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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_integrals.cpp | |
10 | //! \brief quadrature tests that cover the whole range of the Lambert W0 function. | |
11 | ||
12 | #include <boost/config.hpp> // for BOOST_MSVC definition etc. | |
13 | #include <boost/version.hpp> // for BOOST_MSVC versions. | |
14 | ||
15 | // Boost macros | |
16 | #define BOOST_TEST_MAIN | |
17 | #define BOOST_LIB_DIAGNOSTIC "on" // Report library file details. | |
18 | #include <boost/test/included/unit_test.hpp> // Boost.Test | |
19 | // #include <boost/test/unit_test.hpp> // Boost.Test | |
20 | #include <boost/test/tools/floating_point_comparison.hpp> | |
21 | ||
22 | #include <boost/array.hpp> | |
92f5a8d4 | 23 | #include <boost/type_traits/is_constructible.hpp> |
f67539c2 | 24 | #include <boost/math/special_functions/fpclassify.hpp> // isnan, isfinite. |
92f5a8d4 TL |
25 | #include <boost/math/special_functions/next.hpp> // float_next, float_prior |
26 | using boost::math::float_next; | |
27 | using boost::math::float_prior; | |
28 | #include <boost/math/special_functions/ulp.hpp> // ulp | |
29 | ||
30 | #include <boost/math/tools/test_value.hpp> // for create_test_value and macro BOOST_MATH_TEST_VALUE. | |
31 | #include <boost/math/policies/policy.hpp> | |
32 | using boost::math::policies::digits2; | |
33 | using boost::math::policies::digits10; | |
34 | #include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function. | |
35 | using boost::math::lambert_wm1; | |
36 | using boost::math::lambert_w0; | |
37 | ||
38 | #include <limits> | |
39 | #include <cmath> | |
40 | #include <typeinfo> | |
41 | #include <iostream> | |
42 | #include <type_traits> | |
43 | #include <exception> | |
44 | ||
45 | std::string show_versions(void); | |
46 | ||
47 | // Added code and test for Integral of the Lambert W function: by Nick Thompson. | |
48 | // https://en.wikipedia.org/wiki/Lambert_W_function#Definite_integrals | |
49 | ||
50 | #include <boost/math/constants/constants.hpp> // for integral tests. | |
51 | #include <boost/math/quadrature/tanh_sinh.hpp> // for integral tests. | |
52 | #include <boost/math/quadrature/exp_sinh.hpp> // for integral tests. | |
53 | ||
54 | using boost::math::policies::policy; | |
55 | using boost::math::policies::make_policy; | |
56 | ||
57 | // using statements needed for changing error handling policy. | |
58 | using boost::math::policies::evaluation_error; | |
59 | using boost::math::policies::domain_error; | |
60 | using boost::math::policies::overflow_error; | |
61 | using boost::math::policies::ignore_error; | |
62 | using boost::math::policies::throw_on_error; | |
63 | ||
64 | typedef policy< | |
65 | domain_error<throw_on_error>, | |
66 | overflow_error<ignore_error> | |
67 | > no_throw_policy; | |
68 | ||
69 | // Assumes that function has a throw policy, for example: | |
70 | // NOT lambert_w0<T>(1 / (x * x), no_throw_policy()); | |
71 | // Error in function boost::math::quadrature::exp_sinh<double>::integrate: | |
72 | // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf. | |
73 | // Please ensure your function evaluates to a finite number of its entire domain. | |
74 | template <typename T> | |
75 | T debug_integration_proc(T x) | |
76 | { | |
77 | T result; // warning C4701: potentially uninitialized local variable 'result' used | |
78 | // T result = 0 ; // But result may not be assigned below? | |
79 | try | |
80 | { | |
81 | // Assign function call to result in here... | |
82 | if (x <= sqrt(boost::math::tools::min_value<T>()) ) | |
83 | { | |
84 | result = 0; | |
85 | } | |
86 | else | |
87 | { | |
88 | result = lambert_w0<T>(1 / (x * x)); | |
89 | } | |
90 | // result = lambert_w0<T>(1 / (x * x), no_throw_policy()); // Bad idea, less helpful diagnostic message is: | |
91 | // Error in function boost::math::quadrature::exp_sinh<double>::integrate: | |
92 | // The exp_sinh quadrature evaluated your function at a singular point and resulted in inf. | |
93 | // Please ensure your function evaluates to a finite number of its entire domain. | |
94 | ||
95 | } // try | |
96 | catch (const std::exception& e) | |
97 | { | |
98 | std::cout << "Exception " << e.what() << std::endl; | |
99 | // set breakpoint here: | |
100 | std::cout << "Unexpected exception thrown in integration code at abscissa (x): " << x << "." << std::endl; | |
101 | if (!std::isfinite(result)) | |
102 | { | |
103 | // set breakpoint here: | |
104 | std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl; | |
105 | } | |
106 | if (std::isnan(result)) | |
107 | { | |
108 | // set breakpoint here: | |
109 | std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl; | |
110 | } | |
111 | } // catch | |
112 | return result; | |
113 | } // T debug_integration_proc(T x) | |
114 | ||
115 | template<class Real> | |
116 | void test_integrals() | |
117 | { | |
118 | // Integral of the Lambert W function: | |
119 | // https://en.wikipedia.org/wiki/Lambert_W_function | |
120 | using boost::math::quadrature::tanh_sinh; | |
121 | using boost::math::quadrature::exp_sinh; | |
122 | // file:///I:/modular-boost/libs/math/doc/html/math_toolkit/quadrature/double_exponential/de_tanh_sinh.html | |
123 | using std::sqrt; | |
124 | ||
125 | std::cout << "Integration of type " << typeid(Real).name() << std::endl; | |
126 | ||
127 | Real tol = std::numeric_limits<Real>::epsilon(); | |
128 | { // // Integrate for function lambert_W0(z); | |
129 | tanh_sinh<Real> ts; | |
130 | Real a = 0; | |
131 | Real b = boost::math::constants::e<Real>(); | |
132 | auto f = [](Real z)->Real | |
133 | { | |
134 | return lambert_w0<Real>(z); | |
135 | }; | |
136 | Real z = ts.integrate(f, a, b); // OK without any decltype(f) | |
137 | BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::e<Real>() - 1, tol); | |
138 | } | |
139 | { | |
140 | // Integrate for function lambert_W0(z/(z sqrt(z)). | |
141 | exp_sinh<Real> es; | |
142 | auto f = [](Real z)->Real | |
143 | { | |
144 | return lambert_w0<Real>(z)/(z * sqrt(z)); | |
145 | }; | |
146 | Real z = es.integrate(f); // OK | |
147 | BOOST_CHECK_CLOSE_FRACTION(z, 2 * boost::math::constants::root_two_pi<Real>(), tol); | |
148 | } | |
149 | { | |
150 | // Integrate for function lambert_W0(1/z^2). | |
151 | exp_sinh<Real> es; | |
152 | //const Real sqrt_min = sqrt(boost::math::tools::min_value<Real>()); // 1.08420217e-19 fo 32-bit float. | |
153 | // error C3493: 'sqrt_min' cannot be implicitly captured because no default capture mode has been specified | |
154 | auto f = [](Real z)->Real | |
155 | { | |
156 | if (z <= sqrt(boost::math::tools::min_value<Real>()) ) | |
157 | { // Too small would underflow z * z and divide by zero to overflow 1/z^2 for lambert_w0 z parameter. | |
158 | return static_cast<Real>(0); | |
159 | } | |
160 | else | |
161 | { | |
162 | return lambert_w0<Real>(1 / (z * z)); // warning C4756: overflow in constant arithmetic, even though cannot happen. | |
163 | } | |
164 | }; | |
165 | Real z = es.integrate(f); | |
166 | BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::root_two_pi<Real>(), tol); | |
167 | } | |
168 | } // template<class Real> void test_integrals() | |
169 | ||
170 | ||
171 | BOOST_AUTO_TEST_CASE( integrals ) | |
172 | { | |
173 | std::cout << "Macro BOOST_MATH_LAMBERT_W0_INTEGRALS is defined." << std::endl; | |
174 | BOOST_TEST_MESSAGE("\nTest Lambert W0 integrals."); | |
175 | try | |
176 | { | |
177 | // using statements needed to change precision policy. | |
178 | using boost::math::policies::policy; | |
179 | using boost::math::policies::make_policy; | |
180 | using boost::math::policies::precision; | |
181 | using boost::math::policies::digits2; | |
182 | using boost::math::policies::digits10; | |
183 | ||
184 | // using statements needed for changing error handling policy. | |
185 | using boost::math::policies::evaluation_error; | |
186 | using boost::math::policies::domain_error; | |
187 | using boost::math::policies::overflow_error; | |
188 | using boost::math::policies::ignore_error; | |
189 | using boost::math::policies::throw_on_error; | |
190 | ||
191 | /* | |
192 | typedef policy< | |
193 | domain_error<throw_on_error>, | |
194 | overflow_error<ignore_error> | |
195 | > no_throw_policy; | |
196 | ||
197 | // Experiment with better diagnostics. | |
198 | typedef float Real; | |
199 | ||
200 | Real inf = std::numeric_limits<Real>::infinity(); | |
201 | Real max = (std::numeric_limits<Real>::max)(); | |
202 | std::cout.precision(std::numeric_limits<Real>::max_digits10); | |
203 | //std::cout << "lambert_w0(inf) = " << lambert_w0(inf) << std::endl; // lambert_w0(inf) = 1.79769e+308 | |
204 | std::cout << "lambert_w0(inf, throw_policy()) = " << lambert_w0(inf, no_throw_policy()) << std::endl; // inf | |
205 | std::cout << "lambert_w0(max) = " << lambert_w0(max) << std::endl; // lambert_w0(max) = 703.227 | |
206 | //std::cout << lambert_w0(inf) << std::endl; // inf - will throw. | |
207 | std::cout << "lambert_w0(0) = " << lambert_w0(0.) << std::endl; // 0 | |
208 | std::cout << "lambert_w0(std::numeric_limits<Real>::denorm_min()) = " << lambert_w0(std::numeric_limits<Real>::denorm_min()) << std::endl; // 4.94066e-324 | |
209 | std::cout << "lambert_w0(std::numeric_limits<Real>::min()) = " << lambert_w0((std::numeric_limits<Real>::min)()) << std::endl; // 2.22507e-308 | |
210 | ||
211 | // Approximate the largest lambert_w you can get for type T? | |
212 | 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. | |
213 | std::cout << "w max_f " << max_w_f << std::endl; // 84.2879 | |
214 | 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. | |
215 | std::cout << "w max " << max_w << std::endl; // 703.227 | |
216 | ||
217 | std::cout << "lambert_w0(7.2416706213544837e-163) = " << lambert_w0(7.2416706213544837e-163) << std::endl; // | |
218 | std::cout << "test integral 1/z^2" << std::endl; | |
219 | std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16 | |
220 | std::cout << "ULP = " << boost::math::ulp(1e-10, policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16 | |
221 | std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<11> >()) << std::endl; // ULP = 2.2204460492503131e-16 | |
222 | std::cout << "epsilon = " << std::numeric_limits<Real>::epsilon() << std::endl; // | |
223 | std::cout << "sqrt(max) = " << sqrt(boost::math::tools::max_value<float>() ) << std::endl; // sqrt(max) = 1.8446742974197924e+19 | |
224 | std::cout << "sqrt(min) = " << sqrt(boost::math::tools::min_value<float>() ) << std::endl; // sqrt(min) = 1.0842021724855044e-19 | |
225 | ||
226 | ||
227 | ||
228 | // Demo debug version. | |
229 | Real tol = std::numeric_limits<Real>::epsilon(); | |
230 | Real x; | |
231 | { | |
232 | using boost::math::quadrature::exp_sinh; | |
233 | exp_sinh<Real> es; | |
234 | // Function to be integrated, lambert_w0(1/z^2). | |
235 | ||
236 | //auto f = [](Real z)->Real | |
237 | //{ // Naive - no protection against underflow and subsequent divide by zero. | |
238 | // return lambert_w0<Real>(1 / (z * z)); | |
239 | //}; | |
240 | // Diagnostic is: | |
241 | // Error in function boost::math::lambert_w0<Real>: Expected a finite value but got inf | |
242 | ||
243 | auto f = [](Real z)->Real | |
244 | { // Debug with diagnostics for underflow and subsequent divide by zero and other bad things. | |
245 | return debug_integration_proc(z); | |
246 | }; | |
247 | // Exception Error in function boost::math::lambert_w0<double>: Expected a finite value but got inf. | |
248 | ||
249 | // Unexpected exception thrown in integration code at abscissa: 7.2416706213544837e-163. | |
250 | // Unexpected exception thrown in integration code at abscissa (x): 3.478765835953569e-23. | |
251 | x = es.integrate(f); | |
252 | std::cout << "es.integrate(f) = " << x << std::endl; | |
253 | BOOST_CHECK_CLOSE_FRACTION(x, boost::math::constants::root_two_pi<Real>(), tol); | |
254 | // root_two_pi<double = 2.506628274631000502 | |
255 | } | |
256 | */ | |
257 | ||
258 | test_integrals<double>(); | |
259 | } | |
260 | catch (std::exception& ex) | |
261 | { | |
262 | std::cout << ex.what() << std::endl; | |
263 | } | |
264 | } | |
265 |