libs/math/test/test_lambert_w_derivative.cpp

   1 // Copyright Paul A. Bristow 2016, 2017, 2018.
   2 // Copyright John Maddock 2016.
   3
   4 // Use, modification and distribution are subject to the
   5 // Boost Software License, Version 1.0.
   6 // (See accompanying file LICENSE_1_0.txt
   7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   8
   9 // test_lambert_w.cpp
  10 //! \brief Basic sanity tests for Lambert W derivative.
  11
  12 #ifdef BOOST_MATH_TEST_FLOAT128
  13 #include <boost/cstdfloat.hpp> // For float_64_t, float128_t. Must be first include!
  14 #endif // #ifdef #ifdef BOOST_MATH_TEST_FLOAT128
  15 // Needs gnu++17 for BOOST_HAS_FLOAT128
  16 #include <boost/config.hpp>   // for BOOST_MSVC definition etc.
  17 #include <boost/version.hpp>   // for BOOST_MSVC versions.
  18
  19 // Boost macros
  20 #define BOOST_TEST_MAIN
  21 #define BOOST_LIB_DIAGNOSTIC "on" // Report library file details.
  22 #include <boost/test/included/unit_test.hpp> // Boost.Test
  23 // #include <boost/test/unit_test.hpp> // Boost.Test
  24 #include <boost/test/tools/floating_point_comparison.hpp>
  25
  26 #include <boost/array.hpp>
  27 #include <boost/lexical_cast.hpp>
  28 #include <boost/type_traits/is_constructible.hpp>
  29
  30 #ifdef BOOST_MATH_TEST_MULTIPRECISION
  31 #include <boost/multiprecision/cpp_dec_float.hpp> // boost::multiprecision::cpp_dec_float_50
  32 using boost::multiprecision::cpp_dec_float_50;
  33
  34 #include <boost/multiprecision/cpp_bin_float.hpp>
  35 using boost::multiprecision::cpp_bin_float_quad;
  36
  37 #ifdef BOOST_MATH_TEST_FLOAT128
  38
  39 #ifdef BOOST_HAS_FLOAT128
  40 // Including this header below without float128 triggers:
  41 // fatal error C1189: #error:  "Sorry compiler is neither GCC, not Intel, don't know how to configure this header."
  42 #include <boost/multiprecision/float128.hpp>
  43 using boost::multiprecision::float128;
  44 #endif // ifdef BOOST_HAS_FLOAT128
  45 #endif // #ifdef #ifdef BOOST_MATH_TEST_FLOAT128
  46
  47 #endif //   #ifdef BOOST_MATH_TEST_MULTIPRECISION
  48
  49 //#include <boost/fixed_point/fixed_point.hpp> // If available.
  50
  51 #include <boost/math/concepts/real_concept.hpp> // for real_concept tests.
  52 #include <boost/math/special_functions/fpclassify.hpp> // isnan, ifinite.
  53 #include <boost/math/special_functions/next.hpp> // float_next, float_prior
  54 using boost::math::float_next;
  55 using boost::math::float_prior;
  56 #include <boost/math/special_functions/ulp.hpp>  // ulp
  57
  58 #include <boost/math/tools/test_value.hpp>  // for create_test_value and macro BOOST_MATH_TEST_VALUE.
  59 #include <boost/math/policies/policy.hpp>
  60 using boost::math::policies::digits2;
  61 using boost::math::policies::digits10;
  62 #include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
  63 using boost::math::lambert_wm1;
  64 using boost::math::lambert_w0;
  65
  66 #include <limits>
  67 #include <cmath>
  68 #include <typeinfo>
  69 #include <iostream>
  70 #include <exception>
  71
  72 std::string show_versions(void);
  73
  74 BOOST_AUTO_TEST_CASE( Derivatives_of_lambert_w )
  75 {
  76   std::cout << "Macro BOOST_MATH_LAMBERT_W_DERIVATIVES to test 1st derivatives is defined." << std::endl;
  77   BOOST_TEST_MESSAGE("\nTest Lambert W function 1st differentials.");
  78
  79   using boost::math::constants::exp_minus_one;
  80   using boost::math::lambert_w0_prime;
  81   using boost::math::lambert_wm1_prime;
  82
  83   // Derivatives
  84   // https://www.wolframalpha.com/input/?i=derivative+of+productlog(0,+x)
  85   //  d/dx(W_0(x)) = W(x)/(x W(x) + x)
  86   // https://www.wolframalpha.com/input/?i=derivative+of+productlog(-1,+x)
  87   // d/dx(W_(-1)(x)) = (W_(-1)(x))/(x W_(-1)(x) + x)
  88
  89   // 55 decimal digit values added to allow future testing using multiprecision.
  90
  91   typedef double RealType;
  92
  93   int epsilons = 1;
  94   RealType tolerance = boost::math::tools::epsilon<RealType>() * epsilons; // 2 eps as a fraction.
  95
  96   // derivative of productlog(-1, x)   at x = -0.1 == -13.8803
  97   // (derivative of productlog(-1, x) ) at x = N[-0.1, 55] - but the result disappears!
  98   // (derivative of N[productlog(-1, x), 55] ) at x = N[-0.1, 55]
  99
 100   // W0 branch
 101   BOOST_CHECK_CLOSE_FRACTION(lambert_w0_prime(BOOST_MATH_TEST_VALUE(RealType, -0.2)),
 102    // BOOST_MATH_TEST_VALUE(RealType, 1.7491967609218355),
 103     BOOST_MATH_TEST_VALUE(RealType, 1.7491967609218358355273514903396335693828167746571404),
 104     tolerance); //                  1.7491967609218358355273514903396335693828167746571404
 105
 106     BOOST_CHECK_CLOSE_FRACTION(lambert_w0_prime(BOOST_MATH_TEST_VALUE(RealType, 10.)),
 107     BOOST_MATH_TEST_VALUE(RealType, 0.063577133469345105142021311010780887641928338458371618),
 108     tolerance);
 109
 110 // W-1 branch
 111   BOOST_CHECK_CLOSE_FRACTION(lambert_wm1_prime(BOOST_MATH_TEST_VALUE(RealType, -0.1)),
 112     BOOST_MATH_TEST_VALUE(RealType, -13.880252213229780748699361486619519025203815492277715),
 113     tolerance);
 114   // Lambert W_prime -13.880252213229780748699361486619519025203815492277715, double -13.880252213229781
 115
 116   BOOST_CHECK_CLOSE_FRACTION(lambert_wm1_prime(BOOST_MATH_TEST_VALUE(RealType, -0.2)),
 117     BOOST_MATH_TEST_VALUE(RealType, -8.2411940564179044961885598641955579728547896392013239),
 118     tolerance);
 119   // Lambert W_prime -8.2411940564179044961885598641955579728547896392013239, double -8.2411940564179051
 120
 121   // Lambert W_prime 0.063577133469345105142021311010780887641928338458371618, double 0.063577133469345098
 122 }; // BOOST_AUTO_TEST_CASE("Derivatives of lambert_w")
 123
 124