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b4688136 ESR |
1 | // { dg-do run { target c++11 } } |
2 | // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } | |
7c62b943 | 3 | // |
85ec4feb | 4 | // Copyright (C) 2016-2018 Free Software Foundation, Inc. |
7c62b943 BK |
5 | // |
6 | // This file is part of the GNU ISO C++ Library. This library is free | |
7 | // software; you can redistribute it and/or modify it under the | |
8 | // terms of the GNU General Public License as published by the | |
748086b7 | 9 | // Free Software Foundation; either version 3, or (at your option) |
7c62b943 BK |
10 | // any later version. |
11 | // | |
12 | // This library is distributed in the hope that it will be useful, | |
13 | // but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
15 | // GNU General Public License for more details. | |
16 | // | |
17 | // You should have received a copy of the GNU General Public License along | |
748086b7 JJ |
18 | // with this library; see the file COPYING3. If not see |
19 | // <http://www.gnu.org/licenses/>. | |
7c62b943 BK |
20 | |
21 | // sph_legendre | |
7c62b943 BK |
22 | // Compare against values generated by the GNU Scientific Library. |
23 | // The GSL can be found on the web: http://www.gnu.org/software/gsl/ | |
b4688136 | 24 | #include <limits> |
7c62b943 BK |
25 | #include <tr1/cmath> |
26 | #if defined(__TEST_DEBUG) | |
b4688136 ESR |
27 | # include <iostream> |
28 | # define VERIFY(A) \ | |
29 | if (!(A)) \ | |
30 | { \ | |
31 | std::cout << "line " << __LINE__ \ | |
32 | << " max_abs_frac = " << max_abs_frac \ | |
33 | << std::endl; \ | |
34 | } | |
7c62b943 | 35 | #else |
b4688136 | 36 | # include <testsuite_hooks.h> |
7c62b943 | 37 | #endif |
b4688136 | 38 | #include <specfun_testcase.h> |
7c62b943 BK |
39 | |
40 | // Test data for l=0, m=0. | |
b4688136 ESR |
41 | // max(|f - f_GSL|): 0.0000000000000000 at index 0 |
42 | // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 | |
43 | // mean(f - f_GSL): 0.0000000000000000 | |
44 | // variance(f - f_GSL): 0.0000000000000000 | |
45 | // stddev(f - f_GSL): 0.0000000000000000 | |
46 | const testcase_sph_legendre<double> | |
47 | data001[21] = | |
7c62b943 | 48 | { |
b4688136 ESR |
49 | { 0.28209479177387814, 0, 0, |
50 | 0.0000000000000000, 0.0 }, | |
51 | { 0.28209479177387814, 0, 0, | |
52 | 0.15707963267948966, 0.0 }, | |
53 | { 0.28209479177387814, 0, 0, | |
54 | 0.31415926535897931, 0.0 }, | |
55 | { 0.28209479177387814, 0, 0, | |
56 | 0.47123889803846897, 0.0 }, | |
57 | { 0.28209479177387814, 0, 0, | |
58 | 0.62831853071795862, 0.0 }, | |
59 | { 0.28209479177387814, 0, 0, | |
60 | 0.78539816339744828, 0.0 }, | |
61 | { 0.28209479177387814, 0, 0, | |
62 | 0.94247779607693793, 0.0 }, | |
63 | { 0.28209479177387814, 0, 0, | |
64 | 1.0995574287564276, 0.0 }, | |
65 | { 0.28209479177387814, 0, 0, | |
66 | 1.2566370614359172, 0.0 }, | |
67 | { 0.28209479177387814, 0, 0, | |
68 | 1.4137166941154069, 0.0 }, | |
69 | { 0.28209479177387814, 0, 0, | |
70 | 1.5707963267948966, 0.0 }, | |
71 | { 0.28209479177387814, 0, 0, | |
72 | 1.7278759594743862, 0.0 }, | |
73 | { 0.28209479177387814, 0, 0, | |
74 | 1.8849555921538759, 0.0 }, | |
75 | { 0.28209479177387814, 0, 0, | |
76 | 2.0420352248333655, 0.0 }, | |
77 | { 0.28209479177387814, 0, 0, | |
78 | 2.1991148575128552, 0.0 }, | |
79 | { 0.28209479177387814, 0, 0, | |
80 | 2.3561944901923448, 0.0 }, | |
81 | { 0.28209479177387814, 0, 0, | |
82 | 2.5132741228718345, 0.0 }, | |
83 | { 0.28209479177387814, 0, 0, | |
84 | 2.6703537555513241, 0.0 }, | |
85 | { 0.28209479177387814, 0, 0, | |
86 | 2.8274333882308138, 0.0 }, | |
87 | { 0.28209479177387814, 0, 0, | |
88 | 2.9845130209103035, 0.0 }, | |
89 | { 0.28209479177387814, 0, 0, | |
90 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 91 | }; |
b4688136 | 92 | const double toler001 = 2.5000000000000020e-13; |
7c62b943 | 93 | |
b4688136 ESR |
94 | // Test data for l=1, m=0. |
95 | // max(|f - f_GSL|): 0.0000000000000000 at index 0 | |
96 | // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 | |
97 | // mean(f - f_GSL): 0.0000000000000000 | |
98 | // variance(f - f_GSL): 0.0000000000000000 | |
99 | // stddev(f - f_GSL): 0.0000000000000000 | |
100 | const testcase_sph_legendre<double> | |
101 | data002[21] = | |
7c62b943 | 102 | { |
b4688136 ESR |
103 | { 0.48860251190291992, 1, 0, |
104 | 0.0000000000000000, 0.0 }, | |
105 | { 0.48258700419201095, 1, 0, | |
106 | 0.15707963267948966, 0.0 }, | |
107 | { 0.46468860282345237, 1, 0, | |
108 | 0.31415926535897931, 0.0 }, | |
109 | { 0.43534802584032634, 1, 0, | |
110 | 0.47123889803846897, 0.0 }, | |
111 | { 0.39528773562374969, 1, 0, | |
112 | 0.62831853071795862, 0.0 }, | |
113 | { 0.34549414947133550, 1, 0, | |
114 | 0.78539816339744828, 0.0 }, | |
115 | { 0.28719335072959395, 1, 0, | |
116 | 0.94247779607693793, 0.0 }, | |
117 | { 0.22182089855280449, 1, 0, | |
118 | 1.0995574287564276, 0.0 }, | |
119 | { 0.15098647967228981, 1, 0, | |
120 | 1.2566370614359172, 0.0 }, | |
121 | { 0.076434272566846345, 1, 0, | |
122 | 1.4137166941154069, 0.0 }, | |
123 | { 2.9918275112863332e-17, 1, 0, | |
124 | 1.5707963267948966, 0.0 }, | |
125 | { -0.076434272566846290, 1, 0, | |
126 | 1.7278759594743862, 0.0 }, | |
127 | { -0.15098647967228976, 1, 0, | |
128 | 1.8849555921538759, 0.0 }, | |
129 | { -0.22182089855280446, 1, 0, | |
130 | 2.0420352248333655, 0.0 }, | |
131 | { -0.28719335072959384, 1, 0, | |
132 | 2.1991148575128552, 0.0 }, | |
133 | { -0.34549414947133544, 1, 0, | |
134 | 2.3561944901923448, 0.0 }, | |
135 | { -0.39528773562374975, 1, 0, | |
136 | 2.5132741228718345, 0.0 }, | |
137 | { -0.43534802584032628, 1, 0, | |
138 | 2.6703537555513241, 0.0 }, | |
139 | { -0.46468860282345231, 1, 0, | |
140 | 2.8274333882308138, 0.0 }, | |
141 | { -0.48258700419201095, 1, 0, | |
142 | 2.9845130209103035, 0.0 }, | |
143 | { -0.48860251190291992, 1, 0, | |
144 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 145 | }; |
b4688136 | 146 | const double toler002 = 2.5000000000000020e-13; |
7c62b943 | 147 | |
b4688136 ESR |
148 | // Test data for l=1, m=1. |
149 | // max(|f - f_GSL|): 1.9984014443252818e-15 at index 9 | |
150 | // max(|f - f_GSL| / |f_GSL|): 5.9507621559271917e-15 | |
151 | // mean(f - f_GSL): 1.1981156807413147e-15 | |
152 | // variance(f - f_GSL): 7.5362762183006766e-32 | |
153 | // stddev(f - f_GSL): 2.7452278991553101e-16 | |
154 | const testcase_sph_legendre<double> | |
155 | data003[21] = | |
7c62b943 | 156 | { |
b4688136 ESR |
157 | { 0.0000000000000000, 1, 1, |
158 | 0.0000000000000000, 0.0 }, | |
159 | { -0.054047192447078167, 1, 1, | |
160 | 0.15707963267948966, 0.0 }, | |
161 | { -0.10676356364376091, 1, 1, | |
162 | 0.31415926535897931, 0.0 }, | |
163 | { -0.15685106157558129, 1, 1, | |
164 | 0.47123889803846897, 0.0 }, | |
165 | { -0.20307636581258248, 1, 1, | |
166 | 0.62831853071795862, 0.0 }, | |
167 | { -0.24430125595146007, 1, 1, | |
168 | 0.78539816339744828, 0.0 }, | |
169 | { -0.27951063837942880, 1, 1, | |
170 | 0.94247779607693793, 0.0 }, | |
171 | { -0.30783754124787122, 1, 1, | |
172 | 1.0995574287564276, 0.0 }, | |
173 | { -0.32858446219656556, 1, 1, | |
174 | 1.2566370614359172, 0.0 }, | |
175 | { -0.34124054317667202, 1, 1, | |
176 | 1.4137166941154069, 0.0 }, | |
177 | { -0.34549414947133567, 1, 1, | |
178 | 1.5707963267948966, 0.0 }, | |
179 | { -0.34124054317667202, 1, 1, | |
180 | 1.7278759594743862, 0.0 }, | |
181 | { -0.32858446219656556, 1, 1, | |
182 | 1.8849555921538759, 0.0 }, | |
183 | { -0.30783754124787127, 1, 1, | |
184 | 2.0420352248333655, 0.0 }, | |
185 | { -0.27951063837942880, 1, 1, | |
186 | 2.1991148575128552, 0.0 }, | |
187 | { -0.24430125595146013, 1, 1, | |
188 | 2.3561944901923448, 0.0 }, | |
189 | { -0.20307636581258243, 1, 1, | |
190 | 2.5132741228718345, 0.0 }, | |
191 | { -0.15685106157558140, 1, 1, | |
192 | 2.6703537555513241, 0.0 }, | |
193 | { -0.10676356364376104, 1, 1, | |
194 | 2.8274333882308138, 0.0 }, | |
195 | { -0.054047192447078167, 1, 1, | |
196 | 2.9845130209103035, 0.0 }, | |
197 | { 0.0000000000000000, 1, 1, | |
198 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 199 | }; |
b4688136 | 200 | const double toler003 = 5.0000000000000039e-13; |
7c62b943 | 201 | |
b4688136 ESR |
202 | // Test data for l=2, m=0. |
203 | // max(|f - f_GSL|): 1.1102230246251565e-16 at index 0 | |
204 | // max(|f - f_GSL| / |f_GSL|): 3.1667226501700652e-15 | |
205 | // mean(f - f_GSL): -3.0233752009881492e-17 | |
206 | // variance(f - f_GSL): 3.4265646892248527e-34 | |
207 | // stddev(f - f_GSL): 1.8510982386747748e-17 | |
208 | const testcase_sph_legendre<double> | |
209 | data004[21] = | |
7c62b943 | 210 | { |
b4688136 ESR |
211 | { 0.63078313050504009, 2, 0, |
212 | 0.0000000000000000, 0.0 }, | |
213 | { 0.60762858760316585, 2, 0, | |
214 | 0.15707963267948966, 0.0 }, | |
215 | { 0.54043148688396603, 2, 0, | |
216 | 0.31415926535897931, 0.0 }, | |
217 | { 0.43576954875556589, 2, 0, | |
218 | 0.47123889803846897, 0.0 }, | |
219 | { 0.30388781294457567, 2, 0, | |
220 | 0.62831853071795862, 0.0 }, | |
221 | { 0.15769578262626011, 2, 0, | |
222 | 0.78539816339744828, 0.0 }, | |
223 | { 0.011503752307944374, 2, 0, | |
224 | 0.94247779607693793, 0.0 }, | |
225 | { -0.12037798350304570, 2, 0, | |
226 | 1.0995574287564276, 0.0 }, | |
227 | { -0.22503992163144576, 2, 0, | |
228 | 1.2566370614359172, 0.0 }, | |
229 | { -0.29223702235064597, 2, 0, | |
230 | 1.4137166941154069, 0.0 }, | |
231 | { -0.31539156525252005, 2, 0, | |
232 | 1.5707963267948966, 0.0 }, | |
233 | { -0.29223702235064597, 2, 0, | |
234 | 1.7278759594743862, 0.0 }, | |
235 | { -0.22503992163144584, 2, 0, | |
236 | 1.8849555921538759, 0.0 }, | |
237 | { -0.12037798350304577, 2, 0, | |
238 | 2.0420352248333655, 0.0 }, | |
239 | { 0.011503752307944164, 2, 0, | |
240 | 2.1991148575128552, 0.0 }, | |
241 | { 0.15769578262625994, 2, 0, | |
242 | 2.3561944901923448, 0.0 }, | |
243 | { 0.30388781294457579, 2, 0, | |
244 | 2.5132741228718345, 0.0 }, | |
245 | { 0.43576954875556562, 2, 0, | |
246 | 2.6703537555513241, 0.0 }, | |
247 | { 0.54043148688396569, 2, 0, | |
248 | 2.8274333882308138, 0.0 }, | |
249 | { 0.60762858760316585, 2, 0, | |
250 | 2.9845130209103035, 0.0 }, | |
251 | { 0.63078313050504009, 2, 0, | |
252 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 253 | }; |
b4688136 | 254 | const double toler004 = 2.5000000000000020e-13; |
7c62b943 | 255 | |
b4688136 ESR |
256 | // Test data for l=2, m=1. |
257 | // max(|f - f_GSL|): 2.2204460492503131e-15 at index 5 | |
258 | // max(|f - f_GSL| / |f_GSL|): 5.9294218689659490e-15 | |
259 | // mean(f - f_GSL): 6.6084703846736834e-19 | |
260 | // variance(f - f_GSL): 2.2927737433182295e-38 | |
261 | // stddev(f - f_GSL): 1.5141907882820546e-19 | |
262 | const testcase_sph_legendre<double> | |
263 | data005[21] = | |
7c62b943 | 264 | { |
b4688136 ESR |
265 | { 0.0000000000000000, 2, 1, |
266 | 0.0000000000000000, 0.0 }, | |
267 | { -0.11936529291378781, 2, 1, | |
268 | 0.15707963267948966, 0.0 }, | |
269 | { -0.22704627929027421, 2, 1, | |
270 | 0.31415926535897931, 0.0 }, | |
271 | { -0.31250239392538215, 2, 1, | |
272 | 0.47123889803846897, 0.0 }, | |
273 | { -0.36736859691086526, 2, 1, | |
274 | 0.62831853071795862, 0.0 }, | |
275 | { -0.38627420202318979, 2, 1, | |
276 | 0.78539816339744828, 0.0 }, | |
277 | { -0.36736859691086532, 2, 1, | |
278 | 0.94247779607693793, 0.0 }, | |
279 | { -0.31250239392538226, 2, 1, | |
280 | 1.0995574287564276, 0.0 }, | |
281 | { -0.22704627929027438, 2, 1, | |
282 | 1.2566370614359172, 0.0 }, | |
283 | { -0.11936529291378740, 2, 1, | |
284 | 1.4137166941154069, 0.0 }, | |
285 | { -4.7304946510089680e-17, 2, 1, | |
286 | 1.5707963267948966, 0.0 }, | |
287 | { 0.11936529291378731, 2, 1, | |
288 | 1.7278759594743862, 0.0 }, | |
289 | { 0.22704627929027429, 2, 1, | |
290 | 1.8849555921538759, 0.0 }, | |
291 | { 0.31250239392538226, 2, 1, | |
292 | 2.0420352248333655, 0.0 }, | |
293 | { 0.36736859691086521, 2, 1, | |
294 | 2.1991148575128552, 0.0 }, | |
295 | { 0.38627420202318979, 2, 1, | |
296 | 2.3561944901923448, 0.0 }, | |
297 | { 0.36736859691086526, 2, 1, | |
298 | 2.5132741228718345, 0.0 }, | |
299 | { 0.31250239392538232, 2, 1, | |
300 | 2.6703537555513241, 0.0 }, | |
301 | { 0.22704627929027449, 2, 1, | |
302 | 2.8274333882308138, 0.0 }, | |
303 | { 0.11936529291378781, 2, 1, | |
304 | 2.9845130209103035, 0.0 }, | |
305 | { 0.0000000000000000, 2, 1, | |
306 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 307 | }; |
b4688136 | 308 | const double toler005 = 5.0000000000000039e-13; |
7c62b943 | 309 | |
b4688136 ESR |
310 | // Test data for l=2, m=2. |
311 | // max(|f - f_GSL|): 2.2759572004815709e-15 at index 10 | |
312 | // max(|f - f_GSL| / |f_GSL|): 6.0197685443914339e-15 | |
313 | // mean(f - f_GSL): -1.0489294618073093e-15 | |
314 | // variance(f - f_GSL): 5.7763283331987012e-32 | |
315 | // stddev(f - f_GSL): 2.4033993287006430e-16 | |
316 | const testcase_sph_legendre<double> | |
317 | data006[21] = | |
7c62b943 | 318 | { |
b4688136 ESR |
319 | { 0.0000000000000000, 2, 2, |
320 | 0.0000000000000000, 0.0 }, | |
321 | { 0.0094528025561623485, 2, 2, | |
322 | 0.15707963267948966, 0.0 }, | |
323 | { 0.036885904048903732, 2, 2, | |
324 | 0.31415926535897931, 0.0 }, | |
325 | { 0.079613961366457681, 2, 2, | |
326 | 0.47123889803846897, 0.0 }, | |
327 | { 0.13345445455470126, 2, 2, | |
328 | 0.62831853071795862, 0.0 }, | |
329 | { 0.19313710101159490, 2, 2, | |
330 | 0.78539816339744828, 0.0 }, | |
331 | { 0.25281974746848851, 2, 2, | |
332 | 0.94247779607693793, 0.0 }, | |
333 | { 0.30666024065673209, 2, 2, | |
334 | 1.0995574287564276, 0.0 }, | |
335 | { 0.34938829797428600, 2, 2, | |
336 | 1.2566370614359172, 0.0 }, | |
337 | { 0.37682139946702753, 2, 2, | |
338 | 1.4137166941154069, 0.0 }, | |
339 | { 0.38627420202318985, 2, 2, | |
340 | 1.5707963267948966, 0.0 }, | |
341 | { 0.37682139946702753, 2, 2, | |
342 | 1.7278759594743862, 0.0 }, | |
343 | { 0.34938829797428606, 2, 2, | |
344 | 1.8849555921538759, 0.0 }, | |
345 | { 0.30666024065673214, 2, 2, | |
346 | 2.0420352248333655, 0.0 }, | |
347 | { 0.25281974746848856, 2, 2, | |
348 | 2.1991148575128552, 0.0 }, | |
349 | { 0.19313710101159498, 2, 2, | |
350 | 2.3561944901923448, 0.0 }, | |
351 | { 0.13345445455470123, 2, 2, | |
352 | 2.5132741228718345, 0.0 }, | |
353 | { 0.079613961366457764, 2, 2, | |
354 | 2.6703537555513241, 0.0 }, | |
355 | { 0.036885904048903809, 2, 2, | |
356 | 2.8274333882308138, 0.0 }, | |
357 | { 0.0094528025561623485, 2, 2, | |
358 | 2.9845130209103035, 0.0 }, | |
359 | { 0.0000000000000000, 2, 2, | |
360 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 361 | }; |
b4688136 | 362 | const double toler006 = 5.0000000000000039e-13; |
7c62b943 | 363 | |
b4688136 ESR |
364 | // Test data for l=5, m=0. |
365 | // max(|f - f_GSL|): 1.0547118733938987e-15 at index 18 | |
366 | // max(|f - f_GSL| / |f_GSL|): 2.9385557676213648e-15 | |
367 | // mean(f - f_GSL): -4.2955057500378082e-17 | |
368 | // variance(f - f_GSL): 9.6869690655191325e-35 | |
369 | // stddev(f - f_GSL): 9.8422401238331574e-18 | |
370 | const testcase_sph_legendre<double> | |
371 | data007[21] = | |
7c62b943 | 372 | { |
b4688136 ESR |
373 | { 0.93560257962738880, 5, 0, |
374 | 0.0000000000000000, 0.0 }, | |
375 | { 0.77014422942079852, 5, 0, | |
376 | 0.15707963267948966, 0.0 }, | |
377 | { 0.35892185032365348, 5, 0, | |
378 | 0.31415926535897931, 0.0 }, | |
379 | { -0.090214932090594294, 5, 0, | |
380 | 0.47123889803846897, 0.0 }, | |
381 | { -0.36214460396518905, 5, 0, | |
382 | 0.62831853071795862, 0.0 }, | |
383 | { -0.35145955579226906, 5, 0, | |
384 | 0.78539816339744828, 0.0 }, | |
385 | { -0.11441703594725193, 5, 0, | |
386 | 0.94247779607693793, 0.0 }, | |
387 | { 0.17248966720808107, 5, 0, | |
388 | 1.0995574287564276, 0.0 }, | |
389 | { 0.32128384287200523, 5, 0, | |
390 | 1.2566370614359172, 0.0 }, | |
391 | { 0.24377632246714948, 5, 0, | |
392 | 1.4137166941154069, 0.0 }, | |
393 | { 1.0741712853887687e-16, 5, 0, | |
394 | 1.5707963267948966, 0.0 }, | |
395 | { -0.24377632246714936, 5, 0, | |
396 | 1.7278759594743862, 0.0 }, | |
397 | { -0.32128384287200534, 5, 0, | |
398 | 1.8849555921538759, 0.0 }, | |
399 | { -0.17248966720808118, 5, 0, | |
400 | 2.0420352248333655, 0.0 }, | |
401 | { 0.11441703594725151, 5, 0, | |
402 | 2.1991148575128552, 0.0 }, | |
403 | { 0.35145955579226895, 5, 0, | |
404 | 2.3561944901923448, 0.0 }, | |
405 | { 0.36214460396518883, 5, 0, | |
406 | 2.5132741228718345, 0.0 }, | |
407 | { 0.090214932090594752, 5, 0, | |
408 | 2.6703537555513241, 0.0 }, | |
409 | { -0.35892185032365165, 5, 0, | |
410 | 2.8274333882308138, 0.0 }, | |
411 | { -0.77014422942079852, 5, 0, | |
412 | 2.9845130209103035, 0.0 }, | |
413 | { -0.93560257962738880, 5, 0, | |
414 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 415 | }; |
b4688136 | 416 | const double toler007 = 2.5000000000000020e-13; |
7c62b943 | 417 | |
b4688136 ESR |
418 | // Test data for l=5, m=1. |
419 | // max(|f - f_GSL|): 3.3306690738754696e-15 at index 2 | |
420 | // max(|f - f_GSL| / |f_GSL|): 6.7265986294921411e-15 | |
421 | // mean(f - f_GSL): 6.3573485100559560e-16 | |
422 | // variance(f - f_GSL): 2.1218337041113107e-32 | |
423 | // stddev(f - f_GSL): 1.4566515383273072e-16 | |
424 | const testcase_sph_legendre<double> | |
425 | data008[21] = | |
7c62b943 | 426 | { |
b4688136 ESR |
427 | { 0.0000000000000000, 5, 1, |
428 | 0.0000000000000000, 0.0 }, | |
429 | { -0.36712373713318402, 5, 1, | |
430 | 0.15707963267948966, 0.0 }, | |
431 | { -0.54610329010534708, 5, 1, | |
432 | 0.31415926535897931, 0.0 }, | |
433 | { -0.45381991493631763, 5, 1, | |
434 | 0.47123889803846897, 0.0 }, | |
435 | { -0.15679720635769906, 5, 1, | |
436 | 0.62831853071795862, 0.0 }, | |
437 | { 0.16985499419838601, 5, 1, | |
438 | 0.78539816339744828, 0.0 }, | |
439 | { 0.34468004499725169, 5, 1, | |
440 | 0.94247779607693793, 0.0 }, | |
441 | { 0.28349471119605985, 5, 1, | |
442 | 1.0995574287564276, 0.0 }, | |
443 | { 0.044286619339675815, 5, 1, | |
444 | 1.2566370614359172, 0.0 }, | |
445 | { -0.21193784177193470, 5, 1, | |
446 | 1.4137166941154069, 0.0 }, | |
447 | { -0.32028164857621527, 5, 1, | |
448 | 1.5707963267948966, 0.0 }, | |
449 | { -0.21193784177193487, 5, 1, | |
450 | 1.7278759594743862, 0.0 }, | |
451 | { 0.044286619339675592, 5, 1, | |
452 | 1.8849555921538759, 0.0 }, | |
453 | { 0.28349471119605973, 5, 1, | |
454 | 2.0420352248333655, 0.0 }, | |
455 | { 0.34468004499725174, 5, 1, | |
456 | 2.1991148575128552, 0.0 }, | |
457 | { 0.16985499419838640, 5, 1, | |
458 | 2.3561944901923448, 0.0 }, | |
459 | { -0.15679720635769961, 5, 1, | |
460 | 2.5132741228718345, 0.0 }, | |
461 | { -0.45381991493631768, 5, 1, | |
462 | 2.6703537555513241, 0.0 }, | |
463 | { -0.54610329010534753, 5, 1, | |
464 | 2.8274333882308138, 0.0 }, | |
465 | { -0.36712373713318402, 5, 1, | |
466 | 2.9845130209103035, 0.0 }, | |
467 | { 0.0000000000000000, 5, 1, | |
468 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 469 | }; |
b4688136 | 470 | const double toler008 = 5.0000000000000039e-13; |
7c62b943 | 471 | |
b4688136 ESR |
472 | // Test data for l=5, m=2. |
473 | // max(|f - f_GSL|): 2.6645352591003757e-15 at index 4 | |
474 | // max(|f - f_GSL| / |f_GSL|): 6.1144597746666128e-15 | |
475 | // mean(f - f_GSL): -4.3615904538845404e-17 | |
476 | // variance(f - f_GSL): 9.9873224258937960e-35 | |
477 | // stddev(f - f_GSL): 9.9936592026613535e-18 | |
478 | const testcase_sph_legendre<double> | |
479 | data009[21] = | |
7c62b943 | 480 | { |
b4688136 ESR |
481 | { 0.0000000000000000, 5, 2, |
482 | 0.0000000000000000, 0.0 }, | |
483 | { 0.078919441745546909, 5, 2, | |
484 | 0.15707963267948966, 0.0 }, | |
485 | { 0.26373799140437948, 5, 2, | |
486 | 0.31415926535897931, 0.0 }, | |
487 | { 0.43002359842080096, 5, 2, | |
488 | 0.47123889803846897, 0.0 }, | |
489 | { 0.45642486439050983, 5, 2, | |
490 | 0.62831853071795862, 0.0 }, | |
491 | { 0.29959604906083298, 5, 2, | |
492 | 0.78539816339744828, 0.0 }, | |
493 | { 0.023781239849532509, 5, 2, | |
494 | 0.94247779607693793, 0.0 }, | |
495 | { -0.23313989334673826, 5, 2, | |
496 | 1.0995574287564276, 0.0 }, | |
497 | { -0.33799912776303714, 5, 2, | |
498 | 1.2566370614359172, 0.0 }, | |
499 | { -0.23964508489529746, 5, 2, | |
500 | 1.4137166941154069, 0.0 }, | |
501 | { -1.0377480524338157e-16, 5, 2, | |
502 | 1.5707963267948966, 0.0 }, | |
503 | { 0.23964508489529732, 5, 2, | |
504 | 1.7278759594743862, 0.0 }, | |
505 | { 0.33799912776303714, 5, 2, | |
506 | 1.8849555921538759, 0.0 }, | |
507 | { 0.23313989334673843, 5, 2, | |
508 | 2.0420352248333655, 0.0 }, | |
509 | { -0.023781239849531916, 5, 2, | |
510 | 2.1991148575128552, 0.0 }, | |
511 | { -0.29959604906083270, 5, 2, | |
512 | 2.3561944901923448, 0.0 }, | |
513 | { -0.45642486439050983, 5, 2, | |
514 | 2.5132741228718345, 0.0 }, | |
515 | { -0.43002359842080118, 5, 2, | |
516 | 2.6703537555513241, 0.0 }, | |
517 | { -0.26373799140437981, 5, 2, | |
518 | 2.8274333882308138, 0.0 }, | |
519 | { -0.078919441745546909, 5, 2, | |
520 | 2.9845130209103035, 0.0 }, | |
521 | { 0.0000000000000000, 5, 2, | |
522 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 523 | }; |
b4688136 | 524 | const double toler009 = 5.0000000000000039e-13; |
7c62b943 | 525 | |
b4688136 ESR |
526 | // Test data for l=5, m=5. |
527 | // max(|f - f_GSL|): 2.3869795029440866e-15 at index 10 | |
528 | // max(|f - f_GSL| / |f_GSL|): 5.4714279627676651e-15 | |
529 | // mean(f - f_GSL): 7.7966720691209837e-16 | |
530 | // variance(f - f_GSL): 3.1913750060540917e-32 | |
531 | // stddev(f - f_GSL): 1.7864419962747438e-16 | |
532 | const testcase_sph_legendre<double> | |
533 | data010[21] = | |
7c62b943 | 534 | { |
b4688136 ESR |
535 | { 0.0000000000000000, 5, 5, |
536 | 0.0000000000000000, 0.0 }, | |
537 | { -4.3481439097910151e-05, 5, 5, | |
538 | 0.15707963267948966, 0.0 }, | |
539 | { -0.0013078367086431740, 5, 5, | |
540 | 0.31415926535897931, 0.0 }, | |
541 | { -0.0089510818191922761, 5, 5, | |
542 | 0.47123889803846897, 0.0 }, | |
543 | { -0.032563803777573910, 5, 5, | |
544 | 0.62831853071795862, 0.0 }, | |
545 | { -0.082047757105021241, 5, 5, | |
546 | 0.78539816339744828, 0.0 }, | |
547 | { -0.16085328164143806, 5, 5, | |
548 | 0.94247779607693793, 0.0 }, | |
549 | { -0.26064303436645381, 5, 5, | |
550 | 1.0995574287564276, 0.0 }, | |
551 | { -0.36113811790820571, 5, 5, | |
552 | 1.2566370614359172, 0.0 }, | |
553 | { -0.43625592459446139, 5, 5, | |
554 | 1.4137166941154069, 0.0 }, | |
555 | { -0.46413220344085809, 5, 5, | |
556 | 1.5707963267948966, 0.0 }, | |
557 | { -0.43625592459446144, 5, 5, | |
558 | 1.7278759594743862, 0.0 }, | |
559 | { -0.36113811790820577, 5, 5, | |
560 | 1.8849555921538759, 0.0 }, | |
561 | { -0.26064303436645381, 5, 5, | |
562 | 2.0420352248333655, 0.0 }, | |
563 | { -0.16085328164143822, 5, 5, | |
564 | 2.1991148575128552, 0.0 }, | |
565 | { -0.082047757105021310, 5, 5, | |
566 | 2.3561944901923448, 0.0 }, | |
567 | { -0.032563803777573896, 5, 5, | |
568 | 2.5132741228718345, 0.0 }, | |
569 | { -0.0089510818191923004, 5, 5, | |
570 | 2.6703537555513241, 0.0 }, | |
571 | { -0.0013078367086431812, 5, 5, | |
572 | 2.8274333882308138, 0.0 }, | |
573 | { -4.3481439097910151e-05, 5, 5, | |
574 | 2.9845130209103035, 0.0 }, | |
575 | { 0.0000000000000000, 5, 5, | |
576 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 577 | }; |
b4688136 | 578 | const double toler010 = 5.0000000000000039e-13; |
7c62b943 | 579 | |
b4688136 ESR |
580 | // Test data for l=10, m=0. |
581 | // max(|f - f_GSL|): 9.9920072216264089e-16 at index 18 | |
582 | // max(|f - f_GSL| / |f_GSL|): 4.3176588435352323e-15 | |
583 | // mean(f - f_GSL): 5.6171998269725183e-18 | |
584 | // variance(f - f_GSL): 1.6565290295473546e-36 | |
585 | // stddev(f - f_GSL): 1.2870621700397205e-18 | |
586 | const testcase_sph_legendre<double> | |
587 | data011[21] = | |
7c62b943 | 588 | { |
b4688136 ESR |
589 | { 1.2927207364566027, 10, 0, |
590 | 0.0000000000000000, 0.0 }, | |
591 | { 0.55288895150522011, 10, 0, | |
592 | 0.15707963267948966, 0.0 }, | |
593 | { -0.44874428379711329, 10, 0, | |
594 | 0.31415926535897931, 0.0 }, | |
595 | { -0.25532095827149687, 10, 0, | |
596 | 0.47123889803846897, 0.0 }, | |
597 | { 0.36625249688013994, 10, 0, | |
598 | 0.62831853071795862, 0.0 }, | |
599 | { 0.14880806329084206, 10, 0, | |
600 | 0.78539816339744828, 0.0 }, | |
601 | { -0.33533356797848740, 10, 0, | |
602 | 0.94247779607693793, 0.0 }, | |
603 | { -0.080639967662335665, 10, 0, | |
604 | 1.0995574287564276, 0.0 }, | |
605 | { 0.32197986450174521, 10, 0, | |
606 | 1.2566370614359172, 0.0 }, | |
607 | { 0.025713542103667848, 10, 0, | |
608 | 1.4137166941154069, 0.0 }, | |
609 | { -0.31813049373736707, 10, 0, | |
610 | 1.5707963267948966, 0.0 }, | |
611 | { 0.025713542103667528, 10, 0, | |
612 | 1.7278759594743862, 0.0 }, | |
613 | { 0.32197986450174543, 10, 0, | |
614 | 1.8849555921538759, 0.0 }, | |
615 | { -0.080639967662335416, 10, 0, | |
616 | 2.0420352248333655, 0.0 }, | |
617 | { -0.33533356797848757, 10, 0, | |
618 | 2.1991148575128552, 0.0 }, | |
619 | { 0.14880806329084156, 10, 0, | |
620 | 2.3561944901923448, 0.0 }, | |
621 | { 0.36625249688013961, 10, 0, | |
622 | 2.5132741228718345, 0.0 }, | |
623 | { -0.25532095827149576, 10, 0, | |
624 | 2.6703537555513241, 0.0 }, | |
625 | { -0.44874428379711545, 10, 0, | |
626 | 2.8274333882308138, 0.0 }, | |
627 | { 0.55288895150522011, 10, 0, | |
628 | 2.9845130209103035, 0.0 }, | |
629 | { 1.2927207364566027, 10, 0, | |
630 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 631 | }; |
b4688136 | 632 | const double toler011 = 2.5000000000000020e-13; |
7c62b943 | 633 | |
b4688136 ESR |
634 | // Test data for l=10, m=1. |
635 | // max(|f - f_GSL|): 6.2172489379008766e-15 at index 1 | |
636 | // max(|f - f_GSL| / |f_GSL|): 1.0515246092567303e-14 | |
637 | // mean(f - f_GSL): -3.3042351923367698e-17 | |
638 | // variance(f - f_GSL): 5.7319343582953255e-35 | |
639 | // stddev(f - f_GSL): 7.5709539414101082e-18 | |
640 | const testcase_sph_legendre<double> | |
641 | data012[21] = | |
7c62b943 | 642 | { |
b4688136 ESR |
643 | { 0.0000000000000000, 10, 1, |
644 | 0.0000000000000000, 0.0 }, | |
645 | { -0.74373723919064050, 10, 1, | |
646 | 0.15707963267948966, 0.0 }, | |
647 | { -0.29035110456209651, 10, 1, | |
648 | 0.31415926535897931, 0.0 }, | |
649 | { 0.42219282075271530, 10, 1, | |
650 | 0.47123889803846897, 0.0 }, | |
651 | { 0.17109256898931161, 10, 1, | |
652 | 0.62831853071795862, 0.0 }, | |
653 | { -0.35583574648544281, 10, 1, | |
654 | 0.78539816339744828, 0.0 }, | |
655 | { -0.10089212303544023, 10, 1, | |
656 | 0.94247779607693793, 0.0 }, | |
657 | { 0.32997652649321085, 10, 1, | |
658 | 1.0995574287564276, 0.0 }, | |
659 | { 0.047416376890032939, 10, 1, | |
660 | 1.2566370614359172, 0.0 }, | |
661 | { -0.31999356750295660, 10, 1, | |
662 | 1.4137166941154069, 0.0 }, | |
663 | { -2.0430664782290742e-16, 10, 1, | |
664 | 1.5707963267948966, 0.0 }, | |
665 | { 0.31999356750295660, 10, 1, | |
666 | 1.7278759594743862, 0.0 }, | |
667 | { -0.047416376890032544, 10, 1, | |
668 | 1.8849555921538759, 0.0 }, | |
669 | { -0.32997652649321096, 10, 1, | |
670 | 2.0420352248333655, 0.0 }, | |
671 | { 0.10089212303543935, 10, 1, | |
672 | 2.1991148575128552, 0.0 }, | |
673 | { 0.35583574648544292, 10, 1, | |
674 | 2.3561944901923448, 0.0 }, | |
675 | { -0.17109256898931269, 10, 1, | |
676 | 2.5132741228718345, 0.0 }, | |
677 | { -0.42219282075271569, 10, 1, | |
678 | 2.6703537555513241, 0.0 }, | |
679 | { 0.29035110456209601, 10, 1, | |
680 | 2.8274333882308138, 0.0 }, | |
681 | { 0.74373723919064050, 10, 1, | |
682 | 2.9845130209103035, 0.0 }, | |
683 | { 0.0000000000000000, 10, 1, | |
684 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 685 | }; |
b4688136 | 686 | const double toler012 = 1.0000000000000008e-12; |
7c62b943 | 687 | |
b4688136 ESR |
688 | // Test data for l=10, m=2. |
689 | // max(|f - f_GSL|): 3.3306690738754696e-15 at index 2 | |
690 | // max(|f - f_GSL| / |f_GSL|): 7.9132043938587384e-15 | |
691 | // mean(f - f_GSL): -3.3504944850294902e-16 | |
692 | // variance(f - f_GSL): 5.8935519794618406e-33 | |
693 | // stddev(f - f_GSL): 7.6769472965898634e-17 | |
694 | const testcase_sph_legendre<double> | |
695 | data013[21] = | |
7c62b943 | 696 | { |
b4688136 ESR |
697 | { 0.0000000000000000, 10, 2, |
698 | 0.0000000000000000, 0.0 }, | |
699 | { 0.34571695599980556, 10, 2, | |
700 | 0.15707963267948966, 0.0 }, | |
701 | { 0.62485535978198148, 10, 2, | |
702 | 0.31415926535897931, 0.0 }, | |
703 | { 0.098210039644716252, 10, 2, | |
704 | 0.47123889803846897, 0.0 }, | |
705 | { -0.41494799233049695, 10, 2, | |
706 | 0.62831853071795862, 0.0 }, | |
707 | { -0.081698973831472732, 10, 2, | |
708 | 0.78539816339744828, 0.0 }, | |
709 | { 0.35253132222271277, 10, 2, | |
710 | 0.94247779607693793, 0.0 }, | |
711 | { 0.049026298555980979, 10, 2, | |
712 | 1.0995574287564276, 0.0 }, | |
713 | { -0.32791246874130792, 10, 2, | |
714 | 1.2566370614359172, 0.0 }, | |
715 | { -0.016196782433946871, 10, 2, | |
716 | 1.4137166941154069, 0.0 }, | |
717 | { 0.32106263400438334, 10, 2, | |
718 | 1.5707963267948966, 0.0 }, | |
719 | { -0.016196782433946497, 10, 2, | |
720 | 1.7278759594743862, 0.0 }, | |
721 | { -0.32791246874130803, 10, 2, | |
722 | 1.8849555921538759, 0.0 }, | |
723 | { 0.049026298555980730, 10, 2, | |
724 | 2.0420352248333655, 0.0 }, | |
725 | { 0.35253132222271266, 10, 2, | |
726 | 2.1991148575128552, 0.0 }, | |
727 | { -0.081698973831472121, 10, 2, | |
728 | 2.3561944901923448, 0.0 }, | |
729 | { -0.41494799233049684, 10, 2, | |
730 | 2.5132741228718345, 0.0 }, | |
731 | { 0.098210039644715197, 10, 2, | |
732 | 2.6703537555513241, 0.0 }, | |
733 | { 0.62485535978198081, 10, 2, | |
734 | 2.8274333882308138, 0.0 }, | |
735 | { 0.34571695599980556, 10, 2, | |
736 | 2.9845130209103035, 0.0 }, | |
737 | { 0.0000000000000000, 10, 2, | |
738 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 739 | }; |
b4688136 | 740 | const double toler013 = 5.0000000000000039e-13; |
7c62b943 | 741 | |
b4688136 ESR |
742 | // Test data for l=10, m=5. |
743 | // max(|f - f_GSL|): 2.8310687127941492e-15 at index 4 | |
744 | // max(|f - f_GSL| / |f_GSL|): 6.7700052018114004e-15 | |
745 | // mean(f - f_GSL): 3.8329128231106644e-17 | |
746 | // variance(f - f_GSL): 7.7128908725222343e-35 | |
747 | // stddev(f - f_GSL): 8.7823065720357509e-18 | |
748 | const testcase_sph_legendre<double> | |
749 | data014[21] = | |
7c62b943 | 750 | { |
b4688136 ESR |
751 | { 0.0000000000000000, 10, 5, |
752 | 0.0000000000000000, 0.0 }, | |
753 | { -0.0030300124052750873, 10, 5, | |
754 | 0.15707963267948966, 0.0 }, | |
755 | { -0.070348585248056511, 10, 5, | |
756 | 0.31415926535897931, 0.0 }, | |
757 | { -0.30055029290703639, 10, 5, | |
758 | 0.47123889803846897, 0.0 }, | |
759 | { -0.49987818144009138, 10, 5, | |
760 | 0.62831853071795862, 0.0 }, | |
761 | { -0.28108771757150108, 10, 5, | |
762 | 0.78539816339744828, 0.0 }, | |
763 | { 0.22068081187249255, 10, 5, | |
764 | 0.94247779607693793, 0.0 }, | |
765 | { 0.33689502212592121, 10, 5, | |
766 | 1.0995574287564276, 0.0 }, | |
767 | { -0.086095515520764110, 10, 5, | |
768 | 1.2566370614359172, 0.0 }, | |
769 | { -0.33935827318511558, 10, 5, | |
770 | 1.4137166941154069, 0.0 }, | |
771 | { -1.9213014340664546e-16, 10, 5, | |
772 | 1.5707963267948966, 0.0 }, | |
773 | { 0.33935827318511558, 10, 5, | |
774 | 1.7278759594743862, 0.0 }, | |
775 | { 0.086095515520764512, 10, 5, | |
776 | 1.8849555921538759, 0.0 }, | |
777 | { -0.33689502212592104, 10, 5, | |
778 | 2.0420352248333655, 0.0 }, | |
779 | { -0.22068081187249344, 10, 5, | |
780 | 2.1991148575128552, 0.0 }, | |
781 | { 0.28108771757150064, 10, 5, | |
782 | 2.3561944901923448, 0.0 }, | |
783 | { 0.49987818144009155, 10, 5, | |
784 | 2.5132741228718345, 0.0 }, | |
785 | { 0.30055029290703672, 10, 5, | |
786 | 2.6703537555513241, 0.0 }, | |
787 | { 0.070348585248056802, 10, 5, | |
788 | 2.8274333882308138, 0.0 }, | |
789 | { 0.0030300124052750873, 10, 5, | |
790 | 2.9845130209103035, 0.0 }, | |
791 | { 0.0000000000000000, 10, 5, | |
792 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 793 | }; |
b4688136 | 794 | const double toler014 = 5.0000000000000039e-13; |
7c62b943 | 795 | |
b4688136 ESR |
796 | // Test data for l=10, m=10. |
797 | // max(|f - f_GSL|): 2.8865798640254070e-15 at index 10 | |
798 | // max(|f - f_GSL| / |f_GSL|): 5.5362170773729674e-15 | |
799 | // mean(f - f_GSL): -6.6245801611758948e-16 | |
800 | // variance(f - f_GSL): 2.3039657713718755e-32 | |
801 | // stddev(f - f_GSL): 1.5178820017945649e-16 | |
802 | const testcase_sph_legendre<double> | |
803 | data015[21] = | |
7c62b943 | 804 | { |
b4688136 ESR |
805 | { 0.0000000000000000, 10, 10, |
806 | 0.0000000000000000, 0.0 }, | |
807 | { 4.7624282733345673e-09, 10, 10, | |
808 | 0.15707963267948966, 0.0 }, | |
809 | { 4.3085156534549315e-06, 10, 10, | |
810 | 0.31415926535897931, 0.0 }, | |
811 | { 0.00020182347649472387, 10, 10, | |
812 | 0.47123889803846897, 0.0 }, | |
813 | { 0.0026711045506511706, 10, 10, | |
814 | 0.62831853071795862, 0.0 }, | |
815 | { 0.016957196623256909, 10, 10, | |
816 | 0.78539816339744828, 0.0 }, | |
817 | { 0.065174916004990271, 10, 10, | |
818 | 0.94247779607693793, 0.0 }, | |
819 | { 0.17112476903017845, 10, 10, | |
820 | 1.0995574287564276, 0.0 }, | |
821 | { 0.32852414199733554, 10, 10, | |
822 | 1.2566370614359172, 0.0 }, | |
823 | { 0.47940582314838287, 10, 10, | |
824 | 1.4137166941154069, 0.0 }, | |
825 | { 0.54263029194422152, 10, 10, | |
826 | 1.5707963267948966, 0.0 }, | |
827 | { 0.47940582314838293, 10, 10, | |
828 | 1.7278759594743862, 0.0 }, | |
829 | { 0.32852414199733571, 10, 10, | |
830 | 1.8849555921538759, 0.0 }, | |
831 | { 0.17112476903017851, 10, 10, | |
832 | 2.0420352248333655, 0.0 }, | |
833 | { 0.065174916004990410, 10, 10, | |
834 | 2.1991148575128552, 0.0 }, | |
835 | { 0.016957196623256943, 10, 10, | |
836 | 2.3561944901923448, 0.0 }, | |
837 | { 0.0026711045506511684, 10, 10, | |
838 | 2.5132741228718345, 0.0 }, | |
839 | { 0.00020182347649472493, 10, 10, | |
840 | 2.6703537555513241, 0.0 }, | |
841 | { 4.3085156534549772e-06, 10, 10, | |
842 | 2.8274333882308138, 0.0 }, | |
843 | { 4.7624282733345673e-09, 10, 10, | |
844 | 2.9845130209103035, 0.0 }, | |
845 | { 0.0000000000000000, 10, 10, | |
846 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 847 | }; |
b4688136 | 848 | const double toler015 = 5.0000000000000039e-13; |
7c62b943 | 849 | |
b4688136 ESR |
850 | // Test data for l=20, m=0. |
851 | // max(|f - f_GSL|): 1.2212453270876722e-15 at index 1 | |
852 | // max(|f - f_GSL| / |f_GSL|): 2.0731910827878347e-15 | |
853 | // mean(f - f_GSL): 1.1102230246251565e-16 | |
854 | // variance(f - f_GSL): 6.4711246131411122e-34 | |
855 | // stddev(f - f_GSL): 2.5438405243138007e-17 | |
856 | const testcase_sph_legendre<double> | |
857 | data016[21] = | |
7c62b943 | 858 | { |
b4688136 ESR |
859 | { 1.8062879984608917, 20, 0, |
860 | 0.0000000000000000, 0.0 }, | |
861 | { -0.58906549291416732, 20, 0, | |
862 | 0.15707963267948966, 0.0 }, | |
863 | { 0.45624611402342063, 20, 0, | |
864 | 0.31415926535897931, 0.0 }, | |
865 | { -0.39955402700466724, 20, 0, | |
866 | 0.47123889803846897, 0.0 }, | |
867 | { 0.36818552901640805, 20, 0, | |
868 | 0.62831853071795862, 0.0 }, | |
869 | { -0.34873131330857743, 20, 0, | |
870 | 0.78539816339744828, 0.0 }, | |
871 | { 0.33600882829186468, 20, 0, | |
872 | 0.94247779607693793, 0.0 }, | |
873 | { -0.32759286308122931, 20, 0, | |
874 | 1.0995574287564276, 0.0 }, | |
875 | { 0.32222458068091325, 20, 0, | |
876 | 1.2566370614359172, 0.0 }, | |
877 | { -0.31922731037135965, 20, 0, | |
878 | 1.4137166941154069, 0.0 }, | |
879 | { 0.31826262039531755, 20, 0, | |
880 | 1.5707963267948966, 0.0 }, | |
881 | { -0.31922731037135971, 20, 0, | |
882 | 1.7278759594743862, 0.0 }, | |
883 | { 0.32222458068091342, 20, 0, | |
884 | 1.8849555921538759, 0.0 }, | |
885 | { -0.32759286308122926, 20, 0, | |
886 | 2.0420352248333655, 0.0 }, | |
887 | { 0.33600882829186518, 20, 0, | |
888 | 2.1991148575128552, 0.0 }, | |
889 | { -0.34873131330857782, 20, 0, | |
890 | 2.3561944901923448, 0.0 }, | |
891 | { 0.36818552901640772, 20, 0, | |
892 | 2.5132741228718345, 0.0 }, | |
893 | { -0.39955402700466824, 20, 0, | |
894 | 2.6703537555513241, 0.0 }, | |
895 | { 0.45624611402342408, 20, 0, | |
896 | 2.8274333882308138, 0.0 }, | |
897 | { -0.58906549291416732, 20, 0, | |
898 | 2.9845130209103035, 0.0 }, | |
899 | { 1.8062879984608917, 20, 0, | |
900 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 901 | }; |
b4688136 | 902 | const double toler016 = 2.5000000000000020e-13; |
7c62b943 | 903 | |
b4688136 ESR |
904 | // Test data for l=20, m=1. |
905 | // max(|f - f_GSL|): 6.2727600891321345e-15 at index 1 | |
906 | // max(|f - f_GSL| / |f_GSL|): 1.3664592043119372e-14 | |
907 | // mean(f - f_GSL): 2.8416422654096149e-17 | |
908 | // variance(f - f_GSL): 4.2393386513952014e-35 | |
909 | // stddev(f - f_GSL): 6.5110203896126770e-18 | |
910 | const testcase_sph_legendre<double> | |
911 | data017[21] = | |
7c62b943 | 912 | { |
b4688136 ESR |
913 | { 0.0000000000000000, 20, 1, |
914 | 0.0000000000000000, 0.0 }, | |
915 | { -0.45905213045059046, 20, 1, | |
916 | 0.15707963267948966, 0.0 }, | |
917 | { 0.31166370423309414, 20, 1, | |
918 | 0.31415926535897931, 0.0 }, | |
919 | { -0.23278757741246778, 20, 1, | |
920 | 0.47123889803846897, 0.0 }, | |
921 | { 0.17937240823503983, 20, 1, | |
922 | 0.62831853071795862, 0.0 }, | |
923 | { -0.13857299972299839, 20, 1, | |
924 | 0.78539816339744828, 0.0 }, | |
925 | { 0.10495324841927815, 20, 1, | |
926 | 0.94247779607693793, 0.0 }, | |
927 | { -0.075707774352163665, 20, 1, | |
928 | 1.0995574287564276, 0.0 }, | |
929 | { 0.049168697683476224, 20, 1, | |
930 | 1.2566370614359172, 0.0 }, | |
931 | { -0.024216050551253303, 20, 1, | |
932 | 1.4137166941154069, 0.0 }, | |
933 | { 3.9938443510694310e-16, 20, 1, | |
934 | 1.5707963267948966, 0.0 }, | |
935 | { 0.024216050551252380, 20, 1, | |
936 | 1.7278759594743862, 0.0 }, | |
937 | { -0.049168697683475482, 20, 1, | |
938 | 1.8849555921538759, 0.0 }, | |
939 | { 0.075707774352163346, 20, 1, | |
940 | 2.0420352248333655, 0.0 }, | |
941 | { -0.10495324841927638, 20, 1, | |
942 | 2.1991148575128552, 0.0 }, | |
943 | { 0.13857299972299741, 20, 1, | |
944 | 2.3561944901923448, 0.0 }, | |
945 | { -0.17937240823504172, 20, 1, | |
946 | 2.5132741228718345, 0.0 }, | |
947 | { 0.23278757741246703, 20, 1, | |
948 | 2.6703537555513241, 0.0 }, | |
949 | { -0.31166370423309253, 20, 1, | |
950 | 2.8274333882308138, 0.0 }, | |
951 | { 0.45905213045059046, 20, 1, | |
952 | 2.9845130209103035, 0.0 }, | |
953 | { 0.0000000000000000, 20, 1, | |
954 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 955 | }; |
b4688136 | 956 | const double toler017 = 1.0000000000000008e-12; |
7c62b943 | 957 | |
b4688136 ESR |
958 | // Test data for l=20, m=2. |
959 | // max(|f - f_GSL|): 3.2196467714129540e-15 at index 2 | |
960 | // max(|f - f_GSL| / |f_GSL|): 7.1072009465107655e-15 | |
961 | // mean(f - f_GSL): 9.2518585385429716e-17 | |
962 | // variance(f - f_GSL): 4.4938365369035506e-34 | |
963 | // stddev(f - f_GSL): 2.1198671035948340e-17 | |
964 | const testcase_sph_legendre<double> | |
965 | data018[21] = | |
7c62b943 | 966 | { |
b4688136 ESR |
967 | { 0.0000000000000000, 20, 2, |
968 | 0.0000000000000000, 0.0 }, | |
969 | { 0.87399805141574205, 20, 2, | |
970 | 0.15707963267948966, 0.0 }, | |
971 | { -0.55116854080894906, 20, 2, | |
972 | 0.31415926535897931, 0.0 }, | |
973 | { 0.44520137308557572, 20, 2, | |
974 | 0.47123889803846897, 0.0 }, | |
975 | { -0.39321637877908278, 20, 2, | |
976 | 0.62831853071795862, 0.0 }, | |
977 | { 0.36312025711350954, 20, 2, | |
978 | 0.78539816339744828, 0.0 }, | |
979 | { -0.34427103004873089, 20, 2, | |
980 | 0.94247779607693793, 0.0 }, | |
981 | { 0.33214917638387642, 20, 2, | |
982 | 1.0995574287564276, 0.0 }, | |
983 | { -0.32455734448839091, 20, 2, | |
984 | 1.2566370614359172, 0.0 }, | |
985 | { 0.32036529628513255, 20, 2, | |
986 | 1.4137166941154069, 0.0 }, | |
987 | { -0.31902310563819986, 20, 2, | |
988 | 1.5707963267948966, 0.0 }, | |
989 | { 0.32036529628513261, 20, 2, | |
990 | 1.7278759594743862, 0.0 }, | |
991 | { -0.32455734448839102, 20, 2, | |
992 | 1.8849555921538759, 0.0 }, | |
993 | { 0.33214917638387659, 20, 2, | |
994 | 2.0420352248333655, 0.0 }, | |
995 | { -0.34427103004873105, 20, 2, | |
996 | 2.1991148575128552, 0.0 }, | |
997 | { 0.36312025711350981, 20, 2, | |
998 | 2.3561944901923448, 0.0 }, | |
999 | { -0.39321637877908228, 20, 2, | |
1000 | 2.5132741228718345, 0.0 }, | |
1001 | { 0.44520137308557650, 20, 2, | |
1002 | 2.6703537555513241, 0.0 }, | |
1003 | { -0.55116854080895039, 20, 2, | |
1004 | 2.8274333882308138, 0.0 }, | |
1005 | { 0.87399805141574205, 20, 2, | |
1006 | 2.9845130209103035, 0.0 }, | |
1007 | { 0.0000000000000000, 20, 2, | |
1008 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1009 | }; |
b4688136 | 1010 | const double toler018 = 5.0000000000000039e-13; |
7c62b943 | 1011 | |
b4688136 ESR |
1012 | // Test data for l=20, m=5. |
1013 | // max(|f - f_GSL|): 3.7747582837255322e-15 at index 2 | |
1014 | // max(|f - f_GSL| / |f_GSL|): 2.9846361325102863e-14 | |
1015 | // mean(f - f_GSL): -1.9825411154020758e-17 | |
1016 | // variance(f - f_GSL): 2.0634963689863462e-35 | |
1017 | // stddev(f - f_GSL): 4.5425723648460969e-18 | |
1018 | const testcase_sph_legendre<double> | |
1019 | data019[21] = | |
7c62b943 | 1020 | { |
b4688136 ESR |
1021 | { 0.0000000000000000, 20, 5, |
1022 | 0.0000000000000000, 0.0 }, | |
1023 | { -0.10024848623505046, 20, 5, | |
1024 | 0.15707963267948966, 0.0 }, | |
1025 | { -0.68115361075940650, 20, 5, | |
1026 | 0.31415926535897931, 0.0 }, | |
1027 | { 0.31774532551156298, 20, 5, | |
1028 | 0.47123889803846897, 0.0 }, | |
1029 | { -0.16011868165390658, 20, 5, | |
1030 | 0.62831853071795862, 0.0 }, | |
1031 | { 0.085844143304115578, 20, 5, | |
1032 | 0.78539816339744828, 0.0 }, | |
1033 | { -0.047467540840863798, 20, 5, | |
1034 | 0.94247779607693793, 0.0 }, | |
1035 | { 0.026283575189471796, 20, 5, | |
1036 | 1.0995574287564276, 0.0 }, | |
1037 | { -0.013891104052597688, 20, 5, | |
1038 | 1.2566370614359172, 0.0 }, | |
1039 | { 0.0059873308239496957, 20, 5, | |
1040 | 1.4137166941154069, 0.0 }, | |
1041 | { 3.9355286582083051e-16, 20, 5, | |
1042 | 1.5707963267948966, 0.0 }, | |
1043 | { -0.0059873308239503324, 20, 5, | |
1044 | 1.7278759594743862, 0.0 }, | |
1045 | { 0.013891104052598547, 20, 5, | |
1046 | 1.8849555921538759, 0.0 }, | |
1047 | { -0.026283575189472153, 20, 5, | |
1048 | 2.0420352248333655, 0.0 }, | |
1049 | { 0.047467540840865928, 20, 5, | |
1050 | 2.1991148575128552, 0.0 }, | |
1051 | { -0.085844143304117007, 20, 5, | |
1052 | 2.3561944901923448, 0.0 }, | |
1053 | { 0.16011868165390544, 20, 5, | |
1054 | 2.5132741228718345, 0.0 }, | |
1055 | { -0.31774532551156381, 20, 5, | |
1056 | 2.6703537555513241, 0.0 }, | |
1057 | { 0.68115361075940484, 20, 5, | |
1058 | 2.8274333882308138, 0.0 }, | |
1059 | { 0.10024848623505046, 20, 5, | |
1060 | 2.9845130209103035, 0.0 }, | |
1061 | { 0.0000000000000000, 20, 5, | |
1062 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1063 | }; |
b4688136 | 1064 | const double toler019 = 2.5000000000000015e-12; |
7c62b943 | 1065 | |
b4688136 ESR |
1066 | // Test data for l=20, m=10. |
1067 | // max(|f - f_GSL|): 2.3314683517128287e-15 at index 4 | |
1068 | // max(|f - f_GSL| / |f_GSL|): 1.0575432165608034e-14 | |
1069 | // mean(f - f_GSL): -1.4002922808555493e-16 | |
1070 | // variance(f - f_GSL): 1.0294296977074090e-33 | |
1071 | // stddev(f - f_GSL): 3.2084726860414586e-17 | |
1072 | const testcase_sph_legendre<double> | |
1073 | data020[21] = | |
7c62b943 | 1074 | { |
b4688136 ESR |
1075 | { 0.0000000000000000, 20, 10, |
1076 | 0.0000000000000000, 0.0 }, | |
1077 | { 3.0595797603707888e-05, 20, 10, | |
1078 | 0.15707963267948966, 0.0 }, | |
1079 | { 0.015924453916396863, 20, 10, | |
1080 | 0.31415926535897931, 0.0 }, | |
1081 | { 0.26588079118745744, 20, 10, | |
1082 | 0.47123889803846897, 0.0 }, | |
1083 | { 0.54045081420686736, 20, 10, | |
1084 | 0.62831853071795862, 0.0 }, | |
1085 | { -0.28215279394285531, 20, 10, | |
1086 | 0.78539816339744828, 0.0 }, | |
1087 | { 0.0085297337582239223, 20, 10, | |
1088 | 0.94247779607693793, 0.0 }, | |
1089 | { 0.16930127953533738, 20, 10, | |
1090 | 1.0995574287564276, 0.0 }, | |
1091 | { -0.27215134048018325, 20, 10, | |
1092 | 1.2566370614359172, 0.0 }, | |
1093 | { 0.32456597088029526, 20, 10, | |
1094 | 1.4137166941154069, 0.0 }, | |
1095 | { -0.34057893241353715, 20, 10, | |
1096 | 1.5707963267948966, 0.0 }, | |
1097 | { 0.32456597088029493, 20, 10, | |
1098 | 1.7278759594743862, 0.0 }, | |
1099 | { -0.27215134048018291, 20, 10, | |
1100 | 1.8849555921538759, 0.0 }, | |
1101 | { 0.16930127953533702, 20, 10, | |
1102 | 2.0420352248333655, 0.0 }, | |
1103 | { 0.0085297337582257438, 20, 10, | |
1104 | 2.1991148575128552, 0.0 }, | |
1105 | { -0.28215279394285619, 20, 10, | |
1106 | 2.3561944901923448, 0.0 }, | |
1107 | { 0.54045081420686869, 20, 10, | |
1108 | 2.5132741228718345, 0.0 }, | |
1109 | { 0.26588079118745828, 20, 10, | |
1110 | 2.6703537555513241, 0.0 }, | |
1111 | { 0.015924453916397002, 20, 10, | |
1112 | 2.8274333882308138, 0.0 }, | |
1113 | { 3.0595797603707888e-05, 20, 10, | |
1114 | 2.9845130209103035, 0.0 }, | |
1115 | { 0.0000000000000000, 20, 10, | |
1116 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1117 | }; |
b4688136 | 1118 | const double toler020 = 1.0000000000000008e-12; |
7c62b943 | 1119 | |
b4688136 ESR |
1120 | // Test data for l=20, m=20. |
1121 | // max(|f - f_GSL|): 2.6645352591003757e-15 at index 10 | |
1122 | // max(|f - f_GSL| / |f_GSL|): 4.5133454703584717e-15 | |
1123 | // mean(f - f_GSL): -4.3857545834694365e-16 | |
1124 | // variance(f - f_GSL): 1.0098292714872165e-32 | |
1125 | // stddev(f - f_GSL): 1.0049026179124106e-16 | |
1126 | const testcase_sph_legendre<double> | |
1127 | data021[21] = | |
7c62b943 | 1128 | { |
b4688136 ESR |
1129 | { 0.0000000000000000, 20, 20, |
1130 | 0.0000000000000000, 0.0 }, | |
1131 | { 4.9264471419250786e-17, 20, 20, | |
1132 | 0.15707963267948966, 0.0 }, | |
1133 | { 4.0321091681530921e-11, 20, 20, | |
1134 | 0.31415926535897931, 0.0 }, | |
1135 | { 8.8474944184471664e-08, 20, 20, | |
1136 | 0.47123889803846897, 0.0 }, | |
1137 | { 1.5497395129387791e-05, 20, 20, | |
1138 | 0.62831853071795862, 0.0 }, | |
1139 | { 0.00062457564282984495, 20, 20, | |
1140 | 0.78539816339744828, 0.0 }, | |
1141 | { 0.0092265192458967308, 20, 20, | |
1142 | 0.94247779607693793, 0.0 }, | |
1143 | { 0.063606673236323297, 20, 20, | |
1144 | 1.0995574287564276, 0.0 }, | |
1145 | { 0.23442909509776316, 20, 20, | |
1146 | 1.2566370614359172, 0.0 }, | |
1147 | { 0.49921030481087009, 20, 20, | |
1148 | 1.4137166941154069, 0.0 }, | |
1149 | { 0.63956545825776223, 20, 20, | |
1150 | 1.5707963267948966, 0.0 }, | |
1151 | { 0.49921030481087025, 20, 20, | |
1152 | 1.7278759594743862, 0.0 }, | |
1153 | { 0.23442909509776336, 20, 20, | |
1154 | 1.8849555921538759, 0.0 }, | |
1155 | { 0.063606673236323324, 20, 20, | |
1156 | 2.0420352248333655, 0.0 }, | |
1157 | { 0.0092265192458967742, 20, 20, | |
1158 | 2.1991148575128552, 0.0 }, | |
1159 | { 0.00062457564282984766, 20, 20, | |
1160 | 2.3561944901923448, 0.0 }, | |
1161 | { 1.5497395129387764e-05, 20, 20, | |
1162 | 2.5132741228718345, 0.0 }, | |
1163 | { 8.8474944184472617e-08, 20, 20, | |
1164 | 2.6703537555513241, 0.0 }, | |
1165 | { 4.0321091681531780e-11, 20, 20, | |
1166 | 2.8274333882308138, 0.0 }, | |
1167 | { 4.9264471419250786e-17, 20, 20, | |
1168 | 2.9845130209103035, 0.0 }, | |
1169 | { 0.0000000000000000, 20, 20, | |
1170 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1171 | }; |
b4688136 | 1172 | const double toler021 = 2.5000000000000020e-13; |
7c62b943 | 1173 | |
b4688136 ESR |
1174 | // Test data for l=50, m=0. |
1175 | // max(|f - f_GSL|): 4.8849813083506888e-15 at index 1 | |
1176 | // max(|f - f_GSL| / |f_GSL|): 9.1896305557688689e-15 | |
1177 | // mean(f - f_GSL): -4.0592529337857286e-16 | |
1178 | // variance(f - f_GSL): 8.6507055497352237e-33 | |
1179 | // stddev(f - f_GSL): 9.3009169170223341e-17 | |
1180 | const testcase_sph_legendre<double> | |
1181 | data022[21] = | |
7c62b943 | 1182 | { |
b4688136 ESR |
1183 | { 2.8350175706934717, 50, 0, |
1184 | 0.0000000000000000, 0.0 }, | |
1185 | { 0.53157537495172758, 50, 0, | |
1186 | 0.15707963267948966, 0.0 }, | |
1187 | { -0.46056183476300561, 50, 0, | |
1188 | 0.31415926535897931, 0.0 }, | |
1189 | { -0.24876032079677909, 50, 0, | |
1190 | 0.47123889803846897, 0.0 }, | |
1191 | { 0.36926172901532667, 50, 0, | |
1192 | 0.62831853071795862, 0.0 }, | |
1193 | { 0.14571730283563575, 50, 0, | |
1194 | 0.78539816339744828, 0.0 }, | |
1195 | { -0.33636199170850750, 50, 0, | |
1196 | 0.94247779607693793, 0.0 }, | |
1197 | { -0.079132716267091507, 50, 0, | |
1198 | 1.0995574287564276, 0.0 }, | |
1199 | { 0.32232921941301451, 50, 0, | |
1200 | 1.2566370614359172, 0.0 }, | |
1201 | { 0.025253991969481544, 50, 0, | |
1202 | 1.4137166941154069, 0.0 }, | |
1203 | { -0.31830208724152359, 50, 0, | |
1204 | 1.5707963267948966, 0.0 }, | |
1205 | { 0.025253991969479882, 50, 0, | |
1206 | 1.7278759594743862, 0.0 }, | |
1207 | { 0.32232921941301479, 50, 0, | |
1208 | 1.8849555921538759, 0.0 }, | |
1209 | { -0.079132716267090064, 50, 0, | |
1210 | 2.0420352248333655, 0.0 }, | |
1211 | { -0.33636199170850883, 50, 0, | |
1212 | 2.1991148575128552, 0.0 }, | |
1213 | { 0.14571730283563347, 50, 0, | |
1214 | 2.3561944901923448, 0.0 }, | |
1215 | { 0.36926172901532522, 50, 0, | |
1216 | 2.5132741228718345, 0.0 }, | |
1217 | { -0.24876032079677354, 50, 0, | |
1218 | 2.6703537555513241, 0.0 }, | |
1219 | { -0.46056183476301255, 50, 0, | |
1220 | 2.8274333882308138, 0.0 }, | |
1221 | { 0.53157537495172758, 50, 0, | |
1222 | 2.9845130209103035, 0.0 }, | |
1223 | { 2.8350175706934717, 50, 0, | |
1224 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1225 | }; |
b4688136 | 1226 | const double toler022 = 5.0000000000000039e-13; |
7c62b943 | 1227 | |
b4688136 ESR |
1228 | // Test data for l=50, m=1. |
1229 | // max(|f - f_GSL|): 7.8825834748386114e-15 at index 1 | |
1230 | // max(|f - f_GSL| / |f_GSL|): 1.6168319946399610e-14 | |
1231 | // mean(f - f_GSL): -8.8223079635391627e-17 | |
1232 | // variance(f - f_GSL): 4.0862386846851427e-34 | |
1233 | // stddev(f - f_GSL): 2.0214447023564960e-17 | |
1234 | const testcase_sph_legendre<double> | |
1235 | data023[21] = | |
7c62b943 | 1236 | { |
b4688136 ESR |
1237 | { 0.0000000000000000, 50, 1, |
1238 | 0.0000000000000000, 0.0 }, | |
1239 | { -0.63751752155228247, 50, 1, | |
1240 | 0.15707963267948966, 0.0 }, | |
1241 | { -0.32616619317605133, 50, 1, | |
1242 | 0.31415926535897931, 0.0 }, | |
1243 | { 0.40649930826162850, 50, 1, | |
1244 | 0.47123889803846897, 0.0 }, | |
1245 | { 0.18473991408343635, 50, 1, | |
1246 | 0.62831853071795862, 0.0 }, | |
1247 | { -0.35083930302013117, 50, 1, | |
1248 | 0.78539816339744828, 0.0 }, | |
1249 | { -0.10755382110947342, 50, 1, | |
1250 | 0.94247779607693793, 0.0 }, | |
1251 | { 0.32822568316499900, 50, 1, | |
1252 | 1.0995574287564276, 0.0 }, | |
1253 | { 0.050286056609797389, 50, 1, | |
1254 | 1.2566370614359172, 0.0 }, | |
1255 | { -0.31935368562159644, 50, 1, | |
1256 | 1.4137166941154069, 0.0 }, | |
1257 | { -9.8421602686195843e-16, 50, 1, | |
1258 | 1.5707963267948966, 0.0 }, | |
1259 | { 0.31935368562159649, 50, 1, | |
1260 | 1.7278759594743862, 0.0 }, | |
1261 | { -0.050286056609795446, 50, 1, | |
1262 | 1.8849555921538759, 0.0 }, | |
1263 | { -0.32822568316499923, 50, 1, | |
1264 | 2.0420352248333655, 0.0 }, | |
1265 | { 0.10755382110946902, 50, 1, | |
1266 | 2.1991148575128552, 0.0 }, | |
1267 | { 0.35083930302013205, 50, 1, | |
1268 | 2.3561944901923448, 0.0 }, | |
1269 | { -0.18473991408344057, 50, 1, | |
1270 | 2.5132741228718345, 0.0 }, | |
1271 | { -0.40649930826163011, 50, 1, | |
1272 | 2.6703537555513241, 0.0 }, | |
1273 | { 0.32616619317604606, 50, 1, | |
1274 | 2.8274333882308138, 0.0 }, | |
1275 | { 0.63751752155228247, 50, 1, | |
1276 | 2.9845130209103035, 0.0 }, | |
1277 | { 0.0000000000000000, 50, 1, | |
1278 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1279 | }; |
b4688136 | 1280 | const double toler023 = 1.0000000000000008e-12; |
7c62b943 | 1281 | |
b4688136 ESR |
1282 | // Test data for l=50, m=2. |
1283 | // max(|f - f_GSL|): 3.7747582837255322e-15 at index 1 | |
1284 | // max(|f - f_GSL| / |f_GSL|): 1.3049193367556654e-14 | |
1285 | // mean(f - f_GSL): 2.4038311024250043e-16 | |
1286 | // variance(f - f_GSL): 3.0336620837175507e-33 | |
1287 | // stddev(f - f_GSL): 5.5078689923758629e-17 | |
1288 | const testcase_sph_legendre<double> | |
1289 | data024[21] = | |
7c62b943 | 1290 | { |
b4688136 ESR |
1291 | { 0.0000000000000000, 50, 2, |
1292 | 0.0000000000000000, 0.0 }, | |
1293 | { -0.37230261163836259, 50, 2, | |
1294 | 0.15707963267948966, 0.0 }, | |
1295 | { 0.50051599680315517, 50, 2, | |
1296 | 0.31415926535897931, 0.0 }, | |
1297 | { 0.21724795180329495, 50, 2, | |
1298 | 0.47123889803846897, 0.0 }, | |
1299 | { -0.37948127307611107, 50, 2, | |
1300 | 0.62831853071795862, 0.0 }, | |
1301 | { -0.13187372121003413, 50, 2, | |
1302 | 0.78539816339744828, 0.0 }, | |
1303 | { 0.33959009162400128, 50, 2, | |
1304 | 0.94247779607693793, 0.0 }, | |
1305 | { 0.072537503112489563, 50, 2, | |
1306 | 1.0995574287564276, 0.0 }, | |
1307 | { -0.32310306941855266, 50, 2, | |
1308 | 1.2566370614359172, 0.0 }, | |
1309 | { -0.023259822816436636, 50, 2, | |
1310 | 1.4137166941154069, 0.0 }, | |
1311 | { 0.31842698506357275, 50, 2, | |
1312 | 1.5707963267948966, 0.0 }, | |
1313 | { -0.023259822816434638, 50, 2, | |
1314 | 1.7278759594743862, 0.0 }, | |
1315 | { -0.32310306941855316, 50, 2, | |
1316 | 1.8849555921538759, 0.0 }, | |
1317 | { 0.072537503112488411, 50, 2, | |
1318 | 2.0420352248333655, 0.0 }, | |
1319 | { 0.33959009162400267, 50, 2, | |
1320 | 2.1991148575128552, 0.0 }, | |
1321 | { -0.13187372121003124, 50, 2, | |
1322 | 2.3561944901923448, 0.0 }, | |
1323 | { -0.37948127307610924, 50, 2, | |
1324 | 2.5132741228718345, 0.0 }, | |
1325 | { 0.21724795180329090, 50, 2, | |
1326 | 2.6703537555513241, 0.0 }, | |
1327 | { 0.50051599680316095, 50, 2, | |
1328 | 2.8274333882308138, 0.0 }, | |
1329 | { -0.37230261163836259, 50, 2, | |
1330 | 2.9845130209103035, 0.0 }, | |
1331 | { 0.0000000000000000, 50, 2, | |
1332 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1333 | }; |
b4688136 | 1334 | const double toler024 = 1.0000000000000008e-12; |
7c62b943 | 1335 | |
b4688136 ESR |
1336 | // Test data for l=50, m=5. |
1337 | // max(|f - f_GSL|): 6.4254157550180935e-15 at index 18 | |
1338 | // max(|f - f_GSL| / |f_GSL|): 8.3058098108785765e-14 | |
1339 | // mean(f - f_GSL): 3.9419525844577751e-16 | |
1340 | // variance(f - f_GSL): 8.1579698435094999e-33 | |
1341 | // stddev(f - f_GSL): 9.0321480521022794e-17 | |
1342 | const testcase_sph_legendre<double> | |
1343 | data025[21] = | |
7c62b943 | 1344 | { |
b4688136 ESR |
1345 | { 0.0000000000000000, 50, 5, |
1346 | 0.0000000000000000, 0.0 }, | |
1347 | { -0.57750385903191603, 50, 5, | |
1348 | 0.15707963267948966, 0.0 }, | |
1349 | { 0.077360497065570286, 50, 5, | |
1350 | 0.31415926535897931, 0.0 }, | |
1351 | { 0.47707267400540226, 50, 5, | |
1352 | 0.47123889803846897, 0.0 }, | |
1353 | { 0.055370615126626811, 50, 5, | |
1354 | 0.62831853071795862, 0.0 }, | |
1355 | { -0.37629451847202833, 50, 5, | |
1356 | 0.78539816339744828, 0.0 }, | |
1357 | { -0.048042277801963115, 50, 5, | |
1358 | 0.94247779607693793, 0.0 }, | |
1359 | { 0.33619379362228718, 50, 5, | |
1360 | 1.0995574287564276, 0.0 }, | |
1361 | { 0.025265227185718764, 50, 5, | |
1362 | 1.2566370614359172, 0.0 }, | |
1363 | { -0.32083679430964535, 50, 5, | |
1364 | 1.4137166941154069, 0.0 }, | |
1365 | { -9.8189201019751726e-16, 50, 5, | |
1366 | 1.5707963267948966, 0.0 }, | |
1367 | { 0.32083679430964546, 50, 5, | |
1368 | 1.7278759594743862, 0.0 }, | |
1369 | { -0.025265227185716790, 50, 5, | |
1370 | 1.8849555921538759, 0.0 }, | |
1371 | { -0.33619379362228730, 50, 5, | |
1372 | 2.0420352248333655, 0.0 }, | |
1373 | { 0.048042277801958064, 50, 5, | |
1374 | 2.1991148575128552, 0.0 }, | |
1375 | { 0.37629451847202872, 50, 5, | |
1376 | 2.3561944901923448, 0.0 }, | |
1377 | { -0.055370615126630517, 50, 5, | |
1378 | 2.5132741228718345, 0.0 }, | |
1379 | { -0.47707267400540176, 50, 5, | |
1380 | 2.6703537555513241, 0.0 }, | |
1381 | { -0.077360497065588632, 50, 5, | |
1382 | 2.8274333882308138, 0.0 }, | |
1383 | { 0.57750385903191603, 50, 5, | |
1384 | 2.9845130209103035, 0.0 }, | |
1385 | { 0.0000000000000000, 50, 5, | |
1386 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1387 | }; |
b4688136 | 1388 | const double toler025 = 5.0000000000000029e-12; |
7c62b943 | 1389 | |
b4688136 ESR |
1390 | // Test data for l=50, m=10. |
1391 | // max(|f - f_GSL|): 4.2188474935755949e-15 at index 17 | |
1392 | // max(|f - f_GSL| / |f_GSL|): 8.5566462271658482e-15 | |
1393 | // mean(f - f_GSL): 2.1378401694418937e-16 | |
1394 | // variance(f - f_GSL): 2.3994393097916561e-33 | |
1395 | // stddev(f - f_GSL): 4.8984072000923484e-17 | |
1396 | const testcase_sph_legendre<double> | |
1397 | data026[21] = | |
7c62b943 | 1398 | { |
b4688136 ESR |
1399 | { 0.0000000000000000, 50, 10, |
1400 | 0.0000000000000000, 0.0 }, | |
1401 | { 0.15606941844801256, 50, 10, | |
1402 | 0.15707963267948966, 0.0 }, | |
1403 | { -0.53748868836814168, 50, 10, | |
1404 | 0.31415926535897931, 0.0 }, | |
1405 | { -0.49304919025183969, 50, 10, | |
1406 | 0.47123889803846897, 0.0 }, | |
1407 | { -0.26267582750427920, 50, 10, | |
1408 | 0.62831853071795862, 0.0 }, | |
1409 | { 0.22058983666314153, 50, 10, | |
1410 | 0.78539816339744828, 0.0 }, | |
1411 | { 0.32936725160671843, 50, 10, | |
1412 | 0.94247779607693793, 0.0 }, | |
1413 | { -0.092053311559447959, 50, 10, | |
1414 | 1.0995574287564276, 0.0 }, | |
1415 | { -0.32542913495935522, 50, 10, | |
1416 | 1.2566370614359172, 0.0 }, | |
1417 | { 0.025673223789103351, 50, 10, | |
1418 | 1.4137166941154069, 0.0 }, | |
1419 | { 0.32150019350255743, 50, 10, | |
1420 | 1.5707963267948966, 0.0 }, | |
1421 | { 0.025673223789105259, 50, 10, | |
1422 | 1.7278759594743862, 0.0 }, | |
1423 | { -0.32542913495935510, 50, 10, | |
1424 | 1.8849555921538759, 0.0 }, | |
1425 | { -0.092053311559449028, 50, 10, | |
1426 | 2.0420352248333655, 0.0 }, | |
1427 | { 0.32936725160671687, 50, 10, | |
1428 | 2.1991148575128552, 0.0 }, | |
1429 | { 0.22058983666314380, 50, 10, | |
1430 | 2.3561944901923448, 0.0 }, | |
1431 | { -0.26267582750428364, 50, 10, | |
1432 | 2.5132741228718345, 0.0 }, | |
1433 | { -0.49304919025184135, 50, 10, | |
1434 | 2.6703537555513241, 0.0 }, | |
1435 | { -0.53748868836814501, 50, 10, | |
1436 | 2.8274333882308138, 0.0 }, | |
1437 | { 0.15606941844801256, 50, 10, | |
1438 | 2.9845130209103035, 0.0 }, | |
1439 | { 0.0000000000000000, 50, 10, | |
1440 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1441 | }; |
b4688136 | 1442 | const double toler026 = 5.0000000000000039e-13; |
7c62b943 | 1443 | |
b4688136 ESR |
1444 | // Test data for l=50, m=20. |
1445 | // max(|f - f_GSL|): 5.3290705182007514e-15 at index 17 | |
1446 | // max(|f - f_GSL| / |f_GSL|): 8.3091988651062939e-15 | |
1447 | // mean(f - f_GSL): -6.3705667112909982e-16 | |
1448 | // variance(f - f_GSL): 2.1306663117079729e-32 | |
1449 | // stddev(f - f_GSL): 1.4596802087128444e-16 | |
1450 | const testcase_sph_legendre<double> | |
1451 | data027[21] = | |
7c62b943 | 1452 | { |
b4688136 ESR |
1453 | { 0.0000000000000000, 50, 20, |
1454 | 0.0000000000000000, 0.0 }, | |
1455 | { 3.0409598712835887e-07, 50, 20, | |
1456 | 0.15707963267948966, 0.0 }, | |
1457 | { 0.030940518122881844, 50, 20, | |
1458 | 0.31415926535897931, 0.0 }, | |
1459 | { 0.64134588721659802, 50, 20, | |
1460 | 0.47123889803846897, 0.0 }, | |
1461 | { 0.29895244392136594, 50, 20, | |
1462 | 0.62831853071795862, 0.0 }, | |
1463 | { 0.25309324781873871, 50, 20, | |
1464 | 0.78539816339744828, 0.0 }, | |
1465 | { 0.34368634714931567, 50, 20, | |
1466 | 0.94247779607693793, 0.0 }, | |
1467 | { 0.33996764360663945, 50, 20, | |
1468 | 1.0995574287564276, 0.0 }, | |
1469 | { 0.12866267745104024, 50, 20, | |
1470 | 1.2566370614359172, 0.0 }, | |
1471 | { -0.18201114398922874, 50, 20, | |
1472 | 1.4137166941154069, 0.0 }, | |
1473 | { -0.33216683431510857, 50, 20, | |
1474 | 1.5707963267948966, 0.0 }, | |
1475 | { -0.18201114398923010, 50, 20, | |
1476 | 1.7278759594743862, 0.0 }, | |
1477 | { 0.12866267745103857, 50, 20, | |
1478 | 1.8849555921538759, 0.0 }, | |
1479 | { 0.33996764360663895, 50, 20, | |
1480 | 2.0420352248333655, 0.0 }, | |
1481 | { 0.34368634714931812, 50, 20, | |
1482 | 2.1991148575128552, 0.0 }, | |
1483 | { 0.25309324781874126, 50, 20, | |
1484 | 2.3561944901923448, 0.0 }, | |
1485 | { 0.29895244392136405, 50, 20, | |
1486 | 2.5132741228718345, 0.0 }, | |
1487 | { 0.64134588721659869, 50, 20, | |
1488 | 2.6703537555513241, 0.0 }, | |
1489 | { 0.030940518122882274, 50, 20, | |
1490 | 2.8274333882308138, 0.0 }, | |
1491 | { 3.0409598712835887e-07, 50, 20, | |
1492 | 2.9845130209103035, 0.0 }, | |
1493 | { 0.0000000000000000, 50, 20, | |
1494 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1495 | }; |
b4688136 | 1496 | const double toler027 = 5.0000000000000039e-13; |
7c62b943 | 1497 | |
b4688136 ESR |
1498 | // Test data for l=50, m=50. |
1499 | // max(|f - f_GSL|): 8.8817841970012523e-16 at index 10 | |
1500 | // max(|f - f_GSL| / |f_GSL|): 1.6947090122367552e-15 | |
1501 | // mean(f - f_GSL): 8.9876810627650302e-17 | |
1502 | // variance(f - f_GSL): 4.2408665715142198e-34 | |
1503 | // stddev(f - f_GSL): 2.0593364396120950e-17 | |
1504 | const testcase_sph_legendre<double> | |
1505 | data028[21] = | |
7c62b943 | 1506 | { |
b4688136 ESR |
1507 | { 0.0000000000000000, 50, 50, |
1508 | 0.0000000000000000, 0.0 }, | |
1509 | { 4.1649039898161316e-41, 50, 50, | |
1510 | 0.15707963267948966, 0.0 }, | |
1511 | { 2.5240684647722935e-26, 50, 50, | |
1512 | 0.31415926535897931, 0.0 }, | |
1513 | { 5.6927376423967334e-18, 50, 50, | |
1514 | 0.47123889803846897, 0.0 }, | |
1515 | { 2.3116239814797222e-12, 50, 50, | |
1516 | 0.62831853071795862, 0.0 }, | |
1517 | { 2.3835981241325056e-08, 50, 50, | |
1518 | 0.78539816339744828, 0.0 }, | |
1519 | { 1.9992410287270217e-05, 50, 50, | |
1520 | 0.94247779607693793, 0.0 }, | |
1521 | { 0.0024947505670829830, 50, 50, | |
1522 | 1.0995574287564276, 0.0 }, | |
1523 | { 0.065057774647971231, 50, 50, | |
1524 | 1.2566370614359172, 0.0 }, | |
1525 | { 0.43050607056732243, 50, 50, | |
1526 | 1.4137166941154069, 0.0 }, | |
1527 | { 0.79980281171531975, 50, 50, | |
1528 | 1.5707963267948966, 0.0 }, | |
1529 | { 0.43050607056732287, 50, 50, | |
1530 | 1.7278759594743862, 0.0 }, | |
1531 | { 0.065057774647971398, 50, 50, | |
1532 | 1.8849555921538759, 0.0 }, | |
1533 | { 0.0024947505670829878, 50, 50, | |
1534 | 2.0420352248333655, 0.0 }, | |
1535 | { 1.9992410287270430e-05, 50, 50, | |
1536 | 2.1991148575128552, 0.0 }, | |
1537 | { 2.3835981241325311e-08, 50, 50, | |
1538 | 2.3561944901923448, 0.0 }, | |
1539 | { 2.3116239814797057e-12, 50, 50, | |
1540 | 2.5132741228718345, 0.0 }, | |
1541 | { 5.6927376423968952e-18, 50, 50, | |
1542 | 2.6703537555513241, 0.0 }, | |
1543 | { 2.5240684647724192e-26, 50, 50, | |
1544 | 2.8274333882308138, 0.0 }, | |
1545 | { 4.1649039898161316e-41, 50, 50, | |
1546 | 2.9845130209103035, 0.0 }, | |
1547 | { 0.0000000000000000, 50, 50, | |
1548 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1549 | }; |
b4688136 | 1550 | const double toler028 = 2.5000000000000020e-13; |
7c62b943 | 1551 | |
b4688136 ESR |
1552 | // Test data for l=100, m=0. |
1553 | // max(|f - f_GSL|): 2.2759572004815709e-15 at index 18 | |
1554 | // max(|f - f_GSL| / |f_GSL|): 4.9270578369513465e-15 | |
1555 | // mean(f - f_GSL): -2.0618427600181479e-16 | |
1556 | // variance(f - f_GSL): 2.2318776726956083e-33 | |
1557 | // stddev(f - f_GSL): 4.7242752594399153e-17 | |
1558 | const testcase_sph_legendre<double> | |
1559 | data029[21] = | |
7c62b943 | 1560 | { |
b4688136 ESR |
1561 | { 3.9993839251484076, 100, 0, |
1562 | 0.0000000000000000, 0.0 }, | |
1563 | { -0.60770160285939456, 100, 0, | |
1564 | 0.15707963267948966, 0.0 }, | |
1565 | { 0.46193027883954441, 100, 0, | |
1566 | 0.31415926535897931, 0.0 }, | |
1567 | { -0.40218718869815234, 100, 0, | |
1568 | 0.47123889803846897, 0.0 }, | |
1569 | { 0.36960201406911097, 100, 0, | |
1570 | 0.62831853071795862, 0.0 }, | |
1571 | { -0.34953726547378389, 100, 0, | |
1572 | 0.78539816339744828, 0.0 }, | |
1573 | { 0.33646959352497730, 100, 0, | |
1574 | 0.94247779607693793, 0.0 }, | |
1575 | { -0.32784733067663224, 100, 0, | |
1576 | 1.0995574287564276, 0.0 }, | |
1577 | { 0.32235624474047969, 100, 0, | |
1578 | 1.2566370614359172, 0.0 }, | |
1579 | { -0.31929330706601350, 100, 0, | |
1580 | 1.4137166941154069, 0.0 }, | |
1581 | { 0.31830791662110325, 100, 0, | |
1582 | 1.5707963267948966, 0.0 }, | |
1583 | { -0.31929330706601333, 100, 0, | |
1584 | 1.7278759594743862, 0.0 }, | |
1585 | { 0.32235624474048036, 100, 0, | |
1586 | 1.8849555921538759, 0.0 }, | |
1587 | { -0.32784733067663291, 100, 0, | |
1588 | 2.0420352248333655, 0.0 }, | |
1589 | { 0.33646959352498013, 100, 0, | |
1590 | 2.1991148575128552, 0.0 }, | |
1591 | { -0.34953726547378589, 100, 0, | |
1592 | 2.3561944901923448, 0.0 }, | |
1593 | { 0.36960201406910725, 100, 0, | |
1594 | 2.5132741228718345, 0.0 }, | |
1595 | { -0.40218718869815723, 100, 0, | |
1596 | 2.6703537555513241, 0.0 }, | |
1597 | { 0.46193027883955923, 100, 0, | |
1598 | 2.8274333882308138, 0.0 }, | |
1599 | { -0.60770160285939456, 100, 0, | |
1600 | 2.9845130209103035, 0.0 }, | |
1601 | { 3.9993839251484076, 100, 0, | |
1602 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1603 | }; |
b4688136 | 1604 | const double toler029 = 2.5000000000000020e-13; |
7c62b943 | 1605 | |
b4688136 ESR |
1606 | // Test data for l=100, m=1. |
1607 | // max(|f - f_GSL|): 4.7184478546569153e-15 at index 18 | |
1608 | // max(|f - f_GSL| / |f_GSL|): 1.6136152688198031e-14 | |
1609 | // mean(f - f_GSL): 1.7347234759767562e-17 | |
1610 | // variance(f - f_GSL): 1.5798644075050619e-35 | |
1611 | // stddev(f - f_GSL): 3.9747508192401971e-18 | |
1612 | const testcase_sph_legendre<double> | |
1613 | data030[21] = | |
7c62b943 | 1614 | { |
b4688136 ESR |
1615 | { 0.0000000000000000, 100, 1, |
1616 | 0.0000000000000000, 0.0 }, | |
1617 | { -0.50851949013714159, 100, 1, | |
1618 | 0.15707963267948966, 0.0 }, | |
1619 | { 0.33129641402223092, 100, 1, | |
1620 | 0.31415926535897931, 0.0 }, | |
1621 | { -0.24390405750942512, 100, 1, | |
1622 | 0.47123889803846897, 0.0 }, | |
1623 | { 0.18659755088413388, 100, 1, | |
1624 | 0.62831853071795862, 0.0 }, | |
1625 | { -0.14355908970517178, 100, 1, | |
1626 | 0.78539816339744828, 0.0 }, | |
1627 | { 0.10844906813251505, 100, 1, | |
1628 | 0.94247779607693793, 0.0 }, | |
1629 | { -0.078100088690857675, 100, 1, | |
1630 | 1.0995574287564276, 0.0 }, | |
1631 | { 0.050670002998302717, 100, 1, | |
1632 | 1.2566370614359172, 0.0 }, | |
1633 | { -0.024941251747138900, 100, 1, | |
1634 | 1.4137166941154069, 0.0 }, | |
1635 | { 1.9587949830851608e-15, 100, 1, | |
1636 | 1.5707963267948966, 0.0 }, | |
1637 | { 0.024941251747135025, 100, 1, | |
1638 | 1.7278759594743862, 0.0 }, | |
1639 | { -0.050670002998298824, 100, 1, | |
1640 | 1.8849555921538759, 0.0 }, | |
1641 | { 0.078100088690855773, 100, 1, | |
1642 | 2.0420352248333655, 0.0 }, | |
1643 | { -0.10844906813250622, 100, 1, | |
1644 | 2.1991148575128552, 0.0 }, | |
1645 | { 0.14355908970516626, 100, 1, | |
1646 | 2.3561944901923448, 0.0 }, | |
1647 | { -0.18659755088414104, 100, 1, | |
1648 | 2.5132741228718345, 0.0 }, | |
1649 | { 0.24390405750941679, 100, 1, | |
1650 | 2.6703537555513241, 0.0 }, | |
1651 | { -0.33129641402221749, 100, 1, | |
1652 | 2.8274333882308138, 0.0 }, | |
1653 | { 0.50851949013714159, 100, 1, | |
1654 | 2.9845130209103035, 0.0 }, | |
1655 | { 0.0000000000000000, 100, 1, | |
1656 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1657 | }; |
b4688136 | 1658 | const double toler030 = 1.0000000000000008e-12; |
7c62b943 | 1659 | |
b4688136 ESR |
1660 | // Test data for l=100, m=2. |
1661 | // max(|f - f_GSL|): 9.3258734068513149e-15 at index 1 | |
1662 | // max(|f - f_GSL| / |f_GSL|): 1.3884756158405121e-14 | |
1663 | // mean(f - f_GSL): 1.1049362483174177e-15 | |
1664 | // variance(f - f_GSL): 6.4096415924402929e-32 | |
1665 | // stddev(f - f_GSL): 2.5317269980075443e-16 | |
1666 | const testcase_sph_legendre<double> | |
1667 | data031[21] = | |
7c62b943 | 1668 | { |
b4688136 ESR |
1669 | { 0.0000000000000000, 100, 2, |
1670 | 0.0000000000000000, 0.0 }, | |
1671 | { 0.67166274297196848, 100, 2, | |
1672 | 0.15707963267948966, 0.0 }, | |
1673 | { -0.48226933687994433, 100, 2, | |
1674 | 0.31415926535897931, 0.0 }, | |
1675 | { 0.41175421895715525, 100, 2, | |
1676 | 0.47123889803846897, 0.0 }, | |
1677 | { -0.37475021787822776, 100, 2, | |
1678 | 0.62831853071795862, 0.0 }, | |
1679 | { 0.35242909383605286, 100, 2, | |
1680 | 0.78539816339744828, 0.0 }, | |
1681 | { -0.33807110409159863, 100, 2, | |
1682 | 0.94247779607693793, 0.0 }, | |
1683 | { 0.32867180390710077, 100, 2, | |
1684 | 1.0995574287564276, 0.0 }, | |
1685 | { -0.32271583790278502, 100, 2, | |
1686 | 1.2566370614359172, 0.0 }, | |
1687 | { 0.31940354677687466, 100, 2, | |
1688 | 1.4137166941154069, 0.0 }, | |
1689 | { -0.31833943693772526, 100, 2, | |
1690 | 1.5707963267948966, 0.0 }, | |
1691 | { 0.31940354677687455, 100, 2, | |
1692 | 1.7278759594743862, 0.0 }, | |
1693 | { -0.32271583790278552, 100, 2, | |
1694 | 1.8849555921538759, 0.0 }, | |
1695 | { 0.32867180390710116, 100, 2, | |
1696 | 2.0420352248333655, 0.0 }, | |
1697 | { -0.33807110409160157, 100, 2, | |
1698 | 2.1991148575128552, 0.0 }, | |
1699 | { 0.35242909383605503, 100, 2, | |
1700 | 2.3561944901923448, 0.0 }, | |
1701 | { -0.37475021787822438, 100, 2, | |
1702 | 2.5132741228718345, 0.0 }, | |
1703 | { 0.41175421895716052, 100, 2, | |
1704 | 2.6703537555513241, 0.0 }, | |
1705 | { -0.48226933687995360, 100, 2, | |
1706 | 2.8274333882308138, 0.0 }, | |
1707 | { 0.67166274297196848, 100, 2, | |
1708 | 2.9845130209103035, 0.0 }, | |
1709 | { 0.0000000000000000, 100, 2, | |
1710 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1711 | }; |
b4688136 | 1712 | const double toler031 = 1.0000000000000008e-12; |
7c62b943 | 1713 | |
b4688136 ESR |
1714 | // Test data for l=100, m=5. |
1715 | // max(|f - f_GSL|): 1.5432100042289676e-14 at index 1 | |
1716 | // max(|f - f_GSL| / |f_GSL|): 2.4665959612621893e-13 | |
1717 | // mean(f - f_GSL): -8.4885802091131797e-16 | |
1718 | // variance(f - f_GSL): 3.7829396832437676e-32 | |
1719 | // stddev(f - f_GSL): 1.9449780675482609e-16 | |
1720 | const testcase_sph_legendre<double> | |
1721 | data032[21] = | |
7c62b943 | 1722 | { |
b4688136 ESR |
1723 | { 0.0000000000000000, 100, 5, |
1724 | 0.0000000000000000, 0.0 }, | |
1725 | { 0.062564361105954577, 100, 5, | |
1726 | 0.15707963267948966, 0.0 }, | |
1727 | { 0.14179554455882706, 100, 5, | |
1728 | 0.31415926535897931, 0.0 }, | |
1729 | { -0.14356866942905960, 100, 5, | |
1730 | 0.47123889803846897, 0.0 }, | |
1731 | { 0.12355483388447824, 100, 5, | |
1732 | 0.62831853071795862, 0.0 }, | |
1733 | { -0.10090029999681642, 100, 5, | |
1734 | 0.78539816339744828, 0.0 }, | |
1735 | { 0.078905134460235241, 100, 5, | |
1736 | 0.94247779607693793, 0.0 }, | |
1737 | { -0.058040182398185071, 100, 5, | |
1738 | 1.0995574287564276, 0.0 }, | |
1739 | { 0.038142759389482424, 100, 5, | |
1740 | 1.2566370614359172, 0.0 }, | |
1741 | { -0.018906264170660478, 100, 5, | |
1742 | 1.4137166941154069, 0.0 }, | |
1743 | { 1.9576303042914504e-15, 100, 5, | |
1744 | 1.5707963267948966, 0.0 }, | |
1745 | { 0.018906264170657019, 100, 5, | |
1746 | 1.7278759594743862, 0.0 }, | |
1747 | { -0.038142759389478365, 100, 5, | |
1748 | 1.8849555921538759, 0.0 }, | |
1749 | { 0.058040182398183086, 100, 5, | |
1750 | 2.0420352248333655, 0.0 }, | |
1751 | { -0.078905134460225707, 100, 5, | |
1752 | 2.1991148575128552, 0.0 }, | |
1753 | { 0.10090029999681013, 100, 5, | |
1754 | 2.3561944901923448, 0.0 }, | |
1755 | { -0.12355483388448550, 100, 5, | |
1756 | 2.5132741228718345, 0.0 }, | |
1757 | { 0.14356866942904906, 100, 5, | |
1758 | 2.6703537555513241, 0.0 }, | |
1759 | { -0.14179554455879767, 100, 5, | |
1760 | 2.8274333882308138, 0.0 }, | |
1761 | { -0.062564361105954577, 100, 5, | |
1762 | 2.9845130209103035, 0.0 }, | |
1763 | { 0.0000000000000000, 100, 5, | |
1764 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1765 | }; |
b4688136 | 1766 | const double toler032 = 2.5000000000000014e-11; |
7c62b943 | 1767 | |
b4688136 ESR |
1768 | // Test data for l=100, m=10. |
1769 | // max(|f - f_GSL|): 6.9944050551384862e-15 at index 1 | |
1770 | // max(|f - f_GSL| / |f_GSL|): 9.2805170220968737e-15 | |
1771 | // mean(f - f_GSL): -9.1725568939268895e-16 | |
1772 | // variance(f - f_GSL): 4.4171294985470989e-32 | |
1773 | // stddev(f - f_GSL): 2.1016968141354497e-16 | |
1774 | const testcase_sph_legendre<double> | |
1775 | data033[21] = | |
7c62b943 | 1776 | { |
b4688136 ESR |
1777 | { 0.0000000000000000, 100, 10, |
1778 | 0.0000000000000000, 0.0 }, | |
1779 | { -0.75366545187997991, 100, 10, | |
1780 | 0.15707963267948966, 0.0 }, | |
1781 | { -0.35914570017278186, 100, 10, | |
1782 | 0.31415926535897931, 0.0 }, | |
1783 | { 0.43480692911578295, 100, 10, | |
1784 | 0.47123889803846897, 0.0 }, | |
1785 | { -0.40862111080315500, 100, 10, | |
1786 | 0.62831853071795862, 0.0 }, | |
1787 | { 0.37832688692909411, 100, 10, | |
1788 | 0.78539816339744828, 0.0 }, | |
1789 | { -0.35484056194773494, 100, 10, | |
1790 | 0.94247779607693793, 0.0 }, | |
1791 | { 0.33821981171196341, 100, 10, | |
1792 | 1.0995574287564276, 0.0 }, | |
1793 | { -0.32729120767830594, 100, 10, | |
1794 | 1.2566370614359172, 0.0 }, | |
1795 | { 0.32110336937091438, 100, 10, | |
1796 | 1.4137166941154069, 0.0 }, | |
1797 | { -0.31910064020036194, 100, 10, | |
1798 | 1.5707963267948966, 0.0 }, | |
1799 | { 0.32110336937091460, 100, 10, | |
1800 | 1.7278759594743862, 0.0 }, | |
1801 | { -0.32729120767830605, 100, 10, | |
1802 | 1.8849555921538759, 0.0 }, | |
1803 | { 0.33821981171196364, 100, 10, | |
1804 | 2.0420352248333655, 0.0 }, | |
1805 | { -0.35484056194773461, 100, 10, | |
1806 | 2.1991148575128552, 0.0 }, | |
1807 | { 0.37832688692909372, 100, 10, | |
1808 | 2.3561944901923448, 0.0 }, | |
1809 | { -0.40862111080315755, 100, 10, | |
1810 | 2.5132741228718345, 0.0 }, | |
1811 | { 0.43480692911577751, 100, 10, | |
1812 | 2.6703537555513241, 0.0 }, | |
1813 | { -0.35914570017276798, 100, 10, | |
1814 | 2.8274333882308138, 0.0 }, | |
1815 | { -0.75366545187997991, 100, 10, | |
1816 | 2.9845130209103035, 0.0 }, | |
1817 | { 0.0000000000000000, 100, 10, | |
1818 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1819 | }; |
b4688136 | 1820 | const double toler033 = 5.0000000000000039e-13; |
7c62b943 | 1821 | |
b4688136 ESR |
1822 | // Test data for l=100, m=20. |
1823 | // max(|f - f_GSL|): 5.2180482157382357e-15 at index 2 | |
1824 | // max(|f - f_GSL| / |f_GSL|): 3.3114331221145530e-14 | |
1825 | // mean(f - f_GSL): -1.7066374768419445e-16 | |
1826 | // variance(f - f_GSL): 1.5291210256147554e-33 | |
1827 | // stddev(f - f_GSL): 3.9103977107383276e-17 | |
1828 | const testcase_sph_legendre<double> | |
1829 | data034[21] = | |
7c62b943 | 1830 | { |
b4688136 ESR |
1831 | { 0.0000000000000000, 100, 20, |
1832 | 0.0000000000000000, 0.0 }, | |
1833 | { 0.053569660841557079, 100, 20, | |
1834 | 0.15707963267948966, 0.0 }, | |
1835 | { 0.57154926874731338, 100, 20, | |
1836 | 0.31415926535897931, 0.0 }, | |
1837 | { 0.47536909969585633, 100, 20, | |
1838 | 0.47123889803846897, 0.0 }, | |
1839 | { -0.28882554564109575, 100, 20, | |
1840 | 0.62831853071795862, 0.0 }, | |
1841 | { 0.020116179014043743, 100, 20, | |
1842 | 0.78539816339744828, 0.0 }, | |
1843 | { 0.14752195931707024, 100, 20, | |
1844 | 0.94247779607693793, 0.0 }, | |
1845 | { -0.24069428588868366, 100, 20, | |
1846 | 1.0995574287564276, 0.0 }, | |
1847 | { 0.29031796025014306, 100, 20, | |
1848 | 1.2566370614359172, 0.0 }, | |
1849 | { -0.31437256851143458, 100, 20, | |
1850 | 1.4137166941154069, 0.0 }, | |
1851 | { 0.32153954851141792, 100, 20, | |
1852 | 1.5707963267948966, 0.0 }, | |
1853 | { -0.31437256851143375, 100, 20, | |
1854 | 1.7278759594743862, 0.0 }, | |
1855 | { 0.29031796025014139, 100, 20, | |
1856 | 1.8849555921538759, 0.0 }, | |
1857 | { -0.24069428588868241, 100, 20, | |
1858 | 2.0420352248333655, 0.0 }, | |
1859 | { 0.14752195931706186, 100, 20, | |
1860 | 2.1991148575128552, 0.0 }, | |
1861 | { 0.020116179014049562, 100, 20, | |
1862 | 2.3561944901923448, 0.0 }, | |
1863 | { -0.28882554564109075, 100, 20, | |
1864 | 2.5132741228718345, 0.0 }, | |
1865 | { 0.47536909969585545, 100, 20, | |
1866 | 2.6703537555513241, 0.0 }, | |
1867 | { 0.57154926874732348, 100, 20, | |
1868 | 2.8274333882308138, 0.0 }, | |
1869 | { 0.053569660841557079, 100, 20, | |
1870 | 2.9845130209103035, 0.0 }, | |
1871 | { 0.0000000000000000, 100, 20, | |
1872 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1873 | }; |
b4688136 | 1874 | const double toler034 = 2.5000000000000015e-12; |
7c62b943 | 1875 | |
b4688136 ESR |
1876 | // Test data for l=100, m=50. |
1877 | // max(|f - f_GSL|): 2.4980018054066022e-15 at index 15 | |
1878 | // max(|f - f_GSL| / |f_GSL|): 7.4927901205617944e-15 | |
1879 | // mean(f - f_GSL): 1.5662074559583175e-16 | |
1880 | // variance(f - f_GSL): 1.2878280424271984e-33 | |
1881 | // stddev(f - f_GSL): 3.5886321104666028e-17 | |
1882 | const testcase_sph_legendre<double> | |
1883 | data035[21] = | |
7c62b943 | 1884 | { |
b4688136 ESR |
1885 | { 0.0000000000000000, 100, 50, |
1886 | 0.0000000000000000, 0.0 }, | |
1887 | { 3.3047910392597822e-21, 100, 50, | |
1888 | 0.15707963267948966, 0.0 }, | |
1889 | { 1.0592655372554564e-07, 100, 50, | |
1890 | 0.31415926535897931, 0.0 }, | |
1891 | { 0.080418744223952773, 100, 50, | |
1892 | 0.47123889803846897, 0.0 }, | |
1893 | { -0.56450600580392973, 100, 50, | |
1894 | 0.62831853071795862, 0.0 }, | |
1895 | { 0.33338739844742110, 100, 50, | |
1896 | 0.78539816339744828, 0.0 }, | |
1897 | { 0.39741714816514678, 100, 50, | |
1898 | 0.94247779607693793, 0.0 }, | |
1899 | { 0.35223993750972243, 100, 50, | |
1900 | 1.0995574287564276, 0.0 }, | |
1901 | { 0.17885891940721577, 100, 50, | |
1902 | 1.2566370614359172, 0.0 }, | |
1903 | { -0.15341660126461967, 100, 50, | |
1904 | 1.4137166941154069, 0.0 }, | |
1905 | { -0.34175924303503102, 100, 50, | |
1906 | 1.5707963267948966, 0.0 }, | |
1907 | { -0.15341660126462270, 100, 50, | |
1908 | 1.7278759594743862, 0.0 }, | |
1909 | { 0.17885891940721302, 100, 50, | |
1910 | 1.8849555921538759, 0.0 }, | |
1911 | { 0.35223993750972227, 100, 50, | |
1912 | 2.0420352248333655, 0.0 }, | |
1913 | { 0.39741714816514595, 100, 50, | |
1914 | 2.1991148575128552, 0.0 }, | |
1915 | { 0.33338739844741666, 100, 50, | |
1916 | 2.3561944901923448, 0.0 }, | |
1917 | { -0.56450600580393095, 100, 50, | |
1918 | 2.5132741228718345, 0.0 }, | |
1919 | { 0.080418744223953911, 100, 50, | |
1920 | 2.6703537555513241, 0.0 }, | |
1921 | { 1.0592655372554981e-07, 100, 50, | |
1922 | 2.8274333882308138, 0.0 }, | |
1923 | { 3.3047910392597822e-21, 100, 50, | |
1924 | 2.9845130209103035, 0.0 }, | |
1925 | { 0.0000000000000000, 100, 50, | |
1926 | 3.1415926535897931, 0.0 }, | |
7c62b943 | 1927 | }; |
b4688136 | 1928 | const double toler035 = 5.0000000000000039e-13; |
7c62b943 | 1929 | |
b4688136 ESR |
1930 | // Test data for l=100, m=100. |
1931 | // max(|f - f_GSL|): 3.6637359812630166e-15 at index 10 | |
1932 | // max(|f - f_GSL| / |f_GSL|): 3.8591350247394187e-15 | |
1933 | // mean(f - f_GSL): 2.7412914496899967e-16 | |
1934 | // variance(f - f_GSL): 3.9452063763753292e-33 | |
1935 | // stddev(f - f_GSL): 6.2810877850698192e-17 | |
1936 | const testcase_sph_legendre<double> | |
1937 | data036[21] = | |
7c62b943 | 1938 | { |
b4688136 ESR |
1939 | { 0.0000000000000000, 100, 100, |
1940 | 0.0000000000000000, 0.0 }, | |
1941 | { 2.5744136608873899e-81, 100, 100, | |
1942 | 0.15707963267948966, 0.0 }, | |
1943 | { 9.4551974868947092e-52, 100, 100, | |
1944 | 0.31415926535897931, 0.0 }, | |
1945 | { 4.8096190703397596e-35, 100, 100, | |
1946 | 0.47123889803846897, 0.0 }, | |
1947 | { 7.9305393636344023e-24, 100, 100, | |
1948 | 0.62831853071795862, 0.0 }, | |
1949 | { 8.4320740610944858e-16, 100, 100, | |
1950 | 0.78539816339744828, 0.0 }, | |
1951 | { 5.9319660146026674e-10, 100, 100, | |
1952 | 0.94247779607693793, 0.0 }, | |
1953 | { 9.2368225946797243e-06, 100, 100, | |
1954 | 1.0995574287564276, 0.0 }, | |
1955 | { 0.0062815489742044095, 100, 100, | |
1956 | 1.2566370614359172, 0.0 }, | |
1957 | { 0.27505966018176986, 100, 100, | |
1958 | 1.4137166941154069, 0.0 }, | |
1959 | { 0.94936713998764621, 100, 100, | |
1960 | 1.5707963267948966, 0.0 }, | |
1961 | { 0.27505966018177036, 100, 100, | |
1962 | 1.7278759594743862, 0.0 }, | |
1963 | { 0.0062815489742044433, 100, 100, | |
1964 | 1.8849555921538759, 0.0 }, | |
1965 | { 9.2368225946797582e-06, 100, 100, | |
1966 | 2.0420352248333655, 0.0 }, | |
1967 | { 5.9319660146027946e-10, 100, 100, | |
1968 | 2.1991148575128552, 0.0 }, | |
1969 | { 8.4320740610946652e-16, 100, 100, | |
1970 | 2.3561944901923448, 0.0 }, | |
1971 | { 7.9305393636342891e-24, 100, 100, | |
1972 | 2.5132741228718345, 0.0 }, | |
1973 | { 4.8096190703400333e-35, 100, 100, | |
1974 | 2.6703537555513241, 0.0 }, | |
1975 | { 9.4551974868956498e-52, 100, 100, | |
1976 | 2.8274333882308138, 0.0 }, | |
1977 | { 2.5744136608873899e-81, 100, 100, | |
1978 | 2.9845130209103035, 0.0 }, | |
1979 | { 0.0000000000000000, 100, 100, | |
1980 | 3.1415926535897931, 0.0 }, | |
1981 | }; | |
1982 | const double toler036 = 2.5000000000000020e-13; | |
1983 | ||
1984 | template<typename Ret, unsigned int Num> | |
1985 | void | |
1986 | test(const testcase_sph_legendre<Ret> (&data)[Num], Ret toler) | |
1987 | { | |
1988 | bool test __attribute__((unused)) = true; | |
1989 | const Ret eps = std::numeric_limits<Ret>::epsilon(); | |
1990 | Ret max_abs_diff = -Ret(1); | |
1991 | Ret max_abs_frac = -Ret(1); | |
1992 | unsigned int num_datum = Num; | |
1993 | for (unsigned int i = 0; i < num_datum; ++i) | |
1994 | { | |
1995 | const Ret f = std::tr1::sph_legendre(data[i].l, data[i].m, | |
1996 | data[i].theta); | |
1997 | const Ret f0 = data[i].f0; | |
1998 | const Ret diff = f - f0; | |
1999 | if (std::abs(diff) > max_abs_diff) | |
2000 | max_abs_diff = std::abs(diff); | |
2001 | if (std::abs(f0) > Ret(10) * eps | |
2002 | && std::abs(f) > Ret(10) * eps) | |
2003 | { | |
2004 | const Ret frac = diff / f0; | |
2005 | if (std::abs(frac) > max_abs_frac) | |
2006 | max_abs_frac = std::abs(frac); | |
2007 | } | |
2008 | } | |
2009 | VERIFY(max_abs_frac < toler); | |
2010 | } | |
7c62b943 | 2011 | |
b4688136 ESR |
2012 | int |
2013 | main() | |
7c62b943 | 2014 | { |
b4688136 ESR |
2015 | test(data001, toler001); |
2016 | test(data002, toler002); | |
2017 | test(data003, toler003); | |
2018 | test(data004, toler004); | |
2019 | test(data005, toler005); | |
2020 | test(data006, toler006); | |
2021 | test(data007, toler007); | |
2022 | test(data008, toler008); | |
2023 | test(data009, toler009); | |
2024 | test(data010, toler010); | |
2025 | test(data011, toler011); | |
2026 | test(data012, toler012); | |
2027 | test(data013, toler013); | |
2028 | test(data014, toler014); | |
2029 | test(data015, toler015); | |
2030 | test(data016, toler016); | |
2031 | test(data017, toler017); | |
2032 | test(data018, toler018); | |
2033 | test(data019, toler019); | |
2034 | test(data020, toler020); | |
2035 | test(data021, toler021); | |
2036 | test(data022, toler022); | |
2037 | test(data023, toler023); | |
2038 | test(data024, toler024); | |
2039 | test(data025, toler025); | |
2040 | test(data026, toler026); | |
2041 | test(data027, toler027); | |
2042 | test(data028, toler028); | |
2043 | test(data029, toler029); | |
2044 | test(data030, toler030); | |
2045 | test(data031, toler031); | |
2046 | test(data032, toler032); | |
2047 | test(data033, toler033); | |
2048 | test(data034, toler034); | |
2049 | test(data035, toler035); | |
2050 | test(data036, toler036); | |
7c62b943 BK |
2051 | return 0; |
2052 | } |