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327 lines
12 KiB
C++
327 lines
12 KiB
C++
// Copyright Paul A. Bristow 2007.
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// Copyright John Maddock 2007.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// test_normal.cpp
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// http://en.wikipedia.org/wiki/Normal_distribution
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
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// Also:
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// Weisstein, Eric W. "Normal Distribution."
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// From MathWorld--A Wolfram Web Resource.
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// http://mathworld.wolfram.com/NormalDistribution.html
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#ifdef _MSC_VER
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#pragma warning (disable: 4127) // conditional expression is constant
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#endif
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#include <boost/test/included/test_exec_monitor.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/distributions/normal.hpp>
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using boost::math::normal_distribution;
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#include <boost/math/tools/test.hpp>
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#include <iostream>
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using std::cout;
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using std::endl;
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using std::setprecision;
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#include <limits>
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using std::numeric_limits;
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template <class RealType>
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RealType NaivePDF(RealType mean, RealType sd, RealType x)
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{
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// Deliberately naive PDF calculator again which
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// we'll compare our pdf function. However some
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// published values to compare against would be better....
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using namespace std;
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return exp(-(x-mean)*(x-mean)/(2*sd*sd))/(sd * sqrt(2*boost::math::constants::pi<RealType>()));
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}
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template <class RealType>
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void check_normal(RealType mean, RealType sd, RealType x, RealType p, RealType q, RealType tol)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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normal_distribution<RealType>(mean, sd), // distribution.
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x), // random variable.
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p, // probability.
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tol); // %tolerance.
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(
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normal_distribution<RealType>(mean, sd), // distribution.
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x)), // random variable.
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q, // probability complement.
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tol); // %tolerance.
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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normal_distribution<RealType>(mean, sd), // distribution.
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p), // probability.
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x, // random variable.
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tol); // %tolerance.
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(
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normal_distribution<RealType>(mean, sd), // distribution.
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q)), // probability complement.
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x, // random variable.
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tol); // %tolerance.
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}
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template <class RealType>
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void test_spots(RealType)
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{
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// Basic sanity checks
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RealType tolerance = static_cast<RealType>(std::pow(10., -(4-2))); // 1e-4 (as %)
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// Some tests only pass at 1e-4 because values generated by
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// http://faculty.vassar.edu/lowry/VassarStats.html
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// give only 5 or 6 *fixed* places, so small values have fewer digits.
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// Check some bad parameters to the distribution,
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BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
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BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
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// Tests on extreme values of random variate x, if has numeric_limit infinity etc.
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normal_distribution<RealType> N01;
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if(std::numeric_limits<RealType>::has_infinity)
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{
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BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<double>::infinity()), 0); // x = + infinity, pdf = 0
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BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<double>::infinity()), 0); // x = - infinity, pdf = 0
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BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<double>::infinity()), 1); // x = + infinity, cdf = 1
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BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<double>::infinity()), 0); // x = - infinity, cdf = 0
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BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
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BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
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BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
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}
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if (std::numeric_limits<RealType>::has_quiet_NaN)
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{
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// No longer allow x to be NaN, then these tests should throw.
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BOOST_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
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BOOST_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
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BOOST_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
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BOOST_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
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BOOST_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
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}
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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check_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(4.8),
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static_cast<RealType>(0.46017),
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static_cast<RealType>(1 - 0.46017),
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tolerance);
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check_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(5.2),
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static_cast<RealType>(1 - 0.46017),
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static_cast<RealType>(0.46017),
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tolerance);
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check_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(2.2),
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static_cast<RealType>(0.08076),
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static_cast<RealType>(1 - 0.08076),
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tolerance);
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check_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(7.8),
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static_cast<RealType>(1 - 0.08076),
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static_cast<RealType>(0.08076),
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tolerance);
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check_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(-4.5),
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static_cast<RealType>(0.38209),
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static_cast<RealType>(1 - 0.38209),
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tolerance);
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check_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(-1.5),
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static_cast<RealType>(1 - 0.38209),
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static_cast<RealType>(0.38209),
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tolerance);
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check_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(-8.5),
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static_cast<RealType>(0.13567),
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static_cast<RealType>(1 - 0.13567),
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tolerance);
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check_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(2.5),
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static_cast<RealType>(1 - 0.13567),
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static_cast<RealType>(0.13567),
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tolerance);
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//
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// Tests for PDF: we know that the peak value is at 1/sqrt(2*pi)
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//
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tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
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BOOST_CHECK_CLOSE(
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pdf(normal_distribution<RealType>(), static_cast<RealType>(0)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(normal_distribution<RealType>(3), static_cast<RealType>(3)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
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tolerance);
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//
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// Spot checks for mean = -5, sd = 6:
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//
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for(RealType x = -15; x < 5; x += 0.125)
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{
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BOOST_CHECK_CLOSE(
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pdf(normal_distribution<RealType>(-5, 6), x),
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NaivePDF(RealType(-5), RealType(6), x),
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tolerance);
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}
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RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
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normal_distribution<RealType> dist(8, 3);
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RealType x = static_cast<RealType>(0.125);
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using namespace std; // ADL of std names.
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// mean:
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BOOST_CHECK_CLOSE(
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mean(dist)
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, static_cast<RealType>(8), tol2);
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// variance:
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BOOST_CHECK_CLOSE(
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variance(dist)
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, static_cast<RealType>(9), tol2);
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// std deviation:
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BOOST_CHECK_CLOSE(
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standard_deviation(dist)
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, static_cast<RealType>(3), tol2);
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// hazard:
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BOOST_CHECK_CLOSE(
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hazard(dist, x)
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, pdf(dist, x) / cdf(complement(dist, x)), tol2);
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// cumulative hazard:
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BOOST_CHECK_CLOSE(
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chf(dist, x)
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, -log(cdf(complement(dist, x))), tol2);
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// coefficient_of_variation:
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BOOST_CHECK_CLOSE(
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coefficient_of_variation(dist)
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, standard_deviation(dist) / mean(dist), tol2);
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// mode:
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BOOST_CHECK_CLOSE(
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mode(dist)
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, static_cast<RealType>(8), tol2);
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BOOST_CHECK_CLOSE(
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median(dist)
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, static_cast<RealType>(8), tol2);
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// skewness:
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BOOST_CHECK_CLOSE(
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skewness(dist)
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, static_cast<RealType>(0), tol2);
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// kertosis:
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BOOST_CHECK_CLOSE(
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kurtosis(dist)
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, static_cast<RealType>(3), tol2);
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// kertosis excess:
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BOOST_CHECK_CLOSE(
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kurtosis_excess(dist)
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, static_cast<RealType>(0), tol2);
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normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
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BOOST_CHECK_CLOSE(
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mean(norm01),
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static_cast<RealType>(0), 0); // Mean == zero
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normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
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BOOST_CHECK_CLOSE(
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mean(defsd_norm01),
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static_cast<RealType>(0), 0); // Mean == zero
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normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
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BOOST_CHECK_CLOSE(
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mean(def_norm01),
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static_cast<RealType>(0), 0); // Mean == zero
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BOOST_CHECK_CLOSE(
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standard_deviation(def_norm01),
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static_cast<RealType>(1), 0); // Mean == zero
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} // template <class RealType>void test_spots(RealType)
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int test_main(int, char* [])
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{
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// Check that can generate normal distribution using the two convenience methods:
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boost::math::normal myf1(1., 2); // Using typedef
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normal_distribution<> myf2(1., 2); // Using default RealType double.
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boost::math::normal myn01; // Use default values.
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// Note NOT myn01() as the compiler will interpret as a function!
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// Check the synonyms, provided to allow generic use of find_location and find_scale.
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BOOST_CHECK_EQUAL(myn01.mean(), myn01.location());
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BOOST_CHECK_EQUAL(myn01.standard_deviation(), myn01.scale());
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// Basic sanity-check spot values.
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// (Parameter value, arbitrarily zero, only communicates the floating point type).
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test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
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test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L); // Test long double.
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
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test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
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#endif
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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"either because the long double overloads of the usual math functions are "
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"not available at all, or because they are too inaccurate for these tests "
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"to pass.</note>" << std::cout;
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#endif
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return 0;
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} // int test_main(int, char* [])
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/*
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Output:
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe"
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Running 1 test case...
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Tolerance for type float is 0.01 %
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Tolerance for type double is 0.01 %
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Tolerance for type long double is 0.01 %
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Tolerance for type class boost::math::concepts::real_concept is 0.01 %
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*** No errors detected
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*/
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