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986 lines
65 KiB
C++
986 lines
65 KiB
C++
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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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# pragma warning(disable : 4512) // assignment operator could not be generated.
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# pragma warning(disable : 4996) // use -D_SCL_SECURE_NO_WARNINGS.
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#endif
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//#include <pch_light.hpp> // commented out during testing.
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//#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/cstdint.hpp>
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#include <boost/math/special_functions/bessel.hpp>
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#include <boost/math/special_functions/airy.hpp>
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#include <boost/math/tools/test.hpp>
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include <typeinfo>
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#include <iostream>
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#include <iomanip>
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// #include <boost/math/tools/
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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, Neumann 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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// We are most grateful for the invaluable
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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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// and the newer http://www.wolframalpha.com/
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// See also NIST Handbook of Mathematical Function http://dlmf.nist.gov/10.21
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/*
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Tests of cyl Bessel and cyl Neumann zeros.
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==========================================
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The algorithms for estimating the roots of both cyl. Bessel
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as well as cyl. Neumann have the same cross-over points,
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and also use expansions that have the same order of approximation.
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Therefore, tests will be equally effective for both functions in the regions of order.
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I have recently changed a critical cross-over in the algorithms
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from a value of order of 1.2 to a value of order of 2.2.
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In addition, there is a critical cross-over in the rank of the
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zero from rank 1 to rank 2 and above. The first zero is
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treated differently than the remaining ones.
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The test cover various regions of order,
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each one tested with several zeros:
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* Order 219/100: This checks a region just below a critical cutof.
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* Order 221/100: This checks a region just above a critical cutoff.
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* Order 0: Something always tends to go wrong at zero.
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* Order 1/1000: A small order.
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* Order 71/19: Merely an intermediate order.
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* Order 7001/19: A medium-large order, small enough to retain moderate efficiency of calculation.
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There are also a few selected high zeros
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such as the 1000th zero for a few modest orders such as 71/19, etc.
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Tests of Airy zeros.
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====================
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The Airy zeros algorithms use tabulated values for the first 10 zeros,
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whereby algorithms are used for rank 11 and higher.
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So testing the zeros of Ai and Bi from 1 through 20 handles
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this cross-over nicely.
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In addition, the algorithms for the estimates of the zeros
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become increasingly accurate for larger, negative argument.
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On the other hand, the zeros become increasingly close
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for large, negative argument. So another nice test
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involves testing pairs of zeros for different orders of
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magnitude of the zeros, to insure that the program
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properly resolves very closely spaced zeros.
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*/
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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 = 5 * (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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//
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// An extra fudge factor for real_concept which has a less accurate tgamma:
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RealType tolerance_tgamma_extra = std::numeric_limits<RealType>::is_specialized ? 1 : 15;
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// http://www.wolframalpha.com/
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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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BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(0), 0), std::domain_error);
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// BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(-1), 2), std::domain_error);
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// From 83051 negative orders are supported.
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// Abuse with infinity and max.
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if (std::numeric_limits<RealType>::has_infinity)
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{
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//BOOST_CHECK_EQUAL(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::infinity()), 1),
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// static_cast<RealType>(std::numeric_limits<RealType>::infinity()) );
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// unknown location(0): fatal error in "test_main":
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// class boost::exception_detail::clone_impl<struct boost::exception_detail::error_info_injector<class std::domain_error> >:
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// Error in function boost::math::cyl_bessel_j_zero<double>(double, int): Order argument is 1.#INF, but must be finite >= 0 !
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// Note that the reported type long double is not the type of the original call RealType,
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// but the promoted value, here long double, if applicable.
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BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::infinity()), 1),
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std::domain_error);
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BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(-std::numeric_limits<RealType>::infinity()), 1),
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std::domain_error);
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}
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// Test with maximum value of v that will cause evaluation error
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//BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(boost::math::tools::max_value<RealType>(), 1), std::domain_error);
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// unknown location(0): fatal error in "test_main":
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// class boost::exception_detail::clone_impl<struct boost::exception_detail::error_info_injector<class boost::math::evaluation_error> >:
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// Error in function boost::math::bessel_jy<double>(double,double): Order of Bessel function is too large to evaluate: got 3.4028234663852886e+038
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BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(boost::math::tools::max_value<RealType>(), 1), boost::math::evaluation_error);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(boost::math::tools::min_value<RealType>(), 1),
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static_cast<RealType>(2.4048255576957727686216318793264546431242449091460L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(-cyl_bessel_j_zero(boost::math::tools::min_value<RealType>(), 1),
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static_cast<RealType>(-2.4048255576957727686216318793264546431242449091460L), tolerance);
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// Checks on some spot values.
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// http://mathworld.wolfram.com/BesselFunctionZeros.html provides some spot values,
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// evaluation at 50 deciaml digits using WoldramAlpha.
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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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*/
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(0), 1), static_cast<RealType>(2.4048255576957727686216318793264546431242449091460L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(0), 2), static_cast<RealType>(5.5200781102863106495966041128130274252218654787829L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(0), 3), static_cast<RealType>(8.6537279129110122169541987126609466855657952312754L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(0), 4), static_cast<RealType>(11.791534439014281613743044911925458922022924699695L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(0), 5), static_cast<RealType>(14.930917708487785947762593997388682207915850115633L), tolerance);
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{ // Same test using the multiple zeros version.
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std::vector<RealType> zeros;
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cyl_bessel_j_zero(static_cast<RealType>(0.0), 1, 3, std::back_inserter(zeros) );
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BOOST_CHECK_CLOSE_FRACTION(zeros[0], static_cast<RealType>(2.4048255576957727686216318793264546431242449091460L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(zeros[1], static_cast<RealType>(5.5200781102863106495966041128130274252218654787829L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(zeros[2], static_cast<RealType>(8.6537279129110122169541987126609466855657952312754L), tolerance);
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}
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// 1/1000 a small order.
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/* Table[N[BesselJZero[1/1000, n], 50], {n, 1, 4, 1}]
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n |
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1 | 2.4063682720422009275161970278295108254321633626292
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2 | 5.5216426858401848664019464270992222126391378706092
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3 | 8.6552960859298799453893840513333150237193779482071
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4 | 11.793103797689738596231262077785930962647860975357
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Table[N[BesselJZero[1/1000, n], 50], {n, 10, 20, 1}]
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n |
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10 | 30.636177039613574749066837922778438992469950755736
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11 | 33.777390823252864715296422192027816488172667994611
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12 | 36.918668992567585467000743488690258054442556198147
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13 | 40.059996426251227493370316149043896483196561190610
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14 | 43.201362392820317233698309483240359167380135262681
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15 | 46.342759065846108737848449985452774243376260538634
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16 | 49.484180603489984324820981438067325210499739716337
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17 | 52.625622557085775090390071484188995092211215108718
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18 | 55.767081479279692992978326069855684800673801918763
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19 | 58.908554657366270044071505013449016741804538135905
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20 | 62.050039927521244984641179233170843941940575857282
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*/
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1)/1000, 1), static_cast<RealType>(2.4063682720422009275161970278295108254321633626292L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1)/1000, 4), static_cast<RealType>(11.793103797689738596231262077785930962647860975357L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1)/1000, 10), static_cast<RealType>(30.636177039613574749066837922778438992469950755736L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1)/1000, 20), static_cast<RealType>(62.050039927521244984641179233170843941940575857282L), tolerance);
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/*
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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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*/
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1), 1), static_cast<RealType>(3.8317059702075123156144358863081607665645452742878L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1), 2), static_cast<RealType>(7.0155866698156187535370499814765247432763115029142L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1), 3), static_cast<RealType>(10.173468135062722077185711776775844069819512500192L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(1), 4), static_cast<RealType>(13.323691936314223032393684126947876751216644731358L), tolerance);
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/*
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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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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(5), 1), static_cast<RealType>(8.7714838159599540191228671334095605629810770148974L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(5), 2), static_cast<RealType>(12.338604197466943986082097644459004412683491122239L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(5), 3), static_cast<RealType>(15.700174079711671037587715595026422501346662246893L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(5), 4), static_cast<RealType>(18.980133875179921120770736748466932306588828411497L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(5), 5), static_cast<RealType>(22.217799896561267868824764947529187163096116704354L), tolerance);
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// An intermediate order
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/*
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Table[N[BesselJZero[71/19, n], 50], {n, 1, 20, 1}]
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7.27317519383164895031856942622907655889631967016227,
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10.7248583088831417325361727458514166471107495990849,
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14.0185045994523881061204595580426602824274719315813,
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17.2524984591704171821624871665497773491959038386104,
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20.4566788740445175951802340838942858854605020778141,
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23.6436308971423452249455142271473195998540517250404,
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26.8196711402550877454213114709650192615223905192969,
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29.9883431174236747426791417966614320438788681941419,
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33.1517968976905208712508624699734452654447919661140,
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36.3114160002162074157243540350393860813165201842005,
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39.4681324675052365879451978080833378877659670320292,
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42.6225978013912364748550348312979540188444334802274,
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45.7752814645368477533902062078067265814959500124386,
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48.9265304891735661983677668174785539924717398947994,
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52.0766070453430027942797460418789248768734780634716,
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55.2257129449125713935942243278172656890590028901917,
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58.3740061015388864367751881504390252017351514189321,
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61.5216118730009652737267426593531362663909441035715,
|
||
|
|
64.6686310537909303683464822148736607945659662871596,
|
||
|
|
67.8151456196962909255567913755559511651114605854579
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(71)/19, 1), static_cast<RealType>(7.27317519383164895031856942622907655889631967016227L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(71)/19, 4), static_cast<RealType>(17.2524984591704171821624871665497773491959038386104L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(71)/19, 10), static_cast<RealType>(36.3114160002162074157243540350393860813165201842005L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(71)/19, 20), static_cast<RealType>(67.8151456196962909255567913755559511651114605854579L), tolerance);
|
||
|
|
/*
|
||
|
|
|
||
|
|
Table[N[BesselJZero[7001/19, n], 50], {n, 1, 2, 1}]
|
||
|
|
|
||
|
|
1 | 381.92201523024489386917204470434842699154031135348
|
||
|
|
2 | 392.17508657648737502651299853099852567001239217724
|
||
|
|
|
||
|
|
Table[N[BesselJZero[7001/19, n], 50], {n, 19, 20, 1}]
|
||
|
|
|
||
|
|
19 | 491.67809669154347398205298745712766193052308172472
|
||
|
|
20 | 496.39435037938252557535375498577989720272298310802
|
||
|
|
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 1), static_cast<RealType>(381.92201523024489386917204470434842699154031135348L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 2), static_cast<RealType>(392.17508657648737502651299853099852567001239217724L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 20), static_cast<RealType>(496.39435037938252557535375498577989720272298310802L), tolerance);
|
||
|
|
|
||
|
|
// Some non-integral tests.
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(3.73684210526315789473684210526315789473684210526315789L), 1), static_cast<RealType>(7.273175193831648950318569426229076558896319670162279791988152000556091140599946365217211157877052381L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(3.73684210526315789473684210526315789473684210526315789L), 20), static_cast<RealType>(67.81514561969629092555679137555595116511146058545787883557679231060644931096494584364894743334132014L), tolerance);
|
||
|
|
|
||
|
|
// Some non-integral tests in 'tough' regions.
|
||
|
|
// Order 219/100: This checks a region just below a critical cutoff.
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(219)/100, 1), static_cast<RealType>(5.37568854370623186731066365697341253761466705063679L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(219)/100, 2), static_cast<RealType>(8.67632060963888122764226633146460596009874991130394L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(219)/100, 20), static_cast<RealType>(65.4517712237598926858973399895944886397152223643028L), tolerance);
|
||
|
|
// Order 221/100: This checks a region just above a critical cutoff.
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(221)/100, 1), static_cast<RealType>(5.40084731984998184087380740054933778965260387203942L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(221)/100, 2), static_cast<RealType>(8.70347906513509618445695740167369153761310106851599L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(221)/100, 20), static_cast<RealType>(65.4825314862621271716158606625527548818843845600782L), tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 1), static_cast<RealType>(381.922015230244893869172044704348426991540311353476L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 2), static_cast<RealType>(392.175086576487375026512998530998525670012392177242L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(7001)/19, 20), static_cast<RealType>(496.394350379382525575353754985779897202722983108025L), tolerance);
|
||
|
|
|
||
|
|
// Zero'th cases.
|
||
|
|
BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(0), 0), std::domain_error); // Zero'th zero of J0(x).
|
||
|
|
BOOST_CHECK(boost::math::cyl_bessel_j_zero(static_cast<RealType>(1), 0) == 0); // Zero'th zero of J1(x).
|
||
|
|
BOOST_CHECK(boost::math::cyl_bessel_j_zero(static_cast<RealType>(2), 0) == 0); // Zero'th zero of J2(x).
|
||
|
|
|
||
|
|
|
||
|
|
// Negative order cases.
|
||
|
|
// Table[N[BesselJZero[-39, n], 51], {n, 1, 20, 1}]
|
||
|
|
|
||
|
|
// 45.597624026432090522996531982029164361723758769649
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39), 1), static_cast<RealType>(45.597624026432090522996531982029164361723758769649L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39), 2), static_cast<RealType>(50.930599960211455519691708196247756810739999585797L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39), 4), static_cast<RealType>(59.810708207036942166964205243063534405954475825070L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39), 10), static_cast<RealType>(82.490310026657839398140015188318580114553721419436L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39), 15), static_cast<RealType>(99.886172950858129702511715161572827825877395517083L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39), 20), static_cast<RealType>(116.73117751356457774415638043701531989536641098359L), tolerance);
|
||
|
|
|
||
|
|
// Table[N[BesselJZero[-39 - (1/3), n], 51], {n, 1, 20, 1}]
|
||
|
|
|
||
|
|
// 43.803165820025277290601047312311146608776920513241
|
||
|
|
// 49.624678304306778749502719837270544976331123155017
|
||
|
|
|
||
|
|
RealType v = static_cast<RealType>(-39);
|
||
|
|
|
||
|
|
v -= boost::math::constants::third<RealType>();
|
||
|
|
|
||
|
|
// BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 1), static_cast<RealType>(43.803165820025277290601047312311146608776920513241L), tolerance);
|
||
|
|
// BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 1), static_cast<RealType>(43.803165820025277290601047312311146608776920513241L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 2), static_cast<RealType>(49.624678304306778749502719837270544976331123155017L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39) - static_cast<RealType>(0.333333333333333333333333333333333333333333333L), 5), static_cast<RealType>(62.911281619408963609400485687996804820400102193455L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39) - static_cast<RealType>(0.333333333333333333333333333333333333333333333L), 10), static_cast<RealType>(81.705998611506506523381866527389118594062841737382L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(static_cast<RealType>(-39) - static_cast<RealType>(0.333333333333333333333333333333333333333333333L), 20), static_cast<RealType>(116.05368337161392034833932554892349580959931408963L), tolerance * 4);
|
||
|
|
|
||
|
|
|
||
|
|
// Table[N[BesselJZero[-1/3, n], 51], {n, 1, 20, 1}]
|
||
|
|
// 1.86635085887389517154698498025466055044627209492336
|
||
|
|
// 4.98785323143515872689263163814239463653891121063534
|
||
|
|
v = - boost::math::constants::third<RealType>();
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 1), static_cast<RealType>(1.86635085887389517154698498025466055044627209492336L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 2), static_cast<RealType>(4.98785323143515872689263163814239463653891121063534L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 5), static_cast<RealType>(14.4037758801360172217813556328092353168458341692115L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 20), static_cast<RealType>(61.5239847181314647255554392599009248210564008120358L), tolerance);
|
||
|
|
|
||
|
|
// Table[N[BesselJZero[-3 - (999999/1000000), n], 51], {n, 1, 20, 1}]
|
||
|
|
// 0.666908567552422764702292353801313970109968787260547
|
||
|
|
//7.58834489983121936102504707121493271448122800440112
|
||
|
|
|
||
|
|
std::cout.precision(2 + std::numeric_limits<RealType>::digits * 3010/10000);
|
||
|
|
v = -static_cast<RealType>(3);
|
||
|
|
//std::cout << "v = " << v << std::endl;
|
||
|
|
RealType d = static_cast<RealType>(999999)/1000000; // Value very near to unity.
|
||
|
|
//std::cout << "d = " << d << std::endl;
|
||
|
|
v -= d;
|
||
|
|
// std::cout << "v = " << v << std::endl; // v = -3.9999989999999999
|
||
|
|
|
||
|
|
// 1st is much less accurate.
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 1), static_cast<RealType>(0.666908567552422764702292353801313970109968787260547L), tolerance * 500000);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 2), static_cast<RealType>(7.58834489983121936102504707121493271448122800440112L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 5), static_cast<RealType>(17.6159678964372778134202353240221384945968807948928L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 20), static_cast<RealType>(65.0669968910414433560468307554730940098734494938136L), tolerance);
|
||
|
|
|
||
|
|
|
||
|
|
v = -static_cast<RealType>(1)/81799; // Largish prime, so small value.
|
||
|
|
// std::cout << "v = " << v << std::endl; // v = -1.22251e-005
|
||
|
|
|
||
|
|
// Table[N[BesselJZero[-1/81799, n], 51], {n, 1, 20, 1}]
|
||
|
|
|
||
|
|
// 2.40480669570616362235270726259606288441474232101937
|
||
|
|
//5.52005898213436490056801834487410496538653938730884
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 1), static_cast<RealType>(2.40480669570616362235270726259606288441474232101937L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 2), static_cast<RealType>(5.52005898213436490056801834487410496538653938730884L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 5), static_cast<RealType>(14.9308985160466385806685583210609848822943295303368L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 20), static_cast<RealType>(62.0484499877253314338528593349200129641402661038743L), tolerance);
|
||
|
|
|
||
|
|
// Confirm that negative m throws domain_error.
|
||
|
|
BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(0), -1), std::domain_error);
|
||
|
|
// unknown location(0): fatal error in "test_main":
|
||
|
|
// class boost::exception_detail::clone_impl<struct boost::exception_detail::error_info_injector<class std::domain_error> >:
|
||
|
|
// Error in function boost::math::cyl_bessel_j_zero<double>(double, int): Requested the -1'th zero, but must be > 0 !
|
||
|
|
|
||
|
|
// Confirm that a C-style ignore_all policy returns NaN for bad input.
|
||
|
|
typedef boost::math::policies::policy<
|
||
|
|
boost::math::policies::domain_error<boost::math::policies::ignore_error>,
|
||
|
|
boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
|
||
|
|
boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
|
||
|
|
boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
|
||
|
|
boost::math::policies::pole_error<boost::math::policies::ignore_error>,
|
||
|
|
boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
|
||
|
|
> ignore_all_policy;
|
||
|
|
|
||
|
|
if (std::numeric_limits<RealType>::has_quiet_NaN)
|
||
|
|
{
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 1), std::domain_error);
|
||
|
|
// Check that bad m returns NaN if policy is no throws.
|
||
|
|
BOOST_CHECK((boost::math::isnan<RealType>)(cyl_bessel_j_zero(std::numeric_limits<RealType>::quiet_NaN(), 1, ignore_all_policy())) );
|
||
|
|
BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), -1), std::domain_error);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{ // real_concept bad m returns zero.
|
||
|
|
//std::cout << boost::math::cyl_bessel_j_zero(static_cast<RealType>(0), -1, ignore_all_policy()) << std::endl; // 0 for real_concept.
|
||
|
|
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_j_zero(static_cast<RealType>(0), -1, ignore_all_policy() ), 0);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (std::numeric_limits<RealType>::has_infinity)
|
||
|
|
{
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(std::numeric_limits<RealType>::infinity(), 0), std::domain_error);
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_bessel_j_zero(std::numeric_limits<RealType>::infinity(), 1), std::domain_error);
|
||
|
|
// Check that NaN is returned if error ignored.
|
||
|
|
BOOST_CHECK((boost::math::isnan<RealType>)(cyl_bessel_j_zero(std::numeric_limits<RealType>::infinity(), 1, ignore_all_policy())) );
|
||
|
|
}
|
||
|
|
|
||
|
|
// Tests of cyc_neumann zero function (BesselYZero in Wolfram) for spot values.
|
||
|
|
/*
|
||
|
|
Table[N[BesselYZero[0, n], 50], {n, 1, 5, 1}]
|
||
|
|
n |
|
||
|
|
1 | 0.89357696627916752158488710205833824122514686193001
|
||
|
|
2 | 3.9576784193148578683756771869174012814186037655636
|
||
|
|
3 | 7.0860510603017726976236245968203524689715103811778
|
||
|
|
4 | 10.222345043496417018992042276342187125994059613181
|
||
|
|
5 | 13.361097473872763478267694585713786426579135174880
|
||
|
|
|
||
|
|
Table[N[BesselYZero[0, n], 50], {n, 1, 5, 1}]
|
||
|
|
|
||
|
|
n |
|
||
|
|
1 | 0.89357696627916752158488710205833824122514686193001
|
||
|
|
2 | 3.9576784193148578683756771869174012814186037655636
|
||
|
|
3 | 7.0860510603017726976236245968203524689715103811778
|
||
|
|
4 | 10.222345043496417018992042276342187125994059613181
|
||
|
|
5 | 13.361097473872763478267694585713786426579135174880
|
||
|
|
|
||
|
|
So K == Y
|
||
|
|
|
||
|
|
Table[N[BesselYZero[1, n], 50], {n, 1, 5, 1}]
|
||
|
|
n |
|
||
|
|
1 | 2.1971413260310170351490335626989662730530183315003
|
||
|
|
2 | 5.4296810407941351327720051908525841965837574760291
|
||
|
|
3 | 8.5960058683311689264296061801639678511029215669749
|
||
|
|
4 | 11.749154830839881243399421939922350714301165983279
|
||
|
|
5 | 14.897442128336725378844819156429870879807150630875
|
||
|
|
|
||
|
|
Table[N[BesselYZero[2, n], 50], {n, 1, 5, 1}]
|
||
|
|
n |
|
||
|
|
1 | 3.3842417671495934727014260185379031127323883259329
|
||
|
|
2 | 6.7938075132682675382911671098369487124493222183854
|
||
|
|
3 | 10.023477979360037978505391792081418280789658279097
|
||
|
|
4 | 13.209986710206416382780863125329852185107588501072
|
||
|
|
5 | 16.378966558947456561726714466123708444627678549687
|
||
|
|
|
||
|
|
*/
|
||
|
|
// Some simple integer values.
|
||
|
|
|
||
|
|
using boost::math::cyl_neumann_zero;
|
||
|
|
// Bad rank m.
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), 0), std::domain_error); //
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), -1), std::domain_error);
|
||
|
|
|
||
|
|
if (std::numeric_limits<RealType>::has_quiet_NaN)
|
||
|
|
{
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_neumann_zero(std::numeric_limits<RealType>::quiet_NaN(), 1), std::domain_error);
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), -1), std::domain_error);
|
||
|
|
}
|
||
|
|
if (std::numeric_limits<RealType>::has_infinity)
|
||
|
|
{
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_neumann_zero(std::numeric_limits<RealType>::infinity(), 2), std::domain_error);
|
||
|
|
BOOST_MATH_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), -1), std::domain_error);
|
||
|
|
}
|
||
|
|
// else no infinity tests.
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(0), 1), static_cast<RealType>(0.89357696627916752158488710205833824122514686193001L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1), 2), static_cast<RealType>(5.4296810407941351327720051908525841965837574760291L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(2), 3), static_cast<RealType>(10.023477979360037978505391792081418280789658279097L), tolerance);
|
||
|
|
|
||
|
|
/*
|
||
|
|
Table[N[BesselYZero[3, n], 50], {n, 1, 5, 1}]
|
||
|
|
1 | 4.5270246611496438503700268671036276386651555486109
|
||
|
|
2 | 8.0975537628604907044022139901128042290432231369075
|
||
|
|
3 | 11.396466739595866739252048190629504945984969192535
|
||
|
|
4 | 14.623077742393873174076722507725200649352970569915
|
||
|
|
5 | 17.818455232945520262553239064736739443380352162752
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 1), static_cast<RealType>(4.5270246611496438503700268671036276386651555486109L), tolerance * 2);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 2), static_cast<RealType>(8.0975537628604907044022139901128042290432231369075L), tolerance * 2);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 3), static_cast<RealType>(11.396466739595866739252048190629504945984969192535L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 4), static_cast<RealType>(14.623077742393873174076722507725200649352970569915L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 5), static_cast<RealType>(17.818455232945520262553239064736739443380352162752L), tolerance);
|
||
|
|
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 1), static_cast<RealType>(4.5270246611496438503700268671036276386651555486109L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 2), static_cast<RealType>(8.0975537628604907044022139901128042290432231369075L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 3), static_cast<RealType>(11.396466739595866739252048190629504945984969192535L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 4), static_cast<RealType>(14.623077742393873174076722507725200649352970569915L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 5), static_cast<RealType>(17.818455232945520262553239064736739443380352162752L), tolerance);
|
||
|
|
|
||
|
|
{ // Repeat rest using multiple zeros version.
|
||
|
|
std::vector<RealType> zeros;
|
||
|
|
cyl_neumann_zero(static_cast<RealType>(0.0), 1, 3, std::back_inserter(zeros) );
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(zeros[0], static_cast<RealType>(0.89357696627916752158488710205833824122514686193001L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(zeros[1], static_cast<RealType>(3.9576784193148578683756771869174012814186037655636L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(zeros[2], static_cast<RealType>(7.0860510603017726976236245968203524689715103811778L), tolerance);
|
||
|
|
}
|
||
|
|
// Order 0: Something always tends to go wrong at zero.
|
||
|
|
|
||
|
|
/* Order 219/100: This checks accuracy in a region just below a critical cutoff.
|
||
|
|
|
||
|
|
Table[N[BesselKZero[219/100, n], 50], {n, 1, 20, 4}]
|
||
|
|
1 | 3.6039149425338727979151181355741147312162055042157
|
||
|
|
5 | 16.655399111666833825247894251535326778980614938275
|
||
|
|
9 | 29.280564448169163756478439692311605757712873534942
|
||
|
|
13 | 41.870269811145814760551599481942750124112093564643
|
||
|
|
17 | 54.449180021209532654553613813754733514317929678038
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(219)/100, 1), static_cast<RealType>(3.6039149425338727979151181355741147312162055042157L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(219)/100, 5), static_cast<RealType>(16.655399111666833825247894251535326778980614938275L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(219)/100, 17), static_cast<RealType>(54.449180021209532654553613813754733514317929678038L), tolerance);
|
||
|
|
|
||
|
|
/* Order 221/100: This checks a region just above a critical cutoff.
|
||
|
|
Table[N[BesselYZero[220/100, n], 50], {n, 1, 20, 5}]
|
||
|
|
1 | 3.6154383428745996706772556069431792744372398748425
|
||
|
|
6 | 19.833435100254138641131431268153987585842088078470
|
||
|
|
11 | 35.592602956438811360473753622212346081080817891225
|
||
|
|
16 | 51.320322762482062633162699745957897178885350674038
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(220)/100, 1), static_cast<RealType>(3.6154383428745996706772556069431792744372398748425L), 2 * tolerance);
|
||
|
|
// Note * 2 tolerance needed - using cpp_dec_float_50 it computes exactly, probably because of extra guard digits in multiprecision decimal version.
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(220)/100, 6), static_cast<RealType>(19.833435100254138641131431268153987585842088078470L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(220)/100, 11), static_cast<RealType>(35.592602956438811360473753622212346081080817891225L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(220)/100, 16), static_cast<RealType>(51.320322762482062633162699745957897178885350674038L), tolerance);
|
||
|
|
|
||
|
|
/* Order 1/1000: A small order.
|
||
|
|
Table[N[BesselYZero[1/1000, n], 50], {n, 1, 20, 5}]
|
||
|
|
1 | 0.89502371604431360670577815537297733265776195646969
|
||
|
|
6 | 16.502492490954716850993456703662137628148182892787
|
||
|
|
11 | 32.206774708309182755790609144739319753463907110990
|
||
|
|
16 | 47.913467031941494147962476920863688176374357572509
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/1000, 1), static_cast<RealType>(0.89502371604431360670577815537297733265776195646969L), 2 * tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/1000, 6), static_cast<RealType>(16.5024924909547168509934567036621376281481828927870L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/1000, 11), static_cast<RealType>(32.206774708309182755790609144739319753463907110990L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/1000, 16), static_cast<RealType>(47.913467031941494147962476920863688176374357572509L), tolerance);
|
||
|
|
|
||
|
|
/* Order 71/19: Merely an intermediate order.
|
||
|
|
Table[N[BesselYZero[71/19, n], 50], {n, 1, 20, 5}]
|
||
|
|
1 | 5.3527167881149432911848659069476821793319749146616
|
||
|
|
6 | 22.051823727778538215953091664153117627848857279151
|
||
|
|
11 | 37.890091170552491176745048499809370107665221628364
|
||
|
|
16 | 53.651270581421816017744203789836444968181687858095
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(71)/19, 1), static_cast<RealType>(5.3527167881149432911848659069476821793319749146616L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(71)/19, 6), static_cast<RealType>(22.051823727778538215953091664153117627848857279151L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(71)/19, 11), static_cast<RealType>(37.890091170552491176745048499809370107665221628364L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(71)/19, 16), static_cast<RealType>(53.651270581421816017744203789836444968181687858095L), tolerance);
|
||
|
|
|
||
|
|
/* Order 7001/19: A medium-large order, small enough to retain moderate efficiency of calculation.
|
||
|
|
|
||
|
|
Table[N[BesselYZero[7001/19, n], 50], {n, 1}]
|
||
|
|
1 | 375.18866334770357669101711932706658671250621098115
|
||
|
|
|
||
|
|
Table[N[BesselYZero[7001/19, n], 50], {n, 2}]
|
||
|
|
Standard computation time exceeded :-(
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(7001)/19, 1), static_cast<RealType>(375.18866334770357669101711932706658671250621098115L), tolerance);
|
||
|
|
|
||
|
|
/* A high zero such as the 1000th zero for a modest order such as 71/19.
|
||
|
|
Table[N[BesselYZero[71/19, n], 50], {n, 1000}]
|
||
|
|
Standard computation time exceeded :-(
|
||
|
|
*/
|
||
|
|
|
||
|
|
/*
|
||
|
|
Test Negative orders cyl_neumann.
|
||
|
|
|
||
|
|
Table[N[BesselYZero[-1, n], 50], {n, 1, 10, 1}]
|
||
|
|
1 | 2.1971413260310170351490335626989662730530183315003
|
||
|
|
2 | 5.4296810407941351327720051908525841965837574760291
|
||
|
|
3 | 8.5960058683311689264296061801639678511029215669749
|
||
|
|
4 | 11.749154830839881243399421939922350714301165983279
|
||
|
|
5 | 14.897442128336725378844819156429870879807150630875
|
||
|
|
6 | 18.043402276727855564304555507889508902163088324834
|
||
|
|
7 | 21.188068934142213016142481528685423196935024604904
|
||
|
|
8 | 24.331942571356912035992944051850129651414333340303
|
||
|
|
9 | 27.475294980449223512212285525410668235700897307021
|
||
|
|
10 | 30.618286491641114715761625696447448310277939570868
|
||
|
|
11 | 33.761017796109325692471759911249650993879821495802
|
||
|
|
16 | 49.472505679924095824128003887609267273294894411716
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-1), 1), static_cast<RealType>(2.1971413260310170351490335626989662730530183315003L), tolerance * 3);
|
||
|
|
// Note this test passes at tolerance for float, double and long double, but fails for real_concept if tolerance <= 2.
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-1), 6), static_cast<RealType>(18.043402276727855564304555507889508902163088324834L), tolerance * 3);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-1), 11), static_cast<RealType>(33.761017796109325692471759911249650993879821495802L), tolerance * 3);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-1), 16), static_cast<RealType>(49.472505679924095824128003887609267273294894411716L), tolerance * 3);
|
||
|
|
|
||
|
|
/*
|
||
|
|
Table[N[BesselYZero[-2, n], 50], {n, 1, 20, 5}]
|
||
|
|
1 | 3.3842417671495934727014260185379031127323883259329
|
||
|
|
6 | 19.539039990286384411511740683423888947393156497603
|
||
|
|
11 | 35.289793869635804143323234828826075805683602368473
|
||
|
|
16 | 51.014128749483902310217774804582826908060740157564
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 1), static_cast<RealType>(3.3842417671495934727014260185379031127323883259329L), tolerance * 3);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 6), static_cast<RealType>(19.539039990286384411511740683423888947393156497603L), tolerance * 3);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 11), static_cast<RealType>(35.289793869635804143323234828826075805683602368473L), tolerance * 3);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 16), static_cast<RealType>(51.014128749483902310217774804582826908060740157564L), tolerance * 3);
|
||
|
|
|
||
|
|
/*
|
||
|
|
Table[N[BesselYZero[-3, n], 51], {n, 1, 7, 1}]
|
||
|
|
1 | 4.52702466114964385037002686710362763866515554861094
|
||
|
|
2 | 8.09755376286049070440221399011280422904322313690750
|
||
|
|
3 | 11.3964667395958667392520481906295049459849691925349
|
||
|
|
4 | 14.6230777423938731740767225077252006493529705699150
|
||
|
|
5 | 17.8184552329455202625532390647367394433803521627517
|
||
|
|
6 | 20.9972847541877606834525058939528641630713169437070
|
||
|
|
7 | 24.1662357585818282287385597668220226288453739040042
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 1), static_cast<RealType>(4.52702466114964385037002686710362763866515554861094L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 2), static_cast<RealType>(8.09755376286049070440221399011280422904322313690750L), tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 4), static_cast<RealType>(14.6230777423938731740767225077252006493529705699150L), tolerance);
|
||
|
|
|
||
|
|
/* Table[N[BesselKZero[-39, n], 51], {n, 1, 20, 5}]
|
||
|
|
1 | 42.2362394762664681287397356668342141701037684436723
|
||
|
|
6 | 65.8250353430045981408288669790173009159561533403819
|
||
|
|
11 | 84.2674082411341814641248554679382420802125973458922
|
||
|
|
16 | 101.589776978258493441843447810649346266014624868410
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 1), static_cast<RealType>(42.2362394762664681287397356668342141701037684436723L), tolerance );
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 6), static_cast<RealType>(65.8250353430045981408288669790173009159561533403819L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 11), static_cast<RealType>(84.2674082411341814641248554679382420802125973458922L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 16), static_cast<RealType>(101.589776978258493441843447810649346266014624868410L), tolerance);
|
||
|
|
|
||
|
|
/* Table[N[BesselKZero[-39 -(1/3), n], 51], {n, 1, 20, 5}]
|
||
|
|
1 | 39.3336965099558453809241429692683050137281997313679
|
||
|
|
6 | 64.9038181444904768984884565999608291433823953030822
|
||
|
|
11 | 83.4922341795560713832607574604255239776551554961143
|
||
|
|
16 | 100.878386349724826125265571457142254077564666532665
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 1), static_cast<RealType>(39.3336965099558453809241429692683050137281997313679L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 6), static_cast<RealType>(64.9038181444904768984884565999608291433823953030822L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 11), static_cast<RealType>(83.4922341795560713832607574604255239776551554961143L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 16), static_cast<RealType>(100.878386349724826125265571457142254077564666532665L), tolerance * 4);
|
||
|
|
/* Table[N[BesselKZero[-(1/3), n], 51], {n, 1, 20, 5}]
|
||
|
|
n |
|
||
|
|
1 | 0.364442931311036254896373762996743259918847602789703
|
||
|
|
6 | 15.9741013584105984633772025789145590038676373673203
|
||
|
|
11 | 31.6799168750213003020847708007848147516190373648194
|
||
|
|
16 | 47.3871543280673235432396563497681616285970326011211
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/3, 1), static_cast<RealType>(0.364442931311036254896373762996743259918847602789703L), tolerance * 10);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/3, 6), static_cast<RealType>(15.9741013584105984633772025789145590038676373673203L), tolerance * 10);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/3, 11), static_cast<RealType>(31.6799168750213003020847708007848147516190373648194L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/3, 16), static_cast<RealType>(47.3871543280673235432396563497681616285970326011211L), tolerance * 4);
|
||
|
|
|
||
|
|
/* Table[N[BesselKZero[-3 -(9999/10000), n], 51], {n, 1, 20, 5}]
|
||
|
|
1 | 5.64546089250283694562642537496601708928630550185069
|
||
|
|
2 | 9.36184180108088288881787970896747209376324330610979
|
||
|
|
3 | 12.7303431758275183078115963473808796340618061355885
|
||
|
|
4 | 15.9998152121877557837972245675029531998475502716021
|
||
|
|
6 | 9.36184180108088288881787970896747209376324330610979
|
||
|
|
11 | 25.6104419106589739931633042959774157385787405502820
|
||
|
|
16 | 41.4361281441868132581487460354904567452973524446193
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 1), static_cast<RealType>(5.64546089250283694562642537496601708928630550185069L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 2), static_cast<RealType>(9.36184180108088288881787970896747209376324330610979L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 3), static_cast<RealType>(12.7303431758275183078115963473808796340618061355885L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 4), static_cast<RealType>(15.9998152121877557837972245675029531998475502716021L), tolerance * 4);
|
||
|
|
|
||
|
|
/* Table[N[BesselYZero[-3 -(9999/10000), n], 51], {n, 1, 7, 1}]
|
||
|
|
1 | 5.64546089250283694562642537496601708928630550185069
|
||
|
|
2 | 9.36184180108088288881787970896747209376324330610979
|
||
|
|
3 | 12.7303431758275183078115963473808796340618061355885
|
||
|
|
4 | 15.9998152121877557837972245675029531998475502716021
|
||
|
|
|
||
|
|
// but 5 is same as 1!! Acknowledged as fault Wolfram [TS 6475] 26 Feb 13.
|
||
|
|
|
||
|
|
5 | 5.64546089250283694562642537496601708928630550184982
|
||
|
|
6 | 9.36184180108088288881787970896747209376324330610979
|
||
|
|
7 | 12.7303431758275183078115963473808796340618061355885
|
||
|
|
|
||
|
|
In[26]:= FindRoot[BesselY[-3 -9999/10000, r] == 0, {r, 3}] for r = 2,3, 4, 5 = {r->5.64546}
|
||
|
|
|
||
|
|
In[26]:= FindRoot[BesselY[-3 -9999/10000, r] == 0, {r, 19}] = 19.2246
|
||
|
|
|
||
|
|
So no very accurate reference value for these.
|
||
|
|
|
||
|
|
Calculated using cpp_dec_float_50
|
||
|
|
|
||
|
|
5.6454608925028369456264253749660170892863055018498
|
||
|
|
9.3618418010808828888178797089674720937632433061099
|
||
|
|
12.730343175827518307811596347380879634061806135589
|
||
|
|
15.999815212187755783797224567502953199847550271602
|
||
|
|
|
||
|
|
19.224610865671563344572152795434688888375602299773
|
||
|
|
22.424988389021059116212186912990863561607855849204
|
||
|
|
25.610441910658973993163304295977415738578740550282
|
||
|
|
28.786066313968546073981640755202085944374967166411
|
||
|
|
31.954857624676521867923579695253822854717613513587
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 1), static_cast<RealType>(5.64546089250283694562642537496601708928630550185069L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 2), static_cast<RealType>(9.36184180108088288881787970896747209376324330610979L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 3), static_cast<RealType>(12.7303431758275183078115963473808796340618061355885L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 4), static_cast<RealType>(15.9998152121877557837972245675029531998475502716021L), tolerance * 4);
|
||
|
|
//
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 5), static_cast<RealType>(19.224610865671563344572152795434688888375602299773L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 6), static_cast<RealType>(22.424988389021059116212186912990863561607855849204L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 7), static_cast<RealType>(25.610441910658973993163304295977415738578740550282L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 8), static_cast<RealType>(28.786066313968546073981640755202085944374967166411L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 9), static_cast<RealType>(31.954857624676521867923579695253822854717613513587L), tolerance * 4);
|
||
|
|
|
||
|
|
|
||
|
|
// Plot[BesselYZero[-7 - v, 1], {v, 0, 1}] shows discontinuity at the mid-point between integers.
|
||
|
|
|
||
|
|
/* Table[N[BesselYZero[-7 - (4999/10000), n], 51], {n, 1, 4, 1}]
|
||
|
|
1 | 3.59209698655443348407622952525352410710983745802573
|
||
|
|
2 | 11.6573245781899449398248761667833391837824916603434
|
||
|
|
3 | 15.4315262542144355217979771618575628291362029097236
|
||
|
|
4 | 18.9232143766706670333395285892576635207736306576135
|
||
|
|
*/
|
||
|
|
|
||
|
|
/* Table[N[BesselYZero[-7 - (5001/10000), n], 51], {n, 1, 4, 1}]
|
||
|
|
1 | 11.6567397956147934678808863468662427054245897492445
|
||
|
|
2 | 15.4310521624769624067699131497395566368341140531722
|
||
|
|
3 | 18.9227840182910629037411848072684247564491740961847
|
||
|
|
4 | 22.2951449444372591060253508661432751300205474374696
|
||
|
|
*/
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(4999)/10000, 1), static_cast<RealType>(3.59209698655443348407622952525352410710983745802573L), tolerance * 2000);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(4999)/10000, 2), static_cast<RealType>(11.6573245781899449398248761667833391837824916603434L), tolerance * 100);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(4999)/10000, 3), static_cast<RealType>(15.4315262542144355217979771618575628291362029097236L), tolerance * 100);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(4999)/10000, 4), static_cast<RealType>(18.9232143766706670333395285892576635207736306576135L), tolerance * 100);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(5001)/10000, 1), static_cast<RealType>(11.6567397956147934678808863468662427054245897492445L), tolerance * 100);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(5001)/10000, 2), static_cast<RealType>(15.4310521624769624067699131497395566368341140531722L), tolerance * 100);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(5001)/10000, 3), static_cast<RealType>(18.9227840182910629037411848072684247564491740961847L), tolerance * 100);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) -static_cast<RealType>(5001)/10000, 4), static_cast<RealType>(22.2951449444372591060253508661432751300205474374696L), tolerance * 100);
|
||
|
|
|
||
|
|
//BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-(static_cast<RealType>(-3)-static_cast<RealType>(99)/100), 5),
|
||
|
|
// cyl_neumann_zero(+(static_cast<RealType>(-3)-static_cast<RealType>(99)/100), 5), tolerance * 100);
|
||
|
|
{
|
||
|
|
long double x = 1.L;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
||
|
|
cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
|
||
|
|
cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
long double x = 2.L;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
||
|
|
cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
|
||
|
|
cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
long double x = 3.L;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
||
|
|
cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
|
||
|
|
cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
|
||
|
|
}
|
||
|
|
// These are very close but not exactly same.
|
||
|
|
//{
|
||
|
|
// RealType x = static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000;
|
||
|
|
// BOOST_CHECK_CLOSE_FRACTION(
|
||
|
|
// cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
|
||
|
|
// cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
|
||
|
|
// // 19.2242889 and 19.2246113
|
||
|
|
//}
|
||
|
|
//{
|
||
|
|
|
||
|
|
// RealType x = static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000;
|
||
|
|
// BOOST_CHECK_CLOSE_FRACTION(
|
||
|
|
// cyl_neumann_zero(-(static_cast<RealType>(x)), 6),
|
||
|
|
// cyl_neumann_zero(+(static_cast<RealType>(x)), 6), tolerance * 100);
|
||
|
|
// // 22.4246693 and 22.4249878
|
||
|
|
//}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
// 2.5 18.6890354 17.1033592
|
||
|
|
|
||
|
|
|
||
|
|
/*Table[N[BesselYZero[-1/81799, n], 51], {n, 1, 10, 5}]
|
||
|
|
|
||
|
|
1 | 0.893559276290122922836047849416713592133322804889757
|
||
|
|
2 | 3.95765935645507004204986415533750122885237402118726
|
||
|
|
3 | 7.08603190350579828577279552434514387474680226004173
|
||
|
|
4 | 10.2223258629823064789904339889550588869985272176335
|
||
|
|
5 | 13.3610782840659145864973521693322670264135672594988
|
||
|
|
3 | 7.08603190350579828577279552434514387474680226004173
|
||
|
|
5 | 13.3610782840659145864973521693322670264135672594988
|
||
|
|
6 | 16.5009032471619898684110089652474861084220781491575
|
||
|
|
7 | 19.6412905039556082160052482410981245043314155416354
|
||
|
|
9 | 25.9229384536173175152381652048590136247796591153244
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 1), static_cast<RealType>(0.893559276290122922836047849416713592133322804889757L), tolerance * 4);
|
||
|
|
// Doesn't converge!
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 2), static_cast<RealType>(3.95765935645507004204986415533750122885237402118726L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 3), static_cast<RealType>(7.08603190350579828577279552434514387474680226004173L), tolerance * 4);
|
||
|
|
/* try positive x
|
||
|
|
Table[N[BesselYZero[1/81799, n], 51], {n, 1, 5, 1}]
|
||
|
|
|
||
|
|
1 | 0.893594656187326273432267210617481926490785928764963
|
||
|
|
2 | 3.95769748213950546166537901626409026826595687994956
|
||
|
|
3 | 7.08607021707716361104064671367526817399129653285580
|
||
|
|
4 | 10.2223642239960815612515914411615233651316361060338
|
||
|
|
5 | 13.3611166636685056799674772287389749065996094266976
|
||
|
|
*/
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/81799, 2), static_cast<RealType>(3.95769748213950546166537901626409026826595687994956L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/81799, 3), static_cast<RealType>(7.08607021707716361104064671367526817399129653285580L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 4), static_cast<RealType>(10.2223258629823064789904339889550588869985272176335L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 5), static_cast<RealType>(13.3610782840659145864973521693322670264135672594988L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 6), static_cast<RealType>(16.5009032471619898684110089652474861084220781491575L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 9), static_cast<RealType>(25.9229384536173175152381652048590136247796591153244L), tolerance * 4);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) - static_cast<RealType>(1)/3, 1), static_cast<RealType>(7.3352783956690540155848592759652828459644819344081L), tolerance * 1000);
|
||
|
|
|
||
|
|
// Test Data for airy_ai_zero and airy_bi_zero functions.
|
||
|
|
|
||
|
|
using boost::math::airy_ai_zero; //
|
||
|
|
|
||
|
|
using boost::math::isnan;
|
||
|
|
|
||
|
|
BOOST_MATH_CHECK_THROW(airy_ai_zero<RealType>(0), std::domain_error);
|
||
|
|
|
||
|
|
if (std::numeric_limits<RealType>::has_quiet_NaN)
|
||
|
|
{ // If ignore errors, return NaN.
|
||
|
|
BOOST_CHECK((boost::math::isnan)(airy_ai_zero<RealType>(0, ignore_all_policy())));
|
||
|
|
BOOST_CHECK((boost::math::isnan)(airy_ai_zero<RealType>((std::numeric_limits<unsigned>::min)() , ignore_all_policy())));
|
||
|
|
// Can't abuse with NaN as won't compile.
|
||
|
|
//BOOST_MATH_CHECK_THROW(airy_ai_zero<RealType>(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{ // real_concept NaN not available, so return zero.
|
||
|
|
BOOST_CHECK_EQUAL(airy_ai_zero<RealType>(0, ignore_all_policy()), 0);
|
||
|
|
// BOOST_CHECK_EQUAL(airy_ai_zero<RealType>(-1), 0); // warning C4245: 'argument' : conversion from 'int' to 'unsigned int', signed/unsigned mismatch
|
||
|
|
}
|
||
|
|
|
||
|
|
BOOST_MATH_CHECK_THROW(airy_ai_zero<RealType>(-1), std::domain_error);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>((std::numeric_limits<boost::int32_t>::max)()), -static_cast<RealType>(4678579.33301973093739L), tolerance);
|
||
|
|
|
||
|
|
// Can't abuse with infinity because won't compile - no conversion.
|
||
|
|
//if (std::numeric_limits<RealType>::has_infinity)
|
||
|
|
//{
|
||
|
|
// BOOST_CHECK(isnan(airy_bi_zero<RealType>(-1)) );
|
||
|
|
//}
|
||
|
|
|
||
|
|
// WolframAlpha Table[N[AiryAiZero[n], 51], {n, 1, 20, 1}]
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1), static_cast<RealType>(-2.33810741045976703848919725244673544063854014567239L), tolerance * 2 * tolerance_tgamma_extra);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(2), static_cast<RealType>(-4.08794944413097061663698870145739106022476469910853L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(3), static_cast<RealType>(-5.52055982809555105912985551293129357379721428061753L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(4), static_cast<RealType>(-6.78670809007175899878024638449617696605388247739349L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(5), static_cast<RealType>(-7.94413358712085312313828055579826853214067439697221L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(6), static_cast<RealType>(-9.02265085334098038015819083988008925652467753515608L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(7), static_cast<RealType>(-10.0401743415580859305945567373625180940429025691058L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(8), static_cast<RealType>(-11.0085243037332628932354396495901510167308253815040L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(9), static_cast<RealType>(-11.9360155632362625170063649029305843155778862321198L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(10), static_cast<RealType>(-12.8287767528657572004067294072418244773864155995734L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(11), static_cast<RealType>(-13.6914890352107179282956967794669205416653698092008L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(12), static_cast<RealType>(-14.5278299517753349820739814429958933787141648698348L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(13), static_cast<RealType>(-15.3407551359779968571462085134814867051175833202480L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(14), static_cast<RealType>(-16.1326851569457714393459804472025217905182723970763L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(15), static_cast<RealType>(-16.9056339974299426270352387706114765990900510950317L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(16), static_cast<RealType>(-17.6613001056970575092536503040180559521532186681200L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(17), static_cast<RealType>(-18.4011325992071154158613979295043367545938146060201L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(18), static_cast<RealType>(-19.1263804742469521441241486897324946890754583847531L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(19), static_cast<RealType>(-19.8381298917214997009475636160114041983356824945389L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(20), static_cast<RealType>(-20.5373329076775663599826814113081017453042180147375L), tolerance);
|
||
|
|
|
||
|
|
// Table[N[AiryAiZero[n], 51], {n, 1000, 1001, 1}]
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1000), static_cast<RealType>(-281.031519612521552835336363963709689055717463965420L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1001), static_cast<RealType>(-281.218889579130068414512015874511112547569713693446L), tolerance);
|
||
|
|
|
||
|
|
// Table[N[AiryAiZero[n], 51], {n, 1000000, 1000001, 1}]
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1000000), static_cast<RealType>(-28107.8319793795834876064419863203282898723750036048L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1000001), static_cast<RealType>(-28107.8507179357979542838020057465277368471496446555L), tolerance);
|
||
|
|
|
||
|
|
|
||
|
|
// Table[N[AiryAiZero[n], 51], {n, 1000000000, 1000000001, 1}]
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1000000000), static_cast<RealType>(-2.81078366593344513918947921096193426320298300481145E+6L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1000000001), static_cast<RealType>(-2.81078366780730091663459728526906320267920607427246E+6L), tolerance);
|
||
|
|
|
||
|
|
// Test Data for airy_bi
|
||
|
|
using boost::math::airy_bi_zero;
|
||
|
|
|
||
|
|
BOOST_MATH_CHECK_THROW(airy_bi_zero<RealType>(0), std::domain_error);
|
||
|
|
|
||
|
|
if (std::numeric_limits<RealType>::has_quiet_NaN)
|
||
|
|
{ // return NaN.
|
||
|
|
BOOST_CHECK((boost::math::isnan)(airy_bi_zero<RealType>(0, ignore_all_policy())));
|
||
|
|
BOOST_CHECK((boost::math::isnan)(airy_bi_zero<RealType>((std::numeric_limits<unsigned>::min)() , ignore_all_policy())));
|
||
|
|
// Can't abuse with NaN as won't compile.
|
||
|
|
// BOOST_MATH_CHECK_THROW(airy_bi_zero<RealType>(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
|
||
|
|
// cannot convert parameter 1 from 'boost::math::concepts::real_concept' to 'unsigned int'.
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{ // real_concept NaN not available, so return zero.
|
||
|
|
BOOST_CHECK_EQUAL(airy_bi_zero<RealType>(0, ignore_all_policy()), 0);
|
||
|
|
// BOOST_CHECK_EQUAL(airy_bi_zero<RealType>(-1), 0);
|
||
|
|
// warning C4245: 'argument' : conversion from 'int' to 'unsigned int', signed/unsigned mismatch.
|
||
|
|
// If ignore the warning, interpreted as max unsigned:
|
||
|
|
// check airy_bi_zero<RealType>(-1) == 0 has failed [-7.42678e+006 != 0]
|
||
|
|
}
|
||
|
|
|
||
|
|
BOOST_MATH_CHECK_THROW(airy_bi_zero<RealType>(-1), std::domain_error);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>((std::numeric_limits<boost::int32_t>::max)()), -static_cast<RealType>(4678579.33229351984573L), tolerance * 300);
|
||
|
|
|
||
|
|
// Can't abuse with infinity because won't compile - no conversion.
|
||
|
|
//if (std::numeric_limits<RealType>::has_infinity)
|
||
|
|
//{
|
||
|
|
// BOOST_CHECK(isnan(airy_bi_zero<RealType>(std::numeric_limits<RealType>::infinity)) );
|
||
|
|
//}
|
||
|
|
|
||
|
|
// Table[N[AiryBiZero[n], 51], {n, 1, 20, 1}]
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1), static_cast<RealType>(-1.17371322270912792491997996247390210454364638917570L), tolerance * 4 * tolerance_tgamma_extra);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(2), static_cast<RealType>(-3.27109330283635271568022824016641380630093596910028L), tolerance * tolerance_tgamma_extra);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(3), static_cast<RealType>(-4.83073784166201593266770933990517817696614261732301L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(4), static_cast<RealType>(-6.16985212831025125983336452055593667996554943427563L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(5), static_cast<RealType>(-7.37676207936776371359995933044254122209152229939710L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(6), static_cast<RealType>(-8.49194884650938801344803949280977672860508755505546L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(7), static_cast<RealType>(-9.53819437934623888663298854515601962083907207638247L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(8), static_cast<RealType>(-10.5299135067053579244005555984531479995295775946214L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(9), static_cast<RealType>(-11.4769535512787794379234649247328196719482538148877L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(10), static_cast<RealType>(-12.3864171385827387455619015028632809482597983846856L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(11), static_cast<RealType>(-13.2636395229418055541107433243954907752411519609813L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(12), static_cast<RealType>(-14.1127568090686577915873097822240184716840428285509L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(13), static_cast<RealType>(-14.9370574121541640402032143104909046396121763517782L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(14), static_cast<RealType>(-15.7392103511904827708949784797481833807180162767841L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(15), static_cast<RealType>(-16.5214195506343790539179499652105457167110310370581L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(16), static_cast<RealType>(-17.2855316245812425329342366922535392425279753602710L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(17), static_cast<RealType>(-18.0331132872250015721711125433391920008087291416406L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(18), static_cast<RealType>(-18.7655082844800810413429789236105128440267189551421L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(19), static_cast<RealType>(-19.4838801329892340136659986592413575122062977793610L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(20), static_cast<RealType>(-20.1892447853962024202253232258275360764649783583934L), tolerance);
|
||
|
|
|
||
|
|
// Table[N[AiryBiZero[n], 51], {n, 1000, 1001, 1}]
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1000), static_cast<RealType>(-280.937811203415240157883427412260300146245056425646L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1001), static_cast<RealType>(-281.125212400956392021977771104562061554648675044114L), tolerance);
|
||
|
|
|
||
|
|
// Table[N[AiryBiZero[n], 51], {n, 1000000, 1000001, 1}]
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1000000), static_cast<RealType>(-28107.8226100991339342855024130953986989636667226163L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1000001), static_cast<RealType>(-28107.8413486584714939255315213519230566014624895515L), tolerance);
|
||
|
|
|
||
|
|
//Table[N[AiryBiZero[n], 51], {n, 1000000000, 1000000001, 1}]
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1000000000), static_cast<RealType>(-2.81078366499651725023268820158218492845371527054171E+6L), tolerance);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1000000001), static_cast<RealType>(-2.81078366687037302799011557215619265502627118526716E+6L), tolerance);
|
||
|
|
|
||
|
|
// Check the multi-root versions.
|
||
|
|
{
|
||
|
|
unsigned int n_roots = 1U;
|
||
|
|
std::vector<RealType> roots;
|
||
|
|
boost::math::airy_ai_zero<RealType>(2U, n_roots, std::back_inserter(roots));
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(roots[0], static_cast<RealType>(-4.08794944413097061663698870145739106022476469910853L), tolerance);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
unsigned int n_roots = 1U;
|
||
|
|
std::vector<RealType> roots;
|
||
|
|
boost::math::airy_bi_zero<RealType>(2U, n_roots, std::back_inserter(roots));
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(roots[0], static_cast<RealType>(-3.27109330283635271568022824016641380630093596910028L), tolerance * tolerance_tgamma_extra);
|
||
|
|
}
|
||
|
|
} // template <class RealType> void test_spots(RealType)
|
||
|
|
|
||
|
|
#include <boost/multiprecision/cpp_dec_float.hpp>
|
||
|
|
|
||
|
|
BOOST_AUTO_TEST_CASE(test_main)
|
||
|
|
{
|
||
|
|
test_bessel_zeros(0.1F);
|
||
|
|
test_bessel_zeros(0.1);
|
||
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
||
|
|
test_bessel_zeros(0.1L);
|
||
|
|
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
|
||
|
|
test_bessel_zeros(boost::math::concepts::real_concept(0.1));
|
||
|
|
#endif
|
||
|
|
#else
|
||
|
|
std::cout << "<note>The long double tests have been disabled on this platform "
|
||
|
|
"either because the long double overloads of the usual math functions are "
|
||
|
|
"not available at all, or because they are too inaccurate for these tests "
|
||
|
|
"to pass.</note>" << std::endl;
|
||
|
|
#endif
|
||
|
|
}
|