123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468 |
- // Copyright John Maddock 2006.
- // Copyright Paul A. Bristow 2007, 2009
- // Use, modification and distribution are subject to the
- // Boost Software License, Version 1.0. (See accompanying file
- // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
- #include <boost/math/concepts/real_concept.hpp>
- #define BOOST_TEST_MAIN
- #include <boost/test/unit_test.hpp>
- #include <boost/test/tools/floating_point_comparison.hpp>
- #include <boost/math/special_functions/math_fwd.hpp>
- #include <boost/math/constants/constants.hpp>
- #include <boost/array.hpp>
- #include <boost/random.hpp>
- #include "functor.hpp"
- #include "handle_test_result.hpp"
- #include "table_type.hpp"
- #ifndef SC_
- #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
- #endif
- template <class Real, typename T>
- void do_test_ellint_rf(T& data, const char* type_name, const char* test)
- {
- #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RF_FUNCTION_TO_TEST))
- typedef Real value_type;
- std::cout << "Testing: " << test << std::endl;
- #ifdef ELLINT_RF_FUNCTION_TO_TEST
- value_type(*fp)(value_type, value_type, value_type) = ELLINT_RF_FUNCTION_TO_TEST;
- #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
- value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf<value_type, value_type, value_type>;
- #else
- value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf;
- #endif
- boost::math::tools::test_result<value_type> result;
-
- result = boost::math::tools::test_hetero<Real>(
- data,
- bind_func<Real>(fp, 0, 1, 2),
- extract_result<Real>(3));
- handle_test_result(result, data[result.worst()], result.worst(),
- type_name, "ellint_rf", test);
- std::cout << std::endl;
- #endif
- }
- template <class Real, typename T>
- void do_test_ellint_rc(T& data, const char* type_name, const char* test)
- {
- #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RC_FUNCTION_TO_TEST))
- typedef Real value_type;
- std::cout << "Testing: " << test << std::endl;
- #ifdef ELLINT_RC_FUNCTION_TO_TEST
- value_type(*fp)(value_type, value_type) = ELLINT_RC_FUNCTION_TO_TEST;
- #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
- value_type (*fp)(value_type, value_type) = boost::math::ellint_rc<value_type, value_type>;
- #else
- value_type (*fp)(value_type, value_type) = boost::math::ellint_rc;
- #endif
- boost::math::tools::test_result<value_type> result;
-
- result = boost::math::tools::test_hetero<Real>(
- data,
- bind_func<Real>(fp, 0, 1),
- extract_result<Real>(2));
- handle_test_result(result, data[result.worst()], result.worst(),
- type_name, "ellint_rc", test);
- std::cout << std::endl;
- #endif
- }
- template <class Real, typename T>
- void do_test_ellint_rj(T& data, const char* type_name, const char* test)
- {
- #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RJ_FUNCTION_TO_TEST))
- typedef Real value_type;
- std::cout << "Testing: " << test << std::endl;
- #ifdef ELLINT_RJ_FUNCTION_TO_TEST
- value_type(*fp)(value_type, value_type, value_type, value_type) = ELLINT_RJ_FUNCTION_TO_TEST;
- #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
- value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj<value_type, value_type, value_type, value_type>;
- #else
- value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj;
- #endif
- boost::math::tools::test_result<value_type> result;
-
- result = boost::math::tools::test_hetero<Real>(
- data,
- bind_func<Real>(fp, 0, 1, 2, 3),
- extract_result<Real>(4));
- handle_test_result(result, data[result.worst()], result.worst(),
- type_name, "ellint_rj", test);
- std::cout << std::endl;
- #endif
- }
- template <class Real, typename T>
- void do_test_ellint_rd(T& data, const char* type_name, const char* test)
- {
- #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RD_FUNCTION_TO_TEST))
- typedef Real value_type;
- std::cout << "Testing: " << test << std::endl;
- #ifdef ELLINT_RD_FUNCTION_TO_TEST
- value_type(*fp)(value_type, value_type, value_type) = ELLINT_RD_FUNCTION_TO_TEST;
- #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
- value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd<value_type, value_type, value_type>;
- #else
- value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd;
- #endif
- boost::math::tools::test_result<value_type> result;
-
- result = boost::math::tools::test_hetero<Real>(
- data,
- bind_func<Real>(fp, 0, 1, 2),
- extract_result<Real>(3));
- handle_test_result(result, data[result.worst()], result.worst(),
- type_name, "ellint_rd", test);
- std::cout << std::endl;
- #endif
- }
- template <class Real, typename T>
- void do_test_ellint_rg(T& data, const char* type_name, const char* test)
- {
- #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RD_FUNCTION_TO_TEST))
- typedef Real value_type;
- std::cout << "Testing: " << test << std::endl;
- #ifdef ELLINT_RG_FUNCTION_TO_TEST
- value_type(*fp)(value_type, value_type, value_type) = ELLINT_RG_FUNCTION_TO_TEST;
- #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
- value_type(*fp)(value_type, value_type, value_type) = boost::math::ellint_rg<value_type, value_type, value_type>;
- #else
- value_type(*fp)(value_type, value_type, value_type) = boost::math::ellint_rg;
- #endif
- boost::math::tools::test_result<value_type> result;
- result = boost::math::tools::test_hetero<Real>(
- data,
- bind_func<Real>(fp, 0, 1, 2),
- extract_result<Real>(3));
- handle_test_result(result, data[result.worst()], result.worst(),
- type_name, "ellint_rg", test);
- std::cout << std::endl;
- #endif
- }
- #if !defined(TEST1) && !defined(TEST2) && !defined(TEST3) && !defined(TEST4)
- #define TEST1
- #define TEST2
- #define TEST3
- #define TEST4
- #endif
- #ifdef TEST1
- template <typename T>
- void t1(T, const char* type_name)
- {
- #include "ellint_rf_data.ipp"
- do_test_ellint_rf<T>(ellint_rf_data, type_name, "RF: Random data");
- }
- template <typename T>
- void t2(T, const char* type_name)
- {
- #include "ellint_rf_xxx.ipp"
- do_test_ellint_rf<T>(ellint_rf_xxx, type_name, "RF: x = y = z");
- }
- template <typename T>
- void t3(T, const char* type_name)
- {
- #include "ellint_rf_xyy.ipp"
- do_test_ellint_rf<T>(ellint_rf_xyy, type_name, "RF: x = y or y = z or x = z");
- }
- template <typename T>
- void t4(T, const char* type_name)
- {
- #include "ellint_rf_0yy.ipp"
- do_test_ellint_rf<T>(ellint_rf_0yy, type_name, "RF: x = 0, y = z");
- }
- template <typename T>
- void t5(T, const char* type_name)
- {
- #include "ellint_rf_xy0.ipp"
- do_test_ellint_rf<T>(ellint_rf_xy0, type_name, "RF: z = 0");
- }
- #endif
- #ifdef TEST2
- template <typename T>
- void t6(T, const char* type_name)
- {
- #include "ellint_rc_data.ipp"
- do_test_ellint_rc<T>(ellint_rc_data, type_name, "RC: Random data");
- }
- template <typename T>
- void t7(T, const char* type_name)
- {
- #include "ellint_rj_data.ipp"
- do_test_ellint_rj<T>(ellint_rj_data, type_name, "RJ: Random data");
- }
- template <typename T>
- void t8(T, const char* type_name)
- {
- #include "ellint_rj_e4.ipp"
- do_test_ellint_rj<T>(ellint_rj_e4, type_name, "RJ: 4 Equal Values");
- }
- template <typename T>
- void t9(T, const char* type_name)
- {
- #include "ellint_rj_e3.ipp"
- do_test_ellint_rj<T>(ellint_rj_e3, type_name, "RJ: 3 Equal Values");
- }
- template <typename T>
- void t10(T, const char* type_name)
- {
- #include "ellint_rj_e2.ipp"
- do_test_ellint_rj<T>(ellint_rj_e2, type_name, "RJ: 2 Equal Values");
- }
- template <typename T>
- void t11(T, const char* type_name)
- {
- #include "ellint_rj_zp.ipp"
- do_test_ellint_rj<T>(ellint_rj_zp, type_name, "RJ: Equal z and p");
- }
- #endif
- #ifdef TEST3
- template <typename T>
- void t12(T, const char* type_name)
- {
- #include "ellint_rd_data.ipp"
- do_test_ellint_rd<T>(ellint_rd_data, type_name, "RD: Random data");
- }
- template <typename T>
- void t13(T, const char* type_name)
- {
- #include "ellint_rd_xyy.ipp"
- do_test_ellint_rd<T>(ellint_rd_xyy, type_name, "RD: y = z");
- }
- template <typename T>
- void t14(T, const char* type_name)
- {
- #include "ellint_rd_xxz.ipp"
- do_test_ellint_rd<T>(ellint_rd_xxz, type_name, "RD: x = y");
- }
- template <typename T>
- void t15(T, const char* type_name)
- {
- #include "ellint_rd_0yy.ipp"
- do_test_ellint_rd<T>(ellint_rd_0yy, type_name, "RD: x = 0, y = z");
- }
- template <typename T>
- void t16(T, const char* type_name)
- {
- #include "ellint_rd_xxx.ipp"
- do_test_ellint_rd<T>(ellint_rd_xxx, type_name, "RD: x = y = z");
- }
- template <typename T>
- void t17(T, const char* type_name)
- {
- #include "ellint_rd_0xy.ipp"
- do_test_ellint_rd<T>(ellint_rd_0xy, type_name, "RD: x = 0");
- }
- #endif
- #ifdef TEST4
- template <typename T>
- void t18(T, const char* type_name)
- {
- #include "ellint_rg.ipp"
- do_test_ellint_rg<T>(ellint_rg, type_name, "RG: Random Data");
- }
- template <typename T>
- void t19(T, const char* type_name)
- {
- #include "ellint_rg_00x.ipp"
- do_test_ellint_rg<T>(ellint_rg_00x, type_name, "RG: two values 0");
- }
- template <typename T>
- void t20(T, const char* type_name)
- {
- #include "ellint_rg_xxx.ipp"
- do_test_ellint_rg<T>(ellint_rg_xxx, type_name, "RG: All values the same or zero");
- }
- template <typename T>
- void t21(T, const char* type_name)
- {
- #include "ellint_rg_xyy.ipp"
- do_test_ellint_rg<T>(ellint_rg_xyy, type_name, "RG: two values the same");
- }
- template <typename T>
- void t22(T, const char* type_name)
- {
- #include "ellint_rg_xy0.ipp"
- do_test_ellint_rg<T>(ellint_rg_xy0, type_name, "RG: one value zero");
- }
- #endif
- template <typename T>
- void test_spots(T val, const char* type_name)
- {
- #ifndef TEST_UDT
- using namespace boost::math;
- using namespace std;
- // Spot values from Numerical Computation of Real or Complex
- // Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
- // RF:
- T tolerance = (std::max)(T(1e-13f), tools::epsilon<T>() * 5) * 100; // Note 5eps expressed as a persentage!!!
- T eps2 = 5 * tools::epsilon<T>();
- BOOST_CHECK_CLOSE(ellint_rf(T(1), T(2), T(0)), T(1.3110287771461), tolerance);
- BOOST_CHECK_CLOSE(ellint_rf(T(0.5), T(1), T(0)), T(1.8540746773014), tolerance);
- BOOST_CHECK_CLOSE(ellint_rf(T(2), T(3), T(4)), T(0.58408284167715), tolerance);
- // RC:
- BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(0), T(1)/4), boost::math::constants::pi<T>(), eps2);
- BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(9)/4, T(2)), boost::math::constants::ln_two<T>(), eps2);
- BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(1) / 4, T(-2)), boost::math::constants::ln_two<T>() / 3, eps2);
- // RJ:
- BOOST_CHECK_CLOSE(ellint_rj(T(0), T(1), T(2), T(3)), T(0.77688623778582), tolerance);
- BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(5)), T(0.14297579667157), tolerance);
- BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-0.5)), T(0.24723819703052), tolerance);
- BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-5)), T(-0.12711230042964), tolerance);
- // RD:
- BOOST_CHECK_CLOSE(ellint_rd(T(0), T(2), T(1)), T(1.7972103521034), tolerance);
- BOOST_CHECK_CLOSE(ellint_rd(T(2), T(3), T(4)), T(0.16510527294261), tolerance);
- // Sanity/consistency checks from Numerical Computation of Real or Complex
- // Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
- boost::mt19937 ran;
- boost::uniform_real<float> ur(0, 1000);
- T eps40 = 40 * tools::epsilon<T>();
- for(unsigned i = 0; i < 1000; ++i)
- {
- T x = ur(ran);
- T y = ur(ran);
- T z = ur(ran);
- T lambda = ur(ran);
- T mu = x * y / lambda;
- // RF, eq 49:
- T s1 = ellint_rf(x+lambda, y+lambda, lambda) +
- ellint_rf(x + mu, y + mu, mu);
- T s2 = ellint_rf(x, y, T(0));
- BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
- // RC is degenerate case of RF:
- s1 = ellint_rc(x, y);
- s2 = ellint_rf(x, y, y);
- BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
- // RC, eq 50 (Note have to assume y = x):
- T mu2 = x * x / lambda;
- s1 = ellint_rc(lambda, x+lambda)
- + ellint_rc(mu2, x + mu2);
- s2 = ellint_rc(T(0), x);
- BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
- /*
- T p = ????; // no closed form for a, b and p???
- s1 = ellint_rj(x+lambda, y+lambda, lambda, p+lambda)
- + ellint_rj(x+mu, y+mu, mu, p+mu);
- s2 = ellint_rj(x, y, T(0), p)
- - 3 * ellint_rc(a, b);
- */
- // RD, eq 53:
- s1 = ellint_rd(lambda, x+lambda, y+lambda)
- + ellint_rd(mu, x+mu, y+mu);
- s2 = ellint_rd(T(0), x, y)
- - 3 / (y * sqrt(x+y+lambda+mu));
- BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
- // RD is degenerate case of RJ:
- s1 = ellint_rd(x, y, z);
- s2 = ellint_rj(x, y, z, z);
- BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
- }
- #endif
- //
- // Now random spot values:
- //
- #ifdef TEST1
- t1(val, type_name);
- t2(val, type_name);
- t3(val, type_name);
- t4(val, type_name);
- t5(val, type_name);
- #endif
- #ifdef TEST2
- t6(val, type_name);
- t7(val, type_name);
- t8(val, type_name);
- t9(val, type_name);
- t10(val, type_name);
- t11(val, type_name);
- #endif
- #ifdef TEST3
- t12(val, type_name);
- t13(val, type_name);
- t14(val, type_name);
- t15(val, type_name);
- t16(val, type_name);
- t17(val, type_name);
- #endif
- #ifdef TEST4
- t18(val, type_name);
- t19(val, type_name);
- t20(val, type_name);
- t21(val, type_name);
- t22(val, type_name);
- #endif
- }
|