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1 | /* |
2 | * Copyright Nick Thompson, 2020 | |
3 | * Use, modification and distribution are subject to the | |
4 | * Boost Software License, Version 1.0. (See accompanying file | |
5 | * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
6 | */ | |
7 | ||
8 | #include "math_unit_test.hpp" | |
9 | #include <numeric> | |
10 | #include <utility> | |
11 | #include <random> | |
12 | #include <boost/math/interpolators/pchip.hpp> | |
13 | #include <boost/circular_buffer.hpp> | |
14 | #ifdef BOOST_HAS_FLOAT128 | |
15 | #include <boost/multiprecision/float128.hpp> | |
16 | using boost::multiprecision::float128; | |
17 | #endif | |
18 | ||
19 | ||
20 | using boost::math::interpolators::pchip; | |
21 | ||
22 | template<typename Real> | |
23 | void test_constant() | |
24 | { | |
25 | ||
26 | std::vector<Real> x{0,1,2,3, 9, 22, 81}; | |
27 | std::vector<Real> y(x.size()); | |
28 | for (auto & t : y) { | |
29 | t = 7; | |
30 | } | |
31 | ||
32 | auto x_copy = x; | |
33 | auto y_copy = y; | |
34 | auto pchip_spline = pchip(std::move(x_copy), std::move(y_copy)); | |
35 | //std::cout << "Constant value pchip spline = " << pchip_spline << "\n"; | |
36 | ||
37 | for (Real t = x[0]; t <= x.back(); t += 0.25) { | |
38 | CHECK_ULP_CLOSE(Real(7), pchip_spline(t), 2); | |
39 | CHECK_ULP_CLOSE(Real(0), pchip_spline.prime(t), 2); | |
40 | } | |
41 | ||
42 | boost::circular_buffer<Real> x_buf(x.size()); | |
43 | for (auto & t : x) { | |
44 | x_buf.push_back(t); | |
45 | } | |
46 | ||
47 | boost::circular_buffer<Real> y_buf(x.size()); | |
48 | for (auto & t : y) { | |
49 | y_buf.push_back(t); | |
50 | } | |
51 | ||
52 | auto circular_pchip_spline = pchip(std::move(x_buf), std::move(y_buf)); | |
53 | ||
54 | for (Real t = x[0]; t <= x.back(); t += 0.25) { | |
55 | CHECK_ULP_CLOSE(Real(7), circular_pchip_spline(t), 2); | |
56 | CHECK_ULP_CLOSE(Real(0), pchip_spline.prime(t), 2); | |
57 | } | |
58 | ||
59 | circular_pchip_spline.push_back(x.back() + 1, 7); | |
60 | CHECK_ULP_CLOSE(Real(0), circular_pchip_spline.prime(x.back()+1), 2); | |
61 | ||
62 | } | |
63 | ||
64 | template<typename Real> | |
65 | void test_linear() | |
66 | { | |
67 | std::vector<Real> x{0,1,2,3}; | |
68 | std::vector<Real> y{0,1,2,3}; | |
69 | ||
70 | auto x_copy = x; | |
71 | auto y_copy = y; | |
72 | auto pchip_spline = pchip(std::move(x_copy), std::move(y_copy)); | |
73 | ||
74 | CHECK_ULP_CLOSE(y[0], pchip_spline(x[0]), 0); | |
75 | CHECK_ULP_CLOSE(Real(1)/Real(2), pchip_spline(Real(1)/Real(2)), 10); | |
76 | CHECK_ULP_CLOSE(y[1], pchip_spline(x[1]), 0); | |
77 | CHECK_ULP_CLOSE(Real(3)/Real(2), pchip_spline(Real(3)/Real(2)), 10); | |
78 | CHECK_ULP_CLOSE(y[2], pchip_spline(x[2]), 0); | |
79 | CHECK_ULP_CLOSE(Real(5)/Real(2), pchip_spline(Real(5)/Real(2)), 10); | |
80 | CHECK_ULP_CLOSE(y[3], pchip_spline(x[3]), 0); | |
81 | ||
82 | x.resize(45); | |
83 | y.resize(45); | |
84 | for (size_t i = 0; i < x.size(); ++i) { | |
85 | x[i] = i; | |
86 | y[i] = i; | |
87 | } | |
88 | ||
89 | x_copy = x; | |
90 | y_copy = y; | |
91 | pchip_spline = pchip(std::move(x_copy), std::move(y_copy)); | |
92 | for (Real t = 0; t < x.back(); t += 0.5) { | |
93 | CHECK_ULP_CLOSE(t, pchip_spline(t), 0); | |
94 | CHECK_ULP_CLOSE(Real(1), pchip_spline.prime(t), 0); | |
95 | } | |
96 | ||
97 | x_copy = x; | |
98 | y_copy = y; | |
99 | // Test endpoint derivatives: | |
100 | pchip_spline = pchip(std::move(x_copy), std::move(y_copy), Real(1), Real(1)); | |
101 | for (Real t = 0; t < x.back(); t += 0.5) { | |
102 | CHECK_ULP_CLOSE(t, pchip_spline(t), 0); | |
103 | CHECK_ULP_CLOSE(Real(1), pchip_spline.prime(t), 0); | |
104 | } | |
105 | ||
106 | ||
107 | boost::circular_buffer<Real> x_buf(x.size()); | |
108 | for (auto & t : x) { | |
109 | x_buf.push_back(t); | |
110 | } | |
111 | ||
112 | boost::circular_buffer<Real> y_buf(x.size()); | |
113 | for (auto & t : y) { | |
114 | y_buf.push_back(t); | |
115 | } | |
116 | ||
117 | auto circular_pchip_spline = pchip(std::move(x_buf), std::move(y_buf)); | |
118 | ||
119 | for (Real t = x[0]; t <= x.back(); t += 0.25) { | |
120 | CHECK_ULP_CLOSE(t, circular_pchip_spline(t), 2); | |
121 | CHECK_ULP_CLOSE(Real(1), circular_pchip_spline.prime(t), 2); | |
122 | } | |
123 | ||
124 | circular_pchip_spline.push_back(x.back() + 1, y.back()+1); | |
125 | ||
126 | CHECK_ULP_CLOSE(Real(y.back() + 1), circular_pchip_spline(Real(x.back()+1)), 2); | |
127 | CHECK_ULP_CLOSE(Real(1), circular_pchip_spline.prime(Real(x.back()+1)), 2); | |
128 | ||
129 | } | |
130 | ||
131 | template<typename Real> | |
132 | void test_interpolation_condition() | |
133 | { | |
134 | for (size_t n = 4; n < 50; ++n) { | |
135 | std::vector<Real> x(n); | |
136 | std::vector<Real> y(n); | |
137 | std::default_random_engine rd; | |
138 | std::uniform_real_distribution<Real> dis(0,1); | |
139 | Real x0 = dis(rd); | |
140 | x[0] = x0; | |
141 | y[0] = dis(rd); | |
142 | for (size_t i = 1; i < n; ++i) { | |
143 | x[i] = x[i-1] + dis(rd); | |
144 | y[i] = dis(rd); | |
145 | } | |
146 | ||
147 | auto x_copy = x; | |
148 | auto y_copy = y; | |
149 | auto s = pchip(std::move(x_copy), std::move(y_copy)); | |
150 | //std::cout << "s = " << s << "\n"; | |
151 | for (size_t i = 0; i < x.size(); ++i) { | |
152 | CHECK_ULP_CLOSE(y[i], s(x[i]), 2); | |
153 | } | |
154 | ||
155 | x_copy = x; | |
156 | y_copy = y; | |
157 | // The interpolation condition is not affected by the endpoint derivatives, even though these derivatives might be super weird: | |
158 | s = pchip(std::move(x_copy), std::move(y_copy), Real(0), Real(0)); | |
159 | //std::cout << "s = " << s << "\n"; | |
160 | for (size_t i = 0; i < x.size(); ++i) { | |
161 | CHECK_ULP_CLOSE(y[i], s(x[i]), 2); | |
162 | } | |
163 | ||
164 | } | |
165 | } | |
166 | ||
167 | template<typename Real> | |
168 | void test_monotonicity() | |
169 | { | |
170 | for (size_t n = 4; n < 50; ++n) { | |
171 | std::vector<Real> x(n); | |
172 | std::vector<Real> y(n); | |
173 | std::default_random_engine rd; | |
174 | std::uniform_real_distribution<Real> dis(0,1); | |
175 | Real x0 = dis(rd); | |
176 | x[0] = x0; | |
177 | y[0] = dis(rd); | |
178 | // Monotone increasing: | |
179 | for (size_t i = 1; i < n; ++i) { | |
180 | x[i] = x[i-1] + dis(rd); | |
181 | y[i] = y[i-1] + dis(rd); | |
182 | } | |
183 | ||
184 | auto x_copy = x; | |
185 | auto y_copy = y; | |
186 | auto s = pchip(std::move(x_copy), std::move(y_copy)); | |
187 | //std::cout << "s = " << s << "\n"; | |
188 | for (size_t i = 0; i < x.size() - 1; ++i) { | |
189 | Real tmin = x[i]; | |
190 | Real tmax = x[i+1]; | |
191 | Real val = y[i]; | |
192 | CHECK_ULP_CLOSE(y[i], s(x[i]), 2); | |
193 | for (Real t = tmin; t < tmax; t += (tmax-tmin)/16) { | |
194 | Real greater_val = s(t); | |
195 | assert(val <= greater_val); | |
196 | val = greater_val; | |
197 | } | |
198 | } | |
199 | ||
200 | ||
201 | x[0] = dis(rd); | |
202 | y[0] = dis(rd); | |
203 | // Monotone decreasing: | |
204 | for (size_t i = 1; i < n; ++i) { | |
205 | x[i] = x[i-1] + dis(rd); | |
206 | y[i] = y[i-1] - dis(rd); | |
207 | } | |
208 | ||
209 | x_copy = x; | |
210 | y_copy = y; | |
211 | s = pchip(std::move(x_copy), std::move(y_copy)); | |
212 | //std::cout << "s = " << s << "\n"; | |
213 | for (size_t i = 0; i < x.size() - 1; ++i) { | |
214 | Real tmin = x[i]; | |
215 | Real tmax = x[i+1]; | |
216 | Real val = y[i]; | |
217 | CHECK_ULP_CLOSE(y[i], s(x[i]), 2); | |
218 | for (Real t = tmin; t < tmax; t += (tmax-tmin)/16) { | |
219 | Real lesser_val = s(t); | |
220 | assert(val >= lesser_val); | |
221 | val = lesser_val; | |
222 | } | |
223 | } | |
224 | ||
225 | } | |
226 | } | |
227 | ||
228 | ||
229 | int main() | |
230 | { | |
231 | test_constant<float>(); | |
232 | test_linear<float>(); | |
233 | test_interpolation_condition<float>(); | |
234 | test_monotonicity<float>(); | |
235 | ||
236 | test_constant<double>(); | |
237 | test_linear<double>(); | |
238 | test_interpolation_condition<double>(); | |
239 | test_monotonicity<double>(); | |
240 | ||
241 | test_constant<long double>(); | |
242 | test_linear<long double>(); | |
243 | test_interpolation_condition<long double>(); | |
244 | test_monotonicity<long double>(); | |
245 | ||
246 | #ifdef BOOST_HAS_FLOAT128 | |
247 | test_constant<float128>(); | |
248 | test_linear<float128>(); | |
249 | #endif | |
250 | ||
251 | return boost::math::test::report_errors(); | |
252 | } |