123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267 |
- // Copyright Paul A. Bristow 2016, 2017, 2018.
- // Copyright John Maddock 2016.
- // Use, modification and distribution are subject to the
- // Boost Software License, Version 1.0.
- // (See accompanying file LICENSE_1_0.txt
- // or copy at http://www.boost.org/LICENSE_1_0.txt)
- // test_lambert_w_integrals.cpp
- //! \brief quadrature tests that cover the whole range of the Lambert W0 function.
- #include <boost/config.hpp> // for BOOST_MSVC definition etc.
- #include <boost/version.hpp> // for BOOST_MSVC versions.
- // Boost macros
- #define BOOST_TEST_MAIN
- #define BOOST_LIB_DIAGNOSTIC "on" // Report library file details.
- #include <boost/test/included/unit_test.hpp> // Boost.Test
- // #include <boost/test/unit_test.hpp> // Boost.Test
- #include <boost/test/tools/floating_point_comparison.hpp>
- #include <boost/array.hpp>
- #include <boost/lexical_cast.hpp>
- #include <boost/type_traits/is_constructible.hpp>
- #include <boost/math/special_functions/fpclassify.hpp> // isnan, ifinite.
- #include <boost/math/special_functions/next.hpp> // float_next, float_prior
- using boost::math::float_next;
- using boost::math::float_prior;
- #include <boost/math/special_functions/ulp.hpp> // ulp
- #include <boost/math/tools/test_value.hpp> // for create_test_value and macro BOOST_MATH_TEST_VALUE.
- #include <boost/math/policies/policy.hpp>
- using boost::math::policies::digits2;
- using boost::math::policies::digits10;
- #include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
- using boost::math::lambert_wm1;
- using boost::math::lambert_w0;
- #include <limits>
- #include <cmath>
- #include <typeinfo>
- #include <iostream>
- #include <type_traits>
- #include <exception>
- std::string show_versions(void);
- // Added code and test for Integral of the Lambert W function: by Nick Thompson.
- // https://en.wikipedia.org/wiki/Lambert_W_function#Definite_integrals
- #include <boost/math/constants/constants.hpp> // for integral tests.
- #include <boost/math/quadrature/tanh_sinh.hpp> // for integral tests.
- #include <boost/math/quadrature/exp_sinh.hpp> // for integral tests.
- using boost::math::policies::policy;
- using boost::math::policies::make_policy;
- // using statements needed for changing error handling policy.
- using boost::math::policies::evaluation_error;
- using boost::math::policies::domain_error;
- using boost::math::policies::overflow_error;
- using boost::math::policies::ignore_error;
- using boost::math::policies::throw_on_error;
- typedef policy<
- domain_error<throw_on_error>,
- overflow_error<ignore_error>
- > no_throw_policy;
- // Assumes that function has a throw policy, for example:
- // NOT lambert_w0<T>(1 / (x * x), no_throw_policy());
- // Error in function boost::math::quadrature::exp_sinh<double>::integrate:
- // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
- // Please ensure your function evaluates to a finite number of its entire domain.
- template <typename T>
- T debug_integration_proc(T x)
- {
- T result; // warning C4701: potentially uninitialized local variable 'result' used
- // T result = 0 ; // But result may not be assigned below?
- try
- {
- // Assign function call to result in here...
- if (x <= sqrt(boost::math::tools::min_value<T>()) )
- {
- result = 0;
- }
- else
- {
- result = lambert_w0<T>(1 / (x * x));
- }
- // result = lambert_w0<T>(1 / (x * x), no_throw_policy()); // Bad idea, less helpful diagnostic message is:
- // Error in function boost::math::quadrature::exp_sinh<double>::integrate:
- // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
- // Please ensure your function evaluates to a finite number of its entire domain.
- } // try
- catch (const std::exception& e)
- {
- std::cout << "Exception " << e.what() << std::endl;
- // set breakpoint here:
- std::cout << "Unexpected exception thrown in integration code at abscissa (x): " << x << "." << std::endl;
- if (!std::isfinite(result))
- {
- // set breakpoint here:
- std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
- }
- if (std::isnan(result))
- {
- // set breakpoint here:
- std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
- }
- } // catch
- return result;
- } // T debug_integration_proc(T x)
- template<class Real>
- void test_integrals()
- {
- // Integral of the Lambert W function:
- // https://en.wikipedia.org/wiki/Lambert_W_function
- using boost::math::quadrature::tanh_sinh;
- using boost::math::quadrature::exp_sinh;
- // file:///I:/modular-boost/libs/math/doc/html/math_toolkit/quadrature/double_exponential/de_tanh_sinh.html
- using std::sqrt;
- std::cout << "Integration of type " << typeid(Real).name() << std::endl;
- Real tol = std::numeric_limits<Real>::epsilon();
- { // // Integrate for function lambert_W0(z);
- tanh_sinh<Real> ts;
- Real a = 0;
- Real b = boost::math::constants::e<Real>();
- auto f = [](Real z)->Real
- {
- return lambert_w0<Real>(z);
- };
- Real z = ts.integrate(f, a, b); // OK without any decltype(f)
- BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::e<Real>() - 1, tol);
- }
- {
- // Integrate for function lambert_W0(z/(z sqrt(z)).
- exp_sinh<Real> es;
- auto f = [](Real z)->Real
- {
- return lambert_w0<Real>(z)/(z * sqrt(z));
- };
- Real z = es.integrate(f); // OK
- BOOST_CHECK_CLOSE_FRACTION(z, 2 * boost::math::constants::root_two_pi<Real>(), tol);
- }
- {
- // Integrate for function lambert_W0(1/z^2).
- exp_sinh<Real> es;
- //const Real sqrt_min = sqrt(boost::math::tools::min_value<Real>()); // 1.08420217e-19 fo 32-bit float.
- // error C3493: 'sqrt_min' cannot be implicitly captured because no default capture mode has been specified
- auto f = [](Real z)->Real
- {
- if (z <= sqrt(boost::math::tools::min_value<Real>()) )
- { // Too small would underflow z * z and divide by zero to overflow 1/z^2 for lambert_w0 z parameter.
- return static_cast<Real>(0);
- }
- else
- {
- return lambert_w0<Real>(1 / (z * z)); // warning C4756: overflow in constant arithmetic, even though cannot happen.
- }
- };
- Real z = es.integrate(f);
- BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::root_two_pi<Real>(), tol);
- }
- } // template<class Real> void test_integrals()
- BOOST_AUTO_TEST_CASE( integrals )
- {
- std::cout << "Macro BOOST_MATH_LAMBERT_W0_INTEGRALS is defined." << std::endl;
- BOOST_TEST_MESSAGE("\nTest Lambert W0 integrals.");
- try
- {
- // using statements needed to change precision policy.
- using boost::math::policies::policy;
- using boost::math::policies::make_policy;
- using boost::math::policies::precision;
- using boost::math::policies::digits2;
- using boost::math::policies::digits10;
- // using statements needed for changing error handling policy.
- using boost::math::policies::evaluation_error;
- using boost::math::policies::domain_error;
- using boost::math::policies::overflow_error;
- using boost::math::policies::ignore_error;
- using boost::math::policies::throw_on_error;
- /*
- typedef policy<
- domain_error<throw_on_error>,
- overflow_error<ignore_error>
- > no_throw_policy;
- // Experiment with better diagnostics.
- typedef float Real;
- Real inf = std::numeric_limits<Real>::infinity();
- Real max = (std::numeric_limits<Real>::max)();
- std::cout.precision(std::numeric_limits<Real>::max_digits10);
- //std::cout << "lambert_w0(inf) = " << lambert_w0(inf) << std::endl; // lambert_w0(inf) = 1.79769e+308
- std::cout << "lambert_w0(inf, throw_policy()) = " << lambert_w0(inf, no_throw_policy()) << std::endl; // inf
- std::cout << "lambert_w0(max) = " << lambert_w0(max) << std::endl; // lambert_w0(max) = 703.227
- //std::cout << lambert_w0(inf) << std::endl; // inf - will throw.
- std::cout << "lambert_w0(0) = " << lambert_w0(0.) << std::endl; // 0
- std::cout << "lambert_w0(std::numeric_limits<Real>::denorm_min()) = " << lambert_w0(std::numeric_limits<Real>::denorm_min()) << std::endl; // 4.94066e-324
- std::cout << "lambert_w0(std::numeric_limits<Real>::min()) = " << lambert_w0((std::numeric_limits<Real>::min)()) << std::endl; // 2.22507e-308
- // Approximate the largest lambert_w you can get for type T?
- float max_w_f = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<float>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
- std::cout << "w max_f " << max_w_f << std::endl; // 84.2879
- Real max_w = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<Real>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
- std::cout << "w max " << max_w << std::endl; // 703.227
- std::cout << "lambert_w0(7.2416706213544837e-163) = " << lambert_w0(7.2416706213544837e-163) << std::endl; //
- std::cout << "test integral 1/z^2" << std::endl;
- std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16
- std::cout << "ULP = " << boost::math::ulp(1e-10, policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16
- std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<11> >()) << std::endl; // ULP = 2.2204460492503131e-16
- std::cout << "epsilon = " << std::numeric_limits<Real>::epsilon() << std::endl; //
- std::cout << "sqrt(max) = " << sqrt(boost::math::tools::max_value<float>() ) << std::endl; // sqrt(max) = 1.8446742974197924e+19
- std::cout << "sqrt(min) = " << sqrt(boost::math::tools::min_value<float>() ) << std::endl; // sqrt(min) = 1.0842021724855044e-19
- // Demo debug version.
- Real tol = std::numeric_limits<Real>::epsilon();
- Real x;
- {
- using boost::math::quadrature::exp_sinh;
- exp_sinh<Real> es;
- // Function to be integrated, lambert_w0(1/z^2).
- //auto f = [](Real z)->Real
- //{ // Naive - no protection against underflow and subsequent divide by zero.
- // return lambert_w0<Real>(1 / (z * z));
- //};
- // Diagnostic is:
- // Error in function boost::math::lambert_w0<Real>: Expected a finite value but got inf
- auto f = [](Real z)->Real
- { // Debug with diagnostics for underflow and subsequent divide by zero and other bad things.
- return debug_integration_proc(z);
- };
- // Exception Error in function boost::math::lambert_w0<double>: Expected a finite value but got inf.
- // Unexpected exception thrown in integration code at abscissa: 7.2416706213544837e-163.
- // Unexpected exception thrown in integration code at abscissa (x): 3.478765835953569e-23.
- x = es.integrate(f);
- std::cout << "es.integrate(f) = " << x << std::endl;
- BOOST_CHECK_CLOSE_FRACTION(x, boost::math::constants::root_two_pi<Real>(), tol);
- // root_two_pi<double = 2.506628274631000502
- }
- */
- test_integrals<float>();
- }
- catch (std::exception& ex)
- {
- std::cout << ex.what() << std::endl;
- }
- }
|