OpenFPM_pdata  4.1.0
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Kernels.hpp
1/*
2 * Kernels.hpp
3 *
4 * Created on: Jan 12, 2016
5 * Author: i-bird
6 */
7
8#ifndef OPENFPM_NUMERICS_SRC_PSE_KERNELS_HPP_
9#define OPENFPM_NUMERICS_SRC_PSE_KERNELS_HPP_
10
11#include <boost/math/constants/constants.hpp>
12
13// Gaussian kernel
14#define KER_GAUSSIAN 1
15
24template<unsigned int dim, typename T, unsigned int ord=2, unsigned int impl=KER_GAUSSIAN>
25struct Lap_PSE
26{
27 T epsilon;
28
29 Lap_PSE(T epsilon)
30 :epsilon(epsilon)
31 {}
32
39 inline T value(T (&x)[dim], T (&y)[dim])
40 {
41 std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " The laplacian for order:" << ord << " in dimension " << dim << " has not been implemented";
42 return 0.0;
43 }
44
51 inline T value(T (&x)[dim], const Point<dim,T> & y)
52 {
53 std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " The laplacian for order:" << ord << " in dimension " << dim << " has not been implemented";
54 return 0.0;
55 }
56
63 inline T value(const Point<dim,T> & x, T (&y)[dim])
64 {
65 std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " The laplacian for order:" << ord << " in dimension " << dim << " has not been implemented";
66 return 0.0;
67 }
68
75 inline T value(const Point<dim,T> & x, const Point<dim,T> & y)
76 {
77 std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " The laplacian for order:" << ord << " in dimension " << dim << " has not been implemented";
78 return 0.0;
79 }
80};
81
82template<typename T>
83struct Lap_PSE<1,T,2,KER_GAUSSIAN>
84{
85 T epsilon;
86
87 inline Lap_PSE(T epsilon)
88 :epsilon(epsilon)
89 {}
90
97 inline T value(T (&x)[1], T (&y)[1])
98 {
99 T d = 0.0;
100 for (size_t i = 0 ; i < 1 ; i++)
101 d += (x[i] - y[i]) * (x[i] - y[i]);
102 d = sqrt(d) / epsilon;
103
104 return T(4.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d);
105 }
106
113 inline T value(T (&x)[1], const Point<1,T> & y)
114 {
115 T d = 0.0;
116 for (size_t i = 0 ; i < 1 ; i++)
117 d += (x[i] - y.get(i)) * (x[i] - y.get(i));
118 d = sqrt(d) / epsilon;
119
120 return T(4.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d);
121 }
122
129 inline T value(const Point<1,T> & x, T (&y)[1])
130 {
131 T d = 0.0;
132 for (size_t i = 0 ; i < 1 ; i++)
133 d += (x.get(i) - y[i]) * (x.get(i) - y[i]);
134 d = sqrt(d) / epsilon;
135
136 return T(4.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d);
137 }
138
145 inline T value(const Point<1,T> & x, const Point<1,T> & y)
146 {
147 T d = 0.0;
148 for (size_t i = 0 ; i < 1 ; i++)
149 d += (x.get(i) - y.get(i)) * (x.get(i) - y.get(i));
150 d = sqrt(d) / epsilon;
151
152 return T(4.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d);
153 }
154};
155
156template<typename T>
157struct Lap_PSE<1,T,4,KER_GAUSSIAN>
158{
159 T epsilon;
160
161 inline Lap_PSE(T epsilon)
162 :epsilon(epsilon)
163 {}
164
171 inline T value(T (&x)[1], T (&y)[1])
172 {
173 T d = 0.0;
174 for (size_t i = 0 ; i < 1 ; i++)
175 d += (x[i] - y[i]) * (x[i] - y[i]);
176 d = sqrt(d) / epsilon;
177
178 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-4.0*d*d+10.0);
179 }
180
187 inline T value(T (&x)[1], const Point<1,T> & y)
188 {
189 T d = 0.0;
190 for (size_t i = 0 ; i < 1 ; i++)
191 d += (x[i] - y.get(i)) * (x[i] - y.get(i));
192 d = sqrt(d) / epsilon;
193
194 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-4.0*d*d+10.0);
195 }
196
203 inline T value(const Point<1,T> & x, T (&y)[1])
204 {
205 T d = 0.0;
206 for (size_t i = 0 ; i < 1 ; i++)
207 d += (x.get(i) - y[i]) * (x.get(i) - y[i]);
208 d = sqrt(d) / epsilon;
209
210 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-4.0*d*d+10.0);
211 }
212
219 inline T value(const Point<1,T> & x, const Point<1,T> & y)
220 {
221 T d = 0.0;
222 for (size_t i = 0 ; i < 1 ; i++)
223 d += (x.get(i) - y.get(i)) * (x.get(i) - y.get(i));
224 d = sqrt(d) / epsilon;
225
226 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-4.0*d*d+10.0);
227 }
228};
229
230template<typename T>
231struct Lap_PSE<1,T,6,KER_GAUSSIAN>
232{
233 T epsilon;
234
235 inline Lap_PSE(T epsilon)
236 :epsilon(epsilon)
237 {}
238
245 inline T value(T (&x)[1], T (&y)[1])
246 {
247 T d = 0.0;
248 for (size_t i = 0 ; i < 1 ; i++)
249 d += (x[i] - y[i]) * (x[i] - y[i]);
250 d = sqrt(d) / epsilon;
251
252 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (2.0*d*d*d*d-14.0*d*d+35.0/2.0);
253 }
254
261 inline T value(T (&x)[1], const Point<1,T> & y)
262 {
263 T d = 0.0;
264 for (size_t i = 0 ; i < 1 ; i++)
265 d += (x[i] - y.get(i)) * (x[i] - y.get(i));
266 d = sqrt(d) / epsilon;
267
268 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (2.0*d*d*d*d-14.0*d*d+35.0/2.0);
269 }
270
277 inline T value(const Point<1,T> & x, T (&y)[1])
278 {
279 T d = 0.0;
280 for (size_t i = 0 ; i < 1 ; i++)
281 d += (x.get(i) - y[i]) * (x.get(i) - y[i]);
282 d = sqrt(d) / epsilon;
283
284 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (2.0*d*d*d*d-14.0*d*d+35.0/2.0);
285 }
286
293 inline T value(const Point<1,T> & x, const Point<1,T> & y)
294 {
295 T d = 0.0;
296 for (size_t i = 0 ; i < 1 ; i++)
297 d += (x.get(i) - y.get(i)) * (x.get(i) - y.get(i));
298 d = sqrt(d) / epsilon;
299
300 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (2.0*d*d*d*d-14.0*d*d+35.0/2.0);
301 }
302};
303
304template<typename T>
305struct Lap_PSE<1,T,8,KER_GAUSSIAN>
306{
307 T epsilon;
308
309 inline Lap_PSE(T epsilon)
310 :epsilon(epsilon)
311 {}
312
319 inline T value(T (&x)[1], T (&y)[1])
320 {
321 T d = 0.0;
322 for (size_t i = 0 ; i < 1 ; i++)
323 d += (x[i] - y[i]) * (x[i] - y[i]);
324 d = sqrt(d) / epsilon;
325
326 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-T(2.0)/T(3.0)*d*d*d*d*d*d+9.0*d*d*d*d-63.0/2.0*d*d+105.0/4.0);
327 }
328
335 inline T value(T (&x)[1], const Point<1,T> & y)
336 {
337 T d = 0.0;
338 for (size_t i = 0 ; i < 1 ; i++)
339 d += (x[i] - y.get(i)) * (x[i] - y.get(i));
340 d = sqrt(d) / epsilon;
341
342 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-T(2.0)/T(3.0)*d*d*d*d*d*d+9.0*d*d*d*d-63.0/2.0*d*d+105.0/4.0);
343 }
344
351 inline T value(const Point<1,T> & x, T (&y)[1])
352 {
353 T d = 0.0;
354 for (size_t i = 0 ; i < 1 ; i++)
355 d += (x.get(i) - y[i]) * (x.get(i) - y[i]);
356 d = sqrt(d) / epsilon;
357
358 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-T(2.0)/T(3.0)*d*d*d*d*d*d+9.0*d*d*d*d-63.0/2.0*d*d+105.0/4.0);
359 }
360
367 inline T value(const Point<1,T> & x, const Point<1,T> & y)
368 {
369 T d = 0.0;
370 for (size_t i = 0 ; i < 1 ; i++)
371 d += (x.get(i) - y.get(i)) * (x.get(i) - y.get(i));
372 d = sqrt(d) / epsilon;
373
374 return T(1.0) / epsilon / boost::math::constants::root_pi<T>() * exp(-d*d) * (-T(2.0)/T(3.0)*d*d*d*d*d*d+9.0*d*d*d*d-63.0/2.0*d*d+105.0/4.0);
375 }
376};
377
378#endif /* OPENFPM_NUMERICS_SRC_PSE_KERNELS_HPP_ */
Point
This class implement the point shape in an N-dimensional space.
Definition Point.hpp:28
Lap_PSE< 1, T, 2, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:145
Lap_PSE< 1, T, 2, KER_GAUSSIAN >::value
T value(T(&x)[1], T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:97
Lap_PSE< 1, T, 2, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:129
Lap_PSE< 1, T, 2, KER_GAUSSIAN >::value
T value(T(&x)[1], const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:113
Lap_PSE< 1, T, 4, KER_GAUSSIAN >::value
T value(T(&x)[1], const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:187
Lap_PSE< 1, T, 4, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:219
Lap_PSE< 1, T, 4, KER_GAUSSIAN >::value
T value(T(&x)[1], T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:171
Lap_PSE< 1, T, 4, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:203
Lap_PSE< 1, T, 6, KER_GAUSSIAN >::value
T value(T(&x)[1], const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:261
Lap_PSE< 1, T, 6, KER_GAUSSIAN >::value
T value(T(&x)[1], T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:245
Lap_PSE< 1, T, 6, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:277
Lap_PSE< 1, T, 6, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:293
Lap_PSE< 1, T, 8, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:367
Lap_PSE< 1, T, 8, KER_GAUSSIAN >::value
T value(T(&x)[1], T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:319
Lap_PSE< 1, T, 8, KER_GAUSSIAN >::value
T value(T(&x)[1], const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:335
Lap_PSE< 1, T, 8, KER_GAUSSIAN >::value
T value(const Point< 1, T > &x, T(&y)[1])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:351
Lap_PSE
Implementation of the Laplacian kernels for PSE.
Definition Kernels.hpp:26
Lap_PSE::value
T value(const Point< dim, T > &x, const Point< dim, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:75
Lap_PSE::value
T value(T(&x)[dim], const Point< dim, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:51
Lap_PSE::value
T value(const Point< dim, T > &x, T(&y)[dim])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:63
Lap_PSE::value
T value(T(&x)[dim], T(&y)[dim])
From a kernel centered in x, it give the value of the kernel in y.
Definition Kernels.hpp:39