1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
5 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11 #include <cstdlib>
12 #include <cerrno>
13 #include <ctime>
14 #include <iostream>
15 #include <fstream>
16 #include <string>
17 #include <sstream>
18 #include <vector>
19 #include <typeinfo>
20
21 // The following includes of STL headers have to be done _before_ the
22 // definition of macros min() and max(). The reason is that many STL
23 // implementations will not work properly as the min and max symbols collide
24 // with the STL functions std:min() and std::max(). The STL headers may check
25 // for the macro definition of min/max and issue a warning or undefine the
26 // macros.
27 //
28 // Still, Windows defines min() and max() in windef.h as part of the regular
29 // Windows system interfaces and many other Windows APIs depend on these
30 // macros being available. To prevent the macro expansion of min/max and to
31 // make Eigen compatible with the Windows environment all function calls of
32 // std::min() and std::max() have to be written with parenthesis around the
33 // function name.
34 //
35 // All STL headers used by Eigen should be included here. Because main.h is
36 // included before any Eigen header and because the STL headers are guarded
37 // against multiple inclusions, no STL header will see our own min/max macro
38 // definitions.
39 #include <limits>
40 #include <algorithm>
41 #include <complex>
42 #include <deque>
43 #include <queue>
44 #include <cassert>
45 #include <list>
46 #if __cplusplus >= 201103L
47 #include <random>
48 #ifdef EIGEN_USE_THREADS
49 #include <future>
50 #endif
51 #endif
52
53 // To test that all calls from Eigen code to std::min() and std::max() are
54 // protected by parenthesis against macro expansion, the min()/max() macros
55 // are defined here and any not-parenthesized min/max call will cause a
56 // compiler error.
57 #define min(A,B) please_protect_your_min_with_parentheses
58 #define max(A,B) please_protect_your_max_with_parentheses
59 #define isnan(X) please_protect_your_isnan_with_parentheses
60 #define isinf(X) please_protect_your_isinf_with_parentheses
61 #define isfinite(X) please_protect_your_isfinite_with_parentheses
62 #ifdef M_PI
63 #undef M_PI
64 #endif
65 #define M_PI please_use_EIGEN_PI_instead_of_M_PI
66
67 #define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes
68 // B0 is defined in POSIX header termios.h
69 #define B0 FORBIDDEN_IDENTIFIER
70
71 // Unit tests calling Eigen's blas library must preserve the default blocking size
72 // to avoid troubles.
73 #ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
74 #define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
75 #endif
76
77 // shuts down ICC's remark #593: variable "XXX" was set but never used
78 #define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X)
79
80 #ifdef TEST_ENABLE_TEMPORARY_TRACKING
81
82 static long int nb_temporaries;
83 static long int nb_temporaries_on_assert = -1;
84
on_temporary_creation(long int size)85 inline void on_temporary_creation(long int size) {
86 // here's a great place to set a breakpoint when debugging failures in this test!
87 if(size!=0) nb_temporaries++;
88 if(nb_temporaries_on_assert>0) assert(nb_temporaries<nb_temporaries_on_assert);
89 }
90
91 #define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { on_temporary_creation(size); }
92
93 #define VERIFY_EVALUATION_COUNT(XPR,N) {\
94 nb_temporaries = 0; \
95 XPR; \
96 if(nb_temporaries!=N) { std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; }\
97 VERIFY( (#XPR) && nb_temporaries==N ); \
98 }
99
100 #endif
101
102 // the following file is automatically generated by cmake
103 #include "split_test_helper.h"
104
105 #ifdef NDEBUG
106 #undef NDEBUG
107 #endif
108
109 // On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.
110 #ifndef DEBUG
111 #define DEBUG
112 #endif
113
114 // bounds integer values for AltiVec
115 #if defined(__ALTIVEC__) || defined(__VSX__)
116 #define EIGEN_MAKING_DOCS
117 #endif
118
119 #ifndef EIGEN_TEST_FUNC
120 #error EIGEN_TEST_FUNC must be defined
121 #endif
122
123 #define DEFAULT_REPEAT 10
124
125 namespace Eigen
126 {
127 static std::vector<std::string> g_test_stack;
128 // level == 0 <=> abort if test fail
129 // level >= 1 <=> warning message to std::cerr if test fail
130 static int g_test_level = 0;
131 static int g_repeat;
132 static unsigned int g_seed;
133 static bool g_has_set_repeat, g_has_set_seed;
134 }
135
136 #define TRACK std::cerr << __FILE__ << " " << __LINE__ << std::endl
137 // #define TRACK while()
138
139 #define EI_PP_MAKE_STRING2(S) #S
140 #define EI_PP_MAKE_STRING(S) EI_PP_MAKE_STRING2(S)
141
142 #define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, " ", "\n", "", "", "", "")
143
144 #if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__)
145 #define EIGEN_EXCEPTIONS
146 #endif
147
148 #ifndef EIGEN_NO_ASSERTION_CHECKING
149
150 namespace Eigen
151 {
152 static const bool should_raise_an_assert = false;
153
154 // Used to avoid to raise two exceptions at a time in which
155 // case the exception is not properly caught.
156 // This may happen when a second exceptions is triggered in a destructor.
157 static bool no_more_assert = false;
158 static bool report_on_cerr_on_assert_failure = true;
159
160 struct eigen_assert_exception
161 {
eigen_assert_exceptioneigen_assert_exception162 eigen_assert_exception(void) {}
~eigen_assert_exceptioneigen_assert_exception163 ~eigen_assert_exception() { Eigen::no_more_assert = false; }
164 };
165 }
166 // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while
167 // one should have been, then the list of excecuted assertions is printed out.
168 //
169 // EIGEN_DEBUG_ASSERTS is not enabled by default as it
170 // significantly increases the compilation time
171 // and might even introduce side effects that would hide
172 // some memory errors.
173 #ifdef EIGEN_DEBUG_ASSERTS
174
175 namespace Eigen
176 {
177 namespace internal
178 {
179 static bool push_assert = false;
180 }
181 static std::vector<std::string> eigen_assert_list;
182 }
183 #define eigen_assert(a) \
184 if( (!(a)) && (!no_more_assert) ) \
185 { \
186 if(report_on_cerr_on_assert_failure) \
187 std::cerr << #a << " " __FILE__ << "(" << __LINE__ << ")\n"; \
188 Eigen::no_more_assert = true; \
189 EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
190 } \
191 else if (Eigen::internal::push_assert) \
192 { \
193 eigen_assert_list.push_back(std::string(EI_PP_MAKE_STRING(__FILE__) " (" EI_PP_MAKE_STRING(__LINE__) ") : " #a) ); \
194 }
195
196 #ifdef EIGEN_EXCEPTIONS
197 #define VERIFY_RAISES_ASSERT(a) \
198 { \
199 Eigen::no_more_assert = false; \
200 Eigen::eigen_assert_list.clear(); \
201 Eigen::internal::push_assert = true; \
202 Eigen::report_on_cerr_on_assert_failure = false; \
203 try { \
204 a; \
205 std::cerr << "One of the following asserts should have been triggered:\n"; \
206 for (uint ai=0 ; ai<eigen_assert_list.size() ; ++ai) \
207 std::cerr << " " << eigen_assert_list[ai] << "\n"; \
208 VERIFY(Eigen::should_raise_an_assert && # a); \
209 } catch (Eigen::eigen_assert_exception) { \
210 Eigen::internal::push_assert = false; VERIFY(true); \
211 } \
212 Eigen::report_on_cerr_on_assert_failure = true; \
213 Eigen::internal::push_assert = false; \
214 }
215 #endif //EIGEN_EXCEPTIONS
216
217 #elif !defined(__CUDACC__) // EIGEN_DEBUG_ASSERTS
218 // see bug 89. The copy_bool here is working around a bug in gcc <= 4.3
219 #define eigen_assert(a) \
220 if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\
221 { \
222 Eigen::no_more_assert = true; \
223 if(report_on_cerr_on_assert_failure) \
224 eigen_plain_assert(a); \
225 else \
226 EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
227 }
228 #ifdef EIGEN_EXCEPTIONS
229 #define VERIFY_RAISES_ASSERT(a) { \
230 Eigen::no_more_assert = false; \
231 Eigen::report_on_cerr_on_assert_failure = false; \
232 try { \
233 a; \
234 VERIFY(Eigen::should_raise_an_assert && # a); \
235 } \
236 catch (Eigen::eigen_assert_exception&) { VERIFY(true); } \
237 Eigen::report_on_cerr_on_assert_failure = true; \
238 }
239 #endif //EIGEN_EXCEPTIONS
240 #endif // EIGEN_DEBUG_ASSERTS
241
242 #ifndef VERIFY_RAISES_ASSERT
243 #define VERIFY_RAISES_ASSERT(a) \
244 std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled\n";
245 #endif
246
247 #if !defined(__CUDACC__)
248 #define EIGEN_USE_CUSTOM_ASSERT
249 #endif
250
251 #else // EIGEN_NO_ASSERTION_CHECKING
252
253 #define VERIFY_RAISES_ASSERT(a) {}
254
255 #endif // EIGEN_NO_ASSERTION_CHECKING
256
257
258 #define EIGEN_INTERNAL_DEBUGGING
259 #include <Eigen/QR> // required for createRandomPIMatrixOfRank
260
verify_impl(bool condition,const char * testname,const char * file,int line,const char * condition_as_string)261 inline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string)
262 {
263 if (!condition)
264 {
265 if(Eigen::g_test_level>0)
266 std::cerr << "WARNING: ";
267 std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")"
268 << std::endl << " " << condition_as_string << std::endl;
269 std::cerr << "Stack:\n";
270 const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
271 for(int i=test_stack_size-1; i>=0; --i)
272 std::cerr << " - " << Eigen::g_test_stack[i] << "\n";
273 std::cerr << "\n";
274 if(Eigen::g_test_level==0)
275 abort();
276 }
277 }
278
279 #define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a))
280
281 #define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a >= b))
282 #define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a <= b))
283
284
285 #define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true))
286 #define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false))
287 #define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b))
288 #define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
289 #define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
290 #define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
291 #define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
292 #define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))
293
294 #define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))
295
296 #define CALL_SUBTEST(FUNC) do { \
297 g_test_stack.push_back(EI_PP_MAKE_STRING(FUNC)); \
298 FUNC; \
299 g_test_stack.pop_back(); \
300 } while (0)
301
302
303 namespace Eigen {
304
test_precision()305 template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
306 template<> inline float test_precision<float>() { return 1e-3f; }
307 template<> inline double test_precision<double>() { return 1e-6; }
308 template<> inline long double test_precision<long double>() { return 1e-6l; }
309 template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
310 template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
311 template<> inline long double test_precision<std::complex<long double> >() { return test_precision<long double>(); }
312
test_isApprox(const short & a,const short & b)313 inline bool test_isApprox(const short& a, const short& b)
314 { return internal::isApprox(a, b, test_precision<short>()); }
test_isApprox(const unsigned short & a,const unsigned short & b)315 inline bool test_isApprox(const unsigned short& a, const unsigned short& b)
316 { return internal::isApprox(a, b, test_precision<unsigned long>()); }
test_isApprox(const unsigned int & a,const unsigned int & b)317 inline bool test_isApprox(const unsigned int& a, const unsigned int& b)
318 { return internal::isApprox(a, b, test_precision<unsigned int>()); }
test_isApprox(const long & a,const long & b)319 inline bool test_isApprox(const long& a, const long& b)
320 { return internal::isApprox(a, b, test_precision<long>()); }
test_isApprox(const unsigned long & a,const unsigned long & b)321 inline bool test_isApprox(const unsigned long& a, const unsigned long& b)
322 { return internal::isApprox(a, b, test_precision<unsigned long>()); }
323
test_isApprox(const int & a,const int & b)324 inline bool test_isApprox(const int& a, const int& b)
325 { return internal::isApprox(a, b, test_precision<int>()); }
test_isMuchSmallerThan(const int & a,const int & b)326 inline bool test_isMuchSmallerThan(const int& a, const int& b)
327 { return internal::isMuchSmallerThan(a, b, test_precision<int>()); }
test_isApproxOrLessThan(const int & a,const int & b)328 inline bool test_isApproxOrLessThan(const int& a, const int& b)
329 { return internal::isApproxOrLessThan(a, b, test_precision<int>()); }
330
test_isApprox(const float & a,const float & b)331 inline bool test_isApprox(const float& a, const float& b)
332 { return internal::isApprox(a, b, test_precision<float>()); }
test_isMuchSmallerThan(const float & a,const float & b)333 inline bool test_isMuchSmallerThan(const float& a, const float& b)
334 { return internal::isMuchSmallerThan(a, b, test_precision<float>()); }
test_isApproxOrLessThan(const float & a,const float & b)335 inline bool test_isApproxOrLessThan(const float& a, const float& b)
336 { return internal::isApproxOrLessThan(a, b, test_precision<float>()); }
337
test_isApprox(const double & a,const double & b)338 inline bool test_isApprox(const double& a, const double& b)
339 { return internal::isApprox(a, b, test_precision<double>()); }
test_isMuchSmallerThan(const double & a,const double & b)340 inline bool test_isMuchSmallerThan(const double& a, const double& b)
341 { return internal::isMuchSmallerThan(a, b, test_precision<double>()); }
test_isApproxOrLessThan(const double & a,const double & b)342 inline bool test_isApproxOrLessThan(const double& a, const double& b)
343 { return internal::isApproxOrLessThan(a, b, test_precision<double>()); }
344
345 #ifndef EIGEN_TEST_NO_COMPLEX
test_isApprox(const std::complex<float> & a,const std::complex<float> & b)346 inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
347 { return internal::isApprox(a, b, test_precision<std::complex<float> >()); }
test_isMuchSmallerThan(const std::complex<float> & a,const std::complex<float> & b)348 inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
349 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
350
test_isApprox(const std::complex<double> & a,const std::complex<double> & b)351 inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
352 { return internal::isApprox(a, b, test_precision<std::complex<double> >()); }
test_isMuchSmallerThan(const std::complex<double> & a,const std::complex<double> & b)353 inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
354 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
355
356 #ifndef EIGEN_TEST_NO_LONGDOUBLE
test_isApprox(const std::complex<long double> & a,const std::complex<long double> & b)357 inline bool test_isApprox(const std::complex<long double>& a, const std::complex<long double>& b)
358 { return internal::isApprox(a, b, test_precision<std::complex<long double> >()); }
test_isMuchSmallerThan(const std::complex<long double> & a,const std::complex<long double> & b)359 inline bool test_isMuchSmallerThan(const std::complex<long double>& a, const std::complex<long double>& b)
360 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<long double> >()); }
361 #endif
362 #endif
363
364 #ifndef EIGEN_TEST_NO_LONGDOUBLE
test_isApprox(const long double & a,const long double & b)365 inline bool test_isApprox(const long double& a, const long double& b)
366 {
367 bool ret = internal::isApprox(a, b, test_precision<long double>());
368 if (!ret) std::cerr
369 << std::endl << " actual = " << a
370 << std::endl << " expected = " << b << std::endl << std::endl;
371 return ret;
372 }
373
test_isMuchSmallerThan(const long double & a,const long double & b)374 inline bool test_isMuchSmallerThan(const long double& a, const long double& b)
375 { return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }
test_isApproxOrLessThan(const long double & a,const long double & b)376 inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
377 { return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
378 #endif // EIGEN_TEST_NO_LONGDOUBLE
379
test_isApprox(const half & a,const half & b)380 inline bool test_isApprox(const half& a, const half& b)
381 { return internal::isApprox(a, b, test_precision<half>()); }
test_isMuchSmallerThan(const half & a,const half & b)382 inline bool test_isMuchSmallerThan(const half& a, const half& b)
383 { return internal::isMuchSmallerThan(a, b, test_precision<half>()); }
test_isApproxOrLessThan(const half & a,const half & b)384 inline bool test_isApproxOrLessThan(const half& a, const half& b)
385 { return internal::isApproxOrLessThan(a, b, test_precision<half>()); }
386
387 // test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.
388 template<typename T1,typename T2>
test_relative_error(const EigenBase<T1> & a,const EigenBase<T2> & b)389 typename NumTraits<typename T1::RealScalar>::NonInteger test_relative_error(const EigenBase<T1> &a, const EigenBase<T2> &b)
390 {
391 using std::sqrt;
392 typedef typename NumTraits<typename T1::RealScalar>::NonInteger RealScalar;
393 typename internal::nested_eval<T1,2>::type ea(a.derived());
394 typename internal::nested_eval<T2,2>::type eb(b.derived());
395 return sqrt(RealScalar((ea-eb).cwiseAbs2().sum()) / RealScalar((std::min)(eb.cwiseAbs2().sum(),ea.cwiseAbs2().sum())));
396 }
397
398 template<typename T1,typename T2>
399 typename T1::RealScalar test_relative_error(const T1 &a, const T2 &b, const typename T1::Coefficients* = 0)
400 {
401 return test_relative_error(a.coeffs(), b.coeffs());
402 }
403
404 template<typename T1,typename T2>
405 typename T1::Scalar test_relative_error(const T1 &a, const T2 &b, const typename T1::MatrixType* = 0)
406 {
407 return test_relative_error(a.matrix(), b.matrix());
408 }
409
410 template<typename S, int D>
test_relative_error(const Translation<S,D> & a,const Translation<S,D> & b)411 S test_relative_error(const Translation<S,D> &a, const Translation<S,D> &b)
412 {
413 return test_relative_error(a.vector(), b.vector());
414 }
415
416 template <typename S, int D, int O>
test_relative_error(const ParametrizedLine<S,D,O> & a,const ParametrizedLine<S,D,O> & b)417 S test_relative_error(const ParametrizedLine<S,D,O> &a, const ParametrizedLine<S,D,O> &b)
418 {
419 return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin()));
420 }
421
422 template <typename S, int D>
test_relative_error(const AlignedBox<S,D> & a,const AlignedBox<S,D> & b)423 S test_relative_error(const AlignedBox<S,D> &a, const AlignedBox<S,D> &b)
424 {
425 return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)()));
426 }
427
428 template<typename Derived> class SparseMatrixBase;
429 template<typename T1,typename T2>
test_relative_error(const MatrixBase<T1> & a,const SparseMatrixBase<T2> & b)430 typename T1::RealScalar test_relative_error(const MatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
431 {
432 return test_relative_error(a,b.toDense());
433 }
434
435 template<typename Derived> class SparseMatrixBase;
436 template<typename T1,typename T2>
test_relative_error(const SparseMatrixBase<T1> & a,const MatrixBase<T2> & b)437 typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const MatrixBase<T2> &b)
438 {
439 return test_relative_error(a.toDense(),b);
440 }
441
442 template<typename Derived> class SparseMatrixBase;
443 template<typename T1,typename T2>
test_relative_error(const SparseMatrixBase<T1> & a,const SparseMatrixBase<T2> & b)444 typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
445 {
446 return test_relative_error(a.toDense(),b.toDense());
447 }
448
449 template<typename T1,typename T2>
450 typename NumTraits<typename NumTraits<T1>::Real>::NonInteger test_relative_error(const T1 &a, const T2 &b, typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T1>::Real>::value, T1>::type* = 0)
451 {
452 typedef typename NumTraits<typename NumTraits<T1>::Real>::NonInteger RealScalar;
453 return numext::sqrt(RealScalar(numext::abs2(a-b))/RealScalar((numext::mini)(numext::abs2(a),numext::abs2(b))));
454 }
455
456 template<typename T>
test_relative_error(const Rotation2D<T> & a,const Rotation2D<T> & b)457 T test_relative_error(const Rotation2D<T> &a, const Rotation2D<T> &b)
458 {
459 return test_relative_error(a.angle(), b.angle());
460 }
461
462 template<typename T>
test_relative_error(const AngleAxis<T> & a,const AngleAxis<T> & b)463 T test_relative_error(const AngleAxis<T> &a, const AngleAxis<T> &b)
464 {
465 return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis()));
466 }
467
468 template<typename Type1, typename Type2>
469 inline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only
470 {
471 return a.isApprox(b, test_precision<typename Type1::Scalar>());
472 }
473
474 // get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions
475 template<typename T>
476 typename NumTraits<typename T::Scalar>::Real get_test_precision(const T&, const typename T::Scalar* = 0)
477 {
478 return test_precision<typename NumTraits<typename T::Scalar>::Real>();
479 }
480
481 template<typename T>
482 typename NumTraits<T>::Real get_test_precision(const T&,typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0)
483 {
484 return test_precision<typename NumTraits<T>::Real>();
485 }
486
487 // verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails.
488 template<typename Type1, typename Type2>
verifyIsApprox(const Type1 & a,const Type2 & b)489 inline bool verifyIsApprox(const Type1& a, const Type2& b)
490 {
491 bool ret = test_isApprox(a,b);
492 if(!ret)
493 {
494 std::cerr << "Difference too large wrt tolerance " << get_test_precision(a) << ", relative error is: " << test_relative_error(a,b) << std::endl;
495 }
496 return ret;
497 }
498
499 // The idea behind this function is to compare the two scalars a and b where
500 // the scalar ref is a hint about the expected order of magnitude of a and b.
501 // WARNING: the scalar a and b must be positive
502 // Therefore, if for some reason a and b are very small compared to ref,
503 // we won't issue a false negative.
504 // This test could be: abs(a-b) <= eps * ref
505 // However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.
506 template<typename Scalar,typename ScalarRef>
test_isApproxWithRef(const Scalar & a,const Scalar & b,const ScalarRef & ref)507 inline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)
508 {
509 return test_isApprox(a+ref, b+ref);
510 }
511
512 template<typename Derived1, typename Derived2>
test_isMuchSmallerThan(const MatrixBase<Derived1> & m1,const MatrixBase<Derived2> & m2)513 inline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,
514 const MatrixBase<Derived2>& m2)
515 {
516 return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
517 }
518
519 template<typename Derived>
test_isMuchSmallerThan(const MatrixBase<Derived> & m,const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real & s)520 inline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,
521 const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
522 {
523 return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
524 }
525
526 template<typename Derived>
test_isUnitary(const MatrixBase<Derived> & m)527 inline bool test_isUnitary(const MatrixBase<Derived>& m)
528 {
529 return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());
530 }
531
532 // Forward declaration to avoid ICC warning
533 template<typename T, typename U>
534 bool test_is_equal(const T& actual, const U& expected, bool expect_equal=true);
535
536 template<typename T, typename U>
test_is_equal(const T & actual,const U & expected,bool expect_equal)537 bool test_is_equal(const T& actual, const U& expected, bool expect_equal)
538 {
539 if ((actual==expected) == expect_equal)
540 return true;
541 // false:
542 std::cerr
543 << "\n actual = " << actual
544 << "\n expected " << (expect_equal ? "= " : "!=") << expected << "\n\n";
545 return false;
546 }
547
548 /** Creates a random Partial Isometry matrix of given rank.
549 *
550 * A partial isometry is a matrix all of whose singular values are either 0 or 1.
551 * This is very useful to test rank-revealing algorithms.
552 */
553 // Forward declaration to avoid ICC warning
554 template<typename MatrixType>
555 void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
556 template<typename MatrixType>
createRandomPIMatrixOfRank(Index desired_rank,Index rows,Index cols,MatrixType & m)557 void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
558 {
559 typedef typename internal::traits<MatrixType>::Scalar Scalar;
560 enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
561
562 typedef Matrix<Scalar, Dynamic, 1> VectorType;
563 typedef Matrix<Scalar, Rows, Rows> MatrixAType;
564 typedef Matrix<Scalar, Cols, Cols> MatrixBType;
565
566 if(desired_rank == 0)
567 {
568 m.setZero(rows,cols);
569 return;
570 }
571
572 if(desired_rank == 1)
573 {
574 // here we normalize the vectors to get a partial isometry
575 m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
576 return;
577 }
578
579 MatrixAType a = MatrixAType::Random(rows,rows);
580 MatrixType d = MatrixType::Identity(rows,cols);
581 MatrixBType b = MatrixBType::Random(cols,cols);
582
583 // set the diagonal such that only desired_rank non-zero entries reamain
584 const Index diag_size = (std::min)(d.rows(),d.cols());
585 if(diag_size != desired_rank)
586 d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
587
588 HouseholderQR<MatrixAType> qra(a);
589 HouseholderQR<MatrixBType> qrb(b);
590 m = qra.householderQ() * d * qrb.householderQ();
591 }
592
593 // Forward declaration to avoid ICC warning
594 template<typename PermutationVectorType>
595 void randomPermutationVector(PermutationVectorType& v, Index size);
596 template<typename PermutationVectorType>
randomPermutationVector(PermutationVectorType & v,Index size)597 void randomPermutationVector(PermutationVectorType& v, Index size)
598 {
599 typedef typename PermutationVectorType::Scalar Scalar;
600 v.resize(size);
601 for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
602 if(size == 1) return;
603 for(Index n = 0; n < 3 * size; ++n)
604 {
605 Index i = internal::random<Index>(0, size-1);
606 Index j;
607 do j = internal::random<Index>(0, size-1); while(j==i);
608 std::swap(v(i), v(j));
609 }
610 }
611
isNotNaN(const T & x)612 template<typename T> bool isNotNaN(const T& x)
613 {
614 return x==x;
615 }
616
isPlusInf(const T & x)617 template<typename T> bool isPlusInf(const T& x)
618 {
619 return x > NumTraits<T>::highest();
620 }
621
isMinusInf(const T & x)622 template<typename T> bool isMinusInf(const T& x)
623 {
624 return x < NumTraits<T>::lowest();
625 }
626
627 } // end namespace Eigen
628
629 template<typename T> struct GetDifferentType;
630
631 template<> struct GetDifferentType<float> { typedef double type; };
632 template<> struct GetDifferentType<double> { typedef float type; };
633 template<typename T> struct GetDifferentType<std::complex<T> >
634 { typedef std::complex<typename GetDifferentType<T>::type> type; };
635
636 // Forward declaration to avoid ICC warning
637 template<typename T> std::string type_name();
638 template<typename T> std::string type_name() { return "other"; }
639 template<> std::string type_name<float>() { return "float"; }
640 template<> std::string type_name<double>() { return "double"; }
641 template<> std::string type_name<long double>() { return "long double"; }
642 template<> std::string type_name<int>() { return "int"; }
643 template<> std::string type_name<std::complex<float> >() { return "complex<float>"; }
644 template<> std::string type_name<std::complex<double> >() { return "complex<double>"; }
645 template<> std::string type_name<std::complex<long double> >() { return "complex<long double>"; }
646 template<> std::string type_name<std::complex<int> >() { return "complex<int>"; }
647
648 // forward declaration of the main test function
649 void EIGEN_CAT(test_,EIGEN_TEST_FUNC)();
650
651 using namespace Eigen;
652
653 inline void set_repeat_from_string(const char *str)
654 {
655 errno = 0;
656 g_repeat = int(strtoul(str, 0, 10));
657 if(errno || g_repeat <= 0)
658 {
659 std::cout << "Invalid repeat value " << str << std::endl;
660 exit(EXIT_FAILURE);
661 }
662 g_has_set_repeat = true;
663 }
664
665 inline void set_seed_from_string(const char *str)
666 {
667 errno = 0;
668 g_seed = int(strtoul(str, 0, 10));
669 if(errno || g_seed == 0)
670 {
671 std::cout << "Invalid seed value " << str << std::endl;
672 exit(EXIT_FAILURE);
673 }
674 g_has_set_seed = true;
675 }
676
677 int main(int argc, char *argv[])
678 {
679 g_has_set_repeat = false;
680 g_has_set_seed = false;
681 bool need_help = false;
682
683 for(int i = 1; i < argc; i++)
684 {
685 if(argv[i][0] == 'r')
686 {
687 if(g_has_set_repeat)
688 {
689 std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
690 return 1;
691 }
692 set_repeat_from_string(argv[i]+1);
693 }
694 else if(argv[i][0] == 's')
695 {
696 if(g_has_set_seed)
697 {
698 std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
699 return 1;
700 }
701 set_seed_from_string(argv[i]+1);
702 }
703 else
704 {
705 need_help = true;
706 }
707 }
708
709 if(need_help)
710 {
711 std::cout << "This test application takes the following optional arguments:" << std::endl;
712 std::cout << " rN Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
713 std::cout << " sN Use N as seed for random numbers (default: based on current time)" << std::endl;
714 std::cout << std::endl;
715 std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl;
716 std::cout << "will be used as default values for these parameters." << std::endl;
717 return 1;
718 }
719
720 char *env_EIGEN_REPEAT = getenv("EIGEN_REPEAT");
721 if(!g_has_set_repeat && env_EIGEN_REPEAT)
722 set_repeat_from_string(env_EIGEN_REPEAT);
723 char *env_EIGEN_SEED = getenv("EIGEN_SEED");
724 if(!g_has_set_seed && env_EIGEN_SEED)
725 set_seed_from_string(env_EIGEN_SEED);
726
727 if(!g_has_set_seed) g_seed = (unsigned int) time(NULL);
728 if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;
729
730 std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
731 std::stringstream ss;
732 ss << "Seed: " << g_seed;
733 g_test_stack.push_back(ss.str());
734 srand(g_seed);
735 std::cout << "Repeating each test " << g_repeat << " times" << std::endl;
736
737 Eigen::g_test_stack.push_back(std::string(EI_PP_MAKE_STRING(EIGEN_TEST_FUNC)));
738
739 EIGEN_CAT(test_,EIGEN_TEST_FUNC)();
740 return 0;
741 }
742
743 // These warning are disabled here such that they are still ON when parsing Eigen's header files.
744 #if defined __INTEL_COMPILER
745 // remark #383: value copied to temporary, reference to temporary used
746 // -> this warning is raised even for legal usage as: g_test_stack.push_back("foo"); where g_test_stack is a std::vector<std::string>
747 // remark #1418: external function definition with no prior declaration
748 // -> this warning is raised for all our test functions. Declaring them static would fix the issue.
749 // warning #279: controlling expression is constant
750 // remark #1572: floating-point equality and inequality comparisons are unreliable
751 #pragma warning disable 279 383 1418 1572
752 #endif
753
754 #ifdef _MSC_VER
755 // 4503 - decorated name length exceeded, name was truncated
756 #pragma warning( disable : 4503)
757 #endif
758