quaternion_test.cpp

boost库提供标准的C++ API 配合dev c++使用,功能更加强大

                << ::boost::math::multipolar(rho1, theta1, rho2, theta2));
    
    float                         t = 5;
    float                         radius = ::std::sqrt(2.0f);
    float                         longitude = ::std::atan(1.0f);
    float                         lattitude = ::std::atan(::std::sqrt(3.0f));
    
    BOOST_MESSAGE( "The value of the quaternion represented "
                << "in cylindrospherical form by "
                << "t = " << t << " , radius = " << radius
                << " , longitude = " << longitude << " , latitude = "
                << lattitude << " is "
                << ::boost::math::cylindrospherical(t, radius,
                        longitude, lattitude));
    
    float                         r = ::std::sqrt(2.0f);
    float                         angle = ::std::atan(1.0f);
    float                         h1 = 3;
    float                         h2 = 4;
    
    BOOST_MESSAGE( "The value of the quaternion represented "
                << "in cylindrical form by "
                << "r = " << r << " , angle = " << angle
                << " , h1 = " << h1 << " , h2 = " << h2
                << " is "
                << ::boost::math::cylindrical(r, angle, h1, h2));
    
    double                                   real_1(1);
    ::std::complex<double>                   complex_1(1);
    ::std::complex<double>                   complex_i(0,1);
    ::boost::math::quaternion<double>        quaternion_1(1);
    ::boost::math::quaternion<double>        quaternion_i(0,1);
    ::boost::math::quaternion<double>        quaternion_j(0,0,1);
    ::boost::math::quaternion<double>        quaternion_k(0,0,0,1);
    
    BOOST_MESSAGE(" ");
    
    BOOST_MESSAGE( "Real 1: " << real_1 << " ; "
                << "Complex 1: " << complex_1 << " ; "
                << "Quaternion 1: " << quaternion_1 << " .");
    
    BOOST_MESSAGE( "Complex i: " << complex_i << " ; "
                << "Quaternion i: " << quaternion_i << " .");
    
    BOOST_MESSAGE( "Quaternion j: " << quaternion_j << " .");
    
    BOOST_MESSAGE( "Quaternion k: " << quaternion_k << " .");
    
    
    BOOST_MESSAGE(" ");
    
    
    BOOST_MESSAGE( "i*i: " << quaternion_i*quaternion_i << " ; "
                << "j*j: " << quaternion_j*quaternion_j << " ; "
                << "k*k: " << quaternion_k*quaternion_k << " .");
    BOOST_MESSAGE( "i*j: " << quaternion_i*quaternion_j << " ; "
                << "j*i: " << quaternion_j*quaternion_i << " .");
    BOOST_MESSAGE( "j*k: " << quaternion_j*quaternion_k << " ; "
                << "k*j: " << quaternion_k*quaternion_j << " .");
    BOOST_MESSAGE( "k*i: " << quaternion_k*quaternion_i << " ; "
                << "i*k: " << quaternion_i*quaternion_k << " .");
    
    BOOST_MESSAGE(" ");
}


template<typename T>
void    multiplication_test(const char * more_blurb)
{
#if defined(__GNUC__) && (__GNUC__ < 3)
#else   /* defined(__GNUC__) && (__GNUC__ < 3) */
    using ::std::numeric_limits;
    
    using ::boost::math::abs;
#endif /* defined(__GNUC__) && (__GNUC__ < 3) */
    
    
    BOOST_MESSAGE("Testing multiplication for " << more_blurb << ".");
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(1,0,0,0)*
                ::boost::math::quaternion<T>(1,0,0,0)-static_cast<T>(1)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,1,0,0)*
                ::boost::math::quaternion<T>(0,1,0,0)+static_cast<T>(1)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,0,1,0)*
                ::boost::math::quaternion<T>(0,0,1,0)+static_cast<T>(1)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,0,0,1)*
                ::boost::math::quaternion<T>(0,0,0,1)+static_cast<T>(1)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,1,0,0)*
                ::boost::math::quaternion<T>(0,0,1,0)-
                ::boost::math::quaternion<T>(0,0,0,1)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,0,1,0)*
                ::boost::math::quaternion<T>(0,1,0,0)+
                ::boost::math::quaternion<T>(0,0,0,1)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,0,1,0)*
                ::boost::math::quaternion<T>(0,0,0,1)-
                ::boost::math::quaternion<T>(0,1,0,0)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,0,0,1)*
                ::boost::math::quaternion<T>(0,0,1,0)+
                ::boost::math::quaternion<T>(0,1,0,0)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,0,0,1)*
                ::boost::math::quaternion<T>(0,1,0,0)-
                ::boost::math::quaternion<T>(0,0,1,0)),
            numeric_limits<T>::epsilon()
        ));
    
    BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(::boost::math::quaternion<T>(0,1,0,0)*
                ::boost::math::quaternion<T>(0,0,0,1)+
                ::boost::math::quaternion<T>(0,0,1,0)),
            numeric_limits<T>::epsilon()
        ));
}


template<typename T>
void    exp_test(const char * more_blurb)
{
#if defined(__GNUC__) && (__GNUC__ < 3)
#else   /* defined(__GNUC__) && (__GNUC__ < 3) */
    using ::std::numeric_limits;
    
    using ::std::atan;
    
    using ::boost::math::abs;
#endif  /* defined(__GNUC__) && (__GNUC__ < 3) */
    
    
    BOOST_MESSAGE("Testing exp for " << more_blurb << ".");
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(exp(::boost::math::quaternion<T>
                (0,4*atan(static_cast<T>(1)),0,0))+static_cast<T>(1)),
            2*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(exp(::boost::math::quaternion<T>
                (0,0,4*atan(static_cast<T>(1)),0))+static_cast<T>(1)),
            2*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(exp(::boost::math::quaternion<T>
                (0,0,0,4*atan(static_cast<T>(1))))+static_cast<T>(1)),
            2*numeric_limits<T>::epsilon()
        ));
}


template<typename T>
void    cos_test(const char * more_blurb)
{
#if defined(__GNUC__) && (__GNUC__ < 3)
#else   /* defined(__GNUC__) && (__GNUC__ < 3) */
    using ::std::numeric_limits;
    
    using ::std::log;
    
    using ::boost::math::abs;
#endif  /* defined(__GNUC__) && (__GNUC__ < 3) */
    
    
    BOOST_MESSAGE("Testing cos for " << more_blurb << ".");
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(static_cast<T>(4)*cos(::boost::math::quaternion<T>
                (0,log(static_cast<T>(2)),0,0))-static_cast<T>(5)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(static_cast<T>(4)*cos(::boost::math::quaternion<T>
                (0,0,log(static_cast<T>(2)),0))-static_cast<T>(5)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(static_cast<T>(4)*cos(::boost::math::quaternion<T>
                (0,0,0,log(static_cast<T>(2))))-static_cast<T>(5)),
            4*numeric_limits<T>::epsilon()
        ));
}


template<typename T>
void    sin_test(const char * more_blurb)
{
#if defined(__GNUC__) && (__GNUC__ < 3)
#else   /* defined(__GNUC__) && (__GNUC__ < 3) */
    using ::std::numeric_limits;
    
    using ::std::log;
    
    using ::boost::math::abs;
#endif  /* defined(__GNUC__) && (__GNUC__ < 3) */
    
    
    BOOST_MESSAGE("Testing sin for " << more_blurb << ".");
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(static_cast<T>(4)*sin(::boost::math::quaternion<T>
                (0,log(static_cast<T>(2)),0,0))
                -::boost::math::quaternion<T>(0,3,0,0)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(static_cast<T>(4)*sin(::boost::math::quaternion<T>
                (0,0,log(static_cast<T>(2)),0))
                -::boost::math::quaternion<T>(0,0,3,0)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(static_cast<T>(4)*sin(::boost::math::quaternion<T>
                (0,0,0,log(static_cast<T>(2))))
                -::boost::math::quaternion<T>(0,0,0,3)),
            4*numeric_limits<T>::epsilon()
        ));
}


template<typename T>
void    cosh_test(const char * more_blurb)
{
#if defined(__GNUC__) && (__GNUC__ < 3)
#else   /* defined(__GNUC__) && (__GNUC__ < 3) */
    using ::std::numeric_limits;
    
    using ::std::atan;
    
    using ::boost::math::abs;
#endif  /* defined(__GNUC__) && (__GNUC__ < 3) */
    
    
    BOOST_MESSAGE("Testing cosh for " << more_blurb << ".");
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(cosh(::boost::math::quaternion<T>
                (0,4*atan(static_cast<T>(1)),0,0))
                +static_cast<T>(1)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(cosh(::boost::math::quaternion<T>
                (0,0,4*atan(static_cast<T>(1)),0))
                +static_cast<T>(1)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(cosh(::boost::math::quaternion<T>
                (0,0,0,4*atan(static_cast<T>(1))))
                +static_cast<T>(1)),
            4*numeric_limits<T>::epsilon()
        ));
}


template<typename T>
void    sinh_test(const char * more_blurb)
{
#if defined(__GNUC__) && (__GNUC__ < 3)
#else   /* defined(__GNUC__) && (__GNUC__ < 3) */
    using ::std::numeric_limits;
    
    using ::std::atan;
    
    using ::boost::math::abs;
#endif  /* defined(__GNUC__) && (__GNUC__ < 3) */
    
    
    BOOST_MESSAGE("Testing sinh for " << more_blurb << ".");
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(sinh(::boost::math::quaternion<T>
                (0,2*atan(static_cast<T>(1)),0,0))
                -::boost::math::quaternion<T>(0,1,0,0)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(sinh(::boost::math::quaternion<T>
                (0,0,2*atan(static_cast<T>(1)),0))
                -::boost::math::quaternion<T>(0,0,1,0)),
            4*numeric_limits<T>::epsilon()
        ));
    
    BOOST_CHECK_PREDICATE(::std::less_equal<T>(), 2,
        (
            abs(sinh(::boost::math::quaternion<T>
                (0,0,0,2*atan(static_cast<T>(1))))
                -::boost::math::quaternion<T>(0,0,0,1)),
            4*numeric_limits<T>::epsilon()
        ));
}


boost::unit_test_framework::test_suite *    init_unit_test_suite(int, char *[])
{
    //::boost::unit_test_framework::unit_test_log::instance().
    //    set_log_threshold_level_by_name("messages");
    
    boost::unit_test_framework::test_suite *    test =
        BOOST_TEST_SUITE("quaternion_test");
    
#define    BOOST_QUATERNION_COMMON_GENERATOR(fct,type)             \
    test->add(BOOST_TEST_CASE(::boost::bind(static_cast            \
        < void (*) (const char *) >(&fct##_test<type>), #type)));
    
    
#define    BOOST_QUATERNION_TEST(type)                        \
    BOOST_QUATERNION_COMMON_GENERATOR(multiplication,type)    \
    BOOST_QUATERNION_COMMON_GENERATOR(exp,type)               \
    BOOST_QUATERNION_COMMON_GENERATOR(cos,type)               \
    BOOST_QUATERNION_COMMON_GENERATOR(sin,type)               \
    BOOST_QUATERNION_COMMON_GENERATOR(cosh,type)              \
    BOOST_QUATERNION_COMMON_GENERATOR(sinh,type)
    
    
    BOOST_QUATERNION_TEST(float)
    BOOST_QUATERNION_TEST(double)
    BOOST_QUATERNION_TEST(long double)
    
    
#undef    BOOST_QUATERNION_TEST
    
#undef    BOOST_QUATERNION_COMMON_GENERATOR
    
    
#ifdef BOOST_QUATERNION_TEST_VERBOSE
    
    quaternion_manual_test();
    
#endif    /* BOOST_QUATERNION_TEST_VERBOSE */
    
    return(test);
}