1 // Copyright Nick Thompson, 2019
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0.
4 // (See accompanying file LICENSE_1_0.txt
5 // or copy at http://www.boost.org/LICENSE_1_0.txt)
7 #define BOOST_TEST_MODULE vector_barycentric_rational
12 #include <Eigen/Dense>
13 #include <boost/numeric/ublas/vector.hpp>
14 #include <boost/random/uniform_real_distribution.hpp>
15 #include <boost/type_index.hpp>
16 #include <boost/test/included/unit_test.hpp>
17 #include <boost/test/tools/floating_point_comparison.hpp>
18 #include <boost/math/interpolators/barycentric_rational.hpp>
19 #include <boost/math/interpolators/vector_barycentric_rational.hpp>
23 using std::numeric_limits;
26 void test_agreement_with_1d()
28 std::cout << "Testing with 1D interpolation on type "
29 << boost::typeindex::type_id<Real>().pretty_name() << "\n";
30 std::mt19937 gen(4723);
31 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
32 std::vector<Real> t(100);
33 std::vector<Eigen::Vector2d> y(100);
37 for (size_t i = 1; i < t.size(); ++i)
39 t[i] = t[i-1] + dis(gen);
44 std::vector<Eigen::Vector2d> y_copy = y;
45 std::vector<Real> t_copy = t;
46 std::vector<Real> t_copy0 = t;
47 std::vector<Real> t_copy1 = t;
49 std::vector<Real> y_copy0(y.size());
50 std::vector<Real> y_copy1(y.size());
51 for (size_t i = 0; i < y.size(); ++i) {
56 boost::random::uniform_real_distribution<Real> dis2(t[0], t[t.size()-1]);
57 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
58 boost::math::barycentric_rational<Real> scalar_interpolator0(std::move(t_copy0), std::move(y_copy0));
59 boost::math::barycentric_rational<Real> scalar_interpolator1(std::move(t_copy1), std::move(y_copy1));
65 while (samples++ < 1000)
69 BOOST_CHECK_CLOSE(z[0], scalar_interpolator0(t), 10000*numeric_limits<Real>::epsilon());
70 BOOST_CHECK_CLOSE(z[1], scalar_interpolator1(t), 10000*numeric_limits<Real>::epsilon());
76 void test_interpolation_condition_eigen()
78 std::cout << "Testing interpolation condition for barycentric interpolation on Eigen vectors of type "
79 << boost::typeindex::type_id<Real>().pretty_name() << "\n";
80 std::mt19937 gen(4723);
81 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
82 std::vector<Real> t(100);
83 std::vector<Eigen::Vector2d> y(100);
87 for (size_t i = 1; i < t.size(); ++i)
89 t[i] = t[i-1] + dis(gen);
94 std::vector<Eigen::Vector2d> y_copy = y;
95 std::vector<Real> t_copy = t;
96 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
99 for (size_t i = 0; i < t_copy.size(); ++i)
101 interpolator(z, t_copy[i]);
102 BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
103 BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
108 void test_interpolation_condition_std_array()
110 std::cout << "Testing interpolation condition for barycentric interpolation on std::array vectors of type "
111 << boost::typeindex::type_id<Real>().pretty_name() << "\n";
112 std::mt19937 gen(4723);
113 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
114 std::vector<Real> t(100);
115 std::vector<std::array<Real, 2>> y(100);
119 for (size_t i = 1; i < t.size(); ++i)
121 t[i] = t[i-1] + dis(gen);
126 std::vector<std::array<Real, 2>> y_copy = y;
127 std::vector<Real> t_copy = t;
128 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
130 std::array<Real, 2> z;
131 for (size_t i = 0; i < t_copy.size(); ++i)
133 interpolator(z, t_copy[i]);
134 BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
135 BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
141 void test_interpolation_condition_ublas()
143 std::cout << "Testing interpolation condition for barycentric interpolation ublas vectors of type "
144 << boost::typeindex::type_id<Real>().pretty_name() << "\n";
145 std::mt19937 gen(4723);
146 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
147 std::vector<Real> t(100);
148 std::vector<boost::numeric::ublas::vector<Real>> y(100);
153 for (size_t i = 1; i < t.size(); ++i)
155 t[i] = t[i-1] + dis(gen);
161 std::vector<Real> t_copy = t;
162 std::vector<boost::numeric::ublas::vector<Real>> y_copy = y;
164 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
166 boost::numeric::ublas::vector<Real> z(2);
167 for (size_t i = 0; i < t_copy.size(); ++i)
169 interpolator(z, t_copy[i]);
170 BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
171 BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
176 void test_interpolation_condition_high_order()
178 std::cout << "Testing interpolation condition in high order for barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
180 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
181 std::vector<Real> t(100);
182 std::vector<Eigen::Vector2d> y(100);
186 for (size_t i = 1; i < t.size(); ++i)
188 t[i] = t[i-1] + dis(gen);
193 std::vector<Eigen::Vector2d> y_copy = y;
194 std::vector<Real> t_copy = t;
195 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y), 5);
198 for (size_t i = 0; i < t_copy.size(); ++i)
200 interpolator(z, t_copy[i]);
201 BOOST_CHECK_CLOSE(z[0], y_copy[i][0], 100*numeric_limits<Real>::epsilon());
202 BOOST_CHECK_CLOSE(z[1], y_copy[i][1], 100*numeric_limits<Real>::epsilon());
208 void test_constant_eigen()
210 std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on Eigen vectors of type "
211 << boost::typeindex::type_id<Real>().pretty_name() << "\n";
214 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
215 std::vector<Real> t(100);
216 std::vector<Eigen::Vector2d> y(100);
218 Real constant0 = dis(gen);
219 Real constant1 = dis(gen);
222 for (size_t i = 1; i < t.size(); ++i)
224 t[i] = t[i-1] + dis(gen);
229 std::vector<Eigen::Vector2d> y_copy = y;
230 std::vector<Real> t_copy = t;
231 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
234 for (size_t i = 0; i < t_copy.size(); ++i)
236 // Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
237 Real t = t_copy[i] + dis(gen);
239 BOOST_CHECK_CLOSE(z[0], constant0, 100*sqrt(numeric_limits<Real>::epsilon()));
240 BOOST_CHECK_CLOSE(z[1], constant1, 100*sqrt(numeric_limits<Real>::epsilon()));
241 Eigen::Vector2d zprime = interpolator.prime(t);
242 Real zero_0 = zprime[0];
243 Real zero_1 = zprime[1];
244 BOOST_CHECK_SMALL(zero_0, sqrt(numeric_limits<Real>::epsilon()));
245 BOOST_CHECK_SMALL(zero_1, sqrt(numeric_limits<Real>::epsilon()));
251 void test_constant_std_array()
253 std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on std::array vectors of type "
254 << boost::typeindex::type_id<Real>().pretty_name() << "\n";
257 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
258 std::vector<Real> t(100);
259 std::vector<std::array<Real, 2>> y(100);
261 Real constant0 = dis(gen);
262 Real constant1 = dis(gen);
265 for (size_t i = 1; i < t.size(); ++i)
267 t[i] = t[i-1] + dis(gen);
272 std::vector<std::array<Real,2>> y_copy = y;
273 std::vector<Real> t_copy = t;
274 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y));
276 std::array<Real, 2> z;
277 for (size_t i = 0; i < t_copy.size(); ++i)
279 // Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
280 Real t = t_copy[i] + dis(gen);
282 BOOST_CHECK_CLOSE(z[0], constant0, 100*sqrt(numeric_limits<Real>::epsilon()));
283 BOOST_CHECK_CLOSE(z[1], constant1, 100*sqrt(numeric_limits<Real>::epsilon()));
284 std::array<Real, 2> zprime = interpolator.prime(t);
285 Real zero_0 = zprime[0];
286 Real zero_1 = zprime[1];
287 BOOST_CHECK_SMALL(zero_0, sqrt(numeric_limits<Real>::epsilon()));
288 BOOST_CHECK_SMALL(zero_1, sqrt(numeric_limits<Real>::epsilon()));
294 void test_constant_high_order()
296 std::cout << "Testing that constants are interpolated correctly using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
299 boost::random::uniform_real_distribution<Real> dis(0.1f, 1);
300 std::vector<Real> t(100);
301 std::vector<Eigen::Vector2d> y(100);
303 Real constant0 = dis(gen);
304 Real constant1 = dis(gen);
307 for (size_t i = 1; i < t.size(); ++i)
309 t[i] = t[i-1] + dis(gen);
314 std::vector<Eigen::Vector2d> y_copy = y;
315 std::vector<Real> t_copy = t;
316 boost::math::vector_barycentric_rational<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y), 5);
319 for (size_t i = 0; i < t_copy.size(); ++i)
321 // Don't evaluate the constant at x[i]; that's already tested in the interpolation condition test.
322 Real t = t_copy[i] + dis(gen);
324 BOOST_CHECK_CLOSE(z[0], constant0, 100*sqrt(numeric_limits<Real>::epsilon()));
325 BOOST_CHECK_CLOSE(z[1], constant1, 100*sqrt(numeric_limits<Real>::epsilon()));
326 Eigen::Vector2d zprime = interpolator.prime(t);
327 Real zero_0 = zprime[0];
328 Real zero_1 = zprime[1];
329 BOOST_CHECK_SMALL(zero_0, sqrt(numeric_limits<Real>::epsilon()));
330 BOOST_CHECK_SMALL(zero_1, sqrt(numeric_limits<Real>::epsilon()));
338 std::cout << "Testing weights are calculated correctly using barycentric interpolation on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
341 boost::random::uniform_real_distribution<Real> dis(0.005, 0.01);
342 std::vector<Real> t(100);
343 std::vector<Eigen::Vector2d> y(100);
347 for (size_t i = 1; i < t.size(); ++i)
349 t[i] = t[i-1] + dis(gen);
354 std::vector<Eigen::Vector2d> y_copy = y;
355 std::vector<Real> t_copy = t;
356 boost::math::detail::vector_barycentric_rational_imp<decltype(t), decltype(y)> interpolator(std::move(t), std::move(y), 1);
358 for (size_t i = 1; i < t_copy.size() - 1; ++i)
360 Real w = interpolator.weight(i);
361 Real w_expect = 1/(t_copy[i] - t_copy[i - 1]) + 1/(t_copy[i+1] - t_copy[i]);
364 BOOST_CHECK_CLOSE(w, -w_expect, 0.00001);
368 BOOST_CHECK_CLOSE(w, w_expect, 0.00001);
374 BOOST_AUTO_TEST_CASE(vector_barycentric_rational)
376 test_weights<double>();
377 test_constant_eigen<double>();
378 test_constant_std_array<double>();
379 test_constant_high_order<double>();
380 test_interpolation_condition_eigen<double>();
381 test_interpolation_condition_ublas<double>();
382 test_interpolation_condition_std_array<double>();
383 test_interpolation_condition_high_order<double>();
384 test_agreement_with_1d<double>();