]>
git.proxmox.com Git - ceph.git/blob - ceph/src/boost/libs/math/test/test_normal.cpp
1 // Copyright Paul A. Bristow 2010.
2 // Copyright John Maddock 2007.
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)
11 // http://en.wikipedia.org/wiki/Normal_distribution
12 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
14 // Weisstein, Eric W. "Normal Distribution."
15 // From MathWorld--A Wolfram Web Resource.
16 // http://mathworld.wolfram.com/NormalDistribution.html
18 #include <pch.hpp> // include directory /libs/math/src/tr1/ is needed.
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)
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>
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"
41 using std :: setprecision
;
43 using std :: numeric_limits
;
45 template < class RealType
>
46 RealType
NaivePDF ( RealType mean
, RealType sd
, RealType x
)
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....
52 return exp (-( x
- mean
)*( x
- mean
)/( 2 * sd
* sd
))/( sd
* sqrt ( 2 * boost :: math :: constants :: pi
< RealType
>()));
55 template < class RealType
>
56 void check_normal ( RealType mean
, RealType sd
, RealType x
, RealType p
, RealType q
, RealType tol
)
60 normal_distribution
< RealType
>( mean
, sd
), // distribution.
61 x
), // random variable.
67 normal_distribution
< RealType
>( mean
, sd
), // distribution.
68 x
)), // random variable.
69 q
, // probability complement.
72 :: boost :: math :: quantile (
73 normal_distribution
< RealType
>( mean
, sd
), // distribution.
75 x
, // random variable.
78 :: boost :: math :: quantile (
80 normal_distribution
< RealType
>( mean
, sd
), // distribution.
81 q
)), // probability complement.
82 x
, // random variable.
86 template < class RealType
>
87 void test_spots ( RealType
)
89 // Basic sanity checks
90 RealType tolerance
= 1e-2 f
; // 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.
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
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
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
)
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
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
125 if ( std :: numeric_limits
< RealType
>:: has_quiet_NaN
)
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
135 cout
<< "Tolerance for type " << typeid ( RealType
). name () << " is " << tolerance
<< " %" << endl
;
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 ),
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 ),
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 ),
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 ),
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 ),
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 ),
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 ),
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 ),
202 // Tests for PDF: we know that the peak value is at 1/sqrt(2*pi)
204 tolerance
= boost :: math :: tools :: epsilon
< RealType
>() * 5 * 100 ; // 5 eps as a percentage
206 pdf ( normal_distribution
< RealType
>(), static_cast < RealType
>( 0 )),
207 static_cast < RealType
>( 0.3989422804014326779399460599343818684759L ), // 1/sqrt(2*pi)
210 pdf ( normal_distribution
< RealType
>( 3 ), static_cast < RealType
>( 3 )),
211 static_cast < RealType
>( 0.3989422804014326779399460599343818684759L ),
214 pdf ( normal_distribution
< RealType
>( 3 , 5 ), static_cast < RealType
>( 3 )),
215 static_cast < RealType
>( 0.3989422804014326779399460599343818684759L / 5 ),
219 // Spot checks for mean = -5, sd = 6:
221 for ( RealType x
= - 15 ; x
< 5 ; x
+= 0.125 )
224 pdf ( normal_distribution
< RealType
>(- 5 , 6 ), x
),
225 NaivePDF ( RealType (- 5 ), RealType ( 6 ), x
),
229 RealType tol2
= boost :: math :: tools :: epsilon
< RealType
>() * 5 ;
230 normal_distribution
< RealType
> dist ( 8 , 3 );
231 RealType x
= static_cast < RealType
>( 0.125 );
233 BOOST_MATH_STD_USING
// ADL of std math lib names
238 , static_cast < RealType
>( 8 ), tol2
);
242 , static_cast < RealType
>( 9 ), tol2
);
245 standard_deviation ( dist
)
246 , static_cast < RealType
>( 3 ), tol2
);
250 , pdf ( dist
, x
) / cdf ( complement ( dist
, x
)), tol2
);
251 // cumulative hazard:
254 , - log ( cdf ( complement ( dist
, x
))), tol2
);
255 // coefficient_of_variation:
257 coefficient_of_variation ( dist
)
258 , standard_deviation ( dist
) / mean ( dist
), tol2
);
262 , static_cast < RealType
>( 8 ), tol2
);
266 , static_cast < RealType
>( 8 ), tol2
);
271 , static_cast < RealType
>( 0 ), tol2
);
275 , static_cast < RealType
>( 3 ), tol2
);
278 kurtosis_excess ( dist
)
279 , static_cast < RealType
>( 0 ), tol2
);
281 normal_distribution
< RealType
> norm01 ( 0 , 1 ); // Test default (0, 1)
284 static_cast < RealType
>( 0 ), 0 ); // Mean == zero
286 normal_distribution
< RealType
> defsd_norm01 ( 0 ); // Test default (0, sd = 1)
289 static_cast < RealType
>( 0 ), 0 ); // Mean == zero
291 normal_distribution
< RealType
> def_norm01
; // Test default (0, sd = 1)
294 static_cast < RealType
>( 0 ), 0 ); // Mean == zero
297 standard_deviation ( def_norm01
),
298 static_cast < RealType
>( 1 ), 0 ); // Mean == zero
301 check_out_of_range
< boost :: math :: normal_distribution
< RealType
> >( 0 , 1 ); // (All) valid constructor parameter values.
303 BOOST_MATH_CHECK_THROW ( pdf ( normal_distribution
< RealType
>( 0 , 0 ), 0 ), std :: domain_error
);
304 BOOST_MATH_CHECK_THROW ( pdf ( normal_distribution
< RealType
>( 0 , - 1 ), 0 ), std :: domain_error
);
305 BOOST_MATH_CHECK_THROW ( quantile ( normal_distribution
< RealType
>( 0 , 1 ), - 1 ), std :: domain_error
);
306 BOOST_MATH_CHECK_THROW ( quantile ( normal_distribution
< RealType
>( 0 , 1 ), 2 ), std :: domain_error
);
307 } // template <class RealType>void test_spots(RealType)
309 BOOST_AUTO_TEST_CASE ( test_main
)
311 // Check that can generate normal distribution using the two convenience methods:
312 boost :: math :: normal
myf1 ( 1 ., 2 ); // Using typedef
313 normal_distribution
<> myf2 ( 1 ., 2 ); // Using default RealType double.
314 boost :: math :: normal myn01
; // Use default values.
315 // Note NOT myn01() as the compiler will interpret as a function!
317 // Check the synonyms, provided to allow generic use of find_location and find_scale.
318 BOOST_CHECK_EQUAL ( myn01
. mean (), myn01
. location ());
319 BOOST_CHECK_EQUAL ( myn01
. standard_deviation (), myn01
. scale ());
321 // Basic sanity-check spot values.
322 // (Parameter value, arbitrarily zero, only communicates the floating point type).
323 test_spots ( 0.0 F
); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
324 test_spots ( 0.0 ); // Test double. OK at decdigits 7, tolerance = 1e07 %
325 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
326 test_spots ( 0.0L ); // Test long double.
327 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
328 test_spots ( boost :: math :: concepts :: real_concept ( 0 .)); // Test real concept.
331 std :: cout
<< "<note>The long double tests have been disabled on this platform "
332 "either because the long double overloads of the usual math functions are "
333 "not available at all, or because they are too inaccurate for these tests "
334 "to pass.</note>" << std :: endl
;
338 } // BOOST_AUTO_TEST_CASE( test_main )
344 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe"
345 Running 1 test case...
346 Tolerance for type float is 0.01 %
347 Tolerance for type double is 0.01 %
348 Tolerance for type long double is 0.01 %
349 Tolerance for type class boost::math::concepts::real_concept is 0.01 %
350 *** No errors detected
355 ------ Build started: Project: test_normal, Configuration: Release Win32 ------
358 Finished generating code
359 test_normal.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_normal.exe
360 Running 1 test case...
361 Tolerance for type float is 0.01 %
362 Tolerance for type double is 0.01 %
363 Tolerance for type long double is 0.01 %
364 Tolerance for type class boost::math::concepts::real_concept is 0.01 %
366 *** No errors detected
367 Detected memory leaks!
369 {2413} normal block at 0x00321190, 42 bytes long.
370 Data: <class boost::mat> 63 6C 61 73 73 20 62 6F 6F 73 74 3A 3A 6D 61 74
371 {2412} normal block at 0x003231F0, 8 bytes long.
372 Data: < 2 22 > 90 11 32 00 98 32 32 00
373 {1824} normal block at 0x00323180, 12 bytes long.
374 Data: <long double > 6C 6F 6E 67 20 64 6F 75 62 6C 65 00
375 {1823} normal block at 0x00323298, 8 bytes long.
376 Data: < 12 `22 > 80 31 32 00 60 32 32 00
377 {1227} normal block at 0x00323148, 7 bytes long.
378 Data: <double > 64 6F 75 62 6C 65 00
379 {1226} normal block at 0x00323260, 8 bytes long.
380 Data: <H12 02 > 48 31 32 00 A0 30 32 00
381 {633} normal block at 0x003230D8, 6 bytes long.
382 Data: <float > 66 6C 6F 61 74 00
383 {632} normal block at 0x003230A0, 8 bytes long.
384 Data: < 02 > D8 30 32 00 00 00 00 00
385 Object dump complete.
386 ========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========