|
1251 | /* ----------------- C++ stuff ------------------ */ |
---|
1252 | |
---|
1253 | /* |
---|
1254 | * clean m_act from zeros (after elim) |
---|
1255 | */ |
---|
1256 | void sparse_mat::smZeroElim() |
---|
1257 | { |
---|
1258 | int i = 0; |
---|
1259 | int j; |
---|
1260 | |
---|
1261 | loop |
---|
1262 | { |
---|
1263 | i++; |
---|
1264 | if (i > act) return; |
---|
1265 | if (m_act[i] == NULL) break; |
---|
1266 | } |
---|
1267 | j = i; |
---|
1268 | loop |
---|
1269 | { |
---|
1270 | j++; |
---|
1271 | if (j > act) break; |
---|
1272 | if (m_act[j] != NULL) |
---|
1273 | { |
---|
1274 | m_act[i] = m_act[j]; |
---|
1275 | i++; |
---|
1276 | } |
---|
1277 | } |
---|
1278 | act -= (j-i); |
---|
1279 | sign = 0; |
---|
1280 | } |
---|
1281 | |
---|
1282 | /* |
---|
1283 | * clean m_act from cols not to reduced (after elim) |
---|
1284 | * put them to m_res |
---|
1285 | */ |
---|
1286 | void sparse_mat::smToredElim() |
---|
1287 | { |
---|
1288 | int i = 0; |
---|
1289 | int j; |
---|
1290 | |
---|
1291 | loop |
---|
1292 | { |
---|
1293 | i++; |
---|
1294 | if (i > act) return; |
---|
1295 | if (m_act[i]->pos > tored) |
---|
1296 | { |
---|
1297 | m_res[inred] = m_act[i]; |
---|
1298 | inred--; |
---|
1299 | break; |
---|
1300 | } |
---|
1301 | } |
---|
1302 | j = i; |
---|
1303 | loop |
---|
1304 | { |
---|
1305 | j++; |
---|
1306 | if (j > act) break; |
---|
1307 | if (m_act[j]->pos > tored) |
---|
1308 | { |
---|
1309 | m_res[inred] = m_act[j]; |
---|
1310 | inred--; |
---|
1311 | } |
---|
1312 | else |
---|
1313 | { |
---|
1314 | m_act[i] = m_act[j]; |
---|
1315 | i++; |
---|
1316 | } |
---|
1317 | } |
---|
1318 | act -= (j-i); |
---|
1319 | sign = 0; |
---|
1320 | } |
---|
1321 | |
---|
1322 | /* |
---|
1323 | * copy m_act to m_res |
---|
1324 | */ |
---|
1325 | void sparse_mat::smCopToRes() |
---|
1326 | { |
---|
1327 | smpoly a,ap,r,h; |
---|
1328 | int i,j,k,l; |
---|
1329 | |
---|
1330 | i = 0; |
---|
1331 | if (act) |
---|
1332 | { |
---|
1333 | a = m_act[act]; // init perm |
---|
1334 | do |
---|
1335 | { |
---|
1336 | i++; |
---|
1337 | perm[crd+i] = a->pos; |
---|
1338 | a = a->n; |
---|
1339 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1340 | for (j=act-1;j;j--) // load all positions of perm |
---|
1341 | { |
---|
1342 | a = m_act[j]; |
---|
1343 | k = 1; |
---|
1344 | loop |
---|
1345 | { |
---|
1346 | if (perm[crd+k] >= a->pos) |
---|
1347 | { |
---|
1348 | if (perm[crd+k] > a->pos) |
---|
1349 | { |
---|
1350 | for (l=i;l>=k;l--) perm[crd+l+1] = perm[crd+l]; |
---|
1351 | perm[crd+k] = a->pos; |
---|
1352 | i++; |
---|
1353 | } |
---|
1354 | a = a->n; |
---|
1355 | if ((a == NULL) || (a->pos > tored)) break; |
---|
1356 | } |
---|
1357 | k++; |
---|
1358 | if ((k > i) && (a->pos <= tored)) |
---|
1359 | { |
---|
1360 | do |
---|
1361 | { |
---|
1362 | i++; |
---|
1363 | perm[crd+i] = a->pos; |
---|
1364 | a = a->n; |
---|
1365 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1366 | break; |
---|
1367 | } |
---|
1368 | } |
---|
1369 | } |
---|
1370 | } |
---|
1371 | for (j=act;j;j--) // renumber m_act |
---|
1372 | { |
---|
1373 | k = 1; |
---|
1374 | a = m_act[j]; |
---|
1375 | while ((a != NULL) && (a->pos <= tored)) |
---|
1376 | { |
---|
1377 | if (perm[crd+k] == a->pos) |
---|
1378 | { |
---|
1379 | a->pos = crd+k; |
---|
1380 | a = a->n; |
---|
1381 | } |
---|
1382 | k++; |
---|
1383 | } |
---|
1384 | } |
---|
1385 | tored = crd+i; |
---|
1386 | for(k=1;k<=i;k++) // clean this from m_row |
---|
1387 | { |
---|
1388 | j = perm[crd+k]; |
---|
1389 | if (m_row[j] != NULL) |
---|
1390 | { |
---|
1391 | r = m_row[j]; |
---|
1392 | m_row[j] = NULL; |
---|
1393 | do |
---|
1394 | { |
---|
1395 | ap = m_res[r->pos]; |
---|
1396 | loop |
---|
1397 | { |
---|
1398 | a = ap->n; |
---|
1399 | if (a == NULL) |
---|
1400 | { |
---|
1401 | h = ap->n = r; |
---|
1402 | r = r->n; |
---|
1403 | h->n = NULL; |
---|
1404 | h->pos = crd+k; |
---|
1405 | break; |
---|
1406 | } |
---|
1407 | ap = a; |
---|
1408 | } |
---|
1409 | } while (r!=NULL); |
---|
1410 | } |
---|
1411 | } |
---|
1412 | while(act) // clean m_act |
---|
1413 | { |
---|
1414 | crd++; |
---|
1415 | m_res[crd] = m_act[act]; |
---|
1416 | act--; |
---|
1417 | } |
---|
1418 | for (i=1;i<=tored;i++) // take the rest of m_row |
---|
1419 | { |
---|
1420 | if(m_row[i] != NULL) |
---|
1421 | { |
---|
1422 | tored++; |
---|
1423 | r = m_row[i]; |
---|
1424 | m_row[i] = NULL; |
---|
1425 | perm[tored] = i; |
---|
1426 | do |
---|
1427 | { |
---|
1428 | ap = m_res[r->pos]; |
---|
1429 | loop |
---|
1430 | { |
---|
1431 | a = ap->n; |
---|
1432 | if (a == NULL) |
---|
1433 | { |
---|
1434 | h = ap->n = r; |
---|
1435 | r = r->n; |
---|
1436 | h->n = NULL; |
---|
1437 | h->pos = tored; |
---|
1438 | break; |
---|
1439 | } |
---|
1440 | ap = a; |
---|
1441 | } |
---|
1442 | } while (r!=NULL); |
---|
1443 | } |
---|
1444 | } |
---|
1445 | for (i=tored+1;i<=nrows;i++) // take the rest of m_row |
---|
1446 | { |
---|
1447 | if(m_row[i] != NULL) |
---|
1448 | { |
---|
1449 | r = m_row[i]; |
---|
1450 | m_row[i] = NULL; |
---|
1451 | do |
---|
1452 | { |
---|
1453 | ap = m_res[r->pos]; |
---|
1454 | loop |
---|
1455 | { |
---|
1456 | a = ap->n; |
---|
1457 | if (a == NULL) |
---|
1458 | { |
---|
1459 | h = ap->n = r; |
---|
1460 | r = r->n; |
---|
1461 | h->n = NULL; |
---|
1462 | h->pos = i; |
---|
1463 | break; |
---|
1464 | } |
---|
1465 | ap = a; |
---|
1466 | } |
---|
1467 | } while (r!=NULL); |
---|
1468 | } |
---|
1469 | } |
---|
1470 | while (inred < ncols) // take unreducable |
---|
1471 | { |
---|
1472 | crd++; |
---|
1473 | inred++; |
---|
1474 | m_res[crd] = m_res[inred]; |
---|
1475 | } |
---|
1476 | } |
---|
1477 | |
---|
1478 | /* |
---|
1479 | * multiply and divide the column, that goes to result |
---|
1480 | */ |
---|
1481 | void sparse_mat::smMultCol() |
---|
1482 | { |
---|
1483 | smpoly a = m_act[act]; |
---|
1484 | int e = crd; |
---|
1485 | poly ha; |
---|
1486 | int f; |
---|
1487 | |
---|
1488 | while (a != NULL) |
---|
1489 | { |
---|
1490 | f = a->e; |
---|
1491 | if (f < e) |
---|
1492 | { |
---|
1493 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1494 | pDelete(&a->m); |
---|
1495 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1496 | a->m = ha; |
---|
1497 | if (normalize) pNormalize(a->m); |
---|
1498 | } |
---|
1499 | a = a->n; |
---|
1500 | } |
---|
1501 | } |
---|
1502 | |
---|
1503 | /* |
---|
1504 | * multiply and divide the m_act finaly |
---|
1505 | */ |
---|
1506 | void sparse_mat::smFinalMult() |
---|
1507 | { |
---|
1508 | smpoly a; |
---|
1509 | poly ha; |
---|
1510 | int i, f; |
---|
1511 | int e = crd; |
---|
1512 | |
---|
1513 | for (i=act; i; i--) |
---|
1514 | { |
---|
1515 | a = m_act[i]; |
---|
1516 | do |
---|
1517 | { |
---|
1518 | f = a->e; |
---|
1519 | if (f < e) |
---|
1520 | { |
---|
1521 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1522 | pDelete(&a->m); |
---|
1523 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1524 | a->m = ha; |
---|
1525 | } |
---|
1526 | if (normalize) pNormalize(a->m); |
---|
1527 | a = a->n; |
---|
1528 | } while (a != NULL); |
---|
1529 | } |
---|
1530 | } |
---|
1531 | |
---|
1532 | /* |
---|
1533 | * check for denominators |
---|
1534 | */ |
---|
1535 | int sparse_mat::smCheckNormalize() |
---|
1536 | { |
---|
1537 | int i; |
---|
1538 | smpoly a; |
---|
1539 | |
---|
1540 | for (i=act; i; i--) |
---|
1541 | { |
---|
1542 | a = m_act[i]; |
---|
1543 | do |
---|
1544 | { |
---|
1545 | if(smHaveDenom(a->m)) return 1; |
---|
1546 | a = a->n; |
---|
1547 | } while (a != NULL); |
---|
1548 | } |
---|
1549 | return 0; |
---|
1550 | } |
---|
1551 | |
---|
1552 | /* |
---|
1553 | * normalize |
---|
1554 | */ |
---|
1555 | void sparse_mat::smNormalize() |
---|
1556 | { |
---|
1557 | smpoly a; |
---|
1558 | int i; |
---|
1559 | int e = crd; |
---|
1560 | |
---|
1561 | for (i=act; i; i--) |
---|
1562 | { |
---|
1563 | a = m_act[i]; |
---|
1564 | do |
---|
1565 | { |
---|
1566 | if (e == a->e) pNormalize(a->m); |
---|
1567 | a = a->n; |
---|
1568 | } while (a != NULL); |
---|
1569 | } |
---|
1570 | } |
---|
1571 | |
---|
1572 | /* |
---|
1573 | * multiply and divide the element, save poly |
---|
1574 | */ |
---|
1575 | poly sparse_mat::smMultPoly(smpoly a) |
---|
1576 | { |
---|
1577 | int f = a->e; |
---|
1578 | poly r, h; |
---|
1579 | |
---|
1580 | if (f < crd) |
---|
1581 | { |
---|
1582 | h = r = a->m; |
---|
1583 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m); |
---|
1584 | if (f) SM_DIV(h, m_res[f]->m); |
---|
1585 | a->m = h; |
---|
1586 | if (normalize) pNormalize(a->m); |
---|
1587 | a->f = smPolyWeight(a); |
---|
1588 | return r; |
---|
1589 | } |
---|
1590 | else |
---|
1591 | return NULL; |
---|
1592 | } |
---|
1593 | |
---|
1594 | /* |
---|
1595 | * delete the m_act finaly |
---|
1596 | */ |
---|
1597 | void sparse_mat::smActDel() |
---|
1598 | { |
---|
1599 | smpoly a; |
---|
1600 | int i; |
---|
1601 | |
---|
1602 | for (i=act; i; i--) |
---|
1603 | { |
---|
1604 | a = m_act[i]; |
---|
1605 | do |
---|
1606 | { |
---|
1607 | smElemDelete(&a); |
---|
1608 | } while (a != NULL); |
---|
1609 | } |
---|
1610 | } |
---|
1611 | |
---|
1612 | /* |
---|
1613 | * delete the pivotcol |
---|
1614 | */ |
---|
1615 | void sparse_mat::smColDel() |
---|
1616 | { |
---|
1617 | smpoly a = m_act[act]; |
---|
1618 | |
---|
1619 | while (a != NULL) |
---|
1620 | { |
---|
1621 | smElemDelete(&a); |
---|
1622 | } |
---|
1623 | } |
---|
1624 | |
---|
1625 | /* |
---|
1626 | * delete pivot elements |
---|
1627 | */ |
---|
1628 | void sparse_mat::smPivDel() |
---|
1629 | { |
---|
1630 | int i=crd; |
---|
1631 | |
---|
1632 | while (i != 0) |
---|
1633 | { |
---|
1634 | smElemDelete(&m_res[i]); |
---|
1635 | i--; |
---|
1636 | } |
---|
1637 | } |
---|
1638 | |
---|
1639 | /* |
---|
1640 | * the sign of the determinant |
---|
1641 | */ |
---|
1642 | void sparse_mat::smSign() |
---|
1643 | { |
---|
1644 | int j,i; |
---|
1645 | if (act > 2) |
---|
1646 | { |
---|
1647 | if (cpiv!=act) sign=-sign; |
---|
1648 | if ((act%2)==0) sign=-sign; |
---|
1649 | i=1; |
---|
1650 | j=perm[1]; |
---|
1651 | while(j<rpiv) |
---|
1652 | { |
---|
1653 | sign=-sign; |
---|
1654 | i++; |
---|
1655 | j=perm[i]; |
---|
1656 | } |
---|
1657 | while(perm[i]!=0) |
---|
1658 | { |
---|
1659 | perm[i]=perm[i+1]; |
---|
1660 | i++; |
---|
1661 | } |
---|
1662 | } |
---|
1663 | else |
---|
1664 | { |
---|
1665 | if (cpiv!=1) sign=-sign; |
---|
1666 | if (rpiv!=perm[1]) sign=-sign; |
---|
1667 | } |
---|
1668 | } |
---|
1669 | |
---|
1670 | void sparse_mat::smInitPerm() |
---|
1671 | { |
---|
1672 | int i; |
---|
1673 | for (i=act;i;i--) perm[i]=i; |
---|
1674 | } |
---|
1675 | |
---|
1676 | /* ----------------- arithmetic ------------------ */ |
---|
1677 | |
---|
1678 | /* |
---|
1679 | * returns a*b |
---|
1680 | * a,b NOT destroyed |
---|
1681 | */ |
---|
1682 | poly smMult(poly a, poly b) |
---|
1683 | { |
---|
1684 | poly pa, res, r; |
---|
1685 | |
---|
1686 | if (smSmaller(a, b)) |
---|
1687 | { |
---|
1688 | r = a; |
---|
1689 | a = b; |
---|
1690 | b = r; |
---|
1691 | } |
---|
1692 | if (pNext(b) == NULL) |
---|
1693 | { |
---|
1694 | if (pIsConstantComp(b)) |
---|
1695 | return pMultCopyN(a, pGetCoeff(b)); |
---|
1696 | else |
---|
1697 | return smEMult(a, b); |
---|
1698 | } |
---|
1699 | pa = res = smEMult(a, b); |
---|
1700 | pIter(b); |
---|
1701 | do |
---|
1702 | { |
---|
1703 | r = smEMult(a, b); |
---|
1704 | smCombineChain(&pa, r); |
---|
1705 | pIter(b); |
---|
1706 | } while (b != NULL); |
---|
1707 | return res; |
---|
1708 | } |
---|
1709 | |
---|
1710 | /*2 |
---|
1711 | * exact division a/b |
---|
1712 | * a destroyed, b NOT destroyed |
---|
1713 | */ |
---|
1714 | void smPolyDiv(poly a, poly b) |
---|
1715 | { |
---|
1716 | const number x = pGetCoeff(b); |
---|
1717 | number y, yn; |
---|
1718 | poly t, h, dummy; |
---|
1719 | int i; |
---|
1720 | |
---|
1721 | if (pNext(b) == NULL) |
---|
1722 | { |
---|
1723 | do |
---|
1724 | { |
---|
1725 | if (!pIsConstantComp(b)) |
---|
1726 | { |
---|
1727 | for (i=pVariables; i; i--) |
---|
1728 | pSubExp(a,i,pGetExp(b,i)); |
---|
1729 | pSetm(a); |
---|
1730 | } |
---|
1731 | y = nDiv(pGetCoeff(a),x); |
---|
1732 | nNormalize(y); |
---|
1733 | pSetCoeff(a,y); |
---|
1734 | pIter(a); |
---|
1735 | } while (a != NULL); |
---|
1736 | return; |
---|
1737 | } |
---|
1738 | dummy = pInit(); |
---|
1739 | do |
---|
1740 | { |
---|
1741 | for (i=pVariables; i; i--) |
---|
1742 | pSubExp(a,i,pGetExp(b,i)); |
---|
1743 | pSetm(a); |
---|
1744 | y = nDiv(pGetCoeff(a),x); |
---|
1745 | nNormalize(y); |
---|
1746 | pSetCoeff(a,y); |
---|
1747 | yn = nNeg(nCopy(y)); |
---|
1748 | t = pNext(b); |
---|
1749 | h = dummy; |
---|
1750 | do |
---|
1751 | { |
---|
1752 | h = pNext(h) = pInit(); |
---|
1753 | //pSetComp(h,0); |
---|
1754 | for (i=pVariables; i; i--) |
---|
1755 | pSetExp(h,i,pGetExp(a,i)+pGetExp(t,i)); |
---|
1756 | pSetm(h); |
---|
1757 | pSetCoeff0(h,nMult(yn, pGetCoeff(t))); |
---|
1758 | pIter(t); |
---|
1759 | } while (t != NULL); |
---|
1760 | nDelete(&yn); |
---|
1761 | pNext(h) = NULL; |
---|
1762 | a = pNext(a) = pAdd(pNext(a), pNext(dummy)); |
---|
1763 | } while (a!=NULL); |
---|
1764 | pFree1(dummy); |
---|
1765 | } |
---|
1766 | |
---|
1767 | /* |
---|
1768 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1769 | */ |
---|
1770 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1771 | { |
---|
1772 | poly pa, e, res, r; |
---|
1773 | BOOLEAN lead; |
---|
1774 | |
---|
1775 | if (smSmaller(a, b)) |
---|
1776 | { |
---|
1777 | r = a; |
---|
1778 | a = b; |
---|
1779 | b = r; |
---|
1780 | } |
---|
1781 | if ((c == NULL) || pIsConstantComp(c)) |
---|
1782 | { |
---|
1783 | if (pNext(b) == NULL) |
---|
1784 | { |
---|
1785 | if (pIsConstantComp(b)) |
---|
1786 | return pMultCopyN(a, pGetCoeff(b)); |
---|
1787 | else |
---|
1788 | return smEMult(a, b); |
---|
1789 | } |
---|
1790 | pa = res = smEMult(a, b); |
---|
1791 | pIter(b); |
---|
1792 | do |
---|
1793 | { |
---|
1794 | r = smEMult(a, b); |
---|
1795 | smCombineChain(&pa, r); |
---|
1796 | pIter(b); |
---|
1797 | } while (b != NULL); |
---|
1798 | return res; |
---|
1799 | } |
---|
1800 | res = NULL; |
---|
1801 | e = pInit(); |
---|
1802 | lead = FALSE; |
---|
1803 | while (!lead) |
---|
1804 | { |
---|
1805 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1806 | if (smIsNegQuot(e, b, c)) |
---|
1807 | { |
---|
1808 | lead = smCheckLead(a, e); |
---|
1809 | r = smDMult(a, e); |
---|
1810 | smComplete(r, b, c); |
---|
1811 | } |
---|
1812 | else |
---|
1813 | { |
---|
1814 | lead = TRUE; |
---|
1815 | r = smEMult(a, e); |
---|
1816 | } |
---|
1817 | if (lead) |
---|
1818 | { |
---|
1819 | if (res != NULL) |
---|
1820 | { |
---|
1821 | smFindRef(&pa, &res, r); |
---|
1822 | if (pa == NULL) |
---|
1823 | lead = FALSE; |
---|
1824 | } |
---|
1825 | else |
---|
1826 | { |
---|
1827 | pa = res = r; |
---|
1828 | } |
---|
1829 | } |
---|
1830 | else |
---|
1831 | res = pAdd(res, r); |
---|
1832 | pIter(b); |
---|
1833 | if (b == NULL) |
---|
1834 | { |
---|
1835 | pFree1(e); |
---|
1836 | return res; |
---|
1837 | } |
---|
1838 | } |
---|
1839 | do |
---|
1840 | { |
---|
1841 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1842 | if (smIsNegQuot(e, b, c)) |
---|
1843 | { |
---|
1844 | r = smDMult(a, e); |
---|
1845 | smComplete(r, b, c); |
---|
1846 | if (smCheckLead(a, e)) |
---|
1847 | smCombineChain(&pa, r); |
---|
1848 | else |
---|
1849 | pa = pAdd(pa,r); |
---|
1850 | } |
---|
1851 | else |
---|
1852 | { |
---|
1853 | r = smEMult(a, e); |
---|
1854 | smCombineChain(&pa, r); |
---|
1855 | } |
---|
1856 | pIter(b); |
---|
1857 | } while (b != NULL); |
---|
1858 | pFree1(e); |
---|
1859 | return res; |
---|
1860 | } |
---|
1861 | |
---|
1862 | /*n |
---|
1863 | * exact division a/b |
---|
1864 | * a is a result of smMultDiv |
---|
1865 | * a destroyed, b NOT destroyed |
---|
1866 | */ |
---|
1867 | void smSpecialPolyDiv(poly a, poly b) |
---|
1868 | { |
---|
1869 | if (pNext(b) == NULL) |
---|
1870 | { |
---|
1871 | smPolyDivN(a, pGetCoeff(b)); |
---|
1872 | return; |
---|
1873 | } |
---|
1874 | smExactPolyDiv(a, b); |
---|
1875 | } |
---|
1876 | |
---|
1877 | /* ------------ internals arithmetic ------------- */ |
---|
1878 | static void smExactPolyDiv(poly a, poly b) |
---|
1879 | { |
---|
1880 | const number x = pGetCoeff(b); |
---|
1881 | poly tail = pNext(b), e = pInit(); |
---|
1882 | poly h; |
---|
1883 | number y, yn; |
---|
1884 | |
---|
1885 | do |
---|
1886 | { |
---|
1887 | y = nDiv(pGetCoeff(a), x); |
---|
1888 | nNormalize(y); |
---|
1889 | pSetCoeff(a,y); |
---|
1890 | yn = nNeg(nCopy(y)); |
---|
1891 | pSetCoeff0(e,yn); |
---|
1892 | if (smIsNegQuot(e, a, b)) |
---|
1893 | { |
---|
1894 | h = smDMult(tail, e); |
---|
1895 | smComplete(h, a, b); |
---|
1896 | } |
---|
1897 | else |
---|
1898 | h = smEMult(tail, e); |
---|
1899 | nDelete(&yn); |
---|
1900 | a = pNext(a) = pAdd(pNext(a), h); |
---|
1901 | } while (a!=NULL); |
---|
1902 | pFree1(e); |
---|
1903 | } |
---|
1904 | |
---|
1905 | static BOOLEAN smIsNegQuot(poly a, const poly b, const poly c) |
---|
1906 | { |
---|
1907 | int i; |
---|
1908 | |
---|
1909 | i=pVariables; |
---|
1910 | while (i&&(pGetExp(b,i)<pGetExp(c,i))) i--; |
---|
1911 | if(i) |
---|
1912 | { |
---|
1913 | for (i=pVariables; i; i--) |
---|
1914 | { |
---|
1915 | if(pGetExp(b,i)<pGetExp(c,i)) |
---|
1916 | pSetExp(a,i,pGetExp(c,i)-pGetExp(b,i)); |
---|
1917 | else |
---|
1918 | pSetExp(a,i,0); |
---|
1919 | } |
---|
1920 | return TRUE; |
---|
1921 | } |
---|
1922 | else |
---|
1923 | { |
---|
1924 | for (i=pVariables; i; i--) |
---|
1925 | { |
---|
1926 | pSetExp(a,i,pGetExp(b,i)-pGetExp(c,i)); |
---|
1927 | } |
---|
1928 | return FALSE; |
---|
1929 | } |
---|
1930 | } |
---|
1931 | |
---|
1932 | static poly smEMult(poly t, const poly e) |
---|
1933 | { |
---|
1934 | const number y = pGetCoeff(e); |
---|
1935 | poly res, h; |
---|
1936 | int i; |
---|
1937 | |
---|
1938 | h = res = pNew(); |
---|
1939 | loop |
---|
1940 | { |
---|
1941 | pCopy2(h,t); |
---|
1942 | for (i=pVariables; i; i--) |
---|
1943 | pAddExp(h,i,pGetExp(e,i)); |
---|
1944 | pSetm(h); |
---|
1945 | pSetCoeff0(h,nMult(y,pGetCoeff(t))); |
---|
1946 | pIter(t); |
---|
1947 | if (t == NULL) |
---|
1948 | { |
---|
1949 | pNext(h) = NULL; |
---|
1950 | return res; |
---|
1951 | } |
---|
1952 | h = pNext(h) = pNew(); |
---|
1953 | } |
---|
1954 | } |
---|
1955 | |
---|
1956 | static BOOLEAN smCheckLead(const poly t, const poly e) |
---|
1957 | { |
---|
1958 | int i; |
---|
1959 | Exponent_t w; |
---|
1960 | for (i=pVariables; i; i--) |
---|
1961 | { |
---|
1962 | w = pGetExp(e,i); |
---|
1963 | if (w&&(w>pGetExp(t,i))) |
---|
1964 | return FALSE; |
---|
1965 | } |
---|
1966 | return TRUE; |
---|
1967 | } |
---|
1968 | |
---|
1969 | static poly smDMult(poly t, const poly e) |
---|
1970 | { |
---|
1971 | const number y = pGetCoeff(e); |
---|
1972 | poly res, h; |
---|
1973 | |
---|
1974 | loop |
---|
1975 | { |
---|
1976 | if(smCheckLead(t,e)) break; |
---|
1977 | pIter(t); |
---|
1978 | if(t==NULL) return NULL; |
---|
1979 | } |
---|
1980 | h = res = pNew(); |
---|
1981 | loop |
---|
1982 | { |
---|
1983 | pCopy2(h,t); |
---|
1984 | pSetCoeff0(h,nMult(y,pGetCoeff(t))); |
---|
1985 | loop |
---|
1986 | { |
---|
1987 | pIter(t); |
---|
1988 | if(t==NULL) |
---|
1989 | { |
---|
1990 | pNext(h)=NULL; |
---|
1991 | return res; |
---|
1992 | } |
---|
1993 | if(smCheckLead(t,e)) break; |
---|
1994 | } |
---|
1995 | h=pNext(h)=pNew(); |
---|
1996 | } |
---|
1997 | } |
---|
1998 | |
---|
1999 | static void smComplete(poly t, const poly b, const poly c) |
---|
2000 | { |
---|
2001 | int i; |
---|
2002 | while(t!=NULL) |
---|
2003 | { |
---|
2004 | for (i=pVariables; i; i--) |
---|
2005 | { |
---|
2006 | pAddExp(t,i,pGetExp(b,i)); |
---|
2007 | pSubExp(t,i,pGetExp(c,i)); |
---|
2008 | pSetm(t); |
---|
2009 | } |
---|
2010 | pIter(t); |
---|
2011 | } |
---|
2012 | } |
---|
2013 | |
---|
2014 | static void smPolyDivN(poly a, const number x) |
---|
2015 | { |
---|
2016 | number y; |
---|
2017 | |
---|
2018 | do |
---|
2019 | { |
---|
2020 | y = nDiv(pGetCoeff(a),x); |
---|
2021 | nNormalize(y); |
---|
2022 | pSetCoeff(a,y); |
---|
2023 | pIter(a); |
---|
2024 | } while (a != NULL); |
---|
2025 | } |
---|
2026 | |
---|
2027 | static BOOLEAN smSmaller(poly a, poly b) |
---|
2028 | { |
---|
2029 | loop |
---|
2030 | { |
---|
2031 | pIter(b); |
---|
2032 | if (b == NULL) return TRUE; |
---|
2033 | pIter(a); |
---|
2034 | if (a == NULL) return FALSE; |
---|
2035 | } |
---|
2036 | } |
---|
2037 | |
---|
2038 | static void smCombineChain(poly *px, poly r) |
---|
2039 | { |
---|
2040 | poly pa = *px, pb; |
---|
2041 | number x; |
---|
2042 | int i; |
---|
2043 | |
---|
2044 | loop |
---|
2045 | { |
---|
2046 | pb = pNext(pa); |
---|
2047 | if (pb == NULL) |
---|
2048 | { |
---|
2049 | pa = pNext(pa) = r; |
---|
2050 | break; |
---|
2051 | } |
---|
2052 | i = pComp0(pb, r); |
---|
2053 | if (i > 0) |
---|
2054 | pa = pb; |
---|
2055 | else |
---|
2056 | { |
---|
2057 | if (i == 0) |
---|
2058 | { |
---|
2059 | x = nAdd(pGetCoeff(pb), pGetCoeff(r)); |
---|
2060 | pDelete1(&r); |
---|
2061 | if (nIsZero(x)) |
---|
2062 | { |
---|
2063 | pDelete1(&pb); |
---|
2064 | pNext(pa) = pAdd(pb,r); |
---|
2065 | } |
---|
2066 | else |
---|
2067 | { |
---|
2068 | pa = pb; |
---|
2069 | pSetCoeff(pa,x); |
---|
2070 | pNext(pa) = pAdd(pNext(pa), r); |
---|
2071 | } |
---|
2072 | } |
---|
2073 | else |
---|
2074 | { |
---|
2075 | pa = pNext(pa) = r; |
---|
2076 | pNext(pa) = pAdd(pb, pNext(pa)); |
---|
2077 | } |
---|
2078 | break; |
---|
2079 | } |
---|
2080 | } |
---|
2081 | *px = pa; |
---|
2082 | } |
---|
2083 | |
---|
2084 | static void smFindRef(poly *ref, poly *px, poly r) |
---|
2085 | { |
---|
2086 | number x; |
---|
2087 | int i; |
---|
2088 | poly pa = *px, pp = NULL; |
---|
2089 | |
---|
2090 | loop |
---|
2091 | { |
---|
2092 | i = pComp0(pa, r); |
---|
2093 | if (i > 0) |
---|
2094 | { |
---|
2095 | pp = pa; |
---|
2096 | pIter(pa); |
---|
2097 | if (pa==NULL) |
---|
2098 | { |
---|
2099 | pNext(pp) = r; |
---|
2100 | break; |
---|
2101 | } |
---|
2102 | } |
---|
2103 | else |
---|
2104 | { |
---|
2105 | if (i == 0) |
---|
2106 | { |
---|
2107 | x = nAdd(pGetCoeff(pa), pGetCoeff(r)); |
---|
2108 | pDelete1(&r); |
---|
2109 | if (nIsZero(x)) |
---|
2110 | { |
---|
2111 | pDelete1(&pa); |
---|
2112 | if (pp!=NULL) |
---|
2113 | pNext(pp) = pAdd(pa,r); |
---|
2114 | else |
---|
2115 | *px = pAdd(pa,r); |
---|
2116 | } |
---|
2117 | else |
---|
2118 | { |
---|
2119 | pp = pa; |
---|
2120 | pSetCoeff(pp,x); |
---|
2121 | pNext(pp) = pAdd(pNext(pp), r); |
---|
2122 | } |
---|
2123 | } |
---|
2124 | else |
---|
2125 | { |
---|
2126 | if (pp!=NULL) |
---|
2127 | pp = pNext(pp) = r; |
---|
2128 | else |
---|
2129 | *px = pp = r; |
---|
2130 | pNext(pp) = pAdd(pa, pNext(r)); |
---|
2131 | } |
---|
2132 | break; |
---|
2133 | } |
---|
2134 | } |
---|
2135 | *ref = pp; |
---|
2136 | } |
---|
2137 | |
---|
2138 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2139 | |
---|
2140 | static void smElemDelete(smpoly *r) |
---|
2141 | { |
---|
2142 | smpoly a = *r, b = a->n; |
---|
2143 | |
---|
2144 | pDelete(&a->m); |
---|
2145 | omFreeBin((void *)a, smprec_bin); |
---|
2146 | *r = b; |
---|
2147 | } |
---|
2148 | |
---|
2149 | static smpoly smElemCopy(smpoly a) |
---|
2150 | { |
---|
2151 | smpoly r = (smpoly)omAllocBin(smprec_bin); |
---|
2152 | memcpy(r, a, sizeof(smprec)); |
---|
2153 | /* r->m = pCopy(r->m); */ |
---|
2154 | return r; |
---|
2155 | } |
---|
2156 | |
---|
2157 | /* |
---|
2158 | * from poly to smpoly |
---|
2159 | * do not destroy p |
---|
2160 | */ |
---|
2161 | static smpoly smPoly2Smpoly(poly q) |
---|
2162 | { |
---|
2163 | poly pp; |
---|
2164 | smpoly res, a; |
---|
2165 | Exponent_t x; |
---|
2166 | |
---|
2167 | if (q == NULL) |
---|
2168 | return NULL; |
---|
2169 | a = res = (smpoly)omAllocBin(smprec_bin); |
---|
2170 | a->pos = x = pGetComp(q); |
---|
2171 | a->m = q; |
---|
2172 | a->e = 0; |
---|
2173 | loop |
---|
2174 | { |
---|
2175 | pSetComp(q,0); |
---|
2176 | pp = q; |
---|
2177 | pIter(q); |
---|
2178 | if (q == NULL) |
---|
2179 | { |
---|
2180 | a->n = NULL; |
---|
2181 | return res; |
---|
2182 | } |
---|
2183 | if (pGetComp(q) != x) |
---|
2184 | { |
---|
2185 | a = a->n = (smpoly)omAllocBin(smprec_bin); |
---|
2186 | pNext(pp) = NULL; |
---|
2187 | a->pos = x = pGetComp(q); |
---|
2188 | a->m = q; |
---|
2189 | a->e = 0; |
---|
2190 | } |
---|
2191 | } |
---|
2192 | } |
---|
2193 | |
---|
2194 | /* |
---|
2195 | * from smpoly to poly |
---|
2196 | * destroy a |
---|
2197 | */ |
---|
2198 | static poly smSmpoly2Poly(smpoly a) |
---|
2199 | { |
---|
2200 | smpoly b; |
---|
2201 | poly res, pp, q; |
---|
2202 | Exponent_t x; |
---|
2203 | |
---|
2204 | if (a == NULL) |
---|
2205 | return NULL; |
---|
2206 | x = a->pos; |
---|
2207 | q = res = a->m; |
---|
2208 | loop |
---|
2209 | { |
---|
2210 | pSetComp(q,x); |
---|
2211 | pp = q; |
---|
2212 | pIter(q); |
---|
2213 | if (q == NULL) |
---|
2214 | break; |
---|
2215 | } |
---|
2216 | loop |
---|
2217 | { |
---|
2218 | b = a; |
---|
2219 | a = a->n; |
---|
2220 | omFreeBin((void *)b, smprec_bin); |
---|
2221 | if (a == NULL) |
---|
2222 | return res; |
---|
2223 | x = a->pos; |
---|
2224 | q = pNext(pp) = a->m; |
---|
2225 | loop |
---|
2226 | { |
---|
2227 | pSetComp(q,x); |
---|
2228 | pp = q; |
---|
2229 | pIter(q); |
---|
2230 | if (q == NULL) |
---|
2231 | break; |
---|
2232 | } |
---|
2233 | } |
---|
2234 | } |
---|
2235 | |
---|
2236 | /* |
---|
2237 | * weigth of a polynomial, for pivot strategy |
---|
2238 | */ |
---|
2239 | static float smPolyWeight(smpoly a) |
---|
2240 | { |
---|
2241 | poly p = a->m; |
---|
2242 | int i; |
---|
2243 | float res = (float)nSize(pGetCoeff(p)); |
---|
2244 | |
---|
2245 | if (pNext(p) == NULL) |
---|
2246 | { |
---|
2247 | for(i=pVariables; i>0; i--) |
---|
2248 | { |
---|
2249 | if (pGetExp(p,i) != 0) return res+1.0; |
---|
2250 | } |
---|
2251 | return res; |
---|
2252 | } |
---|
2253 | else |
---|
2254 | { |
---|
2255 | i = 0; |
---|
2256 | res = 0.0; |
---|
2257 | do |
---|
2258 | { |
---|
2259 | i++; |
---|
2260 | res += (float)nSize(pGetCoeff(p)); |
---|
2261 | pIter(p); |
---|
2262 | } |
---|
2263 | while (p); |
---|
2264 | return res+(float)i; |
---|
2265 | } |
---|
2266 | } |
---|
2267 | |
---|
2268 | static BOOLEAN smHaveDenom(poly a) |
---|
2269 | { |
---|
2270 | BOOLEAN sw; |
---|
2271 | number x,o=nInit(1); |
---|
2272 | |
---|
2273 | while (a != NULL) |
---|
2274 | { |
---|
2275 | x = nGetDenom(pGetCoeff(a)); |
---|
2276 | sw = nEqual(x,o); |
---|
2277 | nDelete(&x); |
---|
2278 | if (!sw) |
---|
2279 | { |
---|
2280 | nDelete(&o); |
---|
2281 | return TRUE; |
---|
2282 | } |
---|
2283 | pIter(a); |
---|
2284 | } |
---|
2285 | nDelete(&o); |
---|
2286 | return FALSE; |
---|
2287 | } |
---|
2288 | |
---|
2289 | static number smCleardenom(ideal id) |
---|
2290 | { |
---|
2291 | poly a; |
---|
2292 | number x,y,res=nInit(1); |
---|
2293 | BOOLEAN sw=FALSE; |
---|
2294 | |
---|
2295 | for (int i=0; i<IDELEMS(id); i++) |
---|
2296 | { |
---|
2297 | a = id->m[i]; |
---|
2298 | sw = smHaveDenom(a); |
---|
2299 | if (sw) break; |
---|
2300 | } |
---|
2301 | if (!sw) return res; |
---|
2302 | for (int i=0; i<IDELEMS(id); i++) |
---|
2303 | { |
---|
2304 | a = id->m[i]; |
---|
2305 | x = nCopy(pGetCoeff(a)); |
---|
2306 | pCleardenom(a); |
---|
2307 | y = nDiv(x,pGetCoeff(a)); |
---|
2308 | nDelete(&x); |
---|
2309 | x = nMult(res,y); |
---|
2310 | nNormalize(x); |
---|
2311 | nDelete(&res); |
---|
2312 | res = x; |
---|
2313 | } |
---|
2314 | return res; |
---|
2315 | } |
---|
2316 | |
---|
2317 | /* ----------------- gauss elimination ------------------ */ |
---|
2318 | /* in structs.h */ |
---|
2319 | typedef struct smnrec sm_nrec; |
---|
2320 | typedef sm_nrec * smnumber; |
---|
2321 | struct smnrec{ |
---|
2322 | smnumber n; // the next element |
---|
2323 | int pos; // position |
---|
2324 | number m; // the element |
---|
2325 | }; |
---|
2326 | |
---|
2327 | static omBin smnrec_bin = omGetSpecBin(sizeof(smnrec)); |
---|
2328 | |
---|
2329 | /* declare internal 'C' stuff */ |
---|
2330 | static void smNumberDelete(smnumber *); |
---|
2331 | static smnumber smNumberCopy(smnumber); |
---|
2332 | static smnumber smPoly2Smnumber(poly); |
---|
2333 | static poly smSmnumber2Poly(number); |
---|
2334 | static BOOLEAN smCheckSolv(ideal); |
---|
2335 | |
---|
2336 | /* class for sparse number matrix: |
---|
2337 | */ |
---|
2338 | class sparse_number_mat{ |
---|
2339 | private: |
---|
2340 | int nrows, ncols; // dimension of the problem |
---|
2341 | int act; // number of unreduced columns (start: ncols) |
---|
2342 | int crd; // number of reduced columns (start: 0) |
---|
2343 | int tored; // border for rows to reduce |
---|
2344 | int sing; // indicator for singular problem |
---|
2345 | int rpiv; // row-position of the pivot |
---|
2346 | int *perm; // permutation of rows |
---|
2347 | number one; // the "1" |
---|
2348 | number *sol; // field for solution |
---|
2349 | int *wrw, *wcl; // weights of rows and columns |
---|
2350 | smnumber * m_act; // unreduced columns |
---|
2351 | smnumber * m_res; // reduced columns (result) |
---|
2352 | smnumber * m_row; // reduced part of rows |
---|
2353 | smnumber red; // row to reduce |
---|
2354 | smnumber piv; // pivot |
---|
2355 | smnumber dumm; // allocated dummy |
---|
2356 | void smColToRow(); |
---|
2357 | void smRowToCol(); |
---|
2358 | void smSelectPR(); |
---|
2359 | void smRealPivot(); |
---|
2360 | void smZeroToredElim(); |
---|
2361 | void smGElim(); |
---|
2362 | void smAllDel(); |
---|
2363 | public: |
---|
2364 | sparse_number_mat(ideal); |
---|
2365 | ~sparse_number_mat(); |
---|
2366 | int smIsSing() { return sing; } |
---|
2367 | void smTriangular(); |
---|
2368 | void smSolv(); |
---|
2369 | ideal smRes2Ideal(); |
---|
2370 | }; |
---|
2371 | |
---|
2372 | /* ----------------- basics (used from 'C') ------------------ */ |
---|
2373 | /*2 |
---|
2374 | * returns the solution of a linear equation |
---|
2375 | * solution of M*x = r (M has dimension nXn) => |
---|
2376 | * I = module(transprose(M)) + r*gen(n+1) |
---|
2377 | * uses Gauss-elimination |
---|
2378 | */ |
---|
2379 | lists smCallSolv(ideal I) |
---|
2380 | { |
---|
2381 | sparse_number_mat *linsolv; |
---|
2382 | int k; |
---|
2383 | ring origR; |
---|
2384 | sip_sring tmpR; |
---|
2385 | ideal rr, ss; |
---|
2386 | lists res; |
---|
2387 | |
---|
2388 | if (idIsConstant(I)==FALSE) |
---|
2389 | { |
---|
2390 | WerrorS("symbol in equation"); |
---|
2391 | return NULL; |
---|
2392 | } |
---|
2393 | I->rank = idRankFreeModule(I); |
---|
2394 | if (smCheckSolv(I)) return NULL; |
---|
2395 | res=(lists)omAllocBin(slists_bin); |
---|
2396 | rr=smRingCopy(I,&origR,tmpR); |
---|
2397 | ss = NULL; |
---|
2398 | linsolv = new sparse_number_mat(rr); |
---|
2399 | linsolv->smTriangular(); |
---|
2400 | if (linsolv->smIsSing() == 0) |
---|
2401 | { |
---|
2402 | linsolv->smSolv(); |
---|
2403 | ss = linsolv->smRes2Ideal(); |
---|
2404 | } |
---|
2405 | else |
---|
2406 | WerrorS("singular problem for linsolv"); |
---|
2407 | delete linsolv; |
---|
2408 | if ((origR!=NULL) && (ss!=NULL)) |
---|
2409 | { |
---|
2410 | rChangeCurrRing(origR,TRUE); |
---|
2411 | rr = idInit(IDELEMS(ss), 1); |
---|
2412 | for (k=0;k<IDELEMS(ss);k++) |
---|
2413 | rr->m[k] = prCopyR(ss->m[k], &tmpR); |
---|
2414 | rChangeCurrRing(&tmpR,FALSE); |
---|
2415 | idDelete(&ss); |
---|
2416 | ss = rr; |
---|
2417 | } |
---|
2418 | if(origR!=NULL) |
---|
2419 | smRingClean(origR,tmpR); |
---|
2420 | res->Init(1); |
---|
2421 | res->m[0].rtyp=IDEAL_CMD; |
---|
2422 | res->m[0].data=(void *)ss; |
---|
2423 | return res; |
---|
2424 | } |
---|
2425 | |
---|
2426 | /* |
---|
2427 | * constructor, destroy smat |
---|
2428 | */ |
---|
2429 | sparse_number_mat::sparse_number_mat(ideal smat) |
---|
2430 | { |
---|
2431 | int i; |
---|
2432 | polyset pmat; |
---|
2433 | |
---|
2434 | crd = sing = 0; |
---|
2435 | act = ncols = smat->ncols; |
---|
2436 | tored = nrows = smat->rank; |
---|
2437 | i = tored+1; |
---|
2438 | perm = (int *)omAlloc(sizeof(int)*i); |
---|
2439 | m_row = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2440 | wrw = (int *)omAlloc(sizeof(int)*i); |
---|
2441 | i = ncols+1; |
---|
2442 | wcl = (int *)omAlloc(sizeof(int)*i); |
---|
2443 | m_act = (smnumber *)omAlloc(sizeof(smnumber)*i); |
---|
2444 | m_res = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2445 | dumm = (smnumber)omAllocBin(smnrec_bin); |
---|
2446 | pmat = smat->m; |
---|
2447 | for(i=ncols; i; i--) |
---|
2448 | { |
---|
2449 | m_act[i] = smPoly2Smnumber(pmat[i-1]); |
---|
2450 | } |
---|
2451 | omFreeSize((ADDRESS)pmat,smat->ncols*sizeof(poly)); |
---|
2452 | omFreeBin((ADDRESS)smat, sip_sideal_bin); |
---|
2453 | one = nInit(1); |
---|
2454 | } |
---|
2455 | |
---|
2456 | /* |
---|
2457 | * destructor |
---|
2458 | */ |
---|
2459 | sparse_number_mat::~sparse_number_mat() |
---|
2460 | { |
---|
2461 | int i; |
---|
2462 | omFreeBin((ADDRESS)dumm, smnrec_bin); |
---|
2463 | i = ncols+1; |
---|
2464 | omFreeSize((ADDRESS)m_res, sizeof(smnumber)*i); |
---|
2465 | omFreeSize((ADDRESS)m_act, sizeof(smnumber)*i); |
---|
2466 | omFreeSize((ADDRESS)wcl, sizeof(int)*i); |
---|
2467 | i = nrows+1; |
---|
2468 | omFreeSize((ADDRESS)wrw, sizeof(int)*i); |
---|
2469 | omFreeSize((ADDRESS)m_row, sizeof(smnumber)*i); |
---|
2470 | omFreeSize((ADDRESS)perm, sizeof(int)*i); |
---|
2471 | nDelete(&one); |
---|
2472 | } |
---|
2473 | |
---|
2474 | /* |
---|
2475 | * triangularization by Gauss-elimination |
---|
2476 | */ |
---|
2477 | void sparse_number_mat::smTriangular() |
---|
2478 | { |
---|
2479 | tored--; |
---|
2480 | this->smZeroToredElim(); |
---|
2481 | if (sing != 0) return; |
---|
2482 | while (act > 1) |
---|
2483 | { |
---|
2484 | this->smRealPivot(); |
---|
2485 | this->smSelectPR(); |
---|
2486 | this->smGElim(); |
---|
2487 | crd++; |
---|
2488 | this->smColToRow(); |
---|
2489 | act--; |
---|
2490 | this->smRowToCol(); |
---|
2491 | this->smZeroToredElim(); |
---|
2492 | if (sing != 0) return; |
---|
2493 | } |
---|
2494 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
2495 | piv = m_act[1]; |
---|
2496 | rpiv = piv->pos; |
---|
2497 | m_act[1] = piv->n; |
---|
2498 | piv->n = NULL; |
---|
2499 | crd++; |
---|
2500 | this->smColToRow(); |
---|
2501 | act--; |
---|
2502 | this->smRowToCol(); |
---|
2503 | } |
---|
2504 | |
---|
2505 | /* |
---|
2506 | * solve the triangular system |
---|
2507 | */ |
---|
2508 | void sparse_number_mat::smSolv() |
---|
2509 | { |
---|
2510 | int i, j; |
---|
2511 | number x, y, z; |
---|
2512 | smnumber s, d, r = m_row[nrows]; |
---|
2513 | |
---|
2514 | m_row[nrows] = NULL; |
---|
2515 | sol = (number *)omAlloc0(sizeof(number)*(crd+1)); |
---|
2516 | while (r != NULL) // expand the rigth hand side |
---|
2517 | { |
---|
2518 | sol[r->pos] = r->m; |
---|
2519 | s = r; |
---|
2520 | r = r->n; |
---|
2521 | omFreeBin((ADDRESS)s, smnrec_bin); |
---|
2522 | } |
---|
2523 | i = crd; // solve triangular system |
---|
2524 | if (sol[i] != NULL) |
---|
2525 | { |
---|
2526 | x = sol[i]; |
---|
2527 | sol[i] = nDiv(x, m_res[i]->m); |
---|
2528 | nDelete(&x); |
---|
2529 | } |
---|
2530 | i--; |
---|
2531 | while (i > 0) |
---|
2532 | { |
---|
2533 | x = NULL; |
---|
2534 | d = m_res[i]; |
---|
2535 | s = d->n; |
---|
2536 | while (s != NULL) |
---|
2537 | { |
---|
2538 | j = s->pos; |
---|
2539 | if (sol[j] != NULL) |
---|
2540 | { |
---|
2541 | z = nMult(sol[j], s->m); |
---|
2542 | if (x != NULL) |
---|
2543 | { |
---|
2544 | y = x; |
---|
2545 | x = nSub(y, z); |
---|
2546 | nDelete(&y); |
---|
2547 | nDelete(&z); |
---|
2548 | } |
---|
2549 | else |
---|
2550 | x = nNeg(z); |
---|
2551 | } |
---|
2552 | s = s->n; |
---|
2553 | } |
---|
2554 | if (sol[i] != NULL) |
---|
2555 | { |
---|
2556 | if (x != NULL) |
---|
2557 | { |
---|
2558 | y = nAdd(x, sol[i]); |
---|
2559 | nDelete(&x); |
---|
2560 | if (nIsZero(y)) |
---|
2561 | { |
---|
2562 | nDelete(&sol[i]); |
---|
2563 | sol[i] = NULL; |
---|
2564 | } |
---|
2565 | else |
---|
2566 | sol[i] = y; |
---|
2567 | } |
---|
2568 | } |
---|
2569 | else |
---|
2570 | sol[i] = x; |
---|
2571 | if (sol[i] != NULL) |
---|
2572 | { |
---|
2573 | x = sol[i]; |
---|
2574 | sol[i] = nDiv(x, d->m); |
---|
2575 | nDelete(&x); |
---|
2576 | } |
---|
2577 | i--; |
---|
2578 | } |
---|
2579 | this->smAllDel(); |
---|
2580 | } |
---|
2581 | |
---|
2582 | /* |
---|
2583 | * transform the result to an ideal |
---|
2584 | */ |
---|
2585 | ideal sparse_number_mat::smRes2Ideal() |
---|
2586 | { |
---|
2587 | int i, j; |
---|
2588 | ideal res = idInit(crd, 1); |
---|
2589 | |
---|
2590 | for (i=crd; i; i--) |
---|
2591 | { |
---|
2592 | j = perm[i]-1; |
---|
2593 | res->m[j] = smSmnumber2Poly(sol[i]); |
---|
2594 | } |
---|
2595 | omFreeSize((ADDRESS)sol, sizeof(number)*(crd+1)); |
---|
2596 | return res; |
---|
2597 | } |
---|
2598 | |
---|
2599 | /* ----------------- pivot method ------------------ */ |
---|
2600 | |
---|
2601 | /* |
---|
2602 | * compute pivot |
---|
2603 | */ |
---|
2604 | void sparse_number_mat::smRealPivot() |
---|
2605 | { |
---|
2606 | smnumber a; |
---|
2607 | number x, xo; |
---|
2608 | int i, copt, ropt; |
---|
2609 | |
---|
2610 | xo=nInit(0); |
---|
2611 | for (i=act; i; i--) |
---|
2612 | { |
---|
2613 | a = m_act[i]; |
---|
2614 | while ((a!=NULL) && (a->pos<=tored)) |
---|
2615 | { |
---|
2616 | x = a->m; |
---|
2617 | if (nGreaterZero(x)) |
---|
2618 | { |
---|
2619 | if (nGreater(x,xo)) |
---|
2620 | { |
---|
2621 | nDelete(&xo); |
---|
2622 | xo = nCopy(x); |
---|
2623 | copt = i; |
---|
2624 | ropt = a->pos; |
---|
2625 | } |
---|
2626 | } |
---|
2627 | else |
---|
2628 | { |
---|
2629 | xo = nNeg(xo); |
---|
2630 | if (nGreater(xo,x)) |
---|
2631 | { |
---|
2632 | nDelete(&xo); |
---|
2633 | xo = nCopy(x); |
---|
2634 | copt = i; |
---|
2635 | ropt = a->pos; |
---|
2636 | } |
---|
2637 | xo = nNeg(xo); |
---|
2638 | } |
---|
2639 | a = a->n; |
---|
2640 | } |
---|
2641 | } |
---|
2642 | rpiv = ropt; |
---|
2643 | if (copt != act) |
---|
2644 | { |
---|
2645 | a = m_act[act]; |
---|
2646 | m_act[act] = m_act[copt]; |
---|
2647 | m_act[copt] = a; |
---|
2648 | } |
---|
2649 | nDelete(&xo); |
---|
2650 | } |
---|
2651 | |
---|
2652 | /* ----------------- elimination ------------------ */ |
---|
2653 | |
---|
2654 | /* one step of Gauss-elimination */ |
---|
2655 | void sparse_number_mat::smGElim() |
---|
2656 | { |
---|
2657 | number p = nDiv(one,piv->m); // pivotelement |
---|
2658 | smnumber c = m_act[act]; // pivotcolumn |
---|
2659 | smnumber r = red; // row to reduce |
---|
2660 | smnumber res, a, b; |
---|
2661 | number w, ha, hb; |
---|
2662 | |
---|
2663 | if ((c == NULL) || (r == NULL)) |
---|
2664 | { |
---|
2665 | while (r!=NULL) smNumberDelete(&r); |
---|
2666 | return; |
---|
2667 | } |
---|
2668 | do |
---|
2669 | { |
---|
2670 | a = m_act[r->pos]; |
---|
2671 | res = dumm; |
---|
2672 | res->n = NULL; |
---|
2673 | b = c; |
---|
2674 | w = nMult(r->m, p); |
---|
2675 | nDelete(&r->m); |
---|
2676 | r->m = w; |
---|
2677 | loop // combine the chains a and b: a + w*b |
---|
2678 | { |
---|
2679 | if (a == NULL) |
---|
2680 | { |
---|
2681 | do |
---|
2682 | { |
---|
2683 | res = res->n = smNumberCopy(b); |
---|
2684 | res->m = nMult(b->m, w); |
---|
2685 | b = b->n; |
---|
2686 | } while (b != NULL); |
---|
2687 | break; |
---|
2688 | } |
---|
2689 | if (a->pos < b->pos) |
---|
2690 | { |
---|
2691 | res = res->n = a; |
---|
2692 | a = a->n; |
---|
2693 | } |
---|
2694 | else if (a->pos > b->pos) |
---|
2695 | { |
---|
2696 | res = res->n = smNumberCopy(b); |
---|
2697 | res->m = nMult(b->m, w); |
---|
2698 | b = b->n; |
---|
2699 | } |
---|
2700 | else |
---|
2701 | { |
---|
2702 | hb = nMult(b->m, w); |
---|
2703 | ha = nAdd(a->m, hb); |
---|
2704 | nDelete(&hb); |
---|
2705 | nDelete(&a->m); |
---|
2706 | if (nIsZero(ha)) |
---|
2707 | { |
---|
2708 | smNumberDelete(&a); |
---|
2709 | } |
---|
2710 | else |
---|
2711 | { |
---|
2712 | a->m = ha; |
---|
2713 | res = res->n = a; |
---|
2714 | a = a->n; |
---|
2715 | } |
---|
2716 | b = b->n; |
---|
2717 | } |
---|
2718 | if (b == NULL) |
---|
2719 | { |
---|
2720 | res->n = a; |
---|
2721 | break; |
---|
2722 | } |
---|
2723 | } |
---|
2724 | m_act[r->pos] = dumm->n; |
---|
2725 | smNumberDelete(&r); |
---|
2726 | } while (r != NULL); |
---|
2727 | nDelete(&p); |
---|
2728 | } |
---|
2729 | |
---|
2730 | /* ----------------- transfer ------------------ */ |
---|
2731 | |
---|
2732 | /* |
---|
2733 | * select the pivotrow and store it to red and piv |
---|
2734 | */ |
---|
2735 | void sparse_number_mat::smSelectPR() |
---|
2736 | { |
---|
2737 | smnumber b = dumm; |
---|
2738 | smnumber a, ap; |
---|
2739 | int i; |
---|
2740 | |
---|
2741 | if (TEST_OPT_PROT) |
---|
2742 | { |
---|
2743 | if ((crd+1)%10) |
---|
2744 | PrintS("."); |
---|
2745 | else |
---|
2746 | PrintS(".\n"); |
---|
2747 | } |
---|
2748 | a = m_act[act]; |
---|
2749 | if (a->pos < rpiv) |
---|
2750 | { |
---|
2751 | do |
---|
2752 | { |
---|
2753 | ap = a; |
---|
2754 | a = a->n; |
---|
2755 | } while (a->pos < rpiv); |
---|
2756 | ap->n = a->n; |
---|
2757 | } |
---|
2758 | else |
---|
2759 | m_act[act] = a->n; |
---|
2760 | piv = a; |
---|
2761 | a->n = NULL; |
---|
2762 | for (i=1; i<act; i++) |
---|
2763 | { |
---|
2764 | a = m_act[i]; |
---|
2765 | if (a->pos < rpiv) |
---|
2766 | { |
---|
2767 | loop |
---|
2768 | { |
---|
2769 | ap = a; |
---|
2770 | a = a->n; |
---|
2771 | if ((a == NULL) || (a->pos > rpiv)) |
---|
2772 | break; |
---|
2773 | if (a->pos == rpiv) |
---|
2774 | { |
---|
2775 | ap->n = a->n; |
---|
2776 | a->m = nNeg(a->m); |
---|
2777 | b = b->n = a; |
---|
2778 | b->pos = i; |
---|
2779 | break; |
---|
2780 | } |
---|
2781 | } |
---|
2782 | } |
---|
2783 | else if (a->pos == rpiv) |
---|
2784 | { |
---|
2785 | m_act[i] = a->n; |
---|
2786 | a->m = nNeg(a->m); |
---|
2787 | b = b->n = a; |
---|
2788 | b->pos = i; |
---|
2789 | } |
---|
2790 | } |
---|
2791 | b->n = NULL; |
---|
2792 | red = dumm->n; |
---|
2793 | } |
---|
2794 | |
---|
2795 | /* |
---|
2796 | * store the pivotcol in m_row |
---|
2797 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
2798 | */ |
---|
2799 | void sparse_number_mat::smColToRow() |
---|
2800 | { |
---|
2801 | smnumber c = m_act[act]; |
---|
2802 | smnumber h; |
---|
2803 | |
---|
2804 | while (c != NULL) |
---|
2805 | { |
---|
2806 | h = c; |
---|
2807 | c = c->n; |
---|
2808 | h->n = m_row[h->pos]; |
---|
2809 | m_row[h->pos] = h; |
---|
2810 | h->pos = crd; |
---|
2811 | } |
---|
2812 | } |
---|
2813 | |
---|
2814 | /* |
---|
2815 | * store the pivot and the assosiated row in m_row |
---|
2816 | * to m_res (result): |
---|
2817 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
2818 | */ |
---|
2819 | void sparse_number_mat::smRowToCol() |
---|
2820 | { |
---|
2821 | smnumber r = m_row[rpiv]; |
---|
2822 | smnumber a, ap, h; |
---|
2823 | |
---|
2824 | m_row[rpiv] = NULL; |
---|
2825 | perm[crd] = rpiv; |
---|
2826 | piv->pos = crd; |
---|
2827 | m_res[crd] = piv; |
---|
2828 | while (r != NULL) |
---|
2829 | { |
---|
2830 | ap = m_res[r->pos]; |
---|
2831 | loop |
---|
2832 | { |
---|
2833 | a = ap->n; |
---|
2834 | if (a == NULL) |
---|
2835 | { |
---|
2836 | ap->n = h = r; |
---|
2837 | r = r->n; |
---|
2838 | h->n = a; |
---|
2839 | h->pos = crd; |
---|
2840 | break; |
---|
2841 | } |
---|
2842 | ap = a; |
---|
2843 | } |
---|
2844 | } |
---|
2845 | } |
---|
2846 | |
---|
2847 | /* ----------------- C++ stuff ------------------ */ |
---|
2848 | |
---|
2849 | /* |
---|
2850 | * check singularity |
---|
2851 | */ |
---|
2852 | void sparse_number_mat::smZeroToredElim() |
---|
2853 | { |
---|
2854 | smnumber a; |
---|
2855 | int i = act; |
---|
2856 | |
---|
2857 | loop |
---|
2858 | { |
---|
2859 | if (i == 0) return; |
---|
2860 | a = m_act[i]; |
---|
2861 | if ((a==NULL) || (a->pos>tored)) |
---|
2862 | { |
---|
2863 | sing = 1; |
---|
2864 | this->smAllDel(); |
---|
2865 | return; |
---|
2866 | } |
---|
2867 | i--; |
---|
2868 | } |
---|
2869 | } |
---|
2870 | |
---|
2871 | /* |
---|
2872 | * delete all smnumber's |
---|
2873 | */ |
---|
2874 | void sparse_number_mat::smAllDel() |
---|
2875 | { |
---|
2876 | smnumber a; |
---|
2877 | int i; |
---|
2878 | |
---|
2879 | for (i=act; i; i--) |
---|
2880 | { |
---|
2881 | a = m_act[i]; |
---|
2882 | while (a != NULL) |
---|
2883 | smNumberDelete(&a); |
---|
2884 | } |
---|
2885 | for (i=crd; i; i--) |
---|
2886 | { |
---|
2887 | a = m_res[i]; |
---|
2888 | while (a != NULL) |
---|
2889 | smNumberDelete(&a); |
---|
2890 | } |
---|
2891 | if (act) |
---|
2892 | { |
---|
2893 | for (i=nrows; i; i--) |
---|
2894 | { |
---|
2895 | a = m_row[i]; |
---|
2896 | while (a != NULL) |
---|
2897 | smNumberDelete(&a); |
---|
2898 | } |
---|
2899 | } |
---|
2900 | } |
---|
2901 | |
---|
2902 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2903 | |
---|
2904 | static void smNumberDelete(smnumber *r) |
---|
2905 | { |
---|
2906 | smnumber a = *r, b = a->n; |
---|
2907 | |
---|
2908 | nDelete(&a->m); |
---|
2909 | omFreeBin((ADDRESS)a, smnrec_bin); |
---|
2910 | *r = b; |
---|
2911 | } |
---|
2912 | |
---|
2913 | static smnumber smNumberCopy(smnumber a) |
---|
2914 | { |
---|
2915 | smnumber r = (smnumber)omAllocBin(smnrec_bin); |
---|
2916 | memcpy(r, a, sizeof(smnrec)); |
---|
2917 | return r; |
---|
2918 | } |
---|
2919 | |
---|
2920 | /* |
---|
2921 | * from poly to smnumber |
---|
2922 | * do not destroy p |
---|
2923 | */ |
---|
2924 | static smnumber smPoly2Smnumber(poly q) |
---|
2925 | { |
---|
2926 | smnumber a, res; |
---|
2927 | poly p = q; |
---|
2928 | |
---|
2929 | if (p == NULL) |
---|
2930 | return NULL; |
---|
2931 | a = res = (smnumber)omAllocBin(smnrec_bin); |
---|
2932 | a->pos = pGetComp(p); |
---|
2933 | a->m = pGetCoeff(p); |
---|
2934 | nNew(&pGetCoeff(p)); |
---|
2935 | loop |
---|
2936 | { |
---|
2937 | pIter(p); |
---|
2938 | if (p == NULL) |
---|
2939 | { |
---|
2940 | pDelete(&q); |
---|
2941 | a->n = NULL; |
---|
2942 | return res; |
---|
2943 | } |
---|
2944 | a = a->n = (smnumber)omAllocBin(smnrec_bin); |
---|
2945 | a->pos = pGetComp(p); |
---|
2946 | a->m = pGetCoeff(p); |
---|
2947 | nNew(&pGetCoeff(p)); |
---|
2948 | } |
---|
2949 | } |
---|
2950 | |
---|
2951 | /* |
---|
2952 | * from smnumber to poly |
---|
2953 | * destroy a |
---|
2954 | */ |
---|
2955 | static poly smSmnumber2Poly(number a) |
---|
2956 | { |
---|
2957 | poly res; |
---|
2958 | |
---|
2959 | if (a == NULL) return NULL; |
---|
2960 | res = pInit(); |
---|
2961 | pSetCoeff0(res, a); |
---|
2962 | return res; |
---|
2963 | } |
---|
2964 | |
---|
2965 | /*2 |
---|
2966 | * check the input |
---|
2967 | */ |
---|
2968 | static BOOLEAN smCheckSolv(ideal I) |
---|
2969 | { int i = I->ncols; |
---|
2970 | if ((i == 0) || (i != I->rank-1)) |
---|
2971 | { |
---|
2972 | WerrorS("wrong dimensions for linsolv"); |
---|
2973 | return TRUE; |
---|
2974 | } |
---|
2975 | for(;i;i--) |
---|
2976 | { |
---|
2977 | if(I->m[i-1] == NULL) |
---|
2978 | { |
---|
2979 | WerrorS("singular input for linsolv"); |
---|
2980 | return TRUE; |
---|
2981 | } |
---|
2982 | } |
---|
2983 | return FALSE; |
---|
2984 | } |
---|