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196c9e7a | 1 | // { dg-do run { target c++11 } } |
2be75957 ESR |
2 | // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } |
3 | // | |
a945c346 | 4 | // Copyright (C) 2016-2024 Free Software Foundation, Inc. |
2be75957 ESR |
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 | |
9 | // Free Software Foundation; either version 3, or (at your option) | |
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 | |
18 | // with this library; see the file COPYING3. If not see | |
19 | // <http://www.gnu.org/licenses/>. | |
20 | ||
21 | // sph_legendre | |
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/ | |
24 | #include <limits> | |
25 | #include <cmath> | |
26 | #if defined(__TEST_DEBUG) | |
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 | } | |
35 | #else | |
36 | # include <testsuite_hooks.h> | |
37 | #endif | |
38 | #include <specfun_testcase.h> | |
39 | ||
2be75957 | 40 | // Test data for l=0, m=0. |
b4688136 | 41 | // max(|f - f_GSL|): 0.0000000000000000 at index 0 |
2be75957 | 42 | // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 |
b4688136 ESR |
43 | // mean(f - f_GSL): 0.0000000000000000 |
44 | // variance(f - f_GSL): 0.0000000000000000 | |
45 | // stddev(f - f_GSL): 0.0000000000000000 | |
2be75957 ESR |
46 | const testcase_sph_legendre<double> |
47 | data001[21] = | |
48 | { | |
49 | { 0.28209479177387814, 0, 0, | |
b4688136 | 50 | 0.0000000000000000, 0.0 }, |
2be75957 | 51 | { 0.28209479177387814, 0, 0, |
b4688136 | 52 | 0.15707963267948966, 0.0 }, |
2be75957 | 53 | { 0.28209479177387814, 0, 0, |
b4688136 | 54 | 0.31415926535897931, 0.0 }, |
2be75957 | 55 | { 0.28209479177387814, 0, 0, |
b4688136 | 56 | 0.47123889803846897, 0.0 }, |
2be75957 | 57 | { 0.28209479177387814, 0, 0, |
b4688136 | 58 | 0.62831853071795862, 0.0 }, |
2be75957 | 59 | { 0.28209479177387814, 0, 0, |
b4688136 | 60 | 0.78539816339744828, 0.0 }, |
2be75957 | 61 | { 0.28209479177387814, 0, 0, |
b4688136 | 62 | 0.94247779607693793, 0.0 }, |
2be75957 | 63 | { 0.28209479177387814, 0, 0, |
b4688136 | 64 | 1.0995574287564276, 0.0 }, |
2be75957 | 65 | { 0.28209479177387814, 0, 0, |
b4688136 | 66 | 1.2566370614359172, 0.0 }, |
2be75957 | 67 | { 0.28209479177387814, 0, 0, |
b4688136 | 68 | 1.4137166941154069, 0.0 }, |
2be75957 | 69 | { 0.28209479177387814, 0, 0, |
b4688136 | 70 | 1.5707963267948966, 0.0 }, |
2be75957 | 71 | { 0.28209479177387814, 0, 0, |
b4688136 | 72 | 1.7278759594743862, 0.0 }, |
2be75957 | 73 | { 0.28209479177387814, 0, 0, |
b4688136 | 74 | 1.8849555921538759, 0.0 }, |
2be75957 | 75 | { 0.28209479177387814, 0, 0, |
b4688136 | 76 | 2.0420352248333655, 0.0 }, |
2be75957 | 77 | { 0.28209479177387814, 0, 0, |
b4688136 | 78 | 2.1991148575128552, 0.0 }, |
2be75957 | 79 | { 0.28209479177387814, 0, 0, |
b4688136 | 80 | 2.3561944901923448, 0.0 }, |
2be75957 | 81 | { 0.28209479177387814, 0, 0, |
b4688136 | 82 | 2.5132741228718345, 0.0 }, |
2be75957 | 83 | { 0.28209479177387814, 0, 0, |
b4688136 | 84 | 2.6703537555513241, 0.0 }, |
2be75957 | 85 | { 0.28209479177387814, 0, 0, |
b4688136 | 86 | 2.8274333882308138, 0.0 }, |
2be75957 | 87 | { 0.28209479177387814, 0, 0, |
b4688136 | 88 | 2.9845130209103035, 0.0 }, |
2be75957 | 89 | { 0.28209479177387814, 0, 0, |
b4688136 | 90 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
91 | }; |
92 | const double toler001 = 2.5000000000000020e-13; | |
93 | ||
94 | // Test data for l=1, m=0. | |
b4688136 | 95 | // max(|f - f_GSL|): 0.0000000000000000 at index 0 |
2be75957 | 96 | // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 |
b4688136 ESR |
97 | // mean(f - f_GSL): 0.0000000000000000 |
98 | // variance(f - f_GSL): 0.0000000000000000 | |
99 | // stddev(f - f_GSL): 0.0000000000000000 | |
2be75957 ESR |
100 | const testcase_sph_legendre<double> |
101 | data002[21] = | |
102 | { | |
103 | { 0.48860251190291992, 1, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 109 | { 0.43534802584032634, 1, 0, |
b4688136 ESR |
110 | 0.47123889803846897, 0.0 }, |
111 | { 0.39528773562374969, 1, 0, | |
112 | 0.62831853071795862, 0.0 }, | |
2be75957 | 113 | { 0.34549414947133550, 1, 0, |
b4688136 ESR |
114 | 0.78539816339744828, 0.0 }, |
115 | { 0.28719335072959395, 1, 0, | |
116 | 0.94247779607693793, 0.0 }, | |
2be75957 | 117 | { 0.22182089855280449, 1, 0, |
b4688136 | 118 | 1.0995574287564276, 0.0 }, |
2be75957 | 119 | { 0.15098647967228981, 1, 0, |
b4688136 | 120 | 1.2566370614359172, 0.0 }, |
2be75957 | 121 | { 0.076434272566846345, 1, 0, |
b4688136 ESR |
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 }, | |
2be75957 | 127 | { -0.15098647967228976, 1, 0, |
b4688136 ESR |
128 | 1.8849555921538759, 0.0 }, |
129 | { -0.22182089855280446, 1, 0, | |
130 | 2.0420352248333655, 0.0 }, | |
2be75957 | 131 | { -0.28719335072959384, 1, 0, |
b4688136 | 132 | 2.1991148575128552, 0.0 }, |
2be75957 | 133 | { -0.34549414947133544, 1, 0, |
b4688136 ESR |
134 | 2.3561944901923448, 0.0 }, |
135 | { -0.39528773562374975, 1, 0, | |
136 | 2.5132741228718345, 0.0 }, | |
2be75957 | 137 | { -0.43534802584032628, 1, 0, |
b4688136 | 138 | 2.6703537555513241, 0.0 }, |
2be75957 | 139 | { -0.46468860282345231, 1, 0, |
b4688136 | 140 | 2.8274333882308138, 0.0 }, |
2be75957 | 141 | { -0.48258700419201095, 1, 0, |
b4688136 | 142 | 2.9845130209103035, 0.0 }, |
2be75957 | 143 | { -0.48860251190291992, 1, 0, |
b4688136 | 144 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
145 | }; |
146 | const double toler002 = 2.5000000000000020e-13; | |
147 | ||
148 | // Test data for l=1, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
154 | const testcase_sph_legendre<double> |
155 | data003[21] = | |
156 | { | |
157 | { 0.0000000000000000, 1, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 163 | { -0.15685106157558129, 1, 1, |
b4688136 ESR |
164 | 0.47123889803846897, 0.0 }, |
165 | { -0.20307636581258248, 1, 1, | |
166 | 0.62831853071795862, 0.0 }, | |
2be75957 | 167 | { -0.24430125595146007, 1, 1, |
b4688136 | 168 | 0.78539816339744828, 0.0 }, |
2be75957 | 169 | { -0.27951063837942880, 1, 1, |
b4688136 | 170 | 0.94247779607693793, 0.0 }, |
2be75957 | 171 | { -0.30783754124787122, 1, 1, |
b4688136 | 172 | 1.0995574287564276, 0.0 }, |
2be75957 | 173 | { -0.32858446219656556, 1, 1, |
b4688136 | 174 | 1.2566370614359172, 0.0 }, |
2be75957 | 175 | { -0.34124054317667202, 1, 1, |
b4688136 | 176 | 1.4137166941154069, 0.0 }, |
2be75957 | 177 | { -0.34549414947133567, 1, 1, |
b4688136 | 178 | 1.5707963267948966, 0.0 }, |
2be75957 | 179 | { -0.34124054317667202, 1, 1, |
b4688136 | 180 | 1.7278759594743862, 0.0 }, |
2be75957 | 181 | { -0.32858446219656556, 1, 1, |
b4688136 | 182 | 1.8849555921538759, 0.0 }, |
2be75957 | 183 | { -0.30783754124787127, 1, 1, |
b4688136 | 184 | 2.0420352248333655, 0.0 }, |
2be75957 | 185 | { -0.27951063837942880, 1, 1, |
b4688136 | 186 | 2.1991148575128552, 0.0 }, |
2be75957 | 187 | { -0.24430125595146013, 1, 1, |
b4688136 ESR |
188 | 2.3561944901923448, 0.0 }, |
189 | { -0.20307636581258243, 1, 1, | |
190 | 2.5132741228718345, 0.0 }, | |
2be75957 | 191 | { -0.15685106157558140, 1, 1, |
b4688136 | 192 | 2.6703537555513241, 0.0 }, |
2be75957 | 193 | { -0.10676356364376104, 1, 1, |
b4688136 | 194 | 2.8274333882308138, 0.0 }, |
2be75957 | 195 | { -0.054047192447078167, 1, 1, |
b4688136 | 196 | 2.9845130209103035, 0.0 }, |
2be75957 | 197 | { 0.0000000000000000, 1, 1, |
b4688136 | 198 | 3.1415926535897931, 0.0 }, |
2be75957 | 199 | }; |
b4688136 | 200 | const double toler003 = 5.0000000000000039e-13; |
2be75957 ESR |
201 | |
202 | // Test data for l=2, m=0. | |
b4688136 ESR |
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 | |
2be75957 ESR |
208 | const testcase_sph_legendre<double> |
209 | data004[21] = | |
210 | { | |
211 | { 0.63078313050504009, 2, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 217 | { 0.43576954875556589, 2, 0, |
b4688136 ESR |
218 | 0.47123889803846897, 0.0 }, |
219 | { 0.30388781294457567, 2, 0, | |
220 | 0.62831853071795862, 0.0 }, | |
2be75957 | 221 | { 0.15769578262626011, 2, 0, |
b4688136 ESR |
222 | 0.78539816339744828, 0.0 }, |
223 | { 0.011503752307944374, 2, 0, | |
224 | 0.94247779607693793, 0.0 }, | |
2be75957 | 225 | { -0.12037798350304570, 2, 0, |
b4688136 | 226 | 1.0995574287564276, 0.0 }, |
2be75957 | 227 | { -0.22503992163144576, 2, 0, |
b4688136 | 228 | 1.2566370614359172, 0.0 }, |
2be75957 | 229 | { -0.29223702235064597, 2, 0, |
b4688136 | 230 | 1.4137166941154069, 0.0 }, |
2be75957 | 231 | { -0.31539156525252005, 2, 0, |
b4688136 ESR |
232 | 1.5707963267948966, 0.0 }, |
233 | { -0.29223702235064597, 2, 0, | |
234 | 1.7278759594743862, 0.0 }, | |
2be75957 | 235 | { -0.22503992163144584, 2, 0, |
b4688136 ESR |
236 | 1.8849555921538759, 0.0 }, |
237 | { -0.12037798350304577, 2, 0, | |
238 | 2.0420352248333655, 0.0 }, | |
2be75957 | 239 | { 0.011503752307944164, 2, 0, |
b4688136 | 240 | 2.1991148575128552, 0.0 }, |
2be75957 | 241 | { 0.15769578262625994, 2, 0, |
b4688136 ESR |
242 | 2.3561944901923448, 0.0 }, |
243 | { 0.30388781294457579, 2, 0, | |
244 | 2.5132741228718345, 0.0 }, | |
2be75957 | 245 | { 0.43576954875556562, 2, 0, |
b4688136 | 246 | 2.6703537555513241, 0.0 }, |
2be75957 | 247 | { 0.54043148688396569, 2, 0, |
b4688136 | 248 | 2.8274333882308138, 0.0 }, |
2be75957 | 249 | { 0.60762858760316585, 2, 0, |
b4688136 | 250 | 2.9845130209103035, 0.0 }, |
2be75957 | 251 | { 0.63078313050504009, 2, 0, |
b4688136 | 252 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
253 | }; |
254 | const double toler004 = 2.5000000000000020e-13; | |
255 | ||
256 | // Test data for l=2, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
262 | const testcase_sph_legendre<double> |
263 | data005[21] = | |
264 | { | |
265 | { 0.0000000000000000, 2, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 271 | { -0.31250239392538215, 2, 1, |
b4688136 | 272 | 0.47123889803846897, 0.0 }, |
2be75957 | 273 | { -0.36736859691086526, 2, 1, |
b4688136 | 274 | 0.62831853071795862, 0.0 }, |
2be75957 | 275 | { -0.38627420202318979, 2, 1, |
b4688136 ESR |
276 | 0.78539816339744828, 0.0 }, |
277 | { -0.36736859691086532, 2, 1, | |
278 | 0.94247779607693793, 0.0 }, | |
2be75957 | 279 | { -0.31250239392538226, 2, 1, |
b4688136 | 280 | 1.0995574287564276, 0.0 }, |
2be75957 | 281 | { -0.22704627929027438, 2, 1, |
b4688136 | 282 | 1.2566370614359172, 0.0 }, |
2be75957 | 283 | { -0.11936529291378740, 2, 1, |
b4688136 ESR |
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 }, | |
2be75957 | 289 | { 0.22704627929027429, 2, 1, |
b4688136 ESR |
290 | 1.8849555921538759, 0.0 }, |
291 | { 0.31250239392538226, 2, 1, | |
292 | 2.0420352248333655, 0.0 }, | |
2be75957 | 293 | { 0.36736859691086521, 2, 1, |
b4688136 | 294 | 2.1991148575128552, 0.0 }, |
2be75957 | 295 | { 0.38627420202318979, 2, 1, |
b4688136 | 296 | 2.3561944901923448, 0.0 }, |
2be75957 | 297 | { 0.36736859691086526, 2, 1, |
b4688136 | 298 | 2.5132741228718345, 0.0 }, |
2be75957 | 299 | { 0.31250239392538232, 2, 1, |
b4688136 | 300 | 2.6703537555513241, 0.0 }, |
2be75957 | 301 | { 0.22704627929027449, 2, 1, |
b4688136 | 302 | 2.8274333882308138, 0.0 }, |
2be75957 | 303 | { 0.11936529291378781, 2, 1, |
b4688136 | 304 | 2.9845130209103035, 0.0 }, |
2be75957 | 305 | { 0.0000000000000000, 2, 1, |
b4688136 | 306 | 3.1415926535897931, 0.0 }, |
2be75957 | 307 | }; |
b4688136 | 308 | const double toler005 = 5.0000000000000039e-13; |
2be75957 ESR |
309 | |
310 | // Test data for l=2, m=2. | |
b4688136 ESR |
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 | |
2be75957 ESR |
316 | const testcase_sph_legendre<double> |
317 | data006[21] = | |
318 | { | |
319 | { 0.0000000000000000, 2, 2, | |
b4688136 ESR |
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 }, | |
2be75957 | 325 | { 0.079613961366457681, 2, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 331 | { 0.25281974746848851, 2, 2, |
b4688136 | 332 | 0.94247779607693793, 0.0 }, |
2be75957 | 333 | { 0.30666024065673209, 2, 2, |
b4688136 | 334 | 1.0995574287564276, 0.0 }, |
2be75957 | 335 | { 0.34938829797428600, 2, 2, |
b4688136 | 336 | 1.2566370614359172, 0.0 }, |
2be75957 | 337 | { 0.37682139946702753, 2, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 343 | { 0.34938829797428606, 2, 2, |
b4688136 ESR |
344 | 1.8849555921538759, 0.0 }, |
345 | { 0.30666024065673214, 2, 2, | |
346 | 2.0420352248333655, 0.0 }, | |
2be75957 | 347 | { 0.25281974746848856, 2, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 353 | { 0.079613961366457764, 2, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 359 | { 0.0000000000000000, 2, 2, |
b4688136 | 360 | 3.1415926535897931, 0.0 }, |
2be75957 | 361 | }; |
b4688136 | 362 | const double toler006 = 5.0000000000000039e-13; |
2be75957 ESR |
363 | |
364 | // Test data for l=5, m=0. | |
b4688136 | 365 | // max(|f - f_GSL|): 1.0547118733938987e-15 at index 18 |
2be75957 | 366 | // max(|f - f_GSL| / |f_GSL|): 2.9385557676213648e-15 |
b4688136 ESR |
367 | // mean(f - f_GSL): -4.2955057500378082e-17 |
368 | // variance(f - f_GSL): 9.6869690655191325e-35 | |
369 | // stddev(f - f_GSL): 9.8422401238331574e-18 | |
2be75957 ESR |
370 | const testcase_sph_legendre<double> |
371 | data007[21] = | |
372 | { | |
373 | { 0.93560257962738880, 5, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 379 | { -0.090214932090594294, 5, 0, |
b4688136 ESR |
380 | 0.47123889803846897, 0.0 }, |
381 | { -0.36214460396518905, 5, 0, | |
382 | 0.62831853071795862, 0.0 }, | |
2be75957 | 383 | { -0.35145955579226906, 5, 0, |
b4688136 ESR |
384 | 0.78539816339744828, 0.0 }, |
385 | { -0.11441703594725193, 5, 0, | |
386 | 0.94247779607693793, 0.0 }, | |
2be75957 | 387 | { 0.17248966720808107, 5, 0, |
b4688136 | 388 | 1.0995574287564276, 0.0 }, |
2be75957 | 389 | { 0.32128384287200523, 5, 0, |
b4688136 | 390 | 1.2566370614359172, 0.0 }, |
2be75957 | 391 | { 0.24377632246714948, 5, 0, |
b4688136 ESR |
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 }, | |
2be75957 | 397 | { -0.32128384287200534, 5, 0, |
b4688136 ESR |
398 | 1.8849555921538759, 0.0 }, |
399 | { -0.17248966720808118, 5, 0, | |
400 | 2.0420352248333655, 0.0 }, | |
2be75957 | 401 | { 0.11441703594725151, 5, 0, |
b4688136 | 402 | 2.1991148575128552, 0.0 }, |
2be75957 | 403 | { 0.35145955579226895, 5, 0, |
b4688136 ESR |
404 | 2.3561944901923448, 0.0 }, |
405 | { 0.36214460396518883, 5, 0, | |
406 | 2.5132741228718345, 0.0 }, | |
2be75957 | 407 | { 0.090214932090594752, 5, 0, |
b4688136 | 408 | 2.6703537555513241, 0.0 }, |
2be75957 | 409 | { -0.35892185032365165, 5, 0, |
b4688136 | 410 | 2.8274333882308138, 0.0 }, |
2be75957 | 411 | { -0.77014422942079852, 5, 0, |
b4688136 | 412 | 2.9845130209103035, 0.0 }, |
2be75957 | 413 | { -0.93560257962738880, 5, 0, |
b4688136 | 414 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
415 | }; |
416 | const double toler007 = 2.5000000000000020e-13; | |
417 | ||
418 | // Test data for l=5, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
424 | const testcase_sph_legendre<double> |
425 | data008[21] = | |
426 | { | |
427 | { 0.0000000000000000, 5, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 433 | { -0.45381991493631763, 5, 1, |
b4688136 ESR |
434 | 0.47123889803846897, 0.0 }, |
435 | { -0.15679720635769906, 5, 1, | |
436 | 0.62831853071795862, 0.0 }, | |
2be75957 | 437 | { 0.16985499419838601, 5, 1, |
b4688136 ESR |
438 | 0.78539816339744828, 0.0 }, |
439 | { 0.34468004499725169, 5, 1, | |
440 | 0.94247779607693793, 0.0 }, | |
2be75957 | 441 | { 0.28349471119605985, 5, 1, |
b4688136 | 442 | 1.0995574287564276, 0.0 }, |
2be75957 | 443 | { 0.044286619339675815, 5, 1, |
b4688136 | 444 | 1.2566370614359172, 0.0 }, |
2be75957 | 445 | { -0.21193784177193470, 5, 1, |
b4688136 | 446 | 1.4137166941154069, 0.0 }, |
2be75957 | 447 | { -0.32028164857621527, 5, 1, |
b4688136 ESR |
448 | 1.5707963267948966, 0.0 }, |
449 | { -0.21193784177193487, 5, 1, | |
450 | 1.7278759594743862, 0.0 }, | |
2be75957 | 451 | { 0.044286619339675592, 5, 1, |
b4688136 ESR |
452 | 1.8849555921538759, 0.0 }, |
453 | { 0.28349471119605973, 5, 1, | |
454 | 2.0420352248333655, 0.0 }, | |
2be75957 | 455 | { 0.34468004499725174, 5, 1, |
b4688136 | 456 | 2.1991148575128552, 0.0 }, |
2be75957 | 457 | { 0.16985499419838640, 5, 1, |
b4688136 ESR |
458 | 2.3561944901923448, 0.0 }, |
459 | { -0.15679720635769961, 5, 1, | |
460 | 2.5132741228718345, 0.0 }, | |
2be75957 | 461 | { -0.45381991493631768, 5, 1, |
b4688136 | 462 | 2.6703537555513241, 0.0 }, |
2be75957 | 463 | { -0.54610329010534753, 5, 1, |
b4688136 | 464 | 2.8274333882308138, 0.0 }, |
2be75957 | 465 | { -0.36712373713318402, 5, 1, |
b4688136 | 466 | 2.9845130209103035, 0.0 }, |
2be75957 | 467 | { 0.0000000000000000, 5, 1, |
b4688136 | 468 | 3.1415926535897931, 0.0 }, |
2be75957 | 469 | }; |
b4688136 | 470 | const double toler008 = 5.0000000000000039e-13; |
2be75957 ESR |
471 | |
472 | // Test data for l=5, m=2. | |
b4688136 ESR |
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 | |
2be75957 ESR |
478 | const testcase_sph_legendre<double> |
479 | data009[21] = | |
480 | { | |
481 | { 0.0000000000000000, 5, 2, | |
b4688136 ESR |
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 }, | |
2be75957 | 487 | { 0.43002359842080096, 5, 2, |
b4688136 | 488 | 0.47123889803846897, 0.0 }, |
2be75957 | 489 | { 0.45642486439050983, 5, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 495 | { -0.23313989334673826, 5, 2, |
b4688136 | 496 | 1.0995574287564276, 0.0 }, |
2be75957 | 497 | { -0.33799912776303714, 5, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 505 | { 0.33799912776303714, 5, 2, |
b4688136 | 506 | 1.8849555921538759, 0.0 }, |
2be75957 | 507 | { 0.23313989334673843, 5, 2, |
b4688136 | 508 | 2.0420352248333655, 0.0 }, |
2be75957 | 509 | { -0.023781239849531916, 5, 2, |
b4688136 ESR |
510 | 2.1991148575128552, 0.0 }, |
511 | { -0.29959604906083270, 5, 2, | |
512 | 2.3561944901923448, 0.0 }, | |
2be75957 | 513 | { -0.45642486439050983, 5, 2, |
b4688136 | 514 | 2.5132741228718345, 0.0 }, |
2be75957 | 515 | { -0.43002359842080118, 5, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 521 | { 0.0000000000000000, 5, 2, |
b4688136 | 522 | 3.1415926535897931, 0.0 }, |
2be75957 | 523 | }; |
b4688136 | 524 | const double toler009 = 5.0000000000000039e-13; |
2be75957 ESR |
525 | |
526 | // Test data for l=5, m=5. | |
b4688136 ESR |
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 | |
2be75957 ESR |
532 | const testcase_sph_legendre<double> |
533 | data010[21] = | |
534 | { | |
535 | { 0.0000000000000000, 5, 5, | |
b4688136 ESR |
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 }, | |
2be75957 | 541 | { -0.0089510818191922761, 5, 5, |
b4688136 ESR |
542 | 0.47123889803846897, 0.0 }, |
543 | { -0.032563803777573910, 5, 5, | |
544 | 0.62831853071795862, 0.0 }, | |
2be75957 | 545 | { -0.082047757105021241, 5, 5, |
b4688136 ESR |
546 | 0.78539816339744828, 0.0 }, |
547 | { -0.16085328164143806, 5, 5, | |
548 | 0.94247779607693793, 0.0 }, | |
2be75957 | 549 | { -0.26064303436645381, 5, 5, |
b4688136 | 550 | 1.0995574287564276, 0.0 }, |
2be75957 | 551 | { -0.36113811790820571, 5, 5, |
b4688136 | 552 | 1.2566370614359172, 0.0 }, |
2be75957 | 553 | { -0.43625592459446139, 5, 5, |
b4688136 | 554 | 1.4137166941154069, 0.0 }, |
2be75957 | 555 | { -0.46413220344085809, 5, 5, |
b4688136 ESR |
556 | 1.5707963267948966, 0.0 }, |
557 | { -0.43625592459446144, 5, 5, | |
558 | 1.7278759594743862, 0.0 }, | |
2be75957 | 559 | { -0.36113811790820577, 5, 5, |
b4688136 ESR |
560 | 1.8849555921538759, 0.0 }, |
561 | { -0.26064303436645381, 5, 5, | |
562 | 2.0420352248333655, 0.0 }, | |
2be75957 | 563 | { -0.16085328164143822, 5, 5, |
b4688136 | 564 | 2.1991148575128552, 0.0 }, |
2be75957 | 565 | { -0.082047757105021310, 5, 5, |
b4688136 ESR |
566 | 2.3561944901923448, 0.0 }, |
567 | { -0.032563803777573896, 5, 5, | |
568 | 2.5132741228718345, 0.0 }, | |
2be75957 | 569 | { -0.0089510818191923004, 5, 5, |
b4688136 | 570 | 2.6703537555513241, 0.0 }, |
2be75957 | 571 | { -0.0013078367086431812, 5, 5, |
b4688136 | 572 | 2.8274333882308138, 0.0 }, |
2be75957 | 573 | { -4.3481439097910151e-05, 5, 5, |
b4688136 | 574 | 2.9845130209103035, 0.0 }, |
2be75957 | 575 | { 0.0000000000000000, 5, 5, |
b4688136 | 576 | 3.1415926535897931, 0.0 }, |
2be75957 | 577 | }; |
b4688136 | 578 | const double toler010 = 5.0000000000000039e-13; |
2be75957 ESR |
579 | |
580 | // Test data for l=10, m=0. | |
b4688136 ESR |
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 | |
2be75957 ESR |
586 | const testcase_sph_legendre<double> |
587 | data011[21] = | |
588 | { | |
589 | { 1.2927207364566027, 10, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 595 | { -0.25532095827149687, 10, 0, |
b4688136 ESR |
596 | 0.47123889803846897, 0.0 }, |
597 | { 0.36625249688013994, 10, 0, | |
598 | 0.62831853071795862, 0.0 }, | |
2be75957 | 599 | { 0.14880806329084206, 10, 0, |
b4688136 ESR |
600 | 0.78539816339744828, 0.0 }, |
601 | { -0.33533356797848740, 10, 0, | |
602 | 0.94247779607693793, 0.0 }, | |
2be75957 | 603 | { -0.080639967662335665, 10, 0, |
b4688136 | 604 | 1.0995574287564276, 0.0 }, |
2be75957 | 605 | { 0.32197986450174521, 10, 0, |
b4688136 | 606 | 1.2566370614359172, 0.0 }, |
2be75957 | 607 | { 0.025713542103667848, 10, 0, |
b4688136 | 608 | 1.4137166941154069, 0.0 }, |
2be75957 | 609 | { -0.31813049373736707, 10, 0, |
b4688136 ESR |
610 | 1.5707963267948966, 0.0 }, |
611 | { 0.025713542103667528, 10, 0, | |
612 | 1.7278759594743862, 0.0 }, | |
2be75957 | 613 | { 0.32197986450174543, 10, 0, |
b4688136 ESR |
614 | 1.8849555921538759, 0.0 }, |
615 | { -0.080639967662335416, 10, 0, | |
616 | 2.0420352248333655, 0.0 }, | |
2be75957 | 617 | { -0.33533356797848757, 10, 0, |
b4688136 | 618 | 2.1991148575128552, 0.0 }, |
2be75957 | 619 | { 0.14880806329084156, 10, 0, |
b4688136 ESR |
620 | 2.3561944901923448, 0.0 }, |
621 | { 0.36625249688013961, 10, 0, | |
622 | 2.5132741228718345, 0.0 }, | |
2be75957 | 623 | { -0.25532095827149576, 10, 0, |
b4688136 | 624 | 2.6703537555513241, 0.0 }, |
2be75957 | 625 | { -0.44874428379711545, 10, 0, |
b4688136 | 626 | 2.8274333882308138, 0.0 }, |
2be75957 | 627 | { 0.55288895150522011, 10, 0, |
b4688136 | 628 | 2.9845130209103035, 0.0 }, |
2be75957 | 629 | { 1.2927207364566027, 10, 0, |
b4688136 | 630 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
631 | }; |
632 | const double toler011 = 2.5000000000000020e-13; | |
633 | ||
634 | // Test data for l=10, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
640 | const testcase_sph_legendre<double> |
641 | data012[21] = | |
642 | { | |
643 | { 0.0000000000000000, 10, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 649 | { 0.42219282075271530, 10, 1, |
b4688136 ESR |
650 | 0.47123889803846897, 0.0 }, |
651 | { 0.17109256898931161, 10, 1, | |
652 | 0.62831853071795862, 0.0 }, | |
2be75957 | 653 | { -0.35583574648544281, 10, 1, |
b4688136 ESR |
654 | 0.78539816339744828, 0.0 }, |
655 | { -0.10089212303544023, 10, 1, | |
656 | 0.94247779607693793, 0.0 }, | |
2be75957 | 657 | { 0.32997652649321085, 10, 1, |
b4688136 | 658 | 1.0995574287564276, 0.0 }, |
2be75957 | 659 | { 0.047416376890032939, 10, 1, |
b4688136 | 660 | 1.2566370614359172, 0.0 }, |
2be75957 | 661 | { -0.31999356750295660, 10, 1, |
b4688136 ESR |
662 | 1.4137166941154069, 0.0 }, |
663 | { -2.0430664782290742e-16, 10, 1, | |
664 | 1.5707963267948966, 0.0 }, | |
2be75957 | 665 | { 0.31999356750295660, 10, 1, |
b4688136 | 666 | 1.7278759594743862, 0.0 }, |
2be75957 | 667 | { -0.047416376890032544, 10, 1, |
b4688136 ESR |
668 | 1.8849555921538759, 0.0 }, |
669 | { -0.32997652649321096, 10, 1, | |
670 | 2.0420352248333655, 0.0 }, | |
2be75957 | 671 | { 0.10089212303543935, 10, 1, |
b4688136 | 672 | 2.1991148575128552, 0.0 }, |
2be75957 | 673 | { 0.35583574648544292, 10, 1, |
b4688136 ESR |
674 | 2.3561944901923448, 0.0 }, |
675 | { -0.17109256898931269, 10, 1, | |
676 | 2.5132741228718345, 0.0 }, | |
2be75957 | 677 | { -0.42219282075271569, 10, 1, |
b4688136 | 678 | 2.6703537555513241, 0.0 }, |
2be75957 | 679 | { 0.29035110456209601, 10, 1, |
b4688136 | 680 | 2.8274333882308138, 0.0 }, |
2be75957 | 681 | { 0.74373723919064050, 10, 1, |
b4688136 | 682 | 2.9845130209103035, 0.0 }, |
2be75957 | 683 | { 0.0000000000000000, 10, 1, |
b4688136 | 684 | 3.1415926535897931, 0.0 }, |
2be75957 | 685 | }; |
b4688136 | 686 | const double toler012 = 1.0000000000000008e-12; |
2be75957 ESR |
687 | |
688 | // Test data for l=10, m=2. | |
b4688136 ESR |
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 | |
2be75957 ESR |
694 | const testcase_sph_legendre<double> |
695 | data013[21] = | |
696 | { | |
697 | { 0.0000000000000000, 10, 2, | |
b4688136 ESR |
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 }, | |
2be75957 | 703 | { 0.098210039644716252, 10, 2, |
b4688136 ESR |
704 | 0.47123889803846897, 0.0 }, |
705 | { -0.41494799233049695, 10, 2, | |
706 | 0.62831853071795862, 0.0 }, | |
2be75957 | 707 | { -0.081698973831472732, 10, 2, |
b4688136 | 708 | 0.78539816339744828, 0.0 }, |
2be75957 | 709 | { 0.35253132222271277, 10, 2, |
b4688136 | 710 | 0.94247779607693793, 0.0 }, |
2be75957 | 711 | { 0.049026298555980979, 10, 2, |
b4688136 | 712 | 1.0995574287564276, 0.0 }, |
2be75957 | 713 | { -0.32791246874130792, 10, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 721 | { -0.32791246874130803, 10, 2, |
b4688136 ESR |
722 | 1.8849555921538759, 0.0 }, |
723 | { 0.049026298555980730, 10, 2, | |
724 | 2.0420352248333655, 0.0 }, | |
2be75957 | 725 | { 0.35253132222271266, 10, 2, |
b4688136 | 726 | 2.1991148575128552, 0.0 }, |
2be75957 | 727 | { -0.081698973831472121, 10, 2, |
b4688136 ESR |
728 | 2.3561944901923448, 0.0 }, |
729 | { -0.41494799233049684, 10, 2, | |
730 | 2.5132741228718345, 0.0 }, | |
2be75957 | 731 | { 0.098210039644715197, 10, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 737 | { 0.0000000000000000, 10, 2, |
b4688136 | 738 | 3.1415926535897931, 0.0 }, |
2be75957 | 739 | }; |
b4688136 | 740 | const double toler013 = 5.0000000000000039e-13; |
2be75957 ESR |
741 | |
742 | // Test data for l=10, m=5. | |
b4688136 ESR |
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 | |
2be75957 ESR |
748 | const testcase_sph_legendre<double> |
749 | data014[21] = | |
750 | { | |
751 | { 0.0000000000000000, 10, 5, | |
b4688136 ESR |
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 }, | |
2be75957 | 757 | { -0.30055029290703639, 10, 5, |
b4688136 ESR |
758 | 0.47123889803846897, 0.0 }, |
759 | { -0.49987818144009138, 10, 5, | |
760 | 0.62831853071795862, 0.0 }, | |
2be75957 | 761 | { -0.28108771757150108, 10, 5, |
b4688136 ESR |
762 | 0.78539816339744828, 0.0 }, |
763 | { 0.22068081187249255, 10, 5, | |
764 | 0.94247779607693793, 0.0 }, | |
2be75957 | 765 | { 0.33689502212592121, 10, 5, |
b4688136 | 766 | 1.0995574287564276, 0.0 }, |
2be75957 | 767 | { -0.086095515520764110, 10, 5, |
b4688136 | 768 | 1.2566370614359172, 0.0 }, |
2be75957 | 769 | { -0.33935827318511558, 10, 5, |
b4688136 ESR |
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 }, | |
2be75957 | 775 | { 0.086095515520764512, 10, 5, |
b4688136 ESR |
776 | 1.8849555921538759, 0.0 }, |
777 | { -0.33689502212592104, 10, 5, | |
778 | 2.0420352248333655, 0.0 }, | |
2be75957 | 779 | { -0.22068081187249344, 10, 5, |
b4688136 | 780 | 2.1991148575128552, 0.0 }, |
2be75957 | 781 | { 0.28108771757150064, 10, 5, |
b4688136 ESR |
782 | 2.3561944901923448, 0.0 }, |
783 | { 0.49987818144009155, 10, 5, | |
784 | 2.5132741228718345, 0.0 }, | |
2be75957 | 785 | { 0.30055029290703672, 10, 5, |
b4688136 | 786 | 2.6703537555513241, 0.0 }, |
2be75957 | 787 | { 0.070348585248056802, 10, 5, |
b4688136 | 788 | 2.8274333882308138, 0.0 }, |
2be75957 | 789 | { 0.0030300124052750873, 10, 5, |
b4688136 | 790 | 2.9845130209103035, 0.0 }, |
2be75957 | 791 | { 0.0000000000000000, 10, 5, |
b4688136 | 792 | 3.1415926535897931, 0.0 }, |
2be75957 | 793 | }; |
b4688136 | 794 | const double toler014 = 5.0000000000000039e-13; |
2be75957 ESR |
795 | |
796 | // Test data for l=10, m=10. | |
b4688136 ESR |
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 | |
2be75957 ESR |
802 | const testcase_sph_legendre<double> |
803 | data015[21] = | |
804 | { | |
805 | { 0.0000000000000000, 10, 10, | |
b4688136 ESR |
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 }, | |
2be75957 | 811 | { 0.00020182347649472387, 10, 10, |
b4688136 ESR |
812 | 0.47123889803846897, 0.0 }, |
813 | { 0.0026711045506511706, 10, 10, | |
814 | 0.62831853071795862, 0.0 }, | |
2be75957 | 815 | { 0.016957196623256909, 10, 10, |
b4688136 ESR |
816 | 0.78539816339744828, 0.0 }, |
817 | { 0.065174916004990271, 10, 10, | |
818 | 0.94247779607693793, 0.0 }, | |
2be75957 | 819 | { 0.17112476903017845, 10, 10, |
b4688136 | 820 | 1.0995574287564276, 0.0 }, |
2be75957 | 821 | { 0.32852414199733554, 10, 10, |
b4688136 | 822 | 1.2566370614359172, 0.0 }, |
2be75957 | 823 | { 0.47940582314838287, 10, 10, |
b4688136 | 824 | 1.4137166941154069, 0.0 }, |
2be75957 | 825 | { 0.54263029194422152, 10, 10, |
b4688136 ESR |
826 | 1.5707963267948966, 0.0 }, |
827 | { 0.47940582314838293, 10, 10, | |
828 | 1.7278759594743862, 0.0 }, | |
2be75957 | 829 | { 0.32852414199733571, 10, 10, |
b4688136 ESR |
830 | 1.8849555921538759, 0.0 }, |
831 | { 0.17112476903017851, 10, 10, | |
832 | 2.0420352248333655, 0.0 }, | |
2be75957 | 833 | { 0.065174916004990410, 10, 10, |
b4688136 | 834 | 2.1991148575128552, 0.0 }, |
2be75957 | 835 | { 0.016957196623256943, 10, 10, |
b4688136 ESR |
836 | 2.3561944901923448, 0.0 }, |
837 | { 0.0026711045506511684, 10, 10, | |
838 | 2.5132741228718345, 0.0 }, | |
2be75957 | 839 | { 0.00020182347649472493, 10, 10, |
b4688136 | 840 | 2.6703537555513241, 0.0 }, |
2be75957 | 841 | { 4.3085156534549772e-06, 10, 10, |
b4688136 | 842 | 2.8274333882308138, 0.0 }, |
2be75957 | 843 | { 4.7624282733345673e-09, 10, 10, |
b4688136 | 844 | 2.9845130209103035, 0.0 }, |
2be75957 | 845 | { 0.0000000000000000, 10, 10, |
b4688136 | 846 | 3.1415926535897931, 0.0 }, |
2be75957 | 847 | }; |
b4688136 | 848 | const double toler015 = 5.0000000000000039e-13; |
2be75957 ESR |
849 | |
850 | // Test data for l=20, m=0. | |
b4688136 ESR |
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 | |
2be75957 ESR |
856 | const testcase_sph_legendre<double> |
857 | data016[21] = | |
858 | { | |
859 | { 1.8062879984608917, 20, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 865 | { -0.39955402700466724, 20, 0, |
b4688136 ESR |
866 | 0.47123889803846897, 0.0 }, |
867 | { 0.36818552901640805, 20, 0, | |
868 | 0.62831853071795862, 0.0 }, | |
2be75957 | 869 | { -0.34873131330857743, 20, 0, |
b4688136 ESR |
870 | 0.78539816339744828, 0.0 }, |
871 | { 0.33600882829186468, 20, 0, | |
872 | 0.94247779607693793, 0.0 }, | |
2be75957 | 873 | { -0.32759286308122931, 20, 0, |
b4688136 | 874 | 1.0995574287564276, 0.0 }, |
2be75957 | 875 | { 0.32222458068091325, 20, 0, |
b4688136 | 876 | 1.2566370614359172, 0.0 }, |
2be75957 | 877 | { -0.31922731037135965, 20, 0, |
b4688136 | 878 | 1.4137166941154069, 0.0 }, |
2be75957 | 879 | { 0.31826262039531755, 20, 0, |
b4688136 ESR |
880 | 1.5707963267948966, 0.0 }, |
881 | { -0.31922731037135971, 20, 0, | |
882 | 1.7278759594743862, 0.0 }, | |
2be75957 | 883 | { 0.32222458068091342, 20, 0, |
b4688136 ESR |
884 | 1.8849555921538759, 0.0 }, |
885 | { -0.32759286308122926, 20, 0, | |
886 | 2.0420352248333655, 0.0 }, | |
2be75957 | 887 | { 0.33600882829186518, 20, 0, |
b4688136 | 888 | 2.1991148575128552, 0.0 }, |
2be75957 | 889 | { -0.34873131330857782, 20, 0, |
b4688136 ESR |
890 | 2.3561944901923448, 0.0 }, |
891 | { 0.36818552901640772, 20, 0, | |
892 | 2.5132741228718345, 0.0 }, | |
2be75957 | 893 | { -0.39955402700466824, 20, 0, |
b4688136 | 894 | 2.6703537555513241, 0.0 }, |
2be75957 | 895 | { 0.45624611402342408, 20, 0, |
b4688136 | 896 | 2.8274333882308138, 0.0 }, |
2be75957 | 897 | { -0.58906549291416732, 20, 0, |
b4688136 | 898 | 2.9845130209103035, 0.0 }, |
2be75957 | 899 | { 1.8062879984608917, 20, 0, |
b4688136 | 900 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
901 | }; |
902 | const double toler016 = 2.5000000000000020e-13; | |
903 | ||
904 | // Test data for l=20, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
910 | const testcase_sph_legendre<double> |
911 | data017[21] = | |
912 | { | |
913 | { 0.0000000000000000, 20, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 919 | { -0.23278757741246778, 20, 1, |
b4688136 ESR |
920 | 0.47123889803846897, 0.0 }, |
921 | { 0.17937240823503983, 20, 1, | |
922 | 0.62831853071795862, 0.0 }, | |
2be75957 | 923 | { -0.13857299972299839, 20, 1, |
b4688136 ESR |
924 | 0.78539816339744828, 0.0 }, |
925 | { 0.10495324841927815, 20, 1, | |
926 | 0.94247779607693793, 0.0 }, | |
2be75957 | 927 | { -0.075707774352163665, 20, 1, |
b4688136 | 928 | 1.0995574287564276, 0.0 }, |
2be75957 | 929 | { 0.049168697683476224, 20, 1, |
b4688136 | 930 | 1.2566370614359172, 0.0 }, |
2be75957 | 931 | { -0.024216050551253303, 20, 1, |
b4688136 ESR |
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 }, | |
2be75957 | 937 | { -0.049168697683475482, 20, 1, |
b4688136 ESR |
938 | 1.8849555921538759, 0.0 }, |
939 | { 0.075707774352163346, 20, 1, | |
940 | 2.0420352248333655, 0.0 }, | |
2be75957 | 941 | { -0.10495324841927638, 20, 1, |
b4688136 | 942 | 2.1991148575128552, 0.0 }, |
2be75957 | 943 | { 0.13857299972299741, 20, 1, |
b4688136 ESR |
944 | 2.3561944901923448, 0.0 }, |
945 | { -0.17937240823504172, 20, 1, | |
946 | 2.5132741228718345, 0.0 }, | |
2be75957 | 947 | { 0.23278757741246703, 20, 1, |
b4688136 | 948 | 2.6703537555513241, 0.0 }, |
2be75957 | 949 | { -0.31166370423309253, 20, 1, |
b4688136 | 950 | 2.8274333882308138, 0.0 }, |
2be75957 | 951 | { 0.45905213045059046, 20, 1, |
b4688136 | 952 | 2.9845130209103035, 0.0 }, |
2be75957 | 953 | { 0.0000000000000000, 20, 1, |
b4688136 | 954 | 3.1415926535897931, 0.0 }, |
2be75957 | 955 | }; |
b4688136 | 956 | const double toler017 = 1.0000000000000008e-12; |
2be75957 ESR |
957 | |
958 | // Test data for l=20, m=2. | |
b4688136 ESR |
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 | |
2be75957 ESR |
964 | const testcase_sph_legendre<double> |
965 | data018[21] = | |
966 | { | |
967 | { 0.0000000000000000, 20, 2, | |
b4688136 ESR |
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 }, | |
2be75957 | 973 | { 0.44520137308557572, 20, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 981 | { 0.33214917638387642, 20, 2, |
b4688136 | 982 | 1.0995574287564276, 0.0 }, |
2be75957 | 983 | { -0.32455734448839091, 20, 2, |
b4688136 ESR |
984 | 1.2566370614359172, 0.0 }, |
985 | { 0.32036529628513255, 20, 2, | |
986 | 1.4137166941154069, 0.0 }, | |
2be75957 | 987 | { -0.31902310563819986, 20, 2, |
b4688136 ESR |
988 | 1.5707963267948966, 0.0 }, |
989 | { 0.32036529628513261, 20, 2, | |
990 | 1.7278759594743862, 0.0 }, | |
2be75957 | 991 | { -0.32455734448839102, 20, 2, |
b4688136 | 992 | 1.8849555921538759, 0.0 }, |
2be75957 | 993 | { 0.33214917638387659, 20, 2, |
b4688136 | 994 | 2.0420352248333655, 0.0 }, |
2be75957 | 995 | { -0.34427103004873105, 20, 2, |
b4688136 | 996 | 2.1991148575128552, 0.0 }, |
2be75957 | 997 | { 0.36312025711350981, 20, 2, |
b4688136 ESR |
998 | 2.3561944901923448, 0.0 }, |
999 | { -0.39321637877908228, 20, 2, | |
1000 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1001 | { 0.44520137308557650, 20, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 1007 | { 0.0000000000000000, 20, 2, |
b4688136 | 1008 | 3.1415926535897931, 0.0 }, |
2be75957 | 1009 | }; |
b4688136 | 1010 | const double toler018 = 5.0000000000000039e-13; |
2be75957 ESR |
1011 | |
1012 | // Test data for l=20, m=5. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1018 | const testcase_sph_legendre<double> |
1019 | data019[21] = | |
1020 | { | |
1021 | { 0.0000000000000000, 20, 5, | |
b4688136 ESR |
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 }, | |
2be75957 | 1027 | { 0.31774532551156298, 20, 5, |
b4688136 ESR |
1028 | 0.47123889803846897, 0.0 }, |
1029 | { -0.16011868165390658, 20, 5, | |
1030 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1031 | { 0.085844143304115578, 20, 5, |
b4688136 ESR |
1032 | 0.78539816339744828, 0.0 }, |
1033 | { -0.047467540840863798, 20, 5, | |
1034 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1035 | { 0.026283575189471796, 20, 5, |
b4688136 | 1036 | 1.0995574287564276, 0.0 }, |
2be75957 | 1037 | { -0.013891104052597688, 20, 5, |
b4688136 | 1038 | 1.2566370614359172, 0.0 }, |
2be75957 | 1039 | { 0.0059873308239496957, 20, 5, |
b4688136 ESR |
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 }, | |
2be75957 | 1045 | { 0.013891104052598547, 20, 5, |
b4688136 ESR |
1046 | 1.8849555921538759, 0.0 }, |
1047 | { -0.026283575189472153, 20, 5, | |
1048 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1049 | { 0.047467540840865928, 20, 5, |
b4688136 | 1050 | 2.1991148575128552, 0.0 }, |
2be75957 | 1051 | { -0.085844143304117007, 20, 5, |
b4688136 ESR |
1052 | 2.3561944901923448, 0.0 }, |
1053 | { 0.16011868165390544, 20, 5, | |
1054 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1055 | { -0.31774532551156381, 20, 5, |
b4688136 | 1056 | 2.6703537555513241, 0.0 }, |
2be75957 | 1057 | { 0.68115361075940484, 20, 5, |
b4688136 | 1058 | 2.8274333882308138, 0.0 }, |
2be75957 | 1059 | { 0.10024848623505046, 20, 5, |
b4688136 | 1060 | 2.9845130209103035, 0.0 }, |
2be75957 | 1061 | { 0.0000000000000000, 20, 5, |
b4688136 | 1062 | 3.1415926535897931, 0.0 }, |
2be75957 | 1063 | }; |
b4688136 | 1064 | const double toler019 = 2.5000000000000015e-12; |
2be75957 ESR |
1065 | |
1066 | // Test data for l=20, m=10. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1072 | const testcase_sph_legendre<double> |
1073 | data020[21] = | |
1074 | { | |
1075 | { 0.0000000000000000, 20, 10, | |
b4688136 ESR |
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 }, | |
2be75957 | 1081 | { 0.26588079118745744, 20, 10, |
b4688136 ESR |
1082 | 0.47123889803846897, 0.0 }, |
1083 | { 0.54045081420686736, 20, 10, | |
1084 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1085 | { -0.28215279394285531, 20, 10, |
b4688136 ESR |
1086 | 0.78539816339744828, 0.0 }, |
1087 | { 0.0085297337582239223, 20, 10, | |
1088 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1089 | { 0.16930127953533738, 20, 10, |
b4688136 | 1090 | 1.0995574287564276, 0.0 }, |
2be75957 | 1091 | { -0.27215134048018325, 20, 10, |
b4688136 | 1092 | 1.2566370614359172, 0.0 }, |
2be75957 | 1093 | { 0.32456597088029526, 20, 10, |
b4688136 | 1094 | 1.4137166941154069, 0.0 }, |
2be75957 | 1095 | { -0.34057893241353715, 20, 10, |
b4688136 ESR |
1096 | 1.5707963267948966, 0.0 }, |
1097 | { 0.32456597088029493, 20, 10, | |
1098 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1099 | { -0.27215134048018291, 20, 10, |
b4688136 ESR |
1100 | 1.8849555921538759, 0.0 }, |
1101 | { 0.16930127953533702, 20, 10, | |
1102 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1103 | { 0.0085297337582257438, 20, 10, |
b4688136 | 1104 | 2.1991148575128552, 0.0 }, |
2be75957 | 1105 | { -0.28215279394285619, 20, 10, |
b4688136 ESR |
1106 | 2.3561944901923448, 0.0 }, |
1107 | { 0.54045081420686869, 20, 10, | |
1108 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1109 | { 0.26588079118745828, 20, 10, |
b4688136 | 1110 | 2.6703537555513241, 0.0 }, |
2be75957 | 1111 | { 0.015924453916397002, 20, 10, |
b4688136 | 1112 | 2.8274333882308138, 0.0 }, |
2be75957 | 1113 | { 3.0595797603707888e-05, 20, 10, |
b4688136 | 1114 | 2.9845130209103035, 0.0 }, |
2be75957 | 1115 | { 0.0000000000000000, 20, 10, |
b4688136 | 1116 | 3.1415926535897931, 0.0 }, |
2be75957 | 1117 | }; |
b4688136 | 1118 | const double toler020 = 1.0000000000000008e-12; |
2be75957 ESR |
1119 | |
1120 | // Test data for l=20, m=20. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1126 | const testcase_sph_legendre<double> |
1127 | data021[21] = | |
1128 | { | |
1129 | { 0.0000000000000000, 20, 20, | |
b4688136 ESR |
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 }, | |
2be75957 | 1135 | { 8.8474944184471664e-08, 20, 20, |
b4688136 ESR |
1136 | 0.47123889803846897, 0.0 }, |
1137 | { 1.5497395129387791e-05, 20, 20, | |
1138 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1139 | { 0.00062457564282984495, 20, 20, |
b4688136 ESR |
1140 | 0.78539816339744828, 0.0 }, |
1141 | { 0.0092265192458967308, 20, 20, | |
1142 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1143 | { 0.063606673236323297, 20, 20, |
b4688136 | 1144 | 1.0995574287564276, 0.0 }, |
2be75957 | 1145 | { 0.23442909509776316, 20, 20, |
b4688136 | 1146 | 1.2566370614359172, 0.0 }, |
2be75957 | 1147 | { 0.49921030481087009, 20, 20, |
b4688136 | 1148 | 1.4137166941154069, 0.0 }, |
2be75957 | 1149 | { 0.63956545825776223, 20, 20, |
b4688136 ESR |
1150 | 1.5707963267948966, 0.0 }, |
1151 | { 0.49921030481087025, 20, 20, | |
1152 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1153 | { 0.23442909509776336, 20, 20, |
b4688136 ESR |
1154 | 1.8849555921538759, 0.0 }, |
1155 | { 0.063606673236323324, 20, 20, | |
1156 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1157 | { 0.0092265192458967742, 20, 20, |
b4688136 | 1158 | 2.1991148575128552, 0.0 }, |
2be75957 | 1159 | { 0.00062457564282984766, 20, 20, |
b4688136 ESR |
1160 | 2.3561944901923448, 0.0 }, |
1161 | { 1.5497395129387764e-05, 20, 20, | |
1162 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1163 | { 8.8474944184472617e-08, 20, 20, |
b4688136 | 1164 | 2.6703537555513241, 0.0 }, |
2be75957 | 1165 | { 4.0321091681531780e-11, 20, 20, |
b4688136 | 1166 | 2.8274333882308138, 0.0 }, |
2be75957 | 1167 | { 4.9264471419250786e-17, 20, 20, |
b4688136 | 1168 | 2.9845130209103035, 0.0 }, |
2be75957 | 1169 | { 0.0000000000000000, 20, 20, |
b4688136 | 1170 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1171 | }; |
1172 | const double toler021 = 2.5000000000000020e-13; | |
1173 | ||
1174 | // Test data for l=50, m=0. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1180 | const testcase_sph_legendre<double> |
1181 | data022[21] = | |
1182 | { | |
1183 | { 2.8350175706934717, 50, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 1189 | { -0.24876032079677909, 50, 0, |
b4688136 ESR |
1190 | 0.47123889803846897, 0.0 }, |
1191 | { 0.36926172901532667, 50, 0, | |
1192 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1193 | { 0.14571730283563575, 50, 0, |
b4688136 ESR |
1194 | 0.78539816339744828, 0.0 }, |
1195 | { -0.33636199170850750, 50, 0, | |
1196 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1197 | { -0.079132716267091507, 50, 0, |
b4688136 | 1198 | 1.0995574287564276, 0.0 }, |
2be75957 | 1199 | { 0.32232921941301451, 50, 0, |
b4688136 | 1200 | 1.2566370614359172, 0.0 }, |
2be75957 | 1201 | { 0.025253991969481544, 50, 0, |
b4688136 | 1202 | 1.4137166941154069, 0.0 }, |
2be75957 | 1203 | { -0.31830208724152359, 50, 0, |
b4688136 ESR |
1204 | 1.5707963267948966, 0.0 }, |
1205 | { 0.025253991969479882, 50, 0, | |
1206 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1207 | { 0.32232921941301479, 50, 0, |
b4688136 ESR |
1208 | 1.8849555921538759, 0.0 }, |
1209 | { -0.079132716267090064, 50, 0, | |
1210 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1211 | { -0.33636199170850883, 50, 0, |
b4688136 | 1212 | 2.1991148575128552, 0.0 }, |
2be75957 | 1213 | { 0.14571730283563347, 50, 0, |
b4688136 ESR |
1214 | 2.3561944901923448, 0.0 }, |
1215 | { 0.36926172901532522, 50, 0, | |
1216 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1217 | { -0.24876032079677354, 50, 0, |
b4688136 | 1218 | 2.6703537555513241, 0.0 }, |
2be75957 | 1219 | { -0.46056183476301255, 50, 0, |
b4688136 | 1220 | 2.8274333882308138, 0.0 }, |
2be75957 | 1221 | { 0.53157537495172758, 50, 0, |
b4688136 | 1222 | 2.9845130209103035, 0.0 }, |
2be75957 | 1223 | { 2.8350175706934717, 50, 0, |
b4688136 | 1224 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1225 | }; |
1226 | const double toler022 = 5.0000000000000039e-13; | |
1227 | ||
1228 | // Test data for l=50, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1234 | const testcase_sph_legendre<double> |
1235 | data023[21] = | |
1236 | { | |
1237 | { 0.0000000000000000, 50, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 1243 | { 0.40649930826162850, 50, 1, |
b4688136 ESR |
1244 | 0.47123889803846897, 0.0 }, |
1245 | { 0.18473991408343635, 50, 1, | |
1246 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1247 | { -0.35083930302013117, 50, 1, |
b4688136 ESR |
1248 | 0.78539816339744828, 0.0 }, |
1249 | { -0.10755382110947342, 50, 1, | |
1250 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1251 | { 0.32822568316499900, 50, 1, |
b4688136 | 1252 | 1.0995574287564276, 0.0 }, |
2be75957 | 1253 | { 0.050286056609797389, 50, 1, |
b4688136 | 1254 | 1.2566370614359172, 0.0 }, |
2be75957 | 1255 | { -0.31935368562159644, 50, 1, |
b4688136 ESR |
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 }, | |
2be75957 | 1261 | { -0.050286056609795446, 50, 1, |
b4688136 ESR |
1262 | 1.8849555921538759, 0.0 }, |
1263 | { -0.32822568316499923, 50, 1, | |
1264 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1265 | { 0.10755382110946902, 50, 1, |
b4688136 | 1266 | 2.1991148575128552, 0.0 }, |
2be75957 | 1267 | { 0.35083930302013205, 50, 1, |
b4688136 ESR |
1268 | 2.3561944901923448, 0.0 }, |
1269 | { -0.18473991408344057, 50, 1, | |
1270 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1271 | { -0.40649930826163011, 50, 1, |
b4688136 | 1272 | 2.6703537555513241, 0.0 }, |
2be75957 | 1273 | { 0.32616619317604606, 50, 1, |
b4688136 | 1274 | 2.8274333882308138, 0.0 }, |
2be75957 | 1275 | { 0.63751752155228247, 50, 1, |
b4688136 | 1276 | 2.9845130209103035, 0.0 }, |
2be75957 | 1277 | { 0.0000000000000000, 50, 1, |
b4688136 | 1278 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1279 | }; |
1280 | const double toler023 = 1.0000000000000008e-12; | |
1281 | ||
1282 | // Test data for l=50, m=2. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1288 | const testcase_sph_legendre<double> |
1289 | data024[21] = | |
1290 | { | |
1291 | { 0.0000000000000000, 50, 2, | |
b4688136 ESR |
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 }, | |
2be75957 | 1297 | { 0.21724795180329495, 50, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 1305 | { 0.072537503112489563, 50, 2, |
b4688136 | 1306 | 1.0995574287564276, 0.0 }, |
2be75957 | 1307 | { -0.32310306941855266, 50, 2, |
b4688136 ESR |
1308 | 1.2566370614359172, 0.0 }, |
1309 | { -0.023259822816436636, 50, 2, | |
1310 | 1.4137166941154069, 0.0 }, | |
2be75957 | 1311 | { 0.31842698506357275, 50, 2, |
b4688136 ESR |
1312 | 1.5707963267948966, 0.0 }, |
1313 | { -0.023259822816434638, 50, 2, | |
1314 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1315 | { -0.32310306941855316, 50, 2, |
b4688136 ESR |
1316 | 1.8849555921538759, 0.0 }, |
1317 | { 0.072537503112488411, 50, 2, | |
1318 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1319 | { 0.33959009162400267, 50, 2, |
b4688136 | 1320 | 2.1991148575128552, 0.0 }, |
2be75957 | 1321 | { -0.13187372121003124, 50, 2, |
b4688136 ESR |
1322 | 2.3561944901923448, 0.0 }, |
1323 | { -0.37948127307610924, 50, 2, | |
1324 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1325 | { 0.21724795180329090, 50, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 1331 | { 0.0000000000000000, 50, 2, |
b4688136 | 1332 | 3.1415926535897931, 0.0 }, |
2be75957 | 1333 | }; |
b4688136 | 1334 | const double toler024 = 1.0000000000000008e-12; |
2be75957 ESR |
1335 | |
1336 | // Test data for l=50, m=5. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1342 | const testcase_sph_legendre<double> |
1343 | data025[21] = | |
1344 | { | |
1345 | { 0.0000000000000000, 50, 5, | |
b4688136 ESR |
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 }, | |
2be75957 | 1351 | { 0.47707267400540226, 50, 5, |
b4688136 ESR |
1352 | 0.47123889803846897, 0.0 }, |
1353 | { 0.055370615126626811, 50, 5, | |
1354 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1355 | { -0.37629451847202833, 50, 5, |
b4688136 ESR |
1356 | 0.78539816339744828, 0.0 }, |
1357 | { -0.048042277801963115, 50, 5, | |
1358 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1359 | { 0.33619379362228718, 50, 5, |
b4688136 | 1360 | 1.0995574287564276, 0.0 }, |
2be75957 | 1361 | { 0.025265227185718764, 50, 5, |
b4688136 | 1362 | 1.2566370614359172, 0.0 }, |
2be75957 | 1363 | { -0.32083679430964535, 50, 5, |
b4688136 ESR |
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 }, | |
2be75957 | 1369 | { -0.025265227185716790, 50, 5, |
b4688136 ESR |
1370 | 1.8849555921538759, 0.0 }, |
1371 | { -0.33619379362228730, 50, 5, | |
1372 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1373 | { 0.048042277801958064, 50, 5, |
b4688136 | 1374 | 2.1991148575128552, 0.0 }, |
2be75957 | 1375 | { 0.37629451847202872, 50, 5, |
b4688136 ESR |
1376 | 2.3561944901923448, 0.0 }, |
1377 | { -0.055370615126630517, 50, 5, | |
1378 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1379 | { -0.47707267400540176, 50, 5, |
b4688136 | 1380 | 2.6703537555513241, 0.0 }, |
2be75957 | 1381 | { -0.077360497065588632, 50, 5, |
b4688136 | 1382 | 2.8274333882308138, 0.0 }, |
2be75957 | 1383 | { 0.57750385903191603, 50, 5, |
b4688136 | 1384 | 2.9845130209103035, 0.0 }, |
2be75957 | 1385 | { 0.0000000000000000, 50, 5, |
b4688136 | 1386 | 3.1415926535897931, 0.0 }, |
2be75957 | 1387 | }; |
b4688136 | 1388 | const double toler025 = 5.0000000000000029e-12; |
2be75957 ESR |
1389 | |
1390 | // Test data for l=50, m=10. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1396 | const testcase_sph_legendre<double> |
1397 | data026[21] = | |
1398 | { | |
1399 | { 0.0000000000000000, 50, 10, | |
b4688136 ESR |
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 }, | |
2be75957 | 1405 | { -0.49304919025183969, 50, 10, |
b4688136 ESR |
1406 | 0.47123889803846897, 0.0 }, |
1407 | { -0.26267582750427920, 50, 10, | |
1408 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1409 | { 0.22058983666314153, 50, 10, |
b4688136 ESR |
1410 | 0.78539816339744828, 0.0 }, |
1411 | { 0.32936725160671843, 50, 10, | |
1412 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1413 | { -0.092053311559447959, 50, 10, |
b4688136 | 1414 | 1.0995574287564276, 0.0 }, |
2be75957 | 1415 | { -0.32542913495935522, 50, 10, |
b4688136 | 1416 | 1.2566370614359172, 0.0 }, |
2be75957 | 1417 | { 0.025673223789103351, 50, 10, |
b4688136 | 1418 | 1.4137166941154069, 0.0 }, |
2be75957 | 1419 | { 0.32150019350255743, 50, 10, |
b4688136 ESR |
1420 | 1.5707963267948966, 0.0 }, |
1421 | { 0.025673223789105259, 50, 10, | |
1422 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1423 | { -0.32542913495935510, 50, 10, |
b4688136 ESR |
1424 | 1.8849555921538759, 0.0 }, |
1425 | { -0.092053311559449028, 50, 10, | |
1426 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1427 | { 0.32936725160671687, 50, 10, |
b4688136 | 1428 | 2.1991148575128552, 0.0 }, |
2be75957 | 1429 | { 0.22058983666314380, 50, 10, |
b4688136 ESR |
1430 | 2.3561944901923448, 0.0 }, |
1431 | { -0.26267582750428364, 50, 10, | |
1432 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1433 | { -0.49304919025184135, 50, 10, |
b4688136 | 1434 | 2.6703537555513241, 0.0 }, |
2be75957 | 1435 | { -0.53748868836814501, 50, 10, |
b4688136 | 1436 | 2.8274333882308138, 0.0 }, |
2be75957 | 1437 | { 0.15606941844801256, 50, 10, |
b4688136 | 1438 | 2.9845130209103035, 0.0 }, |
2be75957 | 1439 | { 0.0000000000000000, 50, 10, |
b4688136 | 1440 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1441 | }; |
1442 | const double toler026 = 5.0000000000000039e-13; | |
1443 | ||
1444 | // Test data for l=50, m=20. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1450 | const testcase_sph_legendre<double> |
1451 | data027[21] = | |
1452 | { | |
1453 | { 0.0000000000000000, 50, 20, | |
b4688136 ESR |
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 }, | |
2be75957 | 1459 | { 0.64134588721659802, 50, 20, |
b4688136 ESR |
1460 | 0.47123889803846897, 0.0 }, |
1461 | { 0.29895244392136594, 50, 20, | |
1462 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1463 | { 0.25309324781873871, 50, 20, |
b4688136 ESR |
1464 | 0.78539816339744828, 0.0 }, |
1465 | { 0.34368634714931567, 50, 20, | |
1466 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1467 | { 0.33996764360663945, 50, 20, |
b4688136 | 1468 | 1.0995574287564276, 0.0 }, |
2be75957 | 1469 | { 0.12866267745104024, 50, 20, |
b4688136 | 1470 | 1.2566370614359172, 0.0 }, |
2be75957 | 1471 | { -0.18201114398922874, 50, 20, |
b4688136 | 1472 | 1.4137166941154069, 0.0 }, |
2be75957 | 1473 | { -0.33216683431510857, 50, 20, |
b4688136 ESR |
1474 | 1.5707963267948966, 0.0 }, |
1475 | { -0.18201114398923010, 50, 20, | |
1476 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1477 | { 0.12866267745103857, 50, 20, |
b4688136 | 1478 | 1.8849555921538759, 0.0 }, |
2be75957 | 1479 | { 0.33996764360663895, 50, 20, |
b4688136 | 1480 | 2.0420352248333655, 0.0 }, |
2be75957 | 1481 | { 0.34368634714931812, 50, 20, |
b4688136 | 1482 | 2.1991148575128552, 0.0 }, |
2be75957 | 1483 | { 0.25309324781874126, 50, 20, |
b4688136 ESR |
1484 | 2.3561944901923448, 0.0 }, |
1485 | { 0.29895244392136405, 50, 20, | |
1486 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1487 | { 0.64134588721659869, 50, 20, |
b4688136 | 1488 | 2.6703537555513241, 0.0 }, |
2be75957 | 1489 | { 0.030940518122882274, 50, 20, |
b4688136 | 1490 | 2.8274333882308138, 0.0 }, |
2be75957 | 1491 | { 3.0409598712835887e-07, 50, 20, |
b4688136 | 1492 | 2.9845130209103035, 0.0 }, |
2be75957 | 1493 | { 0.0000000000000000, 50, 20, |
b4688136 | 1494 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1495 | }; |
1496 | const double toler027 = 5.0000000000000039e-13; | |
1497 | ||
1498 | // Test data for l=50, m=50. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1504 | const testcase_sph_legendre<double> |
1505 | data028[21] = | |
1506 | { | |
1507 | { 0.0000000000000000, 50, 50, | |
b4688136 ESR |
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 }, | |
2be75957 | 1513 | { 5.6927376423967334e-18, 50, 50, |
b4688136 ESR |
1514 | 0.47123889803846897, 0.0 }, |
1515 | { 2.3116239814797222e-12, 50, 50, | |
1516 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1517 | { 2.3835981241325056e-08, 50, 50, |
b4688136 ESR |
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 }, | |
2be75957 | 1523 | { 0.065057774647971231, 50, 50, |
b4688136 | 1524 | 1.2566370614359172, 0.0 }, |
2be75957 | 1525 | { 0.43050607056732243, 50, 50, |
b4688136 | 1526 | 1.4137166941154069, 0.0 }, |
2be75957 | 1527 | { 0.79980281171531975, 50, 50, |
b4688136 ESR |
1528 | 1.5707963267948966, 0.0 }, |
1529 | { 0.43050607056732287, 50, 50, | |
1530 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1531 | { 0.065057774647971398, 50, 50, |
b4688136 ESR |
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 }, | |
2be75957 | 1537 | { 2.3835981241325311e-08, 50, 50, |
b4688136 ESR |
1538 | 2.3561944901923448, 0.0 }, |
1539 | { 2.3116239814797057e-12, 50, 50, | |
1540 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1541 | { 5.6927376423968952e-18, 50, 50, |
b4688136 | 1542 | 2.6703537555513241, 0.0 }, |
2be75957 | 1543 | { 2.5240684647724192e-26, 50, 50, |
b4688136 | 1544 | 2.8274333882308138, 0.0 }, |
2be75957 | 1545 | { 4.1649039898161316e-41, 50, 50, |
b4688136 | 1546 | 2.9845130209103035, 0.0 }, |
2be75957 | 1547 | { 0.0000000000000000, 50, 50, |
b4688136 | 1548 | 3.1415926535897931, 0.0 }, |
2be75957 | 1549 | }; |
b4688136 | 1550 | const double toler028 = 2.5000000000000020e-13; |
2be75957 ESR |
1551 | |
1552 | // Test data for l=100, m=0. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1558 | const testcase_sph_legendre<double> |
1559 | data029[21] = | |
1560 | { | |
1561 | { 3.9993839251484076, 100, 0, | |
b4688136 ESR |
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 }, | |
2be75957 | 1567 | { -0.40218718869815234, 100, 0, |
b4688136 ESR |
1568 | 0.47123889803846897, 0.0 }, |
1569 | { 0.36960201406911097, 100, 0, | |
1570 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1571 | { -0.34953726547378389, 100, 0, |
b4688136 ESR |
1572 | 0.78539816339744828, 0.0 }, |
1573 | { 0.33646959352497730, 100, 0, | |
1574 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1575 | { -0.32784733067663224, 100, 0, |
b4688136 | 1576 | 1.0995574287564276, 0.0 }, |
2be75957 | 1577 | { 0.32235624474047969, 100, 0, |
b4688136 | 1578 | 1.2566370614359172, 0.0 }, |
2be75957 | 1579 | { -0.31929330706601350, 100, 0, |
b4688136 | 1580 | 1.4137166941154069, 0.0 }, |
2be75957 | 1581 | { 0.31830791662110325, 100, 0, |
b4688136 ESR |
1582 | 1.5707963267948966, 0.0 }, |
1583 | { -0.31929330706601333, 100, 0, | |
1584 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1585 | { 0.32235624474048036, 100, 0, |
b4688136 ESR |
1586 | 1.8849555921538759, 0.0 }, |
1587 | { -0.32784733067663291, 100, 0, | |
1588 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1589 | { 0.33646959352498013, 100, 0, |
b4688136 | 1590 | 2.1991148575128552, 0.0 }, |
2be75957 | 1591 | { -0.34953726547378589, 100, 0, |
b4688136 ESR |
1592 | 2.3561944901923448, 0.0 }, |
1593 | { 0.36960201406910725, 100, 0, | |
1594 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1595 | { -0.40218718869815723, 100, 0, |
b4688136 | 1596 | 2.6703537555513241, 0.0 }, |
2be75957 | 1597 | { 0.46193027883955923, 100, 0, |
b4688136 | 1598 | 2.8274333882308138, 0.0 }, |
2be75957 | 1599 | { -0.60770160285939456, 100, 0, |
b4688136 | 1600 | 2.9845130209103035, 0.0 }, |
2be75957 | 1601 | { 3.9993839251484076, 100, 0, |
b4688136 | 1602 | 3.1415926535897931, 0.0 }, |
2be75957 | 1603 | }; |
b4688136 | 1604 | const double toler029 = 2.5000000000000020e-13; |
2be75957 ESR |
1605 | |
1606 | // Test data for l=100, m=1. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1612 | const testcase_sph_legendre<double> |
1613 | data030[21] = | |
1614 | { | |
1615 | { 0.0000000000000000, 100, 1, | |
b4688136 ESR |
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 }, | |
2be75957 | 1621 | { -0.24390405750942512, 100, 1, |
b4688136 ESR |
1622 | 0.47123889803846897, 0.0 }, |
1623 | { 0.18659755088413388, 100, 1, | |
1624 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1625 | { -0.14355908970517178, 100, 1, |
b4688136 ESR |
1626 | 0.78539816339744828, 0.0 }, |
1627 | { 0.10844906813251505, 100, 1, | |
1628 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1629 | { -0.078100088690857675, 100, 1, |
b4688136 | 1630 | 1.0995574287564276, 0.0 }, |
2be75957 | 1631 | { 0.050670002998302717, 100, 1, |
b4688136 | 1632 | 1.2566370614359172, 0.0 }, |
2be75957 | 1633 | { -0.024941251747138900, 100, 1, |
b4688136 ESR |
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 }, | |
2be75957 | 1639 | { -0.050670002998298824, 100, 1, |
b4688136 ESR |
1640 | 1.8849555921538759, 0.0 }, |
1641 | { 0.078100088690855773, 100, 1, | |
1642 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1643 | { -0.10844906813250622, 100, 1, |
b4688136 | 1644 | 2.1991148575128552, 0.0 }, |
2be75957 | 1645 | { 0.14355908970516626, 100, 1, |
b4688136 ESR |
1646 | 2.3561944901923448, 0.0 }, |
1647 | { -0.18659755088414104, 100, 1, | |
1648 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1649 | { 0.24390405750941679, 100, 1, |
b4688136 | 1650 | 2.6703537555513241, 0.0 }, |
2be75957 | 1651 | { -0.33129641402221749, 100, 1, |
b4688136 | 1652 | 2.8274333882308138, 0.0 }, |
2be75957 | 1653 | { 0.50851949013714159, 100, 1, |
b4688136 | 1654 | 2.9845130209103035, 0.0 }, |
2be75957 | 1655 | { 0.0000000000000000, 100, 1, |
b4688136 | 1656 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1657 | }; |
1658 | const double toler030 = 1.0000000000000008e-12; | |
1659 | ||
1660 | // Test data for l=100, m=2. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1666 | const testcase_sph_legendre<double> |
1667 | data031[21] = | |
1668 | { | |
1669 | { 0.0000000000000000, 100, 2, | |
b4688136 ESR |
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 }, | |
2be75957 | 1675 | { 0.41175421895715525, 100, 2, |
b4688136 ESR |
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 }, | |
2be75957 | 1683 | { 0.32867180390710077, 100, 2, |
b4688136 | 1684 | 1.0995574287564276, 0.0 }, |
2be75957 | 1685 | { -0.32271583790278502, 100, 2, |
b4688136 ESR |
1686 | 1.2566370614359172, 0.0 }, |
1687 | { 0.31940354677687466, 100, 2, | |
1688 | 1.4137166941154069, 0.0 }, | |
2be75957 | 1689 | { -0.31833943693772526, 100, 2, |
b4688136 ESR |
1690 | 1.5707963267948966, 0.0 }, |
1691 | { 0.31940354677687455, 100, 2, | |
1692 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1693 | { -0.32271583790278552, 100, 2, |
b4688136 ESR |
1694 | 1.8849555921538759, 0.0 }, |
1695 | { 0.32867180390710116, 100, 2, | |
1696 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1697 | { -0.33807110409160157, 100, 2, |
b4688136 | 1698 | 2.1991148575128552, 0.0 }, |
2be75957 | 1699 | { 0.35242909383605503, 100, 2, |
b4688136 ESR |
1700 | 2.3561944901923448, 0.0 }, |
1701 | { -0.37475021787822438, 100, 2, | |
1702 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1703 | { 0.41175421895716052, 100, 2, |
b4688136 | 1704 | 2.6703537555513241, 0.0 }, |
2be75957 | 1705 | { -0.48226933687995360, 100, 2, |
b4688136 ESR |
1706 | 2.8274333882308138, 0.0 }, |
1707 | { 0.67166274297196848, 100, 2, | |
1708 | 2.9845130209103035, 0.0 }, | |
2be75957 | 1709 | { 0.0000000000000000, 100, 2, |
b4688136 | 1710 | 3.1415926535897931, 0.0 }, |
2be75957 | 1711 | }; |
b4688136 | 1712 | const double toler031 = 1.0000000000000008e-12; |
2be75957 ESR |
1713 | |
1714 | // Test data for l=100, m=5. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1720 | const testcase_sph_legendre<double> |
1721 | data032[21] = | |
1722 | { | |
1723 | { 0.0000000000000000, 100, 5, | |
b4688136 ESR |
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 }, | |
2be75957 | 1729 | { -0.14356866942905960, 100, 5, |
b4688136 ESR |
1730 | 0.47123889803846897, 0.0 }, |
1731 | { 0.12355483388447824, 100, 5, | |
1732 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1733 | { -0.10090029999681642, 100, 5, |
b4688136 ESR |
1734 | 0.78539816339744828, 0.0 }, |
1735 | { 0.078905134460235241, 100, 5, | |
1736 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1737 | { -0.058040182398185071, 100, 5, |
b4688136 | 1738 | 1.0995574287564276, 0.0 }, |
2be75957 | 1739 | { 0.038142759389482424, 100, 5, |
b4688136 | 1740 | 1.2566370614359172, 0.0 }, |
2be75957 | 1741 | { -0.018906264170660478, 100, 5, |
b4688136 ESR |
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 }, | |
2be75957 | 1747 | { -0.038142759389478365, 100, 5, |
b4688136 ESR |
1748 | 1.8849555921538759, 0.0 }, |
1749 | { 0.058040182398183086, 100, 5, | |
1750 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1751 | { -0.078905134460225707, 100, 5, |
b4688136 | 1752 | 2.1991148575128552, 0.0 }, |
2be75957 | 1753 | { 0.10090029999681013, 100, 5, |
b4688136 ESR |
1754 | 2.3561944901923448, 0.0 }, |
1755 | { -0.12355483388448550, 100, 5, | |
1756 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1757 | { 0.14356866942904906, 100, 5, |
b4688136 | 1758 | 2.6703537555513241, 0.0 }, |
2be75957 | 1759 | { -0.14179554455879767, 100, 5, |
b4688136 | 1760 | 2.8274333882308138, 0.0 }, |
2be75957 | 1761 | { -0.062564361105954577, 100, 5, |
b4688136 | 1762 | 2.9845130209103035, 0.0 }, |
2be75957 | 1763 | { 0.0000000000000000, 100, 5, |
b4688136 | 1764 | 3.1415926535897931, 0.0 }, |
2be75957 | 1765 | }; |
b4688136 | 1766 | const double toler032 = 2.5000000000000014e-11; |
2be75957 ESR |
1767 | |
1768 | // Test data for l=100, m=10. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1774 | const testcase_sph_legendre<double> |
1775 | data033[21] = | |
1776 | { | |
1777 | { 0.0000000000000000, 100, 10, | |
b4688136 ESR |
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 }, | |
2be75957 | 1783 | { 0.43480692911578295, 100, 10, |
b4688136 ESR |
1784 | 0.47123889803846897, 0.0 }, |
1785 | { -0.40862111080315500, 100, 10, | |
1786 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1787 | { 0.37832688692909411, 100, 10, |
b4688136 ESR |
1788 | 0.78539816339744828, 0.0 }, |
1789 | { -0.35484056194773494, 100, 10, | |
1790 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1791 | { 0.33821981171196341, 100, 10, |
b4688136 | 1792 | 1.0995574287564276, 0.0 }, |
2be75957 | 1793 | { -0.32729120767830594, 100, 10, |
b4688136 | 1794 | 1.2566370614359172, 0.0 }, |
2be75957 | 1795 | { 0.32110336937091438, 100, 10, |
b4688136 | 1796 | 1.4137166941154069, 0.0 }, |
2be75957 | 1797 | { -0.31910064020036194, 100, 10, |
b4688136 | 1798 | 1.5707963267948966, 0.0 }, |
2be75957 | 1799 | { 0.32110336937091460, 100, 10, |
b4688136 | 1800 | 1.7278759594743862, 0.0 }, |
2be75957 | 1801 | { -0.32729120767830605, 100, 10, |
b4688136 ESR |
1802 | 1.8849555921538759, 0.0 }, |
1803 | { 0.33821981171196364, 100, 10, | |
1804 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1805 | { -0.35484056194773461, 100, 10, |
b4688136 | 1806 | 2.1991148575128552, 0.0 }, |
2be75957 | 1807 | { 0.37832688692909372, 100, 10, |
b4688136 ESR |
1808 | 2.3561944901923448, 0.0 }, |
1809 | { -0.40862111080315755, 100, 10, | |
1810 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1811 | { 0.43480692911577751, 100, 10, |
b4688136 | 1812 | 2.6703537555513241, 0.0 }, |
2be75957 | 1813 | { -0.35914570017276798, 100, 10, |
b4688136 | 1814 | 2.8274333882308138, 0.0 }, |
2be75957 | 1815 | { -0.75366545187997991, 100, 10, |
b4688136 | 1816 | 2.9845130209103035, 0.0 }, |
2be75957 | 1817 | { 0.0000000000000000, 100, 10, |
b4688136 | 1818 | 3.1415926535897931, 0.0 }, |
2be75957 | 1819 | }; |
b4688136 | 1820 | const double toler033 = 5.0000000000000039e-13; |
2be75957 ESR |
1821 | |
1822 | // Test data for l=100, m=20. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1828 | const testcase_sph_legendre<double> |
1829 | data034[21] = | |
1830 | { | |
1831 | { 0.0000000000000000, 100, 20, | |
b4688136 ESR |
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 }, | |
2be75957 | 1837 | { 0.47536909969585633, 100, 20, |
b4688136 ESR |
1838 | 0.47123889803846897, 0.0 }, |
1839 | { -0.28882554564109575, 100, 20, | |
1840 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1841 | { 0.020116179014043743, 100, 20, |
b4688136 ESR |
1842 | 0.78539816339744828, 0.0 }, |
1843 | { 0.14752195931707024, 100, 20, | |
1844 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1845 | { -0.24069428588868366, 100, 20, |
b4688136 | 1846 | 1.0995574287564276, 0.0 }, |
2be75957 | 1847 | { 0.29031796025014306, 100, 20, |
b4688136 | 1848 | 1.2566370614359172, 0.0 }, |
2be75957 | 1849 | { -0.31437256851143458, 100, 20, |
b4688136 | 1850 | 1.4137166941154069, 0.0 }, |
2be75957 | 1851 | { 0.32153954851141792, 100, 20, |
b4688136 ESR |
1852 | 1.5707963267948966, 0.0 }, |
1853 | { -0.31437256851143375, 100, 20, | |
1854 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1855 | { 0.29031796025014139, 100, 20, |
b4688136 ESR |
1856 | 1.8849555921538759, 0.0 }, |
1857 | { -0.24069428588868241, 100, 20, | |
1858 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1859 | { 0.14752195931706186, 100, 20, |
b4688136 | 1860 | 2.1991148575128552, 0.0 }, |
2be75957 | 1861 | { 0.020116179014049562, 100, 20, |
b4688136 ESR |
1862 | 2.3561944901923448, 0.0 }, |
1863 | { -0.28882554564109075, 100, 20, | |
1864 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1865 | { 0.47536909969585545, 100, 20, |
b4688136 | 1866 | 2.6703537555513241, 0.0 }, |
2be75957 | 1867 | { 0.57154926874732348, 100, 20, |
b4688136 | 1868 | 2.8274333882308138, 0.0 }, |
2be75957 | 1869 | { 0.053569660841557079, 100, 20, |
b4688136 | 1870 | 2.9845130209103035, 0.0 }, |
2be75957 | 1871 | { 0.0000000000000000, 100, 20, |
b4688136 | 1872 | 3.1415926535897931, 0.0 }, |
2be75957 ESR |
1873 | }; |
1874 | const double toler034 = 2.5000000000000015e-12; | |
1875 | ||
1876 | // Test data for l=100, m=50. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1882 | const testcase_sph_legendre<double> |
1883 | data035[21] = | |
1884 | { | |
1885 | { 0.0000000000000000, 100, 50, | |
b4688136 ESR |
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 }, | |
2be75957 | 1891 | { 0.080418744223952773, 100, 50, |
b4688136 ESR |
1892 | 0.47123889803846897, 0.0 }, |
1893 | { -0.56450600580392973, 100, 50, | |
1894 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1895 | { 0.33338739844742110, 100, 50, |
b4688136 ESR |
1896 | 0.78539816339744828, 0.0 }, |
1897 | { 0.39741714816514678, 100, 50, | |
1898 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1899 | { 0.35223993750972243, 100, 50, |
b4688136 | 1900 | 1.0995574287564276, 0.0 }, |
2be75957 | 1901 | { 0.17885891940721577, 100, 50, |
b4688136 | 1902 | 1.2566370614359172, 0.0 }, |
2be75957 | 1903 | { -0.15341660126461967, 100, 50, |
b4688136 | 1904 | 1.4137166941154069, 0.0 }, |
2be75957 | 1905 | { -0.34175924303503102, 100, 50, |
b4688136 ESR |
1906 | 1.5707963267948966, 0.0 }, |
1907 | { -0.15341660126462270, 100, 50, | |
1908 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1909 | { 0.17885891940721302, 100, 50, |
b4688136 ESR |
1910 | 1.8849555921538759, 0.0 }, |
1911 | { 0.35223993750972227, 100, 50, | |
1912 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1913 | { 0.39741714816514595, 100, 50, |
b4688136 | 1914 | 2.1991148575128552, 0.0 }, |
2be75957 | 1915 | { 0.33338739844741666, 100, 50, |
b4688136 ESR |
1916 | 2.3561944901923448, 0.0 }, |
1917 | { -0.56450600580393095, 100, 50, | |
1918 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1919 | { 0.080418744223953911, 100, 50, |
b4688136 | 1920 | 2.6703537555513241, 0.0 }, |
2be75957 | 1921 | { 1.0592655372554981e-07, 100, 50, |
b4688136 | 1922 | 2.8274333882308138, 0.0 }, |
2be75957 | 1923 | { 3.3047910392597822e-21, 100, 50, |
b4688136 | 1924 | 2.9845130209103035, 0.0 }, |
2be75957 | 1925 | { 0.0000000000000000, 100, 50, |
b4688136 | 1926 | 3.1415926535897931, 0.0 }, |
2be75957 | 1927 | }; |
b4688136 | 1928 | const double toler035 = 5.0000000000000039e-13; |
2be75957 ESR |
1929 | |
1930 | // Test data for l=100, m=100. | |
b4688136 ESR |
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 | |
2be75957 ESR |
1936 | const testcase_sph_legendre<double> |
1937 | data036[21] = | |
1938 | { | |
1939 | { 0.0000000000000000, 100, 100, | |
b4688136 ESR |
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 }, | |
2be75957 | 1945 | { 4.8096190703397596e-35, 100, 100, |
b4688136 ESR |
1946 | 0.47123889803846897, 0.0 }, |
1947 | { 7.9305393636344023e-24, 100, 100, | |
1948 | 0.62831853071795862, 0.0 }, | |
2be75957 | 1949 | { 8.4320740610944858e-16, 100, 100, |
b4688136 ESR |
1950 | 0.78539816339744828, 0.0 }, |
1951 | { 5.9319660146026674e-10, 100, 100, | |
1952 | 0.94247779607693793, 0.0 }, | |
2be75957 | 1953 | { 9.2368225946797243e-06, 100, 100, |
b4688136 | 1954 | 1.0995574287564276, 0.0 }, |
2be75957 | 1955 | { 0.0062815489742044095, 100, 100, |
b4688136 | 1956 | 1.2566370614359172, 0.0 }, |
2be75957 | 1957 | { 0.27505966018176986, 100, 100, |
b4688136 | 1958 | 1.4137166941154069, 0.0 }, |
2be75957 | 1959 | { 0.94936713998764621, 100, 100, |
b4688136 ESR |
1960 | 1.5707963267948966, 0.0 }, |
1961 | { 0.27505966018177036, 100, 100, | |
1962 | 1.7278759594743862, 0.0 }, | |
2be75957 | 1963 | { 0.0062815489742044433, 100, 100, |
b4688136 ESR |
1964 | 1.8849555921538759, 0.0 }, |
1965 | { 9.2368225946797582e-06, 100, 100, | |
1966 | 2.0420352248333655, 0.0 }, | |
2be75957 | 1967 | { 5.9319660146027946e-10, 100, 100, |
b4688136 | 1968 | 2.1991148575128552, 0.0 }, |
2be75957 | 1969 | { 8.4320740610946652e-16, 100, 100, |
b4688136 ESR |
1970 | 2.3561944901923448, 0.0 }, |
1971 | { 7.9305393636342891e-24, 100, 100, | |
1972 | 2.5132741228718345, 0.0 }, | |
2be75957 | 1973 | { 4.8096190703400333e-35, 100, 100, |
b4688136 | 1974 | 2.6703537555513241, 0.0 }, |
2be75957 | 1975 | { 9.4551974868956498e-52, 100, 100, |
b4688136 ESR |
1976 | 2.8274333882308138, 0.0 }, |
1977 | { 2.5744136608873899e-81, 100, 100, | |
1978 | 2.9845130209103035, 0.0 }, | |
2be75957 | 1979 | { 0.0000000000000000, 100, 100, |
b4688136 | 1980 | 3.1415926535897931, 0.0 }, |
2be75957 | 1981 | }; |
b4688136 | 1982 | const double toler036 = 2.5000000000000020e-13; |
2be75957 | 1983 | |
b4688136 | 1984 | template<typename Ret, unsigned int Num> |
2be75957 | 1985 | void |
b4688136 | 1986 | test(const testcase_sph_legendre<Ret> (&data)[Num], Ret toler) |
2be75957 | 1987 | { |
b4688136 ESR |
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); | |
2be75957 ESR |
1992 | unsigned int num_datum = Num; |
1993 | for (unsigned int i = 0; i < num_datum; ++i) | |
1994 | { | |
b4688136 | 1995 | const Ret f = std::sph_legendre(data[i].l, data[i].m, |
2be75957 | 1996 | data[i].theta); |
b4688136 ESR |
1997 | const Ret f0 = data[i].f0; |
1998 | const Ret diff = f - f0; | |
2be75957 ESR |
1999 | if (std::abs(diff) > max_abs_diff) |
2000 | max_abs_diff = std::abs(diff); | |
b4688136 ESR |
2001 | if (std::abs(f0) > Ret(10) * eps |
2002 | && std::abs(f) > Ret(10) * eps) | |
2be75957 | 2003 | { |
b4688136 | 2004 | const Ret frac = diff / f0; |
2be75957 ESR |
2005 | if (std::abs(frac) > max_abs_frac) |
2006 | max_abs_frac = std::abs(frac); | |
2007 | } | |
2008 | } | |
2009 | VERIFY(max_abs_frac < toler); | |
2010 | } | |
2011 | ||
2012 | int | |
2013 | main() | |
2014 | { | |
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); | |
2051 | return 0; | |
2052 | } |