1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id: matpol.cc,v 1.14 2008-06-10 10:17:32 motsak Exp $ */ |
---|
5 | |
---|
6 | /* |
---|
7 | * ABSTRACT: |
---|
8 | */ |
---|
9 | |
---|
10 | #include <stdio.h> |
---|
11 | #include <math.h> |
---|
12 | |
---|
13 | #include "mod2.h" |
---|
14 | #include <mylimits.h> |
---|
15 | #include "structs.h" |
---|
16 | #include "kstd1.h" |
---|
17 | #include "polys.h" |
---|
18 | #include "omalloc.h" |
---|
19 | #include "febase.h" |
---|
20 | #include "numbers.h" |
---|
21 | #include "ideals.h" |
---|
22 | #include "intvec.h" |
---|
23 | #include "ring.h" |
---|
24 | #include "sparsmat.h" |
---|
25 | #include "matpol.h" |
---|
26 | #include "prCopy.h" |
---|
27 | |
---|
28 | //omBin ip_smatrix_bin = omGetSpecBin(sizeof(ip_smatrix)); |
---|
29 | #define ip_smatrix_bin sip_sideal_bin |
---|
30 | /*0 implementation*/ |
---|
31 | |
---|
32 | |
---|
33 | typedef int perm[100]; |
---|
34 | static void mpReplace(int j, int n, int &sign, int *perm); |
---|
35 | static int mpNextperm(perm * z, int max); |
---|
36 | static poly mpLeibnitz(matrix a); |
---|
37 | static poly minuscopy (poly p); |
---|
38 | static poly pInsert(poly p1, poly p2); |
---|
39 | static poly mpExdiv ( poly m, poly d, poly vars); |
---|
40 | static poly mpSelect (poly fro, poly what); |
---|
41 | |
---|
42 | static void mpPartClean(matrix, int, int); |
---|
43 | static void mpFinalClean(matrix); |
---|
44 | static int mpPrepareRow (matrix, int, int); |
---|
45 | static int mpPreparePiv (matrix, int, int); |
---|
46 | static int mpPivBar(matrix, int, int); |
---|
47 | static int mpPivRow(matrix, int, int); |
---|
48 | static float mpPolyWeight(poly); |
---|
49 | static void mpSwapRow(matrix, int, int, int); |
---|
50 | static void mpSwapCol(matrix, int, int, int); |
---|
51 | static void mpElimBar(matrix, matrix, poly, int, int); |
---|
52 | |
---|
53 | /*2 |
---|
54 | * create a r x c zero-matrix |
---|
55 | */ |
---|
56 | matrix mpNew(int r, int c) |
---|
57 | { |
---|
58 | if (r<=0) r=1; |
---|
59 | if ( (((int)(INT_MAX/sizeof(poly))) / r) <= c) |
---|
60 | { |
---|
61 | Werror("internal error: creating matrix[%d][%d]",r,c); |
---|
62 | return NULL; |
---|
63 | } |
---|
64 | matrix rc = (matrix)omAllocBin(ip_smatrix_bin); |
---|
65 | rc->nrows = r; |
---|
66 | rc->ncols = c; |
---|
67 | rc->rank = r; |
---|
68 | if (c != 0) |
---|
69 | { |
---|
70 | int s=r*c*sizeof(poly); |
---|
71 | rc->m = (polyset)omAlloc0(s); |
---|
72 | //if (rc->m==NULL) |
---|
73 | //{ |
---|
74 | // Werror("internal error: creating matrix[%d][%d]",r,c); |
---|
75 | // return NULL; |
---|
76 | //} |
---|
77 | } |
---|
78 | return rc; |
---|
79 | } |
---|
80 | |
---|
81 | /*2 |
---|
82 | *copies matrix a to b |
---|
83 | */ |
---|
84 | matrix mpCopy (matrix a) |
---|
85 | { |
---|
86 | idTest((ideal)a); |
---|
87 | poly t; |
---|
88 | int i, m=MATROWS(a), n=MATCOLS(a); |
---|
89 | matrix b = mpNew(m, n); |
---|
90 | |
---|
91 | for (i=m*n-1; i>=0; i--) |
---|
92 | { |
---|
93 | t = a->m[i]; |
---|
94 | if (t!=NULL) |
---|
95 | { |
---|
96 | pNormalize(t); |
---|
97 | b->m[i] = pCopy(t); |
---|
98 | } |
---|
99 | } |
---|
100 | b->rank=a->rank; |
---|
101 | return b; |
---|
102 | } |
---|
103 | |
---|
104 | /*2 |
---|
105 | *copies matrix a from rSrc into rDst |
---|
106 | */ |
---|
107 | matrix mpCopy(const matrix a, const ring rSrc, const ring rDst) |
---|
108 | { |
---|
109 | const ring save = currRing; |
---|
110 | |
---|
111 | if( save != currRing ) |
---|
112 | rChangeCurrRing(rSrc); |
---|
113 | |
---|
114 | idTest((ideal)a); |
---|
115 | |
---|
116 | rChangeCurrRing(rDst); |
---|
117 | |
---|
118 | poly t; |
---|
119 | int i, m=MATROWS(a), n=MATCOLS(a); |
---|
120 | |
---|
121 | matrix b = mpNew(m, n); |
---|
122 | |
---|
123 | for (i=m*n-1; i>=0; i--) |
---|
124 | { |
---|
125 | t = a->m[i]; |
---|
126 | if (t!=NULL) |
---|
127 | { |
---|
128 | b->m[i] = prCopyR_NoSort(t, rSrc, rDst); |
---|
129 | p_Normalize(b->m[i], rDst); |
---|
130 | } |
---|
131 | } |
---|
132 | b->rank=a->rank; |
---|
133 | |
---|
134 | idTest((ideal)b); |
---|
135 | |
---|
136 | if( save != currRing ) |
---|
137 | rChangeCurrRing(save); |
---|
138 | |
---|
139 | return b; |
---|
140 | } |
---|
141 | |
---|
142 | |
---|
143 | |
---|
144 | /*2 |
---|
145 | * make it a p * unit matrix |
---|
146 | */ |
---|
147 | matrix mpInitP(int r, int c, poly p) |
---|
148 | { |
---|
149 | matrix rc = mpNew(r,c); |
---|
150 | int i=si_min(r,c), n = c*(i-1)+i-1, inc = c+1; |
---|
151 | |
---|
152 | pNormalize(p); |
---|
153 | while (n>0) |
---|
154 | { |
---|
155 | rc->m[n] = pCopy(p); |
---|
156 | n -= inc; |
---|
157 | } |
---|
158 | rc->m[0]=p; |
---|
159 | return rc; |
---|
160 | } |
---|
161 | |
---|
162 | /*2 |
---|
163 | * make it a v * unit matrix |
---|
164 | */ |
---|
165 | matrix mpInitI(int r, int c, int v) |
---|
166 | { |
---|
167 | return mpInitP(r,c,pISet(v)); |
---|
168 | } |
---|
169 | |
---|
170 | /*2 |
---|
171 | * c = f*a |
---|
172 | */ |
---|
173 | matrix mpMultI(matrix a, int f) |
---|
174 | { |
---|
175 | int k, n = a->nrows, m = a->ncols; |
---|
176 | poly p = pISet(f); |
---|
177 | matrix c = mpNew(n,m); |
---|
178 | |
---|
179 | for (k=m*n-1; k>0; k--) |
---|
180 | c->m[k] = ppMult_qq(a->m[k], p); |
---|
181 | c->m[0] = pMult(pCopy(a->m[0]), p); |
---|
182 | return c; |
---|
183 | } |
---|
184 | |
---|
185 | /*2 |
---|
186 | * multiply a matrix 'a' by a poly 'p', destroy the args |
---|
187 | */ |
---|
188 | matrix mpMultP(matrix a, poly p) |
---|
189 | { |
---|
190 | int k, n = a->nrows, m = a->ncols; |
---|
191 | |
---|
192 | pNormalize(p); |
---|
193 | for (k=m*n-1; k>0; k--) |
---|
194 | { |
---|
195 | if (a->m[k]!=NULL) |
---|
196 | a->m[k] = pMult(a->m[k], pCopy(p)); |
---|
197 | } |
---|
198 | a->m[0] = pMult(a->m[0], p); |
---|
199 | return a; |
---|
200 | } |
---|
201 | |
---|
202 | matrix mpAdd(matrix a, matrix b) |
---|
203 | { |
---|
204 | int k, n = a->nrows, m = a->ncols; |
---|
205 | if ((n != b->nrows) || (m != b->ncols)) |
---|
206 | { |
---|
207 | /* |
---|
208 | * Werror("cannot add %dx%d matrix and %dx%d matrix", |
---|
209 | * m,n,b->cols(),b->rows()); |
---|
210 | */ |
---|
211 | return NULL; |
---|
212 | } |
---|
213 | matrix c = mpNew(n,m); |
---|
214 | for (k=m*n-1; k>=0; k--) |
---|
215 | c->m[k] = pAdd(pCopy(a->m[k]), pCopy(b->m[k])); |
---|
216 | return c; |
---|
217 | } |
---|
218 | |
---|
219 | matrix mpSub(matrix a, matrix b) |
---|
220 | { |
---|
221 | int k, n = a->nrows, m = a->ncols; |
---|
222 | if ((n != b->nrows) || (m != b->ncols)) |
---|
223 | { |
---|
224 | /* |
---|
225 | * Werror("cannot sub %dx%d matrix and %dx%d matrix", |
---|
226 | * m,n,b->cols(),b->rows()); |
---|
227 | */ |
---|
228 | return NULL; |
---|
229 | } |
---|
230 | matrix c = mpNew(n,m); |
---|
231 | for (k=m*n-1; k>=0; k--) |
---|
232 | c->m[k] = pSub(pCopy(a->m[k]), pCopy(b->m[k])); |
---|
233 | return c; |
---|
234 | } |
---|
235 | |
---|
236 | matrix mpMult(matrix a, matrix b) |
---|
237 | { |
---|
238 | int i, j, k; |
---|
239 | int m = MATROWS(a); |
---|
240 | int p = MATCOLS(a); |
---|
241 | int q = MATCOLS(b); |
---|
242 | |
---|
243 | if (p!=MATROWS(b)) |
---|
244 | { |
---|
245 | /* |
---|
246 | * Werror("cannot multiply %dx%d matrix and %dx%d matrix", |
---|
247 | * m,p,b->rows(),q); |
---|
248 | */ |
---|
249 | return NULL; |
---|
250 | } |
---|
251 | matrix c = mpNew(m,q); |
---|
252 | |
---|
253 | for (i=1; i<=m; i++) |
---|
254 | { |
---|
255 | for (k=1; k<=p; k++) |
---|
256 | { |
---|
257 | poly aik; |
---|
258 | if ((aik=MATELEM(a,i,k))!=NULL) |
---|
259 | { |
---|
260 | for (j=1; j<=q; j++) |
---|
261 | { |
---|
262 | poly bkj; |
---|
263 | if ((bkj=MATELEM(b,k,j))!=NULL) |
---|
264 | { |
---|
265 | poly *cij=&(MATELEM(c,i,j)); |
---|
266 | poly s = ppMult_qq(aik /*MATELEM(a,i,k)*/, bkj/*MATELEM(b,k,j)*/); |
---|
267 | if (/*MATELEM(c,i,j)*/ (*cij)==NULL) (*cij)=s; |
---|
268 | else (*cij) = pAdd((*cij) /*MATELEM(c,i,j)*/ ,s); |
---|
269 | } |
---|
270 | } |
---|
271 | } |
---|
272 | // pNormalize(t); |
---|
273 | // MATELEM(c,i,j) = t; |
---|
274 | } |
---|
275 | } |
---|
276 | for(i=m*q-1;i>=0;i--) pNormalize(c->m[i]); |
---|
277 | return c; |
---|
278 | } |
---|
279 | |
---|
280 | matrix mpTransp(matrix a) |
---|
281 | { |
---|
282 | int i, j, r = MATROWS(a), c = MATCOLS(a); |
---|
283 | poly *p; |
---|
284 | matrix b = mpNew(c,r); |
---|
285 | |
---|
286 | p = b->m; |
---|
287 | for (i=0; i<c; i++) |
---|
288 | { |
---|
289 | for (j=0; j<r; j++) |
---|
290 | { |
---|
291 | if (a->m[j*c+i]!=NULL) *p = pCopy(a->m[j*c+i]); |
---|
292 | p++; |
---|
293 | } |
---|
294 | } |
---|
295 | return b; |
---|
296 | } |
---|
297 | |
---|
298 | /*2 |
---|
299 | *returns the trace of matrix a |
---|
300 | */ |
---|
301 | poly mpTrace ( matrix a) |
---|
302 | { |
---|
303 | int i; |
---|
304 | int n = (MATCOLS(a)<MATROWS(a)) ? MATCOLS(a) : MATROWS(a); |
---|
305 | poly t = NULL; |
---|
306 | |
---|
307 | for (i=1; i<=n; i++) |
---|
308 | t = pAdd(t, pCopy(MATELEM(a,i,i))); |
---|
309 | return t; |
---|
310 | } |
---|
311 | |
---|
312 | /*2 |
---|
313 | *returns the trace of the product of a and b |
---|
314 | */ |
---|
315 | poly TraceOfProd ( matrix a, matrix b, int n) |
---|
316 | { |
---|
317 | int i, j; |
---|
318 | poly p, t = NULL; |
---|
319 | |
---|
320 | for (i=1; i<=n; i++) |
---|
321 | { |
---|
322 | for (j=1; j<=n; j++) |
---|
323 | { |
---|
324 | p = ppMult_qq(MATELEM(a,i,j), MATELEM(b,j,i)); |
---|
325 | t = pAdd(t, p); |
---|
326 | } |
---|
327 | } |
---|
328 | return t; |
---|
329 | } |
---|
330 | |
---|
331 | /* |
---|
332 | * C++ classes for Bareiss algorithm |
---|
333 | */ |
---|
334 | class row_col_weight |
---|
335 | { |
---|
336 | private: |
---|
337 | int ym, yn; |
---|
338 | public: |
---|
339 | float *wrow, *wcol; |
---|
340 | row_col_weight() : ym(0) {} |
---|
341 | row_col_weight(int, int); |
---|
342 | ~row_col_weight(); |
---|
343 | }; |
---|
344 | |
---|
345 | /*2 |
---|
346 | * a submatrix M of a matrix X[m,n]: |
---|
347 | * 0 <= i < s_m <= a_m |
---|
348 | * 0 <= j < s_n <= a_n |
---|
349 | * M = ( Xarray[qrow[i],qcol[j]] ) |
---|
350 | * if a_m = a_n and s_m = s_n |
---|
351 | * det(X) = sign*div^(s_m-1)*det(M) |
---|
352 | * resticted pivot for elimination |
---|
353 | * 0 <= j < piv_s |
---|
354 | */ |
---|
355 | class mp_permmatrix |
---|
356 | { |
---|
357 | private: |
---|
358 | int a_m, a_n, s_m, s_n, sign, piv_s; |
---|
359 | int *qrow, *qcol; |
---|
360 | poly *Xarray; |
---|
361 | void mpInitMat(); |
---|
362 | poly * mpRowAdr(int); |
---|
363 | poly * mpColAdr(int); |
---|
364 | void mpRowWeight(float *); |
---|
365 | void mpColWeight(float *); |
---|
366 | void mpRowSwap(int, int); |
---|
367 | void mpColSwap(int, int); |
---|
368 | public: |
---|
369 | mp_permmatrix() : a_m(0) {} |
---|
370 | mp_permmatrix(matrix); |
---|
371 | mp_permmatrix(mp_permmatrix *); |
---|
372 | ~mp_permmatrix(); |
---|
373 | int mpGetRow(); |
---|
374 | int mpGetCol(); |
---|
375 | int mpGetRdim(); |
---|
376 | int mpGetCdim(); |
---|
377 | int mpGetSign(); |
---|
378 | void mpSetSearch(int s); |
---|
379 | void mpSaveArray(); |
---|
380 | poly mpGetElem(int, int); |
---|
381 | void mpSetElem(poly, int, int); |
---|
382 | void mpDelElem(int, int); |
---|
383 | void mpElimBareiss(poly); |
---|
384 | int mpPivotBareiss(row_col_weight *); |
---|
385 | int mpPivotRow(row_col_weight *, int); |
---|
386 | void mpToIntvec(intvec *); |
---|
387 | void mpRowReorder(); |
---|
388 | void mpColReorder(); |
---|
389 | }; |
---|
390 | |
---|
391 | #ifndef SIZE_OF_SYSTEM_PAGE |
---|
392 | #define SIZE_OF_SYSTEM_PAGE 4096 |
---|
393 | #endif |
---|
394 | /*2 |
---|
395 | * entries of a are minors and go to result (only if not in R) |
---|
396 | */ |
---|
397 | void mpMinorToResult(ideal result, int &elems, matrix a, int r, int c, |
---|
398 | ideal R) |
---|
399 | { |
---|
400 | poly *q1; |
---|
401 | int e=IDELEMS(result); |
---|
402 | int i,j; |
---|
403 | |
---|
404 | if (R != NULL) |
---|
405 | { |
---|
406 | for (i=r-1;i>=0;i--) |
---|
407 | { |
---|
408 | q1 = &(a->m)[i*a->ncols]; |
---|
409 | for (j=c-1;j>=0;j--) |
---|
410 | { |
---|
411 | if (q1[j]!=NULL) q1[j] = kNF(R,currQuotient,q1[j]); |
---|
412 | } |
---|
413 | } |
---|
414 | } |
---|
415 | for (i=r-1;i>=0;i--) |
---|
416 | { |
---|
417 | q1 = &(a->m)[i*a->ncols]; |
---|
418 | for (j=c-1;j>=0;j--) |
---|
419 | { |
---|
420 | if (q1[j]!=NULL) |
---|
421 | { |
---|
422 | if (elems>=e) |
---|
423 | { |
---|
424 | if(e<SIZE_OF_SYSTEM_PAGE) |
---|
425 | { |
---|
426 | pEnlargeSet(&(result->m),e,e); |
---|
427 | e += e; |
---|
428 | } |
---|
429 | else |
---|
430 | { |
---|
431 | pEnlargeSet(&(result->m),e,SIZE_OF_SYSTEM_PAGE); |
---|
432 | e += SIZE_OF_SYSTEM_PAGE; |
---|
433 | } |
---|
434 | IDELEMS(result) =e; |
---|
435 | } |
---|
436 | result->m[elems] = q1[j]; |
---|
437 | q1[j] = NULL; |
---|
438 | elems++; |
---|
439 | } |
---|
440 | } |
---|
441 | } |
---|
442 | } |
---|
443 | |
---|
444 | /*2 |
---|
445 | * produces recursively the ideal of all arxar-minors of a |
---|
446 | */ |
---|
447 | void mpRecMin(int ar,ideal result,int &elems,matrix a,int lr,int lc, |
---|
448 | poly barDiv, ideal R) |
---|
449 | { |
---|
450 | int k; |
---|
451 | int kr=lr-1,kc=lc-1; |
---|
452 | matrix nextLevel=mpNew(kr,kc); |
---|
453 | |
---|
454 | loop |
---|
455 | { |
---|
456 | /*--- look for an optimal row and bring it to last position ------------*/ |
---|
457 | if(mpPrepareRow(a,lr,lc)==0) break; |
---|
458 | /*--- now take all pivots from the last row ------------*/ |
---|
459 | k = lc; |
---|
460 | loop |
---|
461 | { |
---|
462 | if(mpPreparePiv(a,lr,k)==0) break; |
---|
463 | mpElimBar(a,nextLevel,barDiv,lr,k); |
---|
464 | k--; |
---|
465 | if (ar>1) |
---|
466 | { |
---|
467 | mpRecMin(ar-1,result,elems,nextLevel,kr,k,a->m[kr*a->ncols+k],R); |
---|
468 | mpPartClean(nextLevel,kr,k); |
---|
469 | } |
---|
470 | else mpMinorToResult(result,elems,nextLevel,kr,k,R); |
---|
471 | if (ar>k-1) break; |
---|
472 | } |
---|
473 | if (ar>=kr) break; |
---|
474 | /*--- now we have to take out the last row...------------*/ |
---|
475 | lr = kr; |
---|
476 | kr--; |
---|
477 | } |
---|
478 | mpFinalClean(nextLevel); |
---|
479 | } |
---|
480 | |
---|
481 | /*2 |
---|
482 | *returns the determinant of the matrix m; |
---|
483 | *uses Bareiss algorithm |
---|
484 | */ |
---|
485 | poly mpDetBareiss (matrix a) |
---|
486 | { |
---|
487 | int s; |
---|
488 | poly div, res; |
---|
489 | if (MATROWS(a) != MATCOLS(a)) |
---|
490 | { |
---|
491 | Werror("det of %d x %d matrix",MATROWS(a),MATCOLS(a)); |
---|
492 | return NULL; |
---|
493 | } |
---|
494 | matrix c = mpCopy(a); |
---|
495 | mp_permmatrix *Bareiss = new mp_permmatrix(c); |
---|
496 | row_col_weight w(Bareiss->mpGetRdim(), Bareiss->mpGetCdim()); |
---|
497 | |
---|
498 | /* Bareiss */ |
---|
499 | div = NULL; |
---|
500 | while(Bareiss->mpPivotBareiss(&w)) |
---|
501 | { |
---|
502 | Bareiss->mpElimBareiss(div); |
---|
503 | div = Bareiss->mpGetElem(Bareiss->mpGetRdim(), Bareiss->mpGetCdim()); |
---|
504 | } |
---|
505 | Bareiss->mpRowReorder(); |
---|
506 | Bareiss->mpColReorder(); |
---|
507 | Bareiss->mpSaveArray(); |
---|
508 | s = Bareiss->mpGetSign(); |
---|
509 | delete Bareiss; |
---|
510 | |
---|
511 | /* result */ |
---|
512 | res = MATELEM(c,1,1); |
---|
513 | MATELEM(c,1,1) = NULL; |
---|
514 | idDelete((ideal *)&c); |
---|
515 | if (s < 0) |
---|
516 | res = pNeg(res); |
---|
517 | return res; |
---|
518 | } |
---|
519 | |
---|
520 | /*2 |
---|
521 | *returns the determinant of the matrix m; |
---|
522 | *uses Newtons formulea for symmetric functions |
---|
523 | */ |
---|
524 | poly mpDet (matrix m) |
---|
525 | { |
---|
526 | int i,j,k,n; |
---|
527 | poly p,q; |
---|
528 | matrix a, s; |
---|
529 | matrix ma[100]; |
---|
530 | number c=NULL, d=NULL, ONE=NULL; |
---|
531 | |
---|
532 | n = MATROWS(m); |
---|
533 | if (n != MATCOLS(m)) |
---|
534 | { |
---|
535 | Werror("det of %d x %d matrix",n,MATCOLS(m)); |
---|
536 | return NULL; |
---|
537 | } |
---|
538 | k=rChar(); |
---|
539 | if ((k > 0) && (k <= n)) |
---|
540 | return mpLeibnitz(m); |
---|
541 | ONE = nInit(1); |
---|
542 | ma[1]=mpCopy(m); |
---|
543 | k = (n+1) / 2; |
---|
544 | s = mpNew(1, n); |
---|
545 | MATELEM(s,1,1) = mpTrace(m); |
---|
546 | for (i=2; i<=k; i++) |
---|
547 | { |
---|
548 | //ma[i] = mpNew(n,n); |
---|
549 | ma[i]=mpMult(ma[i-1], ma[1]); |
---|
550 | MATELEM(s,1,i) = mpTrace(ma[i]); |
---|
551 | pTest(MATELEM(s,1,i)); |
---|
552 | } |
---|
553 | for (i=k+1; i<=n; i++) |
---|
554 | { |
---|
555 | MATELEM(s,1,i) = TraceOfProd(ma[i / 2], ma[(i+1) / 2], n); |
---|
556 | pTest(MATELEM(s,1,i)); |
---|
557 | } |
---|
558 | for (i=1; i<=k; i++) |
---|
559 | idDelete((ideal *)&(ma[i])); |
---|
560 | /* the array s contains the traces of the powers of the matrix m, |
---|
561 | * these are the power sums of the eigenvalues of m */ |
---|
562 | a = mpNew(1,n); |
---|
563 | MATELEM(a,1,1) = minuscopy(MATELEM(s,1,1)); |
---|
564 | for (i=2; i<=n; i++) |
---|
565 | { |
---|
566 | p = pCopy(MATELEM(s,1,i)); |
---|
567 | for (j=i-1; j>=1; j--) |
---|
568 | { |
---|
569 | q = ppMult_qq(MATELEM(s,1,j), MATELEM(a,1,i-j)); |
---|
570 | pTest(q); |
---|
571 | p = pAdd(p,q); |
---|
572 | } |
---|
573 | // c= -1/i |
---|
574 | d = nInit(-(int)i); |
---|
575 | c = nDiv(ONE, d); |
---|
576 | nDelete(&d); |
---|
577 | |
---|
578 | pMult_nn(p, c); |
---|
579 | pTest(p); |
---|
580 | MATELEM(a,1,i) = p; |
---|
581 | nDelete(&c); |
---|
582 | } |
---|
583 | /* the array a contains the elementary symmetric functions of the |
---|
584 | * eigenvalues of m */ |
---|
585 | for (i=1; i<=n-1; i++) |
---|
586 | { |
---|
587 | //pDelete(&(MATELEM(a,1,i))); |
---|
588 | pDelete(&(MATELEM(s,1,i))); |
---|
589 | } |
---|
590 | pDelete(&(MATELEM(s,1,n))); |
---|
591 | /* up to a sign, the determinant is the n-th elementary symmetric function */ |
---|
592 | if ((n/2)*2 < n) |
---|
593 | { |
---|
594 | d = nInit(-1); |
---|
595 | pMult_nn(MATELEM(a,1,n), d); |
---|
596 | nDelete(&d); |
---|
597 | } |
---|
598 | nDelete(&ONE); |
---|
599 | idDelete((ideal *)&s); |
---|
600 | poly result=MATELEM(a,1,n); |
---|
601 | MATELEM(a,1,n)=NULL; |
---|
602 | idDelete((ideal *)&a); |
---|
603 | return result; |
---|
604 | } |
---|
605 | |
---|
606 | /*2 |
---|
607 | * compute all ar-minors of the matrix a |
---|
608 | */ |
---|
609 | matrix mpWedge(matrix a, int ar) |
---|
610 | { |
---|
611 | int i,j,k,l; |
---|
612 | int *rowchoise,*colchoise; |
---|
613 | BOOLEAN rowch,colch; |
---|
614 | matrix result; |
---|
615 | matrix tmp; |
---|
616 | poly p; |
---|
617 | |
---|
618 | i = binom(a->nrows,ar); |
---|
619 | j = binom(a->ncols,ar); |
---|
620 | |
---|
621 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
622 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
623 | result =mpNew(i,j); |
---|
624 | tmp=mpNew(ar,ar); |
---|
625 | l = 1; /* k,l:the index in result*/ |
---|
626 | idInitChoise(ar,1,a->nrows,&rowch,rowchoise); |
---|
627 | while (!rowch) |
---|
628 | { |
---|
629 | k=1; |
---|
630 | idInitChoise(ar,1,a->ncols,&colch,colchoise); |
---|
631 | while (!colch) |
---|
632 | { |
---|
633 | for (i=1; i<=ar; i++) |
---|
634 | { |
---|
635 | for (j=1; j<=ar; j++) |
---|
636 | { |
---|
637 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
638 | } |
---|
639 | } |
---|
640 | p = mpDetBareiss(tmp); |
---|
641 | if ((k+l) & 1) p=pNeg(p); |
---|
642 | MATELEM(result,l,k) = p; |
---|
643 | k++; |
---|
644 | idGetNextChoise(ar,a->ncols,&colch,colchoise); |
---|
645 | } |
---|
646 | idGetNextChoise(ar,a->nrows,&rowch,rowchoise); |
---|
647 | l++; |
---|
648 | } |
---|
649 | /*delete the matrix tmp*/ |
---|
650 | for (i=1; i<=ar; i++) |
---|
651 | { |
---|
652 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
653 | } |
---|
654 | idDelete((ideal *) &tmp); |
---|
655 | return (result); |
---|
656 | } |
---|
657 | |
---|
658 | ///*2 |
---|
659 | //*homogenize all elements of matrix (not the matrix itself) |
---|
660 | //*/ |
---|
661 | //matrix mpHomogen(matrix a, int v) |
---|
662 | //{ |
---|
663 | // int i,j; |
---|
664 | // poly p; |
---|
665 | // |
---|
666 | // for (i=1;i<=MATROWS(a);i++) |
---|
667 | // { |
---|
668 | // for (j=1;j<=MATCOLS(a);j++) |
---|
669 | // { |
---|
670 | // p=pHomogen(MATELEM(a,i,j),v); |
---|
671 | // pDelete(&(MATELEM(a,i,j))); |
---|
672 | // MATELEM(a,i,j)=p; |
---|
673 | // } |
---|
674 | // } |
---|
675 | // return a; |
---|
676 | //} |
---|
677 | |
---|
678 | /*2 |
---|
679 | * corresponds to Maple's coeffs: |
---|
680 | * var has to be the number of a variable |
---|
681 | */ |
---|
682 | matrix mpCoeffs (ideal I, int var) |
---|
683 | { |
---|
684 | poly h,f; |
---|
685 | int l, i, c, m=0; |
---|
686 | matrix co; |
---|
687 | /* look for maximal power m of x_var in I */ |
---|
688 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
689 | { |
---|
690 | f=I->m[i]; |
---|
691 | while (f!=NULL) |
---|
692 | { |
---|
693 | l=pGetExp(f,var); |
---|
694 | if (l>m) m=l; |
---|
695 | pIter(f); |
---|
696 | } |
---|
697 | } |
---|
698 | co=mpNew((m+1)*I->rank,IDELEMS(I)); |
---|
699 | /* divide each monomial by a power of x_var, |
---|
700 | * remember the power in l and the component in c*/ |
---|
701 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
702 | { |
---|
703 | f=I->m[i]; |
---|
704 | while (f!=NULL) |
---|
705 | { |
---|
706 | l=pGetExp(f,var); |
---|
707 | pSetExp(f,var,0); |
---|
708 | c=si_max((int)pGetComp(f),1); |
---|
709 | pSetComp(f,0); |
---|
710 | pSetm(f); |
---|
711 | /* now add the resulting monomial to co*/ |
---|
712 | h=pNext(f); |
---|
713 | pNext(f)=NULL; |
---|
714 | //MATELEM(co,c*(m+1)-l,i+1) |
---|
715 | // =pAdd(MATELEM(co,c*(m+1)-l,i+1),f); |
---|
716 | MATELEM(co,(c-1)*(m+1)+l+1,i+1) |
---|
717 | =pAdd(MATELEM(co,(c-1)*(m+1)+l+1,i+1),f); |
---|
718 | /* iterate f*/ |
---|
719 | f=h; |
---|
720 | } |
---|
721 | } |
---|
722 | return co; |
---|
723 | } |
---|
724 | |
---|
725 | /*2 |
---|
726 | * given the result c of mpCoeffs(ideal/module i, var) |
---|
727 | * i of rank r |
---|
728 | * build the matrix of the corresponding monomials in m |
---|
729 | */ |
---|
730 | void mpMonomials(matrix c, int r, int var, matrix m) |
---|
731 | { |
---|
732 | /* clear contents of m*/ |
---|
733 | int k,l; |
---|
734 | for (k=MATROWS(m);k>0;k--) |
---|
735 | { |
---|
736 | for(l=MATCOLS(m);l>0;l--) |
---|
737 | { |
---|
738 | pDelete(&MATELEM(m,k,l)); |
---|
739 | } |
---|
740 | } |
---|
741 | omfreeSize((ADDRESS)m->m,MATROWS(m)*MATCOLS(m)*sizeof(poly)); |
---|
742 | /* allocate monoms in the right size r x MATROWS(c)*/ |
---|
743 | m->m=(polyset)omAlloc0(r*MATROWS(c)*sizeof(poly)); |
---|
744 | MATROWS(m)=r; |
---|
745 | MATCOLS(m)=MATROWS(c); |
---|
746 | m->rank=r; |
---|
747 | /* the maximal power p of x_var: MATCOLS(m)=r*(p+1) */ |
---|
748 | int p=MATCOLS(m)/r-1; |
---|
749 | /* fill in the powers of x_var=h*/ |
---|
750 | poly h=pOne(); |
---|
751 | for(k=r;k>0; k--) |
---|
752 | { |
---|
753 | MATELEM(m,k,k*(p+1))=pOne(); |
---|
754 | } |
---|
755 | for(l=p;l>0; l--) |
---|
756 | { |
---|
757 | pSetExp(h,var,l); |
---|
758 | pSetm(h); |
---|
759 | for(k=r;k>0; k--) |
---|
760 | { |
---|
761 | MATELEM(m,k,k*(p+1)-l)=pCopy(h); |
---|
762 | } |
---|
763 | } |
---|
764 | pDelete(&h); |
---|
765 | } |
---|
766 | |
---|
767 | matrix mpCoeffProc (poly f, poly vars) |
---|
768 | { |
---|
769 | assume(vars!=NULL); |
---|
770 | poly sel, h; |
---|
771 | int l, i; |
---|
772 | int pos_of_1 = -1; |
---|
773 | matrix co; |
---|
774 | |
---|
775 | if (f==NULL) |
---|
776 | { |
---|
777 | co = mpNew(2, 1); |
---|
778 | MATELEM(co,1,1) = pOne(); |
---|
779 | MATELEM(co,2,1) = NULL; |
---|
780 | return co; |
---|
781 | } |
---|
782 | sel = mpSelect(f, vars); |
---|
783 | l = pLength(sel); |
---|
784 | co = mpNew(2, l); |
---|
785 | if (pOrdSgn==-1) |
---|
786 | { |
---|
787 | for (i=l; i>=1; i--) |
---|
788 | { |
---|
789 | h = sel; |
---|
790 | pIter(sel); |
---|
791 | pNext(h)=NULL; |
---|
792 | MATELEM(co,1,i) = h; |
---|
793 | MATELEM(co,2,i) = NULL; |
---|
794 | if (pIsConstant(h)) pos_of_1 = i; |
---|
795 | } |
---|
796 | } |
---|
797 | else |
---|
798 | { |
---|
799 | for (i=1; i<=l; i++) |
---|
800 | { |
---|
801 | h = sel; |
---|
802 | pIter(sel); |
---|
803 | pNext(h)=NULL; |
---|
804 | MATELEM(co,1,i) = h; |
---|
805 | MATELEM(co,2,i) = NULL; |
---|
806 | if (pIsConstant(h)) pos_of_1 = i; |
---|
807 | } |
---|
808 | } |
---|
809 | while (f!=NULL) |
---|
810 | { |
---|
811 | i = 1; |
---|
812 | loop |
---|
813 | { |
---|
814 | if (i!=pos_of_1) |
---|
815 | { |
---|
816 | h = mpExdiv(f, MATELEM(co,1,i),vars); |
---|
817 | if (h!=NULL) |
---|
818 | { |
---|
819 | MATELEM(co,2,i) = pAdd(MATELEM(co,2,i), h); |
---|
820 | break; |
---|
821 | } |
---|
822 | } |
---|
823 | if (i == l) |
---|
824 | { |
---|
825 | // check monom 1 last: |
---|
826 | if (pos_of_1 != -1) |
---|
827 | { |
---|
828 | h = mpExdiv(f, MATELEM(co,1,pos_of_1),vars); |
---|
829 | if (h!=NULL) |
---|
830 | { |
---|
831 | MATELEM(co,2,pos_of_1) = pAdd(MATELEM(co,2,pos_of_1), h); |
---|
832 | } |
---|
833 | } |
---|
834 | break; |
---|
835 | } |
---|
836 | i ++; |
---|
837 | } |
---|
838 | pIter(f); |
---|
839 | } |
---|
840 | return co; |
---|
841 | } |
---|
842 | |
---|
843 | /*2 |
---|
844 | *exact divisor: let d == x^i*y^j, m is thought to have only one term; |
---|
845 | * return m/d iff d divides m, and no x^k*y^l (k>i or l>j) divides m |
---|
846 | * consider all variables in vars |
---|
847 | */ |
---|
848 | static poly mpExdiv ( poly m, poly d, poly vars) |
---|
849 | { |
---|
850 | int i; |
---|
851 | poly h = pHead(m); |
---|
852 | for (i=1; i<=pVariables; i++) |
---|
853 | { |
---|
854 | if (pGetExp(vars,i) > 0) |
---|
855 | { |
---|
856 | if (pGetExp(d,i) != pGetExp(h,i)) |
---|
857 | { |
---|
858 | pDelete(&h); |
---|
859 | return NULL; |
---|
860 | } |
---|
861 | pSetExp(h,i,0); |
---|
862 | } |
---|
863 | } |
---|
864 | pSetm(h); |
---|
865 | return h; |
---|
866 | } |
---|
867 | |
---|
868 | void mpCoef2(poly v, poly mon, matrix *c, matrix *m) |
---|
869 | { |
---|
870 | polyset s; |
---|
871 | poly p; |
---|
872 | int sl,i,j; |
---|
873 | int l=0; |
---|
874 | poly sel=mpSelect(v,mon); |
---|
875 | |
---|
876 | pVec2Polys(sel,&s,&sl); |
---|
877 | for (i=0; i<sl; i++) |
---|
878 | l=si_max(l,pLength(s[i])); |
---|
879 | *c=mpNew(sl,l); |
---|
880 | *m=mpNew(sl,l); |
---|
881 | poly h; |
---|
882 | int isConst; |
---|
883 | for (j=1; j<=sl;j++) |
---|
884 | { |
---|
885 | p=s[j-1]; |
---|
886 | if (pIsConstant(p)) /*p != NULL */ |
---|
887 | { |
---|
888 | isConst=-1; |
---|
889 | i=l; |
---|
890 | } |
---|
891 | else |
---|
892 | { |
---|
893 | isConst=1; |
---|
894 | i=1; |
---|
895 | } |
---|
896 | while(p!=NULL) |
---|
897 | { |
---|
898 | h = pHead(p); |
---|
899 | MATELEM(*m,j,i) = h; |
---|
900 | i+=isConst; |
---|
901 | p = p->next; |
---|
902 | } |
---|
903 | } |
---|
904 | while (v!=NULL) |
---|
905 | { |
---|
906 | i = 1; |
---|
907 | j = pGetComp(v); |
---|
908 | loop |
---|
909 | { |
---|
910 | poly mp=MATELEM(*m,j,i); |
---|
911 | if (mp!=NULL) |
---|
912 | { |
---|
913 | h = mpExdiv(v, mp /*MATELEM(*m,j,i)*/, mp); |
---|
914 | if (h!=NULL) |
---|
915 | { |
---|
916 | pSetComp(h,0); |
---|
917 | MATELEM(*c,j,i) = pAdd(MATELEM(*c,j,i), h); |
---|
918 | break; |
---|
919 | } |
---|
920 | } |
---|
921 | if (i < l) |
---|
922 | i++; |
---|
923 | else |
---|
924 | break; |
---|
925 | } |
---|
926 | v = v->next; |
---|
927 | } |
---|
928 | } |
---|
929 | |
---|
930 | |
---|
931 | BOOLEAN mpEqual(matrix a, matrix b) |
---|
932 | { |
---|
933 | if ((MATCOLS(a)!=MATCOLS(b)) || (MATROWS(a)!=MATROWS(b))) |
---|
934 | return FALSE; |
---|
935 | int i=MATCOLS(a)*MATROWS(b)-1; |
---|
936 | while (i>=0) |
---|
937 | { |
---|
938 | if (a->m[i]==NULL) |
---|
939 | { |
---|
940 | if (b->m[i]!=NULL) return FALSE; |
---|
941 | } |
---|
942 | else |
---|
943 | if (b->m[i]==NULL) return FALSE; |
---|
944 | else if (pCmp(a->m[i],b->m[i])!=0) return FALSE; |
---|
945 | i--; |
---|
946 | } |
---|
947 | i=MATCOLS(a)*MATROWS(b)-1; |
---|
948 | while (i>=0) |
---|
949 | { |
---|
950 | #if 0 |
---|
951 | poly tt=pSub(pCopy(a->m[i]),pCopy(b->m[i])); |
---|
952 | if (tt!=NULL) |
---|
953 | { |
---|
954 | pDelete(&tt); |
---|
955 | return FALSE; |
---|
956 | } |
---|
957 | #else |
---|
958 | if(!pEqualPolys(a->m[i],b->m[i])) return FALSE; |
---|
959 | #endif |
---|
960 | i--; |
---|
961 | } |
---|
962 | return TRUE; |
---|
963 | } |
---|
964 | |
---|
965 | /* --------------- internal stuff ------------------- */ |
---|
966 | |
---|
967 | row_col_weight::row_col_weight(int i, int j) |
---|
968 | { |
---|
969 | ym = i; |
---|
970 | yn = j; |
---|
971 | wrow = (float *)omAlloc(i*sizeof(float)); |
---|
972 | wcol = (float *)omAlloc(j*sizeof(float)); |
---|
973 | } |
---|
974 | |
---|
975 | row_col_weight::~row_col_weight() |
---|
976 | { |
---|
977 | if (ym!=0) |
---|
978 | { |
---|
979 | omFreeSize((ADDRESS)wcol, yn*sizeof(float)); |
---|
980 | omFreeSize((ADDRESS)wrow, ym*sizeof(float)); |
---|
981 | } |
---|
982 | } |
---|
983 | |
---|
984 | mp_permmatrix::mp_permmatrix(matrix A) : sign(1) |
---|
985 | { |
---|
986 | a_m = A->nrows; |
---|
987 | a_n = A->ncols; |
---|
988 | this->mpInitMat(); |
---|
989 | Xarray = A->m; |
---|
990 | } |
---|
991 | |
---|
992 | mp_permmatrix::mp_permmatrix(mp_permmatrix *M) |
---|
993 | { |
---|
994 | poly p, *athis, *aM; |
---|
995 | int i, j; |
---|
996 | |
---|
997 | a_m = M->s_m; |
---|
998 | a_n = M->s_n; |
---|
999 | sign = M->sign; |
---|
1000 | this->mpInitMat(); |
---|
1001 | Xarray = (poly *)omAlloc0(a_m*a_n*sizeof(poly)); |
---|
1002 | for (i=a_m-1; i>=0; i--) |
---|
1003 | { |
---|
1004 | athis = this->mpRowAdr(i); |
---|
1005 | aM = M->mpRowAdr(i); |
---|
1006 | for (j=a_n-1; j>=0; j--) |
---|
1007 | { |
---|
1008 | p = aM[M->qcol[j]]; |
---|
1009 | if (p) |
---|
1010 | { |
---|
1011 | athis[j] = pCopy(p); |
---|
1012 | } |
---|
1013 | } |
---|
1014 | } |
---|
1015 | } |
---|
1016 | |
---|
1017 | mp_permmatrix::~mp_permmatrix() |
---|
1018 | { |
---|
1019 | int k; |
---|
1020 | |
---|
1021 | if (a_m != 0) |
---|
1022 | { |
---|
1023 | omFreeSize((ADDRESS)qrow,a_m*sizeof(int)); |
---|
1024 | omFreeSize((ADDRESS)qcol,a_n*sizeof(int)); |
---|
1025 | if (Xarray != NULL) |
---|
1026 | { |
---|
1027 | for (k=a_m*a_n-1; k>=0; k--) |
---|
1028 | pDelete(&Xarray[k]); |
---|
1029 | omFreeSize((ADDRESS)Xarray,a_m*a_n*sizeof(poly)); |
---|
1030 | } |
---|
1031 | } |
---|
1032 | } |
---|
1033 | |
---|
1034 | int mp_permmatrix::mpGetRdim() { return s_m; } |
---|
1035 | |
---|
1036 | int mp_permmatrix::mpGetCdim() { return s_n; } |
---|
1037 | |
---|
1038 | int mp_permmatrix::mpGetSign() { return sign; } |
---|
1039 | |
---|
1040 | void mp_permmatrix::mpSetSearch(int s) { piv_s = s; } |
---|
1041 | |
---|
1042 | void mp_permmatrix::mpSaveArray() { Xarray = NULL; } |
---|
1043 | |
---|
1044 | poly mp_permmatrix::mpGetElem(int r, int c) |
---|
1045 | { |
---|
1046 | return Xarray[a_n*qrow[r]+qcol[c]]; |
---|
1047 | } |
---|
1048 | |
---|
1049 | void mp_permmatrix::mpSetElem(poly p, int r, int c) |
---|
1050 | { |
---|
1051 | Xarray[a_n*qrow[r]+qcol[c]] = p; |
---|
1052 | } |
---|
1053 | |
---|
1054 | void mp_permmatrix::mpDelElem(int r, int c) |
---|
1055 | { |
---|
1056 | pDelete(&Xarray[a_n*qrow[r]+qcol[c]]); |
---|
1057 | } |
---|
1058 | |
---|
1059 | /* |
---|
1060 | * the Bareiss-type elimination with division by div (div != NULL) |
---|
1061 | */ |
---|
1062 | void mp_permmatrix::mpElimBareiss(poly div) |
---|
1063 | { |
---|
1064 | poly piv, elim, q1, q2, *ap, *a; |
---|
1065 | int i, j, jj; |
---|
1066 | |
---|
1067 | ap = this->mpRowAdr(s_m); |
---|
1068 | piv = ap[qcol[s_n]]; |
---|
1069 | for(i=s_m-1; i>=0; i--) |
---|
1070 | { |
---|
1071 | a = this->mpRowAdr(i); |
---|
1072 | elim = a[qcol[s_n]]; |
---|
1073 | if (elim != NULL) |
---|
1074 | { |
---|
1075 | elim = pNeg(elim); |
---|
1076 | for (j=s_n-1; j>=0; j--) |
---|
1077 | { |
---|
1078 | q2 = NULL; |
---|
1079 | jj = qcol[j]; |
---|
1080 | if (ap[jj] != NULL) |
---|
1081 | { |
---|
1082 | q2 = SM_MULT(ap[jj], elim, div); |
---|
1083 | if (a[jj] != NULL) |
---|
1084 | { |
---|
1085 | q1 = SM_MULT(a[jj], piv, div); |
---|
1086 | pDelete(&a[jj]); |
---|
1087 | q2 = pAdd(q2, q1); |
---|
1088 | } |
---|
1089 | } |
---|
1090 | else if (a[jj] != NULL) |
---|
1091 | { |
---|
1092 | q2 = SM_MULT(a[jj], piv, div); |
---|
1093 | } |
---|
1094 | if ((q2!=NULL) && div) |
---|
1095 | SM_DIV(q2, div); |
---|
1096 | a[jj] = q2; |
---|
1097 | } |
---|
1098 | pDelete(&a[qcol[s_n]]); |
---|
1099 | } |
---|
1100 | else |
---|
1101 | { |
---|
1102 | for (j=s_n-1; j>=0; j--) |
---|
1103 | { |
---|
1104 | jj = qcol[j]; |
---|
1105 | if (a[jj] != NULL) |
---|
1106 | { |
---|
1107 | q2 = SM_MULT(a[jj], piv, div); |
---|
1108 | pDelete(&a[jj]); |
---|
1109 | if (div) |
---|
1110 | SM_DIV(q2, div); |
---|
1111 | a[jj] = q2; |
---|
1112 | } |
---|
1113 | } |
---|
1114 | } |
---|
1115 | } |
---|
1116 | } |
---|
1117 | |
---|
1118 | /*2 |
---|
1119 | * pivot strategy for Bareiss algorithm |
---|
1120 | */ |
---|
1121 | int mp_permmatrix::mpPivotBareiss(row_col_weight *C) |
---|
1122 | { |
---|
1123 | poly p, *a; |
---|
1124 | int i, j, iopt, jopt; |
---|
1125 | float sum, f1, f2, fo, r, ro, lp; |
---|
1126 | float *dr = C->wrow, *dc = C->wcol; |
---|
1127 | |
---|
1128 | fo = 1.0e20; |
---|
1129 | ro = 0.0; |
---|
1130 | iopt = jopt = -1; |
---|
1131 | |
---|
1132 | s_n--; |
---|
1133 | s_m--; |
---|
1134 | if (s_m == 0) |
---|
1135 | return 0; |
---|
1136 | if (s_n == 0) |
---|
1137 | { |
---|
1138 | for(i=s_m; i>=0; i--) |
---|
1139 | { |
---|
1140 | p = this->mpRowAdr(i)[qcol[0]]; |
---|
1141 | if (p) |
---|
1142 | { |
---|
1143 | f1 = mpPolyWeight(p); |
---|
1144 | if (f1 < fo) |
---|
1145 | { |
---|
1146 | fo = f1; |
---|
1147 | if (iopt >= 0) |
---|
1148 | pDelete(&(this->mpRowAdr(iopt)[qcol[0]])); |
---|
1149 | iopt = i; |
---|
1150 | } |
---|
1151 | else |
---|
1152 | pDelete(&(this->mpRowAdr(i)[qcol[0]])); |
---|
1153 | } |
---|
1154 | } |
---|
1155 | if (iopt >= 0) |
---|
1156 | mpReplace(iopt, s_m, sign, qrow); |
---|
1157 | return 0; |
---|
1158 | } |
---|
1159 | this->mpRowWeight(dr); |
---|
1160 | this->mpColWeight(dc); |
---|
1161 | sum = 0.0; |
---|
1162 | for(i=s_m; i>=0; i--) |
---|
1163 | sum += dr[i]; |
---|
1164 | for(i=s_m; i>=0; i--) |
---|
1165 | { |
---|
1166 | r = dr[i]; |
---|
1167 | a = this->mpRowAdr(i); |
---|
1168 | for(j=s_n; j>=0; j--) |
---|
1169 | { |
---|
1170 | p = a[qcol[j]]; |
---|
1171 | if (p) |
---|
1172 | { |
---|
1173 | lp = mpPolyWeight(p); |
---|
1174 | ro = r - lp; |
---|
1175 | f1 = ro * (dc[j]-lp); |
---|
1176 | if (f1 != 0.0) |
---|
1177 | { |
---|
1178 | f2 = lp * (sum - ro - dc[j]); |
---|
1179 | f2 += f1; |
---|
1180 | } |
---|
1181 | else |
---|
1182 | f2 = lp-r-dc[j]; |
---|
1183 | if (f2 < fo) |
---|
1184 | { |
---|
1185 | fo = f2; |
---|
1186 | iopt = i; |
---|
1187 | jopt = j; |
---|
1188 | } |
---|
1189 | } |
---|
1190 | } |
---|
1191 | } |
---|
1192 | if (iopt < 0) |
---|
1193 | return 0; |
---|
1194 | mpReplace(iopt, s_m, sign, qrow); |
---|
1195 | mpReplace(jopt, s_n, sign, qcol); |
---|
1196 | return 1; |
---|
1197 | } |
---|
1198 | |
---|
1199 | /*2 |
---|
1200 | * pivot strategy for Bareiss algorithm with defined row |
---|
1201 | */ |
---|
1202 | int mp_permmatrix::mpPivotRow(row_col_weight *C, int row) |
---|
1203 | { |
---|
1204 | poly p, *a; |
---|
1205 | int j, iopt, jopt; |
---|
1206 | float sum, f1, f2, fo, r, ro, lp; |
---|
1207 | float *dr = C->wrow, *dc = C->wcol; |
---|
1208 | |
---|
1209 | fo = 1.0e20; |
---|
1210 | ro = 0.0; |
---|
1211 | iopt = jopt = -1; |
---|
1212 | |
---|
1213 | s_n--; |
---|
1214 | s_m--; |
---|
1215 | if (s_m == 0) |
---|
1216 | return 0; |
---|
1217 | if (s_n == 0) |
---|
1218 | { |
---|
1219 | p = this->mpRowAdr(row)[qcol[0]]; |
---|
1220 | if (p) |
---|
1221 | { |
---|
1222 | f1 = mpPolyWeight(p); |
---|
1223 | if (f1 < fo) |
---|
1224 | { |
---|
1225 | fo = f1; |
---|
1226 | if (iopt >= 0) |
---|
1227 | pDelete(&(this->mpRowAdr(iopt)[qcol[0]])); |
---|
1228 | iopt = row; |
---|
1229 | } |
---|
1230 | else |
---|
1231 | pDelete(&(this->mpRowAdr(row)[qcol[0]])); |
---|
1232 | } |
---|
1233 | if (iopt >= 0) |
---|
1234 | mpReplace(iopt, s_m, sign, qrow); |
---|
1235 | return 0; |
---|
1236 | } |
---|
1237 | this->mpRowWeight(dr); |
---|
1238 | this->mpColWeight(dc); |
---|
1239 | sum = 0.0; |
---|
1240 | for(j=s_m; j>=0; j--) |
---|
1241 | sum += dr[j]; |
---|
1242 | r = dr[row]; |
---|
1243 | a = this->mpRowAdr(row); |
---|
1244 | for(j=s_n; j>=0; j--) |
---|
1245 | { |
---|
1246 | p = a[qcol[j]]; |
---|
1247 | if (p) |
---|
1248 | { |
---|
1249 | lp = mpPolyWeight(p); |
---|
1250 | ro = r - lp; |
---|
1251 | f1 = ro * (dc[j]-lp); |
---|
1252 | if (f1 != 0.0) |
---|
1253 | { |
---|
1254 | f2 = lp * (sum - ro - dc[j]); |
---|
1255 | f2 += f1; |
---|
1256 | } |
---|
1257 | else |
---|
1258 | f2 = lp-r-dc[j]; |
---|
1259 | if (f2 < fo) |
---|
1260 | { |
---|
1261 | fo = f2; |
---|
1262 | iopt = row; |
---|
1263 | jopt = j; |
---|
1264 | } |
---|
1265 | } |
---|
1266 | } |
---|
1267 | if (iopt < 0) |
---|
1268 | return 0; |
---|
1269 | mpReplace(iopt, s_m, sign, qrow); |
---|
1270 | mpReplace(jopt, s_n, sign, qcol); |
---|
1271 | return 1; |
---|
1272 | } |
---|
1273 | |
---|
1274 | void mp_permmatrix::mpToIntvec(intvec *v) |
---|
1275 | { |
---|
1276 | int i; |
---|
1277 | |
---|
1278 | for (i=v->rows()-1; i>=0; i--) |
---|
1279 | (*v)[i] = qcol[i]+1; |
---|
1280 | } |
---|
1281 | |
---|
1282 | void mp_permmatrix::mpRowReorder() |
---|
1283 | { |
---|
1284 | int k, i, i1, i2; |
---|
1285 | |
---|
1286 | if (a_m > a_n) |
---|
1287 | k = a_m - a_n; |
---|
1288 | else |
---|
1289 | k = 0; |
---|
1290 | for (i=a_m-1; i>=k; i--) |
---|
1291 | { |
---|
1292 | i1 = qrow[i]; |
---|
1293 | if (i1 != i) |
---|
1294 | { |
---|
1295 | this->mpRowSwap(i1, i); |
---|
1296 | i2 = 0; |
---|
1297 | while (qrow[i2] != i) i2++; |
---|
1298 | qrow[i2] = i1; |
---|
1299 | } |
---|
1300 | } |
---|
1301 | } |
---|
1302 | |
---|
1303 | void mp_permmatrix::mpColReorder() |
---|
1304 | { |
---|
1305 | int k, j, j1, j2; |
---|
1306 | |
---|
1307 | if (a_n > a_m) |
---|
1308 | k = a_n - a_m; |
---|
1309 | else |
---|
1310 | k = 0; |
---|
1311 | for (j=a_n-1; j>=k; j--) |
---|
1312 | { |
---|
1313 | j1 = qcol[j]; |
---|
1314 | if (j1 != j) |
---|
1315 | { |
---|
1316 | this->mpColSwap(j1, j); |
---|
1317 | j2 = 0; |
---|
1318 | while (qcol[j2] != j) j2++; |
---|
1319 | qcol[j2] = j1; |
---|
1320 | } |
---|
1321 | } |
---|
1322 | } |
---|
1323 | |
---|
1324 | // private |
---|
1325 | void mp_permmatrix::mpInitMat() |
---|
1326 | { |
---|
1327 | int k; |
---|
1328 | |
---|
1329 | s_m = a_m; |
---|
1330 | s_n = a_n; |
---|
1331 | piv_s = 0; |
---|
1332 | qrow = (int *)omAlloc(a_m*sizeof(int)); |
---|
1333 | qcol = (int *)omAlloc(a_n*sizeof(int)); |
---|
1334 | for (k=a_m-1; k>=0; k--) qrow[k] = k; |
---|
1335 | for (k=a_n-1; k>=0; k--) qcol[k] = k; |
---|
1336 | } |
---|
1337 | |
---|
1338 | poly * mp_permmatrix::mpRowAdr(int r) |
---|
1339 | { |
---|
1340 | return &(Xarray[a_n*qrow[r]]); |
---|
1341 | } |
---|
1342 | |
---|
1343 | poly * mp_permmatrix::mpColAdr(int c) |
---|
1344 | { |
---|
1345 | return &(Xarray[qcol[c]]); |
---|
1346 | } |
---|
1347 | |
---|
1348 | void mp_permmatrix::mpRowWeight(float *wrow) |
---|
1349 | { |
---|
1350 | poly p, *a; |
---|
1351 | int i, j; |
---|
1352 | float count; |
---|
1353 | |
---|
1354 | for (i=s_m; i>=0; i--) |
---|
1355 | { |
---|
1356 | a = this->mpRowAdr(i); |
---|
1357 | count = 0.0; |
---|
1358 | for(j=s_n; j>=0; j--) |
---|
1359 | { |
---|
1360 | p = a[qcol[j]]; |
---|
1361 | if (p) |
---|
1362 | count += mpPolyWeight(p); |
---|
1363 | } |
---|
1364 | wrow[i] = count; |
---|
1365 | } |
---|
1366 | } |
---|
1367 | |
---|
1368 | void mp_permmatrix::mpColWeight(float *wcol) |
---|
1369 | { |
---|
1370 | poly p, *a; |
---|
1371 | int i, j; |
---|
1372 | float count; |
---|
1373 | |
---|
1374 | for (j=s_n; j>=0; j--) |
---|
1375 | { |
---|
1376 | a = this->mpColAdr(j); |
---|
1377 | count = 0.0; |
---|
1378 | for(i=s_m; i>=0; i--) |
---|
1379 | { |
---|
1380 | p = a[a_n*qrow[i]]; |
---|
1381 | if (p) |
---|
1382 | count += mpPolyWeight(p); |
---|
1383 | } |
---|
1384 | wcol[j] = count; |
---|
1385 | } |
---|
1386 | } |
---|
1387 | |
---|
1388 | void mp_permmatrix::mpRowSwap(int i1, int i2) |
---|
1389 | { |
---|
1390 | poly p, *a1, *a2; |
---|
1391 | int j; |
---|
1392 | |
---|
1393 | a1 = &(Xarray[a_n*i1]); |
---|
1394 | a2 = &(Xarray[a_n*i2]); |
---|
1395 | for (j=a_n-1; j>= 0; j--) |
---|
1396 | { |
---|
1397 | p = a1[j]; |
---|
1398 | a1[j] = a2[j]; |
---|
1399 | a2[j] = p; |
---|
1400 | } |
---|
1401 | } |
---|
1402 | |
---|
1403 | void mp_permmatrix::mpColSwap(int j1, int j2) |
---|
1404 | { |
---|
1405 | poly p, *a1, *a2; |
---|
1406 | int i, k = a_n*a_m; |
---|
1407 | |
---|
1408 | a1 = &(Xarray[j1]); |
---|
1409 | a2 = &(Xarray[j2]); |
---|
1410 | for (i=0; i< k; i+=a_n) |
---|
1411 | { |
---|
1412 | p = a1[i]; |
---|
1413 | a1[i] = a2[i]; |
---|
1414 | a2[i] = p; |
---|
1415 | } |
---|
1416 | } |
---|
1417 | |
---|
1418 | int mp_permmatrix::mpGetRow() |
---|
1419 | { |
---|
1420 | return qrow[s_m]; |
---|
1421 | } |
---|
1422 | |
---|
1423 | int mp_permmatrix::mpGetCol() |
---|
1424 | { |
---|
1425 | return qcol[s_n]; |
---|
1426 | } |
---|
1427 | |
---|
1428 | /* |
---|
1429 | * perform replacement for pivot strategy in Bareiss algorithm |
---|
1430 | * change sign of determinant |
---|
1431 | */ |
---|
1432 | static void mpReplace(int j, int n, int &sign, int *perm) |
---|
1433 | { |
---|
1434 | int k; |
---|
1435 | |
---|
1436 | if (j != n) |
---|
1437 | { |
---|
1438 | k = perm[n]; |
---|
1439 | perm[n] = perm[j]; |
---|
1440 | perm[j] = k; |
---|
1441 | sign = -sign; |
---|
1442 | } |
---|
1443 | } |
---|
1444 | |
---|
1445 | static int mpNextperm(perm * z, int max) |
---|
1446 | { |
---|
1447 | int s, i, k, t; |
---|
1448 | s = max; |
---|
1449 | do |
---|
1450 | { |
---|
1451 | s--; |
---|
1452 | } |
---|
1453 | while ((s > 0) && ((*z)[s] >= (*z)[s+1])); |
---|
1454 | if (s==0) |
---|
1455 | return 0; |
---|
1456 | do |
---|
1457 | { |
---|
1458 | (*z)[s]++; |
---|
1459 | k = 0; |
---|
1460 | do |
---|
1461 | { |
---|
1462 | k++; |
---|
1463 | } |
---|
1464 | while (((*z)[k] != (*z)[s]) && (k!=s)); |
---|
1465 | } |
---|
1466 | while (k < s); |
---|
1467 | for (i=s+1; i <= max; i++) |
---|
1468 | { |
---|
1469 | (*z)[i]=0; |
---|
1470 | do |
---|
1471 | { |
---|
1472 | (*z)[i]++; |
---|
1473 | k=0; |
---|
1474 | do |
---|
1475 | { |
---|
1476 | k++; |
---|
1477 | } |
---|
1478 | while (((*z)[k] != (*z)[i]) && (k != i)); |
---|
1479 | } |
---|
1480 | while (k < i); |
---|
1481 | } |
---|
1482 | s = max+1; |
---|
1483 | do |
---|
1484 | { |
---|
1485 | s--; |
---|
1486 | } |
---|
1487 | while ((s > 0) && ((*z)[s] > (*z)[s+1])); |
---|
1488 | t = 1; |
---|
1489 | for (i=1; i<max; i++) |
---|
1490 | for (k=i+1; k<=max; k++) |
---|
1491 | if ((*z)[k] < (*z)[i]) |
---|
1492 | t = -t; |
---|
1493 | (*z)[0] = t; |
---|
1494 | return s; |
---|
1495 | } |
---|
1496 | |
---|
1497 | static poly mpLeibnitz(matrix a) |
---|
1498 | { |
---|
1499 | int i, e, n; |
---|
1500 | poly p, d; |
---|
1501 | perm z; |
---|
1502 | |
---|
1503 | n = MATROWS(a); |
---|
1504 | memset(&z,0,(n+2)*sizeof(int)); |
---|
1505 | p = pOne(); |
---|
1506 | for (i=1; i <= n; i++) |
---|
1507 | p = pMult(p, pCopy(MATELEM(a, i, i))); |
---|
1508 | d = p; |
---|
1509 | for (i=1; i<= n; i++) |
---|
1510 | z[i] = i; |
---|
1511 | z[0]=1; |
---|
1512 | e = 1; |
---|
1513 | if (n!=1) |
---|
1514 | { |
---|
1515 | while (e) |
---|
1516 | { |
---|
1517 | e = mpNextperm((perm *)&z, n); |
---|
1518 | p = pOne(); |
---|
1519 | for (i = 1; i <= n; i++) |
---|
1520 | p = pMult(p, pCopy(MATELEM(a, i, z[i]))); |
---|
1521 | if (z[0] > 0) |
---|
1522 | d = pAdd(d, p); |
---|
1523 | else |
---|
1524 | d = pSub(d, p); |
---|
1525 | } |
---|
1526 | } |
---|
1527 | return d; |
---|
1528 | } |
---|
1529 | |
---|
1530 | static poly minuscopy (poly p) |
---|
1531 | { |
---|
1532 | poly w; |
---|
1533 | number e; |
---|
1534 | e = nInit(-1); |
---|
1535 | w = pCopy(p); |
---|
1536 | pMult_nn(w, e); |
---|
1537 | nDelete(&e); |
---|
1538 | return w; |
---|
1539 | } |
---|
1540 | |
---|
1541 | /*2 |
---|
1542 | * insert a monomial into a list, avoid duplicates |
---|
1543 | * arguments are destroyed |
---|
1544 | */ |
---|
1545 | static poly pInsert(poly p1, poly p2) |
---|
1546 | { |
---|
1547 | poly a1, p, a2, a; |
---|
1548 | int c; |
---|
1549 | |
---|
1550 | if (p1==NULL) return p2; |
---|
1551 | if (p2==NULL) return p1; |
---|
1552 | a1 = p1; |
---|
1553 | a2 = p2; |
---|
1554 | a = p = pOne(); |
---|
1555 | loop |
---|
1556 | { |
---|
1557 | c = pCmp(a1, a2); |
---|
1558 | if (c == 1) |
---|
1559 | { |
---|
1560 | a = pNext(a) = a1; |
---|
1561 | pIter(a1); |
---|
1562 | if (a1==NULL) |
---|
1563 | { |
---|
1564 | pNext(a) = a2; |
---|
1565 | break; |
---|
1566 | } |
---|
1567 | } |
---|
1568 | else if (c == -1) |
---|
1569 | { |
---|
1570 | a = pNext(a) = a2; |
---|
1571 | pIter(a2); |
---|
1572 | if (a2==NULL) |
---|
1573 | { |
---|
1574 | pNext(a) = a1; |
---|
1575 | break; |
---|
1576 | } |
---|
1577 | } |
---|
1578 | else |
---|
1579 | { |
---|
1580 | pDeleteLm(&a2); |
---|
1581 | a = pNext(a) = a1; |
---|
1582 | pIter(a1); |
---|
1583 | if (a1==NULL) |
---|
1584 | { |
---|
1585 | pNext(a) = a2; |
---|
1586 | break; |
---|
1587 | } |
---|
1588 | else if (a2==NULL) |
---|
1589 | { |
---|
1590 | pNext(a) = a1; |
---|
1591 | break; |
---|
1592 | } |
---|
1593 | } |
---|
1594 | } |
---|
1595 | pDeleteLm(&p); |
---|
1596 | return p; |
---|
1597 | } |
---|
1598 | |
---|
1599 | /*2 |
---|
1600 | *if what == xy the result is the list of all different power products |
---|
1601 | * x^i*y^j (i, j >= 0) that appear in fro |
---|
1602 | */ |
---|
1603 | static poly mpSelect (poly fro, poly what) |
---|
1604 | { |
---|
1605 | int i; |
---|
1606 | poly h, res; |
---|
1607 | res = NULL; |
---|
1608 | while (fro!=NULL) |
---|
1609 | { |
---|
1610 | h = pOne(); |
---|
1611 | for (i=1; i<=pVariables; i++) |
---|
1612 | pSetExp(h,i, pGetExp(fro,i) * pGetExp(what, i)); |
---|
1613 | pSetComp(h, pGetComp(fro)); |
---|
1614 | pSetm(h); |
---|
1615 | res = pInsert(h, res); |
---|
1616 | fro = fro->next; |
---|
1617 | } |
---|
1618 | return res; |
---|
1619 | } |
---|
1620 | |
---|
1621 | /* |
---|
1622 | *static void ppp(matrix a) |
---|
1623 | *{ |
---|
1624 | * int j,i,r=a->nrows,c=a->ncols; |
---|
1625 | * for(j=1;j<=r;j++) |
---|
1626 | * { |
---|
1627 | * for(i=1;i<=c;i++) |
---|
1628 | * { |
---|
1629 | * if(MATELEM(a,j,i)!=NULL) Print("X"); |
---|
1630 | * else Print("0"); |
---|
1631 | * } |
---|
1632 | * Print("\n"); |
---|
1633 | * } |
---|
1634 | *} |
---|
1635 | */ |
---|
1636 | |
---|
1637 | static void mpPartClean(matrix a, int lr, int lc) |
---|
1638 | { |
---|
1639 | poly *q1; |
---|
1640 | int i,j; |
---|
1641 | |
---|
1642 | for (i=lr-1;i>=0;i--) |
---|
1643 | { |
---|
1644 | q1 = &(a->m)[i*a->ncols]; |
---|
1645 | for (j=lc-1;j>=0;j--) if(q1[j]) pDelete(&q1[j]); |
---|
1646 | } |
---|
1647 | } |
---|
1648 | |
---|
1649 | static void mpFinalClean(matrix a) |
---|
1650 | { |
---|
1651 | omFreeSize((ADDRESS)a->m,a->nrows*a->ncols*sizeof(poly)); |
---|
1652 | omFreeBin((ADDRESS)a, ip_smatrix_bin); |
---|
1653 | } |
---|
1654 | |
---|
1655 | /*2 |
---|
1656 | * prepare one step of 'Bareiss' algorithm |
---|
1657 | * for application in minor |
---|
1658 | */ |
---|
1659 | static int mpPrepareRow (matrix a, int lr, int lc) |
---|
1660 | { |
---|
1661 | int r; |
---|
1662 | |
---|
1663 | r = mpPivBar(a,lr,lc); |
---|
1664 | if(r==0) return 0; |
---|
1665 | if(r<lr) mpSwapRow(a, r, lr, lc); |
---|
1666 | return 1; |
---|
1667 | } |
---|
1668 | |
---|
1669 | /*2 |
---|
1670 | * prepare one step of 'Bareiss' algorithm |
---|
1671 | * for application in minor |
---|
1672 | */ |
---|
1673 | static int mpPreparePiv (matrix a, int lr, int lc) |
---|
1674 | { |
---|
1675 | int c; |
---|
1676 | |
---|
1677 | c = mpPivRow(a, lr, lc); |
---|
1678 | if(c==0) return 0; |
---|
1679 | if(c<lc) mpSwapCol(a, c, lr, lc); |
---|
1680 | return 1; |
---|
1681 | } |
---|
1682 | |
---|
1683 | /* |
---|
1684 | * find best row |
---|
1685 | */ |
---|
1686 | static int mpPivBar(matrix a, int lr, int lc) |
---|
1687 | { |
---|
1688 | float f1, f2; |
---|
1689 | poly *q1; |
---|
1690 | int i,j,io; |
---|
1691 | |
---|
1692 | io = -1; |
---|
1693 | f1 = 1.0e30; |
---|
1694 | for (i=lr-1;i>=0;i--) |
---|
1695 | { |
---|
1696 | q1 = &(a->m)[i*a->ncols]; |
---|
1697 | f2 = 0.0; |
---|
1698 | for (j=lc-1;j>=0;j--) |
---|
1699 | { |
---|
1700 | if (q1[j]!=NULL) |
---|
1701 | f2 += mpPolyWeight(q1[j]); |
---|
1702 | } |
---|
1703 | if ((f2!=0.0) && (f2<f1)) |
---|
1704 | { |
---|
1705 | f1 = f2; |
---|
1706 | io = i; |
---|
1707 | } |
---|
1708 | } |
---|
1709 | if (io<0) return 0; |
---|
1710 | else return io+1; |
---|
1711 | } |
---|
1712 | |
---|
1713 | /* |
---|
1714 | * find pivot in the last row |
---|
1715 | */ |
---|
1716 | static int mpPivRow(matrix a, int lr, int lc) |
---|
1717 | { |
---|
1718 | float f1, f2; |
---|
1719 | poly *q1; |
---|
1720 | int j,jo; |
---|
1721 | |
---|
1722 | jo = -1; |
---|
1723 | f1 = 1.0e30; |
---|
1724 | q1 = &(a->m)[(lr-1)*a->ncols]; |
---|
1725 | for (j=lc-1;j>=0;j--) |
---|
1726 | { |
---|
1727 | if (q1[j]!=NULL) |
---|
1728 | { |
---|
1729 | f2 = mpPolyWeight(q1[j]); |
---|
1730 | if (f2<f1) |
---|
1731 | { |
---|
1732 | f1 = f2; |
---|
1733 | jo = j; |
---|
1734 | } |
---|
1735 | } |
---|
1736 | } |
---|
1737 | if (jo<0) return 0; |
---|
1738 | else return jo+1; |
---|
1739 | } |
---|
1740 | |
---|
1741 | /* |
---|
1742 | * weigth of a polynomial, for pivot strategy |
---|
1743 | */ |
---|
1744 | static float mpPolyWeight(poly p) |
---|
1745 | { |
---|
1746 | int i; |
---|
1747 | float res; |
---|
1748 | |
---|
1749 | if (pNext(p) == NULL) |
---|
1750 | { |
---|
1751 | res = (float)nSize(pGetCoeff(p)); |
---|
1752 | for (i=pVariables;i>0;i--) |
---|
1753 | { |
---|
1754 | if(pGetExp(p,i)!=0) |
---|
1755 | { |
---|
1756 | res += 2.0; |
---|
1757 | break; |
---|
1758 | } |
---|
1759 | } |
---|
1760 | } |
---|
1761 | else |
---|
1762 | { |
---|
1763 | res = 0.0; |
---|
1764 | do |
---|
1765 | { |
---|
1766 | res += (float)nSize(pGetCoeff(p))+2.0; |
---|
1767 | pIter(p); |
---|
1768 | } |
---|
1769 | while (p); |
---|
1770 | } |
---|
1771 | return res; |
---|
1772 | } |
---|
1773 | |
---|
1774 | static void mpSwapRow(matrix a, int pos, int lr, int lc) |
---|
1775 | { |
---|
1776 | poly sw; |
---|
1777 | int j; |
---|
1778 | polyset a2 = a->m, a1 = &a2[a->ncols*(pos-1)]; |
---|
1779 | |
---|
1780 | a2 = &a2[a->ncols*(lr-1)]; |
---|
1781 | for (j=lc-1; j>=0; j--) |
---|
1782 | { |
---|
1783 | sw = a1[j]; |
---|
1784 | a1[j] = a2[j]; |
---|
1785 | a2[j] = sw; |
---|
1786 | } |
---|
1787 | } |
---|
1788 | |
---|
1789 | static void mpSwapCol(matrix a, int pos, int lr, int lc) |
---|
1790 | { |
---|
1791 | poly sw; |
---|
1792 | int j; |
---|
1793 | polyset a2 = a->m, a1 = &a2[pos-1]; |
---|
1794 | |
---|
1795 | a2 = &a2[lc-1]; |
---|
1796 | for (j=a->ncols*(lr-1); j>=0; j-=a->ncols) |
---|
1797 | { |
---|
1798 | sw = a1[j]; |
---|
1799 | a1[j] = a2[j]; |
---|
1800 | a2[j] = sw; |
---|
1801 | } |
---|
1802 | } |
---|
1803 | |
---|
1804 | static void mpElimBar(matrix a0, matrix re, poly div, int lr, int lc) |
---|
1805 | { |
---|
1806 | int r=lr-1, c=lc-1; |
---|
1807 | poly *b = a0->m, *x = re->m; |
---|
1808 | poly piv, elim, q1, q2, *ap, *a, *q; |
---|
1809 | int i, j; |
---|
1810 | |
---|
1811 | ap = &b[r*a0->ncols]; |
---|
1812 | piv = ap[c]; |
---|
1813 | for(j=c-1; j>=0; j--) |
---|
1814 | if (ap[j] != NULL) ap[j] = pNeg(ap[j]); |
---|
1815 | for(i=r-1; i>=0; i--) |
---|
1816 | { |
---|
1817 | a = &b[i*a0->ncols]; |
---|
1818 | q = &x[i*re->ncols]; |
---|
1819 | if (a[c] != NULL) |
---|
1820 | { |
---|
1821 | elim = a[c]; |
---|
1822 | for (j=c-1; j>=0; j--) |
---|
1823 | { |
---|
1824 | q1 = NULL; |
---|
1825 | if (a[j] != NULL) |
---|
1826 | { |
---|
1827 | q1 = SM_MULT(a[j], piv, div); |
---|
1828 | if (ap[j] != NULL) |
---|
1829 | { |
---|
1830 | q2 = SM_MULT(ap[j], elim, div); |
---|
1831 | q1 = pAdd(q1,q2); |
---|
1832 | } |
---|
1833 | } |
---|
1834 | else if (ap[j] != NULL) |
---|
1835 | q1 = SM_MULT(ap[j], elim, div); |
---|
1836 | if (q1 != NULL) |
---|
1837 | { |
---|
1838 | if (div) |
---|
1839 | SM_DIV(q1, div); |
---|
1840 | q[j] = q1; |
---|
1841 | } |
---|
1842 | } |
---|
1843 | } |
---|
1844 | else |
---|
1845 | { |
---|
1846 | for (j=c-1; j>=0; j--) |
---|
1847 | { |
---|
1848 | if (a[j] != NULL) |
---|
1849 | { |
---|
1850 | q1 = SM_MULT(a[j], piv, div); |
---|
1851 | if (div) |
---|
1852 | SM_DIV(q1, div); |
---|
1853 | q[j] = q1; |
---|
1854 | } |
---|
1855 | } |
---|
1856 | } |
---|
1857 | } |
---|
1858 | } |
---|
1859 | |
---|
1860 | BOOLEAN mpIsDiagUnit(matrix U) |
---|
1861 | { |
---|
1862 | if(MATROWS(U)!=MATCOLS(U)) |
---|
1863 | return FALSE; |
---|
1864 | for(int i=MATCOLS(U);i>=1;i--) |
---|
1865 | { |
---|
1866 | for(int j=MATCOLS(U); j>=1; j--) |
---|
1867 | { |
---|
1868 | if (i==j) |
---|
1869 | { |
---|
1870 | if (!pIsUnit(MATELEM(U,i,i))) return FALSE; |
---|
1871 | } |
---|
1872 | else if (MATELEM(U,i,j)!=NULL) return FALSE; |
---|
1873 | } |
---|
1874 | } |
---|
1875 | return TRUE; |
---|
1876 | } |
---|
1877 | |
---|
1878 | void iiWriteMatrix(matrix im, const char *n, int dim,int spaces) |
---|
1879 | { |
---|
1880 | int i,ii = MATROWS(im)-1; |
---|
1881 | int j,jj = MATCOLS(im)-1; |
---|
1882 | poly *pp = im->m; |
---|
1883 | |
---|
1884 | for (i=0; i<=ii; i++) |
---|
1885 | { |
---|
1886 | for (j=0; j<=jj; j++) |
---|
1887 | { |
---|
1888 | if (spaces>0) |
---|
1889 | Print("%-*.*s",spaces,spaces," "); |
---|
1890 | if (dim == 2) Print("%s[%u,%u]=",n,i+1,j+1); |
---|
1891 | else if (dim == 1) Print("%s[%u]=",n,j+1); |
---|
1892 | else if (dim == 0) Print("%s=",n); |
---|
1893 | if ((i<ii)||(j<jj)) pWrite(*pp++); |
---|
1894 | else pWrite0(*pp); |
---|
1895 | } |
---|
1896 | } |
---|
1897 | } |
---|
1898 | |
---|
1899 | char * iiStringMatrix(matrix im, int dim,char ch) |
---|
1900 | { |
---|
1901 | int i,ii = MATROWS(im); |
---|
1902 | int j,jj = MATCOLS(im); |
---|
1903 | poly *pp = im->m; |
---|
1904 | char *s=StringSetS(""); |
---|
1905 | |
---|
1906 | for (i=0; i<ii; i++) |
---|
1907 | { |
---|
1908 | for (j=0; j<jj; j++) |
---|
1909 | { |
---|
1910 | pString0(*pp++); |
---|
1911 | s=StringAppend("%c",ch); |
---|
1912 | if (dim > 1) s = StringAppendS("\n"); |
---|
1913 | } |
---|
1914 | } |
---|
1915 | s[strlen(s)- (dim > 1 ? 2 : 1)]='\0'; |
---|
1916 | return s; |
---|
1917 | } |
---|
1918 | |
---|
1919 | void mpDelete(matrix* a, const ring r) |
---|
1920 | { |
---|
1921 | id_Delete((ideal *) a, r); |
---|
1922 | } |
---|