1 | /* |
---|
2 | * lib_cone.cpp |
---|
3 | * |
---|
4 | * Created on: Sep 29, 2010 |
---|
5 | * Author: anders |
---|
6 | */ |
---|
7 | |
---|
8 | #include "gfanlib_zcone.h" |
---|
9 | |
---|
10 | #include <vector> |
---|
11 | #include <set> |
---|
12 | |
---|
13 | #include "setoper.h" |
---|
14 | #include "cdd.h" |
---|
15 | |
---|
16 | namespace gfan{ |
---|
17 | |
---|
18 | static void cddinitGmp() |
---|
19 | { |
---|
20 | static bool initialized; |
---|
21 | if(!initialized) |
---|
22 | { |
---|
23 | dd_set_global_constants(); /* First, this must be called. */ |
---|
24 | initialized=true; |
---|
25 | } |
---|
26 | } |
---|
27 | |
---|
28 | |
---|
29 | class LpSolver |
---|
30 | { |
---|
31 | static dd_MatrixPtr ZMatrix2MatrixGmp(ZMatrix const &g, dd_ErrorType *Error) |
---|
32 | { |
---|
33 | int n=g.getWidth(); |
---|
34 | dd_MatrixPtr M=NULL; |
---|
35 | dd_rowrange m_input,i; |
---|
36 | dd_colrange d_input,j; |
---|
37 | dd_RepresentationType rep=dd_Inequality; |
---|
38 | dd_boolean found=dd_FALSE, newformat=dd_FALSE, successful=dd_FALSE; |
---|
39 | char command[dd_linelenmax], comsave[dd_linelenmax]; |
---|
40 | dd_NumberType NT; |
---|
41 | |
---|
42 | (*Error)=dd_NoError; |
---|
43 | |
---|
44 | rep=dd_Inequality; newformat=dd_TRUE; |
---|
45 | |
---|
46 | m_input=g.getHeight(); |
---|
47 | d_input=n+1; |
---|
48 | |
---|
49 | NT=dd_Rational; |
---|
50 | |
---|
51 | M=dd_CreateMatrix(m_input, d_input); |
---|
52 | M->representation=rep; |
---|
53 | M->numbtype=NT; |
---|
54 | |
---|
55 | for (i = 0; i < m_input; i++) { |
---|
56 | dd_set_si(M->matrix[i][0],0); |
---|
57 | for (j = 1; j < d_input; j++) { |
---|
58 | g[i][j-1].setGmp(mpq_numref(M->matrix[i][j])); |
---|
59 | mpz_init_set_ui(mpq_denref(M->matrix[i][j]), 1); |
---|
60 | mpq_canonicalize(M->matrix[i][j]); |
---|
61 | } |
---|
62 | } |
---|
63 | |
---|
64 | successful=dd_TRUE; |
---|
65 | |
---|
66 | return M; |
---|
67 | } |
---|
68 | static dd_MatrixPtr ZMatrix2MatrixGmp(ZMatrix const &inequalities, ZMatrix const &equations, dd_ErrorType *err) |
---|
69 | { |
---|
70 | ZMatrix g=inequalities; |
---|
71 | g.append(equations); |
---|
72 | int numberOfInequalities=inequalities.getHeight(); |
---|
73 | int numberOfRows=g.getHeight(); |
---|
74 | dd_MatrixPtr A=NULL; |
---|
75 | cddinitGmp(); |
---|
76 | A=ZMatrix2MatrixGmp(g, err); |
---|
77 | for(int i=numberOfInequalities;i<numberOfRows;i++) |
---|
78 | set_addelem(A->linset,i+1); |
---|
79 | return A; |
---|
80 | } |
---|
81 | static ZMatrix getConstraints(dd_MatrixPtr A, bool returnEquations) |
---|
82 | { |
---|
83 | int rowsize=A->rowsize; |
---|
84 | int n=A->colsize-1; |
---|
85 | |
---|
86 | ZMatrix ret(0,n); |
---|
87 | for(int i=0;i<rowsize;i++) |
---|
88 | { |
---|
89 | bool isEquation=set_member(i+1,A->linset); |
---|
90 | if(isEquation==returnEquations) |
---|
91 | { |
---|
92 | QVector v(n); |
---|
93 | for(int j=0;j<n;j++)v[j]=Rational(A->matrix[i][j+1]); |
---|
94 | ret.appendRow(QToZVectorPrimitive(v)); |
---|
95 | } |
---|
96 | } |
---|
97 | return ret; |
---|
98 | } |
---|
99 | static bool isFacet(ZMatrix const &g, int index) |
---|
100 | { |
---|
101 | bool ret; |
---|
102 | dd_MatrixPtr M=NULL,M2=NULL,M3=NULL; |
---|
103 | dd_colrange d; |
---|
104 | dd_ErrorType err=dd_NoError; |
---|
105 | dd_rowset redrows,linrows,ignoredrows, basisrows; |
---|
106 | dd_colset ignoredcols, basiscols; |
---|
107 | dd_DataFileType inputfile; |
---|
108 | FILE *reading=NULL; |
---|
109 | |
---|
110 | cddinitGmp(); |
---|
111 | |
---|
112 | M=ZMatrix2MatrixGmp(g, &err); |
---|
113 | if (err!=dd_NoError) goto _L99; |
---|
114 | |
---|
115 | d=M->colsize; |
---|
116 | |
---|
117 | static dd_Arow temp; |
---|
118 | dd_InitializeArow(g.getWidth()+1,&temp); |
---|
119 | |
---|
120 | ret= !dd_Redundant(M,index+1,temp,&err); |
---|
121 | |
---|
122 | dd_FreeMatrix(M); |
---|
123 | dd_FreeArow(g.getWidth()+1,temp); |
---|
124 | |
---|
125 | if (err!=dd_NoError) goto _L99; |
---|
126 | return ret; |
---|
127 | _L99: |
---|
128 | assert(0); |
---|
129 | return false; |
---|
130 | } |
---|
131 | |
---|
132 | /* |
---|
133 | Heuristic for checking if inequality of full dimensional cone is a |
---|
134 | facet. If the routine returns true then the inequality is a |
---|
135 | facet. If it returns false it is unknown. |
---|
136 | */ |
---|
137 | static bool fastIsFacetCriterion(ZMatrix const &normals, int i) |
---|
138 | { |
---|
139 | int n=normals.getWidth(); |
---|
140 | for(int j=0;j<n;j++) |
---|
141 | if(normals[i][j].sign()!=0) |
---|
142 | { |
---|
143 | int sign=normals[i][j].sign(); |
---|
144 | bool isTheOnly=true; |
---|
145 | for(int k=0;k<normals.getHeight();k++) |
---|
146 | if(k!=i) |
---|
147 | { |
---|
148 | if(normals[i][j].sign()==sign) |
---|
149 | { |
---|
150 | isTheOnly=false; |
---|
151 | break; |
---|
152 | } |
---|
153 | } |
---|
154 | if(isTheOnly)return true; |
---|
155 | } |
---|
156 | return false; |
---|
157 | } |
---|
158 | |
---|
159 | static bool fastIsFacet(ZMatrix const &normals, int i) |
---|
160 | { |
---|
161 | if(fastIsFacetCriterion(normals,i))return true; |
---|
162 | return isFacet(normals,i); |
---|
163 | } |
---|
164 | |
---|
165 | class MyHashMap |
---|
166 | { |
---|
167 | typedef std::vector<std::set<ZVector> > Container; |
---|
168 | Container container; |
---|
169 | int tableSize; |
---|
170 | public: |
---|
171 | class iterator |
---|
172 | { |
---|
173 | class MyHashMap &hashMap; |
---|
174 | int index; // having index==-1 means that we are before/after the elements. |
---|
175 | std::set<ZVector>::iterator i; |
---|
176 | public: |
---|
177 | bool operator++() |
---|
178 | { |
---|
179 | if(index==-1)goto search; |
---|
180 | i++; |
---|
181 | while(i==hashMap.container[index].end()) |
---|
182 | { |
---|
183 | search: |
---|
184 | index++; |
---|
185 | if(index>=hashMap.tableSize){ |
---|
186 | index=-1; |
---|
187 | return false; |
---|
188 | } |
---|
189 | i=hashMap.container[index].begin(); |
---|
190 | } |
---|
191 | return true; |
---|
192 | } |
---|
193 | ZVector const & operator*()const |
---|
194 | { |
---|
195 | return *i; |
---|
196 | } |
---|
197 | ZVector operator*() |
---|
198 | { |
---|
199 | return *i; |
---|
200 | } |
---|
201 | iterator(MyHashMap &hashMap_): |
---|
202 | hashMap(hashMap_) |
---|
203 | { |
---|
204 | index=-1; |
---|
205 | } |
---|
206 | }; |
---|
207 | unsigned int function(const ZVector &v) |
---|
208 | { |
---|
209 | unsigned int ret=0; |
---|
210 | int n=v.size(); |
---|
211 | for(int i=0;i<n;i++) |
---|
212 | ret=(ret<<3)+(ret>>29)+v.UNCHECKEDACCESS(i).hashValue(); |
---|
213 | return ret%tableSize; |
---|
214 | } |
---|
215 | MyHashMap(int tableSize_): |
---|
216 | container(tableSize_), |
---|
217 | tableSize(tableSize_) |
---|
218 | { |
---|
219 | assert(tableSize_>0); |
---|
220 | } |
---|
221 | void insert(const ZVector &v) |
---|
222 | { |
---|
223 | container[function(v)].insert(v); |
---|
224 | } |
---|
225 | void erase(ZVector const &v) |
---|
226 | { |
---|
227 | container[function(v)].erase(v); |
---|
228 | } |
---|
229 | iterator begin() |
---|
230 | { |
---|
231 | iterator ret(*this); |
---|
232 | ++ ret; |
---|
233 | return ret; |
---|
234 | } |
---|
235 | int size() |
---|
236 | { |
---|
237 | iterator i=begin(); |
---|
238 | int ret=0; |
---|
239 | do{ret++;}while(++i); |
---|
240 | return ret; |
---|
241 | } |
---|
242 | }; |
---|
243 | |
---|
244 | |
---|
245 | static ZMatrix normalizedWithSumsAndDuplicatesRemoved(ZMatrix const &a) |
---|
246 | { |
---|
247 | // TODO: write a version of this function which will work faster if the entries fit in 32bit |
---|
248 | if(a.getHeight()==0)return a; |
---|
249 | int n=a.getWidth(); |
---|
250 | ZVector temp1(n); |
---|
251 | // ZVector temp2(n); |
---|
252 | ZMatrix ret(0,n); |
---|
253 | MyHashMap b(a.getHeight()); |
---|
254 | |
---|
255 | for(int i=0;i<a.getHeight();i++) |
---|
256 | { |
---|
257 | assert(!(a[i].isZero())); |
---|
258 | b.insert(a[i].normalized()); |
---|
259 | } |
---|
260 | |
---|
261 | { |
---|
262 | MyHashMap::iterator i=b.begin(); |
---|
263 | |
---|
264 | do |
---|
265 | { |
---|
266 | MyHashMap::iterator j=i; |
---|
267 | while(++j) |
---|
268 | { |
---|
269 | ZVector const &I=*i; |
---|
270 | ZVector const &J=*j; |
---|
271 | for(int k=0;k<n;k++)temp1[k]=I.UNCHECKEDACCESS(k)+J.UNCHECKEDACCESS(k); |
---|
272 | // normalizedLowLevel(temp1,temp2); |
---|
273 | // b.erase(temp2);//this can never remove *i or *j |
---|
274 | b.erase(temp1.normalized());//this can never remove *i or *j |
---|
275 | } |
---|
276 | } |
---|
277 | while(++i); |
---|
278 | } |
---|
279 | ZMatrix original(0,n); |
---|
280 | { |
---|
281 | MyHashMap::iterator i=b.begin(); |
---|
282 | do |
---|
283 | { |
---|
284 | original.appendRow(*i); |
---|
285 | } |
---|
286 | while(++i); |
---|
287 | } |
---|
288 | |
---|
289 | for(int i=0;i!=original.getHeight();i++) |
---|
290 | for(int j=0;j!=a.getHeight();j++) |
---|
291 | if(!dependent(original[i],a[j])) |
---|
292 | { |
---|
293 | ZVector const &I=original[i]; |
---|
294 | ZVector const &J=a[j]; |
---|
295 | for(int k=0;k<n;k++)temp1[k]=I.UNCHECKEDACCESS(k)+J.UNCHECKEDACCESS(k); |
---|
296 | // normalizedLowLevel(temp1,temp2); |
---|
297 | // b.erase(temp2);//this can never remove *i or *j |
---|
298 | b.erase(temp1.normalized());//this can never remove *i or *j |
---|
299 | } |
---|
300 | { |
---|
301 | MyHashMap::iterator i=b.begin(); |
---|
302 | do |
---|
303 | { |
---|
304 | ZVector temp=*i; |
---|
305 | ret.appendRow(temp); |
---|
306 | } |
---|
307 | while(++i); |
---|
308 | } |
---|
309 | return ret; |
---|
310 | } |
---|
311 | public: |
---|
312 | static ZMatrix fastNormals(ZMatrix const &inequalities) |
---|
313 | { |
---|
314 | ZMatrix normals=normalizedWithSumsAndDuplicatesRemoved(inequalities); |
---|
315 | for(int i=0;i!=normals.getHeight();i++) |
---|
316 | if(!fastIsFacet(normals,i)) |
---|
317 | { |
---|
318 | normals[i]=normals[normals.getHeight()-1]; |
---|
319 | normals.eraseLastRow(); |
---|
320 | i--; |
---|
321 | } |
---|
322 | return normals; |
---|
323 | } |
---|
324 | void removeRedundantRows(ZMatrix &inequalities, ZMatrix &equations, bool removeInequalityRedundancies) |
---|
325 | { |
---|
326 | cddinitGmp(); |
---|
327 | int numberOfEqualities=equations.getHeight(); |
---|
328 | int numberOfInequalities=inequalities.getHeight(); |
---|
329 | int numberOfRows=numberOfEqualities+numberOfInequalities; |
---|
330 | |
---|
331 | if(numberOfRows==0)return;//the full space, so description is already irredundant |
---|
332 | |
---|
333 | dd_rowset r=NULL; |
---|
334 | ZMatrix g=inequalities; |
---|
335 | g.append(equations); |
---|
336 | |
---|
337 | dd_LPSolverType solver=dd_DualSimplex; |
---|
338 | dd_MatrixPtr A=NULL; |
---|
339 | dd_ErrorType err=dd_NoError; |
---|
340 | |
---|
341 | A=ZMatrix2MatrixGmp(g,&err); |
---|
342 | if (err!=dd_NoError) goto _L99; |
---|
343 | |
---|
344 | for(int i=numberOfInequalities;i<numberOfRows;i++) |
---|
345 | set_addelem(A->linset,i+1); |
---|
346 | |
---|
347 | A->objective=dd_LPmax; |
---|
348 | |
---|
349 | dd_rowset impl_linset; |
---|
350 | dd_rowset redset; |
---|
351 | dd_rowindex newpos; |
---|
352 | |
---|
353 | if(removeInequalityRedundancies) |
---|
354 | dd_MatrixCanonicalize(&A, &impl_linset, &redset, &newpos, &err); |
---|
355 | else |
---|
356 | dd_MatrixCanonicalizeLinearity(&A, &impl_linset, &newpos, &err); |
---|
357 | |
---|
358 | if (err!=dd_NoError) goto _L99; |
---|
359 | |
---|
360 | { |
---|
361 | int n=A->colsize-1; |
---|
362 | equations=ZMatrix(0,n); //TODO: the number of rows needed is actually known |
---|
363 | inequalities=ZMatrix(0,n); //is known by set_card(). That might save some copying. |
---|
364 | |
---|
365 | { |
---|
366 | int rowsize=A->rowsize; |
---|
367 | QVector point(n); |
---|
368 | for(int i=0;i<rowsize;i++) |
---|
369 | { |
---|
370 | for(int j=0;j<n;j++)point[j]=Rational(A->matrix[i][j+1]); |
---|
371 | ((set_member(i+1,A->linset))?equations:inequalities).appendRow(QToZVectorPrimitive(point)); |
---|
372 | } |
---|
373 | } |
---|
374 | assert(set_card(A->linset)==equations.getHeight()); |
---|
375 | assert(A->rowsize==equations.getHeight()+inequalities.getHeight()); |
---|
376 | |
---|
377 | set_free(impl_linset); |
---|
378 | if(removeInequalityRedundancies) |
---|
379 | set_free(redset); |
---|
380 | free(newpos); |
---|
381 | |
---|
382 | dd_FreeMatrix(A); |
---|
383 | return; |
---|
384 | } |
---|
385 | _L99: |
---|
386 | assert(!"Cddlib reported error when called by Gfanlib."); |
---|
387 | } |
---|
388 | ZVector relativeInteriorPoint(const ZMatrix &inequalities, const ZMatrix &equations) |
---|
389 | { |
---|
390 | QVector retUnscaled(inequalities.getWidth()); |
---|
391 | cddinitGmp(); |
---|
392 | int numberOfEqualities=equations.getHeight(); |
---|
393 | int numberOfInequalities=inequalities.getHeight(); |
---|
394 | int numberOfRows=numberOfEqualities+numberOfInequalities; |
---|
395 | |
---|
396 | dd_rowset r=NULL; |
---|
397 | ZMatrix g=inequalities; |
---|
398 | g.append(equations); |
---|
399 | |
---|
400 | dd_LPSolverType solver=dd_DualSimplex; |
---|
401 | dd_MatrixPtr A=NULL; |
---|
402 | dd_ErrorType err=dd_NoError; |
---|
403 | |
---|
404 | A=ZMatrix2MatrixGmp(g,&err); |
---|
405 | if (err!=dd_NoError) goto _L99; |
---|
406 | { |
---|
407 | dd_LPSolutionPtr lps1; |
---|
408 | dd_LPPtr lp,lp1; |
---|
409 | |
---|
410 | for(int i=0;i<numberOfInequalities;i++) |
---|
411 | dd_set_si(A->matrix[i][0],-1); |
---|
412 | for(int i=numberOfInequalities;i<numberOfRows;i++) |
---|
413 | set_addelem(A->linset,i+1); |
---|
414 | |
---|
415 | A->objective=dd_LPmax; |
---|
416 | lp=dd_Matrix2LP(A, &err); |
---|
417 | if (err!=dd_NoError) goto _L99; |
---|
418 | |
---|
419 | lp1=dd_MakeLPforInteriorFinding(lp); |
---|
420 | dd_LPSolve(lp1,solver,&err); |
---|
421 | if (err!=dd_NoError) goto _L99; |
---|
422 | |
---|
423 | lps1=dd_CopyLPSolution(lp1); |
---|
424 | |
---|
425 | assert(!dd_Negative(lps1->optvalue)); |
---|
426 | |
---|
427 | for (int j=1; j <(lps1->d)-1; j++) |
---|
428 | retUnscaled[j-1]=Rational(lps1->sol[j]); |
---|
429 | |
---|
430 | dd_FreeLPData(lp); |
---|
431 | dd_FreeLPSolution(lps1); |
---|
432 | dd_FreeLPData(lp1); |
---|
433 | dd_FreeMatrix(A); |
---|
434 | return QToZVectorPrimitive(retUnscaled); |
---|
435 | } |
---|
436 | _L99: |
---|
437 | assert(0); |
---|
438 | return QToZVectorPrimitive(retUnscaled); |
---|
439 | } |
---|
440 | void dual(ZMatrix const &inequalities, ZMatrix const &equations, ZMatrix &dualInequalities, ZMatrix &dualEquations) |
---|
441 | { |
---|
442 | int result; |
---|
443 | |
---|
444 | dd_MatrixPtr A=NULL; |
---|
445 | dd_ErrorType err=dd_NoError; |
---|
446 | |
---|
447 | cddinitGmp(); |
---|
448 | |
---|
449 | A=ZMatrix2MatrixGmp(inequalities, equations, &err); |
---|
450 | |
---|
451 | dd_PolyhedraPtr poly; |
---|
452 | poly=dd_DDMatrix2Poly2(A, dd_LexMin, &err); |
---|
453 | |
---|
454 | if (poly->child==NULL || poly->child->CompStatus!=dd_AllFound) assert(0); |
---|
455 | |
---|
456 | dd_MatrixPtr A2=dd_CopyGenerators(poly); |
---|
457 | |
---|
458 | dualInequalities=getConstraints(A2,false); |
---|
459 | dualEquations=getConstraints(A2,true); |
---|
460 | |
---|
461 | dd_FreeMatrix(A2); |
---|
462 | dd_FreeMatrix(A); |
---|
463 | dd_FreePolyhedra(poly); |
---|
464 | |
---|
465 | return; |
---|
466 | _L99: |
---|
467 | assert(0); |
---|
468 | } |
---|
469 | // this procedure is take from cddio.c. |
---|
470 | static void dd_ComputeAinc(dd_PolyhedraPtr poly) |
---|
471 | { |
---|
472 | /* This generates the input incidence array poly->Ainc, and |
---|
473 | two sets: poly->Ared, poly->Adom. |
---|
474 | */ |
---|
475 | dd_bigrange k; |
---|
476 | dd_rowrange i,m1; |
---|
477 | dd_colrange j; |
---|
478 | dd_boolean redundant; |
---|
479 | dd_MatrixPtr M=NULL; |
---|
480 | mytype sum,temp; |
---|
481 | |
---|
482 | dd_init(sum); dd_init(temp); |
---|
483 | if (poly->AincGenerated==dd_TRUE) goto _L99; |
---|
484 | |
---|
485 | M=dd_CopyOutput(poly); |
---|
486 | poly->n=M->rowsize; |
---|
487 | m1=poly->m1; |
---|
488 | |
---|
489 | /* this number is same as poly->m, except when |
---|
490 | poly is given by nonhomogeneous inequalty: |
---|
491 | !(poly->homogeneous) && poly->representation==Inequality, |
---|
492 | it is poly->m+1. See dd_ConeDataLoad. |
---|
493 | */ |
---|
494 | poly->Ainc=(set_type*)calloc(m1, sizeof(set_type)); |
---|
495 | for(i=1; i<=m1; i++) set_initialize(&(poly->Ainc[i-1]),poly->n); |
---|
496 | set_initialize(&(poly->Ared), m1); |
---|
497 | set_initialize(&(poly->Adom), m1); |
---|
498 | |
---|
499 | for (k=1; k<=poly->n; k++){ |
---|
500 | for (i=1; i<=poly->m; i++){ |
---|
501 | dd_set(sum,dd_purezero); |
---|
502 | for (j=1; j<=poly->d; j++){ |
---|
503 | dd_mul(temp,poly->A[i-1][j-1],M->matrix[k-1][j-1]); |
---|
504 | dd_add(sum,sum,temp); |
---|
505 | } |
---|
506 | if (dd_EqualToZero(sum)) { |
---|
507 | set_addelem(poly->Ainc[i-1], k); |
---|
508 | } |
---|
509 | } |
---|
510 | if (!(poly->homogeneous) && poly->representation==dd_Inequality){ |
---|
511 | if (dd_EqualToZero(M->matrix[k-1][0])) { |
---|
512 | set_addelem(poly->Ainc[m1-1], k); /* added infinity inequality (1,0,0,...,0) */ |
---|
513 | } |
---|
514 | } |
---|
515 | } |
---|
516 | |
---|
517 | for (i=1; i<=m1; i++){ |
---|
518 | if (set_card(poly->Ainc[i-1])==M->rowsize){ |
---|
519 | set_addelem(poly->Adom, i); |
---|
520 | } |
---|
521 | } |
---|
522 | for (i=m1; i>=1; i--){ |
---|
523 | if (set_card(poly->Ainc[i-1])==0){ |
---|
524 | redundant=dd_TRUE; |
---|
525 | set_addelem(poly->Ared, i); |
---|
526 | }else { |
---|
527 | redundant=dd_FALSE; |
---|
528 | for (k=1; k<=m1; k++) { |
---|
529 | if (k!=i && !set_member(k, poly->Ared) && !set_member(k, poly->Adom) && |
---|
530 | set_subset(poly->Ainc[i-1], poly->Ainc[k-1])){ |
---|
531 | if (!redundant){ |
---|
532 | redundant=dd_TRUE; |
---|
533 | } |
---|
534 | set_addelem(poly->Ared, i); |
---|
535 | } |
---|
536 | } |
---|
537 | } |
---|
538 | } |
---|
539 | dd_FreeMatrix(M); |
---|
540 | poly->AincGenerated=dd_TRUE; |
---|
541 | _L99:; |
---|
542 | dd_clear(sum); dd_clear(temp); |
---|
543 | } |
---|
544 | |
---|
545 | |
---|
546 | std::vector<std::vector<int> > extremeRaysInequalityIndices(const ZMatrix &inequalities) |
---|
547 | { |
---|
548 | int dim2=inequalities.getHeight(); |
---|
549 | if(dim2==0)return std::vector<std::vector<int> >(); |
---|
550 | int dimension=inequalities.getWidth(); |
---|
551 | |
---|
552 | dd_MatrixPtr A=NULL; |
---|
553 | dd_ErrorType err=dd_NoError; |
---|
554 | |
---|
555 | cddinitGmp(); |
---|
556 | A=ZMatrix2MatrixGmp(inequalities, &err); |
---|
557 | |
---|
558 | dd_PolyhedraPtr poly; |
---|
559 | poly=dd_DDMatrix2Poly2(A, dd_LexMin, &err); |
---|
560 | |
---|
561 | if (poly->child==NULL || poly->child->CompStatus!=dd_AllFound) assert(0); |
---|
562 | if (poly->AincGenerated==dd_FALSE) dd_ComputeAinc(poly); |
---|
563 | |
---|
564 | std::vector<std::vector<int> > ret; |
---|
565 | |
---|
566 | /* |
---|
567 | How do we interpret the cddlib output? For a long ting gfan has |
---|
568 | been using poly->n as the number of rays of the cone and thus |
---|
569 | returned sets of indices that actually gave the lineality |
---|
570 | space. The mistake was then caught later in PolyhedralCone. On Feb |
---|
571 | 17 2009 gfan was changed to check the length of each set to make |
---|
572 | sure that it does not specify the lineality space and only return |
---|
573 | those sets giving rise to rays. This does not seem to be the best |
---|
574 | strategy and might even be wrong. |
---|
575 | */ |
---|
576 | |
---|
577 | |
---|
578 | for (int k=1; k<=poly->n; k++) |
---|
579 | { |
---|
580 | int length=0; |
---|
581 | for (int i=1; i<=poly->m1; i++) |
---|
582 | if(set_member(k,poly->Ainc[i-1]))length++; |
---|
583 | if(length!=dim2) |
---|
584 | { |
---|
585 | std::vector<int> v(length); |
---|
586 | int j=0; |
---|
587 | for (int i=1; i<=poly->m1; i++) |
---|
588 | if(set_member(k,poly->Ainc[i-1]))v[j++]=i-1; |
---|
589 | ret.push_back(v); |
---|
590 | } |
---|
591 | } |
---|
592 | |
---|
593 | dd_FreeMatrix(A); |
---|
594 | dd_FreePolyhedra(poly); |
---|
595 | |
---|
596 | return ret; |
---|
597 | _L99: |
---|
598 | assert(0); |
---|
599 | return std::vector<std::vector<int> >(); |
---|
600 | } |
---|
601 | |
---|
602 | }; |
---|
603 | |
---|
604 | LpSolver lpSolver; |
---|
605 | |
---|
606 | bool ZCone::isInStateMinimum(int s)const |
---|
607 | { |
---|
608 | return state>=s; |
---|
609 | } |
---|
610 | |
---|
611 | |
---|
612 | bool operator<(ZCone const &a, ZCone const &b) |
---|
613 | { |
---|
614 | assert(a.state>=3); |
---|
615 | assert(b.state>=3); |
---|
616 | |
---|
617 | if(a.n<b.n)return true; |
---|
618 | if(a.n>b.n)return false; |
---|
619 | |
---|
620 | if(a.equations<b.equations)return true; |
---|
621 | if(b.equations<a.equations)return false; |
---|
622 | |
---|
623 | if(a.inequalities<b.inequalities)return true; |
---|
624 | if(b.inequalities<a.inequalities)return false; |
---|
625 | |
---|
626 | return false; |
---|
627 | } |
---|
628 | |
---|
629 | |
---|
630 | bool operator!=(ZCone const &a, ZCone const &b) |
---|
631 | { |
---|
632 | return (a<b)||(b<a); |
---|
633 | } |
---|
634 | |
---|
635 | |
---|
636 | void ZCone::ensureStateAsMinimum(int s)const |
---|
637 | { |
---|
638 | if((state<1) && (s==1)) |
---|
639 | { |
---|
640 | { |
---|
641 | QMatrix m=ZToQMatrix(equations); |
---|
642 | m.reduce(); |
---|
643 | m.removeZeroRows(); |
---|
644 | |
---|
645 | ZMatrix newInequalities(0,inequalities.getWidth()); |
---|
646 | for(int i=0;i<inequalities.getHeight();i++) |
---|
647 | { |
---|
648 | QVector w=ZToQVector(inequalities[i]); |
---|
649 | w=m.canonicalize(w); |
---|
650 | if(!w.isZero()) |
---|
651 | newInequalities.appendRow(QToZVectorPrimitive(w)); |
---|
652 | } |
---|
653 | |
---|
654 | inequalities=newInequalities; |
---|
655 | inequalities.sortAndRemoveDuplicateRows(); |
---|
656 | equations=QToZMatrixPrimitive(m); |
---|
657 | } |
---|
658 | |
---|
659 | if(!(preassumptions&PCP_impliedEquationsKnown)) |
---|
660 | if(inequalities.getHeight()>1)//there can be no implied equation unless we have at least two inequalities |
---|
661 | lpSolver.removeRedundantRows(inequalities,equations,false); |
---|
662 | |
---|
663 | assert(inequalities.getWidth()==equations.getWidth()); |
---|
664 | } |
---|
665 | if((state<2) && (s>=2) && !(preassumptions&PCP_facetsKnown)) |
---|
666 | { |
---|
667 | /* if(inequalities.size()>25) |
---|
668 | { |
---|
669 | IntegerVectorList h1; |
---|
670 | IntegerVectorList h2; |
---|
671 | bool a=false; |
---|
672 | for(IntegerVectorList::const_iterator i=inequalities.begin();i!=inequalities.end();i++) |
---|
673 | { |
---|
674 | if(a) |
---|
675 | h1.push_back(*i); |
---|
676 | else |
---|
677 | h2.push_back(*i); |
---|
678 | a=!a; |
---|
679 | } |
---|
680 | PolyhedralCone c1(h1,equations); |
---|
681 | PolyhedralCone c2(h2,equations); |
---|
682 | c1.ensureStateAsMinimum(2); |
---|
683 | c2.ensureStateAsMinimum(2); |
---|
684 | inequalities=c1.inequalities; |
---|
685 | for(IntegerVectorList::const_iterator i=c2.inequalities.begin();i!=c2.inequalities.end();i++) |
---|
686 | inequalities.push_back(*i); |
---|
687 | } |
---|
688 | */ |
---|
689 | if(equations.getHeight()) |
---|
690 | { |
---|
691 | QMatrix m=ZToQMatrix(equations); |
---|
692 | m.reduce(); |
---|
693 | m.REformToRREform(); |
---|
694 | ZMatrix inequalities2(0,equations.getWidth()); |
---|
695 | for(int i=0;i<inequalities.getHeight();i++) |
---|
696 | { |
---|
697 | inequalities2.appendRow(QToZVectorPrimitive(m.canonicalize(ZToQVector(inequalities[i])))); |
---|
698 | } |
---|
699 | inequalities=LpSolver::fastNormals(inequalities2); |
---|
700 | goto noFallBack; |
---|
701 | fallBack://alternativ (disabled) |
---|
702 | lpSolver.removeRedundantRows(inequalities,equations,true); |
---|
703 | noFallBack:; |
---|
704 | } |
---|
705 | else |
---|
706 | inequalities=LpSolver::fastNormals(inequalities); |
---|
707 | } |
---|
708 | if((state<3) && (s>=3)) |
---|
709 | { |
---|
710 | QMatrix equations2=ZToQMatrix(equations); |
---|
711 | equations2.reduce(false,false,true); |
---|
712 | equations2.REformToRREform(); |
---|
713 | for(int i=0;i<inequalities.getHeight();i++) |
---|
714 | { |
---|
715 | inequalities[i]=QToZVectorPrimitive(equations2.canonicalize(ZToQVector(inequalities[i]))); |
---|
716 | } |
---|
717 | inequalities.sortRows(); |
---|
718 | equations=QToZMatrixPrimitive(equations2); |
---|
719 | } |
---|
720 | if(state<s) |
---|
721 | state=s; |
---|
722 | } |
---|
723 | |
---|
724 | std::ostream &operator<<(std::ostream &f, ZCone const &c) |
---|
725 | { |
---|
726 | f<<"Ambient dimension:"<<c.n<<std::endl; |
---|
727 | f<<"Inequalities:"<<std::endl; |
---|
728 | f<<c.inequalities<<std::endl; |
---|
729 | f<<"Equations:"<<std::endl; |
---|
730 | f<<c.equations<<std::endl; |
---|
731 | } |
---|
732 | |
---|
733 | |
---|
734 | ZCone::ZCone(int ambientDimension): |
---|
735 | inequalities(ZMatrix(0,ambientDimension)), |
---|
736 | equations(ZMatrix(0,ambientDimension)), |
---|
737 | n(ambientDimension), |
---|
738 | state(1), |
---|
739 | preassumptions(PCP_impliedEquationsKnown|PCP_facetsKnown), |
---|
740 | multiplicity(1), |
---|
741 | haveExtremeRaysBeenCached(false), |
---|
742 | linearForms(ZMatrix(0,ambientDimension)) |
---|
743 | { |
---|
744 | } |
---|
745 | |
---|
746 | |
---|
747 | ZCone::ZCone(ZMatrix const &inequalities_, ZMatrix const &equations_, int preassumptions_): |
---|
748 | inequalities(inequalities_), |
---|
749 | equations(equations_), |
---|
750 | state(0), |
---|
751 | preassumptions(preassumptions_), |
---|
752 | multiplicity(1), |
---|
753 | haveExtremeRaysBeenCached(false), |
---|
754 | n(inequalities_.getWidth()), |
---|
755 | linearForms(ZMatrix(0,inequalities_.getWidth())) |
---|
756 | { |
---|
757 | assert(preassumptions_<4);//OTHERWISE WE ARE DOING SOMETHING STUPID LIKE SPECIFYING AMBIENT DIMENSION |
---|
758 | assert(equations_.getWidth()==n); |
---|
759 | ensureStateAsMinimum(1); |
---|
760 | } |
---|
761 | |
---|
762 | void ZCone::canonicalize() |
---|
763 | { |
---|
764 | ensureStateAsMinimum(3); |
---|
765 | } |
---|
766 | |
---|
767 | void ZCone::findFacets() |
---|
768 | { |
---|
769 | ensureStateAsMinimum(2); |
---|
770 | } |
---|
771 | |
---|
772 | ZMatrix ZCone::getFacets()const |
---|
773 | { |
---|
774 | ensureStateAsMinimum(2); |
---|
775 | return inequalities; |
---|
776 | } |
---|
777 | |
---|
778 | void ZCone::findImpliedEquations() |
---|
779 | { |
---|
780 | ensureStateAsMinimum(1); |
---|
781 | } |
---|
782 | |
---|
783 | ZMatrix ZCone::getImpliedEquations()const |
---|
784 | { |
---|
785 | ensureStateAsMinimum(1); |
---|
786 | return equations; |
---|
787 | } |
---|
788 | |
---|
789 | ZVector ZCone::getRelativeInteriorPoint()const |
---|
790 | { |
---|
791 | ensureStateAsMinimum(1); |
---|
792 | // assert(state>=1); |
---|
793 | |
---|
794 | return lpSolver.relativeInteriorPoint(inequalities,equations); |
---|
795 | } |
---|
796 | |
---|
797 | ZVector ZCone::getUniquePoint()const |
---|
798 | { |
---|
799 | ZMatrix rays=extremeRays(); |
---|
800 | ZVector ret(n); |
---|
801 | for(int i=0;i<rays.getHeight();i++) |
---|
802 | ret+=rays[i]; |
---|
803 | |
---|
804 | return ret; |
---|
805 | } |
---|
806 | |
---|
807 | ZVector ZCone::getUniquePointFromExtremeRays(ZMatrix const &extremeRays)const |
---|
808 | { |
---|
809 | ZVector ret(n); |
---|
810 | for(int i=0;i<extremeRays.getHeight();i++) |
---|
811 | if(contains(extremeRays[i]))ret+=extremeRays[i]; |
---|
812 | return ret; |
---|
813 | } |
---|
814 | |
---|
815 | |
---|
816 | int ZCone::ambientDimension()const |
---|
817 | { |
---|
818 | return n; |
---|
819 | } |
---|
820 | |
---|
821 | |
---|
822 | int ZCone::codimension()const |
---|
823 | { |
---|
824 | return ambientDimension()-dimension(); |
---|
825 | } |
---|
826 | |
---|
827 | |
---|
828 | int ZCone::dimension()const |
---|
829 | { |
---|
830 | // assert(state>=1); |
---|
831 | ensureStateAsMinimum(1); |
---|
832 | return ambientDimension()-equations.getHeight(); |
---|
833 | } |
---|
834 | |
---|
835 | |
---|
836 | int ZCone::dimensionOfLinealitySpace()const |
---|
837 | { |
---|
838 | ZMatrix temp=inequalities; |
---|
839 | temp.append(equations); |
---|
840 | ZCone temp2(ZMatrix(0,n),temp); |
---|
841 | return temp2.dimension(); |
---|
842 | } |
---|
843 | |
---|
844 | |
---|
845 | bool ZCone::isOrigin()const |
---|
846 | { |
---|
847 | return dimension()==0; |
---|
848 | } |
---|
849 | |
---|
850 | |
---|
851 | bool ZCone::isFullSpace()const |
---|
852 | { |
---|
853 | for(int i=0;i<inequalities.getHeight();i++) |
---|
854 | if(!inequalities[i].isZero())return false; |
---|
855 | for(int i=0;i<equations.getHeight();i++) |
---|
856 | if(!equations[i].isZero())return false; |
---|
857 | return true; |
---|
858 | } |
---|
859 | |
---|
860 | |
---|
861 | ZCone intersection(const ZCone &a, const ZCone &b) |
---|
862 | { |
---|
863 | assert(a.ambientDimension()==b.ambientDimension()); |
---|
864 | ZMatrix inequalities=a.inequalities; |
---|
865 | inequalities.append(b.inequalities); |
---|
866 | ZMatrix equations=a.equations; |
---|
867 | equations.append(b.equations); |
---|
868 | |
---|
869 | equations.sortAndRemoveDuplicateRows(); |
---|
870 | inequalities.sortAndRemoveDuplicateRows(); |
---|
871 | |
---|
872 | { |
---|
873 | ZMatrix Aequations=a.equations; |
---|
874 | ZMatrix Ainequalities=a.inequalities; |
---|
875 | Aequations.sortAndRemoveDuplicateRows(); |
---|
876 | Ainequalities.sortAndRemoveDuplicateRows(); |
---|
877 | if((Ainequalities.getHeight()==inequalities.getHeight()) && (Aequations.getHeight()==equations.getHeight()))return a; |
---|
878 | ZMatrix Bequations=b.equations; |
---|
879 | ZMatrix Binequalities=b.inequalities; |
---|
880 | Bequations.sortAndRemoveDuplicateRows(); |
---|
881 | Binequalities.sortAndRemoveDuplicateRows(); |
---|
882 | if((Binequalities.getHeight()==inequalities.getHeight()) && (Bequations.getHeight()==equations.getHeight()))return b; |
---|
883 | } |
---|
884 | |
---|
885 | return ZCone(inequalities,equations); |
---|
886 | } |
---|
887 | |
---|
888 | /* |
---|
889 | PolyhedralCone product(const PolyhedralCone &a, const PolyhedralCone &b) |
---|
890 | { |
---|
891 | IntegerVectorList equations2; |
---|
892 | IntegerVectorList inequalities2; |
---|
893 | |
---|
894 | int n1=a.n; |
---|
895 | int n2=b.n; |
---|
896 | |
---|
897 | for(IntegerVectorList::const_iterator i=a.equations.begin();i!=a.equations.end();i++) |
---|
898 | equations2.push_back(concatenation(*i,IntegerVector(n2))); |
---|
899 | for(IntegerVectorList::const_iterator i=b.equations.begin();i!=b.equations.end();i++) |
---|
900 | equations2.push_back(concatenation(IntegerVector(n1),*i)); |
---|
901 | for(IntegerVectorList::const_iterator i=a.inequalities.begin();i!=a.inequalities.end();i++) |
---|
902 | inequalities2.push_back(concatenation(*i,IntegerVector(n2))); |
---|
903 | for(IntegerVectorList::const_iterator i=b.inequalities.begin();i!=b.inequalities.end();i++) |
---|
904 | inequalities2.push_back(concatenation(IntegerVector(n1),*i)); |
---|
905 | |
---|
906 | PolyhedralCone ret(inequalities2,equations2,n1+n2); |
---|
907 | ret.setMultiplicity(a.getMultiplicity()*b.getMultiplicity()); |
---|
908 | ret.setLinearForm(concatenation(a.getLinearForm(),b.getLinearForm())); |
---|
909 | |
---|
910 | ret.ensureStateAsMinimum(a.state); |
---|
911 | ret.ensureStateAsMinimum(b.state); |
---|
912 | |
---|
913 | return ret; |
---|
914 | }*/ |
---|
915 | |
---|
916 | |
---|
917 | ZCone ZCone::positiveOrthant(int dimension) |
---|
918 | { |
---|
919 | return ZCone(ZMatrix::identity(dimension),ZMatrix(0,dimension)); |
---|
920 | } |
---|
921 | |
---|
922 | |
---|
923 | ZCone ZCone::givenByRays(ZMatrix const &generators, ZMatrix const &linealitySpace) |
---|
924 | { |
---|
925 | ZCone dual(generators,linealitySpace); |
---|
926 | ZMatrix inequalities=dual.extremeRays(); |
---|
927 | ZMatrix equations=dual.generatorsOfLinealitySpace(); |
---|
928 | |
---|
929 | return ZCone(inequalities,equations,3); |
---|
930 | } |
---|
931 | |
---|
932 | |
---|
933 | bool ZCone::containsPositiveVector()const |
---|
934 | { |
---|
935 | ZCone temp=intersection(*this,ZCone::positiveOrthant(n)); |
---|
936 | return temp.getRelativeInteriorPoint().isPositive(); |
---|
937 | } |
---|
938 | |
---|
939 | |
---|
940 | bool ZCone::contains(ZVector const &v)const |
---|
941 | { |
---|
942 | for(int i=0;i<equations.getHeight();i++) |
---|
943 | { |
---|
944 | if(!dot(equations[i],v).isZero())return false; |
---|
945 | } |
---|
946 | for(int i=0;i<inequalities.getHeight();i++) |
---|
947 | { |
---|
948 | if(dot(inequalities[i],v).sign()<0)return false; |
---|
949 | } |
---|
950 | return true; |
---|
951 | } |
---|
952 | |
---|
953 | |
---|
954 | bool ZCone::containsRowsOf(ZMatrix const &m)const |
---|
955 | { |
---|
956 | for(int i=0;i<m.getHeight();i++) |
---|
957 | if(!contains(m[i]))return false; |
---|
958 | return true; |
---|
959 | } |
---|
960 | |
---|
961 | |
---|
962 | bool ZCone::contains(ZCone const &c)const |
---|
963 | { |
---|
964 | ZCone c2=intersection(*this,c); |
---|
965 | ZCone c3=c; |
---|
966 | c2.canonicalize(); |
---|
967 | c3.canonicalize(); |
---|
968 | return !(c2!=c3); |
---|
969 | } |
---|
970 | |
---|
971 | |
---|
972 | bool ZCone::containsRelatively(ZVector const &v)const |
---|
973 | { |
---|
974 | ensureStateAsMinimum(1); |
---|
975 | // assert(state>=1); |
---|
976 | for(int i=0;i<equations.getHeight();i++) |
---|
977 | { |
---|
978 | if(!dot(equations[i],v).isZero())return false; |
---|
979 | } |
---|
980 | for(int i=0;i<inequalities.getHeight();i++) |
---|
981 | { |
---|
982 | if(dot(inequalities[i],v).sign()<=0)return false; |
---|
983 | } |
---|
984 | return true; |
---|
985 | } |
---|
986 | |
---|
987 | |
---|
988 | bool ZCone::isSimplicial()const |
---|
989 | { |
---|
990 | // assert(state>=2); |
---|
991 | ensureStateAsMinimum(2); |
---|
992 | return codimension()+inequalities.getHeight()+dimensionOfLinealitySpace()==n; |
---|
993 | } |
---|
994 | |
---|
995 | |
---|
996 | ZCone ZCone::linealitySpace()const |
---|
997 | { |
---|
998 | ZCone ret(ZMatrix(0,n),combineOnTop(equations,inequalities)); |
---|
999 | // ret.ensureStateAsMinimum(state); |
---|
1000 | return ret; |
---|
1001 | } |
---|
1002 | |
---|
1003 | |
---|
1004 | ZCone ZCone::dualCone()const |
---|
1005 | { |
---|
1006 | ensureStateAsMinimum(1); |
---|
1007 | // assert(state>=1); |
---|
1008 | |
---|
1009 | ZMatrix dualInequalities,dualEquations; |
---|
1010 | lpSolver.dual(inequalities,equations,dualInequalities,dualEquations); |
---|
1011 | ZCone ret(dualInequalities,dualEquations); |
---|
1012 | ret.ensureStateAsMinimum(state); |
---|
1013 | |
---|
1014 | return ret; |
---|
1015 | } |
---|
1016 | |
---|
1017 | |
---|
1018 | ZCone ZCone::negated()const |
---|
1019 | { |
---|
1020 | ZCone ret(-inequalities,equations,(areFacetsKnown()?PCP_facetsKnown:0)|(areImpliedEquationsKnown()?PCP_impliedEquationsKnown:0)); |
---|
1021 | // ret.ensureStateAsMinimum(state); |
---|
1022 | return ret; |
---|
1023 | } |
---|
1024 | |
---|
1025 | |
---|
1026 | ZMatrix ZCone::extremeRays(ZMatrix const *generatorsOfLinealitySpace)const |
---|
1027 | { |
---|
1028 | // assert((dimension()==ambientDimension()) || (state>=3)); |
---|
1029 | if(dimension()!=ambientDimension()) |
---|
1030 | ensureStateAsMinimum(3); |
---|
1031 | |
---|
1032 | if(haveExtremeRaysBeenCached)return cachedExtremeRays; |
---|
1033 | ZMatrix ret(0,n); |
---|
1034 | std::vector<std::vector<int> > indices=lpSolver.extremeRaysInequalityIndices(inequalities); |
---|
1035 | |
---|
1036 | for(int i=0;i<indices.size();i++) |
---|
1037 | { |
---|
1038 | /* At this point we know lineality space, implied equations and |
---|
1039 | also inequalities for the ray. To construct a vector on the |
---|
1040 | ray which is stable under (or indendent of) angle and |
---|
1041 | linarity preserving transformation we find the dimension 1 |
---|
1042 | subspace orthorgonal to the implied equations and the |
---|
1043 | lineality space and pick a suitable primitive generator */ |
---|
1044 | |
---|
1045 | /* To be more precise, |
---|
1046 | * let E be the set of equations, and v the inequality defining a ray R. |
---|
1047 | * We wish to find a vector satisfying these, but it must also be orthogonal |
---|
1048 | * to the lineality space of the cone, that is, in the span of {E,v}. |
---|
1049 | * One way to get such a vector is to project v to E an get a vector p. |
---|
1050 | * Then v-p is in the span of {E,v} by construction. |
---|
1051 | * The vector v-p is also in the orthogonal complement to E by construction, |
---|
1052 | * that is, the span of R. |
---|
1053 | * We wish to argue that it is not zero. |
---|
1054 | * That would imply that v=p, meaning that v is in the span of the equations. |
---|
1055 | * However, that would contradict that R is a ray. |
---|
1056 | * In case v-p does not satisfy the inequality v (is this possible?), we change the sign. |
---|
1057 | * |
---|
1058 | * As a consequence we need the following procedure |
---|
1059 | * primitiveProjection(): |
---|
1060 | * Input: E,v |
---|
1061 | * Output: A primitive representation of the vector v-p, where p is the projection of v onto E |
---|
1062 | * |
---|
1063 | * Notice that the output is a Q linear combination of the input and that p is |
---|
1064 | * a linear combination of E. The check that p has been computed correctly, |
---|
1065 | * it suffices to check that v-p satisfies the equations E. |
---|
1066 | * The routine will actually first compute a multiple of v-p. |
---|
1067 | * It will do this using floating point arithmetics. It will then transform |
---|
1068 | * the coefficients to get the multiple of v-p into integers. Then it |
---|
1069 | * verifies in exact arithmetics, that with these coefficients we get a point |
---|
1070 | * satisfying E. It then returns the primitive vector on the ray v-p. |
---|
1071 | * In case of a failure it falls back to an implementation using rational arithmetics. |
---|
1072 | */ |
---|
1073 | |
---|
1074 | |
---|
1075 | std::vector<int> asVector(inequalities.getHeight()); |
---|
1076 | for(int j=0;j<indices[i].size();j++){asVector[indices[i][j]]=1;} |
---|
1077 | ZMatrix equations=this->equations; |
---|
1078 | ZVector theInequality; |
---|
1079 | |
---|
1080 | for(int j=0;j<asVector.size();j++) |
---|
1081 | if(asVector[j]) |
---|
1082 | equations.appendRow(inequalities[j]); |
---|
1083 | else |
---|
1084 | theInequality=inequalities[j]; |
---|
1085 | |
---|
1086 | assert(!theInequality.isZero()); |
---|
1087 | |
---|
1088 | ZVector thePrimitiveVector; |
---|
1089 | if(generatorsOfLinealitySpace) |
---|
1090 | { |
---|
1091 | QMatrix temp=ZToQMatrix(combineOnTop(equations,*generatorsOfLinealitySpace)); |
---|
1092 | thePrimitiveVector=QToZVectorPrimitive(temp.reduceAndComputeVectorInKernel()); |
---|
1093 | } |
---|
1094 | else |
---|
1095 | { |
---|
1096 | QMatrix linealitySpaceOrth=ZToQMatrix(combineOnTop(this->equations,inequalities)); |
---|
1097 | |
---|
1098 | |
---|
1099 | QMatrix temp=combineOnTop(linealitySpaceOrth.reduceAndComputeKernel(),ZToQMatrix(equations)); |
---|
1100 | thePrimitiveVector=QToZVectorPrimitive(temp.reduceAndComputeVectorInKernel()); |
---|
1101 | } |
---|
1102 | if(!contains(thePrimitiveVector))thePrimitiveVector=-thePrimitiveVector; |
---|
1103 | ret.appendRow(thePrimitiveVector); |
---|
1104 | } |
---|
1105 | |
---|
1106 | cachedExtremeRays=ret; |
---|
1107 | haveExtremeRaysBeenCached=true; |
---|
1108 | |
---|
1109 | return ret; |
---|
1110 | } |
---|
1111 | |
---|
1112 | |
---|
1113 | Integer ZCone::getMultiplicity()const |
---|
1114 | { |
---|
1115 | return multiplicity; |
---|
1116 | } |
---|
1117 | |
---|
1118 | |
---|
1119 | void ZCone::setMultiplicity(Integer const &m) |
---|
1120 | { |
---|
1121 | multiplicity=m; |
---|
1122 | } |
---|
1123 | |
---|
1124 | |
---|
1125 | ZMatrix ZCone::getLinearForms()const |
---|
1126 | { |
---|
1127 | return linearForms; |
---|
1128 | } |
---|
1129 | |
---|
1130 | |
---|
1131 | void ZCone::setLinearForms(ZMatrix const &linearForms_) |
---|
1132 | { |
---|
1133 | linearForms=linearForms_; |
---|
1134 | } |
---|
1135 | |
---|
1136 | |
---|
1137 | ZMatrix ZCone::quotientLatticeBasis()const |
---|
1138 | { |
---|
1139 | // assert(isInStateMinimum(1));// Implied equations must have been computed in order to know the span of the cone |
---|
1140 | ensureStateAsMinimum(1); |
---|
1141 | |
---|
1142 | |
---|
1143 | int a=equations.getHeight(); |
---|
1144 | int b=inequalities.getHeight(); |
---|
1145 | |
---|
1146 | // Implementation below could be moved to nonLP part of code. |
---|
1147 | |
---|
1148 | // small vector space defined by a+b equations.... big by a equations. |
---|
1149 | |
---|
1150 | ZMatrix M=combineLeftRight(combineLeftRight( |
---|
1151 | equations.transposed(), |
---|
1152 | inequalities.transposed()), |
---|
1153 | ZMatrix::identity(n)); |
---|
1154 | M.reduce(false,true); |
---|
1155 | /* |
---|
1156 | [A|B|I] is reduced to [A'|B'|C'] meaning [A'|B']=C'[A|B] and A'=C'A. |
---|
1157 | |
---|
1158 | [A'|B'] is in row echelon form, implying that the rows of C' corresponding to zero rows |
---|
1159 | of [A'|B'] generate the lattice cokernel of [A|B] - that is the linealityspace intersected with Z^n. |
---|
1160 | |
---|
1161 | [A'] is in row echelon form, implying that the rows of C' corresponding to zero rows of [A'] generate |
---|
1162 | the lattice cokernel of [A] - that is the span of the cone intersected with Z^n. |
---|
1163 | |
---|
1164 | It is clear that the second row set is a superset of the first. Their difference is a basis for the quotient. |
---|
1165 | */ |
---|
1166 | ZMatrix ret(0,n); |
---|
1167 | |
---|
1168 | for(int i=0;i<M.getHeight();i++) |
---|
1169 | if(M[i].subvector(0,a).isZero()&&!M[i].subvector(a,a+b).isZero()) |
---|
1170 | { |
---|
1171 | ret.appendRow(M[i].subvector(a+b,a+b+n)); |
---|
1172 | } |
---|
1173 | |
---|
1174 | return ret; |
---|
1175 | } |
---|
1176 | |
---|
1177 | |
---|
1178 | ZVector ZCone::semiGroupGeneratorOfRay()const |
---|
1179 | { |
---|
1180 | ZMatrix temp=quotientLatticeBasis(); |
---|
1181 | assert(temp.getHeight()==1); |
---|
1182 | for(int i=0;i<inequalities.getHeight();i++) |
---|
1183 | if(dot(temp[0],inequalities[i]).sign()<0) |
---|
1184 | { |
---|
1185 | temp[0]=-temp[0]; |
---|
1186 | break; |
---|
1187 | } |
---|
1188 | return temp[0]; |
---|
1189 | } |
---|
1190 | |
---|
1191 | |
---|
1192 | ZCone ZCone::link(ZVector const &w)const |
---|
1193 | { |
---|
1194 | /* Observe that the inequalities giving rise to facets |
---|
1195 | * also give facets in the link, if they are kept as |
---|
1196 | * inequalities. This means that the state cannot decrease |
---|
1197 | * when taking links - that is why we specify the PCP flags. |
---|
1198 | */ |
---|
1199 | ZMatrix inequalities2(0,n); |
---|
1200 | for(int j=0;j<inequalities.getHeight();j++) |
---|
1201 | if(dot(w,inequalities[j]).sign()==0)inequalities2.appendRow(inequalities[j]); |
---|
1202 | ZCone C(inequalities2,equations,(areImpliedEquationsKnown()?PCP_impliedEquationsKnown:0)|(areFacetsKnown()?PCP_facetsKnown:0)); |
---|
1203 | C.ensureStateAsMinimum(state); |
---|
1204 | |
---|
1205 | C.setLinearForms(getLinearForms()); |
---|
1206 | C.setMultiplicity(getMultiplicity()); |
---|
1207 | |
---|
1208 | return C; |
---|
1209 | } |
---|
1210 | |
---|
1211 | bool ZCone::hasFace(ZCone const &f)const |
---|
1212 | { |
---|
1213 | if(!contains(f.getRelativeInteriorPoint()))return false; |
---|
1214 | ZCone temp1=faceContaining(f.getRelativeInteriorPoint()); |
---|
1215 | temp1.canonicalize(); |
---|
1216 | ZCone temp2=f; |
---|
1217 | temp2.canonicalize(); |
---|
1218 | |
---|
1219 | return !(temp2!=temp1); |
---|
1220 | } |
---|
1221 | |
---|
1222 | ZCone ZCone::faceContaining(ZVector const &v)const |
---|
1223 | { |
---|
1224 | assert(n==v.size()); |
---|
1225 | assert(contains(v)); |
---|
1226 | ZMatrix newEquations=equations; |
---|
1227 | ZMatrix newInequalities(0,n); |
---|
1228 | for(int i=0;i<inequalities.getHeight();i++) |
---|
1229 | if(dot(inequalities[i],v).sign()!=0) |
---|
1230 | newInequalities.appendRow(inequalities[i]); |
---|
1231 | else |
---|
1232 | newEquations.appendRow(inequalities[i]); |
---|
1233 | |
---|
1234 | ZCone ret(newInequalities,newEquations,(state>=1)?PCP_impliedEquationsKnown:0); |
---|
1235 | ret.ensureStateAsMinimum(state); |
---|
1236 | return ret; |
---|
1237 | } |
---|
1238 | |
---|
1239 | |
---|
1240 | ZMatrix ZCone::getInequalities()const |
---|
1241 | { |
---|
1242 | return inequalities; |
---|
1243 | } |
---|
1244 | |
---|
1245 | |
---|
1246 | ZMatrix ZCone::getEquations()const |
---|
1247 | { |
---|
1248 | return equations; |
---|
1249 | } |
---|
1250 | |
---|
1251 | |
---|
1252 | ZMatrix ZCone::generatorsOfSpan()const |
---|
1253 | { |
---|
1254 | ensureStateAsMinimum(1); |
---|
1255 | QMatrix l=ZToQMatrix(equations); |
---|
1256 | return QToZMatrixPrimitive(l.reduceAndComputeKernel()); |
---|
1257 | } |
---|
1258 | |
---|
1259 | |
---|
1260 | ZMatrix ZCone::generatorsOfLinealitySpace()const |
---|
1261 | { |
---|
1262 | QMatrix l=ZToQMatrix(combineOnTop(inequalities,equations)); |
---|
1263 | return QToZMatrixPrimitive(l.reduceAndComputeKernel()); |
---|
1264 | } |
---|
1265 | |
---|
1266 | }; |
---|