GCC Code Coverage Report

Directory: Bembel/src/
File: Quadrature/GaussLegendreRule.hpp
Date: 2024-12-18 07:36:36
Exec Total Coverage
Lines: 92 129 71.3%
Functions: 51 51 100.0%
Branches: 54 104 51.9%
Line Branch Exec Source
1 // This file is part of Bembel, the higher order C++ boundary element library.
2 //
3 // Copyright (C) 2022 see <http://www.bembel.eu>
4 //
5 // It was written as part of a cooperation of J. Doelz, H. Harbrecht, S. Kurz,
6 // M. Multerer, S. Schoeps, and F. Wolf at Technische Universitaet Darmstadt,
7 // Universitaet Basel, and Universita della Svizzera italiana, Lugano. This
8 // source code is subject to the GNU General Public License version 3 and
9 // provided WITHOUT ANY WARRANTY, see <http://www.bembel.eu> for further
10 // information.
11
12 #ifndef BEMBEL_SRC_QUADRATURE_GAUSSLEGENDRERULE_HPP_
13 #define BEMBEL_SRC_QUADRATURE_GAUSSLEGENDRERULE_HPP_
14
15 namespace Bembel {
16 /**
17 * \ingroup Quadrature
18 * \brief Gauss Legendre quadrature rules. The first 20 are hard coded.
19 * Afterwards, the programmer in charge lost his interest and
20 * provided a method to compute arbitrary order Legendre rules
21 * by solving the corresponding eigenvalue problem.
22 *
23 * In addition, to make use of the bracket initializer, std::vector
24 * had to be used in the template specializations. However, this
25 * is taken care of by the quadrature struct.
26 **/
27 template <unsigned int Order>
28 struct GaussLegendreRule {
29 3800 GaussLegendreRule() {
30
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 3800 Eigen::MatrixXd A(Order, Order);
31
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 3800 A.setZero();
32
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 136530 for (auto i = 1; i < Order; ++i) A(i, i - 1) = i / (sqrt(4. * i * i - 1));
33
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 3800 Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> es;
34
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 3800 es.compute(A);
35
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 3800 xi_.resize(Order);
36
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 3800 w_.resize(Order);
37
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 140330 for (auto i = 0; i < Order; ++i) {
38
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 136530 xi_[i] = 0.5 * (es.eigenvalues()(i) + 1);
39
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 136530 w_[i] = es.eigenvectors()(0, i) * es.eigenvectors()(0, i);
40 }
41 3800 }
42 std::vector<double> xi_;
43 std::vector<double> w_;
44 };
45 /**
46 * \brief Gauss Legendre Rule - Unused base case
47 */
48 template <>
49 struct GaussLegendreRule<0> {
50 GaussLegendreRule() {
51 assert(false && "Order of GaussLegendre Quadrature has to be at least 1");
52 }
53 };
54 /**
55 * \brief Gauss Legendre Rule using 1 point.
56 */
57 template <>
58 struct GaussLegendreRule<1> {
59 76 GaussLegendreRule() {
60
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 76 xi_ = {0.5};
61
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 76 w_ = {1.0};
62 76 }
63 std::vector<double> xi_;
64 std::vector<double> w_;
65 };
66 /**
67 * \brief Gauss Legendre Rule using 2 point.
68 */
69 template <>
70 struct GaussLegendreRule<2> {
71 76 GaussLegendreRule() {
72 ✗ xi_ = {0.2113248654051871177454256097490212721762,
73
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 76 0.7886751345948128822545743902509787278238};
74
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 76 w_ = {0.5, 0.5};
75 76 }
76 std::vector<double> xi_;
77 std::vector<double> w_;
78 };
79 /**
80 * \brief Gauss Legendre Rule using 3 point.
81 */
82 template <>
83 struct GaussLegendreRule<3> {
84 76 GaussLegendreRule() {
85 ✗ xi_ = {0.1127016653792583114820734600217600389167, 0.5,
86
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 76 0.8872983346207416885179265399782399610833};
87
88 ✗ w_ = {.2777777777777777777777777777777777777778,
89 .4444444444444444444444444444444444444444,
90
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 76 .2777777777777777777777777777777777777778};
91 76 }
92 std::vector<double> xi_;
93 std::vector<double> w_;
94 };
95 /**
96 * \brief Gauss Legendre Rule using 4 point.
97 */
98 template <>
99 struct GaussLegendreRule<4> {
100 76 GaussLegendreRule() {
101 ✗ xi_ = {0.06943184420297371238802675555359524745214,
102 0.3300094782075718675986671204483776563997,
103 0.6699905217924281324013328795516223436003,
104
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 76 0.9305681557970262876119732444464047525479};
105
106 ✗ w_ = {.1739274225687269286865319746109997036177,
107 .3260725774312730713134680253890002963823,
108 .3260725774312730713134680253890002963823,
109
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 76 .1739274225687269286865319746109997036177};
110 76 }
111 std::vector<double> xi_;
112 std::vector<double> w_;
113 };
114 /**
115 * \brief Gauss Legendre Rule using 5 point.
116 */
117 template <>
118 struct GaussLegendreRule<5> {
119 76 GaussLegendreRule() {
120 ✗ xi_ = {0.04691007703066800360118656085030351743717,
121 0.2307653449471584544818427896498955975164, 0.5,
122 0.7692346550528415455181572103501044024836,
123
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 76 0.9530899229693319963988134391496964825628};
124
125 ✗ w_ = {.1184634425280945437571320203599586813216,
126 .2393143352496832340206457574178190964561,
127 .2844444444444444444444444444444444444444,
128 .2393143352496832340206457574178190964561,
129
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 76 .1184634425280945437571320203599586813216};
130 76 }
131 std::vector<double> xi_;
132 std::vector<double> w_;
133 };
134 /**
135 * \brief Gauss Legendre Rule using 6 point.
136 */
137 template <>
138 struct GaussLegendreRule<6> {
139 76 GaussLegendreRule() {
140 ✗ xi_ = {0.03376524289842398609384922275300269543262,
141 0.1693953067668677431693002024900473264968,
142 0.3806904069584015456847491391596440322907,
143 0.6193095930415984543152508608403559677093,
144 0.8306046932331322568306997975099526735032,
145
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 76 0.9662347571015760139061507772469973045674};
146
147 ✗ w_ = {.08566224618958517252014807108636644676341,
148 .1803807865240693037849167569188580558308,
149 .2339569672863455236949351719947754974058,
150 .2339569672863455236949351719947754974058,
151 .1803807865240693037849167569188580558308,
152
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 76 .08566224618958517252014807108636644676341};
153 76 }
154 std::vector<double> xi_;
155 std::vector<double> w_;
156 };
157 /**
158 * \brief Gauss Legendre Rule using 7 point.
159 */
160 template <>
161 struct GaussLegendreRule<7> {
162 76 GaussLegendreRule() {
163 ✗ xi_ = {0.02544604382862073773690515797607436879961,
164 0.1292344072003027800680676133596057964629,
165 0.2970774243113014165466967939615192683263,
166 0.5,
167 0.7029225756886985834533032060384807316737,
168 0.8707655927996972199319323866403942035371,
169
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 76 0.9745539561713792622630948420239256312004};
170
171 ✗ w_ = {0.06474248308443484663530571633954100916429,
172 0.1398526957446383339507338857118897912435,
173 0.1909150252525594724751848877444875669392,
174 0.2089795918367346938775510204081632653061,
175 0.1909150252525594724751848877444875669392,
176 0.1398526957446383339507338857118897912435,
177
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 76 0.06474248308443484663530571633954100916429};
178 76 }
179 std::vector<double> xi_;
180 std::vector<double> w_;
181 };
182 /**
183 * \brief Gauss Legendre Rule using 8 point.
184 */
185 template <>
186 struct GaussLegendreRule<8> {
187 76 GaussLegendreRule() {
188 ✗ xi_ = {0.01985507175123188415821956571526350478588,
189 0.1016667612931866302042230317620847815814,
190 0.237233795041835507091130475405376825479,
191 0.4082826787521750975302619288199080096666,
192 0.5917173212478249024697380711800919903334,
193 0.762766204958164492908869524594623174521,
194 0.8983332387068133697957769682379152184186,
195
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 76 0.9801449282487681158417804342847364952141};
196
197 ✗ w_ = {0.0506142681451881295762656771549810950577,
198 0.1111905172266872352721779972131204422151,
199 0.1568533229389436436689811009933006566302,
200 0.1813418916891809914825752246385978060971,
201 0.1813418916891809914825752246385978060971,
202 0.1568533229389436436689811009933006566302,
203 0.1111905172266872352721779972131204422151,
204
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 76 0.0506142681451881295762656771549810950577};
205 76 }
206 std::vector<double> xi_;
207 std::vector<double> w_;
208 };
209 /**
210 * \brief Gauss Legendre Rule using 9 point.
211 */
212 template <>
213 struct GaussLegendreRule<9> {
214 76 GaussLegendreRule() {
215 ✗ xi_ = {0.0159198802461869550822118985481635649753,
216 0.08198444633668210285028510596513256172795,
217 0.1933142836497048013456489803292629076071,
218 0.337873288298095535480730992678331695714,
219 0.5,
220 0.662126711701904464519269007321668304286,
221 0.8066857163502951986543510196707370923929,
222 0.9180155536633178971497148940348674382721,
223
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 76 0.9840801197538130449177881014518364350247};
224
225 ✗ w_ = {.04063719418078720598594607905526182533783,
226 .09032408034742870202923601562145640475717,
227 .1303053482014677311593714347093164248859,
228 .1561735385200014200343152032922218327994,
229 .1651196775006298815822625346434870244394,
230 .1561735385200014200343152032922218327994,
231 .1303053482014677311593714347093164248859,
232 .09032408034742870202923601562145640475717,
233
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 76 .04063719418078720598594607905526182533783};
234 76 }
235 std::vector<double> xi_;
236 std::vector<double> w_;
237 };
238 /**
239 * \brief Gauss Legendre Rule using 10 point.
240 */
241 template <>
242 struct GaussLegendreRule<10> {
243 76 GaussLegendreRule() {
244 ✗ xi_ = {0.01304673574141413996101799395777397328587,
245 0.06746831665550774463395165578825347573623,
246 0.1602952158504877968828363174425632121154,
247 0.2833023029353764046003670284171079189,
248 0.4255628305091843945575869994351400076912,
249 0.5744371694908156054424130005648599923088,
250 0.7166976970646235953996329715828920811,
251 0.8397047841495122031171636825574367878846,
252 0.9325316833444922553660483442117465242638,
253
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 76 0.9869532642585858600389820060422260267141};
254
255 ✗ w_ = {0.03333567215434406879678440494666589642893,
256 0.07472567457529029657288816982884866620128,
257 0.1095431812579910219977674671140815962294,
258 0.1346333596549981775456134607847346764299,
259 0.1477621123573764350869464973256691647105,
260 0.1477621123573764350869464973256691647105,
261 0.1346333596549981775456134607847346764299,
262 0.1095431812579910219977674671140815962294,
263 0.07472567457529029657288816982884866620128,
264
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 76 0.03333567215434406879678440494666589642893};
265 76 }
266 std::vector<double> xi_;
267 std::vector<double> w_;
268 };
269 /**
270 * \brief Gauss Legendre Rule using 11 point.
271 */
272 template <>
273 struct GaussLegendreRule<11> {
274 76 GaussLegendreRule() {
275 ✗ xi_ = {0.01088567092697150359803099943857130461429,
276 0.05646870011595235046242111534803636668416,
277 0.1349239972129753379532918739844232709752,
278 0.2404519353965940920371371652706952227599,
279 0.3652284220238275138342340072995692376602,
280 0.5,
281 0.6347715779761724861657659927004307623398,
282 0.7595480646034059079628628347293047772401,
283 0.8650760027870246620467081260155767290248,
284 0.9435312998840476495375788846519636333158,
285
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 76 0.9891143290730284964019690005614286953857};
286
287 ✗ w_ = {0.02783428355808683324137686022127428936426,
288 0.06279018473245231231734714961197005009881,
289 0.09314510546386712571304882071582794584564,
290 0.1165968822959952399592618524215875697159,
291 0.1314022722551233310903444349452545976864,
292 0.136462543388950315357241764168171094578,
293 0.1314022722551233310903444349452545976864,
294 0.1165968822959952399592618524215875697159,
295 0.09314510546386712571304882071582794584564,
296 0.06279018473245231231734714961197005009881,
297
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 76 0.02783428355808683324137686022127428936426};
298 76 }
299 std::vector<double> xi_;
300 std::vector<double> w_;
301 };
302 /**
303 * \brief Gauss Legendre Rule using 12 point.
304 */
305 template <>
306 struct GaussLegendreRule<12> {
307 76 GaussLegendreRule() {
308 ✗ xi_ = {0.009219682876640374654725454925359588519922,
309 0.0479413718147625716607670669404519037312,
310 0.1150486629028476564815530833935909620075,
311 0.2063410228566912763516487905297328598155,
312 0.3160842505009099031236542316781412193718,
313 0.4373832957442655422637793152680734350083,
314 0.5626167042557344577362206847319265649917,
315 0.6839157494990900968763457683218587806282,
316 0.7936589771433087236483512094702671401845,
317 0.8849513370971523435184469166064090379925,
318 0.9520586281852374283392329330595480962688,
319
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 76 0.9907803171233596253452745450746404114801};
320
321 ✗ w_ = {0.02358766819325591359730798074250853015851,
322 0.05346966299765921548012735909699811210729,
323 0.08003916427167311316732626477167953593601,
324 0.1015837133615329608745322279048991882533,
325 0.1167462682691774043804249494624390281297,
326 0.1245735229067013925002812180214756054152,
327 0.1245735229067013925002812180214756054152,
328 0.1167462682691774043804249494624390281297,
329 0.1015837133615329608745322279048991882533,
330 0.08003916427167311316732626477167953593601,
331 0.05346966299765921548012735909699811210729,
332
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 76 0.02358766819325591359730798074250853015851};
333 76 }
334 std::vector<double> xi_;
335 std::vector<double> w_;
336 };
337 /**
338 * \brief Gauss Legendre Rule using 13 point.
339 */
340 template <>
341 struct GaussLegendreRule<13> {
342 76 GaussLegendreRule() {
343 ✗ xi_ = {0.007908472640705925263585275596445194467505,
344 0.04120080038851101739672608174964024380476,
345 0.09921095463334504360289675520857005484719,
346 0.1788253302798298896780076965022421749642,
347 0.275753624481776573561043573936180066099,
348 0.3847708420224326029672359394510055823942,
349 0.5,
350 0.6152291579775673970327640605489944176058,
351 0.724246375518223426438956426063819933901,
352 0.8211746697201701103219923034977578250358,
353 0.9007890453666549563971032447914299451528,
354 0.9587991996114889826032739182503597561952,
355
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 76 0.9920915273592940747364147244035548055325};
356
357 ✗ w_ = {0.02024200238265793976001079610049303002099,
358 0.04606074991886422395721088797689856046184,
359 0.06943675510989361923180088843443573381093,
360 0.08907299038097286914002334599804899775641,
361 0.1039080237684442511562616096530263816933,
362 0.1131415901314486192060450930198883092174,
363 0.1162757766154369550972947576344179740783,
364 0.1131415901314486192060450930198883092174,
365 0.1039080237684442511562616096530263816933,
366 0.08907299038097286914002334599804899775641,
367 0.06943675510989361923180088843443573381093,
368 0.04606074991886422395721088797689856046184,
369
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 76 0.02024200238265793976001079610049303002099};
370 76 }
371 std::vector<double> xi_;
372 std::vector<double> w_;
373 };
374 /**
375 * \brief Gauss Legendre Rule using 14 point.
376 */
377 template <>
378 struct GaussLegendreRule<14> {
379 76 GaussLegendreRule() {
380 ✗ xi_ = {0.006858095651593830579201366647973599161954,
381 0.03578255816821324133180443031106286776148,
382 0.08639934246511750340510262867480251948015,
383 0.1563535475941572649259900984903329312308,
384 0.2423756818209229540173546407244056688456,
385 0.3404438155360551197821640879157622665829,
386 0.445972525646328168966877674890082626194,
387 0.554027474353671831033122325109917373806,
388 0.6595561844639448802178359120842377334171,
389 0.7576243181790770459826453592755943311544,
390 0.8436464524058427350740099015096670687692,
391 0.9136006575348824965948973713251974805199,
392 0.9642174418317867586681955696889371322385,
393
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 76 0.993141904348406169420798633352026400838};
394
395 ✗ w_ = {0.01755973016587593151591643806909589030985,
396 0.04007904357988010490281663853142715479185,
397 0.06075928534395159234470740453623831297833,
398 0.07860158357909676728480096931192107830283,
399 0.09276919873896890687085829506257851812446,
400 0.1025992318606478019829620328306090278552,
401 0.1076319267315788950979382216581300176375,
402 0.1076319267315788950979382216581300176375,
403 0.1025992318606478019829620328306090278552,
404 0.09276919873896890687085829506257851812446,
405 0.07860158357909676728480096931192107830283,
406 0.06075928534395159234470740453623831297833,
407 0.04007904357988010490281663853142715479185,
408
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 76 0.01755973016587593151591643806909589030985};
409 76 }
410 std::vector<double> xi_;
411 std::vector<double> w_;
412 };
413 /**
414 * \brief Gauss Legendre Rule using 15 point.
415 */
416 template <>
417 struct GaussLegendreRule<15> {
418 76 GaussLegendreRule() {
419 ✗ xi_ = {0.006003740989757285755217140706693709426514,
420 0.031363303799647047846120526144895264378,
421 0.07589670829478639189967583961289157431687,
422 0.1377911343199149762919069726930309951846,
423 0.2145139136957305762313866313730446793808,
424 0.3029243264612183150513963145094772658186,
425 0.3994029530012827388496858483027018960936,
426 0.5,
427 0.6005970469987172611503141516972981039064,
428 0.6970756735387816849486036854905227341814,
429 0.7854860863042694237686133686269553206192,
430 0.8622088656800850237080930273069690048154,
431 0.9241032917052136081003241603871084256831,
432 0.968636696200352952153879473855104735622,
433
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434
435 ✗ w_ = {0.01537662099805863417731419678860220886087,
436 0.03518302374405406235463370822533366923335,
437 0.05357961023358596750593477334293465170777,
438 0.06978533896307715722390239725551416126043,
439 0.08313460290849696677660043024060440556545,
440 0.09308050000778110551340028093321141225311,
441 0.09921574266355578822805916322191966240935,
442 0.1012891209627806364403100999837596574193,
443 0.09921574266355578822805916322191966240935,
444 0.09308050000778110551340028093321141225311,
445 0.08313460290849696677660043024060440556545,
446 0.06978533896307715722390239725551416126043,
447 0.05357961023358596750593477334293465170777,
448 0.03518302374405406235463370822533366923335,
449
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 76 0.01537662099805863417731419678860220886087};
450 76 }
451 std::vector<double> xi_;
452 std::vector<double> w_;
453 };
454 /**
455 * \brief Gauss Legendre Rule using 16 point.
456 */
457 template <>
458 struct GaussLegendreRule<16> {
459 76 GaussLegendreRule() {
460 ✗ xi_ = {0.005299532504175033701922913274833686286863,
461 0.02771248846338371196100579223269582745443,
462 0.06718439880608412805976605114380343380633,
463 0.1222977958224984830524494025762788658231,
464 0.1910618777986781257766641179756044905041,
465 0.27099161117138630682879027850821121323,
466 0.359198224610370543384769749269751946757,
467 0.4524937450811812799073403322875209684348,
468 0.5475062549188187200926596677124790315652,
469 0.640801775389629456615230250730248053243,
470 0.72900838882861369317120972149178878677,
471 0.8089381222013218742233358820243955094959,
472 0.8777022041775015169475505974237211341769,
473 0.9328156011939158719402339488561965661937,
474 0.9722875115366162880389942077673041725456,
475
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476
477 ✗ w_ = {0.01357622970587704742589028622800905175613,
478 0.03112676196932394643142191849718884713749,
479 0.04757925584124639240496255380112311317763,
480 0.06231448562776693602623814109600821007244,
481 0.07479799440828836604075086527373927448525,
482 0.08457825969750126909465603951517998110582,
483 0.09130170752246179443338183398460996969178,
484 0.09472530522753424814269836160414155257345,
485 0.09472530522753424814269836160414155257345,
486 0.09130170752246179443338183398460996969178,
487 0.08457825969750126909465603951517998110582,
488 0.07479799440828836604075086527373927448525,
489 0.06231448562776693602623814109600821007244,
490 0.04757925584124639240496255380112311317763,
491 0.03112676196932394643142191849718884713749,
492
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 76 0.01357622970587704742589028622800905175613};
493 76 }
494 std::vector<double> xi_;
495 std::vector<double> w_;
496 };
497 /**
498 * \brief Gauss Legendre Rule using 17 point.
499 */
500 template <>
501 struct GaussLegendreRule<17> {
502 76 GaussLegendreRule() {
503 ✗ xi_ = {0.004712262342791332162282990029667361746105,
504 0.02466223911561611938864152105209848927831,
505 0.05988042313650704893852215275592215368829,
506 0.109242998051599296537384972239761974888,
507 0.1711644203916546170748488916784988324261,
508 0.2436547314567615160568767156852240627085,
509 0.3243841182730618423514072414523269974797,
510 0.4107579092520760720746612531729672212623,
511 0.5,
512 0.5892420907479239279253387468270327787377,
513 0.6756158817269381576485927585476730025203,
514 0.7563452685432384839431232843147759372915,
515 0.8288355796083453829251511083215011675739,
516 0.890757001948400703462615027760238025112,
517 0.9401195768634929510614778472440778463117,
518 0.9753377608843838806113584789479015107217,
519
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520
521 ✗ w_ = {0.01207415143427396598005501314378266234585,
522 0.02772976468699360056472008267912233025642,
523 0.04251807415858959044176768509553103692525,
524 0.05594192359670198554739419281317796336792,
525 0.06756818423426273664315999085117509868606,
526 0.07702288053840514404071579740097930597024,
527 0.0840020510782250222549853318941615775106,
528 0.08828135268349632316263549505659861957546,
529 0.08972323517810326272913282213094281072439,
530 0.08828135268349632316263549505659861957546,
531 0.0840020510782250222549853318941615775106,
532 0.07702288053840514404071579740097930597024,
533 0.06756818423426273664315999085117509868606,
534 0.05594192359670198554739419281317796336792,
535 0.04251807415858959044176768509553103692525,
536 0.02772976468699360056472008267912233025642,
537
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 76 0.01207415143427396598005501314378266234585};
538 76 }
539 std::vector<double> xi_;
540 std::vector<double> w_;
541 };
542 /**
543 * \brief Gauss Legendre Rule using 18 point.
544 */
545 template <>
546 struct GaussLegendreRule<18> {
547 76 GaussLegendreRule() {
548 ✗ xi_ = {0.004217415789534526634991997646924614873711,
549 0.02208802521430112240940205353511184501358,
550 0.05369876675122213039696970443642724229605,
551 0.09814752051373844215879127249270460144835,
552 0.1541564784698233960625544593555758052739,
553 0.2201145844630262326960642257373354315362,
554 0.2941244192685786769820341030834741814605,
555 0.3740568871542472452055135725610443849186,
556 0.4576124934791323493788690735321080941333,
557 0.5423875065208676506211309264678919058667,
558 0.6259431128457527547944864274389556150814,
559 0.7058755807314213230179658969165258185395,
560 0.7798854155369737673039357742626645684638,
561 0.8458435215301766039374455406444241947261,
562 0.9018524794862615578412087275072953985516,
563 0.9463012332487778696030302955635727577039,
564 0.9779119747856988775905979464648881549864,
565
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566
567 ✗ w_ = {0.01080800676324165515667135513322623469384,
568 0.02485727444748489822666747310131932084043,
569 0.03821286512744452826456483880831826280266,
570 0.0504710220531435827814069924624173035314,
571 0.06127760335573923009225956340010077761408,
572 0.07032145733532532560236565187597361404775,
573 0.07734233756313262246270900191818738609661,
574 0.08213824187291636149302688823296379520617,
575 0.08457119148157179592032823506749330516705,
576 0.08457119148157179592032823506749330516705,
577 0.08213824187291636149302688823296379520617,
578 0.07734233756313262246270900191818738609661,
579 0.07032145733532532560236565187597361404775,
580 0.06127760335573923009225956340010077761408,
581 0.0504710220531435827814069924624173035314,
582 0.03821286512744452826456483880831826280266,
583 0.02485727444748489822666747310131932084043,
584
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 76 0.01080800676324165515667135513322623469384};
585 76 }
586 std::vector<double> xi_;
587 std::vector<double> w_;
588 };
589 /**
590 * \brief Gauss Legendre Rule using 19 point.
591 */
592 template <>
593 struct GaussLegendreRule<19> {
594 71 GaussLegendreRule() {
595 ✗ xi_ = {0.003796578078207798405491164873369753205342,
596 0.01989592393258498457361057965617423669245,
597 0.0484220481925910491786695357338437560953,
598 0.08864267173142858751053875664364304911273,
599 0.1395169113323853106914520695881091851714,
600 0.1997273476691594882651809175268803600658,
601 0.2677146293120195271413664259479488160119,
602 0.3417179500181850840049413355750775410539,
603 0.4198206771798873120659519421296282252476,
604 0.5,
605 0.5801793228201126879340480578703717747524,
606 0.6582820499818149159950586644249224589461,
607 0.7322853706879804728586335740520511839881,
608 0.8002726523308405117348190824731196399342,
609 0.8604830886676146893085479304118908148286,
610 0.9113573282685714124894612433563569508873,
611 0.9515779518074089508213304642661562439047,
612 0.9801040760674150154263894203438257633075,
613
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614
615 ✗ w_ = {0.009730894114863238518156020732219217876453,
616 0.02240711338284980016641907870099710597588,
617 0.03452227136882061329035412900300652248092,
618 0.04574501081122499973223104706191982633046,
619 0.05578332277366699735801195084088299874067,
620 0.06437698126966811383775789242843855852792,
621 0.07130335108680330588787305472095148623783,
622 0.0763830210329298333894277004488314992305,
623 0.07948442169697717382497821973252360083939,
624 0.08052722492439184798958181266045836751995,
625 0.07948442169697717382497821973252360083939,
626 0.0763830210329298333894277004488314992305,
627 0.07130335108680330588787305472095148623783,
628 0.06437698126966811383775789242843855852792,
629 0.05578332277366699735801195084088299874067,
630 0.04574501081122499973223104706191982633046,
631 0.03452227136882061329035412900300652248092,
632 0.02240711338284980016641907870099710597588,
633
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 71 0.009730894114863238518156020732219217876453};
634 71 }
635 std::vector<double> xi_;
636 std::vector<double> w_;
637 };
638 /**
639 * \brief Gauss Legendre Rule using 20 point.
640 */
641 template <>
642 struct GaussLegendreRule<20> {
643 71 GaussLegendreRule() {
644 ✗ xi_ = {0.003435700407452537606938805764339860888676,
645 0.01801403636104310436616693440136138904397,
646 0.04388278587433704706612377939835094347541,
647 0.08044151408889058830273546914923965733519,
648 0.1268340467699246036928474648221792048446,
649 0.1819731596367424872735816518868570316283,
650 0.2445664990245864509978179745223745007873,
651 0.3131469556422902196637259114875363813021,
652 0.3861070744291774609597519023157126876285,
653 0.4617367394332513331226797953005808944976,
654 0.5382632605667486668773202046994191055024,
655 0.6138929255708225390402480976842873123715,
656 0.6868530443577097803362740885124636186979,
657 0.7554335009754135490021820254776254992127,
658 0.8180268403632575127264183481131429683717,
659 0.8731659532300753963071525351778207951554,
660 0.9195584859111094116972645308507603426648,
661 0.9561172141256629529338762206016490565246,
662 0.981985963638956895633833065598638610956,
663
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 71 0.9965642995925474623930611942356601391113};
664
665 ✗ w_ = {0.008807003569576059155930981175926408181072,
666 0.02030071490019347066551997613746605493955,
667 0.0313360241670545317847532675935208031758,
668 0.04163837078835237436237907161102310305009,
669 0.05096505990862021751837506774017493808335,
670 0.05909726598075920865618868885569114350252,
671 0.06584431922458831344924724987408156745806,
672 0.07104805465919102566464916253358246651726,
673 0.07458649323630187339391436850098471834634,
674 0.07637669356536292534904216597754879674597,
675 0.07637669356536292534904216597754879674597,
676 0.07458649323630187339391436850098471834634,
677 0.07104805465919102566464916253358246651726,
678 0.06584431922458831344924724987408156745806,
679 0.05909726598075920865618868885569114350252,
680 0.05096505990862021751837506774017493808335,
681 0.04163837078835237436237907161102310305009,
682 0.0313360241670545317847532675935208031758,
683 0.02030071490019347066551997613746605493955,
684
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 71 0.008807003569576059155930981175926408181072};
685 71 }
686 std::vector<double> xi_;
687 std::vector<double> w_;
688 };
689
690 } // namespace Bembel
691 #endif // BEMBEL_SRC_QUADRATURE_GAUSSLEGENDRERULE_HPP_
692