1 // Copyright Nick Thompson, 2017
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)
6
7 #define BOOST_TEST_MODULE test_cubic_b_spline
8
9 #include <random>
10 #include <functional>
11 #include <boost/random/uniform_real_distribution.hpp>
12 #include <boost/type_index.hpp>
13 #include <boost/test/included/unit_test.hpp>
14 #include <boost/test/tools/floating_point_comparison.hpp>
15 #include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
16 #include <boost/math/interpolators/detail/cardinal_cubic_b_spline_detail.hpp>
17 #include <boost/multiprecision/cpp_bin_float.hpp>
18
19 using boost::multiprecision::cpp_bin_float_50;
20 using boost::math::constants::third;
21 using boost::math::constants::half;
22
23 template<class Real>
test_b3_spline()24 void test_b3_spline()
25 {
26 std::cout << "Testing evaluation of spline basis functions on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
27 // Outside the support:
28 Real eps = std::numeric_limits<Real>::epsilon();
29 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(2.5), (Real) 0);
30 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(-2.5), (Real) 0);
31 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(2.5), (Real) 0);
32 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(-2.5), (Real) 0);
33 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(2.5), (Real) 0);
34 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(-2.5), (Real) 0);
35
36
37 // On the boundary of support:
38 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(2), (Real) 0);
39 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(-2), (Real) 0);
40 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(2), (Real) 0);
41 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(-2), (Real) 0);
42
43 // Special values:
44 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(-1), third<Real>()*half<Real>(), eps);
45 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>( 1), third<Real>()*half<Real>(), eps);
46 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(0), 2*third<Real>(), eps);
47
48 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>(-1), half<Real>(), eps);
49 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>( 1), -half<Real>(), eps);
50 BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(0), eps);
51
52 // Properties: B3 is an even function, B3' is an odd function.
53 for (size_t i = 1; i < 200; ++i)
54 {
55 Real arg = i*0.01;
56 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(arg), boost::math::interpolators::detail::b3_spline<Real>(arg), eps);
57 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>(-arg), -boost::math::interpolators::detail::b3_spline_prime<Real>(arg), eps);
58 BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_double_prime<Real>(-arg), boost::math::interpolators::detail::b3_spline_double_prime<Real>(arg), eps);
59 }
60
61 }
62 /*
63 * This test ensures that the interpolant s(x_j) = f(x_j) at all grid points.
64 */
65 template<class Real>
test_interpolation_condition()66 void test_interpolation_condition()
67 {
68 using std::sqrt;
69 std::cout << "Testing interpolation condition for cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
70 std::random_device rd;
71 std::mt19937 gen(rd());
72 boost::random::uniform_real_distribution<Real> dis(1, 10);
73 std::vector<Real> v(5000);
74 for (size_t i = 0; i < v.size(); ++i)
75 {
76 v[i] = dis(gen);
77 }
78
79 Real step = 0.01;
80 Real a = 5;
81 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), a, step);
82
83 for (size_t i = 0; i < v.size(); ++i)
84 {
85 Real y = spline(i*step + a);
86 // This seems like a very large tolerance, but I don't know of any other interpolators
87 // that will be able to do much better on random data.
88 BOOST_CHECK_CLOSE(y, v[i], 10000*sqrt(std::numeric_limits<Real>::epsilon()));
89 }
90
91 }
92
93
94 template<class Real>
test_constant_function()95 void test_constant_function()
96 {
97 std::cout << "Testing that constants are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
98 std::vector<Real> v(500);
99 Real constant = 50.2;
100 for (size_t i = 0; i < v.size(); ++i)
101 {
102 v[i] = 50.2;
103 }
104
105 Real step = 0.02;
106 Real a = 5;
107 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), a, step);
108
109 for (size_t i = 0; i < v.size(); ++i)
110 {
111 // Do not test at interpolation point; we already know it works there:
112 Real y = spline(i*step + a + 0.001);
113 BOOST_CHECK_CLOSE(y, constant, 10*std::numeric_limits<Real>::epsilon());
114 Real y_prime = spline.prime(i*step + a + 0.002);
115 BOOST_CHECK_SMALL(y_prime, 5000*std::numeric_limits<Real>::epsilon());
116 Real y_double_prime = spline.double_prime(i*step + a + 0.002);
117 BOOST_CHECK_SMALL(y_double_prime, 5000*std::numeric_limits<Real>::epsilon());
118
119 }
120
121 // Test that correctly specified left and right-derivatives work properly:
122 spline = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), a, step, 0, 0);
123
124 for (size_t i = 0; i < v.size(); ++i)
125 {
126 Real y = spline(i*step + a + 0.002);
127 BOOST_CHECK_CLOSE(y, constant, std::numeric_limits<Real>::epsilon());
128 Real y_prime = spline.prime(i*step + a + 0.002);
129 BOOST_CHECK_SMALL(y_prime, std::numeric_limits<Real>::epsilon());
130 }
131
132 //
133 // Again with iterator constructor:
134 //
135 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline2(v.begin(), v.end(), a, step);
136
137 for (size_t i = 0; i < v.size(); ++i)
138 {
139 // Do not test at interpolation point; we already know it works there:
140 Real y = spline2(i*step + a + 0.001);
141 BOOST_CHECK_CLOSE(y, constant, 10 * std::numeric_limits<Real>::epsilon());
142 Real y_prime = spline2.prime(i*step + a + 0.002);
143 BOOST_CHECK_SMALL(y_prime, 5000 * std::numeric_limits<Real>::epsilon());
144 }
145
146 // Test that correctly specified left and right-derivatives work properly:
147 spline2 = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.begin(), v.end(), a, step, 0, 0);
148
149 for (size_t i = 0; i < v.size(); ++i)
150 {
151 Real y = spline2(i*step + a + 0.002);
152 BOOST_CHECK_CLOSE(y, constant, std::numeric_limits<Real>::epsilon());
153 Real y_prime = spline2.prime(i*step + a + 0.002);
154 BOOST_CHECK_SMALL(y_prime, std::numeric_limits<Real>::epsilon());
155 }
156 }
157
158
159 template<class Real>
test_affine_function()160 void test_affine_function()
161 {
162 using std::sqrt;
163 std::cout << "Testing that affine functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
164 std::vector<Real> v(500);
165 Real a = 10;
166 Real b = 8;
167 Real step = 0.005;
168
169 auto f = [a, b](Real x) { return a*x + b; };
170 for (size_t i = 0; i < v.size(); ++i)
171 {
172 v[i] = f(i*step);
173 }
174
175 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), 0, step);
176
177 for (size_t i = 0; i < v.size() - 1; ++i)
178 {
179 Real arg = i*step + 0.0001;
180 Real y = spline(arg);
181 BOOST_CHECK_CLOSE(y, f(arg), sqrt(std::numeric_limits<Real>::epsilon()));
182 Real y_prime = spline.prime(arg);
183 BOOST_CHECK_CLOSE(y_prime, a, 100*sqrt(std::numeric_limits<Real>::epsilon()));
184 }
185
186 // Test that correctly specified left and right-derivatives work properly:
187 spline = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), 0, step, a, a);
188
189 for (size_t i = 0; i < v.size() - 1; ++i)
190 {
191 Real arg = i*step + 0.0001;
192 Real y = spline(arg);
193 BOOST_CHECK_CLOSE(y, f(arg), sqrt(std::numeric_limits<Real>::epsilon()));
194 Real y_prime = spline.prime(arg);
195 BOOST_CHECK_CLOSE(y_prime, a, 100*sqrt(std::numeric_limits<Real>::epsilon()));
196 }
197 }
198
199
200 template<class Real>
test_quadratic_function()201 void test_quadratic_function()
202 {
203 using std::sqrt;
204 std::cout << "Testing that quadratic functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
205 std::vector<Real> v(500);
206 Real a = 1.2;
207 Real b = -3.4;
208 Real c = -8.6;
209 Real step = 0.01;
210
211 auto f = [a, b, c](Real x) { return a*x*x + b*x + c; };
212 for (size_t i = 0; i < v.size(); ++i)
213 {
214 v[i] = f(i*step);
215 }
216
217 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), 0, step);
218
219 for (size_t i = 0; i < v.size() -1; ++i)
220 {
221 Real arg = i*step + 0.001;
222 Real y = spline(arg);
223 BOOST_CHECK_CLOSE(y, f(arg), 0.1);
224 Real y_prime = spline.prime(arg);
225 BOOST_CHECK_CLOSE(y_prime, 2*a*arg + b, 2.0);
226 }
227 }
228
229
230 template<class Real>
test_trig_function()231 void test_trig_function()
232 {
233 std::cout << "Testing that sine functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
234 std::mt19937 gen;
235 std::vector<Real> v(500);
236 Real x0 = 1;
237 Real step = 0.125;
238
239 for (size_t i = 0; i < v.size(); ++i)
240 {
241 v[i] = sin(x0 + step * i);
242 }
243
244 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), x0, step);
245
246 boost::random::uniform_real_distribution<Real> absissa(x0, x0 + 499 * step);
247
248 for (size_t i = 0; i < v.size(); ++i)
249 {
250 Real x = absissa(gen);
251 Real y = spline(x);
252 BOOST_CHECK_CLOSE(y, sin(x), 1.0);
253 auto y_prime = spline.prime(x);
254 BOOST_CHECK_CLOSE(y_prime, cos(x), 2.0);
255 }
256 }
257
258 template<class Real>
test_copy_move()259 void test_copy_move()
260 {
261 std::cout << "Testing that copy/move operation succeed on cubic b spline\n";
262 std::vector<Real> v(500);
263 Real x0 = 1;
264 Real step = 0.125;
265
266 for (size_t i = 0; i < v.size(); ++i)
267 {
268 v[i] = sin(x0 + step * i);
269 }
270
271 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), x0, step);
272
273
274 // Default constructor should compile so that splines can be member variables:
275 boost::math::interpolators::cardinal_cubic_b_spline<Real> d;
276 d = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), x0, step);
277 BOOST_CHECK_CLOSE(d(x0), sin(x0), 0.01);
278 // Passing to lambda should compile:
279 auto f = [=](Real x) { return d(x); };
280 // Make sure this variable is used.
281 BOOST_CHECK_CLOSE(f(x0), sin(x0), 0.01);
282
283 // Move operations should compile.
284 auto s = std::move(spline);
285
286 // Copy operations should compile:
287 boost::math::interpolators::cardinal_cubic_b_spline<Real> c = d;
288 BOOST_CHECK_CLOSE(c(x0), sin(x0), 0.01);
289
290 // Test with std::bind:
291 auto h = std::bind(&boost::math::interpolators::cardinal_cubic_b_spline<double>::operator(), &s, std::placeholders::_1);
292 BOOST_CHECK_CLOSE(h(x0), sin(x0), 0.01);
293 }
294
295 template<class Real>
test_outside_interval()296 void test_outside_interval()
297 {
298 std::cout << "Testing that the spline can be evaluated outside the interpolation interval\n";
299 std::vector<Real> v(400);
300 Real x0 = 1;
301 Real step = 0.125;
302
303 for (size_t i = 0; i < v.size(); ++i)
304 {
305 v[i] = sin(x0 + step * i);
306 }
307
308 boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), x0, step);
309
310 // There's no test here; it simply does it's best to be an extrapolator.
311 //
312 std::ostream cnull(0);
313 cnull << spline(0);
314 cnull << spline(2000);
315 }
316
BOOST_AUTO_TEST_CASE(test_cubic_b_spline)317 BOOST_AUTO_TEST_CASE(test_cubic_b_spline)
318 {
319 test_b3_spline<float>();
320 test_b3_spline<double>();
321 test_b3_spline<long double>();
322 test_b3_spline<cpp_bin_float_50>();
323
324 test_interpolation_condition<float>();
325 test_interpolation_condition<double>();
326 test_interpolation_condition<long double>();
327 test_interpolation_condition<cpp_bin_float_50>();
328
329 test_constant_function<float>();
330 test_constant_function<double>();
331 test_constant_function<long double>();
332 test_constant_function<cpp_bin_float_50>();
333
334 test_affine_function<float>();
335 test_affine_function<double>();
336 test_affine_function<long double>();
337 test_affine_function<cpp_bin_float_50>();
338
339 test_quadratic_function<float>();
340 test_quadratic_function<double>();
341 test_quadratic_function<long double>();
342 test_affine_function<cpp_bin_float_50>();
343
344 test_trig_function<float>();
345 test_trig_function<double>();
346 test_trig_function<long double>();
347 test_trig_function<cpp_bin_float_50>();
348
349 test_copy_move<double>();
350 test_outside_interval<double>();
351 }
352