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Drafted some tests for single value Bessel zeros, but domain_error exceptions not right yet.
TODO airy zeros. [SVN r82680]
This commit is contained in:
Paul A. Bristow
152
test/test_bessel_airy_zeros.cpp
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152
test/test_bessel_airy_zeros.cpp
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// Copyright John Maddock 2013
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// Copyright Christopher Kormanyos 2013.
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// Copyright Paul A. Bristow 2013.
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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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#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 <pch_light.hpp> // commente dout during testing.
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#include <boost/math/special_functions/bessel.hpp>
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#include <boost/test/test_exec_monitor.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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//
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// DESCRIPTION:
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// ~~~~~~~~~~~~
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//
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// This file tests the functions that evaluate zeros (or roots) of Bessel and Airy functions.
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// Spot tests which compare our results with selected values computed
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// using the online special function calculator at functions.wolfram.com,
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// and values generated with Boost.Multiprecision at about 1000-bit or 100 decimal digits precision.
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// Weisstein, Eric W. "Bessel Function Zeros." From MathWorld--A Wolfram Web Resource.
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// http://mathworld.wolfram.com/BesselFunctionZeros.html
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// See also http://dlmf.nist.gov/10.21
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template <class RealType>
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void test_bessel_zeros(RealType)
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{
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// Basic sanity checks for finding zeros of Bessel and Airy function.
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// where template parameter RealType can be float, double, long double,
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// or real_concept, a prototype for user-defined floating-point types.
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// Parameter RealType is only used to communicate the RealType, float, double...
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// and is an arbitrary zero for all tests.
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RealType tolerance = (std::max)(
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static_cast<RealType>(boost::math::tools::epsilon<long double>()),
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boost::math::tools::epsilon<RealType>());
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std::cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << "." << std::endl;
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// http://www.wolframalpha.com/
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/*
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Table[N[BesselJZero[0, n], 50], {n, 1, 5, 1}]
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n |
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1 | 2.4048255576957727686216318793264546431242449091460
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2 | 5.5200781102863106495966041128130274252218654787829
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3 | 8.6537279129110122169541987126609466855657952312754
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4 | 11.791534439014281613743044911925458922022924699695
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5 | 14.930917708487785947762593997388682207915850115633
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Table[N[BesselJZero[1, n], 50], {n, 1, 4, 1}]
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n |
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1 | 3.8317059702075123156144358863081607665645452742878
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2 | 7.0155866698156187535370499814765247432763115029142
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3 | 10.173468135062722077185711776775844069819512500192
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4 | 13.323691936314223032393684126947876751216644731358
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Table[N[BesselJZero[5, n], 50], {n, 1, 5, 1}]
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n |
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1 | 8.7714838159599540191228671334095605629810770148974
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2 | 12.338604197466943986082097644459004412683491122239
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3 | 15.700174079711671037587715595026422501346662246893
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4 | 18.980133875179921120770736748466932306588828411497
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5 | 22.217799896561267868824764947529187163096116704354
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*/
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using boost::math::cyl_bessel_j_zero; // (nu, j)
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using boost::math::isnan;
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if (std::numeric_limits<RealType>::has_quiet_NaN)
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{
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BOOST_CHECK(isnan(cyl_bessel_j_zero(static_cast<RealType>(0), 0U))); // yes - returns NaN - is this right?
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}
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(0), 1U), static_cast<RealType>(2.4048255576957727686216318793264546431242449091460L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1), 1U), static_cast<RealType>(3.8317059702075123156144358863081607665645452742878L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1), 2U), static_cast<RealType>(7.0155866698156187535370499814765247432763115029142L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(5), 5U), static_cast<RealType>(22.217799896561267868824764947529187163096116704354L), tolerance);
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// Some none integral tests.
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(3.736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105L), 1U), static_cast<RealType>(7.273175193831648950318569426229076558896319670162279791988152000556091140599946365217211157877052381L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(3.736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105L), 20U), static_cast<RealType>(67.81514561969629092555679137555595116511146058545787883557679231060644931096494584364894743334132014L), tolerance);
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// Some none integral tests in 'tough' regions.
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(219)/100, 1U), static_cast<RealType>(5.37568854370623186731066365697341253761466705063679L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(219)/100, 2U), static_cast<RealType>(8.67632060963888122764226633146460596009874991130394L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(219)/100, 20U), static_cast<RealType>(65.4517712237598926858973399895944886397152223643028L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(221)/100, 1U), static_cast<RealType>(5.40084731984998184087380740054933778965260387203942L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(221)/100, 2U), static_cast<RealType>(8.70347906513509618445695740167369153761310106851599L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(221)/100, 20U), static_cast<RealType>(65.4825314862621271716158606625527548818843845600782L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 1U), static_cast<RealType>(381.922015230244893869172044704348426991540311353476L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 2U), static_cast<RealType>(392.175086576487375026512998530998525670012392177242L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 20U), static_cast<RealType>(496.394350379382525575353754985779897202722983108025L), tolerance);
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// Check expected exceptions :
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//BOOST_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(0), 0L), std::domain_error);
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//BOOST_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(0), -1), std::domain_error);
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// warning C4245: 'argument' : conversion from 'int' to 'unsigned int', signed/unsigned mismatch
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// BOOST_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0U), std::domain_error); // No exception?
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//BOOST_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), -1), std::domain_error); // OK if unsigned.
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if (std::numeric_limits<RealType>::has_quiet_NaN)
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{
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BOOST_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 1U), std::domain_error);
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}
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// BOOST_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::infinity()), 0U), std::domain_error);
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//BOOST_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::infinity()), -1), std::domain_error); // OK if unsigned.
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if (std::numeric_limits<RealType>::has_infinity)
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{
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BOOST_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::infinity()), 1U), std::domain_error);
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}
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// BOOST_CHECK_THROW(static_cast<RealType>(0.L), 0L, std::domain_error);
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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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#ifdef TEST_GSL
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gsl_set_error_handler_off();
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#endif
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//expected_results();
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BOOST_MATH_CONTROL_FP;
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test_bessel_zeros(0.1F);
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test_bessel_zeros(0.1);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_bessel_zeros(0.1L);
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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test_bessel_zeros(boost::math::concepts::real_concept(0.1));
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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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