1 // Copyright Paul A. Bristow 2010.
2 // Copyright John Maddock 2007.
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_normal.cpp
10
11 // http://en.wikipedia.org/wiki/Normal_distribution
12 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
13 // Also:
14 // Weisstein, Eric W. "Normal Distribution."
15 // From MathWorld--A Wolfram Web Resource.
16 // http://mathworld.wolfram.com/NormalDistribution.html
17
18 #include <pch.hpp> // include directory /libs/math/src/tr1/ is needed.
19
20 #ifdef _MSC_VER
21 # pragma warning (disable: 4127) // conditional expression is constant
22 // caused by using if(std::numeric_limits<RealType>::has_infinity)
23 // and if (std::numeric_limits<RealType>::has_quiet_NaN)
24 #endif
25
26 #include <boost/math/tools/test.hpp>
27 #include <boost/math/concepts/real_concept.hpp> // for real_concept
28 #define BOOST_TEST_MAIN
29 #include <boost/test/unit_test.hpp> // Boost.Test
30 #include <boost/test/tools/floating_point_comparison.hpp>
31
32 #include <boost/math/distributions/normal.hpp>
33 using boost::math::normal_distribution;
34 #include <boost/math/tools/test.hpp>
35 #include "test_out_of_range.hpp"
36
37 #include <iostream>
38 #include <iomanip>
39 using std::cout;
40 using std::endl;
41 using std::setprecision;
42 #include <limits>
43 using std::numeric_limits;
44
45 template <class RealType>
NaivePDF(RealType mean,RealType sd,RealType x)46 RealType NaivePDF(RealType mean, RealType sd, RealType x)
47 {
48 // Deliberately naive PDF calculator again which
49 // we'll compare our pdf function. However some
50 // published values to compare against would be better....
51 using namespace std;
52 return exp(-(x-mean)*(x-mean)/(2*sd*sd))/(sd * sqrt(2*boost::math::constants::pi<RealType>()));
53 }
54
55 template <class RealType>
check_normal(RealType mean,RealType sd,RealType x,RealType p,RealType q,RealType tol)56 void check_normal(RealType mean, RealType sd, RealType x, RealType p, RealType q, RealType tol)
57 {
58 BOOST_CHECK_CLOSE(
59 ::boost::math::cdf(
60 normal_distribution<RealType>(mean, sd), // distribution.
61 x), // random variable.
62 p, // probability.
63 tol); // %tolerance.
64 BOOST_CHECK_CLOSE(
65 ::boost::math::cdf(
66 complement(
67 normal_distribution<RealType>(mean, sd), // distribution.
68 x)), // random variable.
69 q, // probability complement.
70 tol); // %tolerance.
71 BOOST_CHECK_CLOSE(
72 ::boost::math::quantile(
73 normal_distribution<RealType>(mean, sd), // distribution.
74 p), // probability.
75 x, // random variable.
76 tol); // %tolerance.
77 BOOST_CHECK_CLOSE(
78 ::boost::math::quantile(
79 complement(
80 normal_distribution<RealType>(mean, sd), // distribution.
81 q)), // probability complement.
82 x, // random variable.
83 tol); // %tolerance.
84 }
85
86 template <class RealType>
test_spots(RealType)87 void test_spots(RealType)
88 {
89 // Basic sanity checks
90 RealType tolerance = 1e-2f; // 1e-4 (as %)
91 // Some tests only pass at 1e-4 because values generated by
92 // http://faculty.vassar.edu/lowry/VassarStats.html
93 // give only 5 or 6 *fixed* places, so small values have fewer digits.
94
95 // Check some bad parameters to the distribution,
96 #ifndef BOOST_NO_EXCEPTIONS
97 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
98 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
99 #else
100 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, 0), std::domain_error); // zero sd
101 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, -1), std::domain_error); // negative sd
102 #endif
103
104 // Tests on extreme values of random variate x, if has std::numeric_limits infinity etc.
105 normal_distribution<RealType> N01;
106 if(std::numeric_limits<RealType>::has_infinity)
107 {
108 BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
109 BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
110 BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
111 BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
112 BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
113 BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
114 #ifndef BOOST_NO_EXCEPTIONS
115 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
116 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
117 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
118 #else
119 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
120 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
121 BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
122 #endif
123 }
124
125 if (std::numeric_limits<RealType>::has_quiet_NaN)
126 {
127 // No longer allow x to be NaN, then these tests should throw.
128 BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
129 BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
130 BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
131 BOOST_MATH_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
132 BOOST_MATH_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
133 }
134
135 cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
136
137 check_normal(
138 static_cast<RealType>(5),
139 static_cast<RealType>(2),
140 static_cast<RealType>(4.8),
141 static_cast<RealType>(0.46017),
142 static_cast<RealType>(1 - 0.46017),
143 tolerance);
144
145 check_normal(
146 static_cast<RealType>(5),
147 static_cast<RealType>(2),
148 static_cast<RealType>(5.2),
149 static_cast<RealType>(1 - 0.46017),
150 static_cast<RealType>(0.46017),
151 tolerance);
152
153 check_normal(
154 static_cast<RealType>(5),
155 static_cast<RealType>(2),
156 static_cast<RealType>(2.2),
157 static_cast<RealType>(0.08076),
158 static_cast<RealType>(1 - 0.08076),
159 tolerance);
160
161 check_normal(
162 static_cast<RealType>(5),
163 static_cast<RealType>(2),
164 static_cast<RealType>(7.8),
165 static_cast<RealType>(1 - 0.08076),
166 static_cast<RealType>(0.08076),
167 tolerance);
168
169 check_normal(
170 static_cast<RealType>(-3),
171 static_cast<RealType>(5),
172 static_cast<RealType>(-4.5),
173 static_cast<RealType>(0.38209),
174 static_cast<RealType>(1 - 0.38209),
175 tolerance);
176
177 check_normal(
178 static_cast<RealType>(-3),
179 static_cast<RealType>(5),
180 static_cast<RealType>(-1.5),
181 static_cast<RealType>(1 - 0.38209),
182 static_cast<RealType>(0.38209),
183 tolerance);
184
185 check_normal(
186 static_cast<RealType>(-3),
187 static_cast<RealType>(5),
188 static_cast<RealType>(-8.5),
189 static_cast<RealType>(0.13567),
190 static_cast<RealType>(1 - 0.13567),
191 tolerance);
192
193 check_normal(
194 static_cast<RealType>(-3),
195 static_cast<RealType>(5),
196 static_cast<RealType>(2.5),
197 static_cast<RealType>(1 - 0.13567),
198 static_cast<RealType>(0.13567),
199 tolerance);
200
201 //
202 // Tests for PDF: we know that the peak value is at 1/sqrt(2*pi)
203 //
204 tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
205 BOOST_CHECK_CLOSE(
206 pdf(normal_distribution<RealType>(), static_cast<RealType>(0)),
207 static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
208 tolerance);
209 BOOST_CHECK_CLOSE(
210 pdf(normal_distribution<RealType>(3), static_cast<RealType>(3)),
211 static_cast<RealType>(0.3989422804014326779399460599343818684759L),
212 tolerance);
213 BOOST_CHECK_CLOSE(
214 pdf(normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
215 static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
216 tolerance);
217
218 //
219 // Spot checks for mean = -5, sd = 6:
220 //
221 for(RealType x = -15; x < 5; x += 0.125)
222 {
223 BOOST_CHECK_CLOSE(
224 pdf(normal_distribution<RealType>(-5, 6), x),
225 NaivePDF(RealType(-5), RealType(6), x),
226 tolerance);
227 }
228
229 RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
230 normal_distribution<RealType> dist(8, 3);
231 RealType x = static_cast<RealType>(0.125);
232
233 BOOST_MATH_STD_USING // ADL of std math lib names
234
235 // mean:
236 BOOST_CHECK_CLOSE(
237 mean(dist)
238 , static_cast<RealType>(8), tol2);
239 // variance:
240 BOOST_CHECK_CLOSE(
241 variance(dist)
242 , static_cast<RealType>(9), tol2);
243 // std deviation:
244 BOOST_CHECK_CLOSE(
245 standard_deviation(dist)
246 , static_cast<RealType>(3), tol2);
247 // hazard:
248 BOOST_CHECK_CLOSE(
249 hazard(dist, x)
250 , pdf(dist, x) / cdf(complement(dist, x)), tol2);
251 // cumulative hazard:
252 BOOST_CHECK_CLOSE(
253 chf(dist, x)
254 , -log(cdf(complement(dist, x))), tol2);
255 // coefficient_of_variation:
256 BOOST_CHECK_CLOSE(
257 coefficient_of_variation(dist)
258 , standard_deviation(dist) / mean(dist), tol2);
259 // mode:
260 BOOST_CHECK_CLOSE(
261 mode(dist)
262 , static_cast<RealType>(8), tol2);
263
264 BOOST_CHECK_CLOSE(
265 median(dist)
266 , static_cast<RealType>(8), tol2);
267
268 // skewness:
269 BOOST_CHECK_CLOSE(
270 skewness(dist)
271 , static_cast<RealType>(0), tol2);
272 // kurtosis:
273 BOOST_CHECK_CLOSE(
274 kurtosis(dist)
275 , static_cast<RealType>(3), tol2);
276 // kurtosis excess:
277 BOOST_CHECK_CLOSE(
278 kurtosis_excess(dist)
279 , static_cast<RealType>(0), tol2);
280
281 RealType expected_entropy = log(boost::math::constants::two_pi<RealType>()*boost::math::constants::e<RealType>()*9)/2;
282 BOOST_CHECK_CLOSE(
283 entropy(dist)
284 ,expected_entropy, tol2);
285
286 normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
287 BOOST_CHECK_CLOSE(
288 mean(norm01),
289 static_cast<RealType>(0), 0); // Mean == zero
290
291 normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
292 BOOST_CHECK_CLOSE(
293 mean(defsd_norm01),
294 static_cast<RealType>(0), 0); // Mean == zero
295
296 normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
297 BOOST_CHECK_CLOSE(
298 mean(def_norm01),
299 static_cast<RealType>(0), 0); // Mean == zero
300
301 BOOST_CHECK_CLOSE(
302 standard_deviation(def_norm01),
303 static_cast<RealType>(1), 0); // Mean == zero
304
305 // Error tests:
306 check_out_of_range<boost::math::normal_distribution<RealType> >(0, 1); // (All) valid constructor parameter values.
307
308 BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, 0), 0), std::domain_error);
309 BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, -1), 0), std::domain_error);
310 BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), -1), std::domain_error);
311 BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), 2), std::domain_error);
312 } // template <class RealType>void test_spots(RealType)
313
BOOST_AUTO_TEST_CASE(test_main)314 BOOST_AUTO_TEST_CASE( test_main )
315 {
316 // Check that can generate normal distribution using the two convenience methods:
317 boost::math::normal myf1(1., 2); // Using typedef
318 normal_distribution<> myf2(1., 2); // Using default RealType double.
319 boost::math::normal myn01; // Use default values.
320 // Note NOT myn01() as the compiler will interpret as a function!
321
322 // Check the synonyms, provided to allow generic use of find_location and find_scale.
323 BOOST_CHECK_EQUAL(myn01.mean(), myn01.location());
324 BOOST_CHECK_EQUAL(myn01.standard_deviation(), myn01.scale());
325
326 // Basic sanity-check spot values.
327 // (Parameter value, arbitrarily zero, only communicates the floating point type).
328 test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
329 test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
330 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
331 test_spots(0.0L); // Test long double.
332 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
333 test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
334 #endif
335 #else
336 std::cout << "<note>The long double tests have been disabled on this platform "
337 "either because the long double overloads of the usual math functions are "
338 "not available at all, or because they are too inaccurate for these tests "
339 "to pass.</note>" << std::endl;
340 #endif
341
342
343 } // BOOST_AUTO_TEST_CASE( test_main )
344
345 /*
346
347 Output:
348
349 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe"
350 Running 1 test case...
351 Tolerance for type float is 0.01 %
352 Tolerance for type double is 0.01 %
353 Tolerance for type long double is 0.01 %
354 Tolerance for type class boost::math::concepts::real_concept is 0.01 %
355 *** No errors detected
356
357
358
359
360 ------ Build started: Project: test_normal, Configuration: Release Win32 ------
361 test_normal.cpp
362 Generating code
363 Finished generating code
364 test_normal.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_normal.exe
365 Running 1 test case...
366 Tolerance for type float is 0.01 %
367 Tolerance for type double is 0.01 %
368 Tolerance for type long double is 0.01 %
369 Tolerance for type class boost::math::concepts::real_concept is 0.01 %
370
371 *** No errors detected
372 Detected memory leaks!
373 Dumping objects ->
374 {2413} normal block at 0x00321190, 42 bytes long.
375 Data: <class boost::mat> 63 6C 61 73 73 20 62 6F 6F 73 74 3A 3A 6D 61 74
376 {2412} normal block at 0x003231F0, 8 bytes long.
377 Data: < 2 22 > 90 11 32 00 98 32 32 00
378 {1824} normal block at 0x00323180, 12 bytes long.
379 Data: <long double > 6C 6F 6E 67 20 64 6F 75 62 6C 65 00
380 {1823} normal block at 0x00323298, 8 bytes long.
381 Data: < 12 `22 > 80 31 32 00 60 32 32 00
382 {1227} normal block at 0x00323148, 7 bytes long.
383 Data: <double > 64 6F 75 62 6C 65 00
384 {1226} normal block at 0x00323260, 8 bytes long.
385 Data: <H12 02 > 48 31 32 00 A0 30 32 00
386 {633} normal block at 0x003230D8, 6 bytes long.
387 Data: <float > 66 6C 6F 61 74 00
388 {632} normal block at 0x003230A0, 8 bytes long.
389 Data: < 02 > D8 30 32 00 00 00 00 00
390 Object dump complete.
391 ========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
392
393
394 */
395
396
397