aboutsummaryrefslogtreecommitdiffhomepage
path: root/test/main.h
blob: 786673dead8ec4facaa4712f1f67758861500ef7 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include <cstdlib>
#include <cerrno>
#include <ctime>
#include <iostream>
#include <fstream>
#include <string>
#include <sstream>
#include <vector>
#include <typeinfo>
#include <functional>

// The following includes of STL headers have to be done _before_ the
// definition of macros min() and max().  The reason is that many STL
// implementations will not work properly as the min and max symbols collide
// with the STL functions std:min() and std::max().  The STL headers may check
// for the macro definition of min/max and issue a warning or undefine the
// macros.
//
// Still, Windows defines min() and max() in windef.h as part of the regular
// Windows system interfaces and many other Windows APIs depend on these
// macros being available.  To prevent the macro expansion of min/max and to
// make Eigen compatible with the Windows environment all function calls of
// std::min() and std::max() have to be written with parenthesis around the
// function name.
//
// All STL headers used by Eigen should be included here.  Because main.h is
// included before any Eigen header and because the STL headers are guarded
// against multiple inclusions, no STL header will see our own min/max macro
// definitions.
#include <limits>
#include <algorithm>
// Disable ICC's std::complex operator specializations so we can use our own.
#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
#include <complex>
#include <deque>
#include <queue>
#include <cassert>
#include <list>
#if __cplusplus >= 201103L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201103L)
#include <random>
#include <chrono>
#ifdef EIGEN_USE_THREADS
#include <future>
#endif
#endif

// Same for cuda_fp16.h
#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
  // Means the compiler is either nvcc or clang with CUDA enabled
  #define EIGEN_CUDACC __CUDACC__
#endif
#if defined(EIGEN_CUDACC)
#include <cuda.h>
  #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
#else
  #define EIGEN_CUDA_SDK_VER 0
#endif
#if EIGEN_CUDA_SDK_VER >= 70500
#include <cuda_fp16.h>
#endif

// To test that all calls from Eigen code to std::min() and std::max() are
// protected by parenthesis against macro expansion, the min()/max() macros
// are defined here and any not-parenthesized min/max call will cause a
// compiler error.
#if !defined(__HIPCC__) && !defined(EIGEN_USE_SYCL)
  //
  // HIP header files include the following files
  //  <thread>
  //  <regex>
  //  <unordered_map>
  // which seem to contain not-parenthesized calls to "max"/"min", triggering the following check and causing the compile to fail
  //
  // Including those header files before the following macro definition for "min" / "max", only partially resolves the issue
  // This is because other HIP header files also define "isnan" / "isinf" / "isfinite" functions, which are needed in other
  // headers.
  //
  // So instead choosing to simply disable this check for HIP
  //
  #define min(A,B) please_protect_your_min_with_parentheses
  #define max(A,B) please_protect_your_max_with_parentheses
  #define isnan(X) please_protect_your_isnan_with_parentheses
  #define isinf(X) please_protect_your_isinf_with_parentheses
  #define isfinite(X) please_protect_your_isfinite_with_parentheses
#endif


// test possible conflicts
struct real {};
struct imag {};

#ifdef M_PI
#undef M_PI
#endif
#define M_PI please_use_EIGEN_PI_instead_of_M_PI

#define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes
// B0 is defined in POSIX header termios.h
#define B0 FORBIDDEN_IDENTIFIER
// `I` may be defined by complex.h:
#define I  FORBIDDEN_IDENTIFIER

// Unit tests calling Eigen's blas library must preserve the default blocking size
// to avoid troubles.
#ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
#define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
#endif

// shuts down ICC's remark #593: variable "XXX" was set but never used
#define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X)

#ifdef TEST_ENABLE_TEMPORARY_TRACKING

static long int nb_temporaries;
static long int nb_temporaries_on_assert = -1;

inline void on_temporary_creation(long int size) {
  // here's a great place to set a breakpoint when debugging failures in this test!
  if(size!=0) nb_temporaries++;
  if(nb_temporaries_on_assert>0) assert(nb_temporaries<nb_temporaries_on_assert);
}

#define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { on_temporary_creation(size); }

#define VERIFY_EVALUATION_COUNT(XPR,N) {\
    nb_temporaries = 0; \
    XPR; \
    if(nb_temporaries!=(N)) { std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; }\
    VERIFY( (#XPR) && nb_temporaries==(N) ); \
  }

#endif

#include "split_test_helper.h"

#ifdef NDEBUG
#undef NDEBUG
#endif

// On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.
#ifndef DEBUG
#define DEBUG
#endif

// bounds integer values for AltiVec
#if defined(__ALTIVEC__) || defined(__VSX__)
#define EIGEN_MAKING_DOCS
#endif

#define DEFAULT_REPEAT 10

namespace Eigen
{
  static std::vector<std::string> g_test_stack;
  // level == 0 <=> abort if test fail
  // level >= 1 <=> warning message to std::cerr if test fail
  static int g_test_level = 0;
  static int g_repeat = 1;
  static unsigned int g_seed = 0;
  static bool g_has_set_repeat = false, g_has_set_seed = false;

  class EigenTest
  {
  public:
    EigenTest() : m_func(0) {}
    EigenTest(const char* a_name, void (*func)(void))
      : m_name(a_name), m_func(func)
    {
      get_registered_tests().push_back(this);
    }
    const std::string& name() const { return m_name; }
    void operator()() const { m_func(); }

    static const std::vector<EigenTest*>& all() { return get_registered_tests(); }
  protected:
    static std::vector<EigenTest*>& get_registered_tests()
    {
      static std::vector<EigenTest*>* ms_registered_tests = new std::vector<EigenTest*>();
      return *ms_registered_tests;
    }
    std::string m_name;
    void (*m_func)(void);
  };

  // Declare and register a test, e.g.:
  //    EIGEN_DECLARE_TEST(mytest) { ... }
  // will create a function:
  //    void test_mytest() { ... }
  // that will be automatically called.
  #define EIGEN_DECLARE_TEST(X) \
    void EIGEN_CAT(test_,X) (); \
    static EigenTest EIGEN_CAT(test_handler_,X) (EIGEN_MAKESTRING(X), & EIGEN_CAT(test_,X)); \
    void EIGEN_CAT(test_,X) ()
}

#define TRACK std::cerr << __FILE__ << " " << __LINE__ << std::endl
// #define TRACK while()

#define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, "  ", "\n", "", "", "", "")

#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(__HIP_DEVICE_COMPILE__) && !defined(__SYCL_DEVICE_ONLY__)
  #define EIGEN_EXCEPTIONS
#endif

#ifndef EIGEN_NO_ASSERTION_CHECKING

  namespace Eigen
  {
    static const bool should_raise_an_assert = false;

    // Used to avoid to raise two exceptions at a time in which
    // case the exception is not properly caught.
    // This may happen when a second exceptions is triggered in a destructor.
    static bool no_more_assert = false;
    static bool report_on_cerr_on_assert_failure = true;

    struct eigen_assert_exception
    {
      eigen_assert_exception(void) {}
      ~eigen_assert_exception() { Eigen::no_more_assert = false; }
    };

    struct eigen_static_assert_exception
    {
      eigen_static_assert_exception(void) {}
      ~eigen_static_assert_exception() { Eigen::no_more_assert = false; }
    };
  }
  // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while
  // one should have been, then the list of executed assertions is printed out.
  //
  // EIGEN_DEBUG_ASSERTS is not enabled by default as it
  // significantly increases the compilation time
  // and might even introduce side effects that would hide
  // some memory errors.
  #ifdef EIGEN_DEBUG_ASSERTS

    namespace Eigen
    {
      namespace internal
      {
        static bool push_assert = false;
      }
      static std::vector<std::string> eigen_assert_list;
    }
    #define eigen_assert(a)                       \
      if( (!(a)) && (!no_more_assert) )     \
      { \
        if(report_on_cerr_on_assert_failure) \
          std::cerr <<  #a << " " __FILE__ << "(" << __LINE__ << ")\n"; \
        Eigen::no_more_assert = true;       \
        EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
      }                                     \
      else if (Eigen::internal::push_assert)       \
      {                                     \
        eigen_assert_list.push_back(std::string(EIGEN_MAKESTRING(__FILE__) " (" EIGEN_MAKESTRING(__LINE__) ") : " #a) ); \
      }

    #ifdef EIGEN_EXCEPTIONS
    #define VERIFY_RAISES_ASSERT(a)                                                   \
      {                                                                               \
        Eigen::no_more_assert = false;                                                \
        Eigen::eigen_assert_list.clear();                                             \
        Eigen::internal::push_assert = true;                                          \
        Eigen::report_on_cerr_on_assert_failure = false;                              \
        try {                                                                         \
          a;                                                                          \
          std::cerr << "One of the following asserts should have been triggered:\n";  \
          for (uint ai=0 ; ai<eigen_assert_list.size() ; ++ai)                        \
            std::cerr << "  " << eigen_assert_list[ai] << "\n";                       \
          VERIFY(Eigen::should_raise_an_assert && # a);                               \
        } catch (Eigen::eigen_assert_exception) {                                     \
          Eigen::internal::push_assert = false; VERIFY(true);                         \
        }                                                                             \
        Eigen::report_on_cerr_on_assert_failure = true;                               \
        Eigen::internal::push_assert = false;                                         \
      }
    #endif //EIGEN_EXCEPTIONS

  #elif !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY) // EIGEN_DEBUG_ASSERTS
    // see bug 89. The copy_bool here is working around a bug in gcc <= 4.3
    #define eigen_assert(a) \
      if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\
      {                                       \
        Eigen::no_more_assert = true;         \
        if(report_on_cerr_on_assert_failure)  \
          eigen_plain_assert(a);              \
        else                                  \
          EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
      }

    #ifdef EIGEN_EXCEPTIONS
      #define VERIFY_RAISES_ASSERT(a) {                           \
        Eigen::no_more_assert = false;                            \
        Eigen::report_on_cerr_on_assert_failure = false;          \
        try {                                                     \
          a;                                                      \
          VERIFY(Eigen::should_raise_an_assert && # a);           \
        }                                                         \
        catch (Eigen::eigen_assert_exception&) { VERIFY(true); }  \
        Eigen::report_on_cerr_on_assert_failure = true;           \
      }
    #endif // EIGEN_EXCEPTIONS
  #endif // EIGEN_DEBUG_ASSERTS

  #if defined(TEST_CHECK_STATIC_ASSERTIONS) && defined(EIGEN_EXCEPTIONS)
    #define EIGEN_STATIC_ASSERT(a,MSG) \
      if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\
      {                                       \
        Eigen::no_more_assert = true;         \
        if(report_on_cerr_on_assert_failure)  \
          eigen_plain_assert((a) && #MSG);      \
        else                                  \
          EIGEN_THROW_X(Eigen::eigen_static_assert_exception()); \
      }
    #define VERIFY_RAISES_STATIC_ASSERT(a) {                    \
      Eigen::no_more_assert = false;                            \
      Eigen::report_on_cerr_on_assert_failure = false;          \
      try {                                                     \
        a;                                                      \
        VERIFY(Eigen::should_raise_an_assert && # a);           \
      }                                                         \
      catch (Eigen::eigen_static_assert_exception&) { VERIFY(true); }  \
      Eigen::report_on_cerr_on_assert_failure = true;           \
    }
  #endif // TEST_CHECK_STATIC_ASSERTIONS

#ifndef VERIFY_RAISES_ASSERT
  #define VERIFY_RAISES_ASSERT(a) \
    std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled\n";
#endif
#ifndef VERIFY_RAISES_STATIC_ASSERT
  #define VERIFY_RAISES_STATIC_ASSERT(a) \
    std::cout << "Can't VERIFY_RAISES_STATIC_ASSERT( " #a " ) with exceptions disabled\n";
#endif

  #if !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY)
  #define EIGEN_USE_CUSTOM_ASSERT
  #endif

#else // EIGEN_NO_ASSERTION_CHECKING

  #define VERIFY_RAISES_ASSERT(a) {}
  #define VERIFY_RAISES_STATIC_ASSERT(a) {}

#endif // EIGEN_NO_ASSERTION_CHECKING

#define EIGEN_INTERNAL_DEBUGGING
#include <Eigen/QR> // required for createRandomPIMatrixOfRank

inline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string)
{
  if (!condition)
  {
    if(Eigen::g_test_level>0)
      std::cerr << "WARNING: ";
    std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")"
      << std::endl << "    " << condition_as_string << std::endl;
    std::cerr << "Stack:\n";
    const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
    for(int i=test_stack_size-1; i>=0; --i)
      std::cerr << "  - " << Eigen::g_test_stack[i] << "\n";
    std::cerr << "\n";
    if(Eigen::g_test_level==0)
      abort();
  }
}

#define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a))

#define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a >= b))
#define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a <= b))


#define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true))
#define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false))
#define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b))
#define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))

#define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))

#define STATIC_CHECK(COND) EIGEN_STATIC_ASSERT( (COND) , EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT )

#define CALL_SUBTEST(FUNC) do { \
    g_test_stack.push_back(EIGEN_MAKESTRING(FUNC)); \
    FUNC; \
    g_test_stack.pop_back(); \
  } while (0)


namespace Eigen {

template<typename T1,typename T2>
typename internal::enable_if<internal::is_same<T1,T2>::value,bool>::type
is_same_type(const T1&, const T2&)
{
  return true;
}

template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
template<> inline float test_precision<float>() { return 1e-3f; }
template<> inline double test_precision<double>() { return 1e-6; }
template<> inline long double test_precision<long double>() { return 1e-6l; }
template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
template<> inline long double test_precision<std::complex<long double> >() { return test_precision<long double>(); }

#define EIGEN_TEST_SCALAR_TEST_OVERLOAD(TYPE)                             \
  inline bool test_isApprox(TYPE a, TYPE b)                               \
  { return internal::isApprox(a, b, test_precision<TYPE>()); }            \
  inline bool test_isMuchSmallerThan(TYPE a, TYPE b)                      \
  { return internal::isMuchSmallerThan(a, b, test_precision<TYPE>()); }   \
  inline bool test_isApproxOrLessThan(TYPE a, TYPE b)                     \
  { return internal::isApproxOrLessThan(a, b, test_precision<TYPE>()); }

EIGEN_TEST_SCALAR_TEST_OVERLOAD(short)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned short)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(int)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned int)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(long)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long)
#if EIGEN_HAS_CXX11
EIGEN_TEST_SCALAR_TEST_OVERLOAD(long long)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long long)
#endif
EIGEN_TEST_SCALAR_TEST_OVERLOAD(float)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(double)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(half)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(bfloat16)

#undef EIGEN_TEST_SCALAR_TEST_OVERLOAD

#ifndef EIGEN_TEST_NO_COMPLEX
inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
{ return internal::isApprox(a, b, test_precision<std::complex<float> >()); }
inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }

inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
{ return internal::isApprox(a, b, test_precision<std::complex<double> >()); }
inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }

#ifndef EIGEN_TEST_NO_LONGDOUBLE
inline bool test_isApprox(const std::complex<long double>& a, const std::complex<long double>& b)
{ return internal::isApprox(a, b, test_precision<std::complex<long double> >()); }
inline bool test_isMuchSmallerThan(const std::complex<long double>& a, const std::complex<long double>& b)
{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<long double> >()); }
#endif
#endif

#ifndef EIGEN_TEST_NO_LONGDOUBLE
inline bool test_isApprox(const long double& a, const long double& b)
{
    bool ret = internal::isApprox(a, b, test_precision<long double>());
    if (!ret) std::cerr
        << std::endl << "    actual   = " << a
        << std::endl << "    expected = " << b << std::endl << std::endl;
    return ret;
}

inline bool test_isMuchSmallerThan(const long double& a, const long double& b)
{ return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }
inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
{ return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
#endif // EIGEN_TEST_NO_LONGDOUBLE

// test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.
template<typename T1,typename T2>
typename NumTraits<typename T1::RealScalar>::NonInteger test_relative_error(const EigenBase<T1> &a, const EigenBase<T2> &b)
{
  using std::sqrt;
  typedef typename NumTraits<typename T1::RealScalar>::NonInteger RealScalar;
  typename internal::nested_eval<T1,2>::type ea(a.derived());
  typename internal::nested_eval<T2,2>::type eb(b.derived());
  return sqrt(RealScalar((ea-eb).cwiseAbs2().sum()) / RealScalar((std::min)(eb.cwiseAbs2().sum(),ea.cwiseAbs2().sum())));
}

template<typename T1,typename T2>
typename T1::RealScalar test_relative_error(const T1 &a, const T2 &b, const typename T1::Coefficients* = 0)
{
  return test_relative_error(a.coeffs(), b.coeffs());
}

template<typename T1,typename T2>
typename T1::Scalar test_relative_error(const T1 &a, const T2 &b, const typename T1::MatrixType* = 0)
{
  return test_relative_error(a.matrix(), b.matrix());
}

template<typename S, int D>
S test_relative_error(const Translation<S,D> &a, const Translation<S,D> &b)
{
  return test_relative_error(a.vector(), b.vector());
}

template <typename S, int D, int O>
S test_relative_error(const ParametrizedLine<S,D,O> &a, const ParametrizedLine<S,D,O> &b)
{
  return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin()));
}

template <typename S, int D>
S test_relative_error(const AlignedBox<S,D> &a, const AlignedBox<S,D> &b)
{
  return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)()));
}

template<typename Derived> class SparseMatrixBase;
template<typename T1,typename T2>
typename T1::RealScalar test_relative_error(const MatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
{
  return test_relative_error(a,b.toDense());
}

template<typename Derived> class SparseMatrixBase;
template<typename T1,typename T2>
typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const MatrixBase<T2> &b)
{
  return test_relative_error(a.toDense(),b);
}

template<typename Derived> class SparseMatrixBase;
template<typename T1,typename T2>
typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
{
  return test_relative_error(a.toDense(),b.toDense());
}

template<typename T1,typename T2>
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)
{
  typedef typename NumTraits<typename NumTraits<T1>::Real>::NonInteger RealScalar;
  return numext::sqrt(RealScalar(numext::abs2(a-b))/(numext::mini)(RealScalar(numext::abs2(a)),RealScalar(numext::abs2(b))));
}

template<typename T>
T test_relative_error(const Rotation2D<T> &a, const Rotation2D<T> &b)
{
  return test_relative_error(a.angle(), b.angle());
}

template<typename T>
T test_relative_error(const AngleAxis<T> &a, const AngleAxis<T> &b)
{
  return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis()));
}

template<typename Type1, typename Type2>
inline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only
{
  return a.isApprox(b, test_precision<typename Type1::Scalar>());
}

// get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions
template<typename T>
typename NumTraits<typename T::Scalar>::Real get_test_precision(const T&, const typename T::Scalar* = 0)
{
  return test_precision<typename NumTraits<typename T::Scalar>::Real>();
}

template<typename T>
typename NumTraits<T>::Real get_test_precision(const T&,typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0)
{
  return test_precision<typename NumTraits<T>::Real>();
}

// verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails.
template<typename Type1, typename Type2>
inline bool verifyIsApprox(const Type1& a, const Type2& b)
{
  bool ret = test_isApprox(a,b);
  if(!ret)
  {
    std::cerr << "Difference too large wrt tolerance " << get_test_precision(a)  << ", relative error is: " << test_relative_error(a,b) << std::endl;
  }
  return ret;
}

// The idea behind this function is to compare the two scalars a and b where
// the scalar ref is a hint about the expected order of magnitude of a and b.
// WARNING: the scalar a and b must be positive
// Therefore, if for some reason a and b are very small compared to ref,
// we won't issue a false negative.
// This test could be: abs(a-b) <= eps * ref
// However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.
template<typename Scalar,typename ScalarRef>
inline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)
{
  return test_isApprox(a+ref, b+ref);
}

template<typename Derived1, typename Derived2>
inline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,
                                   const MatrixBase<Derived2>& m2)
{
  return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
}

template<typename Derived>
inline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,
                                   const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
{
  return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
}

template<typename Derived>
inline bool test_isUnitary(const MatrixBase<Derived>& m)
{
  return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());
}

// Forward declaration to avoid ICC warning
template<typename T, typename U>
bool test_is_equal(const T& actual, const U& expected, bool expect_equal=true);

template<typename T, typename U>
bool test_is_equal(const T& actual, const U& expected, bool expect_equal)
{
    if ((actual==expected) == expect_equal)
        return true;
    // false:
    std::cerr
        << "\n    actual   = " << actual
        << "\n    expected " << (expect_equal ? "= " : "!=") << expected << "\n\n";
    return false;
}

// Forward declaration to avoid ICC warning
template<typename MatrixType>
void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
/**
 * Creates a random partial isometry matrix of given rank.
 *
 * A partial isometry is a matrix all of whose singular values are either 0 or 1.
 * This is very useful to test rank-revealing algorithms.
 *
 * @tparam MatrixType type of random partial isometry matrix
 * @param desired_rank rank requested for the random partial isometry matrix
 * @param rows row dimension of requested random partial isometry matrix
 * @param cols column dimension of requested random partial isometry matrix
 * @param m random partial isometry matrix
 */
template<typename MatrixType>
void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
{
  typedef typename internal::traits<MatrixType>::Scalar Scalar;
  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };

  typedef Matrix<Scalar, Dynamic, 1> VectorType;
  typedef Matrix<Scalar, Rows, Rows> MatrixAType;
  typedef Matrix<Scalar, Cols, Cols> MatrixBType;

  if(desired_rank == 0)
  {
    m.setZero(rows,cols);
    return;
  }

  if(desired_rank == 1)
  {
    // here we normalize the vectors to get a partial isometry
    m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
    return;
  }

  MatrixAType a = MatrixAType::Random(rows,rows);
  MatrixType d = MatrixType::Identity(rows,cols);
  MatrixBType  b = MatrixBType::Random(cols,cols);

  // set the diagonal such that only desired_rank non-zero entries reamain
  const Index diag_size = (std::min)(d.rows(),d.cols());
  if(diag_size != desired_rank)
    d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);

  HouseholderQR<MatrixAType> qra(a);
  HouseholderQR<MatrixBType> qrb(b);
  m = qra.householderQ() * d * qrb.householderQ();
}

// Forward declaration to avoid ICC warning
template<typename PermutationVectorType>
void randomPermutationVector(PermutationVectorType& v, Index size);
/**
 * Generate random permutation vector.
 *
 * @tparam PermutationVectorType type of vector used to store permutation
 * @param v permutation vector
 * @param size length of permutation vector
 */
template<typename PermutationVectorType>
void randomPermutationVector(PermutationVectorType& v, Index size)
{
  typedef typename PermutationVectorType::Scalar Scalar;
  v.resize(size);
  for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
  if(size == 1) return;
  for(Index n = 0; n < 3 * size; ++n)
  {
    Index i = internal::random<Index>(0, size-1);
    Index j;
    do j = internal::random<Index>(0, size-1); while(j==i);
    std::swap(v(i), v(j));
  }
}

/**
 * Check if number is "not a number" (NaN).
 *
 * @tparam T input type
 * @param x input value
 * @return true, if input value is "not a number" (NaN)
 */
template<typename T> bool isNotNaN(const T& x)
{
  return x==x;
}

/**
 * Check if number is plus infinity.
 *
 * @tparam T input type
 * @param x input value
 * @return true, if input value is plus infinity
 */
template<typename T> bool isPlusInf(const T& x)
{
  return x > NumTraits<T>::highest();
}

/**
 * Check if number is minus infinity.
 *
 * @tparam T input type
 * @param x input value
 * @return true, if input value is minus infinity
 */
template<typename T> bool isMinusInf(const T& x)
{
  return x < NumTraits<T>::lowest();
}

} // end namespace Eigen

template<typename T> struct GetDifferentType;

template<> struct GetDifferentType<float> { typedef double type; };
template<> struct GetDifferentType<double> { typedef float type; };
template<typename T> struct GetDifferentType<std::complex<T> >
{ typedef std::complex<typename GetDifferentType<T>::type> type; };

// Forward declaration to avoid ICC warning
template<typename T> std::string type_name();
template<typename T> std::string type_name()                    { return "other"; }
template<> std::string type_name<float>()                       { return "float"; }
template<> std::string type_name<double>()                      { return "double"; }
template<> std::string type_name<long double>()                 { return "long double"; }
template<> std::string type_name<int>()                         { return "int"; }
template<> std::string type_name<std::complex<float> >()        { return "complex<float>"; }
template<> std::string type_name<std::complex<double> >()       { return "complex<double>"; }
template<> std::string type_name<std::complex<long double> >()  { return "complex<long double>"; }
template<> std::string type_name<std::complex<int> >()          { return "complex<int>"; }

using namespace Eigen;

/**
 * Set number of repetitions for unit test from input string.
 *
 * @param str input string
 */
inline void set_repeat_from_string(const char *str)
{
  errno = 0;
  g_repeat = int(strtoul(str, 0, 10));
  if(errno || g_repeat <= 0)
  {
    std::cout << "Invalid repeat value " << str << std::endl;
    exit(EXIT_FAILURE);
  }
  g_has_set_repeat = true;
}

/**
 * Set seed for randomized unit tests from input string.
 *
 * @param str input string
 */
inline void set_seed_from_string(const char *str)
{
  errno = 0;
  g_seed = int(strtoul(str, 0, 10));
  if(errno || g_seed == 0)
  {
    std::cout << "Invalid seed value " << str << std::endl;
    exit(EXIT_FAILURE);
  }
  g_has_set_seed = true;
}

int main(int argc, char *argv[])
{
    g_has_set_repeat = false;
    g_has_set_seed = false;
    bool need_help = false;

    for(int i = 1; i < argc; i++)
    {
      if(argv[i][0] == 'r')
      {
        if(g_has_set_repeat)
        {
          std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
          return 1;
        }
        set_repeat_from_string(argv[i]+1);
      }
      else if(argv[i][0] == 's')
      {
        if(g_has_set_seed)
        {
          std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
          return 1;
        }
         set_seed_from_string(argv[i]+1);
      }
      else
      {
        need_help = true;
      }
    }

    if(need_help)
    {
      std::cout << "This test application takes the following optional arguments:" << std::endl;
      std::cout << "  rN     Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
      std::cout << "  sN     Use N as seed for random numbers (default: based on current time)" << std::endl;
      std::cout << std::endl;
      std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl;
      std::cout << "will be used as default values for these parameters." << std::endl;
      return 1;
    }

    char *env_EIGEN_REPEAT = getenv("EIGEN_REPEAT");
    if(!g_has_set_repeat && env_EIGEN_REPEAT)
      set_repeat_from_string(env_EIGEN_REPEAT);
    char *env_EIGEN_SEED = getenv("EIGEN_SEED");
    if(!g_has_set_seed && env_EIGEN_SEED)
      set_seed_from_string(env_EIGEN_SEED);

    if(!g_has_set_seed) g_seed = (unsigned int) time(NULL);
    if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;

    std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
    std::stringstream ss;
    ss << "Seed: " << g_seed;
    g_test_stack.push_back(ss.str());
    srand(g_seed);
    std::cout << "Repeating each test " << g_repeat << " times" << std::endl;

    VERIFY(EigenTest::all().size()>0);

    for(std::size_t i=0; i<EigenTest::all().size(); ++i)
    {
      const EigenTest& current_test = *EigenTest::all()[i];
      Eigen::g_test_stack.push_back(current_test.name());
      current_test();
      Eigen::g_test_stack.pop_back();
    }

    return 0;
}

// These warning are disabled here such that they are still ON when parsing Eigen's header files.
#if defined __INTEL_COMPILER
  // remark #383: value copied to temporary, reference to temporary used
  //  -> 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>
  // remark #1418: external function definition with no prior declaration
  //  -> this warning is raised for all our test functions. Declaring them static would fix the issue.
  // warning #279: controlling expression is constant
  // remark #1572: floating-point equality and inequality comparisons are unreliable
  #pragma warning disable 279 383 1418 1572
#endif

#ifdef _MSC_VER
  // 4503 - decorated name length exceeded, name was truncated
  #pragma warning( disable : 4503)
#endif