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1 | // test_find_scale.cpp |
2 | ||
3 | // Copyright John Maddock 2007. | |
4 | // Copyright Paul A. Bristow 2007. | |
5 | ||
6 | // Use, modification and distribution are subject to the | |
7 | // Boost Software License, Version 1.0. | |
8 | // (See accompanying file LICENSE_1_0.txt | |
9 | // or copy at http://www.boost.org/LICENSE_1_0.txt) | |
10 | ||
11 | // Basic sanity test for find_scale function. | |
12 | ||
13 | // Default distribution domain error policy is | |
14 | // #define BOOST_MATH_DOMAIN_ERROR_POLICY throw_on_error | |
15 | ||
16 | #include <pch.hpp> | |
17 | ||
18 | #include <boost/math/tools/test.hpp> | |
19 | #include <boost/math/concepts/real_concept.hpp> // for real_concept | |
20 | #include <boost/math/distributions/normal.hpp> // for normal_distribution | |
21 | using boost::math::normal; // Default type double. | |
22 | using boost::math::normal_distribution; // All floating-point types. | |
23 | #include <boost/math/distributions/cauchy.hpp> // for cauchy_distribution | |
24 | using boost::math::cauchy; | |
25 | #include <boost/math/distributions/pareto.hpp> // for cauchy_distribution | |
26 | using boost::math::pareto; | |
27 | #include <boost/math/distributions/find_scale.hpp> | |
28 | using boost::math::find_scale; | |
29 | using boost::math::complement;// will be needed by users who want complement, | |
30 | #include <boost/math/policies/policy.hpp> | |
31 | using boost::math::policies::policy; | |
32 | ||
33 | #define BOOST_TEST_MAIN | |
34 | #include <boost/test/unit_test.hpp> // for test_main | |
92f5a8d4 | 35 | #include <boost/test/tools/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION, BOOST_CHECK_EQUAL... |
7c673cae FG |
36 | |
37 | #include <iostream> | |
38 | #include <iomanip> | |
39 | using std::cout; using std::endl; using std::fixed; | |
40 | using std::right; using std::left; using std::showpoint; | |
41 | using std::showpos; using std::setw; using std::setprecision; | |
42 | ||
43 | #include <limits> | |
44 | using std::numeric_limits; | |
45 | ||
46 | template <class RealType> // Any floating-point type RealType. | |
47 | void test_spots(RealType) | |
48 | { // Parameter only provides the type, float, double... value ignored. | |
49 | ||
50 | // Basic sanity checks, test data may be to double precision only | |
51 | // so set tolerance to 100 eps expressed as a fraction, | |
52 | // or 100 eps of type double expressed as a fraction, | |
53 | // whichever is the larger. | |
54 | ||
55 | RealType tolerance = (std::max) | |
56 | (boost::math::tools::epsilon<RealType>(), | |
57 | static_cast<RealType>(std::numeric_limits<double>::epsilon())); | |
58 | tolerance *= 100; // 100 eps as a fraction. | |
59 | ||
60 | cout << "Tolerance for type " << typeid(RealType).name() << " is " | |
61 | << setprecision(3) << tolerance << " (or " << tolerance * 100 << "%)." << endl; | |
62 | ||
63 | BOOST_MATH_CHECK_THROW( // Probability outside 0 to 1. | |
64 | find_scale<normal_distribution<RealType> >( | |
65 | static_cast<RealType>(0.), static_cast<RealType>(-1.), static_cast<RealType>(0.) ), | |
66 | std::domain_error); | |
67 | ||
68 | normal_distribution<RealType> n; // standard N(0,1) | |
69 | BOOST_CHECK_EQUAL(n.location(), 0); // aka mean. | |
70 | BOOST_CHECK_EQUAL(n.scale(), 1); // aka standard_deviation. | |
71 | ||
72 | // Check for 'bad' arguments. | |
73 | BOOST_MATH_CHECK_THROW(find_scale<normal>(0., -1., 0.), std::domain_error); // p below 0 to 1. | |
74 | BOOST_MATH_CHECK_THROW(find_scale<normal>(0., 2., 0.), std::domain_error); // p above 0 to 1. | |
75 | BOOST_MATH_CHECK_THROW(find_scale<normal>(numeric_limits<double>::infinity(), 0.5, 0.), | |
76 | std::domain_error); // z not finite. | |
77 | BOOST_MATH_CHECK_THROW(find_scale<normal>(numeric_limits<double>::quiet_NaN(), -1., 0.), | |
78 | std::domain_error); // z not finite | |
79 | BOOST_MATH_CHECK_THROW(find_scale<normal>(0., -1., numeric_limits<double>::quiet_NaN()), | |
80 | std::domain_error); // scale not finite | |
81 | ||
82 | ||
83 | BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., -1., 0.)), std::domain_error); // p below 0 to 1. | |
84 | BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., 2., 0.)), std::domain_error); // p above 0 to 1. | |
85 | BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(numeric_limits<double>::infinity(), 0.5, 0.)), | |
86 | std::domain_error); // z not finite. | |
87 | BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(numeric_limits<double>::quiet_NaN(), -1., 0.)), | |
88 | std::domain_error); // z not finite | |
89 | BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., -1., numeric_limits<double>::quiet_NaN())), | |
90 | std::domain_error); // scale not finite | |
91 | ||
92 | BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., -1., 0.)), std::domain_error); // p below 0 to 1. | |
93 | ||
94 | ||
95 | // Check for ab-use with unsuitable distribution(s), for example, | |
96 | // pareto distribution (and most others) can't be used with find_scale (or find_location) | |
97 | // because they lack the scale and location attributes. | |
98 | // BOOST_MATH_CHECK_THROW(find_scale<pareto>(0., 0.5, 0.), std::domain_error); | |
99 | // correctly fails to compile in find_scale() at | |
1e59de90 | 100 | // static_assert(::boost::math::tools::is_scaled_distribution<Dist>::value); |
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101 | |
102 | // Check doesn't throw when an ignore_error for domain_error policy is used. | |
103 | using boost::math::policies::policy; | |
104 | using boost::math::policies::domain_error; | |
105 | using boost::math::policies::ignore_error; | |
106 | ||
107 | // Define a (bad?) policy to ignore domain errors ('bad' arguments): | |
108 | typedef policy<domain_error<ignore_error> > ignore_domain_policy; | |
109 | // Using a typedef is convenient, especially if it is re-used. | |
110 | #ifndef BOOST_NO_EXCEPTIONS | |
111 | BOOST_CHECK_NO_THROW(find_scale<normal>(0, -1, 1, | |
112 | ignore_domain_policy())); // probability outside [0, 1] | |
113 | BOOST_CHECK_NO_THROW(find_scale<normal>(numeric_limits<double>::infinity(), -1, 1, | |
114 | ignore_domain_policy())); // z not finite. | |
115 | BOOST_CHECK_NO_THROW(find_scale<normal>(complement(0, -1, 1, ignore_domain_policy()))); // probability outside [0, 1] | |
116 | BOOST_CHECK_NO_THROW(find_scale<normal>(complement(numeric_limits<double>::infinity(), -1, 1, | |
117 | ignore_domain_policy()))); // z not finite. | |
118 | #endif | |
119 | RealType l = 0.; // standard normal distribution. | |
120 | RealType sd = static_cast<RealType>(1); // normal default standard deviation = 1. | |
121 | normal_distribution<RealType> n01(l, sd); // mean(location) = 0, standard_deviation (scale) = 1. | |
122 | RealType z = static_cast<RealType>(-2); // z to give prob p | |
123 | //cout << "Standard normal distribution with standard deviation = " << sd | |
124 | // << " has " << "fraction <= " << z << " = " << cdf(n01, z) << endl; | |
125 | // Standard normal distribution with standard deviation = 1 has fraction <= -2 = 0.0227501 | |
126 | ||
127 | //normal_distribution<RealType> np001pc(l, sd); // Same mean(location) but with standard_deviation (scale) changed. | |
128 | //cout << "Normal distribution with standard deviation = " << s | |
129 | // << " has " << "fraction <= " << z << " = " << cdf(np001pc, z) << endl; | |
130 | ||
131 | // Find scale to give a probability p (0.001) of z (-2) | |
132 | RealType p = static_cast<RealType>(0.001); // only 0.1% to be below z (-2). | |
133 | // location (mean) remains at zero. | |
134 | RealType s = find_scale<normal_distribution<RealType> >(z, p, l); | |
135 | //cout << "Mean " << l << ", z " << z << ", p " << p | |
136 | // << ", sd " << sd << ", find_scale " << s | |
137 | // << ", difference in sd " << s - sd << endl; | |
138 | // Mean 0, z -2, p 0.001, sd 1, find_scale 0.64720053440907599, difference in sd -0.352799 | |
139 | ||
140 | cout.precision(17); | |
141 | BOOST_CHECK_CLOSE_FRACTION(s, static_cast<RealType>(0.64720053440907599L), tolerance); | |
142 | ||
143 | normal_distribution<RealType> np001pc(l, s); // Same mean(location) but with standard_deviation (scale) changed. | |
144 | //cout << "Normal distribution with standard deviation = " << s | |
145 | // << " has " << "fraction <= " << z << " = " << cdf(np001pc, z) << endl; | |
146 | // Normal distribution with standard deviation = 0.647201 has fraction <= -2 = 0.001 | |
147 | ||
148 | // Check cdf such that only fraction p really is below changed standard deviation s. | |
149 | BOOST_CHECK_CLOSE_FRACTION(p, cdf(np001pc, z), tolerance); | |
150 | ||
151 | // Check that some policies can be applied (though results not used here). | |
152 | s = find_scale<normal_distribution<RealType> >(z, p, l, policy<>()); // Default policy, needs using boost::math::policies::policy; | |
153 | s = find_scale<normal_distribution<RealType> >(z, p, l, boost::math::policies::policy<>()); // Default policy, fully specified. | |
154 | s = find_scale<normal_distribution<RealType> >(z, p, l, ignore_domain_policy()); // find_scale with new policy, using typedef. | |
155 | s = find_scale<normal_distribution<RealType> >(z, p, l, policy<domain_error<ignore_error> >()); // New policy, without typedef. | |
156 | ||
157 | // Check that can use the complement version too. | |
158 | RealType q = 1 - p; // complement. | |
159 | s = find_scale<normal_distribution<RealType> >(complement(z, q, l)); // Implicit default policy. | |
160 | BOOST_CHECK_CLOSE_FRACTION(s, static_cast<RealType>(0.64720053440907599L), tolerance); | |
161 | s = find_scale<normal_distribution<RealType> >(complement(z, q, l, policy<>())); // Explicit default policy. | |
162 | BOOST_CHECK_CLOSE_FRACTION(s, static_cast<RealType>(0.64720053440907599L), tolerance); | |
163 | ||
164 | normal_distribution<RealType> np95pc(l, s); // Same mean(location) but with new standard_deviation (scale). | |
165 | ||
166 | //cout << "Mean " << l << ", z " << z << ", q " << q | |
167 | //<< ", sd " << sd << ", find_scale " << s | |
168 | //<< ", difference in sd " << s - sd << endl; | |
169 | ||
170 | //cout << "Normal distribution with standard deviation = " << s | |
171 | // << " has " << "fraction <= " << z << " = " << cdf(np001pc, z) << endl; | |
172 | BOOST_CHECK_CLOSE_FRACTION(q, cdf(complement(np95pc, z)), tolerance); | |
173 | ||
174 | } // template <class RealType>void test_spots(RealType) | |
175 | ||
176 | BOOST_AUTO_TEST_CASE( test_main ) | |
177 | { | |
178 | // Basic sanity-check spot values. | |
179 | ||
180 | // (Parameter value, arbitrarily zero, only communicates the floating-point type). | |
181 | test_spots(0.0F); // Test float. | |
182 | test_spots(0.0); // Test double. | |
183 | #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS | |
184 | test_spots(0.0L); // Test long double. | |
1e59de90 | 185 | #if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x0582)) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS) |
7c673cae FG |
186 | test_spots(boost::math::concepts::real_concept(0.)); // Test real concept. |
187 | #endif | |
188 | #else | |
189 | std::cout << "<note>The long double tests have been disabled on this platform " | |
190 | "either because the long double overloads of the usual math functions are " | |
191 | "not available at all, or because they are too inaccurate for these tests " | |
192 | "to pass.</note>" << std::endl; | |
193 | #endif | |
194 | ||
195 | } // BOOST_AUTO_TEST_CASE( test_main ) | |
196 | ||
197 | /* | |
198 | ||
199 | Output is: | |
200 | ||
201 | Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_find_scale.exe" | |
202 | Running 1 test case... | |
203 | Tolerance for type float is 1.19e-005 (or 0.00119%). | |
204 | Tolerance for type double is 2.22e-014 (or 2.22e-012%). | |
205 | Tolerance for type long double is 2.22e-014 (or 2.22e-012%). | |
206 | Tolerance for type class boost::math::concepts::real_concept is 2.22e-014 (or 2.22e-012%). | |
207 | *** No errors detected | |
208 | ||
209 | ||
210 | */ | |
211 | ||
212 |