296 lines
9.3 KiB
C++
296 lines
9.3 KiB
C++
// Copyright Nick Thompson, 2017
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#define BOOST_TEST_MODULE barycentric_rational
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#include <cmath>
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#include <random>
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#include <boost/random/uniform_real_distribution.hpp>
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#include <boost/type_index.hpp>
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#include <boost/test/included/unit_test.hpp>
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include <boost/math/interpolators/barycentric_rational.hpp>
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#include <boost/multiprecision/cpp_bin_float.hpp>
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#ifdef BOOST_HAS_FLOAT128
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#include <boost/multiprecision/float128.hpp>
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#endif
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using std::sqrt;
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using std::abs;
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using std::numeric_limits;
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using boost::multiprecision::cpp_bin_float_50;
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template<class Real>
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void test_interpolation_condition()
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{
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std::cout << "Testing interpolation condition for barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
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std::mt19937 gen(4);
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boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
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std::vector<Real> x(100);
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std::vector<Real> y(100);
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x[0] = dis(gen);
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y[0] = dis(gen);
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for (size_t i = 1; i < x.size(); ++i)
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{
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x[i] = x[i-1] + dis(gen);
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y[i] = dis(gen);
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}
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boost::math::barycentric_rational<Real> interpolator(x.data(), y.data(), y.size());
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for (size_t i = 0; i < x.size(); ++i)
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{
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Real z = interpolator(x[i]);
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BOOST_CHECK_CLOSE(z, y[i], 100*numeric_limits<Real>::epsilon());
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}
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// Make sure that the move constructor does the same thing:
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std::vector<Real> x_copy = x;
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std::vector<Real> y_copy = y;
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boost::math::barycentric_rational<Real> move_interpolator(std::move(x), std::move(y));
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for (size_t i = 0; i < x_copy.size(); ++i)
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{
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Real z = move_interpolator(x_copy[i]);
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BOOST_CHECK_CLOSE(z, y_copy[i], 100*numeric_limits<Real>::epsilon());
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}
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}
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template<class Real>
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void test_interpolation_condition_high_order()
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{
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std::cout << "Testing interpolation condition in high order for barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
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std::mt19937 gen(5);
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boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
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std::vector<Real> x(100);
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std::vector<Real> y(100);
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x[0] = dis(gen);
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y[0] = dis(gen);
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for (size_t i = 1; i < x.size(); ++i)
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{
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x[i] = x[i-1] + dis(gen);
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y[i] = dis(gen);
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}
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// Order 5 approximation:
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boost::math::barycentric_rational<Real> interpolator(x.data(), y.data(), y.size(), 5);
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for (size_t i = 0; i < x.size(); ++i)
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{
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Real z = interpolator(x[i]);
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BOOST_CHECK_CLOSE(z, y[i], 100*numeric_limits<Real>::epsilon());
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}
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}
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template<class Real>
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void test_constant()
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{
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std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
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std::mt19937 gen(6);
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boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
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std::vector<Real> x(100);
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std::vector<Real> y(100);
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Real constant = -8;
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x[0] = dis(gen);
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y[0] = constant;
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for (size_t i = 1; i < x.size(); ++i)
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{
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x[i] = x[i-1] + dis(gen);
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y[i] = y[0];
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}
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boost::math::barycentric_rational<Real> interpolator(x.data(), y.data(), y.size());
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for (size_t i = 0; i < x.size(); ++i)
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{
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// Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
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Real t = x[i] + dis(gen);
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Real z = interpolator(t);
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BOOST_CHECK_CLOSE(z, constant, 100*sqrt(numeric_limits<Real>::epsilon()));
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BOOST_CHECK_SMALL(interpolator.prime(t), sqrt(numeric_limits<Real>::epsilon()));
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}
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}
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template<class Real>
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void test_constant_high_order()
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{
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std::cout << "Testing that constants are interpolated correctly in high order using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
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std::mt19937 gen(7);
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boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
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std::vector<Real> x(100);
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std::vector<Real> y(100);
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Real constant = 5;
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x[0] = dis(gen);
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y[0] = constant;
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for (size_t i = 1; i < x.size(); ++i)
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{
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x[i] = x[i-1] + dis(gen);
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y[i] = y[0];
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}
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// Set interpolation order to 7:
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boost::math::barycentric_rational<Real> interpolator(x.data(), y.data(), y.size(), 7);
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for (size_t i = 0; i < x.size(); ++i)
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{
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Real t = x[i] + dis(gen);
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Real z = interpolator(t);
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BOOST_CHECK_CLOSE(z, constant, 1000*sqrt(numeric_limits<Real>::epsilon()));
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BOOST_CHECK_SMALL(interpolator.prime(t), 100*sqrt(numeric_limits<Real>::epsilon()));
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}
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}
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template<class Real>
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void test_runge()
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{
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std::cout << "Testing interpolation of Runge's 1/(1+25x^2) function using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
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std::mt19937 gen(8);
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boost::random::uniform_real_distribution<Real> dis(0.005f, 0.01f);
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std::vector<Real> x(100);
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std::vector<Real> y(100);
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x[0] = -2;
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y[0] = 1/(1+25*x[0]*x[0]);
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for (size_t i = 1; i < x.size(); ++i)
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{
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x[i] = x[i-1] + dis(gen);
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y[i] = 1/(1+25*x[i]*x[i]);
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}
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boost::math::barycentric_rational<Real> interpolator(x.data(), y.data(), y.size(), 5);
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for (size_t i = 0; i < x.size(); ++i)
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{
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Real t = x[i];
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Real z = interpolator(t);
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BOOST_CHECK_CLOSE(z, y[i], 0.03);
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Real z_prime = interpolator.prime(t);
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Real num = -50*t;
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Real denom = (1+25*t*t)*(1+25*t*t);
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if (abs(num/denom) > 0.00001)
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{
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BOOST_CHECK_CLOSE_FRACTION(z_prime, num/denom, 0.03);
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}
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}
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Real tol = 0.0001;
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for (size_t i = 0; i < x.size(); ++i)
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{
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Real t = x[i] + dis(gen);
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Real z = interpolator(t);
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BOOST_CHECK_CLOSE(z, 1/(1+25*t*t), tol);
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Real z_prime = interpolator.prime(t);
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Real num = -50*t;
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Real denom = (1+25*t*t)*(1+25*t*t);
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Real runge_prime = num/denom;
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if (abs(runge_prime) > 0 && abs(z_prime - runge_prime)/abs(runge_prime) > tol)
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{
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std::cout << "Error too high for t = " << t << " which is a distance " << t - x[i] << " from node " << i << "/" << x.size() << " associated with data (" << x[i] << ", " << y[i] << ")\n";
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BOOST_CHECK_CLOSE_FRACTION(z_prime, runge_prime, tol);
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}
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}
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}
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template<class Real>
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void test_weights()
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{
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std::cout << "Testing weights are calculated correctly using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
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std::mt19937 gen(9);
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boost::random::uniform_real_distribution<Real> dis(0.005, 0.01);
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std::vector<Real> x(100);
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std::vector<Real> y(100);
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x[0] = -2;
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y[0] = 1/(1+25*x[0]*x[0]);
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for (size_t i = 1; i < x.size(); ++i)
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{
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x[i] = x[i-1] + dis(gen);
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y[i] = 1/(1+25*x[i]*x[i]);
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}
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boost::math::detail::barycentric_rational_imp<Real> interpolator(x.data(), x.data() + x.size(), y.data(), 0);
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for (size_t i = 0; i < x.size(); ++i)
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{
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Real w = interpolator.weight(i);
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if (i % 2 == 0)
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{
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BOOST_CHECK_CLOSE(w, 1, 0.00001);
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}
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else
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{
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BOOST_CHECK_CLOSE(w, -1, 0.00001);
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}
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}
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// d = 1:
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interpolator = boost::math::detail::barycentric_rational_imp<Real>(x.data(), x.data() + x.size(), y.data(), 1);
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for (size_t i = 1; i < x.size() -1; ++i)
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{
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Real w = interpolator.weight(i);
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Real w_expect = 1/(x[i] - x[i - 1]) + 1/(x[i+1] - x[i]);
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if (i % 2 == 0)
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{
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BOOST_CHECK_CLOSE(w, -w_expect, 0.00001);
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}
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else
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{
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BOOST_CHECK_CLOSE(w, w_expect, 0.00001);
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}
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}
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}
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BOOST_AUTO_TEST_CASE(barycentric_rational)
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{
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// The tests took too long at the higher precisions.
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// They still pass, but the CI system is starting to time out,
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// so I figured it'd be polite to comment out the most expensive tests.
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test_weights<double>();
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test_constant<float>();
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//test_constant<double>();
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test_constant<long double>();
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//test_constant<cpp_bin_float_50>();
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//test_constant_high_order<float>();
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test_constant_high_order<double>();
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//test_constant_high_order<long double>();
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//test_constant_high_order<cpp_bin_float_50>();
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test_interpolation_condition<float>();
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test_interpolation_condition<double>();
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//test_interpolation_condition<long double>();
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//test_interpolation_condition<cpp_bin_float_50>();
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//test_interpolation_condition_high_order<float>();
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test_interpolation_condition_high_order<double>();
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//test_interpolation_condition_high_order<long double>();
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//test_interpolation_condition_high_order<cpp_bin_float_50>();
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test_runge<double>();
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//test_runge<long double>();
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//test_runge<cpp_bin_float_50>();
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#ifdef BOOST_HAS_FLOAT128
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//test_interpolation_condition<boost::multiprecision::float128>();
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//test_constant<boost::multiprecision::float128>();
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//test_constant_high_order<boost::multiprecision::float128>();
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//test_interpolation_condition_high_order<boost::multiprecision::float128>();
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//test_runge<boost::multiprecision::float128>();
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#endif
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}
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