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1 | // Copyright John Maddock 2006. |
2 | // Copyright Paul A. Bristow 2007, 2009 | |
3 | // Use, modification and distribution are subject to the | |
4 | // Boost Software License, Version 1.0. (See accompanying file | |
5 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
6 | ||
7 | #include <boost/math/concepts/real_concept.hpp> | |
8 | #include <boost/math/special_functions/math_fwd.hpp> | |
9 | #define BOOST_TEST_MAIN | |
10 | #include <boost/test/unit_test.hpp> | |
11 | #include <boost/test/results_collector.hpp> | |
12 | #include <boost/test/unit_test.hpp> | |
92f5a8d4 | 13 | #include <boost/test/tools/floating_point_comparison.hpp> |
7c673cae FG |
14 | #include <boost/math/tools/stats.hpp> |
15 | #include <boost/math/tools/test.hpp> | |
16 | #include <boost/math/constants/constants.hpp> | |
17 | #include <boost/type_traits/is_floating_point.hpp> | |
18 | #include <boost/array.hpp> | |
19 | #include "functor.hpp" | |
20 | ||
21 | #include "handle_test_result.hpp" | |
22 | #include "table_type.hpp" | |
23 | ||
24 | #ifndef SC_ | |
25 | #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L)) | |
26 | #endif | |
27 | ||
28 | #define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \ | |
29 | {\ | |
30 | unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\ | |
31 | BOOST_CHECK_CLOSE(a, b, prec); \ | |
32 | if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\ | |
33 | {\ | |
34 | std::cerr << "Failure was at row " << i << std::endl;\ | |
35 | std::cerr << std::setprecision(35); \ | |
36 | std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\ | |
37 | std::cerr << " , " << data[i][3] << " , " << data[i][4] << " , " << data[i][5] << " } " << std::endl;\ | |
38 | }\ | |
39 | } | |
40 | ||
41 | template <class Real, class T> | |
42 | void do_test_gamma_2(const T& data, const char* type_name, const char* test_name) | |
43 | { | |
44 | // | |
45 | // test gamma_p_inv(T, T) against data: | |
46 | // | |
47 | using namespace std; | |
48 | typedef Real value_type; | |
49 | ||
50 | std::cout << test_name << " with type " << type_name << std::endl; | |
51 | ||
52 | // | |
53 | // These sanity checks test for a round trip accuracy of one half | |
54 | // of the bits in T, unless T is type float, in which case we check | |
55 | // for just one decimal digit. The problem here is the sensitivity | |
56 | // of the functions, not their accuracy. This test data was generated | |
57 | // for the forward functions, which means that when it is used as | |
58 | // the input to the inverses then it is necessarily inexact. This rounding | |
59 | // of the input is what makes the data unsuitable for use as an accuracy check, | |
60 | // and also demonstrates that you can't in general round-trip these functions. | |
61 | // It is however a useful sanity check. | |
62 | // | |
63 | value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100; | |
64 | if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50) | |
65 | precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float | |
66 | ||
67 | for(unsigned i = 0; i < data.size(); ++i) | |
68 | { | |
69 | // | |
70 | // These inverse tests are thrown off if the output of the | |
71 | // incomplete gamma is too close to 1: basically there is insuffient | |
72 | // information left in the value we're using as input to the inverse | |
73 | // to be able to get back to the original value. | |
74 | // | |
75 | if(Real(data[i][5]) == 0) | |
76 | BOOST_CHECK_EQUAL(boost::math::gamma_p_inv(Real(data[i][0]), Real(data[i][5])), value_type(0)); | |
77 | else if((1 - Real(data[i][5]) > 0.001) | |
78 | && (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<value_type>()) | |
79 | && (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<double>())) | |
80 | { | |
81 | value_type inv = boost::math::gamma_p_inv(Real(data[i][0]), Real(data[i][5])); | |
82 | BOOST_CHECK_CLOSE_EX(Real(data[i][1]), inv, precision, i); | |
83 | } | |
84 | else if(1 == Real(data[i][5])) | |
85 | BOOST_CHECK_EQUAL(boost::math::gamma_p_inv(Real(data[i][0]), Real(data[i][5])), std::numeric_limits<value_type>::has_infinity ? std::numeric_limits<value_type>::infinity() : boost::math::tools::max_value<value_type>()); | |
86 | else | |
87 | { | |
88 | // not enough bits in our input to get back to x, but we should be in | |
89 | // the same ball park: | |
90 | value_type inv = boost::math::gamma_p_inv(Real(data[i][0]), Real(data[i][5])); | |
91 | BOOST_CHECK_CLOSE_EX(Real(data[i][1]), inv, 100000, i); | |
92 | } | |
93 | ||
94 | if(Real(data[i][3]) == 0) | |
95 | BOOST_CHECK_EQUAL(boost::math::gamma_q_inv(Real(data[i][0]), Real(data[i][3])), std::numeric_limits<value_type>::has_infinity ? std::numeric_limits<value_type>::infinity() : boost::math::tools::max_value<value_type>()); | |
96 | else if((1 - Real(data[i][3]) > 0.001) && (fabs(Real(data[i][3])) > 2 * boost::math::tools::min_value<value_type>())) | |
97 | { | |
98 | value_type inv = boost::math::gamma_q_inv(Real(data[i][0]), Real(data[i][3])); | |
99 | BOOST_CHECK_CLOSE_EX(Real(data[i][1]), inv, precision, i); | |
100 | } | |
101 | else if(1 == Real(data[i][3])) | |
102 | BOOST_CHECK_EQUAL(boost::math::gamma_q_inv(Real(data[i][0]), Real(data[i][3])), value_type(0)); | |
103 | else if(fabs(Real(data[i][3])) > 2 * boost::math::tools::min_value<value_type>()) | |
104 | { | |
105 | // not enough bits in our input to get back to x, but we should be in | |
106 | // the same ball park: | |
107 | value_type inv = boost::math::gamma_q_inv(Real(data[i][0]), Real(data[i][3])); | |
108 | BOOST_CHECK_CLOSE_EX(Real(data[i][1]), inv, 100, i); | |
109 | } | |
110 | } | |
111 | std::cout << std::endl; | |
112 | } | |
113 | ||
114 | template <class Real, class T> | |
115 | void do_test_gamma_inv(const T& data, const char* type_name, const char* test_name) | |
116 | { | |
117 | #if !(defined(ERROR_REPORTING_MODE) && !defined(GAMMAP_INV_FUNCTION_TO_TEST)) | |
118 | typedef Real value_type; | |
119 | ||
120 | typedef value_type (*pg)(value_type, value_type); | |
121 | #ifdef GAMMAP_INV_FUNCTION_TO_TEST | |
122 | pg funcp = GAMMAP_INV_FUNCTION_TO_TEST; | |
123 | #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) | |
124 | pg funcp = boost::math::gamma_p_inv<value_type, value_type>; | |
125 | #else | |
126 | pg funcp = boost::math::gamma_p_inv; | |
127 | #endif | |
128 | ||
129 | boost::math::tools::test_result<value_type> result; | |
130 | ||
131 | std::cout << "Testing " << test_name << " with type " << type_name | |
132 | << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; | |
133 | ||
134 | // | |
135 | // test gamma_p_inv(T, T) against data: | |
136 | // | |
137 | result = boost::math::tools::test_hetero<Real>( | |
138 | data, | |
139 | bind_func<Real>(funcp, 0, 1), | |
140 | extract_result<Real>(2)); | |
141 | handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_p_inv", test_name); | |
142 | // | |
143 | // test gamma_q_inv(T, T) against data: | |
144 | // | |
145 | #ifdef GAMMAQ_INV_FUNCTION_TO_TEST | |
146 | funcp = GAMMAQ_INV_FUNCTION_TO_TEST; | |
147 | #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) | |
148 | funcp = boost::math::gamma_q_inv<value_type, value_type>; | |
149 | #else | |
150 | funcp = boost::math::gamma_q_inv; | |
151 | #endif | |
152 | result = boost::math::tools::test_hetero<Real>( | |
153 | data, | |
154 | bind_func<Real>(funcp, 0, 1), | |
155 | extract_result<Real>(3)); | |
156 | handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_q_inv", test_name); | |
157 | #endif | |
158 | } | |
159 | ||
160 | template <class T> | |
161 | void test_gamma(T, const char* name) | |
162 | { | |
163 | #if !defined(TEST_UDT) && !defined(ERROR_REPORTING_MODE) | |
164 | // | |
165 | // The actual test data is rather verbose, so it's in a separate file | |
166 | // | |
167 | // First the data for the incomplete gamma function, each | |
168 | // row has the following 6 entries: | |
169 | // Parameter a, parameter z, | |
170 | // Expected tgamma(a, z), Expected gamma_q(a, z) | |
171 | // Expected tgamma_lower(a, z), Expected gamma_p(a, z) | |
172 | // | |
173 | # include "igamma_med_data.ipp" | |
174 | ||
175 | do_test_gamma_2<T>(igamma_med_data, name, "Running round trip sanity checks on incomplete gamma medium sized values"); | |
176 | ||
177 | # include "igamma_small_data.ipp" | |
178 | ||
179 | do_test_gamma_2<T>(igamma_small_data, name, "Running round trip sanity checks on incomplete gamma small values"); | |
180 | ||
181 | # include "igamma_big_data.ipp" | |
182 | ||
183 | do_test_gamma_2<T>(igamma_big_data, name, "Running round trip sanity checks on incomplete gamma large values"); | |
184 | ||
185 | #endif | |
186 | ||
187 | # include "gamma_inv_data.ipp" | |
188 | ||
189 | do_test_gamma_inv<T>(gamma_inv_data, name, "incomplete gamma inverse(a, z) medium values"); | |
190 | ||
191 | # include "gamma_inv_big_data.ipp" | |
192 | ||
193 | do_test_gamma_inv<T>(gamma_inv_big_data, name, "incomplete gamma inverse(a, z) large values"); | |
194 | ||
195 | # include "gamma_inv_small_data.ipp" | |
196 | ||
197 | do_test_gamma_inv<T>(gamma_inv_small_data, name, "incomplete gamma inverse(a, z) small values"); | |
198 | } | |
199 | ||
200 | template <class T> | |
201 | void test_spots(T, const char* type_name) | |
202 | { | |
203 | std::cout << "Running spot checks for type " << type_name << std::endl; | |
204 | // | |
205 | // basic sanity checks, tolerance is 150 epsilon expressed as a percentage: | |
206 | // | |
207 | T tolerance = boost::math::tools::epsilon<T>() * 15000; | |
208 | if(tolerance < 1e-25f) | |
209 | tolerance = 1e-25f; // limit of test data? | |
210 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1)/100, static_cast<T>(1.0/128)), static_cast<T>(0.35767144525455121503672919307647515332256996883787L), tolerance); | |
211 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1)/100, static_cast<T>(0.5)), static_cast<T>(4.4655350189103486773248562646452806745879516124613e-31L), tolerance*10); | |
212 | // | |
213 | // We can't test in this region against Mathworld's data as the results produced | |
214 | // by functions.wolfram.com appear to be in error, and do *not* round trip with | |
215 | // their own version of gamma_q. Using our output from the inverse as input to | |
216 | // their version of gamma_q *does* round trip however. It should be pointed out | |
217 | // that the functions in this area are very sensitive with nearly infinite | |
218 | // first derivatives, it's also questionable how useful these functions are | |
219 | // in this part of the domain. | |
220 | // | |
221 | //BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1e-2), static_cast<T>(1.0-1.0/128)), static_cast<T>(3.8106736649978161389878528903698068142257930575497e-181L), tolerance); | |
222 | // | |
223 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0/128)), static_cast<T>(3.5379794687984498627918583429482809311448951189097L), tolerance); | |
224 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0/2)), static_cast<T>(0.22746821155978637597125832348982469815821055329511L), tolerance); | |
225 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0-1.0/128)), static_cast<T>(0.000047938431649305382237483273209405461203600840052182L), tolerance); | |
226 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0/128)), static_cast<T>(19.221865946801723949866005318845155649972164294057L), tolerance); | |
227 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0/2)), static_cast<T>(9.6687146147141311517500637401166726067778162022664L), tolerance); | |
228 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0-1.0/128)), static_cast<T>(3.9754602513640844712089002210120603689809432130520L), tolerance); | |
229 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0/128)), static_cast<T>(10243.369973939134157953734588122880006091919872879L), tolerance); | |
230 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0/2)), static_cast<T>(9999.6666686420474237369661574633153551436435884101L), tolerance); | |
231 | BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0-1.0/128)), static_cast<T>(9759.8597223369324083191194574874497413261589080204L), tolerance); | |
232 | } | |
233 |