EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/math/test/cardinal_cubic_b_spline_test.cpp

// Copyright Nick Thompson, 2017
// 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)

#define BOOST_TEST_MODULE test_cubic_b_spline

#include <random>
#include <functional>
#include <boost/random/uniform_real_distribution.hpp>
#include <boost/type_index.hpp>
#include <boost/test/included/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
#include <boost/math/interpolators/detail/cardinal_cubic_b_spline_detail.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>

using boost::multiprecision::cpp_bin_float_50;
using boost::math::constants::third;
using boost::math::constants::half;

template<class Real>
void test_b3_spline()
{
    std::cout << "Testing evaluation of spline basis functions on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
    // Outside the support:
    Real eps = std::numeric_limits<Real>::epsilon();
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(2.5), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(-2.5), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(2.5), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(-2.5), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(2.5), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(-2.5), (Real) 0);


    // On the boundary of support:
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(2), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(-2), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(2), (Real) 0);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(-2), (Real) 0);

    // Special values:
    BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(-1), third<Real>()*half<Real>(), eps);
    BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>( 1), third<Real>()*half<Real>(), eps);
    BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(0), 2*third<Real>(), eps);

    BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>(-1), half<Real>(), eps);
    BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>( 1), -half<Real>(), eps);
    BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(0), eps);

    // Properties: B3 is an even function, B3' is an odd function.
    for (size_t i = 1; i < 200; ++i)
    {
        Real arg = i*0.01;
        BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(arg), boost::math::interpolators::detail::b3_spline<Real>(arg), eps);
        BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>(-arg), -boost::math::interpolators::detail::b3_spline_prime<Real>(arg), eps);
        BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_double_prime<Real>(-arg), boost::math::interpolators::detail::b3_spline_double_prime<Real>(arg), eps);
    }

}
/*
 * This test ensures that the interpolant s(x_j) = f(x_j) at all grid points.
 */
template<class Real>
void test_interpolation_condition()
{
    using std::sqrt;
    std::cout << "Testing interpolation condition for cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
    std::random_device rd;
    std::mt19937 gen(rd());
    boost::random::uniform_real_distribution<Real> dis(1, 10);
    std::vector<Real> v(5000);
    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = dis(gen);
    }

    Real step = 0.01;
    Real a = 5;
    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), a, step);

    for (size_t i = 0; i < v.size(); ++i)
    {
        Real y = spline(i*step + a);
        // This seems like a very large tolerance, but I don't know of any other interpolators
        // that will be able to do much better on random data.
        BOOST_CHECK_CLOSE(y, v[i], 10000*sqrt(std::numeric_limits<Real>::epsilon()));
    }

}


template<class Real>
void test_constant_function()
{
    std::cout << "Testing that constants are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
    std::vector<Real> v(500);
    Real constant = 50.2;
    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = 50.2;
    }

    Real step = 0.02;
    Real a = 5;
    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), a, step);

    for (size_t i = 0; i < v.size(); ++i)
    {
        // Do not test at interpolation point; we already know it works there:
        Real y = spline(i*step + a + 0.001);
        BOOST_CHECK_CLOSE(y, constant, 10*std::numeric_limits<Real>::epsilon());
        Real y_prime = spline.prime(i*step + a + 0.002);
        BOOST_CHECK_SMALL(y_prime, 5000*std::numeric_limits<Real>::epsilon());
        Real y_double_prime = spline.double_prime(i*step + a + 0.002);
        BOOST_CHECK_SMALL(y_double_prime, 5000*std::numeric_limits<Real>::epsilon());

    }

    // Test that correctly specified left and right-derivatives work properly:
    spline = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), a, step, 0, 0);

    for (size_t i = 0; i < v.size(); ++i)
    {
        Real y = spline(i*step + a + 0.002);
        BOOST_CHECK_CLOSE(y, constant, std::numeric_limits<Real>::epsilon());
        Real y_prime = spline.prime(i*step + a + 0.002);
        BOOST_CHECK_SMALL(y_prime, std::numeric_limits<Real>::epsilon());
    }

    //
    // Again with iterator constructor:
    //
    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline2(v.begin(), v.end(), a, step);

    for (size_t i = 0; i < v.size(); ++i)
    {
       // Do not test at interpolation point; we already know it works there:
       Real y = spline2(i*step + a + 0.001);
       BOOST_CHECK_CLOSE(y, constant, 10 * std::numeric_limits<Real>::epsilon());
       Real y_prime = spline2.prime(i*step + a + 0.002);
       BOOST_CHECK_SMALL(y_prime, 5000 * std::numeric_limits<Real>::epsilon());
    }

    // Test that correctly specified left and right-derivatives work properly:
    spline2 = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.begin(), v.end(), a, step, 0, 0);

    for (size_t i = 0; i < v.size(); ++i)
    {
       Real y = spline2(i*step + a + 0.002);
       BOOST_CHECK_CLOSE(y, constant, std::numeric_limits<Real>::epsilon());
       Real y_prime = spline2.prime(i*step + a + 0.002);
       BOOST_CHECK_SMALL(y_prime, std::numeric_limits<Real>::epsilon());
    }
}


template<class Real>
void test_affine_function()
{
    using std::sqrt;
    std::cout << "Testing that affine functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
    std::vector<Real> v(500);
    Real a = 10;
    Real b = 8;
    Real step = 0.005;

    auto f = [a, b](Real x) { return a*x + b; };
    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = f(i*step);
    }

    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), 0, step);

    for (size_t i = 0; i < v.size() - 1; ++i)
    {
        Real arg = i*step + 0.0001;
        Real y = spline(arg);
        BOOST_CHECK_CLOSE(y, f(arg), sqrt(std::numeric_limits<Real>::epsilon()));
        Real y_prime = spline.prime(arg);
        BOOST_CHECK_CLOSE(y_prime, a, 100*sqrt(std::numeric_limits<Real>::epsilon()));
    }

    // Test that correctly specified left and right-derivatives work properly:
    spline = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), 0, step, a, a);

    for (size_t i = 0; i < v.size() - 1; ++i)
    {
        Real arg = i*step + 0.0001;
        Real y = spline(arg);
        BOOST_CHECK_CLOSE(y, f(arg), sqrt(std::numeric_limits<Real>::epsilon()));
        Real y_prime = spline.prime(arg);
        BOOST_CHECK_CLOSE(y_prime, a, 100*sqrt(std::numeric_limits<Real>::epsilon()));
    }
}


template<class Real>
void test_quadratic_function()
{
    using std::sqrt;
    std::cout << "Testing that quadratic functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
    std::vector<Real> v(500);
    Real a = 1.2;
    Real b = -3.4;
    Real c = -8.6;
    Real step = 0.01;

    auto f = [a, b, c](Real x) { return a*x*x + b*x + c; };
    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = f(i*step);
    }

    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), 0, step);

    for (size_t i = 0; i < v.size() -1; ++i)
    {
        Real arg = i*step + 0.001;
        Real y = spline(arg);
        BOOST_CHECK_CLOSE(y, f(arg), 0.1);
        Real y_prime = spline.prime(arg);
        BOOST_CHECK_CLOSE(y_prime, 2*a*arg + b, 2.0);
    }
}


template<class Real>
void test_trig_function()
{
    std::cout << "Testing that sine functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
    std::mt19937 gen;
    std::vector<Real> v(500);
    Real x0 = 1;
    Real step = 0.125;

    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = sin(x0 + step * i);
    }

    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), x0, step);

    boost::random::uniform_real_distribution<Real> absissa(x0, x0 + 499 * step);

    for (size_t i = 0; i < v.size(); ++i)
    {
        Real x = absissa(gen);
        Real y = spline(x);
        BOOST_CHECK_CLOSE(y, sin(x), 1.0);
        auto y_prime = spline.prime(x);
        BOOST_CHECK_CLOSE(y_prime, cos(x), 2.0);
    }
}

template<class Real>
void test_copy_move()
{
    std::cout << "Testing that copy/move operation succeed on cubic b spline\n";
    std::vector<Real> v(500);
    Real x0 = 1;
    Real step = 0.125;

    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = sin(x0 + step * i);
    }

    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), x0, step);


    // Default constructor should compile so that splines can be member variables:
    boost::math::interpolators::cardinal_cubic_b_spline<Real> d;
    d = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), x0, step);
    BOOST_CHECK_CLOSE(d(x0), sin(x0), 0.01);
    // Passing to lambda should compile:
    auto f = [=](Real x) { return d(x); };
    // Make sure this variable is used.
    BOOST_CHECK_CLOSE(f(x0), sin(x0), 0.01);

    // Move operations should compile.
    auto s = std::move(spline);

    // Copy operations should compile:
    boost::math::interpolators::cardinal_cubic_b_spline<Real> c = d;
    BOOST_CHECK_CLOSE(c(x0), sin(x0), 0.01);

    // Test with std::bind:
    auto h = std::bind(&boost::math::interpolators::cardinal_cubic_b_spline<double>::operator(), &s, std::placeholders::_1);
    BOOST_CHECK_CLOSE(h(x0), sin(x0), 0.01);
}

template<class Real>
void test_outside_interval()
{
    std::cout << "Testing that the spline can be evaluated outside the interpolation interval\n";
    std::vector<Real> v(400);
    Real x0 = 1;
    Real step = 0.125;

    for (size_t i = 0; i < v.size(); ++i)
    {
        v[i] = sin(x0 + step * i);
    }

    boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), x0, step);

    // There's no test here; it simply does it's best to be an extrapolator.
    //
    std::ostream cnull(0);
    cnull << spline(0);
    cnull << spline(2000);
}

BOOST_AUTO_TEST_CASE(test_cubic_b_spline)
{
    test_b3_spline<float>();
    test_b3_spline<double>();
    test_b3_spline<long double>();
    test_b3_spline<cpp_bin_float_50>();

    test_interpolation_condition<float>();
    test_interpolation_condition<double>();
    test_interpolation_condition<long double>();
    test_interpolation_condition<cpp_bin_float_50>();

    test_constant_function<float>();
    test_constant_function<double>();
    test_constant_function<long double>();
    test_constant_function<cpp_bin_float_50>();

    test_affine_function<float>();
    test_affine_function<double>();
    test_affine_function<long double>();
    test_affine_function<cpp_bin_float_50>();

    test_quadratic_function<float>();
    test_quadratic_function<double>();
    test_quadratic_function<long double>();
    test_affine_function<cpp_bin_float_50>();

    test_trig_function<float>();
    test_trig_function<double>();
    test_trig_function<long double>();
    test_trig_function<cpp_bin_float_50>();

    test_copy_move<double>();
    test_outside_interval<double>();
}