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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 
24 template<unsigned int dim, typename T, unsigned int ord=2, unsigned int impl=KER_GAUSSIAN>
25 struct 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 
82 template<typename T>
83 struct 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 
156 template<typename T>
157 struct 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 
230 template<typename T>
231 struct 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 
304 template<typename T>
305 struct 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_ */
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, 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, 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
Point
This class implement the point shape in an N-dimensional space.
Definition: Point.hpp:22
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
Implementation of the Laplacian kernels for PSE.
Definition: Kernels.hpp:25
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::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< 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, 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::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< 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
Point::get
const T & get(size_t i) const
Get coordinate.
Definition: Point.hpp:142
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< 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, 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, 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, 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, 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::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
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< 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], const Point< 1, T > &y)
From a kernel centered in x, it give the value of the kernel in y.
Definition: Kernels.hpp:335