DGtal 1.4.0
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DECCommon.h
1#if !defined(__DEC_TESTS_COMMON_H__)
2#define __DEC_TESTS_COMMON_H__
3
4#include <list>
5
6#include "DGtal/dec/DiscreteExteriorCalculusFactory.h"
7#include "DGtal/base/Common.h"
8#include "DGtal/helpers/StdDefs.h"
9#include "DGtal/math/linalg/EigenSupport.h"
10#include "DGtal/dec/DiscreteExteriorCalculus.h"
11#include "DGtal/dec/DiscreteExteriorCalculusSolver.h"
12#include "DGtal/dec/CDiscreteExteriorCalculusVectorSpace.h"
13#include "DGtal/kernel/sets/DigitalSetBySTLSet.h"
14
15template <typename Container>
16bool
17is_all_zero(const Container& container)
18{
19 for (typename Container::Index ii=0; ii<container.rows(); ii++)
20 for (typename Container::Index jj=0; jj<container.cols(); jj++)
21 if (container.coeff(ii,jj) != 0)
22 return false;
23 return true;
24}
25
26template <typename Container>
27bool
28equal(const Container& aa, const Container& bb)
29{
30 if (aa.rows() != bb.rows()) return false;
31 if (aa.cols() != bb.cols()) return false;
32 for (typename Container::Index ii=0; ii<aa.rows(); ii++)
33 for (typename Container::Index jj=0; jj<aa.cols(); jj++)
34 if (aa.coeff(ii,jj) != bb.coeff(ii,jj))
35 return false;
36 return true;
37}
38
39template <typename Container, typename Value>
40bool
41is_identity(const Container& container, const Value& value)
42{
43 for (typename Container::Index ii=0; ii<container.rows(); ii++)
44 for (typename Container::Index jj=0; jj<container.cols(); jj++)
45 {
46 const Value foo = static_cast<Value>(container.coeff(ii,jj));
47 if ((ii != jj && foo != 0) || (ii == jj && foo != value))
48 return false;
49 }
50 return true;
51}
52
53//DC: changing order to int (to match with -1 specialization)
54template <typename Calculus, int order>
55struct HodgeTester
56{
57 BOOST_STATIC_ASSERT(( order <= Calculus::dimensionEmbedded ));
58
59 static bool test(const Calculus& calculus)
60 {
61 DGtal::trace.info() << "testing identity operators " << order << std::endl;
62
63 { // test identity operator
64 typedef DGtal::LinearOperator<Calculus, order, DGtal::PRIMAL, order, DGtal::PRIMAL> PrimalIdentity;
65 PrimalIdentity primal_identity = calculus.template identity<order, DGtal::PRIMAL>();
66 if (!is_identity(primal_identity.myContainer, 1)) return false;
67
68 typedef DGtal::KForm<Calculus, order, DGtal::PRIMAL> SolveForm;
69 SolveForm input(calculus);
70 SolveForm output = primal_identity * input;
71 typedef typename Calculus::LinearAlgebraBackend LinearAlgebraBackend;
72 typedef typename LinearAlgebraBackend::SolverConjugateGradient LinearSolver;
73 typedef DGtal::DiscreteExteriorCalculusSolver<Calculus, LinearSolver, order, DGtal::PRIMAL, order, DGtal::PRIMAL> Solver;
74 Solver solver;
75 SolveForm input_solved = solver.compute(primal_identity).solve(output);
76 //if (input_solved != input) return false;
77
78 typedef DGtal::LinearOperator<Calculus, order, DGtal::DUAL, order, DGtal::DUAL> DualIdentity;
79 DualIdentity dual_identity = calculus.template identity<order, DGtal::DUAL>();
80 if (!is_identity(dual_identity.myContainer, 1)) return false;
81 }
82
83 typedef DGtal::LinearOperator<Calculus, order, DGtal::PRIMAL, Calculus::dimensionEmbedded-order, DGtal::DUAL> PrimalHodge;
84 typedef DGtal::LinearOperator<Calculus, Calculus::dimensionEmbedded-order, DGtal::DUAL, order, DGtal::PRIMAL> DualHodge;
85 const PrimalHodge primal_hodge = calculus.template hodge<order, DGtal::PRIMAL>();
86 const DualHodge dual_hodge= calculus.template hodge<Calculus::dimensionEmbedded-order, DGtal::DUAL>();
87
88 DGtal::trace.info() << "testing primal to primal hodge composition order " << order << std::endl;
89
90 { // test primal to primal composition
91 typedef DGtal::LinearOperator<Calculus, order, DGtal::PRIMAL, order, DGtal::PRIMAL> PrimalPrimal;
92 PrimalPrimal primal_primal = dual_hodge * primal_hodge;
93 if (!is_identity(primal_primal.myContainer, pow(-1, order*(Calculus::dimensionEmbedded-order)))) return false;
94 }
95
96 DGtal::trace.info() << "testing dual to dual hodge composition order " << order << std::endl;
97
98 { // test dual to dual composition
99 typedef DGtal::LinearOperator<Calculus, Calculus::dimensionEmbedded-order, DGtal::DUAL, Calculus::dimensionEmbedded-order, DGtal::DUAL> DualDual;
100 DualDual dual_dual = primal_hodge * dual_hodge;
101 if (!is_identity(dual_dual.myContainer, pow(-1, order*(Calculus::dimensionEmbedded-order)))) return false;
102 }
103
104 return HodgeTester<Calculus, order-1>::test(calculus);
105 }
106};
107
108template <typename Calculus>
109struct HodgeTester<Calculus, -1>
110{
111 static bool test(const Calculus& calculus)
112 {
113 boost::ignore_unused_variable_warning( calculus );
114 return true;
115 }
116};
117
118template <typename DigitalSet, typename LinearAlgebraBackend>
119void
120test_hodge(int domain_size)
121{
122 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDigitalSet<DigitalSet> ));
123
124 typedef typename DigitalSet::Domain Domain;
125 typedef typename DigitalSet::Point Point;
126 DGtal::trace.info() << "dimension=" << Point::dimension << std::endl;
127 Domain domain(Point(), Point::diagonal(domain_size-1));
128 DGtal::trace.info() << "domain=" << domain << std::endl;
129
130 DigitalSet set(domain);
131 for (typename Domain::ConstIterator di=domain.begin(), die=domain.end(); di!=die; di++)
132 {
133 if (std::rand()%4!=0) continue;
134 const typename Domain::Point& point = *di;
135 set.insertNew(point);
136 }
137 DGtal::trace.info() << "domain.size()=" << domain.size() << std::endl;
138 DGtal::trace.info() << "set.size()=" << set.size() << std::endl;
139
140 typedef DGtal::DiscreteExteriorCalculus<Domain::Space::dimension, Domain::Space::dimension, LinearAlgebraBackend> Calculus;
141 Calculus calculus = DGtal::DiscreteExteriorCalculusFactory<LinearAlgebraBackend>::createFromDigitalSet(set);
142 {
143 DGtal::trace.beginBlock("testing indexes");
144
145 {
146 typename Calculus::Properties properties = calculus.getProperties();
147 DGtal::trace.info() << "properties.size()=" << properties.size() << std::endl;
148 }
149
150 typedef typename Calculus::ConstIterator ConstIterator;
151 typedef typename Calculus::Cell Cell;
152 typedef typename Calculus::SCell SCell;
153 typedef typename Calculus::Index Index;
154 typedef typename Calculus::KSpace KSpace;
155
156 bool test_result = true;
157 for (ConstIterator iter = calculus.begin(), iter_end = calculus.end(); test_result && iter!=iter_end; iter++)
158 {
159 const Cell& cell = iter->first;
160 const Index& index = calculus.getCellIndex(cell);
161 test_result &= (iter->second.index == index);
162 const SCell& signed_cell = calculus.myKSpace.signs(cell, iter->second.flipped ? KSpace::NEG : KSpace::POS);
163 const SCell& primal_signed_cell = calculus.getSCell(calculus.myKSpace.uDim(cell), DGtal::PRIMAL, index);
164 test_result &= (signed_cell == primal_signed_cell);
165 const SCell& dual_signed_cell = calculus.getSCell(Calculus::dimensionEmbedded-calculus.myKSpace.uDim(cell), DGtal::DUAL, index);
166 test_result &= (signed_cell == dual_signed_cell);
167 }
168 DGtal::trace.endBlock();
169
170 FATAL_ERROR(test_result);
171 }
172
173 {
174 DGtal::trace.beginBlock("testing laplace sign");
175
176 const typename Calculus::PrimalIdentity0 primal_laplace = calculus.template laplace<DGtal::PRIMAL>();
177 DGtal::trace.info() << "primal_laplace_trace=" << primal_laplace.myContainer.diagonal().sum() << std::endl;
178 FATAL_ERROR( ( primal_laplace.myContainer.diagonal().array() >= 0 ).prod() == true );
179
180 const typename Calculus::DualIdentity0 dual_laplace = calculus.template laplace<DGtal::DUAL>();
181 DGtal::trace.info() << "dual_laplace_trace=" << dual_laplace.myContainer.diagonal().sum() << std::endl;
182 FATAL_ERROR( ( dual_laplace.myContainer.diagonal().array() >= 0 ).prod() == true );
183
184 DGtal::trace.endBlock();
185 }
186
187 DGtal::trace.beginBlock("testing hodge");
188 bool test_result = HodgeTester<Calculus, Calculus::dimensionEmbedded>::test(calculus);
189 DGtal::trace.endBlock();
190
191 FATAL_ERROR(test_result);
192}
193
194//DC Order->int (see above)
195template <typename Calculus, int order>
196struct DerivativeTester
197{
198 BOOST_STATIC_ASSERT(( order < (int)Calculus::dimensionEmbedded - 1 ));
199
200 static bool test(const Calculus& calculus)
201 {
202 DGtal::trace.info() << "testing primal derivative composition order " << order << std::endl;
203
204 { // test primal composition
205 typedef DGtal::LinearOperator<Calculus, order, DGtal::PRIMAL, order+1, DGtal::PRIMAL> FirstDerivative;
206 FirstDerivative first_derivative = calculus.template derivative<order, DGtal::PRIMAL>();
207 typedef DGtal::LinearOperator<Calculus, order+1, DGtal::PRIMAL, order+2, DGtal::PRIMAL> SecondDerivative;
208 SecondDerivative second_derivative = calculus.template derivative<order+1, DGtal::PRIMAL>();
209 typedef DGtal::LinearOperator<Calculus, order, DGtal::PRIMAL, order+2, DGtal::PRIMAL> DoubleDerivative;
210 DoubleDerivative double_derivative = second_derivative * first_derivative;
211 if (!is_all_zero(double_derivative.myContainer)) return false;
212 }
213
214 DGtal::trace.info() << "testing dual derivative composition order " << order << std::endl;
215
216 { // test dual composition
217 typedef DGtal::LinearOperator<Calculus, order, DGtal::DUAL, order+1, DGtal::DUAL> FirstDerivative;
218 FirstDerivative first_derivative = calculus.template derivative<order, DGtal::DUAL>();
219 typedef DGtal::LinearOperator<Calculus, order+1, DGtal::DUAL, order+2, DGtal::DUAL> SecondDerivative;
220 SecondDerivative second_derivative = calculus.template derivative<order+1, DGtal::DUAL>();
221 typedef DGtal::LinearOperator<Calculus, order, DGtal::DUAL, order+2, DGtal::DUAL> DoubleDerivative;
222 DoubleDerivative double_derivative = second_derivative * first_derivative;
223 if (!is_all_zero(double_derivative.myContainer)) return false;
224 }
225
226 /*
227 DGtal::trace.info() << "testing liebnitz rule order " << order << std::endl;
228
229 {
230 typedef DGtal::LinearOperator<Calculus, order, DGtal::PRIMAL, order+1, DGtal::PRIMAL> Derivative;
231 Derivative derivative = calculus.template derivative<order, DGtal::PRIMAL>();
232
233 typedef DGtal::KForm<Calculus, order, DGtal::PRIMAL> InputForm;
234 typedef DGtal::KForm<Calculus, order+1, DGtal::PRIMAL> OutputForm;
235 InputForm alpha(calculus), beta(calculus), gamma(calculus);
236
237 for (int kk=0; kk<calculus.kFormLength(order, DGtal::PRIMAL); kk++)
238 {
239 const double ak = static_cast<double>(random())/RAND_MAX;
240 const double bk = static_cast<double>(random())/RAND_MAX;
241 alpha.myContainer(kk) = ak;
242 beta.myContainer(kk) = bk;
243 gamma.myContainer(kk) = ak*bk;
244 }
245
246 }
247 */
248
249 return DerivativeTester<Calculus, order-1>::test(calculus);
250 }
251};
252
253template <typename Calculus>
254struct DerivativeTester<Calculus, -1>
255{
256 static bool test(const Calculus& )
257 {
258 return true;
259 }
260};
261
262template <typename DigitalSet, typename LinearAlgebraBackend>
263void
264test_derivative(int domain_size)
265{
266 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDigitalSet<DigitalSet> ));
267
268 typedef typename DigitalSet::Domain Domain;
269 typedef typename DigitalSet::Point Point;
270 DGtal::trace.info() << "dimension=" << Point::dimension << std::endl;
271 Domain domain(Point(), Point::diagonal(domain_size-1));
272 DGtal::trace.info() << "domain=" << domain << std::endl;
273
274 DigitalSet set(domain);
275 for (typename Domain::ConstIterator di=domain.begin(), die=domain.end(); di!=die; di++)
276 {
277 if (std::rand()%3!=0) continue;
278 const typename Domain::Point& point = *di;
279 set.insertNew(point);
280 }
281 DGtal::trace.info() << "domain.size()=" << domain.size() << std::endl;
282 DGtal::trace.info() << "set.size()=" << set.size() << std::endl;
283
284 typedef DGtal::DiscreteExteriorCalculusFactory<LinearAlgebraBackend> CalculusFactory;
285 typedef DGtal::DiscreteExteriorCalculus<Domain::Space::dimension, Domain::Space::dimension, LinearAlgebraBackend> Calculus;
286
287 {
288 DGtal::trace.beginBlock("testing derivative without border");
289 Calculus calculus = CalculusFactory::createFromDigitalSet(set, false);
290
291 typename Calculus::Properties properties = calculus.getProperties();
292 DGtal::trace.info() << "properties.size()=" << properties.size() << std::endl;
293
294 bool test_result = DerivativeTester<Calculus, (int)Calculus::dimensionEmbedded-2>::test(calculus);
295 FATAL_ERROR(test_result);
296
297 DGtal::trace.endBlock();
298 }
299
300 {
301 DGtal::trace.beginBlock("testing derivative with border");
302 Calculus calculus = CalculusFactory::createFromDigitalSet(set, true);
303
304 typename Calculus::Properties properties = calculus.getProperties();
305 DGtal::trace.info() << "properties.size()=" << properties.size() << std::endl;
306
307 bool test_result = DerivativeTester<Calculus, (int)Calculus::dimensionEmbedded-2>::test(calculus);
308 FATAL_ERROR(test_result);
309
310 DGtal::trace.endBlock();
311 }
312}
313
314template <typename LinearAlgebraBackend>
315void
316test_concepts()
317{
318 DGtal::trace.beginBlock("concepts");
319
320 //FIXME add 1d
321
322 { // 2d
323 typedef DGtal::DiscreteExteriorCalculus<2, 2, LinearAlgebraBackend> Calculus;
324 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm0> ));
325 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm1> ));
326 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm2> ));
327 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm0> ));
328 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm1> ));
329 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm2> ));
330
331 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalVectorField> ));
332 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualVectorField> ));
333
334 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative0> ));
335 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative1> ));
336 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative0> ));
337 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative1> ));
338
339 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge0> ));
340 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge1> ));
341 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge2> ));
342 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge0> ));
343 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge1> ));
344 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge2> ));
345
346 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity0> ));
347 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity1> ));
348 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity2> ));
349 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity0> ));
350 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity1> ));
351 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity2> ));
352 }
353
354 { // 2d embedded in 3d
355 typedef DGtal::DiscreteExteriorCalculus<2, 3, LinearAlgebraBackend> Calculus;
356 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm0> ));
357 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm1> ));
358 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm2> ));
359 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm0> ));
360 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm1> ));
361 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm2> ));
362
363 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalVectorField> ));
364 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualVectorField> ));
365
366 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative0> ));
367 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative1> ));
368 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative0> ));
369 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative1> ));
370
371 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge0> ));
372 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge1> ));
373 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge2> ));
374 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge0> ));
375 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge1> ));
376 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge2> ));
377
378 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity0> ));
379 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity1> ));
380 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity2> ));
381 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity0> ));
382 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity1> ));
383 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity2> ));
384 }
385
386 { // 3d
387 typedef DGtal::DiscreteExteriorCalculus<3, 3, LinearAlgebraBackend> Calculus;
388 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm0> ));
389 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm1> ));
390 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm2> ));
391 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalForm3> ));
392 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm0> ));
393 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm1> ));
394 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm2> ));
395 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualForm3> ));
396
397 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalVectorField> ));
398 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualVectorField> ));
399
400 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative0> ));
401 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative1> ));
402 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalDerivative2> ));
403 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative0> ));
404 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative1> ));
405 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualDerivative2> ));
406
407 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge0> ));
408 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge1> ));
409 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge2> ));
410 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalHodge3> ));
411 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge0> ));
412 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge1> ));
413 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge2> ));
414 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualHodge3> ));
415
416 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity0> ));
417 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity1> ));
418 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity2> ));
419 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::PrimalIdentity3> ));
420 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity0> ));
421 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity1> ));
422 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity2> ));
423 BOOST_CONCEPT_ASSERT(( DGtal::concepts::CDiscreteExteriorCalculusVectorSpace<typename Calculus::DualIdentity3> ));
424 }
425
426 DGtal::trace.endBlock();
427}
428
429template <typename LinearAlgebraBackend>
430void
431test_hodge_sign()
432{
433 typedef DGtal::DiscreteExteriorCalculusFactory<LinearAlgebraBackend> CalculusFactory;
434
435 DGtal::trace.beginBlock("testing hodge sign");
436
437 {
438 typedef DGtal::DiscreteExteriorCalculus<2, 2, LinearAlgebraBackend> Calculus;
439 const DGtal::Z2i::Domain domain;
440 const DGtal::Z2i::DigitalSet set(domain);
441 const Calculus calculus = CalculusFactory::createFromDigitalSet(set);
442 typedef DGtal::Z2i::Point Point;
443
444 // primal point, dual cell
445 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,0)), DGtal::PRIMAL ) == 1 );
446 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,0)), DGtal::DUAL ) == 1 );
447 // primal horizontal edge, dual vertical edge
448 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,0)), DGtal::PRIMAL ) == 1 );
449 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,0)), DGtal::DUAL ) == -1 );
450 // primal vectical edge, dual horizontal edge
451 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,1)), DGtal::PRIMAL ) == 1 );
452 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,1)), DGtal::DUAL ) == -1 );
453 // primal cell, dual point
454 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,1)), DGtal::PRIMAL ) == 1 );
455 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,1)), DGtal::DUAL ) == 1 );
456 }
457
458 {
459 typedef DGtal::DiscreteExteriorCalculus<3, 3, LinearAlgebraBackend> Calculus;
460 const DGtal::Z3i::Domain domain;
461 const DGtal::Z3i::DigitalSet set(domain);
462 const Calculus calculus = CalculusFactory::createFromDigitalSet(set);
463 typedef DGtal::Z3i::Point Point;
464
465 // primal point, dual cell
466 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,0,0)), DGtal::PRIMAL ) == 1 );
467 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,0,0)), DGtal::DUAL ) == 1 );
468 // primal edge, dual surfel
469 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,0,0)), DGtal::PRIMAL ) == 1 );
470 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,0,0)), DGtal::DUAL ) == 1 );
471 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,1,0)), DGtal::PRIMAL ) == 1 );
472 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,1,0)), DGtal::DUAL ) == 1 );
473 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,0,1)), DGtal::PRIMAL ) == 1 );
474 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,0,1)), DGtal::DUAL ) == 1 );
475 // primal surfel, dual edge
476 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,1,0)), DGtal::PRIMAL ) == 1 );
477 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,1,0)), DGtal::DUAL ) == 1 );
478 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,1,1)), DGtal::PRIMAL ) == 1 );
479 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(0,1,1)), DGtal::DUAL ) == 1 );
480 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,0,1)), DGtal::PRIMAL ) == 1 );
481 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,0,1)), DGtal::DUAL ) == 1 );
482 // primal cell, dual point
483 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,1,1)), DGtal::PRIMAL ) == 1 );
484 FATAL_ERROR( calculus.hodgeSign( calculus.myKSpace.uFirst(Point(1,1,1)), DGtal::DUAL ) == 1 );
485 }
486
487 DGtal::trace.endBlock();
488}
489
490void
491test_duality()
492{
493 DGtal::trace.beginBlock("testing duality");
494
495 BOOST_STATIC_ASSERT(( DGtal::OppositeDuality<DGtal::PRIMAL>::duality == DGtal::DUAL ));
496 BOOST_STATIC_ASSERT(( DGtal::OppositeDuality<DGtal::DUAL>::duality == DGtal::PRIMAL ));
497
498 DGtal::trace.endBlock();
499}
500
501template <typename LinearAlgebraBackend>
502void
503test_backend(const int& ntime, const int& maxdim)
504{
505 test_duality();
506
507 test_hodge_sign<LinearAlgebraBackend>();
508
509 for (int kk=0; kk<ntime; kk++)
510 {
511 typedef DGtal::SpaceND<1, int> Space1;
512 typedef DGtal::HyperRectDomain<Space1> Domain1;
513 typedef DGtal::DigitalSetBySTLSet<Domain1> DigitalSet1;
514
515 typedef DGtal::SpaceND<4, int> Space4;
516 typedef DGtal::HyperRectDomain<Space4> Domain4;
517 typedef DGtal::DigitalSetBySTLSet<Domain4> DigitalSet4;
518
519 typedef DGtal::SpaceND<5, int> Space5;
520 typedef DGtal::HyperRectDomain<Space5> Domain5;
521 typedef DGtal::DigitalSetBySTLSet<Domain5> DigitalSet5;
522
523 typedef DGtal::SpaceND<6, int> Space6;
524 typedef DGtal::HyperRectDomain<Space6> Domain6;
525 typedef DGtal::DigitalSetBySTLSet<Domain6> DigitalSet6;
526
527 typedef DGtal::SpaceND<7, int> Space7;
528 typedef DGtal::HyperRectDomain<Space7> Domain7;
529 typedef DGtal::DigitalSetBySTLSet<Domain7> DigitalSet7;
530
531 DGtal::trace.beginBlock("testing hodges");
532 if (maxdim>=1) test_hodge<DigitalSet1, LinearAlgebraBackend>(10);
533 if (maxdim>=2) test_hodge<DGtal::Z2i::DigitalSet, LinearAlgebraBackend>(5);
534 if (maxdim>=3) test_hodge<DGtal::Z3i::DigitalSet, LinearAlgebraBackend>(5);
535 if (maxdim>=4) test_hodge<DigitalSet4, LinearAlgebraBackend>(4);
536 if (maxdim>=5) test_hodge<DigitalSet5, LinearAlgebraBackend>(3);
537 if (maxdim>=6) test_hodge<DigitalSet6, LinearAlgebraBackend>(3);
538 if (maxdim>=7) test_hodge<DigitalSet7, LinearAlgebraBackend>(2);
539 DGtal::trace.endBlock();
540
541 DGtal::trace.beginBlock("testing derivatives");
542 if (maxdim>=1) test_derivative<DigitalSet1, LinearAlgebraBackend>(10);
543 if (maxdim>=2) test_derivative<DGtal::Z2i::DigitalSet, LinearAlgebraBackend>(5);
544 if (maxdim>=3) test_derivative<DGtal::Z3i::DigitalSet, LinearAlgebraBackend>(5);
545 if (maxdim>=4) test_derivative<DigitalSet4, LinearAlgebraBackend>(4);
546 if (maxdim>=5) test_derivative<DigitalSet5, LinearAlgebraBackend>(3);
547 if (maxdim>=6) test_derivative<DigitalSet6, LinearAlgebraBackend>(3);
548 if (maxdim>=7) test_derivative<DigitalSet7, LinearAlgebraBackend>(2);
549 DGtal::trace.endBlock();
550 }
551
552 test_concepts<LinearAlgebraBackend>();
553}
554
555#endif
556
DGtal::DigitalSetByAssociativeContainer
Aim: A wrapper class around a STL associative container for storing sets of digital points within som...
Definition DigitalSetByAssociativeContainer.h:90
DGtal::DigitalSetBySTLSet
Aim: A container class for storing sets of digital points within some given domain.
Definition DigitalSetBySTLSet.h:85
DGtal::DiscreteExteriorCalculusFactory
Aim: This class provides static members to create DEC structures from various other DGtal structures.
Definition DiscreteExteriorCalculusFactory.h:62
DGtal::DiscreteExteriorCalculusFactory::createFromDigitalSet
static DiscreteExteriorCalculus< TDigitalSet::Point::dimension, TDigitalSet::Point::dimension, TLinearAlgebraBackend, TInteger > createFromDigitalSet(const TDigitalSet &set, const bool add_border=true)
DGtal::DiscreteExteriorCalculusSolver
Aim: This wraps a linear algebra solver around a discrete exterior calculus.
Definition DiscreteExteriorCalculusSolver.h:70
DGtal::DiscreteExteriorCalculusSolver::solve
SolutionKForm solve(const InputKForm &input_kform) const
DGtal::DiscreteExteriorCalculusSolver::compute
DiscreteExteriorCalculusSolver & compute(const Operator &linear_operator)
DGtal::DiscreteExteriorCalculus
Aim: DiscreteExteriorCalculus represents a calculus in the dec package. This is the main structure in...
Definition DiscreteExteriorCalculus.h:98
DGtal::KForm
Aim: KForm represents discrete kforms in the dec package.
Definition KForm.h:66
DGtal::KhalimskySpaceND::NEG
static const constexpr Sign NEG
Definition KhalimskySpaceND.h:433
DGtal::LinearOperator
Aim: LinearOperator represents discrete linear operator between discrete kforms in the DEC package.
Definition LinearOperator.h:69
DGtal::Trace::beginBlock
void beginBlock(const std::string &keyword="")
DGtal::Trace::info
std::ostream & info()
DGtal::Trace::endBlock
double endBlock()
calculus
PolyCalculus * calculus
Definition dgtalCalculus-geodesic.cpp:70
SCell
Z3i::SCell SCell
Definition digitalPolyhedronBuilder3D.cpp:79
Index
SMesh::Index Index
Definition fullConvexitySphereGeodesics.cpp:117
ConstIterator
MyDigitalSurface::ConstIterator ConstIterator
Definition greedy-plane-segmentation-ex2.cpp:93
DGtal::trace
Trace trace
Definition Common.h:153
DGtal::PRIMAL
@ PRIMAL
Definition Duality.h:61
DGtal::DUAL
@ DUAL
Definition Duality.h:62
DGtal::concepts::CDigitalSet
Aim: Represents a set of points within the given domain. This set of points is modifiable by the user...
Definition CDigitalSet.h:141
DGtal::concepts::CDiscreteExteriorCalculusVectorSpace
Aim: Lift linear algebra container concept into the dec package.
Definition CDiscreteExteriorCalculusVectorSpace.h:90
DerivativeTester< Calculus, -1 >::test
static bool test(const Calculus &)
Definition DECCommon.h:256
DerivativeTester::test
static bool test(const Calculus &calculus)
Definition DECCommon.h:200
DerivativeTester::BOOST_STATIC_ASSERT
BOOST_STATIC_ASSERT((order<(int) Calculus::dimensionEmbedded - 1))
HodgeTester< Calculus, -1 >::test
static bool test(const Calculus &calculus)
Definition DECCommon.h:111
HodgeTester::test
static bool test(const Calculus &calculus)
Definition DECCommon.h:59
HodgeTester::BOOST_STATIC_ASSERT
BOOST_STATIC_ASSERT((order<=Calculus::dimensionEmbedded))
Point
MyPointD Point
Definition testClone2.cpp:383
Cell
KSpace::Cell Cell
Definition testCubicalComplex.cpp:56
test
bool test(const I &itb, const I &ite)
Definition testMostCenteredMSEstimator.cpp:71
domain
Domain domain
Definition testProjection.cpp:88
Domain
HyperRectDomain< Space > Domain
Definition testSimpleRandomAccessRangeFromPoint.cpp:44
DigitalSet
Z2i::DigitalSet DigitalSet
Definition testVoronoiMapComplete.cpp:40