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448 lines
18 KiB
C++
448 lines
18 KiB
C++
// (C) 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. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
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#include <boost/math/concepts/real_concept.hpp>
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp>
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/distributions/non_central_chi_squared.hpp>
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#include <boost/type_traits/is_floating_point.hpp>
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#include <boost/array.hpp>
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#include "functor.hpp"
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#include "handle_test_result.hpp"
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#include "table_type.hpp"
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#include <iostream>
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#include <iomanip>
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#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
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{\
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unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
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BOOST_CHECK_CLOSE(a, b, prec); \
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if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
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{\
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std::cerr << "Failure was at row " << i << std::endl;\
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std::cerr << std::setprecision(35); \
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std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
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std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
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}\
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}
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#define BOOST_CHECK_EX(a, i) \
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{\
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unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
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BOOST_CHECK(a); \
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if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
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{\
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std::cerr << "Failure was at row " << i << std::endl;\
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std::cerr << std::setprecision(35); \
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std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
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std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
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}\
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}
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template <class RealType>
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RealType naive_pdf(RealType v, RealType lam, RealType x)
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{
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// Formula direct from
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// http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html
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// with no simplification:
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RealType sum, term, prefix(1);
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RealType eps = boost::math::tools::epsilon<RealType>();
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term = sum = pdf(boost::math::chi_squared_distribution<RealType>(v), x);
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for(int i = 1;; ++i)
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{
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prefix *= lam / (2 * i);
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term = prefix * pdf(boost::math::chi_squared_distribution<RealType>(v + 2 * i), x);
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sum += term;
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if(term / sum < eps)
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break;
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}
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return sum * exp(-lam / 2);
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}
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template <class RealType>
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void test_spot(
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RealType df, // Degrees of freedom
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RealType ncp, // non-centrality param
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RealType cs, // Chi Square statistic
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RealType P, // CDF
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RealType Q, // Complement of CDF
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RealType tol) // Test tolerance
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{
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boost::math::non_central_chi_squared_distribution<RealType> dist(df, ncp);
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BOOST_CHECK_CLOSE(
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cdf(dist, cs), P, tol);
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#ifndef BOOST_NO_EXCEPTIONS
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try{
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BOOST_CHECK_CLOSE(
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pdf(dist, cs), naive_pdf(dist.degrees_of_freedom(), ncp, cs), tol * 150);
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}
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catch(const std::overflow_error&)
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{
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}
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#endif
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if((P < 0.99) && (Q < 0.99))
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{
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//
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// We can only check this if P is not too close to 1,
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// so that we can guarantee Q is reasonably free of error:
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//
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BOOST_CHECK_CLOSE(
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cdf(complement(dist, cs)), Q, tol);
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BOOST_CHECK_CLOSE(
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quantile(dist, P), cs, tol * 10);
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BOOST_CHECK_CLOSE(
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quantile(complement(dist, Q)), cs, tol * 10);
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BOOST_CHECK_CLOSE(
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dist.find_degrees_of_freedom(ncp, cs, P), df, tol * 10);
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BOOST_CHECK_CLOSE(
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dist.find_degrees_of_freedom(boost::math::complement(ncp, cs, Q)), df, tol * 10);
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BOOST_CHECK_CLOSE(
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dist.find_non_centrality(df, cs, P), ncp, tol * 10);
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BOOST_CHECK_CLOSE(
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dist.find_non_centrality(boost::math::complement(df, cs, Q)), ncp, tol * 10);
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}
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}
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template <class RealType> // Any floating-point type RealType.
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void test_spots(RealType)
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{
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#ifndef ERROR_REPORTING_MODE
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RealType tolerance = (std::max)(
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boost::math::tools::epsilon<RealType>(),
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(RealType)boost::math::tools::epsilon<double>() * 5) * 150;
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//
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// At float precision we need to up the tolerance, since
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// the input values are rounded off to inexact quantities
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// the results get thrown off by a noticeable amount.
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//
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if(boost::math::tools::digits<RealType>() < 50)
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tolerance *= 50;
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if(boost::is_floating_point<RealType>::value != 1)
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tolerance *= 20; // real_concept special functions are less accurate
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std::cout << "Tolerance = " << tolerance << "%." << std::endl;
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using boost::math::chi_squared_distribution;
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using ::boost::math::chi_squared;
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using ::boost::math::cdf;
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using ::boost::math::pdf;
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//
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// Test against the data from Table 6 of:
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//
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// "Self-Validating Computations of Probabilities for Selected
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// Central and Noncentral Univariate Probability Functions."
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// Morgan C. Wang; William J. Kennedy
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// Journal of the American Statistical Association,
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// Vol. 89, No. 427. (Sep., 1994), pp. 878-887.
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//
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test_spot(
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static_cast<RealType>(1), // degrees of freedom
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static_cast<RealType>(6), // non centrality
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static_cast<RealType>(0.00393), // Chi Squared statistic
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static_cast<RealType>(0.2498463724258039e-2), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.2498463724258039e-2), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(5), // degrees of freedom
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static_cast<RealType>(1), // non centrality
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static_cast<RealType>(9.23636), // Chi Squared statistic
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static_cast<RealType>(0.8272918751175548), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.8272918751175548), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(11), // degrees of freedom
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static_cast<RealType>(21), // non centrality
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static_cast<RealType>(24.72497), // Chi Squared statistic
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static_cast<RealType>(0.2539481822183126), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.2539481822183126), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(31), // degrees of freedom
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static_cast<RealType>(6), // non centrality
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static_cast<RealType>(44.98534), // Chi Squared statistic
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static_cast<RealType>(0.8125198785064969), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.8125198785064969), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(51), // degrees of freedom
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static_cast<RealType>(1), // non centrality
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static_cast<RealType>(38.56038), // Chi Squared statistic
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static_cast<RealType>(0.8519497361859118e-1), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.8519497361859118e-1), // Q = 1 - P
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tolerance * 2);
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test_spot(
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static_cast<RealType>(100), // degrees of freedom
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static_cast<RealType>(16), // non centrality
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static_cast<RealType>(82.35814), // Chi Squared statistic
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static_cast<RealType>(0.1184348822747824e-1), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.1184348822747824e-1), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(300), // degrees of freedom
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static_cast<RealType>(16), // non centrality
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static_cast<RealType>(331.78852), // Chi Squared statistic
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static_cast<RealType>(0.7355956710306709), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.7355956710306709), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(500), // degrees of freedom
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static_cast<RealType>(21), // non centrality
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static_cast<RealType>(459.92612), // Chi Squared statistic
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static_cast<RealType>(0.2797023600800060e-1), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.2797023600800060e-1), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(1), // degrees of freedom
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static_cast<RealType>(1), // non centrality
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static_cast<RealType>(0.00016), // Chi Squared statistic
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static_cast<RealType>(0.6121428929881423e-2), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.6121428929881423e-2), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(1), // degrees of freedom
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static_cast<RealType>(1), // non centrality
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static_cast<RealType>(0.00393), // Chi Squared statistic
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static_cast<RealType>(0.3033814229753780e-1), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.3033814229753780e-1), // Q = 1 - P
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tolerance);
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RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
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boost::math::non_central_chi_squared_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(12));
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RealType x = 7;
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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 + 12), 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>(64), 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>(8), 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>(17.184201184730857030170788677340294070728990862663L), sqrt(tolerance * 500));
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BOOST_CHECK_CLOSE(
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median(dist),
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quantile(
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boost::math::non_central_chi_squared_distribution<RealType>(
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static_cast<RealType>(8),
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static_cast<RealType>(12)),
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static_cast<RealType>(0.5)), static_cast<RealType>(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>(0.6875), tol2);
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// kurtosis:
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BOOST_CHECK_CLOSE(
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kurtosis(dist)
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, static_cast<RealType>(3.65625), tol2);
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// kurtosis excess:
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BOOST_CHECK_CLOSE(
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kurtosis_excess(dist)
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, static_cast<RealType>(0.65625), tol2);
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// Error handling checks:
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check_out_of_range<boost::math::non_central_chi_squared_distribution<RealType> >(1, 1);
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BOOST_MATH_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution<RealType>(0, 1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution<RealType>(-1, 1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution<RealType>(1, -1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(quantile(boost::math::non_central_chi_squared_distribution<RealType>(1, 1), -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(quantile(boost::math::non_central_chi_squared_distribution<RealType>(1, 1), 2), std::domain_error);
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#endif
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} // template <class RealType>void test_spots(RealType)
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template <class T>
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T nccs_cdf(T df, T nc, T x)
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{
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return cdf(boost::math::non_central_chi_squared_distribution<T>(df, nc), x);
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}
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template <class T>
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T nccs_ccdf(T df, T nc, T x)
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{
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return cdf(complement(boost::math::non_central_chi_squared_distribution<T>(df, nc), x));
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}
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template <typename Real, typename T>
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void do_test_nc_chi_squared(T& data, const char* type_name, const char* test)
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{
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typedef typename T::value_type row_type;
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typedef Real value_type;
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std::cout << "Testing: " << test << std::endl;
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#ifdef NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST
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value_type(*fp1)(value_type, value_type, value_type) = NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST;
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#else
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value_type(*fp1)(value_type, value_type, value_type) = nccs_cdf;
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#endif
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boost::math::tools::test_result<value_type> result;
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#if !(defined(ERROR_REPORTING_MODE) && !defined(NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST))
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result = boost::math::tools::test_hetero<Real>(
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data,
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bind_func<Real>(fp1, 0, 1, 2),
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extract_result<Real>(3));
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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "non central chi squared CDF", test);
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#endif
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#if !(defined(ERROR_REPORTING_MODE) && !defined(NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST))
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#ifdef NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST
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fp1 = NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST;
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#else
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fp1 = nccs_ccdf;
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#endif
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result = boost::math::tools::test_hetero<Real>(
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data,
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bind_func<Real>(fp1, 0, 1, 2),
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extract_result<Real>(4));
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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "non central chi squared CDF complement", test);
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std::cout << std::endl;
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#endif
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}
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template <typename Real, typename T>
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void quantile_sanity_check(T& data, const char* type_name, const char* test)
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{
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#ifndef ERROR_REPORTING_MODE
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typedef typename T::value_type row_type;
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typedef Real value_type;
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//
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// Tests with type real_concept take rather too long to run, so
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// for now we'll disable them:
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//
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if(!boost::is_floating_point<value_type>::value)
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return;
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std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
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//
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// These sanity checks test for a round trip accuracy of one half
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// of the bits in T, unless T is type float, in which case we check
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// for just one decimal digit. The problem here is the sensitivity
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// of the functions, not their accuracy. This test data was generated
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// for the forward functions, which means that when it is used as
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// the input to the inverses then it is necessarily inexact. This rounding
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// of the input is what makes the data unsuitable for use as an accuracy check,
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// and also demonstrates that you can't in general round-trip these functions.
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// It is however a useful sanity check.
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//
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value_type precision = static_cast<value_type>(ldexp(1.0, 1 - boost::math::policies::digits<value_type, boost::math::policies::policy<> >() / 2)) * 100;
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if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
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precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float
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for(unsigned i = 0; i < data.size(); ++i)
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{
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if(Real(data[i][3]) == 0)
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{
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BOOST_CHECK(0 == quantile(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][3]));
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}
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else if(data[i][3] < 0.9999f)
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{
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value_type p = quantile(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][3]);
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value_type pt = data[i][2];
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BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
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}
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if(data[i][4] == 0)
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{
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BOOST_CHECK(0 == quantile(complement(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][3])));
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}
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else if(data[i][4] < 0.9999f)
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{
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value_type p = quantile(complement(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][4]));
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value_type pt = data[i][2];
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BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
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}
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if(boost::math::tools::digits<value_type>() > 50)
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{
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//
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// Sanity check mode, the accuracy of
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// the mode is at *best* the square root of the accuracy of the PDF:
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//
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#ifndef BOOST_NO_EXCEPTIONS
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try{
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value_type m = mode(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]));
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value_type p = pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m);
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BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m * (1 + sqrt(precision) * 50)) <= p, i);
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BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m * (1 - sqrt(precision)) * 50) <= p, i);
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}
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catch(const boost::math::evaluation_error&) {}
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#endif
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//
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// Sanity check degrees-of-freedom finder, don't bother at float
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// precision though as there's not enough data in the probability
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// values to get back to the correct degrees of freedom or
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|
// non-cenrality parameter:
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|
//
|
|
#ifndef BOOST_NO_EXCEPTIONS
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|
try{
|
|
#endif
|
|
if((data[i][3] < 0.99) && (data[i][3] != 0))
|
|
{
|
|
BOOST_CHECK_CLOSE_EX(
|
|
boost::math::non_central_chi_squared_distribution<value_type>::find_degrees_of_freedom(data[i][1], data[i][2], data[i][3]),
|
|
data[i][0], precision, i);
|
|
BOOST_CHECK_CLOSE_EX(
|
|
boost::math::non_central_chi_squared_distribution<value_type>::find_non_centrality(data[i][0], data[i][2], data[i][3]),
|
|
data[i][1], precision, i);
|
|
}
|
|
if((data[i][4] < 0.99) && (data[i][4] != 0))
|
|
{
|
|
BOOST_CHECK_CLOSE_EX(
|
|
boost::math::non_central_chi_squared_distribution<value_type>::find_degrees_of_freedom(boost::math::complement(data[i][1], data[i][2], data[i][4])),
|
|
data[i][0], precision, i);
|
|
BOOST_CHECK_CLOSE_EX(
|
|
boost::math::non_central_chi_squared_distribution<value_type>::find_non_centrality(boost::math::complement(data[i][0], data[i][2], data[i][4])),
|
|
data[i][1], precision, i);
|
|
}
|
|
#ifndef BOOST_NO_EXCEPTIONS
|
|
}
|
|
catch(const std::exception& e)
|
|
{
|
|
BOOST_ERROR(e.what());
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
#endif
|
|
}
|
|
|
|
template <typename T>
|
|
void test_accuracy(T, const char* type_name)
|
|
{
|
|
#include "nccs.ipp"
|
|
do_test_nc_chi_squared<T>(nccs, type_name, "Non Central Chi Squared, medium parameters");
|
|
quantile_sanity_check<T>(nccs, type_name, "Non Central Chi Squared, medium parameters");
|
|
|
|
#include "nccs_big.ipp"
|
|
do_test_nc_chi_squared<T>(nccs_big, type_name, "Non Central Chi Squared, large parameters");
|
|
quantile_sanity_check<T>(nccs_big, type_name, "Non Central Chi Squared, large parameters");
|
|
}
|
|
|