cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
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main.h (33109B)


      1 
      2 // This file is part of Eigen, a lightweight C++ template library
      3 // for linear algebra.
      4 //
      5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
      6 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
      7 //
      8 // This Source Code Form is subject to the terms of the Mozilla
      9 // Public License v. 2.0. If a copy of the MPL was not distributed
     10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     11 
     12 #include <cstdlib>
     13 #include <cerrno>
     14 #include <ctime>
     15 #include <iostream>
     16 #include <fstream>
     17 #include <string>
     18 #include <sstream>
     19 #include <vector>
     20 #include <typeinfo>
     21 #include <functional>
     22 
     23 // The following includes of STL headers have to be done _before_ the
     24 // definition of macros min() and max().  The reason is that many STL
     25 // implementations will not work properly as the min and max symbols collide
     26 // with the STL functions std:min() and std::max().  The STL headers may check
     27 // for the macro definition of min/max and issue a warning or undefine the
     28 // macros.
     29 //
     30 // Still, Windows defines min() and max() in windef.h as part of the regular
     31 // Windows system interfaces and many other Windows APIs depend on these
     32 // macros being available.  To prevent the macro expansion of min/max and to
     33 // make Eigen compatible with the Windows environment all function calls of
     34 // std::min() and std::max() have to be written with parenthesis around the
     35 // function name.
     36 //
     37 // All STL headers used by Eigen should be included here.  Because main.h is
     38 // included before any Eigen header and because the STL headers are guarded
     39 // against multiple inclusions, no STL header will see our own min/max macro
     40 // definitions.
     41 #include <limits>
     42 #include <algorithm>
     43 // Disable ICC's std::complex operator specializations so we can use our own.
     44 #define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
     45 #include <complex>
     46 #include <deque>
     47 #include <queue>
     48 #include <cassert>
     49 #include <list>
     50 #if __cplusplus >= 201103L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201103L)
     51 #include <random>
     52 #include <chrono>
     53 #ifdef EIGEN_USE_THREADS
     54 #include <future>
     55 #endif
     56 #endif
     57 
     58 // Same for cuda_fp16.h
     59 #if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
     60   // Means the compiler is either nvcc or clang with CUDA enabled
     61   #define EIGEN_CUDACC __CUDACC__
     62 #endif
     63 #if defined(EIGEN_CUDACC)
     64 #include <cuda.h>
     65   #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
     66 #else
     67   #define EIGEN_CUDA_SDK_VER 0
     68 #endif
     69 #if EIGEN_CUDA_SDK_VER >= 70500
     70 #include <cuda_fp16.h>
     71 #endif
     72 
     73 // To test that all calls from Eigen code to std::min() and std::max() are
     74 // protected by parenthesis against macro expansion, the min()/max() macros
     75 // are defined here and any not-parenthesized min/max call will cause a
     76 // compiler error.
     77 #if !defined(__HIPCC__) && !defined(EIGEN_USE_SYCL)
     78   //
     79   // HIP header files include the following files
     80   //  <thread>
     81   //  <regex>
     82   //  <unordered_map>
     83   // which seem to contain not-parenthesized calls to "max"/"min", triggering the following check and causing the compile to fail
     84   //
     85   // Including those header files before the following macro definition for "min" / "max", only partially resolves the issue
     86   // This is because other HIP header files also define "isnan" / "isinf" / "isfinite" functions, which are needed in other
     87   // headers.
     88   //
     89   // So instead choosing to simply disable this check for HIP
     90   //
     91   #define min(A,B) please_protect_your_min_with_parentheses
     92   #define max(A,B) please_protect_your_max_with_parentheses
     93   #define isnan(X) please_protect_your_isnan_with_parentheses
     94   #define isinf(X) please_protect_your_isinf_with_parentheses
     95   #define isfinite(X) please_protect_your_isfinite_with_parentheses
     96 #endif
     97 
     98 
     99 // test possible conflicts
    100 struct real {};
    101 struct imag {};
    102 
    103 #ifdef M_PI
    104 #undef M_PI
    105 #endif
    106 #define M_PI please_use_EIGEN_PI_instead_of_M_PI
    107 
    108 #define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes
    109 // B0 is defined in POSIX header termios.h
    110 #define B0 FORBIDDEN_IDENTIFIER
    111 // `I` may be defined by complex.h:
    112 #define I  FORBIDDEN_IDENTIFIER
    113 
    114 // Unit tests calling Eigen's blas library must preserve the default blocking size
    115 // to avoid troubles.
    116 #ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
    117 #define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
    118 #endif
    119 
    120 // shuts down ICC's remark #593: variable "XXX" was set but never used
    121 #define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X)
    122 
    123 #ifdef TEST_ENABLE_TEMPORARY_TRACKING
    124 
    125 static long int nb_temporaries;
    126 static long int nb_temporaries_on_assert = -1;
    127 
    128 inline void on_temporary_creation(long int size) {
    129   // here's a great place to set a breakpoint when debugging failures in this test!
    130   if(size!=0) nb_temporaries++;
    131   if(nb_temporaries_on_assert>0) assert(nb_temporaries<nb_temporaries_on_assert);
    132 }
    133 
    134 #define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { on_temporary_creation(size); }
    135 
    136 #define VERIFY_EVALUATION_COUNT(XPR,N) {\
    137     nb_temporaries = 0; \
    138     XPR; \
    139     if(nb_temporaries!=(N)) { std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; }\
    140     VERIFY( (#XPR) && nb_temporaries==(N) ); \
    141   }
    142 
    143 #endif
    144 
    145 #include "split_test_helper.h"
    146 
    147 #ifdef NDEBUG
    148 #undef NDEBUG
    149 #endif
    150 
    151 // On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.
    152 #ifndef DEBUG
    153 #define DEBUG
    154 #endif
    155 
    156 // bounds integer values for AltiVec
    157 #if defined(__ALTIVEC__) || defined(__VSX__)
    158 #define EIGEN_MAKING_DOCS
    159 #endif
    160 
    161 #define DEFAULT_REPEAT 10
    162 
    163 namespace Eigen
    164 {
    165   static std::vector<std::string> g_test_stack;
    166   // level == 0 <=> abort if test fail
    167   // level >= 1 <=> warning message to std::cerr if test fail
    168   static int g_test_level = 0;
    169   static int g_repeat = 1;
    170   static unsigned int g_seed = 0;
    171   static bool g_has_set_repeat = false, g_has_set_seed = false;
    172 
    173   class EigenTest
    174   {
    175   public:
    176     EigenTest() : m_func(0) {}
    177     EigenTest(const char* a_name, void (*func)(void))
    178       : m_name(a_name), m_func(func)
    179     {
    180       get_registered_tests().push_back(this);
    181     }
    182     const std::string& name() const { return m_name; }
    183     void operator()() const { m_func(); }
    184 
    185     static const std::vector<EigenTest*>& all() { return get_registered_tests(); }
    186   protected:
    187     static std::vector<EigenTest*>& get_registered_tests()
    188     {
    189       static std::vector<EigenTest*>* ms_registered_tests = new std::vector<EigenTest*>();
    190       return *ms_registered_tests;
    191     }
    192     std::string m_name;
    193     void (*m_func)(void);
    194   };
    195 
    196   // Declare and register a test, e.g.:
    197   //    EIGEN_DECLARE_TEST(mytest) { ... }
    198   // will create a function:
    199   //    void test_mytest() { ... }
    200   // that will be automatically called.
    201   #define EIGEN_DECLARE_TEST(X) \
    202     void EIGEN_CAT(test_,X) (); \
    203     static EigenTest EIGEN_CAT(test_handler_,X) (EIGEN_MAKESTRING(X), & EIGEN_CAT(test_,X)); \
    204     void EIGEN_CAT(test_,X) ()
    205 }
    206 
    207 #define TRACK std::cerr << __FILE__ << " " << __LINE__ << std::endl
    208 // #define TRACK while()
    209 
    210 #define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, "  ", "\n", "", "", "", "")
    211 
    212 #if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(__HIP_DEVICE_COMPILE__) && !defined(__SYCL_DEVICE_ONLY__)
    213   #define EIGEN_EXCEPTIONS
    214 #endif
    215 
    216 #ifndef EIGEN_NO_ASSERTION_CHECKING
    217 
    218   namespace Eigen
    219   {
    220     static const bool should_raise_an_assert = false;
    221 
    222     // Used to avoid to raise two exceptions at a time in which
    223     // case the exception is not properly caught.
    224     // This may happen when a second exceptions is triggered in a destructor.
    225     static bool no_more_assert = false;
    226     static bool report_on_cerr_on_assert_failure = true;
    227 
    228     struct eigen_assert_exception
    229     {
    230       eigen_assert_exception(void) {}
    231       ~eigen_assert_exception() { Eigen::no_more_assert = false; }
    232     };
    233 
    234     struct eigen_static_assert_exception
    235     {
    236       eigen_static_assert_exception(void) {}
    237       ~eigen_static_assert_exception() { Eigen::no_more_assert = false; }
    238     };
    239   }
    240   // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while
    241   // one should have been, then the list of executed assertions is printed out.
    242   //
    243   // EIGEN_DEBUG_ASSERTS is not enabled by default as it
    244   // significantly increases the compilation time
    245   // and might even introduce side effects that would hide
    246   // some memory errors.
    247   #ifdef EIGEN_DEBUG_ASSERTS
    248 
    249     namespace Eigen
    250     {
    251       namespace internal
    252       {
    253         static bool push_assert = false;
    254       }
    255       static std::vector<std::string> eigen_assert_list;
    256     }
    257     #define eigen_assert(a)                       \
    258       if( (!(a)) && (!no_more_assert) )     \
    259       { \
    260         if(report_on_cerr_on_assert_failure) \
    261           std::cerr <<  #a << " " __FILE__ << "(" << __LINE__ << ")\n"; \
    262         Eigen::no_more_assert = true;       \
    263         EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
    264       }                                     \
    265       else if (Eigen::internal::push_assert)       \
    266       {                                     \
    267         eigen_assert_list.push_back(std::string(EIGEN_MAKESTRING(__FILE__) " (" EIGEN_MAKESTRING(__LINE__) ") : " #a) ); \
    268       }
    269 
    270     #ifdef EIGEN_EXCEPTIONS
    271     #define VERIFY_RAISES_ASSERT(a)                                                   \
    272       {                                                                               \
    273         Eigen::no_more_assert = false;                                                \
    274         Eigen::eigen_assert_list.clear();                                             \
    275         Eigen::internal::push_assert = true;                                          \
    276         Eigen::report_on_cerr_on_assert_failure = false;                              \
    277         try {                                                                         \
    278           a;                                                                          \
    279           std::cerr << "One of the following asserts should have been triggered:\n";  \
    280           for (uint ai=0 ; ai<eigen_assert_list.size() ; ++ai)                        \
    281             std::cerr << "  " << eigen_assert_list[ai] << "\n";                       \
    282           VERIFY(Eigen::should_raise_an_assert && # a);                               \
    283         } catch (Eigen::eigen_assert_exception) {                                     \
    284           Eigen::internal::push_assert = false; VERIFY(true);                         \
    285         }                                                                             \
    286         Eigen::report_on_cerr_on_assert_failure = true;                               \
    287         Eigen::internal::push_assert = false;                                         \
    288       }
    289     #endif //EIGEN_EXCEPTIONS
    290 
    291   #elif !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY) // EIGEN_DEBUG_ASSERTS
    292     // see bug 89. The copy_bool here is working around a bug in gcc <= 4.3
    293     #define eigen_assert(a) \
    294       if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\
    295       {                                       \
    296         Eigen::no_more_assert = true;         \
    297         if(report_on_cerr_on_assert_failure)  \
    298           eigen_plain_assert(a);              \
    299         else                                  \
    300           EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
    301       }
    302 
    303     #ifdef EIGEN_EXCEPTIONS
    304       #define VERIFY_RAISES_ASSERT(a) {                           \
    305         Eigen::no_more_assert = false;                            \
    306         Eigen::report_on_cerr_on_assert_failure = false;          \
    307         try {                                                     \
    308           a;                                                      \
    309           VERIFY(Eigen::should_raise_an_assert && # a);           \
    310         }                                                         \
    311         catch (Eigen::eigen_assert_exception&) { VERIFY(true); }  \
    312         Eigen::report_on_cerr_on_assert_failure = true;           \
    313       }
    314     #endif // EIGEN_EXCEPTIONS
    315   #endif // EIGEN_DEBUG_ASSERTS
    316 
    317   #if defined(TEST_CHECK_STATIC_ASSERTIONS) && defined(EIGEN_EXCEPTIONS)
    318     #define EIGEN_STATIC_ASSERT(a,MSG) \
    319       if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\
    320       {                                       \
    321         Eigen::no_more_assert = true;         \
    322         if(report_on_cerr_on_assert_failure)  \
    323           eigen_plain_assert((a) && #MSG);      \
    324         else                                  \
    325           EIGEN_THROW_X(Eigen::eigen_static_assert_exception()); \
    326       }
    327     #define VERIFY_RAISES_STATIC_ASSERT(a) {                    \
    328       Eigen::no_more_assert = false;                            \
    329       Eigen::report_on_cerr_on_assert_failure = false;          \
    330       try {                                                     \
    331         a;                                                      \
    332         VERIFY(Eigen::should_raise_an_assert && # a);           \
    333       }                                                         \
    334       catch (Eigen::eigen_static_assert_exception&) { VERIFY(true); }  \
    335       Eigen::report_on_cerr_on_assert_failure = true;           \
    336     }
    337   #endif // TEST_CHECK_STATIC_ASSERTIONS
    338 
    339 #ifndef VERIFY_RAISES_ASSERT
    340   #define VERIFY_RAISES_ASSERT(a) \
    341     std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled\n";
    342 #endif
    343 #ifndef VERIFY_RAISES_STATIC_ASSERT
    344   #define VERIFY_RAISES_STATIC_ASSERT(a) \
    345     std::cout << "Can't VERIFY_RAISES_STATIC_ASSERT( " #a " ) with exceptions disabled\n";
    346 #endif
    347 
    348   #if !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY)
    349   #define EIGEN_USE_CUSTOM_ASSERT
    350   #endif
    351 
    352 #else // EIGEN_NO_ASSERTION_CHECKING
    353 
    354   #define VERIFY_RAISES_ASSERT(a) {}
    355   #define VERIFY_RAISES_STATIC_ASSERT(a) {}
    356 
    357 #endif // EIGEN_NO_ASSERTION_CHECKING
    358 
    359 #define EIGEN_INTERNAL_DEBUGGING
    360 #include <Eigen/QR> // required for createRandomPIMatrixOfRank
    361 
    362 inline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string)
    363 {
    364   if (!condition)
    365   {
    366     if(Eigen::g_test_level>0)
    367       std::cerr << "WARNING: ";
    368     std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")"
    369       << std::endl << "    " << condition_as_string << std::endl;
    370     std::cerr << "Stack:\n";
    371     const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
    372     for(int i=test_stack_size-1; i>=0; --i)
    373       std::cerr << "  - " << Eigen::g_test_stack[i] << "\n";
    374     std::cerr << "\n";
    375     if(Eigen::g_test_level==0)
    376       abort();
    377   }
    378 }
    379 
    380 #define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a))
    381 
    382 #define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a >= b))
    383 #define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a <= b))
    384 
    385 
    386 #define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true))
    387 #define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false))
    388 #define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b))
    389 #define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
    390 #define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
    391 #define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
    392 #define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
    393 #define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))
    394 
    395 #define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))
    396 
    397 #define STATIC_CHECK(COND) EIGEN_STATIC_ASSERT( (COND) , EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT )
    398 
    399 #define CALL_SUBTEST(FUNC) do { \
    400     g_test_stack.push_back(EIGEN_MAKESTRING(FUNC)); \
    401     FUNC; \
    402     g_test_stack.pop_back(); \
    403   } while (0)
    404 
    405 
    406 namespace Eigen {
    407 
    408 template<typename T1,typename T2>
    409 typename internal::enable_if<internal::is_same<T1,T2>::value,bool>::type
    410 is_same_type(const T1&, const T2&)
    411 {
    412   return true;
    413 }
    414 
    415 template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
    416 template<> inline float test_precision<float>() { return 1e-3f; }
    417 template<> inline double test_precision<double>() { return 1e-6; }
    418 template<> inline long double test_precision<long double>() { return 1e-6l; }
    419 template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
    420 template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
    421 template<> inline long double test_precision<std::complex<long double> >() { return test_precision<long double>(); }
    422 
    423 #define EIGEN_TEST_SCALAR_TEST_OVERLOAD(TYPE)                             \
    424   inline bool test_isApprox(TYPE a, TYPE b)                               \
    425   { return internal::isApprox(a, b, test_precision<TYPE>()); }            \
    426   inline bool test_isMuchSmallerThan(TYPE a, TYPE b)                      \
    427   { return internal::isMuchSmallerThan(a, b, test_precision<TYPE>()); }   \
    428   inline bool test_isApproxOrLessThan(TYPE a, TYPE b)                     \
    429   { return internal::isApproxOrLessThan(a, b, test_precision<TYPE>()); }
    430 
    431 EIGEN_TEST_SCALAR_TEST_OVERLOAD(short)
    432 EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned short)
    433 EIGEN_TEST_SCALAR_TEST_OVERLOAD(int)
    434 EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned int)
    435 EIGEN_TEST_SCALAR_TEST_OVERLOAD(long)
    436 EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long)
    437 #if EIGEN_HAS_CXX11
    438 EIGEN_TEST_SCALAR_TEST_OVERLOAD(long long)
    439 EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long long)
    440 #endif
    441 EIGEN_TEST_SCALAR_TEST_OVERLOAD(float)
    442 EIGEN_TEST_SCALAR_TEST_OVERLOAD(double)
    443 EIGEN_TEST_SCALAR_TEST_OVERLOAD(half)
    444 EIGEN_TEST_SCALAR_TEST_OVERLOAD(bfloat16)
    445 
    446 #undef EIGEN_TEST_SCALAR_TEST_OVERLOAD
    447 
    448 #ifndef EIGEN_TEST_NO_COMPLEX
    449 inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
    450 { return internal::isApprox(a, b, test_precision<std::complex<float> >()); }
    451 inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
    452 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
    453 
    454 inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
    455 { return internal::isApprox(a, b, test_precision<std::complex<double> >()); }
    456 inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
    457 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
    458 
    459 #ifndef EIGEN_TEST_NO_LONGDOUBLE
    460 inline bool test_isApprox(const std::complex<long double>& a, const std::complex<long double>& b)
    461 { return internal::isApprox(a, b, test_precision<std::complex<long double> >()); }
    462 inline bool test_isMuchSmallerThan(const std::complex<long double>& a, const std::complex<long double>& b)
    463 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<long double> >()); }
    464 #endif
    465 #endif
    466 
    467 #ifndef EIGEN_TEST_NO_LONGDOUBLE
    468 inline bool test_isApprox(const long double& a, const long double& b)
    469 {
    470     bool ret = internal::isApprox(a, b, test_precision<long double>());
    471     if (!ret) std::cerr
    472         << std::endl << "    actual   = " << a
    473         << std::endl << "    expected = " << b << std::endl << std::endl;
    474     return ret;
    475 }
    476 
    477 inline bool test_isMuchSmallerThan(const long double& a, const long double& b)
    478 { return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }
    479 inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
    480 { return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
    481 #endif // EIGEN_TEST_NO_LONGDOUBLE
    482 
    483 // test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.
    484 template<typename T1,typename T2>
    485 typename NumTraits<typename T1::RealScalar>::NonInteger test_relative_error(const EigenBase<T1> &a, const EigenBase<T2> &b)
    486 {
    487   using std::sqrt;
    488   typedef typename NumTraits<typename T1::RealScalar>::NonInteger RealScalar;
    489   typename internal::nested_eval<T1,2>::type ea(a.derived());
    490   typename internal::nested_eval<T2,2>::type eb(b.derived());
    491   return sqrt(RealScalar((ea-eb).cwiseAbs2().sum()) / RealScalar((std::min)(eb.cwiseAbs2().sum(),ea.cwiseAbs2().sum())));
    492 }
    493 
    494 template<typename T1,typename T2>
    495 typename T1::RealScalar test_relative_error(const T1 &a, const T2 &b, const typename T1::Coefficients* = 0)
    496 {
    497   return test_relative_error(a.coeffs(), b.coeffs());
    498 }
    499 
    500 template<typename T1,typename T2>
    501 typename T1::Scalar test_relative_error(const T1 &a, const T2 &b, const typename T1::MatrixType* = 0)
    502 {
    503   return test_relative_error(a.matrix(), b.matrix());
    504 }
    505 
    506 template<typename S, int D>
    507 S test_relative_error(const Translation<S,D> &a, const Translation<S,D> &b)
    508 {
    509   return test_relative_error(a.vector(), b.vector());
    510 }
    511 
    512 template <typename S, int D, int O>
    513 S test_relative_error(const ParametrizedLine<S,D,O> &a, const ParametrizedLine<S,D,O> &b)
    514 {
    515   return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin()));
    516 }
    517 
    518 template <typename S, int D>
    519 S test_relative_error(const AlignedBox<S,D> &a, const AlignedBox<S,D> &b)
    520 {
    521   return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)()));
    522 }
    523 
    524 template<typename Derived> class SparseMatrixBase;
    525 template<typename T1,typename T2>
    526 typename T1::RealScalar test_relative_error(const MatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
    527 {
    528   return test_relative_error(a,b.toDense());
    529 }
    530 
    531 template<typename Derived> class SparseMatrixBase;
    532 template<typename T1,typename T2>
    533 typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const MatrixBase<T2> &b)
    534 {
    535   return test_relative_error(a.toDense(),b);
    536 }
    537 
    538 template<typename Derived> class SparseMatrixBase;
    539 template<typename T1,typename T2>
    540 typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
    541 {
    542   return test_relative_error(a.toDense(),b.toDense());
    543 }
    544 
    545 template<typename T1,typename T2>
    546 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)
    547 {
    548   typedef typename NumTraits<typename NumTraits<T1>::Real>::NonInteger RealScalar;
    549   return numext::sqrt(RealScalar(numext::abs2(a-b))/(numext::mini)(RealScalar(numext::abs2(a)),RealScalar(numext::abs2(b))));
    550 }
    551 
    552 template<typename T>
    553 T test_relative_error(const Rotation2D<T> &a, const Rotation2D<T> &b)
    554 {
    555   return test_relative_error(a.angle(), b.angle());
    556 }
    557 
    558 template<typename T>
    559 T test_relative_error(const AngleAxis<T> &a, const AngleAxis<T> &b)
    560 {
    561   return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis()));
    562 }
    563 
    564 template<typename Type1, typename Type2>
    565 inline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only
    566 {
    567   return a.isApprox(b, test_precision<typename Type1::Scalar>());
    568 }
    569 
    570 // get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions
    571 template<typename T>
    572 typename NumTraits<typename T::Scalar>::Real get_test_precision(const T&, const typename T::Scalar* = 0)
    573 {
    574   return test_precision<typename NumTraits<typename T::Scalar>::Real>();
    575 }
    576 
    577 template<typename T>
    578 typename NumTraits<T>::Real get_test_precision(const T&,typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0)
    579 {
    580   return test_precision<typename NumTraits<T>::Real>();
    581 }
    582 
    583 // verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails.
    584 template<typename Type1, typename Type2>
    585 inline bool verifyIsApprox(const Type1& a, const Type2& b)
    586 {
    587   bool ret = test_isApprox(a,b);
    588   if(!ret)
    589   {
    590     std::cerr << "Difference too large wrt tolerance " << get_test_precision(a)  << ", relative error is: " << test_relative_error(a,b) << std::endl;
    591   }
    592   return ret;
    593 }
    594 
    595 // The idea behind this function is to compare the two scalars a and b where
    596 // the scalar ref is a hint about the expected order of magnitude of a and b.
    597 // WARNING: the scalar a and b must be positive
    598 // Therefore, if for some reason a and b are very small compared to ref,
    599 // we won't issue a false negative.
    600 // This test could be: abs(a-b) <= eps * ref
    601 // However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.
    602 template<typename Scalar,typename ScalarRef>
    603 inline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)
    604 {
    605   return test_isApprox(a+ref, b+ref);
    606 }
    607 
    608 template<typename Derived1, typename Derived2>
    609 inline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,
    610                                    const MatrixBase<Derived2>& m2)
    611 {
    612   return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
    613 }
    614 
    615 template<typename Derived>
    616 inline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,
    617                                    const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
    618 {
    619   return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
    620 }
    621 
    622 template<typename Derived>
    623 inline bool test_isUnitary(const MatrixBase<Derived>& m)
    624 {
    625   return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());
    626 }
    627 
    628 // Forward declaration to avoid ICC warning
    629 template<typename T, typename U>
    630 bool test_is_equal(const T& actual, const U& expected, bool expect_equal=true);
    631 
    632 template<typename T, typename U>
    633 bool test_is_equal(const T& actual, const U& expected, bool expect_equal)
    634 {
    635     if ((actual==expected) == expect_equal)
    636         return true;
    637     // false:
    638     std::cerr
    639         << "\n    actual   = " << actual
    640         << "\n    expected " << (expect_equal ? "= " : "!=") << expected << "\n\n";
    641     return false;
    642 }
    643 
    644 /** Creates a random Partial Isometry matrix of given rank.
    645   *
    646   * A partial isometry is a matrix all of whose singular values are either 0 or 1.
    647   * This is very useful to test rank-revealing algorithms.
    648   */
    649 // Forward declaration to avoid ICC warning
    650 template<typename MatrixType>
    651 void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
    652 template<typename MatrixType>
    653 void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
    654 {
    655   typedef typename internal::traits<MatrixType>::Scalar Scalar;
    656   enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
    657 
    658   typedef Matrix<Scalar, Dynamic, 1> VectorType;
    659   typedef Matrix<Scalar, Rows, Rows> MatrixAType;
    660   typedef Matrix<Scalar, Cols, Cols> MatrixBType;
    661 
    662   if(desired_rank == 0)
    663   {
    664     m.setZero(rows,cols);
    665     return;
    666   }
    667 
    668   if(desired_rank == 1)
    669   {
    670     // here we normalize the vectors to get a partial isometry
    671     m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
    672     return;
    673   }
    674 
    675   MatrixAType a = MatrixAType::Random(rows,rows);
    676   MatrixType d = MatrixType::Identity(rows,cols);
    677   MatrixBType  b = MatrixBType::Random(cols,cols);
    678 
    679   // set the diagonal such that only desired_rank non-zero entries reamain
    680   const Index diag_size = (std::min)(d.rows(),d.cols());
    681   if(diag_size != desired_rank)
    682     d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
    683 
    684   HouseholderQR<MatrixAType> qra(a);
    685   HouseholderQR<MatrixBType> qrb(b);
    686   m = qra.householderQ() * d * qrb.householderQ();
    687 }
    688 
    689 // Forward declaration to avoid ICC warning
    690 template<typename PermutationVectorType>
    691 void randomPermutationVector(PermutationVectorType& v, Index size);
    692 template<typename PermutationVectorType>
    693 void randomPermutationVector(PermutationVectorType& v, Index size)
    694 {
    695   typedef typename PermutationVectorType::Scalar Scalar;
    696   v.resize(size);
    697   for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
    698   if(size == 1) return;
    699   for(Index n = 0; n < 3 * size; ++n)
    700   {
    701     Index i = internal::random<Index>(0, size-1);
    702     Index j;
    703     do j = internal::random<Index>(0, size-1); while(j==i);
    704     std::swap(v(i), v(j));
    705   }
    706 }
    707 
    708 template<typename T> bool isNotNaN(const T& x)
    709 {
    710   return x==x;
    711 }
    712 
    713 template<typename T> bool isPlusInf(const T& x)
    714 {
    715   return x > NumTraits<T>::highest();
    716 }
    717 
    718 template<typename T> bool isMinusInf(const T& x)
    719 {
    720   return x < NumTraits<T>::lowest();
    721 }
    722 
    723 } // end namespace Eigen
    724 
    725 template<typename T> struct GetDifferentType;
    726 
    727 template<> struct GetDifferentType<float> { typedef double type; };
    728 template<> struct GetDifferentType<double> { typedef float type; };
    729 template<typename T> struct GetDifferentType<std::complex<T> >
    730 { typedef std::complex<typename GetDifferentType<T>::type> type; };
    731 
    732 // Forward declaration to avoid ICC warning
    733 template<typename T> std::string type_name();
    734 template<typename T> std::string type_name()                    { return "other"; }
    735 template<> std::string type_name<float>()                       { return "float"; }
    736 template<> std::string type_name<double>()                      { return "double"; }
    737 template<> std::string type_name<long double>()                 { return "long double"; }
    738 template<> std::string type_name<int>()                         { return "int"; }
    739 template<> std::string type_name<std::complex<float> >()        { return "complex<float>"; }
    740 template<> std::string type_name<std::complex<double> >()       { return "complex<double>"; }
    741 template<> std::string type_name<std::complex<long double> >()  { return "complex<long double>"; }
    742 template<> std::string type_name<std::complex<int> >()          { return "complex<int>"; }
    743 
    744 using namespace Eigen;
    745 
    746 inline void set_repeat_from_string(const char *str)
    747 {
    748   errno = 0;
    749   g_repeat = int(strtoul(str, 0, 10));
    750   if(errno || g_repeat <= 0)
    751   {
    752     std::cout << "Invalid repeat value " << str << std::endl;
    753     exit(EXIT_FAILURE);
    754   }
    755   g_has_set_repeat = true;
    756 }
    757 
    758 inline void set_seed_from_string(const char *str)
    759 {
    760   errno = 0;
    761   g_seed = int(strtoul(str, 0, 10));
    762   if(errno || g_seed == 0)
    763   {
    764     std::cout << "Invalid seed value " << str << std::endl;
    765     exit(EXIT_FAILURE);
    766   }
    767   g_has_set_seed = true;
    768 }
    769 
    770 int main(int argc, char *argv[])
    771 {
    772     g_has_set_repeat = false;
    773     g_has_set_seed = false;
    774     bool need_help = false;
    775 
    776     for(int i = 1; i < argc; i++)
    777     {
    778       if(argv[i][0] == 'r')
    779       {
    780         if(g_has_set_repeat)
    781         {
    782           std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
    783           return 1;
    784         }
    785         set_repeat_from_string(argv[i]+1);
    786       }
    787       else if(argv[i][0] == 's')
    788       {
    789         if(g_has_set_seed)
    790         {
    791           std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
    792           return 1;
    793         }
    794          set_seed_from_string(argv[i]+1);
    795       }
    796       else
    797       {
    798         need_help = true;
    799       }
    800     }
    801 
    802     if(need_help)
    803     {
    804       std::cout << "This test application takes the following optional arguments:" << std::endl;
    805       std::cout << "  rN     Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
    806       std::cout << "  sN     Use N as seed for random numbers (default: based on current time)" << std::endl;
    807       std::cout << std::endl;
    808       std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl;
    809       std::cout << "will be used as default values for these parameters." << std::endl;
    810       return 1;
    811     }
    812 
    813     char *env_EIGEN_REPEAT = getenv("EIGEN_REPEAT");
    814     if(!g_has_set_repeat && env_EIGEN_REPEAT)
    815       set_repeat_from_string(env_EIGEN_REPEAT);
    816     char *env_EIGEN_SEED = getenv("EIGEN_SEED");
    817     if(!g_has_set_seed && env_EIGEN_SEED)
    818       set_seed_from_string(env_EIGEN_SEED);
    819 
    820     if(!g_has_set_seed) g_seed = (unsigned int) time(NULL);
    821     if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;
    822 
    823     std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
    824     std::stringstream ss;
    825     ss << "Seed: " << g_seed;
    826     g_test_stack.push_back(ss.str());
    827     srand(g_seed);
    828     std::cout << "Repeating each test " << g_repeat << " times" << std::endl;
    829 
    830     VERIFY(EigenTest::all().size()>0);
    831 
    832     for(std::size_t i=0; i<EigenTest::all().size(); ++i)
    833     {
    834       const EigenTest& current_test = *EigenTest::all()[i];
    835       Eigen::g_test_stack.push_back(current_test.name());
    836       current_test();
    837       Eigen::g_test_stack.pop_back();
    838     }
    839 
    840     return 0;
    841 }
    842 
    843 // These warning are disabled here such that they are still ON when parsing Eigen's header files.
    844 #if defined __INTEL_COMPILER
    845   // remark #383: value copied to temporary, reference to temporary used
    846   //  -> 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>
    847   // remark #1418: external function definition with no prior declaration
    848   //  -> this warning is raised for all our test functions. Declaring them static would fix the issue.
    849   // warning #279: controlling expression is constant
    850   // remark #1572: floating-point equality and inequality comparisons are unreliable
    851   #pragma warning disable 279 383 1418 1572
    852 #endif
    853 
    854 #ifdef _MSC_VER
    855   // 4503 - decorated name length exceeded, name was truncated
    856   #pragma warning( disable : 4503)
    857 #endif