GCC Code Coverage Report

Line	Branch	Exec	Source
1			// Copyright (C) 2025 Tiago V. L. Amorim (@tiagovla)
2			//
3			// This file is part of oiseau (https://github.com/tiagovla/oiseau)
4			//
5			// SPDX-License-Identifier: GPL-3.0-or-later
6
7			#include "oiseau/utils/integration.hpp"
8
9			#include <array>
10			#include <cmath>
11			#include <cstddef>
12			#include <stdexcept>
13			#include <string>
14			#include <utility>
15			#include <xtensor-blas/xlinalg.hpp>
16			#include <xtensor/containers/xadapt.hpp>
17			#include <xtensor/containers/xarray.hpp>
18			#include <xtensor/core/xeval.hpp>
19			#include <xtensor/core/xmath.hpp>
20			#include <xtensor/core/xtensor_forward.hpp>
21			#include <xtensor/generators/xbuilder.hpp>
22			#include <xtensor/io/xio.hpp>
23			#include <xtensor/misc/xcomplex.hpp>
24			#include <xtensor/misc/xmanipulation.hpp>
25			#include <xtensor/misc/xpad.hpp>
26			#include <xtensor/misc/xsort.hpp>
27			#include <xtensor/views/xslice.hpp>
28			#include <xtensor/views/xstrided_view.hpp>
29			#include <xtensor/views/xview.hpp>
30
31			#include "oiseau/dg/nodal/utils.hpp"
32
33			namespace {
34
35			// Cools, R. "Monomial Cubature Rules Since "Stroud":
36			// A Compilation--Part 2."
37			//
38			// J. Comput. Appl. Math. 112, 21-27, 1999.
39			//
40			// Cools, R. "Encyclopaedia of Cubature Formulas."
41			// http://www.cs.kuleuven.ac.be/~nines/research/ecf/ecf.html
42
43			// For cub2D_1: 1 point
44			static const std::array<double, 1 * 2> cub2D_1_nodes_data = {
45			{-0.333333333333333, -0.333333333333333}};
46			static const std::array<double, 1> cub2D_1_weights_data = {{2.000000000000000}};
47
48			// For cub2D_2: 3 points
49			static const std::array<double, 3 * 2> cub2D_2_nodes_data = {
50			{-0.666666666666667, -0.666666666666667, 0.333333333333333, -0.666666666666667,
51			-0.666666666666667, 0.333333333333333}};
52			static const std::array<double, 3> cub2D_2_weights_data = {
53			{0.666666666666667, 0.666666666666667, 0.666666666666667}};
54
55			// For cub2D_3: 6 points
56			static const std::array<double, 6 * 2> cub2D_3_nodes_data = {
57			{-0.816847572980458, -0.816847572980458, 0.633695145960917, -0.816847572980459,
58			-0.816847572980459, 0.633695145960917, -0.108103018168070, -0.108103018168070,
59			-0.783793963663860, -0.108103018168070, -0.108103018168070, -0.783793963663860}};
60			static const std::array<double, 6> cub2D_3_weights_data = {{0.219903487310644, 0.219903487310644,
61			0.219903487310644, 0.446763179356023,
62			0.446763179356023, 0.446763179356023}};
63
64			// For cub2D_4: 6 points
65			static const std::array<double, 6 * 2> cub2D_4_nodes_data = {
66			{-0.816847572980458, -0.816847572980458, 0.633695145960917, -0.816847572980459,
67			-0.816847572980459, 0.633695145960917, -0.108103018168070, -0.108103018168070,
68			-0.783793963663860, -0.108103018168070, -0.108103018168070, -0.783793963663860}};
69			static const std::array<double, 6> cub2D_4_weights_data = {{0.219903487310644, 0.219903487310644,
70			0.219903487310644, 0.446763179356023,
71			0.446763179356023, 0.446763179356023}};
72
73			// For cub2D_5: 7 points
74			static const std::array<double, 7 * 2> cub2D_5_nodes_data = {
75			{-0.333333333333333, -0.333333333333333, -0.059715871789770, -0.059715871789770,
76			-0.880568256420460, -0.059715871789770, -0.059715871789770, -0.880568256420460,
77			-0.797426985353087, -0.797426985353087, 0.594853970706175, -0.797426985353087,
78			-0.797426985353087, 0.594853970706175}};
79			static const std::array<double, 7> cub2D_5_weights_data = {
80			{0.450000000000000, 0.264788305577012, 0.264788305577012, 0.264788305577012, 0.251878361089654,
81			0.251878361089654, 0.251878361089654}};
82
83			// For cub2D_6: 12 points
84			static const std::array<double, 12 * 2> cub2D_6_nodes_data = {
85			{-0.501426509658179, -0.501426509658179, 0.002853019316358, -0.501426509658179,
86			-0.501426509658179, 0.002853019316358, -0.873821971016996, -0.873821971016996,
87			0.747643942033991, -0.873821971016996, -0.873821971016996, 0.747643942033991,
88			-0.379295097932431, -0.893709900310366, -0.893709900310366, -0.379295097932431,
89			0.273004998242797, -0.893709900310366, -0.893709900310366, 0.273004998242797,
90			0.273004998242797, -0.379295097932431, -0.379295097932431, 0.273004998242797}};
91			static const std::array<double, 12> cub2D_6_weights_data = {
92			{0.233572551452759, 0.233572551452759, 0.233572551452759, 0.101689812740414, 0.101689812740414,
93			0.101689812740414, 0.165702151236747, 0.165702151236747, 0.165702151236747, 0.165702151236747,
94			0.165702151236747, 0.165702151236747}};
95
96			// For cub2D_7: 15 points
97			static const std::array<double, 15 * 2> cub2D_7_nodes_data = {
98			{-0.158765070723907, -0.158765070723907, -0.682469858552186, -0.158765070723907,
99			-0.158765070723907, -0.682469858552186, -0.901937632421608, -0.901937632421608,
100			0.803875264843215, -0.901937632421608, -0.901937632421608, 0.803875264843215,
101			-0.696696002590528, -0.696696002590528, 0.393392005181056, -0.696696002590528,
102			-0.696696002590528, 0.393392005181056, 0.348275575962283, -0.375762055856278,
103			-0.375762055856278, 0.348275575962283, -0.972513520106005, -0.375762055856278,
104			-0.375762055856278, -0.972513520106005, -0.972513520106005, 0.348275575962283,
105			0.348275575962283, -0.972513520106005}};
106			static const std::array<double, 15> cub2D_7_weights_data = {
107			{0.278402959350494, 0.278402959350494, 0.278402959350494, 0.063653882657145, 0.063653882657145,
108			0.063653882657145, 0.168642646759703, 0.168642646759703, 0.168642646759703, 0.077983588949662,
109			0.077983588949662, 0.077983588949662, 0.077983588949662, 0.077983588949662,
110			0.077983588949662}};
111
112			// For cub2D_8: 16 points
113			static const std::array<double, 16 * 2> cub2D_8_nodes_data = {
114			{-0.333333333333333, -0.333333333333333, -0.081414823414554, -0.081414823414554,
115			-0.837170353170893, -0.081414823414554, -0.081414823414554, -0.837170353170893,
116			-0.658861384496480, -0.658861384496480, 0.317722768992959, -0.658861384496480,
117			-0.658861384496480, 0.317722768992959, -0.898905543365938, -0.898905543365938,
118			0.797811086731876, -0.898905543365938, -0.898905543365938, 0.797811086731876,
119			-0.473774340730724, 0.456984785910809, 0.456984785910809, -0.473774340730724,
120			-0.983210445180085, 0.456984785910809, 0.456984785910809, -0.983210445180085,
121			-0.983210445180085, -0.473774340730724, -0.473774340730724, -0.983210445180085}};
122			static const std::array<double, 16> cub2D_8_weights_data = {
123			{0.288631215355574, 0.190183268534569, 0.190183268534569, 0.190183268534569, 0.206434741069437,
124			0.206434741069437, 0.206434741069437, 0.064916995246396, 0.064916995246396, 0.064916995246396,
125			0.054460628348870, 0.054460628348870, 0.054460628348870, 0.054460628348870, 0.054460628348870,
126			0.054460628348870}};
127
128			// For cub2D_9: 19 points (19*3 = 57 elements)
129			static const std::array<double, 19 * 2> cub2D_9_nodes_data = {
130			{-0.333333333333333, -0.333333333333333, -0.020634961602525, -0.020634961602525,
131			-0.958730076794950, -0.020634961602525, -0.020634961602525, -0.958730076794950,
132			-0.125820817014127, -0.125820817014127, -0.748358365971746, -0.125820817014127,
133			-0.125820817014127, -0.748358365971746, -0.623592928761935, -0.623592928761935,
134			0.247185857523869, -0.623592928761935, -0.623592928761935, 0.247185857523869,
135			-0.910540973211095, -0.910540973211095, 0.821081946422189, -0.910540973211095,
136			-0.910540973211095, 0.821081946422189, 0.482397197568996, -0.556074021678469,
137			-0.556074021678469, 0.482397197568996, -0.926323175890527, -0.556074021678469,
138			-0.556074021678469, -0.926323175890527, -0.926323175890527, 0.482397197568996,
139			0.482397197568996, -0.926323175890527}};
140			static const std::array<double, 19> cub2D_9_weights_data = {
141			{0.194271592565598, 0.062669400454278, 0.062669400454278, 0.062669400454278, 0.155655082009549,
142			0.155655082009549, 0.155655082009549, 0.159295477854420, 0.159295477854420, 0.159295477854420,
143			0.051155351317396, 0.051155351317396, 0.051155351317396, 0.086567078754579, 0.086567078754579,
144			0.086567078754579, 0.086567078754579, 0.086567078754579, 0.086567078754579}};
145
146			// For cub2D_10: 25 points (25*3 = 75 elements)
147			static const std::array<double, 25 * 2> cub2D_10_nodes_data = {
148			{-0.333333333333333, -0.333333333333333, -0.004269134091050, -0.004269134091050,
149			-0.991461731817899, -0.004269134091050, -0.004269134091050, -0.991461731817899,
150			-0.143975100541888, -0.143975100541888, -0.712049798916225, -0.143975100541888,
151			-0.143975100541888, -0.712049798916225, -0.630487174513551, -0.630487174513551,
152			0.260974349027102, -0.630487174513551, -0.630487174513551, 0.260974349027102,
153			-0.959037562856645, -0.959037562856645, 0.918075125713290, -0.959037562856645,
154			-0.959037562856645, 0.918075125713290, -0.726852847487933, 0.656846867693389,
155			0.656846867693389, -0.726852847487933, -0.929994020205456, 0.656846867693389,
156			0.656846867693389, -0.929994020205456, -0.929994020205456, -0.726852847487933,
157			-0.726852847487933, -0.929994020205456, -0.334512798822723, 0.259414658305837,
158			0.259414658305837, -0.334512798822723, -0.924901859483115, 0.259414658305837,
159			0.259414658305837, -0.924901859483115, -0.924901859483115, -0.334512798822723,
160			-0.334512798822723, -0.924901859483115}};
161			static const std::array<double, 25> cub2D_10_weights_data = {
162			{0.167046799610393, 0.014459701184113, 0.014459701184113, 0.014459701184113,
163			0.148984355841961, 0.148984355841961, 0.148984355841961, 0.157292946806217,
164			0.157292946806217, 0.157292946806217, 0.013856646174215, 0.013856646174215,
165			0.013856646174215, 0.059036640669559, 0.059036640669559, 0.059036640669559,
166			0.059036640669559, 0.059036640669559, 0.059036640669559, 0.079158734392122,
167			0.079158734392122, 0.079158734392122, 0.079158734392122, 0.079158734392122,
168			0.079158734392122}};
169
170			// For cub2D_11: 28 points (28*3 = 84 elements)
171			static const std::array<double, 28 * 2> cub2D_11_nodes_data = {
172			{-0.333333333333333, -0.333333333333333, -0.008227986519701, -0.008227986519701,
173			-0.983544026960598, -0.008227986519701, -0.008227986519701, -0.983544026960598,
174			-0.123062767323470, -0.123062767323470, -0.753874465353061, -0.123062767323470,
175			-0.123062767323470, -0.753874465353061, -0.579583807314522, -0.579583807314522,
176			0.159167614629044, -0.579583807314522, -0.579583807314522, 0.159167614629044,
177			-0.794793191450311, -0.794793191450311, 0.589586382900622, -0.794793191450311,
178			-0.794793191450311, 0.589586382900622, -0.943045809035533, -0.943045809035533,
179			0.886091618071066, -0.943045809035533, -0.943045809035533, 0.886091618071066,
180			-0.701412405190965, 0.686811031831200, 0.686811031831200, -0.701412405190965,
181			-0.985398626640235, 0.686811031831200, 0.686811031831200, -0.985398626640235,
182			-0.985398626640235, -0.701412405190966, -0.701412405190966, -0.985398626640235,
183			-0.420944470627256, 0.328932876191794, 0.328932876191794, -0.420944470627256,
184			-0.907988405564538, 0.328932876191794, 0.328932876191794, -0.907988405564538,
185			-0.907988405564538, -0.420944470627256, -0.420944470627256, -0.907988405564538}};
186			static const std::array<double, 28> cub2D_11_weights_data = {
187			{0.171542269659139, 0.033232309648099, 0.033232309648099, 0.033232309648099, 0.134650934561697,
188			0.134650934561697, 0.134650934561697, 0.141045284213931, 0.141045284213931, 0.141045284213931,
189			0.077255352409353, 0.077255352409353, 0.077255352409353, 0.020851693311810, 0.020851693311810,
190			0.020851693311810, 0.020556454130106, 0.020556454130106, 0.020556454130106, 0.020556454130106,
191			0.020556454130106, 0.020556454130106, 0.080668713854259, 0.080668713854259, 0.080668713854259,
192			0.080668713854259, 0.080668713854259, 0.080668713854259}};
193
194			// For cub2D_12: 36 points (36*3 = 108 elements)
195			static const std::array<double, 36 * 2> cub2D_12_nodes_data = {
196			{-0.115127288420454, -0.115127288420454, -0.769745423159092, -0.115127288420454,
197			-0.115127288420454, -0.769745423159092, -0.241326933740970, -0.241326933740970,
198			-0.517346132518060, -0.241326933740970, -0.241326933740970, -0.517346132518060,
199			-0.773435586772427, -0.773435586772427, 0.546871173544855, -0.773435586772427,
200			-0.773435586772427, 0.546871173544855, -0.550360151853422, -0.550360151853422,
201			0.100720303706844, -0.550360151853422, -0.550360151853422, 0.100720303706844,
202			-0.949850839686919, -0.949850839686919, 0.899701679373837, -0.949850839686919,
203			-0.949850839686919, 0.899701679373837, -0.023247583079632, -0.023247583079632,
204			-0.953504833840737, -0.023247583079632, -0.023247583079632, -0.953504833840737,
205			0.701114686742190, -0.956341185792092, -0.956341185792092, 0.701114686742190,
206			-0.744773500950097, -0.956341185792092, -0.956341185792092, -0.744773500950097,
207			-0.744773500950097, 0.701114686742189, 0.701114686742189, -0.744773500950097,
208			0.280974603820889, -0.820754518409649, -0.820754518409649, 0.280974603820889,
209			-0.460220085411240, -0.820754518409649, -0.820754518409649, -0.460220085411240,
210			-0.460220085411240, 0.280974603820889, 0.280974603820889, -0.460220085411240,
211			0.380092839755442, -0.412599349012509, -0.412599349012509, 0.380092839755442,
212			-0.967493490742933, -0.412599349012509, -0.412599349012509, -0.967493490742933,
213			-0.967493490742933, 0.380092839755442, 0.380092839755442, -0.967493490742933}};
214			static const std::array<double, 36> cub2D_12_weights_data = {
215			{0.088694050812375, 0.088694050812375, 0.088694050812375, 0.083486638970495, 0.083486638970495,
216			0.083486638970495, 0.061949370456958, 0.061949370456958, 0.061949370456958, 0.096926744607805,
217			0.096926744607805, 0.096926744607805, 0.016284715813394, 0.016284715813394, 0.016284715813394,
218			0.047730162209543, 0.047730162209543, 0.047730162209543, 0.030740478172077, 0.030740478172077,
219			0.030740478172077, 0.030740478172077, 0.030740478172077, 0.030740478172077, 0.073364295183933,
220			0.073364295183933, 0.073364295183933, 0.073364295183933, 0.073364295183933, 0.073364295183933,
221			0.031692718542038, 0.031692718542038, 0.031692718542038, 0.031692718542038, 0.031692718542038,
222			0.031692718542038}};
223
224			// For cub2D_13: 40 points (40*3 = 120 elements)
225			static const std::array<double, 40 * 2> cub2D_13_nodes_data = {
226			{-0.333333333333333, -0.333333333333333, -0.178369512906405, -0.178369512906405,
227			-0.643260974187191, -0.178369512906405, -0.178369512906405, -0.643260974187191,
228			-0.542160866418819, -0.542160866418819, 0.084321732837639, -0.542160866418819,
229			-0.542160866418819, 0.084321732837639, -0.771083702251175, -0.771083702251175,
230			0.542167404502350, -0.771083702251175, -0.771083702251175, 0.542167404502350,
231			-0.951222762153923, -0.951222762153923, 0.902445524307847, -0.951222762153923,
232			-0.951222762153923, 0.902445524307847, -0.071124044893491, -0.071124044893491,
233			-0.857751910213018, -0.071124044893491, -0.071124044893491, -0.857751910213018,
234			0.089497598920545, -0.972567007080596, -0.972567007080596, 0.089497598920545,
235			-0.116930591839948, -0.972567007080596, -0.972567007080596, -0.116930591839948,
236			-0.116930591839948, 0.089497598920545, 0.089497598920545, -0.116930591839948,
237			0.708303576893352, -0.752827405974001, -0.752827405974001, 0.708303576893352,
238			-0.955476170919351, -0.752827405974001, -0.752827405974001, -0.955476170919351,
239			-0.955476170919351, 0.708303576893352, 0.708303576893352, -0.955476170919351,
240			0.400693795223418, -0.438009873048077, -0.438009873048077, 0.400693795223418,
241			-0.962683922175342, -0.438009873048076, -0.438009873048076, -0.962683922175342,
242			-0.962683922175342, 0.400693795223419, 0.400693795223419, -0.962683922175342,
243			-0.461147708177324, -0.809703416305633, -0.809703416305633, -0.461147708177324,
244			0.270851124482956, -0.809703416305633, -0.809703416305633, 0.270851124482956,
245			0.270851124482956, -0.461147708177324, -0.461147708177324, 0.270851124482956}};
246			static const std::array<double, 40> cub2D_13_weights_data = {
247			{0.097649880256618, 0.090830392435257, 0.090830392435257, 0.090830392435257,
248			0.093688172298398, 0.093688172298398, 0.093688172298398, 0.062636625766914,
249			0.062636625766914, 0.062636625766914, 0.015384123058757, 0.015384123058757,
250			0.015384123058757, 0.063336411850675, 0.063336411850675, 0.063336411850675,
251			0.017363112895214, 0.017363112895214, 0.017363112895214, 0.017363112895214,
252			0.017363112895214, 0.017363112895214, 0.030203519313196, 0.030203519313196,
253			0.030203519313196, 0.030203519313196, 0.030203519313196, 0.030203519313196,
254			0.032954120635442, 0.032954120635442, 0.032954120635442, 0.032954120635442,
255			0.032954120635442, 0.032954120635442, 0.073599737741711, 0.073599737741711,
256			0.073599737741711, 0.073599737741711, 0.073599737741711, 0.073599737741711}};
257
258			// For cub2D_14: 46 points (46*3 = 138 elements)
259			static const std::array<double, 46 * 2> cub2D_14_nodes_data = {
260			{-0.333333333333333, -0.333333333333333, -0.031437623162377, -0.031437623162377,
261			-0.937124753675245, -0.031437623162377, -0.031437623162377, -0.937124753675245,
262			-0.190179067155837, -0.190179067155837, -0.619641865688325, -0.190179067155837,
263			-0.190179067155837, -0.619641865688325, -0.544945017724160, -0.544945017724160,
264			0.089890035448320, -0.544945017724160, -0.544945017724160, 0.089890035448320,
265			-0.829084434528895, -0.829084434528895, 0.658168869057790, -0.829084434528895,
266			-0.829084434528895, 0.658168869057790, -0.961731843229187, -0.961731843229187,
267			0.923463686458374, -0.961731843229187, -0.961731843229187, 0.923463686458374,
268			-0.228055909294146, 0.200257489743243, 0.200257489743243, -0.228055909294146,
269			-0.972201580449098, 0.200257489743243, 0.200257489743243, -0.972201580449098,
270			-0.972201580449097, -0.228055909294146, -0.228055909294146, -0.972201580449097,
271			-0.801926305237733, 0.769518568627872, 0.769518568627872, -0.801926305237733,
272			-0.967592263390139, 0.769518568627872, 0.769518568627872, -0.967592263390139,
273			-0.967592263390139, -0.801926305237733, -0.801926305237733, -0.967592263390139,
274			-0.544893784145096, 0.504355701557747, 0.504355701557747, -0.544893784145096,
275			-0.959461917412651, 0.504355701557747, 0.504355701557747, -0.959461917412651,
276			-0.959461917412651, -0.544893784145095, -0.544893784145095, -0.959461917412651,
277			-0.288429073961769, 0.109399611316741, 0.109399611316741, -0.288429073961769,
278			-0.820970537354972, 0.109399611316741, 0.109399611316741, -0.820970537354972,
279			-0.820970537354972, -0.288429073961769, -0.288429073961769, -0.820970537354972,
280			-0.593507885280605, 0.397658756992448, 0.397658756992448, -0.593507885280605,
281			-0.804150871711842, 0.397658756992447, 0.397658756992447, -0.804150871711842,
282			-0.804150871711842, -0.593507885280605, -0.593507885280605, -0.804150871711842}};
283			static const std::array<double, 46> cub2D_14_weights_data = {
284			{0.086016161940337, 0.020861042581505, 0.020861042581505, 0.020861042581505, 0.084906577433761,
285			0.084906577433761, 0.084906577433761, 0.094412955694385, 0.094412955694385, 0.094412955694385,
286			0.036931420530108, 0.036931420530108, 0.036931420530108, 0.009566859223433, 0.009566859223433,
287			0.009566859223433, 0.023873332102599, 0.023873332102599, 0.023873332102599, 0.023873332102599,
288			0.023873332102599, 0.023873332102599, 0.018006541968931, 0.018006541968931, 0.018006541968931,
289			0.018006541968931, 0.018006541968931, 0.018006541968931, 0.030117913357456, 0.030117913357456,
290			0.030117913357456, 0.030117913357456, 0.030117913357456, 0.030117913357456, 0.067035335144205,
291			0.067035335144205, 0.067035335144205, 0.067035335144205, 0.067035335144205, 0.067035335144205,
292			0.056624756038490, 0.056624756038490, 0.056624756038490, 0.056624756038490, 0.056624756038490,
293			0.056624756038490}};
294
295			static const std::array<double, 54 * 2> cub2D_15_nodes_data = {
296			{-0.083438407261750, -0.083438407261750, -0.833123185476500, -0.083438407261750,
297			-0.083438407261750, -0.833123185476500, -0.192779070841739, -0.192779070841739,
298			-0.614441858316522, -0.192779070841739, -0.192779070841739, -0.614441858316522,
299			-0.413605664173949, -0.413605664173949, -0.172788671652101, -0.413605664173949,
300			-0.413605664173949, -0.172788671652101, -0.707064426114454, -0.707064426114454,
301			0.414128852228908, -0.707064426114454, -0.707064426114454, 0.414128852228908,
302			-0.887274264668793, -0.887274264668793, 0.774548529337586, -0.887274264668793,
303			-0.887274264668793, 0.774548529337586, -0.966849746283259, -0.966849746283259,
304			0.933699492566519, -0.966849746283259, -0.966849746283259, 0.933699492566519,
305			-0.520930891690411, 0.501106485071962, 0.501106485071962, -0.520930891690411,
306			-0.980175593381550, 0.501106485071962, 0.501106485071962, -0.980175593381550,
307			-0.980175593381550, -0.520930891690411, -0.520930891690411, -0.980175593381550,
308			-0.190242385363320, 0.158634844102864, 0.158634844102864, -0.190242385363320,
309			-0.968392458739544, 0.158634844102864, 0.158634844102864, -0.968392458739544,
310			-0.968392458739544, -0.190242385363320, -0.190242385363320, -0.968392458739544,
311			-0.809995773773910, 0.799708556139969, 0.799708556139969, -0.809995773773910,
312			-0.989712782366059, 0.799708556139969, 0.799708556139969, -0.989712782366059,
313			-0.989712782366059, -0.809995773773910, -0.809995773773910, -0.989712782366059,
314			-0.700493785355452, 0.602649133849474, 0.602649133849474, -0.700493785355452,
315			-0.902155348494022, 0.602649133849474, 0.602649133849474, -0.902155348494022,
316			-0.902155348494023, -0.700493785355452, -0.700493785355452, -0.902155348494023,
317			-0.426160775117330, 0.288623277852292, 0.288623277852292, -0.426160775117330,
318			-0.862462502734962, 0.288623277852292, 0.288623277852292, -0.862462502734962,
319			-0.862462502734962, -0.426160775117330, -0.426160775117330, -0.862462502734962,
320			-0.436328663801831, 0.099519827552432, 0.099519827552432, -0.436328663801831,
321			-0.663191163750602, 0.099519827552432, 0.099519827552432, -0.663191163750602,
322			-0.663191163750602, -0.436328663801831, -0.436328663801831, -0.663191163750602}};
323			static const std::array<double, 54> cub2D_15_weights_data = {
324			{0.065323637697611, 0.065323637697611, 0.065323637697611, 0.054825636062729, 0.054825636062729,
325			0.054825636062729, 0.053020073197407, 0.053020073197407, 0.053020073197407, 0.058431924272972,
326			0.058431924272972, 0.058431924272972, 0.021169216132488, 0.021169216132488, 0.021169216132488,
327			0.007229286128184, 0.007229286128184, 0.007229286128184, 0.017055496203419, 0.017055496203419,
328			0.017055496203419, 0.017055496203419, 0.017055496203419, 0.017055496203419, 0.027832353033384,
329			0.027832353033384, 0.027832353033384, 0.027832353033384, 0.027832353033384, 0.027832353033384,
330			0.008583865881470, 0.008583865881470, 0.008583865881470, 0.008583865881470, 0.008583865881470,
331			0.008583865881470, 0.032470658563550, 0.032470658563550, 0.032470658563550, 0.032470658563550,
332			0.032470658563550, 0.032470658563550, 0.051214681842525, 0.051214681842525, 0.051214681842525,
333			0.051214681842525, 0.051214681842525, 0.051214681842525, 0.066176391063291, 0.066176391063291,
334			0.066176391063291, 0.066176391063291, 0.066176391063291, 0.066176391063291}};
335
336			// For cub2D_16: 58 points (58*3 = 174 elements)
337			static const std::array<double, 58 * 2> cub2D_16_nodes_data = {
338			{-0.333333333333333, -0.333333333333333, -0.015796436959213, -0.015796436959213,
339			-0.968407126081574, -0.015796436959213, -0.015796436959213, -0.968407126081574,
340			-0.087376299046785, -0.087376299046785, -0.825247401906431, -0.087376299046785,
341			-0.087376299046785, -0.825247401906431, -0.640498098534045, -0.640498098534045,
342			0.280996197068091, -0.640498098534045, -0.640498098534045, 0.280996197068091,
343			-0.828211591878549, -0.828211591878549, 0.656423183757099, -0.828211591878549,
344			-0.828211591878549, 0.656423183757099, -0.977882767295650, -0.977882767295650,
345			0.955765534591299, -0.977882767295650, -0.977882767295650, 0.955765534591299,
346			-0.648594849699253, 0.619534954455185, 0.619534954455185, -0.648594849699253,
347			-0.970940104755933, 0.619534954455185, 0.619534954455185, -0.970940104755933,
348			-0.970940104755933, -0.648594849699253, -0.648594849699253, -0.970940104755933,
349			-0.355089058161032, 0.324703448463838, 0.324703448463838, -0.355089058161032,
350			-0.969614390302806, 0.324703448463838, 0.324703448463838, -0.969614390302806,
351			-0.969614390302806, -0.355089058161032, -0.355089058161032, -0.969614390302806,
352			-0.863082725186344, 0.829810165174004, 0.829810165174004, -0.863082725186344,
353			-0.966727439987660, 0.829810165174004, 0.829810165174004, -0.966727439987660,
354			-0.966727439987660, -0.863082725186344, -0.863082725186344, -0.966727439987660,
355			-0.650110471151428, 0.511910525190604, 0.511910525190604, -0.650110471151428,
356			-0.861800054039176, 0.511910525190604, 0.511910525190604, -0.861800054039176,
357			-0.861800054039176, -0.650110471151428, -0.650110471151428, -0.861800054039176,
358			-0.282624366842035, 0.131065359625217, 0.131065359625217, -0.282624366842035,
359			-0.848440992783182, 0.131065359625217, 0.131065359625217, -0.848440992783182,
360			-0.848440992783182, -0.282624366842035, -0.282624366842035, -0.848440992783182,
361			-0.500121711290305, 0.333566061453817, 0.333566061453817, -0.500121711290305,
362			-0.833444350163512, 0.333566061453817, 0.333566061453817, -0.833444350163512,
363			-0.833444350163512, -0.500121711290305, -0.500121711290305, -0.833444350163512,
364			-0.353308953197778, -0.027538833736648, -0.027538833736648, -0.353308953197778,
365			-0.619152213065573, -0.027538833736648, -0.027538833736648, -0.619152213065573,
366			-0.619152213065573, -0.353308953197778, -0.353308953197778, -0.619152213065573}};
367			static const std::array<double, 58> cub2D_16_weights_data = {
368			{0.092421202321849, 0.027991652734724, 0.027991652734724, 0.027991652734724, 0.036406763596424,
369			0.036406763596424, 0.036406763596424, 0.062729423327251, 0.062729423327251, 0.062729423327251,
370			0.032217170192673, 0.032217170192673, 0.032217170192673, 0.003676792575648, 0.003676792575648,
371			0.003676792575648, 0.019075686313307, 0.019075686313307, 0.019075686313307, 0.019075686313307,
372			0.019075686313307, 0.019075686313307, 0.025111336723323, 0.025111336723323, 0.025111336723323,
373			0.025111336723323, 0.025111336723323, 0.025111336723323, 0.014134510743040, 0.014134510743040,
374			0.014134510743040, 0.014134510743040, 0.014134510743040, 0.014134510743040, 0.025255543672496,
375			0.025255543672496, 0.025255543672496, 0.025255543672496, 0.025255543672496, 0.025255543672496,
376			0.038432852520849, 0.038432852520849, 0.038432852520849, 0.038432852520849, 0.038432852520849,
377			0.038432852520849, 0.032993291211606, 0.032993291211606, 0.032993291211606, 0.032993291211606,
378			0.032993291211606, 0.032993291211606, 0.081415677215044, 0.081415677215044, 0.081415677215044,
379			0.081415677215044, 0.081415677215044, 0.081415677215044}};
380
381			// For cub2D_17: 66 points (66*3 = 198 elements)
382			static const std::array<double, 66 * 2> cub2D_17_nodes_data = {
383			{-0.013565183960096, -0.013565183960096, -0.972869632079808, -0.013565183960096,
384			-0.013565183960096, -0.972869632079808, -0.918012666387151, -0.918012666387151,
385			0.836025332774302, -0.918012666387151, -0.918012666387151, 0.836025332774302,
386			-0.469265478050798, -0.469265478050798, -0.061469043898404, -0.469265478050798,
387			-0.469265478050798, -0.061469043898404, -0.278161974512876, -0.278161974512876,
388			-0.443676050974249, -0.278161974512876, -0.278161974512876, -0.443676050974249,
389			-0.743831619059579, -0.743831619059579, 0.487663238119159, -0.743831619059579,
390			-0.743831619059579, 0.487663238119159, -0.975086972700342, -0.975086972700342,
391			0.950173945400684, -0.975086972700342, -0.975086972700342, 0.950173945400684,
392			-0.331485915788080, 0.305875449252880, 0.305875449252880, -0.331485915788080,
393			-0.974389533464800, 0.305875449252880, 0.305875449252880, -0.974389533464800,
394			-0.974389533464800, -0.331485915788080, -0.331485915788080, -0.974389533464800,
395			-0.617368143234940, 0.598534426856625, 0.598534426856625, -0.617368143234940,
396			-0.981166283621686, 0.598534426856625, 0.598534426856625, -0.981166283621686,
397			-0.981166283621686, -0.617368143234940, -0.617368143234940, -0.981166283621686,
398			-0.846737941679184, 0.837351785097968, 0.837351785097968, -0.846737941679184,
399			-0.990613843418784, 0.837351785097968, 0.837351785097968, -0.990613843418784,
400			-0.990613843418784, -0.846737941679184, -0.846737941679184, -0.990613843418784,
401			-0.530582382227094, 0.412831673770520, 0.412831673770520, -0.530582382227094,
402			-0.882249291543426, 0.412831673770520, 0.412831673770520, -0.882249291543426,
403			-0.882249291543426, -0.530582382227094, -0.530582382227094, -0.882249291543426,
404			-0.230167008731505, 0.092655855430620, 0.092655855430620, -0.230167008731505,
405			-0.862488846699115, 0.092655855430620, 0.092655855430620, -0.862488846699115,
406			-0.862488846699115, -0.230167008731505, -0.230167008731505, -0.862488846699115,
407			-0.769841956364772, 0.681416462088999, 0.681416462088999, -0.769841956364772,
408			-0.911574505724228, 0.681416462088999, 0.681416462088999, -0.911574505724228,
409			-0.911574505724228, -0.769841956364772, -0.769841956364772, -0.911574505724228,
410			-0.502901760016855, 0.206946937904245, 0.206946937904245, -0.502901760016855,
411			-0.704045177887389, 0.206946937904245, 0.206946937904245, -0.704045177887389,
412			-0.704045177887389, -0.502901760016855, -0.502901760016855, -0.704045177887389,
413			-0.258115377755090, -0.067105414124881, -0.067105414124881, -0.258115377755090,
414			-0.674779208120030, -0.067105414124880, -0.067105414124880, -0.674779208120030,
415			-0.674779208120030, -0.258115377755090, -0.258115377755090, -0.674779208120030}};
416			static const std::array<double, 66> cub2D_17_weights_data = {
417			{0.022448424077156, 0.022448424077156, 0.022448424077156, 0.011377816766740, 0.011377816766740,
418			0.011377816766740, 0.056148078797670, 0.056148078797670, 0.056148078797670, 0.031804753050686,
419			0.031804753050686, 0.031804753050686, 0.042944604159838, 0.042944604159838, 0.042944604159838,
420			0.004138336267131, 0.004138336267131, 0.004138336267131, 0.020094111670483, 0.020094111670483,
421			0.020094111670483, 0.020094111670483, 0.020094111670483, 0.020094111670483, 0.013023443943004,
422			0.013023443943004, 0.013023443943004, 0.013023443943004, 0.013023443943004, 0.013023443943004,
423			0.005856954369545, 0.005856954369545, 0.005856954369545, 0.005856954369545, 0.005856954369545,
424			0.005856954369545, 0.037746172643499, 0.037746172643499, 0.037746172643499, 0.037746172643499,
425			0.037746172643499, 0.037746172643499, 0.048362752988591, 0.048362752988591, 0.048362752988591,
426			0.048362752988591, 0.048362752988591, 0.048362752988591, 0.023467126169388, 0.023467126169388,
427			0.023467126169388, 0.023467126169388, 0.023467126169388, 0.023467126169388, 0.054703428836887,
428			0.054703428836887, 0.054703428836887, 0.054703428836887, 0.054703428836887, 0.054703428836887,
429			0.045648336152327, 0.045648336152327, 0.045648336152327, 0.045648336152327, 0.045648336152327,
430			0.045648336152327}};
431
432			// For cub2D_18: 73 points (73*3 = 219 elements)
433			static const std::array<double, 73 * 2> cub2D_18_nodes_data = {
434			{-0.333333333333333, -0.333333333333333, -0.012131216528029, -0.012131216528029,
435			-0.975737566943942, -0.012131216528029, -0.012131216528029, -0.975737566943942,
436			-0.230136518749796, -0.230136518749796, -0.539726962500408, -0.230136518749796,
437			-0.230136518749796, -0.539726962500408, -0.499402807850562, -0.499402807850562,
438			-0.001194384298875, -0.499402807850563, -0.499402807850563, -0.001194384298875,
439			-0.710045241598598, -0.710045241598598, 0.420090483197196, -0.710045241598598,
440			-0.710045241598598, 0.420090483197196, -0.903019171569391, -0.903019171569391,
441			0.806038343138783, -0.903019171569391, -0.903019171569391, 0.806038343138783,
442			-0.972866921676664, -0.972866921676664, 0.945733843353328, -0.972866921676664,
443			-0.972866921676664, 0.945733843353328, -0.859848143426920, 0.852682278520227,
444			0.852682278520227, -0.859848143426920, -0.992834135093306, 0.852682278520227,
445			0.852682278520227, -0.992834135093306, -0.992834135093306, -0.859848143426920,
446			-0.859848143426920, -0.992834135093306, -0.592208428296456, 0.573110619333459,
447			0.573110619333459, -0.592208428296456, -0.980902191037003, 0.573110619333459,
448			0.573110619333459, -0.980902191037003, -0.980902191037003, -0.592208428296456,
449			-0.592208428296456, -0.980902191037003, -0.316660705097116, 0.294011442575493,
450			0.294011442575493, -0.316660705097116, -0.977350737478378, 0.294011442575493,
451			0.294011442575493, -0.977350737478378, -0.977350737478378, -0.316660705097116,
452			-0.316660705097116, -0.977350737478378, -0.762708275393600, 0.720805143081058,
453			0.720805143081058, -0.762708275393600, -0.958096867687458, 0.720805143081058,
454			0.720805143081058, -0.958096867687458, -0.958096867687458, -0.762708275393600,
455			-0.762708275393600, -0.958096867687458, -0.499464753852078, 0.389673957377540,
456			0.389673957377540, -0.499464753852078, -0.890209203525462, 0.389673957377540,
457			0.389673957377540, -0.890209203525462, -0.890209203525462, -0.499464753852078,
458			-0.499464753852078, -0.890209203525462, -0.730193961187213, 0.595225312221749,
459			0.595225312221749, -0.730193961187213, -0.865031351034536, 0.595225312221749,
460			0.595225312221749, -0.865031351034536, -0.865031351034535, -0.730193961187213,
461			-0.730193961187213, -0.865031351034535, -0.213662181077459, 0.092159471784540,
462			0.092159471784540, -0.213662181077459, -0.878497290707081, 0.092159471784540,
463			0.092159471784540, -0.878497290707081, -0.878497290707081, -0.213662181077459,
464			-0.213662181077459, -0.878497290707081, -0.268906542375276, -0.010964677486621,
465			-0.010964677486621, -0.268906542375276, -0.720128780138103, -0.010964677486621,
466			-0.010964677486621, -0.720128780138103, -0.720128780138103, -0.268906542375276,
467			-0.268906542375276, -0.720128780138103, -0.507963230765286, 0.233062121320884,
468			0.233062121320884, -0.507963230765286, -0.725098890555598, 0.233062121320884,
469			0.233062121320884, -0.725098890555598, -0.725098890555598, -0.507963230765286,
470			-0.507963230765286, -0.725098890555598}};
471			static const std::array<double, 73> cub2D_18_weights_data = {
472			{0.044365924378076, 0.019118866558615, 0.019118866558615, 0.019118866558615, 0.049294282264207,
473			0.049294282264207, 0.049294282264207, 0.060654125981259, 0.060654125981259, 0.060654125981259,
474			0.031366231844497, 0.031366231844497, 0.031366231844497, 0.016173035699059, 0.016173035699059,
475			0.016173035699059, 0.004750076743416, 0.004750076743416, 0.004750076743416, 0.004329998364046,
476			0.004329998364046, 0.004329998364046, 0.004329998364046, 0.004329998364046, 0.004329998364046,
477			0.012300136592151, 0.012300136592151, 0.012300136592151, 0.012300136592151, 0.012300136592151,
478			0.012300136592151, 0.017146550496094, 0.017146550496094, 0.017146550496094, 0.017146550496094,
479			0.017146550496094, 0.017146550496094, 0.010992784367686, 0.010992784367686, 0.010992784367686,
480			0.010992784367686, 0.010992784367686, 0.010992784367686, 0.033988423627451, 0.033988423627451,
481			0.033988423627451, 0.033988423627451, 0.033988423627451, 0.033988423627451, 0.025768775250048,
482			0.025768775250048, 0.025768775250048, 0.025768775250048, 0.025768775250048, 0.025768775250048,
483			0.040023698716305, 0.040023698716305, 0.040023698716305, 0.040023698716305, 0.040023698716305,
484			0.040023698716305, 0.045277248097616, 0.045277248097616, 0.045277248097616, 0.045277248097616,
485			0.045277248097616, 0.045277248097616, 0.045433087546729, 0.045433087546729, 0.045433087546729,
486			0.045433087546729, 0.045433087546729, 0.045433087546729}};
487
488			// For cub2D_19: 82 points (82*3 = 246 elements)
489			static const std::array<double, 82 * 2> cub2D_19_nodes_data = {
490			{-0.333333333333333, -0.333333333333333, -0.121193890022463, -0.121193890022463,
491			-0.757612219955075, -0.121193890022463, -0.121193890022463, -0.757612219955075,
492			-0.227921589064499, -0.227921589064499, -0.544156821871001, -0.227921589064499,
493			-0.227921589064499, -0.544156821871001, -0.480832787187258, -0.480832787187258,
494			-0.038334425625484, -0.480832787187258, -0.480832787187258, -0.038334425625484,
495			-0.607587000462791, -0.607587000462791, 0.215174000925582, -0.607587000462791,
496			-0.607587000462791, 0.215174000925582, -0.728032884013154, -0.728032884013154,
497			0.456065768026307, -0.728032884013154, -0.728032884013154, 0.456065768026307,
498			-0.884999963315497, -0.884999963315497, 0.769999926630994, -0.884999963315497,
499			-0.884999963315497, 0.769999926630994, -0.973927705240279, -0.973927705240279,
500			0.947855410480559, -0.973927705240279, -0.973927705240279, 0.947855410480559,
501			-0.419340397282846, 0.418549313572482, 0.418549313572482, -0.419340397282846,
502			-0.999208916289636, 0.418549313572482, 0.418549313572482, -0.999208916289636,
503			-0.999208916289636, -0.419340397282846, -0.419340397282846, -0.999208916289636,
504			-0.154285565801825, 0.131285016869205, 0.131285016869205, -0.154285565801825,
505			-0.976999451067380, 0.131285016869205, 0.131285016869205, -0.976999451067380,
506			-0.976999451067380, -0.154285565801825, -0.154285565801825, -0.976999451067380,
507			-0.864328042937615, 0.842262778125134, 0.842262778125134, -0.864328042937615,
508			-0.977934735187519, 0.842262778125134, 0.842262778125134, -0.977934735187519,
509			-0.977934735187519, -0.864328042937615, -0.864328042937615, -0.977934735187519,
510			-0.676980679779850, 0.654351228666662, 0.654351228666662, -0.676980679779850,
511			-0.977370548886812, 0.654351228666662, 0.654351228666662, -0.977370548886812,
512			-0.977370548886812, -0.676980679779850, -0.676980679779850, -0.977370548886812,
513			-0.451038034994882, 0.391933493150074, 0.391933493150074, -0.451038034994882,
514			-0.940895458155192, 0.391933493150074, 0.391933493150074, -0.940895458155192,
515			-0.940895458155192, -0.451038034994882, -0.451038034994882, -0.940895458155192,
516			-0.755079003035426, 0.643775758022122, 0.643775758022122, -0.755079003035426,
517			-0.888696754986697, 0.643775758022122, 0.643775758022122, -0.888696754986697,
518			-0.888696754986697, -0.755079003035426, -0.755079003035426, -0.888696754986697,
519			-0.668500025831376, 0.544622467980326, 0.544622467980326, -0.668500025831376,
520			-0.876122442148950, 0.544622467980326, 0.544622467980326, -0.876122442148950,
521			-0.876122442148950, -0.668500025831376, -0.668500025831376, -0.876122442148950,
522			-0.205954158284095, 0.090524206162520, 0.090524206162520, -0.205954158284095,
523			-0.884570047878425, 0.090524206162520, 0.090524206162520, -0.884570047878425,
524			-0.884570047878425, -0.205954158284095, -0.205954158284095, -0.884570047878425,
525			-0.488476686471250, 0.295757669634562, 0.295757669634562, -0.488476686471250,
526			-0.807280983163311, 0.295757669634562, 0.295757669634562, -0.807280983163311,
527			-0.807280983163311, -0.488476686471250, -0.488476686471250, -0.807280983163311,
528			-0.342507806805715, 0.042214391480752, 0.042214391480752, -0.342507806805715,
529			-0.699706584675037, 0.042214391480751, 0.042214391480751, -0.699706584675037,
530			-0.699706584675037, -0.342507806805715, -0.342507806805715, -0.699706584675037}};
531			static const std::array<double, 82> cub2D_19_weights_data = {
532			{0.041424760048010, 0.031784855337689, 0.031784855337689, 0.031784855337689, 0.048406599909930,
533			0.048406599909930, 0.048406599909930, 0.048177661858475, 0.048177661858475, 0.048177661858475,
534			0.042691162490028, 0.042691162490028, 0.042691162490028, 0.031889013978028, 0.031889013978028,
535			0.031889013978028, 0.015529272923518, 0.015529272923518, 0.015529272923518, 0.004442852871415,
536			0.004442852871415, 0.004442852871415, 0.004599409024561, 0.004599409024561, 0.004599409024561,
537			0.004599409024561, 0.004599409024561, 0.004599409024561, 0.016608327001253, 0.016608327001253,
538			0.016608327001253, 0.016608327001253, 0.016608327001253, 0.016608327001253, 0.008508350664254,
539			0.008508350664254, 0.008508350664254, 0.008508350664254, 0.008508350664254, 0.008508350664254,
540			0.012752760516072, 0.012752760516072, 0.012752760516072, 0.012752760516072, 0.012752760516072,
541			0.012752760516072, 0.024864731137205, 0.024864731137205, 0.024864731137205, 0.024864731137205,
542			0.024864731137205, 0.024864731137205, 0.012779469878381, 0.012779469878381, 0.012779469878381,
543			0.012779469878381, 0.012779469878381, 0.012779469878381, 0.017801502950615, 0.017801502950615,
544			0.017801502950615, 0.017801502950615, 0.017801502950615, 0.017801502950615, 0.035738233266717,
545			0.035738233266717, 0.035738233266717, 0.035738233266717, 0.035738233266717, 0.035738233266717,
546			0.038344199404453, 0.038344199404453, 0.038344199404453, 0.038344199404453, 0.038344199404453,
547			0.038344199404453, 0.042971513130613, 0.042971513130613, 0.042971513130613, 0.042971513130613,
548			0.042971513130613, 0.042971513130613}};
549
550			// For cub2D_20: 85 points (85*3 = 255 elements)
551			static const std::array<double, 85 * 2> cub2D_20_nodes_data = {
552			{-0.333333333333333, -0.333333333333333, -0.001500649324429, -0.001500649324429,
553			-0.996998701351142, -0.001500649324429, -0.001500649324429, -0.996998701351142,
554			-0.094139751938951, -0.094139751938951, -0.811720496122098, -0.094139751938951,
555			-0.094139751938951, -0.811720496122098, -0.204472124089526, -0.204472124089526,
556			-0.591055751820947, -0.204472124089526, -0.204472124089526, -0.591055751820947,
557			-0.470999594934425, -0.470999594934425, -0.058000810131149, -0.470999594934425,
558			-0.470999594934425, -0.058000810131149, -0.577962071815846, -0.577962071815846,
559			0.155924143631693, -0.577962071815846, -0.577962071815846, 0.155924143631693,
560			-0.784528785657457, -0.784528785657457, 0.569057571314915, -0.784528785657457,
561			-0.784528785657457, 0.569057571314915, -0.921861824324395, -0.921861824324395,
562			0.843723648648789, -0.921861824324395, -0.921861824324395, 0.843723648648789,
563			-0.977651240541341, -0.977651240541341, 0.955302481082681, -0.977651240541341,
564			-0.977651240541341, 0.955302481082681, -0.872900668183296, 0.862201431808621,
565			0.862201431808621, -0.872900668183296, -0.989300763625325, 0.862201431808621,
566			0.862201431808621, -0.989300763625325, -0.989300763625325, -0.872900668183295,
567			-0.872900668183295, -0.989300763625325, -0.685786162118586, 0.669876527986188,
568			0.669876527986188, -0.685786162118586, -0.984090365867602, 0.669876527986188,
569			0.669876527986188, -0.984090365867602, -0.984090365867602, -0.685786162118586,
570			-0.685786162118586, -0.984090365867602, -0.208715771271252, 0.187870974708724,
571			0.187870974708724, -0.208715771271252, -0.979155203437472, 0.187870974708724,
572			0.187870974708724, -0.979155203437472, -0.979155203437472, -0.208715771271252,
573			-0.208715771271252, -0.979155203437472, -0.453664858574179, 0.431736028981932,
574			0.431736028981932, -0.453664858574179, -0.978071170407753, 0.431736028981932,
575			0.431736028981932, -0.978071170407753, -0.978071170407753, -0.453664858574179,
576			-0.453664858574179, -0.978071170407753, -0.796429235029966, 0.719295810859041,
577			0.719295810859041, -0.796429235029966, -0.922866575829075, 0.719295810859041,
578			0.719295810859041, -0.922866575829075, -0.922866575829075, -0.796429235029966,
579			-0.796429235029966, -0.922866575829075, -0.106682901647172, 0.035521886012736,
580			0.035521886012736, -0.106682901647172, -0.928838984365563, 0.035521886012736,
581			0.035521886012736, -0.928838984365563, -0.928838984365564, -0.106682901647172,
582			-0.106682901647172, -0.928838984365564, -0.601978411700994, 0.502636778975466,
583			0.502636778975466, -0.601978411700994, -0.900658367274472, 0.502636778975466,
584			0.502636778975466, -0.900658367274472, -0.900658367274472, -0.601978411700994,
585			-0.601978411700994, -0.900658367274472, -0.351477632615435, 0.234438182446771,
586			0.234438182446771, -0.351477632615435, -0.882960549831337, 0.234438182446771,
587			0.234438182446771, -0.882960549831337, -0.882960549831337, -0.351477632615435,
588			-0.351477632615435, -0.882960549831337, -0.582937273579734, 0.339941699570946,
589			0.339941699570946, -0.582937273579734, -0.757004425991211, 0.339941699570946,
590			0.339941699570946, -0.757004425991211, -0.757004425991211, -0.582937273579734,
591			-0.582937273579734, -0.757004425991211, -0.353658866927485, 0.072237177039608,
592			0.072237177039608, -0.353658866927485, -0.718578310112123, 0.072237177039608,
593			0.072237177039608, -0.718578310112123, -0.718578310112123, -0.353658866927485,
594			-0.353658866927485, -0.718578310112123}};
595			static const std::array<double, 85> cub2D_20_weights_data = {
596			{0.055220853995399, 0.003558059094653, 0.003558059094653, 0.003558059094653,
597			0.040224796227922, 0.040224796227922, 0.040224796227922, 0.053635694518663,
598			0.053635694518663, 0.053635694518663, 0.049046267603004, 0.049046267603004,
599			0.049046267603004, 0.032789156821391, 0.032789156821391, 0.032789156821391,
600			0.029591814797299, 0.029591814797299, 0.029591814797299, 0.009158564555409,
601			0.009158564555409, 0.009158564555409, 0.003303653031152, 0.003303653031152,
602			0.003303653031152, 0.004698341817151, 0.004698341817151, 0.004698341817151,
603			0.004698341817151, 0.004698341817151, 0.004698341817151, 0.008931851508364,
604			0.008931851508364, 0.008931851508364, 0.008931851508364, 0.008931851508364,
605			0.008931851508364, 0.012199133615816, 0.012199133615816, 0.012199133615816,
606			0.012199133615816, 0.012199133615816, 0.012199133615816, 0.013782162654376,
607			0.013782162654376, 0.013782162654376, 0.013782162654376, 0.013782162654376,
608			0.013782162654376, 0.015994950144956, 0.015994950144956, 0.015994950144956,
609			0.015994950144956, 0.015994950144956, 0.015994950144956, 0.014772268570672,
610			0.014772268570672, 0.014772268570672, 0.014772268570672, 0.014772268570672,
611			0.014772268570672, 0.025598663757297, 0.025598663757297, 0.025598663757297,
612			0.025598663757297, 0.025598663757297, 0.025598663757297, 0.034516142351393,
613			0.034516142351393, 0.034516142351393, 0.034516142351393, 0.034516142351393,
614			0.034516142351393, 0.037345891805871, 0.037345891805871, 0.037345891805871,
615			0.037345891805871, 0.037345891805871, 0.037345891805871, 0.045636448116791,
616			0.045636448116791, 0.045636448116791, 0.045636448116791, 0.045636448116791,
617			0.045636448116791}};
618
619			// For cub2D_21: 93 points (93*3 = 279 elements)
620			static const std::array<double, 93 * 2> cub2D_21_nodes_data = {
621			{-0.006427416686680, -0.006427416686680, -0.987145166626641, -0.006427416686680,
622			-0.006427416686680, -0.987145166626641, -0.037371238381685, -0.037371238381685,
623			-0.925257523236629, -0.037371238381685, -0.037371238381685, -0.925257523236629,
624			-0.101972641308225, -0.101972641308225, -0.796054717383551, -0.101972641308225,
625			-0.101972641308225, -0.796054717383551, -0.405469125577621, -0.405469125577621,
626			-0.189061748844758, -0.405469125577621, -0.405469125577621, -0.189061748844758,
627			-0.556282620757932, -0.556282620757932, 0.112565241515865, -0.556282620757932,
628			-0.556282620757932, 0.112565241515865, -0.787490889149774, -0.787490889149774,
629			0.574981778299548, -0.787490889149774, -0.787490889149774, 0.574981778299548,
630			-0.892713038713217, -0.892713038713217, 0.785426077426434, -0.892713038713217,
631			-0.892713038713217, 0.785426077426434, -0.975095902008750, 0.956581360464913,
632			0.956581360464913, -0.975095902008750, -0.981485458456163, 0.956581360464913,
633			0.956581360464913, -0.981485458456163, -0.981485458456163, -0.975095902008750,
634			-0.975095902008750, -0.981485458456163, -0.734190363492767, 0.718759150923754,
635			0.718759150923754, -0.734190363492767, -0.984568787430988, 0.718759150923754,
636			0.718759150923754, -0.984568787430988, -0.984568787430988, -0.734190363492767,
637			-0.734190363492767, -0.984568787430988, -0.279909645448207, 0.260066127858194,
638			0.260066127858194, -0.279909645448207, -0.980156482409987, 0.260066127858194,
639			0.260066127858194, -0.980156482409987, -0.980156482409987, -0.279909645448207,
640			-0.279909645448207, -0.980156482409987, -0.527626383829046, 0.508213994286434,
641			0.508213994286434, -0.527626383829046, -0.980587610457388, 0.508213994286434,
642			0.508213994286434, -0.980587610457388, -0.980587610457388, -0.527626383829046,
643			-0.527626383829046, -0.980587610457388, -0.887945885434766, 0.867094084690673,
644			0.867094084690673, -0.887945885434766, -0.979148199255907, 0.867094084690673,
645			0.867094084690673, -0.979148199255907, -0.979148199255907, -0.887945885434766,
646			-0.887945885434766, -0.979148199255907, -0.738154400021390, 0.655149643679198,
647			0.655149643679198, -0.738154400021390, -0.916995243657807, 0.655149643679198,
648			0.655149643679198, -0.916995243657807, -0.916995243657807, -0.738154400021390,
649			-0.738154400021390, -0.916995243657807, -0.296840355384531, 0.194393499586184,
650			0.194393499586184, -0.296840355384531, -0.897553144201652, 0.194393499586184,
651			0.194393499586184, -0.897553144201652, -0.897553144201652, -0.296840355384531,
652			-0.296840355384531, -0.897553144201652, -0.531632641825188, 0.431035654635683,
653			0.431035654635683, -0.531632641825188, -0.899403012810496, 0.431035654635683,
654			0.431035654635683, -0.899403012810496, -0.899403012810496, -0.531632641825188,
655			-0.531632641825188, -0.899403012810496, -0.682130525363537, 0.500223407469218,
656			0.500223407469218, -0.682130525363537, -0.818092882105681, 0.500223407469218,
657			0.500223407469218, -0.818092882105681, -0.818092882105681, -0.682130525363537,
658			-0.682130525363537, -0.818092882105681, -0.376270450471865, 0.138207573987544,
659			0.138207573987544, -0.376270450471865, -0.761937123515678, 0.138207573987544,
660			0.138207573987544, -0.761937123515678, -0.761937123515678, -0.376270450471865,
661			-0.376270450471865, -0.761937123515678, -0.590719081005038, 0.339375331943743,
662			0.339375331943743, -0.590719081005038, -0.748656250938705, 0.339375331943743,
663			0.339375331943743, -0.748656250938705, -0.748656250938705, -0.590719081005038,
664			-0.590719081005038, -0.748656250938705, -0.305527033262063, -0.081590222620926,
665			-0.081590222620926, -0.305527033262063, -0.612882744117011, -0.081590222620926,
666			-0.081590222620926, -0.612882744117011, -0.612882744117011, -0.305527033262063,
667			-0.305527033262063, -0.612882744117011}};
668
669			static const std::array<double, 93> cub2D_21_weights_data = {
670			{0.009411977990382, 0.009411977990382, 0.009411977990382, 0.023551229711283, 0.023551229711283,
671			0.023551229711283, 0.041353961937512, 0.041353961937512, 0.041353961937512, 0.045947520102707,
672			0.045947520102707, 0.045947520102707, 0.047724273523632, 0.047724273523632, 0.047724273523632,
673			0.019906824503099, 0.019906824503099, 0.019906824503099, 0.014287994054933, 0.014287994054933,
674			0.014287994054933, 0.001538784565604, 0.001538784565604, 0.001538784565604, 0.001538784565604,
675			0.001538784565604, 0.001538784565604, 0.007257720730941, 0.007257720730941, 0.007257720730941,
676			0.007257720730941, 0.007257720730941, 0.007257720730941, 0.013303360825119, 0.013303360825119,
677			0.013303360825119, 0.013303360825119, 0.013303360825119, 0.013303360825119, 0.011413497063052,
678			0.011413497063052, 0.011413497063052, 0.011413497063052, 0.011413497063052, 0.011413497063052,
679			0.006552521291655, 0.006552521291655, 0.006552521291655, 0.006552521291655, 0.006552521291655,
680			0.006552521291655, 0.017432381135646, 0.017432381135646, 0.017432381135646, 0.017432381135646,
681			0.017432381135646, 0.017432381135646, 0.027402609499462, 0.027402609499462, 0.027402609499462,
682			0.027402609499462, 0.027402609499462, 0.027402609499462, 0.025014173853794, 0.025014173853794,
683			0.025014173853794, 0.025014173853794, 0.025014173853794, 0.025014173853794, 0.008690112508894,
684			0.008690112508894, 0.008690112508894, 0.008690112508894, 0.008690112508894, 0.008690112508894,
685			0.037386369243416, 0.037386369243416, 0.037386369243416, 0.037386369243416, 0.037386369243416,
686			0.037386369243416, 0.032509611084921, 0.032509611084921, 0.032509611084921, 0.032509611084921,
687			0.032509611084921, 0.032509611084921, 0.043740300619054, 0.043740300619054, 0.043740300619054,
688			0.043740300619054, 0.043740300619054, 0.043740300619054}};
689
690			// For cub2D_22: 100 points (100*3 = 300 elements)
691			static const std::array<double, 100 * 2> cub2D_22_nodes_data = {
692			{-0.333333333333333, -0.333333333333333, -0.005980679319437, -0.005980679319437,
693			-0.988038641361126, -0.005980679319437, -0.005980679319437, -0.988038641361126,
694			-0.112289615572167, -0.112289615572167, -0.775420768855665, -0.112289615572167,
695			-0.112289615572167, -0.775420768855665, -0.209082673923590, -0.209082673923590,
696			-0.581834652152820, -0.209082673923590, -0.209082673923590, -0.581834652152820,
697			-0.467712894350161, -0.467712894350161, -0.064574211299679, -0.467712894350161,
698			-0.467712894350161, -0.064574211299679, -0.616276252022817, -0.616276252022817,
699			0.232552504045635, -0.616276252022817, -0.616276252022817, 0.232552504045635,
700			-0.755246756631224, -0.755246756631224, 0.510493513262448, -0.755246756631224,
701			-0.755246756631224, 0.510493513262448, -0.893562558892192, -0.893562558892192,
702			0.787125117784384, -0.893562558892192, -0.893562558892192, 0.787125117784384,
703			-0.943105536827199, -0.943105536827199, 0.886211073654399, -0.943105536827199,
704			-0.943105536827199, 0.886211073654399, -0.991786296535875, -0.991786296535875,
705			0.983572593071750, -0.991786296535875, -0.991786296535875, 0.983572593071750,
706			-0.413667191986728, 0.401491377065593, 0.401491377065593, -0.413667191986728,
707			-0.987824185078864, 0.401491377065593, 0.401491377065593, -0.987824185078864,
708			-0.987824185078865, -0.413667191986728, -0.413667191986728, -0.987824185078865,
709			-0.932052869826067, 0.918490219898898, 0.918490219898898, -0.932052869826067,
710			-0.986437350072830, 0.918490219898898, 0.918490219898898, -0.986437350072830,
711			-0.986437350072830, -0.932052869826067, -0.932052869826067, -0.986437350072830,
712			-0.640599464469824, 0.623868058857117, 0.623868058857117, -0.640599464469824,
713			-0.983268594387293, 0.623868058857116, 0.623868058857116, -0.983268594387293,
714			-0.983268594387293, -0.640599464469824, -0.640599464469824, -0.983268594387293,
715			-0.158411570812104, 0.140890429939385, 0.140890429939385, -0.158411570812104,
716			-0.982478859127282, 0.140890429939385, 0.140890429939385, -0.982478859127282,
717			-0.982478859127282, -0.158411570812104, -0.158411570812104, -0.982478859127282,
718			-0.814806216564922, 0.793459188393794, 0.793459188393794, -0.814806216564922,
719			-0.978652971828873, 0.793459188393795, 0.793459188393795, -0.978652971828873,
720			-0.978652971828873, -0.814806216564922, -0.814806216564922, -0.978652971828873,
721			-0.363960589331557, 0.295112627690632, 0.295112627690632, -0.363960589331557,
722			-0.931152038359075, 0.295112627690632, 0.295112627690632, -0.931152038359075,
723			-0.931152038359075, -0.363960589331557, -0.363960589331557, -0.931152038359075,
724			-0.570323384314285, 0.491002374048080, 0.491002374048080, -0.570323384314285,
725			-0.920678989733795, 0.491002374048080, 0.491002374048080, -0.920678989733795,
726			-0.920678989733795, -0.570323384314285, -0.570323384314285, -0.920678989733795,
727			-0.134636707603169, 0.047157943371727, 0.047157943371727, -0.134636707603169,
728			-0.912521235768557, 0.047157943371727, 0.047157943371727, -0.912521235768557,
729			-0.912521235768557, -0.134636707603169, -0.134636707603169, -0.912521235768557,
730			-0.752804662376914, 0.649201355096884, 0.649201355096884, -0.752804662376914,
731			-0.896396692719970, 0.649201355096884, 0.649201355096884, -0.896396692719970,
732			-0.896396692719970, -0.752804662376914, -0.752804662376914, -0.896396692719970,
733			-0.328638645186542, 0.161176552903625, 0.161176552903625, -0.328638645186542,
734			-0.832537907717083, 0.161176552903625, 0.161176552903625, -0.832537907717083,
735			-0.832537907717083, -0.328638645186542, -0.328638645186542, -0.832537907717083,
736			-0.559939069093864, 0.361861076343249, 0.361861076343249, -0.559939069093864,
737			-0.801922007249385, 0.361861076343249, 0.361861076343249, -0.801922007249385,
738			-0.801922007249385, -0.559939069093864, -0.559939069093864, -0.801922007249385,
739			-0.388196135129182, 0.068617773977901, 0.068617773977901, -0.388196135129182,
740			-0.680421638848718, 0.068617773977901, 0.068617773977901, -0.680421638848718,
741			-0.680421638848718, -0.388196135129182, -0.388196135129182, -0.680421638848718}};
742			static const std::array<double, 100> cub2D_22_weights_data = {
743			{0.052134891986775, 0.002127559342619, 0.002127559342619, 0.002127559342619,
744			0.040243429730281, 0.040243429730281, 0.040243429730281, 0.048340550896214,
745			0.048340550896214, 0.048340550896214, 0.047378470721283, 0.047378470721283,
746			0.047378470721283, 0.040231109011798, 0.040231109011798, 0.040231109011798,
747			0.027899919845537, 0.027899919845537, 0.027899919845537, 0.012350949744993,
748			0.012350949744993, 0.012350949744993, 0.003039705316805, 0.003039705316805,
749			0.003039705316805, 0.000691671630889, 0.000691671630889, 0.000691671630889,
750			0.008022198405286, 0.008022198405286, 0.008022198405286, 0.008022198405286,
751			0.008022198405286, 0.008022198405286, 0.003090974933637, 0.003090974933637,
752			0.003090974933637, 0.003090974933637, 0.003090974933637, 0.003090974933637,
753			0.008631214056178, 0.008631214056178, 0.008631214056178, 0.008631214056178,
754			0.008631214056178, 0.008631214056178, 0.010897457944070, 0.010897457944070,
755			0.010897457944070, 0.010897457944070, 0.010897457944070, 0.010897457944070,
756			0.008001551263950, 0.008001551263950, 0.008001551263950, 0.008001551263950,
757			0.008001551263950, 0.008001551263950, 0.017745434082141, 0.017745434082141,
758			0.017745434082141, 0.017745434082141, 0.017745434082141, 0.017745434082141,
759			0.017950672107247, 0.017950672107247, 0.017950672107247, 0.017950672107247,
760			0.017950672107247, 0.017950672107247, 0.019228676191702, 0.019228676191702,
761			0.019228676191702, 0.019228676191702, 0.019228676191702, 0.019228676191702,
762			0.019100455942623, 0.019100455942623, 0.019100455942623, 0.019100455942623,
763			0.019100455942623, 0.019100455942623, 0.028083739150636, 0.028083739150636,
764			0.028083739150636, 0.028083739150636, 0.028083739150636, 0.028083739150636,
765			0.031874915632607, 0.031874915632607, 0.031874915632607, 0.031874915632607,
766			0.031874915632607, 0.031874915632607, 0.040865211838584, 0.040865211838584,
767			0.040865211838584, 0.040865211838584, 0.040865211838584, 0.040865211838584}};
768
769			// For cub2D_23: 106 points (106*3 = 318 elements)
770			static const std::array<double, 106 * 2> cub2D_23_nodes_data = {
771			{-0.333333333333333, -0.333333333333333, -0.023538910955543, -0.023538910955543,
772			-0.952922178088914, -0.023538910955543, -0.023538910955543, -0.952922178088914,
773			-0.112255282121933, -0.112255282121933, -0.775489435756134, -0.112255282121933,
774			-0.112255282121933, -0.775489435756134, -0.212088442838205, -0.212088442838205,
775			-0.575823114323591, -0.212088442838205, -0.212088442838205, -0.575823114323591,
776			-0.467032671065063, -0.467032671065063, -0.065934657869875, -0.467032671065063,
777			-0.467032671065063, -0.065934657869875, -0.602458675644835, -0.602458675644835,
778			0.204917351289670, -0.602458675644835, -0.602458675644835, 0.204917351289670,
779			-0.729340080155585, -0.729340080155585, 0.458680160311169, -0.729340080155585,
780			-0.729340080155585, 0.458680160311169, -0.835032835950571, -0.835032835950571,
781			0.670065671901142, -0.835032835950571, -0.835032835950571, 0.670065671901142,
782			-0.916650365183127, -0.916650365183127, 0.833300730366254, -0.916650365183127,
783			-0.916650365183127, 0.833300730366254, -0.982250743407210, -0.982250743407210,
784			0.964501486814420, -0.982250743407210, -0.982250743407210, 0.964501486814420,
785			-0.105601712649592, 0.098292547426640, 0.098292547426640, -0.105601712649592,
786			-0.992690834777047, 0.098292547426640, 0.098292547426640, -0.992690834777047,
787			-0.992690834777047, -0.105601712649592, -0.105601712649592, -0.992690834777047,
788			-0.775227228315076, 0.773362241907340, 0.773362241907340, -0.775227228315076,
789			-0.998135013592264, 0.773362241907340, 0.773362241907340, -0.998135013592264,
790			-0.998135013592264, -0.775227228315076, -0.775227228315076, -0.998135013592264,
791			-0.399056075238285, 0.392811698367078, 0.392811698367078, -0.399056075238285,
792			-0.993755623128794, 0.392811698367078, 0.392811698367078, -0.993755623128794,
793			-0.993755623128794, -0.399056075238285, -0.399056075238285, -0.993755623128794,
794			-0.907633572417643, 0.891831436837026, 0.891831436837026, -0.907633572417643,
795			-0.984197864419384, 0.891831436837026, 0.891831436837026, -0.984197864419384,
796			-0.984197864419383, -0.907633572417642, -0.907633572417642, -0.984197864419383,
797			-0.610008084404048, 0.588812673873118, 0.588812673873118, -0.610008084404048,
798			-0.978804589469070, 0.588812673873118, 0.588812673873118, -0.978804589469070,
799			-0.978804589469070, -0.610008084404048, -0.610008084404048, -0.978804589469070,
800			-0.243171741354056, 0.207960140279272, 0.207960140279272, -0.243171741354056,
801			-0.964788398925216, 0.207960140279272, 0.207960140279272, -0.964788398925216,
802			-0.964788398925216, -0.243171741354055, -0.243171741354055, -0.964788398925216,
803			-0.789506197850739, 0.739925802118596, 0.739925802118596, -0.789506197850739,
804			-0.950419604267857, 0.739925802118596, 0.739925802118596, -0.950419604267857,
805			-0.950419604267857, -0.789506197850739, -0.789506197850739, -0.950419604267857,
806			-0.455884762353173, 0.385117794610837, 0.385117794610837, -0.455884762353173,
807			-0.929233032257664, 0.385117794610837, 0.385117794610837, -0.929233032257664,
808			-0.929233032257664, -0.455884762353173, -0.455884762353173, -0.929233032257664,
809			-0.112482048478797, 0.019740291196956, 0.019740291196956, -0.112482048478797,
810			-0.907258242718159, 0.019740291196956, 0.019740291196956, -0.907258242718159,
811			-0.907258242718159, -0.112482048478797, -0.112482048478797, -0.907258242718159,
812			-0.664205324633765, 0.550530931038120, 0.550530931038120, -0.664205324633765,
813			-0.886325606404355, 0.550530931038120, 0.550530931038120, -0.886325606404355,
814			-0.886325606404354, -0.664205324633765, -0.664205324633765, -0.886325606404354,
815			-0.295594853518405, 0.152149871080588, 0.152149871080588, -0.295594853518405,
816			-0.856555017562183, 0.152149871080588, 0.152149871080588, -0.856555017562183,
817			-0.856555017562183, -0.295594853518405, -0.295594853518405, -0.856555017562183,
818			-0.525935282564036, 0.319991164262401, 0.319991164262401, -0.525935282564036,
819			-0.794055881698366, 0.319991164262401, 0.319991164262401, -0.794055881698366,
820			-0.794055881698366, -0.525935282564036, -0.525935282564036, -0.794055881698366,
821			-0.368673747852155, 0.056982821883363, 0.056982821883363, -0.368673747852155,
822			-0.688309074031208, 0.056982821883363, 0.056982821883363, -0.688309074031208,
823			-0.688309074031208, -0.368673747852155, -0.368673747852155, -0.688309074031208}};
824			static const std::array<double, 106> cub2D_23_weights_data = {
825			{0.049993627092845, 0.008227775544650, 0.008227775544650, 0.008227775544650, 0.037662477311797,
826			0.037662477311797, 0.037662477311797, 0.046916667243031, 0.046916667243031, 0.046916667243031,
827			0.047191879210718, 0.047191879210718, 0.047191879210718, 0.039689081561875, 0.039689081561875,
828			0.039689081561875, 0.029223692430473, 0.029223692430473, 0.029223692430473, 0.018566057479642,
829			0.018566057479642, 0.018566057479642, 0.008784960019827, 0.008784960019827, 0.008784960019827,
830			0.002061552741126, 0.002061552741126, 0.002061552741126, 0.004448377162851, 0.004448377162851,
831			0.004448377162851, 0.004448377162851, 0.004448377162851, 0.004448377162851, 0.002318973002522,
832			0.002318973002522, 0.002318973002522, 0.002318973002522, 0.002318973002522, 0.002318973002522,
833			0.005127488569570, 0.005127488569570, 0.005127488569570, 0.005127488569570, 0.005127488569570,
834			0.005127488569570, 0.004167853762943, 0.004167853762943, 0.004167853762943, 0.004167853762943,
835			0.004167853762943, 0.004167853762943, 0.010245094978581, 0.010245094978581, 0.010245094978581,
836			0.010245094978581, 0.010245094978581, 0.010245094978581, 0.012823590639281, 0.012823590639281,
837			0.012823590639281, 0.012823590639281, 0.012823590639281, 0.012823590639281, 0.011635516794817,
838			0.011635516794817, 0.011635516794817, 0.011635516794817, 0.011635516794817, 0.011635516794817,
839			0.019844273900077, 0.019844273900077, 0.019844273900077, 0.019844273900077, 0.019844273900077,
840			0.019844273900077, 0.011754407449188, 0.011754407449188, 0.011754407449188, 0.011754407449188,
841			0.011754407449188, 0.011754407449188, 0.021600208906600, 0.021600208906600, 0.021600208906600,
842			0.021600208906600, 0.021600208906600, 0.021600208906600, 0.028495796363599, 0.028495796363599,
843			0.028495796363599, 0.028495796363599, 0.028495796363599, 0.028495796363599, 0.031988381018369,
844			0.031988381018369, 0.031988381018369, 0.031988381018369, 0.031988381018369, 0.031988381018369,
845			0.041389027831224, 0.041389027831224, 0.041389027831224, 0.041389027831224, 0.041389027831224,
846			0.041389027831224}};
847
848			// For cub2D_24: 118 points (118*3 = 354 elements)
849			static const std::array<double, 118 * 2> cub2D_24_nodes_data = {
850			{-0.333333333333333, -0.333333333333333, -0.031382760283421, -0.031382760283421,
851			-0.937234479433159, -0.031382760283421, -0.031382760283421, -0.937234479433159,
852			-0.120096233850662, -0.120096233850662, -0.759807532298676, -0.120096233850662,
853			-0.120096233850662, -0.759807532298676, -0.217343938317536, -0.217343938317536,
854			-0.565312123364928, -0.217343938317536, -0.217343938317536, -0.565312123364928,
855			-0.429818284439074, -0.429818284439074, -0.140363431121852, -0.429818284439074,
856			-0.429818284439074, -0.140363431121852, -0.522392801883300, -0.522392801883300,
857			0.044785603766601, -0.522392801883300, -0.522392801883300, 0.044785603766601,
858			-0.704274510649686, -0.704274510649686, 0.408549021299373, -0.704274510649686,
859			-0.704274510649686, 0.408549021299373, -0.843105586121546, -0.843105586121546,
860			0.686211172243092, -0.843105586121546, -0.843105586121546, 0.686211172243092,
861			-0.936285318267427, -0.936285318267427, 0.872570636534854, -0.936285318267427,
862			-0.936285318267427, 0.872570636534854, -0.983008712604130, -0.983008712604130,
863			0.966017425208259, -0.983008712604130, -0.983008712604130, 0.966017425208259,
864			-0.133936561710478, 0.120327965916980, 0.120327965916980, -0.133936561710478,
865			-0.986391404206501, 0.120327965916980, 0.120327965916980, -0.986391404206501,
866			-0.986391404206501, -0.133936561710478, -0.133936561710478, -0.986391404206501,
867			-0.589559941056661, 0.574991625876557, 0.574991625876557, -0.589559941056661,
868			-0.985431684819897, 0.574991625876557, 0.574991625876557, -0.985431684819897,
869			-0.985431684819897, -0.589559941056661, -0.589559941056661, -0.985431684819897,
870			-0.375079684130172, 0.361371712031196, 0.361371712031196, -0.375079684130172,
871			-0.986292027901024, 0.361371712031196, 0.361371712031196, -0.986292027901024,
872			-0.986292027901024, -0.375079684130172, -0.375079684130172, -0.986292027901024,
873			-0.906832105591067, 0.897244066241012, 0.897244066241012, -0.906832105591067,
874			-0.990411960649945, 0.897244066241012, 0.897244066241012, -0.990411960649945,
875			-0.990411960649945, -0.906832105591067, -0.906832105591067, -0.990411960649945,
876			-0.768281564078976, 0.757477531703546, 0.757477531703546, -0.768281564078976,
877			-0.989195967624570, 0.757477531703546, 0.757477531703546, -0.989195967624570,
878			-0.989195967624570, -0.768281564078975, -0.768281564078975, -0.989195967624570,
879			-0.498678726055310, 0.424585822926150, 0.424585822926150, -0.498678726055310,
880			-0.925907096870839, 0.424585822926150, 0.424585822926150, -0.925907096870839,
881			-0.925907096870839, -0.498678726055310, -0.498678726055310, -0.925907096870839,
882			-0.279607664483490, 0.208396882316209, 0.208396882316209, -0.279607664483490,
883			-0.928789217832719, 0.208396882316209, 0.208396882316209, -0.928789217832719,
884			-0.928789217832719, -0.279607664483490, -0.279607664483490, -0.928789217832719,
885			-0.837737372642508, 0.780926628976898, 0.780926628976898, -0.837737372642508,
886			-0.943189256334389, 0.780926628976898, 0.780926628976898, -0.943189256334389,
887			-0.943189256334389, -0.837737372642508, -0.837737372642508, -0.943189256334389,
888			-0.693711793201882, 0.625024627714433, 0.625024627714433, -0.693711793201882,
889			-0.931312834512551, 0.625024627714433, 0.625024627714433, -0.931312834512551,
890			-0.931312834512551, -0.693711793201882, -0.693711793201882, -0.931312834512551,
891			0.004700993829951, -0.135567929734853, -0.135567929734853, 0.004700993829951,
892			-0.869133064095098, -0.135567929734853, -0.135567929734853, -0.869133064095098,
893			-0.869133064095098, 0.004700993829951, 0.004700993829951, -0.869133064095098,
894			-0.521976982650353, 0.349105045944945, 0.349105045944945, -0.521976982650353,
895			-0.827128063294591, 0.349105045944945, 0.349105045944945, -0.827128063294591,
896			-0.827128063294591, -0.521976982650353, -0.521976982650353, -0.827128063294591,
897			-0.326968721136217, 0.144732602043697, 0.144732602043697, -0.326968721136217,
898			-0.817763880907480, 0.144732602043697, 0.144732602043697, -0.817763880907480,
899			-0.817763880907480, -0.326968721136217, -0.326968721136217, -0.817763880907480,
900			-0.696116803866709, 0.531011336134871, 0.531011336134871, -0.696116803866709,
901			-0.834894532268162, 0.531011336134871, 0.531011336134871, -0.834894532268162,
902			-0.834894532268162, -0.696116803866709, -0.696116803866709, -0.834894532268162,
903			-0.536404917748559, 0.226734558438523, 0.226734558438523, -0.536404917748559,
904			-0.690329640689964, 0.226734558438523, 0.226734558438523, -0.690329640689964,
905			-0.690329640689964, -0.536404917748559, -0.536404917748559, -0.690329640689964,
906			-0.344489563789357, 0.009282127094255, 0.009282127094255, -0.344489563789357,
907			-0.664792563304898, 0.009282127094255, 0.009282127094255, -0.664792563304898,
908			-0.664792563304898, -0.344489563789357, -0.344489563789357, -0.664792563304898}};
909			static const std::array<double, 118> cub2D_24_weights_data = {
910			{0.031330242175782, 0.014717653847587, 0.014717653847587, 0.014717653847587, 0.030963348398970,
911			0.030963348398970, 0.030963348398970, 0.037986940843648, 0.037986940843648, 0.037986940843648,
912			0.033466254011049, 0.033466254011049, 0.033466254011049, 0.029203686754054, 0.029203686754054,
913			0.029203686754054, 0.022147482605586, 0.022147482605586, 0.022147482605586, 0.015827753677335,
914			0.015827753677335, 0.015827753677335, 0.005897827695084, 0.005897827695084, 0.005897827695084,
915			0.001905131297570, 0.001905131297570, 0.001905131297570, 0.008627443386199, 0.008627443386199,
916			0.008627443386199, 0.008627443386199, 0.008627443386199, 0.008627443386199, 0.007292016855628,
917			0.007292016855628, 0.007292016855628, 0.007292016855628, 0.007292016855628, 0.007292016855628,
918			0.008117703702749, 0.008117703702749, 0.008117703702749, 0.008117703702749, 0.008117703702749,
919			0.008117703702749, 0.002858359515171, 0.002858359515171, 0.002858359515171, 0.002858359515171,
920			0.002858359515171, 0.002858359515171, 0.004596788633153, 0.004596788633153, 0.004596788633153,
921			0.004596788633153, 0.004596788633153, 0.004596788633153, 0.017097477649229, 0.017097477649229,
922			0.017097477649229, 0.017097477649229, 0.017097477649229, 0.017097477649229, 0.018575372163249,
923			0.018575372163249, 0.018575372163249, 0.018575372163249, 0.018575372163249, 0.018575372163249,
924			0.008711688567270, 0.008711688567270, 0.008711688567270, 0.008711688567270, 0.008711688567270,
925			0.008711688567270, 0.013292883787775, 0.013292883787775, 0.013292883787775, 0.013292883787775,
926			0.013292883787775, 0.013292883787775, 0.012281001510740, 0.012281001510740, 0.012281001510740,
927			0.012281001510740, 0.012281001510740, 0.012281001510740, 0.021820885555420, 0.021820885555420,
928			0.021820885555420, 0.021820885555420, 0.021820885555420, 0.021820885555420, 0.027371090249668,
929			0.027371090249668, 0.027371090249668, 0.027371090249668, 0.027371090249668, 0.027371090249668,
930			0.018737543889147, 0.018737543889147, 0.018737543889147, 0.018737543889147, 0.018737543889147,
931			0.018737543889147, 0.028700757241388, 0.028700757241388, 0.028700757241388, 0.028700757241388,
932			0.028700757241388, 0.028700757241388, 0.033972574031807, 0.033972574031807, 0.033972574031807,
933			0.033972574031807, 0.033972574031807, 0.033972574031807}};
934
935			// For cub2D_25: 126 points (126*3 = 378 elements)
936			static const std::array<double, 126 * 2> cub2D_25_nodes_data = {
937			{-0.027946483073174, -0.027946483073174, -0.944107033853652, -0.027946483073174,
938			-0.027946483073174, -0.944107033853652, -0.131178601327651, -0.131178601327651,
939			-0.737642797344697, -0.131178601327651, -0.131178601327651, -0.737642797344697,
940			-0.220221729512072, -0.220221729512072, -0.559556540975855, -0.220221729512072,
941			-0.220221729512072, -0.559556540975855, -0.403113531960391, -0.403113531960391,
942			-0.193772936079218, -0.403113531960391, -0.403113531960391, -0.193772936079218,
943			-0.531911655325256, -0.531911655325256, 0.063823310650513, -0.531911655325256,
944			-0.531911655325256, 0.063823310650513, -0.697063330781965, -0.697063330781965,
945			0.394126661563930, -0.697063330781965, -0.697063330781965, 0.394126661563930,
946			-0.774532212908013, -0.774532212908013, 0.549064425816026, -0.774532212908013,
947			-0.774532212908013, 0.549064425816026, -0.844568615816947, -0.844568615816947,
948			0.689137231633895, -0.844568615816948, -0.844568615816948, 0.689137231633895,
949			-0.930213812771406, -0.930213812771406, 0.860427625542812, -0.930213812771406,
950			-0.930213812771406, 0.860427625542812, -0.985483630758135, -0.985483630758135,
951			0.970967261516271, -0.985483630758135, -0.985483630758135, 0.970967261516271,
952			-0.545571095693272, 0.542986390284387, 0.542986390284387, -0.545571095693272,
953			-0.997415294591116, 0.542986390284387, 0.542986390284387, -0.997415294591116,
954			-0.997415294591116, -0.545571095693272, -0.545571095693272, -0.997415294591116,
955			-0.129978890292857, 0.119179487748624, 0.119179487748624, -0.129978890292857,
956			-0.989200597455768, 0.119179487748624, 0.119179487748624, -0.989200597455768,
957			-0.989200597455768, -0.129978890292857, -0.129978890292857, -0.989200597455768,
958			-0.359380801455591, 0.346612795387641, 0.346612795387641, -0.359380801455591,
959			-0.987231993932050, 0.346612795387641, 0.346612795387641, -0.987231993932050,
960			-0.987231993932050, -0.359380801455591, -0.359380801455591, -0.987231993932050,
961			-0.816499355439990, 0.806442932436004, 0.806442932436004, -0.816499355439990,
962			-0.989943576996014, 0.806442932436004, 0.806442932436004, -0.989943576996014,
963			-0.989943576996014, -0.816499355439990, -0.816499355439990, -0.989943576996014,
964			-0.923978328282551, 0.910324811038988, 0.910324811038988, -0.923978328282551,
965			-0.986346482756436, 0.910324811038988, 0.910324811038988, -0.986346482756436,
966			-0.986346482756436, -0.923978328282551, -0.923978328282551, -0.986346482756436,
967			-0.685149563029377, 0.665117163749518, 0.665117163749518, -0.685149563029377,
968			-0.979967600720141, 0.665117163749517, 0.665117163749517, -0.979967600720141,
969			-0.979967600720141, -0.685149563029376, -0.685149563029376, -0.979967600720141,
970			-0.520220680442934, 0.468705054096154, 0.468705054096154, -0.520220680442934,
971			-0.948484373653220, 0.468705054096154, 0.468705054096154, -0.948484373653220,
972			-0.948484373653220, -0.520220680442934, -0.520220680442934, -0.948484373653220,
973			-0.276113763747879, 0.215657967508047, 0.215657967508047, -0.276113763747879,
974			-0.939544203760168, 0.215657967508047, 0.215657967508047, -0.939544203760168,
975			-0.939544203760168, -0.276113763747879, -0.276113763747879, -0.939544203760168,
976			-0.832896078090343, 0.771886097876019, 0.771886097876019, -0.832896078090343,
977			-0.938990019785676, 0.771886097876019, 0.771886097876019, -0.938990019785676,
978			-0.938990019785676, -0.832896078090343, -0.832896078090343, -0.938990019785676,
979			-0.703113558535164, 0.611200463810025, 0.611200463810025, -0.703113558535164,
980			-0.908086905274861, 0.611200463810025, 0.611200463810025, -0.908086905274861,
981			-0.908086905274861, -0.703113558535164, -0.703113558535164, -0.908086905274861,
982			-0.432520582544930, 0.297634981464375, 0.297634981464375, -0.432520582544930,
983			-0.865114398919445, 0.297634981464375, 0.297634981464375, -0.865114398919445,
984			-0.865114398919445, -0.432520582544930, -0.432520582544930, -0.865114398919445,
985			-0.186201249762425, 0.046111066930604, 0.046111066930604, -0.186201249762425,
986			-0.859909817168179, 0.046111066930604, 0.046111066930604, -0.859909817168179,
987			-0.859909817168179, -0.186201249762425, -0.186201249762425, -0.859909817168179,
988			-0.611772025950215, 0.443948976669982, 0.443948976669982, -0.611772025950215,
989			-0.832176950719767, 0.443948976669982, 0.443948976669982, -0.832176950719767,
990			-0.832176950719767, -0.611772025950215, -0.611772025950215, -0.832176950719767,
991			-0.351731305998594, 0.110980234644288, 0.110980234644288, -0.351731305998594,
992			-0.759248928645695, 0.110980234644288, 0.110980234644288, -0.759248928645695,
993			-0.759248928645695, -0.351731305998594, -0.351731305998594, -0.759248928645695,
994			-0.541445032888038, 0.245311234573305, 0.245311234573305, -0.541445032888038,
995			-0.703866201685267, 0.245311234573305, 0.245311234573305, -0.703866201685267,
996			-0.703866201685267, -0.541445032888038, -0.541445032888038, -0.703866201685267,
997			-0.348763754808032, -0.034779976926618, -0.034779976926618, -0.348763754808032,
998			-0.616456268265350, -0.034779976926618, -0.034779976926618, -0.616456268265350,
999			-0.616456268265350, -0.348763754808032, -0.348763754808032, -0.616456268265350}};
1000			static const std::array<double, 126> cub2D_25_weights_data = {
1001			{0.016011163760041, 0.016011163760041, 0.016011163760041, 0.031894153664781, 0.031894153664781,
1002			0.031894153664781, 0.026218282461591, 0.026218282461591, 0.026218282461591, 0.039166001931271,
1003			0.039166001931271, 0.039166001931271, 0.032941770883075, 0.032941770883075, 0.032941770883075,
1004			0.017094558148184, 0.017094558148184, 0.017094558148184, 0.016323771714453, 0.016323771714453,
1005			0.016323771714453, 0.012242293079968, 0.012242293079968, 0.012242293079968, 0.005816996529873,
1006			0.005816996529873, 0.005816996529873, 0.001384550491324, 0.001384550491324, 0.001384550491324,
1007			0.002496578398555, 0.002496578398555, 0.002496578398555, 0.002496578398555, 0.002496578398555,
1008			0.002496578398555, 0.006809505817606, 0.006809505817606, 0.006809505817606, 0.006809505817606,
1009			0.006809505817606, 0.006809505817606, 0.006719308652128, 0.006719308652128, 0.006719308652128,
1010			0.006719308652128, 0.006719308652128, 0.006719308652128, 0.003432313078994, 0.003432313078994,
1011			0.003432313078994, 0.003432313078994, 0.003432313078994, 0.003432313078994, 0.002961712633431,
1012			0.002961712633431, 0.002961712633431, 0.002961712633431, 0.002961712633431, 0.002961712633431,
1013			0.007022625221457, 0.007022625221457, 0.007022625221457, 0.007022625221457, 0.007022625221457,
1014			0.007022625221457, 0.014787100299413, 0.014787100299413, 0.014787100299413, 0.014787100299413,
1015			0.014787100299413, 0.014787100299413, 0.015966174954753, 0.015966174954753, 0.015966174954753,
1016			0.015966174954753, 0.015966174954753, 0.015966174954753, 0.008711925226316, 0.008711925226316,
1017			0.008711925226316, 0.008711925226316, 0.008711925226316, 0.008711925226316, 0.014730113402836,
1018			0.014730113402836, 0.014730113402836, 0.014730113402836, 0.014730113402836, 0.014730113402836,
1019			0.021927145692839, 0.021927145692839, 0.021927145692839, 0.021927145692839, 0.021927145692839,
1020			0.021927145692839, 0.023499923487082, 0.023499923487082, 0.023499923487082, 0.023499923487082,
1021			0.023499923487082, 0.023499923487082, 0.020031201427597, 0.020031201427597, 0.020031201427597,
1022			0.020031201427597, 0.020031201427597, 0.020031201427597, 0.026619281575257, 0.026619281575257,
1023			0.026619281575257, 0.026619281575257, 0.026619281575257, 0.026619281575257, 0.028308893010452,
1024			0.028308893010452, 0.028308893010452, 0.028308893010452, 0.028308893010452, 0.028308893010452,
1025			0.029762759122336, 0.029762759122336, 0.029762759122336, 0.029762759122336, 0.029762759122336,
1026			0.029762759122336}};
1027
1028			// For cub2D_26: 138 points (138*3 = 414 elements)
1029			static const std::array<double, 138 * 2> cub2D_26_nodes_data = {
1030			{-0.027285103318006, -0.027285103318006, -0.945429793363989, -0.027285103318006,
1031			-0.027285103318006, -0.945429793363989, -0.068629018183452, -0.068629018183452,
1032			-0.862741963633096, -0.068629018183452, -0.068629018183452, -0.862741963633096,
1033			-0.136174624247252, -0.136174624247252, -0.727650751505495, -0.136174624247252,
1034			-0.136174624247252, -0.727650751505495, -0.214440393597162, -0.214440393597162,
1035			-0.571119212805675, -0.214440393597162, -0.214440393597162, -0.571119212805675,
1036			-0.392927303733924, -0.392927303733924, -0.214145392532152, -0.392927303733924,
1037			-0.392927303733924, -0.214145392532152, -0.541283541373341, -0.541283541373341,
1038			0.082567082746682, -0.541283541373341, -0.541283541373341, 0.082567082746682,
1039			-0.710171670270578, -0.710171670270578, 0.420343340541156, -0.710171670270578,
1040			-0.710171670270578, 0.420343340541156, -0.832251071789951, -0.832251071789951,
1041			0.664502143579902, -0.832251071789951, -0.832251071789951, 0.664502143579902,
1042			-0.931928355163542, -0.931928355163542, 0.863856710327084, -0.931928355163542,
1043			-0.931928355163542, 0.863856710327084, -0.987078078630829, -0.987078078630829,
1044			0.974156157261657, -0.987078078630829, -0.987078078630829, 0.974156157261657,
1045			-0.932113855389598, 0.919072286067742, 0.919072286067742, -0.932113855389598,
1046			-0.986958430678145, 0.919072286067742, 0.919072286067742, -0.986958430678145,
1047			-0.986958430678145, -0.932113855389597, -0.932113855389597, -0.986958430678145,
1048			-0.331832115907669, 0.318412220533634, 0.318412220533634, -0.331832115907669,
1049			-0.986580104625965, 0.318412220533634, 0.318412220533634, -0.986580104625965,
1050			-0.986580104625965, -0.331832115907669, -0.331832115907669, -0.986580104625965,
1051			-0.117284648816543, 0.105635324925259, 0.105635324925259, -0.117284648816543,
1052			-0.988350676108717, 0.105635324925259, 0.105635324925259, -0.988350676108717,
1053			-0.988350676108717, -0.117284648816543, -0.117284648816543, -0.988350676108717,
1054			-0.528179583523521, 0.515363521190658, 0.515363521190658, -0.528179583523521,
1055			-0.987183937667137, 0.515363521190658, 0.515363521190658, -0.987183937667137,
1056			-0.987183937667137, -0.528179583523521, -0.528179583523521, -0.987183937667137,
1057			-0.698183069548291, 0.685666877859863, 0.685666877859863, -0.698183069548291,
1058			-0.987483808311572, 0.685666877859863, 0.685666877859863, -0.987483808311572,
1059			-0.987483808311572, -0.698183069548291, -0.698183069548291, -0.987483808311572,
1060			-0.834663613179069, 0.821127985248516, 0.821127985248516, -0.834663613179069,
1061			-0.986464372069447, 0.821127985248516, 0.821127985248516, -0.986464372069447,
1062			-0.986464372069447, -0.834663613179069, -0.834663613179069, -0.986464372069447,
1063			-0.700166221086294, 0.634916644768372, 0.634916644768372, -0.700166221086294,
1064			-0.934750423682077, 0.634916644768372, 0.634916644768372, -0.934750423682077,
1065			-0.934750423682078, -0.700166221086294, -0.700166221086294, -0.934750423682078,
1066			-0.160245113591115, 0.096801406370527, 0.096801406370527, -0.160245113591115,
1067			-0.936556292779412, 0.096801406370527, 0.096801406370527, -0.936556292779412,
1068			-0.936556292779412, -0.160245113591115, -0.160245113591115, -0.936556292779412,
1069			-0.348814552390868, 0.279444440434072, 0.279444440434072, -0.348814552390868,
1070			-0.930629888043204, 0.279444440434072, 0.279444440434072, -0.930629888043204,
1071			-0.930629888043204, -0.348814552390868, -0.348814552390868, -0.930629888043204,
1072			-0.835149343614232, 0.764834325997890, 0.764834325997890, -0.835149343614232,
1073			-0.929684982383659, 0.764834325997890, 0.764834325997890, -0.929684982383659,
1074			-0.929684982383659, -0.835149343614232, -0.835149343614232, -0.929684982383659,
1075			-0.534046892746188, 0.466663082505331, 0.466663082505331, -0.534046892746188,
1076			-0.932616189759143, 0.466663082505331, 0.466663082505331, -0.932616189759143,
1077			-0.932616189759143, -0.534046892746188, -0.534046892746188, -0.932616189759143,
1078			-0.704373154566392, 0.546726033293271, 0.546726033293271, -0.704373154566392,
1079			-0.842352878726879, 0.546726033293271, 0.546726033293271, -0.842352878726879,
1080			-0.842352878726879, -0.704373154566392, -0.704373154566392, -0.842352878726879,
1081			-0.220224863280788, 0.060870104244893, 0.060870104244893, -0.220224863280788,
1082			-0.840645240964104, 0.060870104244893, 0.060870104244893, -0.840645240964104,
1083			-0.840645240964104, -0.220224863280788, -0.220224863280788, -0.840645240964104,
1084			-0.394989254221112, 0.230609434358343, 0.230609434358343, -0.394989254221112,
1085			-0.835620180137232, 0.230609434358343, 0.230609434358343, -0.835620180137232,
1086			-0.835620180137232, -0.394989254221112, -0.394989254221112, -0.835620180137232,
1087			-0.557563751773578, 0.393274056332418, 0.393274056332418, -0.557563751773578,
1088			-0.835710304558840, 0.393274056332418, 0.393274056332418, -0.835710304558840,
1089			-0.835710304558840, -0.557563751773578, -0.557563751773578, -0.835710304558840,
1090			-0.350522450436603, 0.060630141977535, 0.060630141977535, -0.350522450436603,
1091			-0.710107691540932, 0.060630141977535, 0.060630141977535, -0.710107691540932,
1092			-0.710107691540932, -0.350522450436603, -0.350522450436603, -0.710107691540932,
1093			-0.544246685468649, 0.246315777233803, 0.246315777233803, -0.544246685468649,
1094			-0.702069091765154, 0.246315777233803, 0.246315777233803, -0.702069091765154,
1095			-0.702069091765154, -0.544246685468649, -0.544246685468649, -0.702069091765154,
1096			-0.373996265063702, -0.064072130507071, -0.064072130507071, -0.373996265063702,
1097			-0.561931604429227, -0.064072130507071, -0.064072130507071, -0.561931604429227,
1098			-0.561931604429227, -0.373996265063702, -0.373996265063702, -0.561931604429227}};
1099			static const std::array<double, 138> cub2D_26_weights_data = {
1100			{0.005361616431413, 0.005361616431413, 0.005361616431413, 0.012732191427031, 0.012732191427031,
1101			0.012732191427031, 0.029707048808635, 0.029707048808635, 0.029707048808635, 0.026709487358142,
1102			0.026709487358142, 0.026709487358142, 0.031691197689589, 0.031691197689589, 0.031691197689589,
1103			0.028281596577704, 0.028281596577704, 0.028281596577704, 0.022460561269283, 0.022460561269283,
1104			0.022460561269283, 0.013160382318625, 0.013160382318625, 0.013160382318625, 0.005828465225510,
1105			0.005828465225510, 0.005828465225510, 0.001098762787251, 0.001098762787251, 0.001098762787251,
1106			0.002557622023150, 0.002557622023150, 0.002557622023150, 0.002557622023150, 0.002557622023150,
1107			0.002557622023150, 0.007088900226242, 0.007088900226242, 0.007088900226242, 0.007088900226242,
1108			0.007088900226242, 0.007088900226242, 0.006588000446609, 0.006588000446609, 0.006588000446609,
1109			0.006588000446609, 0.006588000446609, 0.006588000446609, 0.006069708653929, 0.006069708653929,
1110			0.006069708653929, 0.006069708653929, 0.006069708653929, 0.006069708653929, 0.004942128706706,
1111			0.004942128706706, 0.004942128706706, 0.004942128706706, 0.004942128706706, 0.004942128706706,
1112			0.004076340070443, 0.004076340070443, 0.004076340070443, 0.004076340070443, 0.004076340070443,
1113			0.004076340070443, 0.011120280239045, 0.011120280239045, 0.011120280239045, 0.011120280239045,
1114			0.011120280239045, 0.011120280239045, 0.012755358640694, 0.012755358640694, 0.012755358640694,
1115			0.012755358640694, 0.012755358640694, 0.012755358640694, 0.014549157045387, 0.014549157045387,
1116			0.014549157045387, 0.014549157045387, 0.014549157045387, 0.014549157045387, 0.009121880355576,
1117			0.009121880355576, 0.009121880355576, 0.009121880355576, 0.009121880355576, 0.009121880355576,
1118			0.013582808914065, 0.013582808914065, 0.013582808914065, 0.013582808914065, 0.013582808914065,
1119			0.013582808914065, 0.015585248954434, 0.015585248954434, 0.015585248954434, 0.015585248954434,
1120			0.015585248954434, 0.015585248954434, 0.018960151369388, 0.018960151369388, 0.018960151369388,
1121			0.018960151369388, 0.018960151369388, 0.018960151369388, 0.019206200353033, 0.019206200353033,
1122			0.019206200353033, 0.019206200353033, 0.019206200353033, 0.019206200353033, 0.018121839059318,
1123			0.018121839059318, 0.018121839059318, 0.018121839059318, 0.018121839059318, 0.018121839059318,
1124			0.028403705951863, 0.028403705951863, 0.028403705951863, 0.028403705951863, 0.028403705951863,
1125			0.028403705951863, 0.026986162760930, 0.026986162760930, 0.026986162760930, 0.026986162760930,
1126			0.026986162760930, 0.026986162760930, 0.025102184615930, 0.025102184615930, 0.025102184615930,
1127			0.025102184615930, 0.025102184615930, 0.025102184615930}};
1128
1129			// For cub2D_27: 145 points (145*3 = 435 elements)
1130			static const std::array<double, 145 * 2> cub2D_27_nodes_data = {
1131			{-0.333333333333333, -0.333333333333333, -0.029244446609137, -0.029244446609137,
1132			-0.941511106781726, -0.029244446609137, -0.029244446609137, -0.941511106781726,
1133			-0.132843721814340, -0.132843721814340, -0.734312556371321, -0.132843721814340,
1134			-0.132843721814340, -0.734312556371321, -0.224940014502969, -0.224940014502969,
1135			-0.550119970994063, -0.224940014502969, -0.224940014502969, -0.550119970994063,
1136			-0.427786783949924, -0.427786783949924, -0.144426432100151, -0.427786783949924,
1137			-0.427786783949924, -0.144426432100151, -0.532776206162091, -0.532776206162091,
1138			0.065552412324182, -0.532776206162091, -0.532776206162091, 0.065552412324182,
1139			-0.690368113175391, -0.690368113175391, 0.380736226350782, -0.690368113175391,
1140			-0.690368113175391, 0.380736226350782, -0.781499070170348, -0.781499070170348,
1141			0.562998140340695, -0.781499070170348, -0.781499070170348, 0.562998140340695,
1142			-0.862704525220276, -0.862704525220276, 0.725409050440551, -0.862704525220276,
1143			-0.862704525220276, 0.725409050440551, -0.932961091535336, -0.932961091535336,
1144			0.865922183070671, -0.932961091535336, -0.932961091535336, 0.865922183070671,
1145			-0.986811381964774, -0.986811381964774, 0.973622763929549, -0.986811381964774,
1146			-0.986811381964774, 0.973622763929549, -0.717055503863097, 0.716419063026126,
1147			0.716419063026126, -0.717055503863097, -0.999363559163030, 0.716419063026126,
1148			0.716419063026126, -0.999363559163030, -0.999363559163030, -0.717055503863097,
1149			-0.717055503863097, -0.999363559163030, -0.838822221132805, 0.827544031058903,
1150			0.827544031058903, -0.838822221132805, -0.988721809926098, 0.827544031058903,
1151			0.827544031058903, -0.988721809926098, -0.988721809926098, -0.838822221132805,
1152			-0.838822221132805, -0.988721809926098, -0.537630806497654, 0.526128943172145,
1153			0.526128943172145, -0.537630806497654, -0.988498136674491, 0.526128943172145,
1154			0.526128943172145, -0.988498136674491, -0.988498136674491, -0.537630806497654,
1155			-0.537630806497654, -0.988498136674491, -0.113842988120976, 0.103273580134309,
1156			0.103273580134309, -0.113842988120976, -0.989430592013333, 0.103273580134310,
1157			0.103273580134310, -0.989430592013333, -0.989430592013333, -0.113842988120976,
1158			-0.113842988120976, -0.989430592013333, -0.330849908839651, 0.320515152715889,
1159			0.320515152715889, -0.330849908839651, -0.989665243876238, 0.320515152715889,
1160			0.320515152715889, -0.989665243876238, -0.989665243876238, -0.330849908839651,
1161			-0.330849908839651, -0.989665243876238, -0.931869179489789, 0.919222453867072,
1162			0.919222453867072, -0.931869179489789, -0.987353274377283, 0.919222453867072,
1163			0.919222453867072, -0.987353274377283, -0.987353274377283, -0.931869179489789,
1164			-0.931869179489789, -0.987353274377283, -0.695123977280935, 0.663705924287710,
1165			0.663705924287710, -0.695123977280935, -0.968581947006775, 0.663705924287710,
1166			0.663705924287710, -0.968581947006775, -0.968581947006775, -0.695123977280935,
1167			-0.695123977280935, -0.968581947006775, -0.831869809255826, 0.777736654895860,
1168			0.777736654895860, -0.831869809255826, -0.945866845640035, 0.777736654895860,
1169			0.777736654895860, -0.945866845640035, -0.945866845640035, -0.831869809255826,
1170			-0.831869809255826, -0.945866845640035, -0.423211420319719, 0.374995160760160,
1171			0.374995160760160, -0.423211420319719, -0.951783740440441, 0.374995160760160,
1172			0.374995160760160, -0.951783740440441, -0.951783740440441, -0.423211420319719,
1173			-0.423211420319719, -0.951783740440441, -0.223962554104902, 0.171509638849087,
1174			0.171509638849087, -0.223962554104902, -0.947547084744185, 0.171509638849087,
1175			0.171509638849087, -0.947547084744185, -0.947547084744185, -0.223962554104902,
1176			-0.223962554104902, -0.947547084744185, -0.566926820194262, 0.490923426439871,
1177			0.490923426439871, -0.566926820194262, -0.923996606245609, 0.490923426439871,
1178			0.490923426439871, -0.923996606245609, -0.923996606245609, -0.566926820194262,
1179			-0.566926820194262, -0.923996606245609, -0.350787336349322, 0.245677528944182,
1180			0.245677528944182, -0.350787336349322, -0.894890192594860, 0.245677528944182,
1181			0.245677528944182, -0.894890192594860, -0.894890192594860, -0.350787336349322,
1182			-0.350787336349322, -0.894890192594860, -0.729613610936203, 0.622255871516285,
1183			0.622255871516285, -0.729613610936203, -0.892642260580081, 0.622255871516285,
1184			0.622255871516285, -0.892642260580081, -0.892642260580081, -0.729613610936203,
1185			-0.729613610936203, -0.892642260580081, -0.176209680235251, 0.035410146457445,
1186			0.035410146457445, -0.176209680235251, -0.859200466222194, 0.035410146457445,
1187			0.035410146457445, -0.859200466222194, -0.859200466222194, -0.176209680235251,
1188			-0.176209680235251, -0.859200466222194, -0.469171656648510, 0.304686011244002,
1189			0.304686011244002, -0.469171656648510, -0.835514354595492, 0.304686011244002,
1190			0.304686011244002, -0.835514354595492, -0.835514354595492, -0.469171656648510,
1191			-0.469171656648510, -0.835514354595492, -0.623736093891471, 0.443479545725970,
1192			0.443479545725970, -0.623736093891471, -0.819743451834499, 0.443479545725970,
1193			0.443479545725970, -0.819743451834499, -0.819743451834499, -0.623736093891471,
1194			-0.623736093891471, -0.819743451834499, -0.336632062394500, 0.104847567508036,
1195			0.104847567508036, -0.336632062394500, -0.768215505113536, 0.104847567508036,
1196			0.104847567508036, -0.768215505113536, -0.768215505113536, -0.336632062394500,
1197			-0.336632062394500, -0.768215505113536, -0.530404689974552, 0.224195004863778,
1198			0.224195004863778, -0.530404689974552, -0.693790314889227, 0.224195004863778,
1199			0.224195004863778, -0.693790314889227, -0.693790314889227, -0.530404689974552,
1200			-0.530404689974552, -0.693790314889227, -0.350831684137242, -0.019508133770036,
1201			-0.019508133770036, -0.350831684137242, -0.629660182092722, -0.019508133770036,
1202			-0.019508133770036, -0.629660182092722, -0.629660182092722, -0.350831684137242,
1203			-0.350831684137242, -0.629660182092722}};
1204			static const std::array<double, 145> cub2D_27_weights_data = {
1205			{0.029215421142604, 0.013615273717612, 0.013615273717612, 0.013615273717612,
1206			0.030951102870660, 0.030951102870660, 0.030951102870660, 0.031733186724762,
1207			0.031733186724762, 0.031733186724762, 0.031559855928489, 0.031559855928489,
1208			0.031559855928489, 0.027863700370354, 0.027863700370354, 0.027863700370354,
1209			0.019750305737275, 0.019750305737275, 0.019750305737275, 0.015635498945203,
1210			0.015635498945203, 0.015635498945203, 0.010432865446986, 0.010432865446986,
1211			0.010432865446986, 0.005852724472600, 0.005852724472600, 0.005852724472600,
1212			0.001134879007165, 0.001134879007165, 0.001134879007165, 0.001375795459783,
1213			0.001375795459783, 0.001375795459783, 0.001375795459783, 0.001375795459783,
1214			0.001375795459783, 0.003088879415937, 0.003088879415937, 0.003088879415937,
1215			0.003088879415937, 0.003088879415937, 0.003088879415937, 0.005625149324346,
1216			0.005625149324346, 0.005625149324346, 0.005625149324346, 0.005625149324346,
1217			0.005625149324346, 0.005913105372899, 0.005913105372899, 0.005913105372899,
1218			0.005913105372899, 0.005913105372899, 0.005913105372899, 0.005565783438844,
1219			0.005565783438844, 0.005565783438844, 0.005565783438844, 0.005565783438844,
1220			0.005565783438844, 0.002449540456172, 0.002449540456172, 0.002449540456172,
1221			0.002449540456172, 0.002449540456172, 0.002449540456172, 0.007906643758942,
1222			0.007906643758942, 0.007906643758942, 0.007906643758942, 0.007906643758942,
1223			0.007906643758942, 0.007221969465327, 0.007221969465327, 0.007221969465327,
1224			0.007221969465327, 0.007221969465327, 0.007221969465327, 0.008707930088036,
1225			0.008707930088036, 0.008707930088036, 0.008707930088036, 0.008707930088036,
1226			0.008707930088036, 0.011256464740666, 0.011256464740666, 0.011256464740666,
1227			0.011256464740666, 0.011256464740666, 0.011256464740666, 0.013269437724243,
1228			0.013269437724243, 0.013269437724243, 0.013269437724243, 0.013269437724243,
1229			0.013269437724243, 0.013046146795576, 0.013046146795576, 0.013046146795576,
1230			0.013046146795576, 0.013046146795576, 0.013046146795576, 0.012947418329903,
1231			0.012947418329903, 0.012947418329903, 0.012947418329903, 0.012947418329903,
1232			0.012947418329903, 0.021313811627966, 0.021313811627966, 0.021313811627966,
1233			0.021313811627966, 0.021313811627966, 0.021313811627966, 0.017176891528936,
1234			0.017176891528936, 0.017176891528936, 0.017176891528936, 0.017176891528936,
1235			0.017176891528936, 0.017763399981969, 0.017763399981969, 0.017763399981969,
1236			0.017763399981969, 0.017763399981969, 0.017763399981969, 0.023828398561090,
1237			0.023828398561090, 0.023828398561090, 0.023828398561090, 0.023828398561090,
1238			0.023828398561090, 0.026764788789016, 0.026764788789016, 0.026764788789016,
1239			0.026764788789016, 0.026764788789016, 0.026764788789016, 0.028977845006028,
1240			0.028977845006028, 0.028977845006028, 0.028977845006028, 0.028977845006028,
1241			0.028977845006028}};
1242
1243			// For cub2D_28: 225 points (225*3 = 675 elements)
1244			static const std::array<double, 225 * 2> cub2D_28_nodes_data = {
1245			{-0.988064607832230, 0.987992518020485, -0.937649986705898, 0.937273392400706,
1246			-0.849117911767581, 0.848206583410427, -0.726072255922453, 0.724417731360170,
1247			-0.573547944561595, 0.570972172608539, -0.397788705468703, 0.394151347077563,
1248			-0.205989917758162, 0.201194093997435, -0.006003740989757, 0.000000000000000,
1249			0.193982435778648, -0.201194093997435, 0.385781223489189, -0.394151347077563,
1250			0.561540462582081, -0.570972172608539, 0.714064773942939, -0.724417731360170,
1251			0.837110429788067, -0.848206583410427, 0.925642504726384, -0.937273392400706,
1252			0.976057125852715, -0.987992518020485, -0.988369112325678, 0.987992518020485,
1253			-0.939240706051164, 0.937273392400706, -0.852967326449712, 0.848206583410427,
1254			-0.733060901773317, 0.724417731360170, -0.584427902697520, 0.570972172608539,
1255			-0.413152762435777, 0.394151347077563, -0.226247286304345, 0.201194093997435,
1256			-0.031363303799647, 0.000000000000000, 0.163520678705051, -0.201194093997435,
1257			0.350426154836483, -0.394151347077563, 0.521701295098226, -0.570972172608539,
1258			0.670334294174023, -0.724417731360170, 0.790240718850418, -0.848206583410427,
1259			0.876514098451870, -0.937273392400706, 0.925642504726384, -0.987992518020485,
1260			-0.988903846377640, 0.987992518020485, -0.942034135439991, 0.937273392400706,
1261			-0.859727204070395, 0.848206583410427, -0.745333518414343, 0.724417731360170,
1262			-0.603533972474414, 0.570972172608539, -0.440133265559207, 0.394151347077563,
1263			-0.261820832829464, 0.201194093997435, -0.075896708294786, 0.000000000000000,
1264			0.110027416239891, -0.201194093997435, 0.288339848969634, -0.394151347077563,
1265			0.451740555884842, -0.570972172608539, 0.593540101824770, -0.724417731360170,
1266			0.707933787480822, -0.848206583410427, 0.790240718850418, -0.937273392400706,
1267			0.837110429788067, -0.987992518020485, -0.989647042582769, 0.987992518020485,
1268			-0.945916562813853, 0.937273392400706, -0.869122370464600, 0.848206583410427,
1269			-0.762390524754508, 0.724417731360170, -0.630088403599617, 0.570972172608539,
1270			-0.477631920189938, 0.394151347077563, -0.311262465886975, 0.201194093997435,
1271			-0.137791134319915, 0.000000000000000, 0.035680197247145, -0.201194093997435,
1272			0.202049651550108, -0.394151347077563, 0.354506134959787, -0.570972172608539,
1273			0.486808256114678, -0.724417731360170, 0.593540101824770, -0.848206583410427,
1274			0.670334294174023, -0.937273392400706, 0.714064773942939, -0.987992518020485,
1275			-0.990568289973542, 0.987992518020485, -0.950729122489687, 0.937273392400706,
1276			-0.880768383276303, 0.848206583410427, -0.783533962351248, 0.724417731360170,
1277			-0.663004610946658, 0.570972172608539, -0.524114312723242, 0.394151347077563,
1278			-0.372549075177309, 0.201194093997435, -0.214513913695731, 0.000000000000000,
1279			-0.056478752214152, -0.201194093997435, 0.095086485331781, -0.394151347077563,
1280			0.233976783555196, -0.570972172608539, 0.354506134959787, -0.724417731360170,
1281			0.451740555884842, -0.848206583410427, 0.521701295098226, -0.937273392400706,
1282			0.561540462582081, -0.987992518020485, -0.991629876411625, 0.987992518020485,
1283			-0.956274807758919, 0.937273392400706, -0.894188501892071, 0.848206583410427,
1284			-0.807898304472545, 0.724417731360170, -0.700935138254217, 0.570972172608539,
1285			-0.577677642201529, 0.394151347077563, -0.443171835046505, 0.201194093997435,
1286			-0.302924326461218, 0.000000000000000, -0.162676817875932, -0.201194093997435,
1287			-0.028171010720908, -0.394151347077563, 0.095086485331781, -0.570972172608539,
1288			0.202049651550108, -0.724417731360170, 0.288339848969634, -0.848206583410427,
1289			0.350426154836483, -0.937273392400706, 0.385781223489189, -0.987992518020485,
1290			-0.992788341781213, 0.987992518020485, -0.962326584707617, 0.937273392400706,
1291			-0.908833322242456, 0.848206583410427, -0.834486103249711, 0.724417731360170,
1292			-0.742327153788413, 0.570972172608539, -0.636129088126634, 0.394151347077563,
1293			-0.520239531729724, 0.201194093997435, -0.399402953001283, 0.000000000000000,
1294			-0.278566374272841, -0.201194093997435, -0.162676817875932, -0.394151347077563,
1295			-0.056478752214152, -0.570972172608539, 0.035680197247145, -0.724417731360170,
1296			0.110027416239891, -0.848206583410427, 0.163520678705051, -0.937273392400706,
1297			0.193982435778648, -0.987992518020485, -0.993996259010243, 0.987992518020485,
1298			-0.968636696200353, 0.937273392400706, -0.924103291705214, 0.848206583410427,
1299			-0.862208865680085, 0.724417731360170, -0.785486086304269, 0.570972172608539,
1300			-0.697075673538782, 0.394151347077563, -0.600597046998717, 0.201194093997435,
1301			-0.500000000000000, 0.000000000000000, -0.399402953001283, -0.201194093997435,
1302			-0.302924326461218, -0.394151347077563, -0.214513913695731, -0.570972172608539,
1303			-0.137791134319915, -0.724417731360170, -0.075896708294786, -0.848206583410427,
1304			-0.031363303799647, -0.937273392400706, -0.006003740989757, -0.987992518020485,
1305			-0.995204176239272, 0.987992518020485, -0.974946807693089, 0.937273392400706,
1306			-0.939373261167971, 0.848206583410427, -0.889931628110459, 0.724417731360170,
1307			-0.828645018820126, 0.570972172608539, -0.758022258950930, 0.394151347077563,
1308			-0.680954562267710, 0.201194093997435, -0.600597046998717, 0.000000000000000,
1309			-0.520239531729724, -0.201194093997435, -0.443171835046505, -0.394151347077563,
1310			-0.372549075177309, -0.570972172608539, -0.311262465886975, -0.724417731360170,
1311			-0.261820832829464, -0.848206583410427, -0.226247286304345, -0.937273392400706,
1312			-0.205989917758162, -0.987992518020485, -0.996362641608860, 0.987992518020485,
1313			-0.980998584641787, 0.937273392400706, -0.954018081518357, 0.848206583410427,
1314			-0.916519426887625, 0.724417731360170, -0.870037034354322, 0.570972172608539,
1315			-0.816473704876034, 0.394151347077563, -0.758022258950930, 0.201194093997435,
1316			-0.697075673538782, 0.000000000000000, -0.636129088126634, -0.201194093997435,
1317			-0.577677642201529, -0.394151347077563, -0.524114312723242, -0.570972172608539,
1318			-0.477631920189938, -0.724417731360170, -0.440133265559207, -0.848206583410427,
1319			-0.413152762435777, -0.937273392400706, -0.397788705468703, -0.987992518020485,
1320			-0.997424228046943, 0.987992518020485, -0.986544269911019, 0.937273392400706,
1321			-0.967438200134124, 0.848206583410427, -0.940883769008922, 0.724417731360170,
1322			-0.907967561661881, 0.570972172608539, -0.870037034354322, 0.394151347077563,
1323			-0.828645018820126, 0.201194093997435, -0.785486086304269, 0.000000000000000,
1324			-0.742327153788413, -0.201194093997435, -0.700935138254217, -0.394151347077563,
1325			-0.663004610946658, -0.570972172608539, -0.630088403599617, -0.724417731360170,
1326			-0.603533972474414, -0.848206583410427, -0.584427902697520, -0.937273392400706,
1327			-0.573547944561595, -0.987992518020485, -0.998345475437717, 0.987992518020485,
1328			-0.991356829586853, 0.937273392400706, -0.979084212945827, 0.848206583410427,
1329			-0.962027206605662, 0.724417731360170, -0.940883769008922, 0.570972172608539,
1330			-0.916519426887625, 0.394151347077563, -0.889931628110459, 0.201194093997435,
1331			-0.862208865680085, 0.000000000000000, -0.834486103249711, -0.201194093997435,
1332			-0.807898304472545, -0.394151347077563, -0.783533962351248, -0.570972172608539,
1333			-0.762390524754508, -0.724417731360170, -0.745333518414343, -0.848206583410427,
1334			-0.733060901773317, -0.937273392400706, -0.726072255922453, -0.987992518020485,
1335			-0.999088671642846, 0.987992518020485, -0.995239256960715, 0.937273392400706,
1336			-0.988479379340032, 0.848206583410427, -0.979084212945827, 0.724417731360170,
1337			-0.967438200134124, 0.570972172608539, -0.954018081518357, 0.394151347077563,
1338			-0.939373261167971, 0.201194093997435, -0.924103291705214, 0.000000000000000,
1339			-0.908833322242456, -0.201194093997435, -0.894188501892071, -0.394151347077563,
1340			-0.880768383276303, -0.570972172608539, -0.869122370464600, -0.724417731360170,
1341			-0.859727204070395, -0.848206583410427, -0.852967326449712, -0.937273392400706,
1342			-0.849117911767581, -0.987992518020485, -0.999623405694808, 0.987992518020485,
1343			-0.998032686349542, 0.937273392400706, -0.995239256960715, 0.848206583410427,
1344			-0.991356829586853, 0.724417731360170, -0.986544269911019, 0.570972172608539,
1345			-0.980998584641787, 0.394151347077563, -0.974946807693089, 0.201194093997435,
1346			-0.968636696200353, 0.000000000000000, -0.962326584707617, -0.201194093997435,
1347			-0.956274807758919, -0.394151347077563, -0.950729122489687, -0.570972172608539,
1348			-0.945916562813853, -0.724417731360170, -0.942034135439991, -0.848206583410427,
1349			-0.939240706051164, -0.937273392400706, -0.937649986705898, -0.987992518020485,
1350			-0.999927910188256, 0.987992518020485, -0.999623405694808, 0.937273392400706,
1351			-0.999088671642846, 0.848206583410427, -0.998345475437717, 0.724417731360170,
1352			-0.997424228046943, 0.570972172608539, -0.996362641608860, 0.394151347077563,
1353			-0.995204176239272, 0.201194093997435, -0.993996259010243, 0.000000000000000,
1354			-0.992788341781213, -0.201194093997435, -0.991629876411625, -0.394151347077563,
1355			-0.990568289973542, -0.570972172608539, -0.989647042582769, -0.724417731360170,
1356			-0.988903846377640, -0.848206583410427, -0.988369112325678, -0.937273392400706,
1357			-0.988064607832230, -0.987992518020485}};
1358			static const std::array<double, 225> cub2D_28_weights_data = {
1359			{0.000005678109445, 0.000067869690329, 0.000250117104238, 0.000591434111178,
1360			0.001096877668021, 0.001734258212849, 0.002437321168702, 0.003114968848543,
1361			0.003665090319212, 0.003990796070869, 0.004016439454972, 0.003700816722647,
1362			0.003045376334904, 0.002096114396383, 0.000940083783827, 0.000012991999963,
1363			0.000155291655212, 0.000572289322752, 0.001353251821662, 0.002509749901695,
1364			0.003968131092565, 0.005576799256556, 0.007127315095696, 0.008386040063107,
1365			0.009131282674963, 0.009189956930633, 0.008467785129237, 0.006968081473429,
1366			0.004796088983887, 0.002150992086750, 0.000019785289042, 0.000236490940043,
1367			0.000871529379538, 0.002060843481789, 0.003822054138805, 0.006042997294437,
1368			0.008492809847469, 0.010854063244177, 0.012770953436328, 0.013905870348620,
1369			0.013995224344240, 0.012895441564853, 0.010611569151594, 0.007303879856139,
1370			0.003275708150100, 0.000025769562269, 0.000308020165519, 0.001135132803359,
1371			0.002684167732828, 0.004978075474027, 0.007870766747028, 0.011061551425453,
1372			0.014136991279319, 0.016633665503545, 0.018111850228555, 0.018228230300094,
1373			0.016795806403939, 0.013821152243283, 0.009513016785380, 0.004266481271556,
1374			0.000030699031605, 0.000366941459749, 0.001352272787635, 0.003197623195991,
1375			0.005930333418609, 0.009376368701824, 0.013177519790991, 0.016841261700383,
1376			0.019815525683434, 0.021576472924861, 0.021715115384404, 0.020008682578130,
1377			0.016465005695410, 0.011332765372579, 0.005082618091388, 0.000034371743072,
1378			0.000410840893588, 0.001514053388316, 0.003580174265665, 0.006639815197344,
1379			0.010498120595869, 0.014754026459451, 0.018856084049129, 0.022186177283618,
1380			0.024157797330925, 0.024313026429341, 0.022402442709917, 0.018434814254740,
1381			0.012688572873940, 0.005690682540646, 0.000036637297986, 0.000437920771488,
1382			0.001613849639200, 0.003816155355883, 0.007077467309460, 0.011190086338209,
1383			0.015726512989614, 0.020098950720122, 0.023648541379510, 0.025750117404859,
1384			0.025915578164965, 0.023879061573116, 0.019649913644597, 0.013524918548175,
1385			0.006065774189928, 0.000037402932316, 0.000447072297244, 0.001647575343713,
1386			0.003895904128496, 0.007225369917846, 0.011423933120557, 0.016055160539688,
1387			0.020518972050826, 0.024142740900556, 0.026288234977700, 0.026457153482920,
1388			0.024378078430143, 0.020060551144640, 0.013807557894147, 0.006192534764769,
1389			0.000036637297986, 0.000437920771488, 0.001613849639200, 0.003816155355883,
1390			0.007077467309460, 0.011190086338209, 0.015726512989614, 0.020098950720122,
1391			0.023648541379510, 0.025750117404859, 0.025915578164965, 0.023879061573116,
1392			0.019649913644597, 0.013524918548175, 0.006065774189928, 0.000034371743072,
1393			0.000410840893588, 0.001514053388316, 0.003580174265665, 0.006639815197344,
1394			0.010498120595869, 0.014754026459451, 0.018856084049129, 0.022186177283618,
1395			0.024157797330925, 0.024313026429341, 0.022402442709917, 0.018434814254740,
1396			0.012688572873940, 0.005690682540646, 0.000030699031605, 0.000366941459749,
1397			0.001352272787635, 0.003197623195991, 0.005930333418609, 0.009376368701824,
1398			0.013177519790991, 0.016841261700383, 0.019815525683434, 0.021576472924861,
1399			0.021715115384404, 0.020008682578130, 0.016465005695410, 0.011332765372579,
1400			0.005082618091388, 0.000025769562269, 0.000308020165519, 0.001135132803359,
1401			0.002684167732828, 0.004978075474027, 0.007870766747028, 0.011061551425453,
1402			0.014136991279319, 0.016633665503545, 0.018111850228555, 0.018228230300094,
1403			0.016795806403939, 0.013821152243283, 0.009513016785380, 0.004266481271556,
1404			0.000019785289042, 0.000236490940043, 0.000871529379538, 0.002060843481789,
1405			0.003822054138805, 0.006042997294437, 0.008492809847469, 0.010854063244177,
1406			0.012770953436328, 0.013905870348620, 0.013995224344240, 0.012895441564853,
1407			0.010611569151594, 0.007303879856139, 0.003275708150100, 0.000012991999963,
1408			0.000155291655212, 0.000572289322752, 0.001353251821662, 0.002509749901695,
1409			0.003968131092565, 0.005576799256556, 0.007127315095696, 0.008386040063107,
1410			0.009131282674963, 0.009189956930633, 0.008467785129237, 0.006968081473429,
1411			0.004796088983887, 0.002150992086750, 0.000005678109445, 0.000067869690329,
1412			0.000250117104238, 0.000591434111178, 0.001096877668021, 0.001734258212849,
1413			0.002437321168702, 0.003114968848543, 0.003665090319212, 0.003990796070869,
1414			0.004016439454972, 0.003700816722647, 0.003045376334904, 0.002096114396383,
1415			0.000940083783827}};
1416			} // namespace
1417
1418			namespace oiseau::utils::integration {
1419		42	std::pair<xt::xarray<double>, xt::xarray<double>> cubature(int order) {
1420	2/2 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 40 times.	42	if (order <= 0) {
1421		2	throw std::out_of_range("cubature: n must be a positive integer, but got " +
1422	2/4 ✓ Branch 3 taken 2 times. ✗ Branch 4 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken.	4	std::to_string(order));
1423			}
1424	29/29 ✓ Branch 0 taken 1 times. ✓ Branch 1 taken 1 times. ✓ Branch 2 taken 1 times. ✓ Branch 3 taken 1 times. ✓ Branch 4 taken 1 times. ✓ Branch 5 taken 1 times. ✓ Branch 6 taken 1 times. ✓ Branch 7 taken 1 times. ✓ Branch 8 taken 1 times. ✓ Branch 9 taken 1 times. ✓ Branch 10 taken 1 times. ✓ Branch 11 taken 1 times. ✓ Branch 12 taken 1 times. ✓ Branch 13 taken 1 times. ✓ Branch 14 taken 1 times. ✓ Branch 15 taken 1 times. ✓ Branch 16 taken 1 times. ✓ Branch 17 taken 1 times. ✓ Branch 18 taken 1 times. ✓ Branch 19 taken 1 times. ✓ Branch 20 taken 1 times. ✓ Branch 21 taken 1 times. ✓ Branch 22 taken 1 times. ✓ Branch 23 taken 1 times. ✓ Branch 24 taken 1 times. ✓ Branch 25 taken 1 times. ✓ Branch 26 taken 1 times. ✓ Branch 27 taken 1 times. ✓ Branch 28 taken 12 times.	40	switch (order) {
1425		1	case 1:
1426	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_1_nodes_data.data(), {1ul, 2ul}),
1427	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_1_weights_data.data(), {1ul})};
1428		1	case 2:
1429	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_2_nodes_data.data(), {3ul, 2ul}),
1430	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_2_weights_data.data(), {3ul})};
1431		1	case 3:
1432	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_3_nodes_data.data(), {6ul, 2ul}),
1433	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_3_weights_data.data(), {6ul})};
1434		1	case 4:
1435	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_4_nodes_data.data(), {6ul, 2ul}),
1436	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_4_weights_data.data(), {6ul})};
1437		1	case 5:
1438	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_5_nodes_data.data(), {7ul, 2ul}),
1439	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_5_weights_data.data(), {7ul})};
1440		1	case 6:
1441	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_6_nodes_data.data(), {12ul, 2ul}),
1442	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_6_weights_data.data(), {12ul})};
1443		1	case 7:
1444	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_7_nodes_data.data(), {15ul, 2ul}),
1445	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_7_weights_data.data(), {15ul})};
1446		1	case 8:
1447	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_8_nodes_data.data(), {16ul, 2ul}),
1448	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_8_weights_data.data(), {16ul})};
1449		1	case 9:
1450	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_9_nodes_data.data(), {19ul, 2ul}),
1451	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_9_weights_data.data(), {19ul})};
1452		1	case 10:
1453	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_10_nodes_data.data(), {25ul, 2ul}),
1454	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_10_weights_data.data(), {25ul})};
1455		1	case 11:
1456	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_11_nodes_data.data(), {28ul, 2ul}),
1457	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_11_weights_data.data(), {28ul})};
1458		1	case 12:
1459	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_12_nodes_data.data(), {36ul, 2ul}),
1460	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_12_weights_data.data(), {36ul})};
1461		1	case 13:
1462	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_13_nodes_data.data(), {40ul, 2ul}),
1463	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_13_weights_data.data(), {40ul})};
1464		1	case 14:
1465	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_14_nodes_data.data(), {46ul, 2ul}),
1466	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_14_weights_data.data(), {46ul})};
1467		1	case 15:
1468	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_15_nodes_data.data(), {54ul, 2ul}),
1469	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_15_weights_data.data(), {54ul})};
1470		1	case 16:
1471	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_16_nodes_data.data(), {58ul, 2ul}),
1472	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_16_weights_data.data(), {58ul})};
1473		1	case 17:
1474	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_17_nodes_data.data(), {66ul, 2ul}),
1475	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_17_weights_data.data(), {66ul})};
1476		1	case 18:
1477	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_18_nodes_data.data(), {73ul, 2ul}),
1478	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_18_weights_data.data(), {73ul})};
1479		1	case 19:
1480	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_19_nodes_data.data(), {82ul, 2ul}),
1481	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_19_weights_data.data(), {82ul})};
1482		1	case 20:
1483	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_20_nodes_data.data(), {85ul, 2ul}),
1484	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_20_weights_data.data(), {85ul})};
1485		1	case 21:
1486	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_21_nodes_data.data(), {93ul, 2ul}),
1487	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_21_weights_data.data(), {93ul})};
1488		1	case 22:
1489	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_22_nodes_data.data(), {100ul, 2ul}),
1490	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_22_weights_data.data(), {100ul})};
1491		1	case 23:
1492	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_23_nodes_data.data(), {106ul, 2ul}),
1493	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_23_weights_data.data(), {106ul})};
1494		1	case 24:
1495	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_24_nodes_data.data(), {118ul, 2ul}),
1496	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_24_weights_data.data(), {118ul})};
1497		1	case 25:
1498	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_25_nodes_data.data(), {126ul, 2ul}),
1499	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_25_weights_data.data(), {126ul})};
1500		1	case 26:
1501	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_26_nodes_data.data(), {138ul, 2ul}),
1502	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_26_weights_data.data(), {138ul})};
1503		1	case 27:
1504	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_27_nodes_data.data(), {145ul, 2ul}),
1505	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_27_weights_data.data(), {145ul})};
1506		1	case 28:
1507	1/2 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken.	3	return std::pair{xt::adapt(cub2D_28_nodes_data.data(), {225ul, 2ul}),
1508	2/4 ✓ Branch 2 taken 1 times. ✗ Branch 3 not taken. ✓ Branch 6 taken 1 times. ✗ Branch 7 not taken.	2	xt::adapt(cub2D_28_weights_data.data(), {225ul})};
1509		12	default:
1510			// TODO(tiagovla): check order/number of nodes relationship
1511		12	int cubNA = std::ceil((order + 1) / 2);
1512	1/2 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken.	12	auto [cubA, cubWA] = oiseau::dg::nodal::utils::jacobi_gq(cubNA - 1, 0, 0);
1513	1/2 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken.	12	auto [cubB, cubWB] = oiseau::dg::nodal::utils::jacobi_gq(cubNA - 1, 1, 0);
1514	2/4 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 12 times. ✗ Branch 5 not taken.	12	auto r0 = xt::reshape_view(xt::tile(cubA, {cubNA}), {cubNA, cubNA});
1515	2/4 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 12 times. ✗ Branch 5 not taken.	12	auto r1 = xt::transpose(xt::reshape_view(xt::tile(cubB, {cubNA}), {cubNA, cubNA}));
1516	3/6 ✓ Branch 6 taken 12 times. ✗ Branch 7 not taken. ✓ Branch 9 taken 12 times. ✗ Branch 10 not taken. ✓ Branch 12 taken 12 times. ✗ Branch 13 not taken.	24	xt::xarray<double> cubR = xt::flatten(xt::eval((0.5 * ((1.0 + r0) * (1.0 - r1)) - 1.0)));
1517	3/6 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 12 times. ✗ Branch 5 not taken. ✓ Branch 7 taken 12 times. ✗ Branch 8 not taken.	24	xt::xarray<double> cubS = xt::flatten(xt::eval(r1));
1518	2/4 ✓ Branch 2 taken 12 times. ✗ Branch 3 not taken. ✓ Branch 5 taken 12 times. ✗ Branch 6 not taken.	24	xt::xarray<double> nodes = xt::stack(xt::xtuple(cubR, cubS), 1);
1519	3/6 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 12 times. ✗ Branch 5 not taken. ✓ Branch 8 taken 12 times. ✗ Branch 9 not taken.	24	xt::xarray<double> weights = 0.5 * xt::flatten(xt::linalg::outer(cubWB, cubWA));
1520	1/2 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken.	12	return std::pair{nodes, weights};
1521		12	}
1522			}
1523
1524		51	std::pair<xt::xarray<double>, xt::xarray<double>> quadrature(int order) {
1525	2/2 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 49 times.	51	if (order <= 0) {
1526		2	throw std::out_of_range("quadrature: n must be a positive integer, but got " +
1527	2/4 ✓ Branch 3 taken 2 times. ✗ Branch 4 not taken. ✓ Branch 6 taken 2 times. ✗ Branch 7 not taken.	4	std::to_string(order));
1528			}
1529			// TODO(tiagovla): check order/number of nodes relationship
1530		49	int n = std::ceil((order + 1) / 2);
1531
1532			// Recurrence coefficients for Legendre polynomials
1533	1/2 ✓ Branch 2 taken 49 times. ✗ Branch 3 not taken.	49	xt::xarray<double> a = xt::zeros<double>({n});
1534	1/2 ✓ Branch 2 taken 49 times. ✗ Branch 3 not taken.	49	xt::xarray<double> b = xt::zeros<double>({n - 1});
1535	2/2 ✓ Branch 0 taken 576 times. ✓ Branch 1 taken 49 times.	625	for (int i = 1; i < n; ++i) {
1536	1/2 ✓ Branch 1 taken 576 times. ✗ Branch 2 not taken.	576	b[i - 1] = static_cast<double>(i) / std::sqrt(4.0 * i * i - 1.0);
1537			}
1538
1539			// Jacobi matrix construction
1540	1/2 ✓ Branch 2 taken 49 times. ✗ Branch 3 not taken.	49	xt::xarray<double> J = xt::zeros<double>({n, n});
1541	2/2 ✓ Branch 0 taken 625 times. ✓ Branch 1 taken 49 times.	674	for (int i = 0; i < n; ++i) {
1542	2/4 ✓ Branch 1 taken 625 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 625 times. ✗ Branch 5 not taken.	625	J(i, i) = a[i];
1543	2/2 ✓ Branch 0 taken 576 times. ✓ Branch 1 taken 49 times.	625	if (i < n - 1) {
1544	2/4 ✓ Branch 1 taken 576 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 576 times. ✗ Branch 5 not taken.	576	J(i, i + 1) = b[i];
1545	2/4 ✓ Branch 1 taken 576 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 576 times. ✗ Branch 5 not taken.	576	J(i + 1, i) = b[i];
1546			}
1547			}
1548
1549			// Solve eigenvalue problem
1550	1/2 ✓ Branch 1 taken 49 times. ✗ Branch 2 not taken.	49	auto eig_result = xt::linalg::eig(J);
1551	1/2 ✓ Branch 3 taken 49 times. ✗ Branch 4 not taken.	49	xt::xarray<double> eigenvalues = xt::real(std::get<0>(eig_result));
1552	1/2 ✓ Branch 3 taken 49 times. ✗ Branch 4 not taken.	49	xt::xarray<double> eigenvectors = xt::real(std::get<1>(eig_result));
1553	1/2 ✓ Branch 1 taken 49 times. ✗ Branch 2 not taken.	49	xt::xarray<std::size_t> sorted_indices = xt::argsort(eigenvalues);
1554
1555	3/6 ✓ Branch 1 taken 49 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 49 times. ✗ Branch 5 not taken. ✓ Branch 7 taken 49 times. ✗ Branch 8 not taken.	49	xt::xarray<double> nodes = xt::view(eigenvalues, xt::keep(sorted_indices));
1556	3/6 ✓ Branch 1 taken 49 times. ✗ Branch 2 not taken. ✓ Branch 5 taken 49 times. ✗ Branch 6 not taken. ✓ Branch 8 taken 49 times. ✗ Branch 9 not taken.	49	xt::xarray<double> sorted_vectors = xt::view(eigenvectors, xt::all(), xt::keep(sorted_indices));
1557
1558			// // Weights are 2 * (first row of eigenvectors)^2
1559	2/4 ✓ Branch 1 taken 49 times. ✗ Branch 2 not taken. ✓ Branch 6 taken 49 times. ✗ Branch 7 not taken.	49	xt::xarray<double> weights = 2.0 * xt::square(xt::row(sorted_vectors, 0));
1560
1561	1/2 ✓ Branch 1 taken 49 times. ✗ Branch 2 not taken.	98	return std::make_pair(nodes, weights);
1562		49	}
1563
1564		14	std::pair<xt::xarray<double>, xt::xarray<double>> jacobi_gq(unsigned n, double alpha, double beta) {
1565	2/2 ✓ Branch 0 taken 2 times. ✓ Branch 1 taken 12 times.	14	if (n == 0) {
1566	1/2 ✓ Branch 1 taken 2 times. ✗ Branch 2 not taken.	2	xt::xarray<double> x = {(alpha - beta) / (alpha + beta + 2)};
1567	1/2 ✓ Branch 1 taken 2 times. ✗ Branch 2 not taken.	2	xt::xarray<double> w = {2};
1568		2	return make_pair(std::move(x), std::move(w));
1569		2	}
1570	1/2 ✓ Branch 5 taken 12 times. ✗ Branch 6 not taken.	12	xt::xarray<double> h1 = 2 * xt::linspace<double>(0, n, n + 1) + alpha + beta;
1571	2/4 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken. ✓ Branch 4 taken 12 times. ✗ Branch 5 not taken.	12	auto h1s = xt::view(h1, xt::range(0, n));
1572		12	auto lins = xt::arange<double>(1, n + 1);
1573			xt::xarray<double> m =
1574	1/2 ✓ Branch 6 taken 12 times. ✗ Branch 7 not taken.	24	xt::diag(-1.0 / 2.0 * (std::pow(alpha, 2) - std::pow(beta, 2)) / (h1 + 2) / h1) +
1575	1/2 ✓ Branch 3 taken 12 times. ✗ Branch 4 not taken.	36	xt::diag(2. / (h1s + 2) *
1576		48	xt::sqrt(lins * (lins + alpha + beta) * (lins + alpha) * (lins + beta) /
1577		60	(h1s + 1) / (h1s + 3)),
1578	1/2 ✓ Branch 2 taken 12 times. ✗ Branch 3 not taken.	12	1);
1579	1/4 ✗ Branch 0 not taken. ✓ Branch 1 taken 12 times. ✗ Branch 3 not taken. ✗ Branch 4 not taken.	12	if (alpha + beta == 0) m(0, 0) = 0;
1580	1/2 ✓ Branch 2 taken 12 times. ✗ Branch 3 not taken.	12	m += xt::transpose(m);
1581	1/2 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken.	12	auto [d, v] = xt::linalg::eigh(m);
1582		12	double cte = std::pow(2, (alpha + beta + 1)) / (alpha + beta + 1) * std::tgamma(alpha + 1) *
1583		12	std::tgamma(beta + 1) / std::tgamma(alpha + beta + 1);
1584	3/6 ✓ Branch 2 taken 12 times. ✗ Branch 3 not taken. ✓ Branch 7 taken 12 times. ✗ Branch 8 not taken. ✓ Branch 13 taken 12 times. ✗ Branch 14 not taken.	12	xt::xarray<double> w = cte * xt::square(xt::view(v, 0, xt::all())), x = d;
1585	1/2 ✓ Branch 1 taken 12 times. ✗ Branch 2 not taken.	12	return {x, w};
1586		12	}
1587
1588			} // namespace oiseau::utils::integration
1589