bessel_functions.cpp
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #include "main.h"
11 #include "../Eigen/SpecialFunctions"
12 
13 template<typename X, typename Y>
14 void verify_component_wise(const X& x, const Y& y)
15 {
16  for(Index i=0; i<x.size(); ++i)
17  {
18  if((numext::isfinite)(y(i))) {
19  VERIFY_IS_APPROX( x(i), y(i) );
20  }
21  else if((numext::isnan)(y(i)))
22  VERIFY((numext::isnan)(x(i)));
23  else
24  VERIFY_IS_EQUAL( x(i), y(i) );
25  }
26 }
27 
28 template<typename ArrayType> void array_bessel_functions()
29 {
30  // Test Bessel function i0. Reference results obtained with SciPy.
31  {
32  ArrayType x(21);
33  ArrayType expected(21);
34  ArrayType res(21);
35 
36  x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
37  2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
38 
39  expected << 4.35582826e+07, 6.21841242e+06, 8.93446228e+05, 1.29418563e+05,
40  1.89489253e+04, 2.81571663e+03, 4.27564116e+02, 6.72344070e+01,
41  1.13019220e+01, 2.27958530e+00, 1.00000000e+00, 2.27958530e+00,
42  1.13019220e+01, 6.72344070e+01, 4.27564116e+02, 2.81571663e+03,
43  1.89489253e+04, 1.29418563e+05, 8.93446228e+05, 6.21841242e+06,
44  4.35582826e+07;
45 
46  CALL_SUBTEST(res = bessel_i0(x);
47  verify_component_wise(res, expected););
48  }
49 
50  // Test Bessel function i0e. Reference results obtained with SciPy.
51  {
52  ArrayType x(21);
53  ArrayType expected(21);
54  ArrayType res(21);
55 
56  x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
57  2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
58 
59  expected << 0.0897803118848, 0.0947062952128, 0.100544127361,
60  0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
61  0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
62  0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
63  0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
64  0.0897803118848;
65 
66  CALL_SUBTEST(res = bessel_i0e(x);
67  verify_component_wise(res, expected););
68  }
69 
70  // Test Bessel function i1. Reference results obtained with SciPy.
71  {
72  ArrayType x(21);
73  ArrayType expected(21);
74  ArrayType res(21);
75 
76  x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
77  2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
78 
79  expected << -4.24549734e+07, -6.04313324e+06, -8.65059436e+05, -1.24707259e+05,
80  -1.81413488e+04, -2.67098830e+03, -3.99873137e+02, -6.13419368e+01,
81  -9.75946515e+00, -1.59063685e+00, 0.00000000e+00, 1.59063685e+00,
82  9.75946515e+00, 6.13419368e+01, 3.99873137e+02, 2.67098830e+03,
83  1.81413488e+04, 1.24707259e+05, 8.65059436e+05, 6.04313324e+06,
84  4.24549734e+07;
85 
86  CALL_SUBTEST(res = bessel_i1(x);
87  verify_component_wise(res, expected););
88  }
89 
90  // Test Bessel function i1e. Reference results obtained with SciPy.
91  {
92  ArrayType x(21);
93  ArrayType expected(21);
94  ArrayType res(21);
95 
96  x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
97  2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
98 
99  expected << -0.0875062221833, -0.092036796872, -0.0973496147565,
100  -0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
101  -0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
102  0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
103  0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
104  0.0875062221833;
105 
106  CALL_SUBTEST(res = bessel_i1e(x);
107  verify_component_wise(res, expected););
108  }
109 
110  // Test Bessel function j0. Reference results obtained with SciPy.
111  {
112  ArrayType x(77);
113  ArrayType expected(77);
114  ArrayType res(77);
115 
116  x << -38., -37., -36., -35., -34., -33., -32., -31., -30.,
117  -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
118  -18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8.,
119  -7., -6., -5., -4., -3., -2., -1., 0., 1., 2., 3.,
120  4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14.,
121  15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
122  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
123  37., 38.;
124 
125  expected << 0.11433274, 0.01086237, -0.10556738,
126  -0.12684568, -0.03042119, 0.09727067, 0.13807901, 0.05120815,
127  -0.08636798, -0.14784876, -0.07315701, 0.07274192, 0.15599932,
128  0.09626678, -0.05623027, -0.16241278, -0.12065148, 0.03657907,
129  0.16702466, 0.14662944, -0.01335581, -0.16985425, -0.17489907,
130  -0.01422447, 0.17107348, 0.2069261 , 0.04768931, -0.1711903 ,
131  -0.24593576, -0.09033361, 0.17165081, 0.30007927, 0.15064526,
132  -0.17759677, -0.39714981, -0.26005195, 0.22389078, 0.76519769,
133  1. , 0.76519769, 0.22389078, -0.26005195, -0.39714981,
134  -0.17759677, 0.15064526, 0.30007927, 0.17165081, -0.09033361,
135  -0.24593576, -0.1711903 , 0.04768931, 0.2069261 , 0.17107348,
136  -0.01422447, -0.17489907, -0.16985425, -0.01335581, 0.14662944,
137  0.16702466, 0.03657907, -0.12065148, -0.16241278, -0.05623027,
138  0.09626678, 0.15599932, 0.07274192, -0.07315701, -0.14784876,
139  -0.08636798, 0.05120815, 0.13807901, 0.09727067, -0.03042119,
140  -0.12684568, -0.10556738, 0.01086237, 0.11433274;
141 
142  CALL_SUBTEST(res = bessel_j0(x);
143  verify_component_wise(res, expected););
144  }
145 
146  // Test Bessel function j1. Reference results obtained with SciPy.
147  {
148  ArrayType x(81);
149  ArrayType expected(81);
150  ArrayType res(81);
151 
152  x << -40., -39., -38., -37., -36., -35., -34., -33., -32., -31., -30.,
153  -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
154  -18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8.,
155  -7., -6., -5., -4., -3., -2., -1., 0., 1., 2., 3.,
156  4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14.,
157  15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
158  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
159  37., 38., 39., 40.;
160 
161  expected << -0.12603832, -0.0640561 , 0.05916189, 0.13058004, 0.08232981,
162  -0.04399094, -0.13297118, -0.10061965, 0.02658903, 0.13302432,
163  0.11875106, -0.0069342 , -0.13055149, -0.13658472, -0.01504573,
164  0.12535025, 0.15403807, 0.03951932, -0.11717779, -0.17112027,
165  -0.06683312, 0.10570143, 0.18799489, 0.09766849, -0.09039718,
166  -0.20510404, -0.13337515, 0.07031805, 0.2234471 , 0.1767853 ,
167  -0.04347275, -0.24531179, -0.23463635, 0.00468282, 0.27668386,
168  0.32757914, 0.06604333, -0.33905896, -0.57672481, -0.44005059,
169  0. , 0.44005059, 0.57672481, 0.33905896, -0.06604333,
170  -0.32757914, -0.27668386, -0.00468282, 0.23463635, 0.24531179,
171  0.04347275, -0.1767853 , -0.2234471 , -0.07031805, 0.13337515,
172  0.20510404, 0.09039718, -0.09766849, -0.18799489, -0.10570143,
173  0.06683312, 0.17112027, 0.11717779, -0.03951932, -0.15403807,
174  -0.12535025, 0.01504573, 0.13658472, 0.13055149, 0.0069342 ,
175  -0.11875106, -0.13302432, -0.02658903, 0.10061965, 0.13297118,
176  0.04399094, -0.08232981, -0.13058004, -0.05916189, 0.0640561 ,
177  0.12603832;
178 
179  CALL_SUBTEST(res = bessel_j1(x);
180  verify_component_wise(res, expected););
181  }
182  // Test Bessel function k0e. Reference results obtained with SciPy.
183  {
184  ArrayType x(42);
185  ArrayType expected(42);
186  ArrayType res(42);
187 
188  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
189  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
190  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
191  39., 40.;
192 
193  expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822,
194  0.6977616 , 0.60929767, 0.54780756, 0.50186313, 0.4658451 ,
195  0.43662302, 0.41229555, 0.39163193, 0.3737955 , 0.35819488,
196  0.34439865, 0.33208364, 0.32100235, 0.31096159, 0.30180802,
197  0.29341821, 0.28569149, 0.27854488, 0.2719092 , 0.26572635,
198  0.25994703, 0.25452917, 0.2494366 , 0.24463801, 0.24010616,
199  0.23581722, 0.23175022, 0.22788667, 0.22421014, 0.22070602,
200  0.21736123, 0.21416406, 0.21110397, 0.20817141, 0.20535778,
201  0.20265524, 0.20005668, 0.19755558;
202 
203  CALL_SUBTEST(res = bessel_k0e(x);
204  verify_component_wise(res, expected););
205  }
206 
207  // Test Bessel function k0. Reference results obtained with SciPy.
208  {
209  ArrayType x(42);
210  ArrayType expected(42);
211  ArrayType res(42);
212 
213  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
214  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
215  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
216  39., 40.;
217 
218  expected << 1.54150675, 0.92441907, 4.21024438e-01, 1.13893873e-01,
219  3.47395044e-02, 1.11596761e-02, 3.69109833e-03, 1.24399433e-03,
220  4.24795742e-04, 1.46470705e-04, 5.08813130e-05, 1.77800623e-05,
221  6.24302055e-06, 2.20082540e-06, 7.78454386e-07, 2.76137082e-07,
222  9.81953648e-08, 3.49941166e-08, 1.24946640e-08, 4.46875334e-09,
223  1.60067129e-09, 5.74123782e-10, 2.06176797e-10, 7.41235161e-11,
224  2.66754511e-11, 9.60881878e-12, 3.46416156e-12, 1.24987740e-12,
225  4.51286453e-13, 1.63053459e-13, 5.89495073e-14, 2.13247750e-14,
226  7.71838266e-15, 2.79505752e-15, 1.01266123e-15, 3.67057597e-16,
227  1.33103515e-16, 4.82858338e-17, 1.75232770e-17, 6.36161716e-18,
228  2.31029936e-18, 8.39286110e-19;
229 
230  CALL_SUBTEST(res = bessel_k0(x);
231  verify_component_wise(res, expected););
232  }
233 
234  // Test Bessel function k0e. Reference results obtained with SciPy.
235  {
236  ArrayType x(42);
237  ArrayType expected(42);
238  ArrayType res(42);
239 
240  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
241  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
242  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
243  39., 40.;
244 
245  expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822,
246  0.6977616 , 0.60929767, 0.54780756, 0.50186313,
247  0.4658451 , 0.43662302, 0.41229555, 0.39163193,
248  0.3737955 , 0.35819488, 0.34439865, 0.33208364,
249  0.32100235, 0.31096159, 0.30180802, 0.29341821,
250  0.28569149, 0.27854488, 0.2719092 , 0.26572635,
251  0.25994703, 0.25452917, 0.2494366 , 0.24463801,
252  0.24010616, 0.23581722, 0.23175022, 0.22788667,
253  0.22421014, 0.22070602, 0.21736123, 0.21416406,
254  0.21110397, 0.20817141, 0.20535778, 0.20265524,
255  0.20005668, 0.19755558;
256 
257  CALL_SUBTEST(res = bessel_k0e(x);
258  verify_component_wise(res, expected););
259  }
260 
261  // Test Bessel function k1. Reference results obtained with SciPy.
262  {
263  ArrayType x(42);
264  ArrayType expected(42);
265  ArrayType res(42);
266 
267  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
268  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
269  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
270  39., 40.;
271 
272  expected << 3.74702597, 1.65644112, 6.01907230e-01, 1.39865882e-01,
273  4.01564311e-02, 1.24834989e-02, 4.04461345e-03, 1.34391972e-03,
274  4.54182487e-04, 1.55369212e-04, 5.36370164e-05, 1.86487735e-05,
275  6.52086067e-06, 2.29075746e-06, 8.07858841e-07, 2.85834365e-07,
276  1.01417294e-07, 3.60715712e-08, 1.28570417e-08, 4.59124963e-09,
277  1.64226697e-09, 5.88305797e-10, 2.11029922e-10, 7.57898116e-11,
278  2.72493059e-11, 9.80699893e-12, 3.53277807e-12, 1.27369078e-12,
279  4.59568940e-13, 1.65940011e-13, 5.99574032e-14, 2.16773200e-14,
280  7.84189960e-15, 2.83839927e-15, 1.02789171e-15, 3.72416929e-16,
281  1.34991783e-16, 4.89519373e-17, 1.77585196e-17, 6.44478588e-18,
282  2.33973340e-18, 8.49713195e-19;
283 
284  CALL_SUBTEST(res = bessel_k1(x);
285  verify_component_wise(res, expected););
286  }
287 
288  // Test Bessel function k1e. Reference results obtained with SciPy.
289  {
290  ArrayType x(42);
291  ArrayType expected(42);
292  ArrayType res(42);
293 
294  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
295  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
296  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
297  39., 40.;
298 
299  expected << 4.81127659, 2.73100971, 1.63615349, 1.03347685,
300  0.80656348, 0.68157595, 0.60027386, 0.54217591,
301  0.49807158, 0.46314909, 0.43462525, 0.41076657,
302  0.39043094, 0.37283175, 0.35740757, 0.34374563,
303  0.33153489, 0.32053597, 0.31056123, 0.30146131,
304  0.29311559, 0.2854255 , 0.27830958, 0.27169987,
305  0.26553913, 0.25977879, 0.25437733, 0.249299 ,
306  0.24451285, 0.23999191, 0.2357126 , 0.23165413,
307  0.22779816, 0.22412841, 0.22063036, 0.21729103,
308  0.21409878, 0.21104314, 0.20811462, 0.20530466,
309  0.20260547, 0.20000997;
310 
311  CALL_SUBTEST(res = bessel_k1e(x);
312  verify_component_wise(res, expected););
313  }
314 
315  // Test Bessel function y0. Reference results obtained with SciPy.
316  {
317  ArrayType x(42);
318  ArrayType expected(42);
319  ArrayType res(42);
320 
321  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
322  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
323  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
324  39., 40.;
325 
326  expected << -0.93157302, -0.44451873, 0.08825696, 0.51037567, 0.37685001,
327  -0.01694074, -0.30851763, -0.28819468, -0.02594974, 0.22352149,
328  0.2499367 , 0.05567117, -0.16884732, -0.22523731, -0.07820786,
329  0.12719257, 0.2054643 , 0.095811 , -0.0926372 , -0.18755216,
330  -0.10951969, 0.0626406 , 0.17020176, 0.1198876 , -0.03598179,
331  -0.15283403, -0.12724943, 0.01204463, 0.13521498, 0.13183647,
332  0.00948116, -0.11729573, -0.13383266, -0.02874248, 0.09913483,
333  0.13340405, 0.04579799, -0.08085609, -0.13071488, -0.06066076,
334  0.06262353, 0.12593642;
335 
336  CALL_SUBTEST(res = bessel_y0(x);
337  verify_component_wise(res, expected););
338  }
339 
340  // Test Bessel function y1. Reference results obtained with SciPy.
341  {
342  ArrayType x(42);
343  ArrayType expected(42);
344  ArrayType res(42);
345 
346  x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
347  13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
348  26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
349  39., 40.;
350 
351  expected << -2.70410523, -1.47147239, -0.78121282, -0.10703243,
352  0.32467442, 0.39792571, 0.14786314, -0.17501034, -0.30266724,
353  -0.15806046, 0.10431458, 0.24901542, 0.16370554, -0.05709922,
354  -0.21008141, -0.16664484, 0.02107363, 0.17797517, 0.16720504,
355  0.00815513, -0.14956011, -0.16551161, -0.03253926, 0.12340586,
356  0.1616692 , 0.05305978, -0.09882996, -0.15579655, -0.07025124,
357  0.07552213, 0.14803412, 0.08442557, -0.05337283, -0.13854483,
358  -0.09578012, 0.03238588, 0.12751273, 0.10445477, -0.01262946,
359  -0.11514066, -0.11056411, -0.00579351;
360 
361  CALL_SUBTEST(res = bessel_y1(x);
362  verify_component_wise(res, expected););
363  }
364 }
365 
366 EIGEN_DECLARE_TEST(bessel_functions)
367 {
368  CALL_SUBTEST_1(array_bessel_functions<ArrayXf>());
369  CALL_SUBTEST_2(array_bessel_functions<ArrayXd>());
370 }
Eigen::bessel_k1e
EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1e_op< typename Derived::Scalar >, const Derived > bessel_k1e(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:190
Eigen::bessel_i1e
EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1e_op< typename Derived::Scalar >, const Derived > bessel_i1e(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:100
Y
const char Y
Definition: test/EulerAngles.cpp:31
y
Scalar * y
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autogenerated on Tue Jul 4 2023 02:33:58