125 lines
5.0 KiB
C++
125 lines
5.0 KiB
C++
// Copyright Paul A. Bristow 2016, 2017, 2018.
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// Copyright John Maddock 2016.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// test_lambert_w.cpp
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//! \brief Basic sanity tests for Lambert W derivative.
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#ifdef BOOST_MATH_TEST_FLOAT128
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#include <boost/cstdfloat.hpp> // For float_64_t, float128_t. Must be first include!
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#endif // #ifdef #ifdef BOOST_MATH_TEST_FLOAT128
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// Needs gnu++17 for BOOST_HAS_FLOAT128
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#include <boost/config.hpp> // for BOOST_MSVC definition etc.
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#include <boost/version.hpp> // for BOOST_MSVC versions.
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// Boost macros
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#define BOOST_TEST_MAIN
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#define BOOST_LIB_DIAGNOSTIC "on" // Report library file details.
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#include <boost/test/included/unit_test.hpp> // Boost.Test
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// #include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include <boost/array.hpp>
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#include <boost/lexical_cast.hpp>
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#include <boost/type_traits/is_constructible.hpp>
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#ifdef BOOST_MATH_TEST_MULTIPRECISION
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#include <boost/multiprecision/cpp_dec_float.hpp> // boost::multiprecision::cpp_dec_float_50
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using boost::multiprecision::cpp_dec_float_50;
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#include <boost/multiprecision/cpp_bin_float.hpp>
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using boost::multiprecision::cpp_bin_float_quad;
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#ifdef BOOST_MATH_TEST_FLOAT128
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#ifdef BOOST_HAS_FLOAT128
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// Including this header below without float128 triggers:
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// fatal error C1189: #error: "Sorry compiler is neither GCC, not Intel, don't know how to configure this header."
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#include <boost/multiprecision/float128.hpp>
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using boost::multiprecision::float128;
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#endif // ifdef BOOST_HAS_FLOAT128
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#endif // #ifdef #ifdef BOOST_MATH_TEST_FLOAT128
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#endif // #ifdef BOOST_MATH_TEST_MULTIPRECISION
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//#include <boost/fixed_point/fixed_point.hpp> // If available.
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#include <boost/math/concepts/real_concept.hpp> // for real_concept tests.
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#include <boost/math/special_functions/fpclassify.hpp> // isnan, ifinite.
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#include <boost/math/special_functions/next.hpp> // float_next, float_prior
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using boost::math::float_next;
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using boost::math::float_prior;
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#include <boost/math/special_functions/ulp.hpp> // ulp
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#include <boost/math/tools/test_value.hpp> // for create_test_value and macro BOOST_MATH_TEST_VALUE.
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#include <boost/math/policies/policy.hpp>
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using boost::math::policies::digits2;
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using boost::math::policies::digits10;
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#include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
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using boost::math::lambert_wm1;
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using boost::math::lambert_w0;
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#include <limits>
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#include <cmath>
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#include <typeinfo>
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#include <iostream>
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#include <exception>
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std::string show_versions(void);
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BOOST_AUTO_TEST_CASE( Derivatives_of_lambert_w )
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{
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std::cout << "Macro BOOST_MATH_LAMBERT_W_DERIVATIVES to test 1st derivatives is defined." << std::endl;
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BOOST_TEST_MESSAGE("\nTest Lambert W function 1st differentials.");
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using boost::math::constants::exp_minus_one;
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using boost::math::lambert_w0_prime;
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using boost::math::lambert_wm1_prime;
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// Derivatives
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// https://www.wolframalpha.com/input/?i=derivative+of+productlog(0,+x)
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// d/dx(W_0(x)) = W(x)/(x W(x) + x)
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// https://www.wolframalpha.com/input/?i=derivative+of+productlog(-1,+x)
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// d/dx(W_(-1)(x)) = (W_(-1)(x))/(x W_(-1)(x) + x)
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// 55 decimal digit values added to allow future testing using multiprecision.
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typedef double RealType;
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int epsilons = 1;
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RealType tolerance = boost::math::tools::epsilon<RealType>() * epsilons; // 2 eps as a fraction.
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// derivative of productlog(-1, x) at x = -0.1 == -13.8803
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// (derivative of productlog(-1, x) ) at x = N[-0.1, 55] - but the result disappears!
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// (derivative of N[productlog(-1, x), 55] ) at x = N[-0.1, 55]
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// W0 branch
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BOOST_CHECK_CLOSE_FRACTION(lambert_w0_prime(BOOST_MATH_TEST_VALUE(RealType, -0.2)),
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// BOOST_MATH_TEST_VALUE(RealType, 1.7491967609218355),
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BOOST_MATH_TEST_VALUE(RealType, 1.7491967609218358355273514903396335693828167746571404),
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tolerance); // 1.7491967609218358355273514903396335693828167746571404
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BOOST_CHECK_CLOSE_FRACTION(lambert_w0_prime(BOOST_MATH_TEST_VALUE(RealType, 10.)),
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BOOST_MATH_TEST_VALUE(RealType, 0.063577133469345105142021311010780887641928338458371618),
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tolerance);
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// W-1 branch
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BOOST_CHECK_CLOSE_FRACTION(lambert_wm1_prime(BOOST_MATH_TEST_VALUE(RealType, -0.1)),
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BOOST_MATH_TEST_VALUE(RealType, -13.880252213229780748699361486619519025203815492277715),
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tolerance);
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// Lambert W_prime -13.880252213229780748699361486619519025203815492277715, double -13.880252213229781
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BOOST_CHECK_CLOSE_FRACTION(lambert_wm1_prime(BOOST_MATH_TEST_VALUE(RealType, -0.2)),
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BOOST_MATH_TEST_VALUE(RealType, -8.2411940564179044961885598641955579728547896392013239),
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tolerance);
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// Lambert W_prime -8.2411940564179044961885598641955579728547896392013239, double -8.2411940564179051
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// Lambert W_prime 0.063577133469345105142021311010780887641928338458371618, double 0.063577133469345098
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}; // BOOST_AUTO_TEST_CASE("Derivatives of lambert_w")
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