ceph/src/boost/libs/math/test/test_hankel.cpp

   1 //  Copyright John Maddock 2012
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #include <pch_light.hpp>
   7
   8 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
   9 #define BOOST_TEST_MAIN
  10 #include <boost/test/unit_test.hpp>
  11 #include <boost/test/floating_point_comparison.hpp>
  12 #include <boost/math/special_functions/math_fwd.hpp>
  13 #include <boost/math/concepts/real_concept.hpp>
  14 #include <boost/array.hpp>
  15 #include <boost/math/special_functions/hankel.hpp>
  16 #include <iostream>
  17 #include <iomanip>
  18
  19 #ifdef _MSC_VER
  20 #  pragma warning(disable : 4756 4127) // overflow in constant arithmetic
  21 // Constants are too big for float case, but this doesn't matter for test.
  22 #endif
  23
  24 //
  25 // DESCRIPTION:
  26 // ~~~~~~~~~~~~
  27 //
  28 // This file tests the Hankel H1 and H2 functions.
  29 // These are basically just a few spot tests, since the underlying implementation
  30 // is the same as for the Bessel functions.
  31 //
  32 template <class T>
  33 void check_close(const std::complex<T>& a, const std::complex<T>& b)
  34 {
  35    T tol = boost::math::tools::epsilon<T>() * 3000;
  36    BOOST_CHECK_CLOSE_FRACTION(a.real(), b.real(), tol);
  37    BOOST_CHECK_CLOSE_FRACTION(a.imag(), b.imag(), tol);
  38 }
  39
  40 template <class T>
  41 void test_hankel(T, const char* name)
  42 {
  43    std::cout << "Testing type " << name << std::endl;
  44
  45    static const boost::array<boost::array<std::complex<T>, 4>, 16> data =
  46    {{
  47       // Values are v, z, J, and Y.
  48       // H1 and H2 are calculated from functions.wolfram.com.
  49       {{ 0, 1, static_cast<T>(0.765197686557966551449717526102663220909274289755325241861548L), static_cast<T>(0.0882569642156769579829267660235151628278175230906755467110438L) }},
  50       {{ 20, 15.5, static_cast<T>(0.0114685669049540880132573889173945340441319848974792913849131L), static_cast<T>(-2.23357703561803241011539677726233479433825678625142168545338L) }},
  51       {{ 202, 65, static_cast<T>(4.03123907894335908039069177339845754619082182624766366629474e-77L), static_cast<T>(-4.12853948338543234456930697819285129000267780751856135651604e73L) }},
  52       {{ 1.25, 2.25, static_cast<T>(0.548918751190427983177518806565451279306141559548962787802891L), static_cast<T>(-0.125900744882628421758627761371862848797979705547465002154794L) }},
  53       {{ -20, 15.5, static_cast<T>(0.0114685669049540880132573889173945340441319848974792913849131L), static_cast<T>(-2.23357703561803241011539677726233479433825678625142168545338L) }},
  54       {{ -20, -15.5,  static_cast<T>(0.0114685669049540880132573889173945340441319848974792913849131L), std::complex<T>(static_cast<T>(-2.23357703561803241011539677726233479433825678625142168545338L), static_cast<T>(0.02293713380990817602651477783478906808826396979495858276983L))}},
  55       {{ 1.25, -1.5, std::complex<T>(static_cast<T>(-0.335713500965919366139805990226845134897000581426417882156072L),  static_cast<T>(-0.335713500965919366139805990226845134897000581426417882156072L)), std::complex<T>(static_cast<T>(0.392747687664481978664420363126684555843062241632017696636768L), static_cast<T>(-1.064174689596320710944032343580374825637063404484853460948911L)) }},
  56       {{ -1.25, -1.5, std::complex<T>(static_cast<T>(0.515099846311769525023685454389374962206960751452481078650112L),  static_cast<T>(-0.515099846311769525023685454389374962206960751452481078650112L)), std::complex<T>(static_cast<T>(-0.040329260174013212604062774398331485097569895404765001721544L), static_cast<T>(0.989870432449525837443308134380418439316351607500197155578680L)) }},
  57       {{ 4, 4, static_cast<T>(0.281129064961360106322277160229942806897088617059328870629222L), static_cast<T>(-0.488936768533842510615657398339913206218740182079627974737267L) }},
  58       {{ 4, -4, static_cast<T>(0.281129064961360106322277160229942806897088617059328870629222L), std::complex<T>(static_cast<T>(-0.488936768533842510615657398339913206218740182079627974737267L), static_cast<T>(0.562258129922720212644554320459885613794177234118657741258443L)) }},
  59       {{ -4, 4, static_cast<T>(0.281129064961360106322277160229942806897088617059328870629222L), static_cast<T>(-0.488936768533842510615657398339913206218740182079627974737267L) }},
  60       {{ -4, -4, static_cast<T>(0.281129064961360106322277160229942806897088617059328870629222), std::complex<T>(static_cast<T>(-0.488936768533842510615657398339913206218740182079627974737267), static_cast<T>(0.562258129922720212644554320459885613794177234118657741258443L)) }},
  61       {{ 3, 3, static_cast<T>(0.309062722255251643618260194946833149429135935993056794354475L), static_cast<T>(-0.538541616105031618004703905338594463807957863604859251481262L) }},
  62       {{ 3, -3, static_cast<T>(-0.309062722255251643618260194946833149429135935993056794354475L), std::complex<T>(static_cast<T>(0.538541616105031618004703905338594463807957863604859251481262L), static_cast<T>(-0.618125444510503287236520389893666298858271871986113588708949L)) }},
  63       {{ -3, 3, static_cast<T>(-0.309062722255251643618260194946833149429135935993056794354475L), static_cast<T>(0.538541616105031618004703905338594463807957863604859251481262L) }},
  64       {{ -3, -3, static_cast<T>(0.309062722255251643618260194946833149429135935993056794354475L), std::complex<T>(static_cast<T>(-0.538541616105031618004703905338594463807957863604859251481262L), static_cast<T>(0.618125444510503287236520389893666298858271871986113588708949L)) }},
  65    }};
  66
  67    std::complex<T> im(0, 1);
  68    for(unsigned i = 0; i < data.size(); ++i)
  69    {
  70       if((i != 2) || (std::numeric_limits<T>::max_exponent10 > 80))
  71       {
  72          check_close(boost::math::cyl_hankel_1(data[i][0].real(), data[i][1].real()), data[i][2] + im * data[i][3]);
  73          check_close(boost::math::cyl_hankel_2(data[i][0].real(), data[i][1].real()), data[i][2] - im * data[i][3]);
  74
  75          check_close(
  76             boost::math::cyl_hankel_1(data[i][0].real() + 0.5f, data[i][1].real()) * boost::math::constants::root_half_pi<T>() / sqrt(data[i][1]),
  77             boost::math::sph_hankel_1(data[i][0].real(), data[i][1].real()));
  78          check_close(
  79             boost::math::cyl_hankel_2(data[i][0].real() + 0.5f, data[i][1].real()) * boost::math::constants::root_half_pi<T>() / sqrt(data[i][1]),
  80             boost::math::sph_hankel_2(data[i][0].real(), data[i][1].real()));
  81       }
  82    }
  83 }
  84
  85 //
  86 // Instantiate a few instances to check our error handling code can cope with std::complex:
  87 //
  88 typedef boost::math::policies::policy<
  89    boost::math::policies::overflow_error<boost::math::policies::throw_on_error>,
  90    boost::math::policies::denorm_error<boost::math::policies::throw_on_error>,
  91    boost::math::policies::underflow_error<boost::math::policies::throw_on_error>,
  92    boost::math::policies::domain_error<boost::math::policies::throw_on_error>,
  93    boost::math::policies::pole_error<boost::math::policies::throw_on_error>,
  94    boost::math::policies::rounding_error<boost::math::policies::throw_on_error>,
  95    boost::math::policies::evaluation_error<boost::math::policies::throw_on_error>,
  96    boost::math::policies::indeterminate_result_error<boost::math::policies::throw_on_error> > pol1;
  97
  98 template std::complex<double> boost::math::cyl_hankel_1<double, double, pol1>(double, double, const pol1&);
  99
 100 typedef boost::math::policies::policy<
 101    boost::math::policies::overflow_error<boost::math::policies::errno_on_error>,
 102    boost::math::policies::denorm_error<boost::math::policies::errno_on_error>,
 103    boost::math::policies::underflow_error<boost::math::policies::errno_on_error>,
 104    boost::math::policies::domain_error<boost::math::policies::errno_on_error>,
 105    boost::math::policies::pole_error<boost::math::policies::errno_on_error>,
 106    boost::math::policies::rounding_error<boost::math::policies::errno_on_error>,
 107    boost::math::policies::evaluation_error<boost::math::policies::errno_on_error>,
 108    boost::math::policies::indeterminate_result_error<boost::math::policies::errno_on_error> > pol2;
 109
 110 template std::complex<double> boost::math::cyl_hankel_1<double, double, pol2>(double, double, const pol2&);
 111
 112 typedef boost::math::policies::policy<
 113    boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
 114    boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
 115    boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
 116    boost::math::policies::domain_error<boost::math::policies::ignore_error>,
 117    boost::math::policies::pole_error<boost::math::policies::ignore_error>,
 118    boost::math::policies::rounding_error<boost::math::policies::ignore_error>,
 119    boost::math::policies::evaluation_error<boost::math::policies::ignore_error>,
 120    boost::math::policies::indeterminate_result_error<boost::math::policies::ignore_error> > pol3;
 121
 122 template std::complex<double> boost::math::cyl_hankel_1<double, double, pol3>(double, double, const pol3&);
 123
 124
 125 BOOST_AUTO_TEST_CASE( test_main )
 126 {
 127 #ifdef TEST_GSL
 128    gsl_set_error_handler_off();
 129 #endif
 130    BOOST_MATH_CONTROL_FP;
 131
 132 #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
 133    test_hankel(0.1F, "float");
 134 #endif
 135    test_hankel(0.1, "double");
 136 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 137    test_hankel(0.1L, "long double");
 138 #else
 139    std::cout << "<note>The long double tests have been disabled on this platform "
 140       "either because the long double overloads of the usual math functions are "
 141       "not available at all, or because they are too inaccurate for these tests "
 142       "to pass.</note>" << std::endl;
 143 #endif
 144
 145 }
 146
 147
 148
 149