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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 | #ifndef BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP | |
8 | #define BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP | |
9 | #include <algorithm> | |
10 | #include <stdexcept> | |
11 | #include <sstream> | |
1e59de90 | 12 | #include <limits> |
f67539c2 TL |
13 | #include <cmath> |
14 | ||
20effc67 TL |
15 | namespace boost { |
16 | namespace math { | |
17 | namespace interpolators { | |
18 | namespace detail { | |
f67539c2 TL |
19 | |
20 | template<class RandomAccessContainer> | |
21 | class quintic_hermite_detail { | |
22 | public: | |
23 | using Real = typename RandomAccessContainer::value_type; | |
24 | quintic_hermite_detail(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2) : x_{std::move(x)}, y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)} | |
25 | { | |
26 | if (x_.size() != y_.size()) | |
27 | { | |
28 | throw std::domain_error("Number of abscissas must = number of ordinates."); | |
29 | } | |
30 | if (x_.size() != dydx_.size()) | |
31 | { | |
32 | throw std::domain_error("Numbers of derivatives must = number of abscissas."); | |
33 | } | |
34 | if (x_.size() != d2ydx2_.size()) | |
35 | { | |
36 | throw std::domain_error("Number of second derivatives must equal number of abscissas."); | |
37 | } | |
38 | if (x_.size() < 2) | |
39 | { | |
40 | throw std::domain_error("At least 2 abscissas are required."); | |
41 | } | |
42 | Real x0 = x_[0]; | |
43 | for (decltype(x_.size()) i = 1; i < x_.size(); ++i) | |
44 | { | |
45 | Real x1 = x_[i]; | |
46 | if (x1 <= x0) | |
47 | { | |
48 | throw std::domain_error("Abscissas must be sorted in strictly increasing order x0 < x1 < ... < x_{n-1}"); | |
49 | } | |
50 | x0 = x1; | |
51 | } | |
52 | } | |
53 | ||
54 | void push_back(Real x, Real y, Real dydx, Real d2ydx2) | |
55 | { | |
56 | using std::abs; | |
57 | using std::isnan; | |
58 | if (x <= x_.back()) | |
59 | { | |
60 | throw std::domain_error("Calling push_back must preserve the monotonicity of the x's"); | |
61 | } | |
62 | x_.push_back(x); | |
63 | y_.push_back(y); | |
64 | dydx_.push_back(dydx); | |
65 | d2ydx2_.push_back(d2ydx2); | |
66 | } | |
67 | ||
68 | inline Real operator()(Real x) const | |
69 | { | |
70 | if (x < x_[0] || x > x_.back()) | |
71 | { | |
72 | std::ostringstream oss; | |
73 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
74 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
75 | << x_[0] << ", " << x_.back() << "]"; | |
76 | throw std::domain_error(oss.str()); | |
77 | } | |
78 | // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work. | |
79 | // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf. | |
80 | if (x == x_.back()) | |
81 | { | |
82 | return y_.back(); | |
83 | } | |
84 | ||
85 | auto it = std::upper_bound(x_.begin(), x_.end(), x); | |
86 | auto i = std::distance(x_.begin(), it) -1; | |
87 | Real x0 = *(it-1); | |
88 | Real x1 = *it; | |
89 | Real y0 = y_[i]; | |
90 | Real y1 = y_[i+1]; | |
91 | Real v0 = dydx_[i]; | |
92 | Real v1 = dydx_[i+1]; | |
93 | Real a0 = d2ydx2_[i]; | |
94 | Real a1 = d2ydx2_[i+1]; | |
95 | ||
96 | Real dx = (x1-x0); | |
97 | Real t = (x-x0)/dx; | |
98 | Real t2 = t*t; | |
99 | Real t3 = t2*t; | |
100 | ||
101 | // See the 'Basis functions' section of: | |
102 | // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf | |
103 | // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs | |
104 | Real y = (1- t3*(10 + t*(-15 + 6*t)))*y0; | |
105 | y += t*(1+ t2*(-6 + t*(8 -3*t)))*v0*dx; | |
106 | y += t2*(1 + t*(-3 + t*(3-t)))*a0*dx*dx/2; | |
107 | y += t3*((1 + t*(-2 + t))*a1*dx*dx/2 + (-4 + t*(7 - 3*t))*v1*dx + (10 + t*(-15 + 6*t))*y1); | |
108 | return y; | |
109 | } | |
110 | ||
111 | inline Real prime(Real x) const | |
112 | { | |
113 | if (x < x_[0] || x > x_.back()) | |
114 | { | |
115 | std::ostringstream oss; | |
116 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
117 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
118 | << x_[0] << ", " << x_.back() << "]"; | |
119 | throw std::domain_error(oss.str()); | |
120 | } | |
121 | if (x == x_.back()) | |
122 | { | |
123 | return dydx_.back(); | |
124 | } | |
125 | ||
126 | auto it = std::upper_bound(x_.begin(), x_.end(), x); | |
127 | auto i = std::distance(x_.begin(), it) -1; | |
128 | Real x0 = *(it-1); | |
129 | Real x1 = *it; | |
130 | Real dx = x1 - x0; | |
131 | ||
132 | Real y0 = y_[i]; | |
133 | Real y1 = y_[i+1]; | |
134 | Real v0 = dydx_[i]; | |
135 | Real v1 = dydx_[i+1]; | |
136 | Real a0 = d2ydx2_[i]; | |
137 | Real a1 = d2ydx2_[i+1]; | |
138 | Real t= (x-x0)/dx; | |
139 | Real t2 = t*t; | |
140 | ||
141 | Real dydx = 30*t2*(1 - 2*t + t*t)*(y1-y0)/dx; | |
142 | dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1; | |
143 | dydx += (t*dx/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1); | |
144 | return dydx; | |
145 | } | |
146 | ||
147 | inline Real double_prime(Real x) const | |
148 | { | |
149 | if (x < x_[0] || x > x_.back()) | |
150 | { | |
151 | std::ostringstream oss; | |
152 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
153 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
154 | << x_[0] << ", " << x_.back() << "]"; | |
155 | throw std::domain_error(oss.str()); | |
156 | } | |
157 | if (x == x_.back()) | |
158 | { | |
159 | return d2ydx2_.back(); | |
160 | } | |
161 | ||
162 | auto it = std::upper_bound(x_.begin(), x_.end(), x); | |
163 | auto i = std::distance(x_.begin(), it) -1; | |
164 | Real x0 = *(it-1); | |
165 | Real x1 = *it; | |
166 | Real dx = x1 - x0; | |
167 | ||
168 | Real y0 = y_[i]; | |
169 | Real y1 = y_[i+1]; | |
170 | Real v0 = dydx_[i]; | |
171 | Real v1 = dydx_[i+1]; | |
172 | Real a0 = d2ydx2_[i]; | |
173 | Real a1 = d2ydx2_[i+1]; | |
174 | Real t = (x-x0)/dx; | |
175 | ||
176 | Real d2ydx2 = 60*t*(1 + t*(-3 + 2*t))*(y1-y0)/(dx*dx); | |
177 | d2ydx2 += 12*t*(-3 + t*(8 - 5*t))*v0/dx; | |
178 | d2ydx2 -= 12*t*(2 + t*(-7 + 5*t))*v1/dx; | |
179 | d2ydx2 += (1 + t*(-9 + t*(18 - 10*t)))*a0; | |
180 | d2ydx2 += t*(3 + t*(-12 + 10*t))*a1; | |
181 | ||
182 | return d2ydx2; | |
183 | } | |
184 | ||
185 | friend std::ostream& operator<<(std::ostream & os, const quintic_hermite_detail & m) | |
186 | { | |
187 | os << "(x,y,y') = {"; | |
188 | for (size_t i = 0; i < m.x_.size() - 1; ++i) { | |
189 | os << "(" << m.x_[i] << ", " << m.y_[i] << ", " << m.dydx_[i] << ", " << m.d2ydx2_[i] << "), "; | |
190 | } | |
191 | auto n = m.x_.size()-1; | |
192 | os << "(" << m.x_[n] << ", " << m.y_[n] << ", " << m.dydx_[n] << ", " << m.d2ydx2_[n] << ")}"; | |
193 | return os; | |
194 | } | |
195 | ||
196 | int64_t bytes() const | |
197 | { | |
198 | return 4*x_.size()*sizeof(x_); | |
199 | } | |
200 | ||
201 | std::pair<Real, Real> domain() const | |
202 | { | |
203 | return {x_.front(), x_.back()}; | |
204 | } | |
205 | ||
206 | private: | |
207 | RandomAccessContainer x_; | |
208 | RandomAccessContainer y_; | |
209 | RandomAccessContainer dydx_; | |
210 | RandomAccessContainer d2ydx2_; | |
211 | }; | |
212 | ||
213 | ||
214 | template<class RandomAccessContainer> | |
215 | class cardinal_quintic_hermite_detail { | |
216 | public: | |
217 | using Real = typename RandomAccessContainer::value_type; | |
218 | cardinal_quintic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx) | |
219 | : y_{std::move(y)}, dy_{std::move(dydx)}, d2y_{std::move(d2ydx2)}, x0_{x0}, inv_dx_{1/dx} | |
220 | { | |
221 | if (y_.size() != dy_.size()) | |
222 | { | |
223 | throw std::domain_error("Numbers of derivatives must = number of abscissas."); | |
224 | } | |
225 | if (y_.size() != d2y_.size()) | |
226 | { | |
227 | throw std::domain_error("Number of second derivatives must equal number of abscissas."); | |
228 | } | |
229 | if (y_.size() < 2) | |
230 | { | |
231 | throw std::domain_error("At least 2 abscissas are required."); | |
232 | } | |
233 | if (dx <= 0) | |
234 | { | |
235 | throw std::domain_error("dx > 0 is required."); | |
236 | } | |
237 | ||
238 | for (auto & dy : dy_) | |
239 | { | |
240 | dy *= dx; | |
241 | } | |
242 | ||
243 | for (auto & d2y : d2y_) | |
244 | { | |
245 | d2y *= (dx*dx)/2; | |
246 | } | |
247 | } | |
248 | ||
249 | ||
250 | inline Real operator()(Real x) const | |
251 | { | |
252 | const Real xf = x0_ + (y_.size()-1)/inv_dx_; | |
253 | if (x < x0_ || x > xf) | |
254 | { | |
255 | std::ostringstream oss; | |
256 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
257 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
258 | << x0_ << ", " << xf << "]"; | |
259 | throw std::domain_error(oss.str()); | |
260 | } | |
261 | if (x == xf) | |
262 | { | |
263 | return y_.back(); | |
264 | } | |
265 | return this->unchecked_evaluation(x); | |
266 | } | |
267 | ||
268 | inline Real unchecked_evaluation(Real x) const | |
269 | { | |
270 | using std::floor; | |
271 | Real s = (x-x0_)*inv_dx_; | |
272 | Real ii = floor(s); | |
273 | auto i = static_cast<decltype(y_.size())>(ii); | |
274 | Real t = s - ii; | |
275 | if (t == 0) | |
276 | { | |
277 | return y_[i]; | |
278 | } | |
279 | Real y0 = y_[i]; | |
280 | Real y1 = y_[i+1]; | |
281 | Real dy0 = dy_[i]; | |
282 | Real dy1 = dy_[i+1]; | |
283 | Real d2y0 = d2y_[i]; | |
284 | Real d2y1 = d2y_[i+1]; | |
285 | ||
286 | // See the 'Basis functions' section of: | |
287 | // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf | |
288 | // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs | |
289 | Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0; | |
290 | y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0; | |
291 | y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0; | |
292 | y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1); | |
293 | return y; | |
294 | } | |
295 | ||
296 | inline Real prime(Real x) const | |
297 | { | |
298 | const Real xf = x0_ + (y_.size()-1)/inv_dx_; | |
299 | if (x < x0_ || x > xf) | |
300 | { | |
301 | std::ostringstream oss; | |
302 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
303 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
304 | << x0_ << ", " << xf << "]"; | |
305 | throw std::domain_error(oss.str()); | |
306 | } | |
307 | if (x == xf) | |
308 | { | |
309 | return dy_.back()*inv_dx_; | |
310 | } | |
311 | ||
312 | return this->unchecked_prime(x); | |
313 | } | |
314 | ||
315 | inline Real unchecked_prime(Real x) const | |
316 | { | |
317 | using std::floor; | |
318 | Real s = (x-x0_)*inv_dx_; | |
319 | Real ii = floor(s); | |
320 | auto i = static_cast<decltype(y_.size())>(ii); | |
321 | Real t = s - ii; | |
322 | if (t == 0) | |
323 | { | |
324 | return dy_[i]*inv_dx_; | |
325 | } | |
326 | Real y0 = y_[i]; | |
327 | Real y1 = y_[i+1]; | |
328 | Real dy0 = dy_[i]; | |
329 | Real dy1 = dy_[i+1]; | |
330 | Real d2y0 = d2y_[i]; | |
331 | Real d2y1 = d2y_[i+1]; | |
332 | ||
333 | Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0); | |
334 | dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*dy0 - t*t*(12 - 28*t + 15*t*t)*dy1; | |
335 | dydx += t*((2 - 9*t + 12*t*t - 5*t*t*t)*d2y0 + t*(3 - 8*t + 5*t*t)*d2y1); | |
336 | dydx *= inv_dx_; | |
337 | return dydx; | |
338 | } | |
339 | ||
340 | inline Real double_prime(Real x) const | |
341 | { | |
342 | const Real xf = x0_ + (y_.size()-1)/inv_dx_; | |
343 | if (x < x0_ || x > xf) { | |
344 | std::ostringstream oss; | |
345 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
346 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
347 | << x0_ << ", " << xf << "]"; | |
348 | throw std::domain_error(oss.str()); | |
349 | } | |
350 | if (x == xf) | |
351 | { | |
352 | return d2y_.back()*2*inv_dx_*inv_dx_; | |
353 | } | |
354 | ||
355 | return this->unchecked_double_prime(x); | |
356 | } | |
357 | ||
358 | inline Real unchecked_double_prime(Real x) const | |
359 | { | |
360 | using std::floor; | |
361 | Real s = (x-x0_)*inv_dx_; | |
362 | Real ii = floor(s); | |
363 | auto i = static_cast<decltype(y_.size())>(ii); | |
364 | Real t = s - ii; | |
365 | if (t==0) | |
366 | { | |
367 | return d2y_[i]*2*inv_dx_*inv_dx_; | |
368 | } | |
369 | ||
370 | Real y0 = y_[i]; | |
371 | Real y1 = y_[i+1]; | |
372 | Real dy0 = dy_[i]; | |
373 | Real dy1 = dy_[i+1]; | |
374 | Real d2y0 = d2y_[i]; | |
375 | Real d2y1 = d2y_[i+1]; | |
376 | ||
377 | Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)*inv_dx_*inv_dx_; | |
378 | d2ydx2 += (12*t)*((-3 + 8*t - 5*t*t)*dy0 - (2 - 7*t + 5*t*t)*dy1); | |
379 | d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*d2y0*(2*inv_dx_*inv_dx_) + t*(3 - 12*t + 10*t*t)*d2y1*(2*inv_dx_*inv_dx_); | |
380 | return d2ydx2; | |
381 | } | |
382 | ||
383 | int64_t bytes() const | |
384 | { | |
385 | return 3*y_.size()*sizeof(Real) + 2*sizeof(Real); | |
386 | } | |
387 | ||
388 | std::pair<Real, Real> domain() const | |
389 | { | |
390 | Real xf = x0_ + (y_.size()-1)/inv_dx_; | |
391 | return {x0_, xf}; | |
392 | } | |
393 | ||
394 | private: | |
395 | RandomAccessContainer y_; | |
396 | RandomAccessContainer dy_; | |
397 | RandomAccessContainer d2y_; | |
398 | Real x0_; | |
399 | Real inv_dx_; | |
400 | }; | |
401 | ||
402 | ||
403 | template<class RandomAccessContainer> | |
404 | class cardinal_quintic_hermite_detail_aos { | |
405 | public: | |
406 | using Point = typename RandomAccessContainer::value_type; | |
407 | using Real = typename Point::value_type; | |
408 | cardinal_quintic_hermite_detail_aos(RandomAccessContainer && data, Real x0, Real dx) | |
409 | : data_{std::move(data)} , x0_{x0}, inv_dx_{1/dx} | |
410 | { | |
411 | if (data_.size() < 2) | |
412 | { | |
413 | throw std::domain_error("At least two points are required to interpolate using cardinal_quintic_hermite_aos"); | |
414 | } | |
415 | ||
416 | if (data_[0].size() != 3) | |
417 | { | |
418 | throw std::domain_error("Each datum passed to the cardinal_quintic_hermite_aos must have three elements: {y, y', y''}"); | |
419 | } | |
420 | if (dx <= 0) | |
421 | { | |
422 | throw std::domain_error("dx > 0 is required."); | |
423 | } | |
424 | ||
425 | for (auto & datum : data_) | |
426 | { | |
427 | datum[1] *= dx; | |
428 | datum[2] *= (dx*dx/2); | |
429 | } | |
430 | } | |
431 | ||
432 | ||
433 | inline Real operator()(Real x) const | |
434 | { | |
435 | const Real xf = x0_ + (data_.size()-1)/inv_dx_; | |
436 | if (x < x0_ || x > xf) | |
437 | { | |
438 | std::ostringstream oss; | |
439 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
440 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
441 | << x0_ << ", " << xf << "]"; | |
442 | throw std::domain_error(oss.str()); | |
443 | } | |
444 | if (x == xf) | |
445 | { | |
446 | return data_.back()[0]; | |
447 | } | |
448 | return this->unchecked_evaluation(x); | |
449 | } | |
450 | ||
451 | inline Real unchecked_evaluation(Real x) const | |
452 | { | |
453 | using std::floor; | |
454 | Real s = (x-x0_)*inv_dx_; | |
455 | Real ii = floor(s); | |
456 | auto i = static_cast<decltype(data_.size())>(ii); | |
457 | Real t = s - ii; | |
458 | if (t == 0) | |
459 | { | |
460 | return data_[i][0]; | |
461 | } | |
462 | ||
463 | Real y0 = data_[i][0]; | |
464 | Real dy0 = data_[i][1]; | |
465 | Real d2y0 = data_[i][2]; | |
466 | Real y1 = data_[i+1][0]; | |
467 | Real dy1 = data_[i+1][1]; | |
468 | Real d2y1 = data_[i+1][2]; | |
469 | ||
470 | Real y = (1 - t*t*t*(10 + t*(-15 + 6*t)))*y0; | |
471 | y += t*(1 + t*t*(-6 + t*(8 - 3*t)))*dy0; | |
472 | y += t*t*(1 + t*(-3 + t*(3 - t)))*d2y0; | |
473 | y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 - 3*t))*dy1 + (10 + t*(-15 + 6*t))*y1); | |
474 | return y; | |
475 | } | |
476 | ||
477 | inline Real prime(Real x) const | |
478 | { | |
479 | const Real xf = x0_ + (data_.size()-1)/inv_dx_; | |
480 | if (x < x0_ || x > xf) | |
481 | { | |
482 | std::ostringstream oss; | |
483 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
484 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
485 | << x0_ << ", " << xf << "]"; | |
486 | throw std::domain_error(oss.str()); | |
487 | } | |
488 | if (x == xf) | |
489 | { | |
490 | return data_.back()[1]*inv_dx_; | |
491 | } | |
492 | ||
493 | return this->unchecked_prime(x); | |
494 | } | |
495 | ||
496 | inline Real unchecked_prime(Real x) const | |
497 | { | |
498 | using std::floor; | |
499 | Real s = (x-x0_)*inv_dx_; | |
500 | Real ii = floor(s); | |
501 | auto i = static_cast<decltype(data_.size())>(ii); | |
502 | Real t = s - ii; | |
503 | if (t == 0) | |
504 | { | |
505 | return data_[i][1]*inv_dx_; | |
506 | } | |
507 | ||
508 | ||
509 | Real y0 = data_[i][0]; | |
510 | Real y1 = data_[i+1][0]; | |
511 | Real v0 = data_[i][1]; | |
512 | Real v1 = data_[i+1][1]; | |
513 | Real a0 = data_[i][2]; | |
514 | Real a1 = data_[i+1][2]; | |
515 | ||
516 | Real dy = 30*t*t*(1 - 2*t + t*t)*(y1-y0); | |
517 | dy += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1; | |
518 | dy += t*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1); | |
519 | return dy*inv_dx_; | |
520 | } | |
521 | ||
522 | inline Real double_prime(Real x) const | |
523 | { | |
524 | const Real xf = x0_ + (data_.size()-1)/inv_dx_; | |
525 | if (x < x0_ || x > xf) | |
526 | { | |
527 | std::ostringstream oss; | |
528 | oss.precision(std::numeric_limits<Real>::digits10+3); | |
529 | oss << "Requested abscissa x = " << x << ", which is outside of allowed range [" | |
530 | << x0_ << ", " << xf << "]"; | |
531 | throw std::domain_error(oss.str()); | |
532 | } | |
533 | if (x == xf) | |
534 | { | |
535 | return data_.back()[2]*2*inv_dx_*inv_dx_; | |
536 | } | |
537 | ||
538 | return this->unchecked_double_prime(x); | |
539 | } | |
540 | ||
541 | inline Real unchecked_double_prime(Real x) const | |
542 | { | |
543 | using std::floor; | |
544 | Real s = (x-x0_)*inv_dx_; | |
545 | Real ii = floor(s); | |
546 | auto i = static_cast<decltype(data_.size())>(ii); | |
547 | Real t = s - ii; | |
548 | if (t == 0) { | |
549 | return data_[i][2]*2*inv_dx_*inv_dx_; | |
550 | } | |
551 | Real y0 = data_[i][0]; | |
552 | Real dy0 = data_[i][1]; | |
553 | Real d2y0 = data_[i][2]; | |
554 | Real y1 = data_[i+1][0]; | |
555 | Real dy1 = data_[i+1][1]; | |
556 | Real d2y1 = data_[i+1][2]; | |
557 | ||
558 | Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)*inv_dx_*inv_dx_; | |
559 | d2ydx2 += (12*t)*((-3 + 8*t - 5*t*t)*dy0 - (2 - 7*t + 5*t*t)*dy1); | |
560 | d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*d2y0*(2*inv_dx_*inv_dx_) + t*(3 - 12*t + 10*t*t)*d2y1*(2*inv_dx_*inv_dx_); | |
561 | return d2ydx2; | |
562 | } | |
563 | ||
564 | int64_t bytes() const | |
565 | { | |
566 | return data_.size()*data_[0].size()*sizeof(Real) + 2*sizeof(Real); | |
567 | } | |
568 | ||
569 | std::pair<Real, Real> domain() const | |
570 | { | |
571 | Real xf = x0_ + (data_.size()-1)/inv_dx_; | |
572 | return {x0_, xf}; | |
573 | } | |
574 | ||
575 | private: | |
576 | RandomAccessContainer data_; | |
577 | Real x0_; | |
578 | Real inv_dx_; | |
579 | }; | |
580 | ||
20effc67 TL |
581 | } |
582 | } | |
583 | } | |
f67539c2 TL |
584 | } |
585 | #endif |