1565 const unsigned int n_points_1D,
1566 const bool use_odd_order)
1578 std::array<double, dim + 1> centroid;
1579 std::fill(centroid.begin(), centroid.end(), 1.0 / (dim + 1.0));
1580 std::vector<std::vector<std::array<double, dim + 1>>> b_point_permutations;
1581 std::vector<double> b_weights;
1591 auto process_point_1 = [&](
const double a,
const double w) {
1592 const double b = 1.0 - dim * a;
1593 std::array<double, dim + 1> b_point;
1594 std::fill(b_point.begin(), b_point.begin() + dim, a);
1597 b_weights.push_back(w);
1598 b_point_permutations.push_back(all_permutations(b_point));
1603 auto process_point_2 = [&](
const double a,
const double w) {
1605 const double b = (1.0 - 2.0 * a) / 2.0;
1606 std::array<double, dim + 1> b_point;
1607 std::fill(b_point.begin(), b_point.begin() + dim - 1, a);
1608 b_point[dim - 1] = b;
1611 b_weights.push_back(w);
1612 b_point_permutations.push_back(all_permutations(b_point));
1618 auto process_point_3 = [&](
const double a,
const double b,
const double w) {
1619 const double c = 1.0 - (dim - 1.0) * a - b;
1620 std::array<double, dim + 1> b_point;
1621 std::fill(b_point.begin(), b_point.begin() + dim - 1, a);
1622 b_point[dim - 1] = b;
1625 b_weights.push_back(w);
1626 b_point_permutations.push_back(all_permutations(b_point));
1629 switch (n_points_1D)
1638 b_point_permutations.push_back({centroid});
1639 b_weights.push_back(1.0000000000000000e+00);
1644 process_point_1(1.6666666666666669e-01,
1645 3.3333333333333331e-01);
1652 b_point_permutations.push_back({centroid});
1653 b_weights.push_back(1.0000000000000000e+00);
1658 process_point_1(1.3819660112501050e-01,
1659 2.5000000000000000e-01);
1671 process_point_1(9.1576213509770743e-02, 1.0995174365532187e-01);
1672 process_point_1(4.4594849091596489e-01, 2.2338158967801147e-01);
1678 process_point_1(3.2816330251638171e-01,
1679 1.3621784253708741e-01);
1680 process_point_1(1.0804724989842859e-01,
1681 1.1378215746291261e-01);
1700 b_point_permutations.push_back({centroid});
1701 b_weights.push_back(2.2500000000000001e-01);
1702 process_point_1(1.0128650732345634e-01,
1703 1.2593918054482714e-01);
1704 process_point_1(4.7014206410511511e-01,
1705 1.3239415278850619e-01);
1710 process_point_1(6.3089014491502227e-02,
1711 5.0844906370206819e-02);
1712 process_point_1(2.4928674517091043e-01,
1713 1.1678627572637937e-01);
1714 process_point_3(5.3145049844816938e-02,
1715 3.1035245103378439e-01,
1716 8.2851075618373571e-02);
1723 process_point_1(3.1088591926330061e-01,
1724 1.1268792571801590e-01);
1725 process_point_1(9.2735250310891248e-02,
1726 7.3493043116361956e-02);
1727 process_point_2(4.5503704125649642e-02,
1728 4.2546020777081472e-02);
1733 process_point_1(4.0673958534611372e-02,
1734 1.0077211055320640e-02);
1735 process_point_1(3.2233789014227548e-01,
1736 5.5357181543654717e-02);
1737 process_point_1(2.1460287125915201e-01,
1738 3.9922750258167487e-02);
1739 process_point_3(6.3661001875017442e-02,
1740 6.0300566479164919e-01,
1741 4.8214285714285710e-02);
1755 process_point_1(3.3730648554587850e-02,
1756 1.6545050110792131e-02);
1757 process_point_1(4.7430969250471822e-01,
1758 7.7086646185986069e-02);
1759 process_point_1(2.4157738259540357e-01,
1760 1.2794417123015558e-01);
1761 process_point_3(4.7036644652595216e-02,
1762 1.9868331479735168e-01,
1763 5.5878732903199779e-02);
1768 b_point_permutations.push_back({centroid});
1769 b_weights.push_back(1.4431560767778717e-01);
1770 process_point_1(5.0547228317030957e-02,
1771 3.2458497623198079e-02);
1772 process_point_1(4.5929258829272313e-01,
1773 9.5091634267284619e-02);
1774 process_point_1(1.7056930775176021e-01,
1775 1.0321737053471824e-01);
1776 process_point_3(8.3947774099575878e-03,
1777 2.6311282963463811e-01,
1778 2.7230314174434993e-02);
1785 b_point_permutations.push_back({centroid});
1786 b_weights.push_back(9.5485289464130846e-02);
1787 process_point_1(3.1570114977820279e-01,
1788 4.2329581209967028e-02);
1789 process_point_2(5.0489822598396350e-02,
1790 3.1896927832857580e-02);
1791 process_point_3(1.8883383102600099e-01,
1792 5.7517163758699996e-01,
1793 3.7207130728334620e-02);
1794 process_point_3(2.1265472541483140e-02,
1795 8.1083024109854862e-01,
1796 8.1107708299033420e-03);
1801 process_point_1(1.0795272496221089e-01,
1802 2.6426650908408830e-02);
1803 process_point_1(1.8510948778258660e-01,
1804 5.2031747563738531e-02);
1805 process_point_1(4.2316543684767283e-02,
1806 7.5252561535401989e-03);
1807 process_point_1(3.1418170912403898e-01,
1808 4.1763782856934897e-02);
1809 process_point_2(4.3559132858383021e-01,
1810 3.6280930261308818e-02);
1811 process_point_3(2.1433930127130570e-02,
1812 7.1746406342630831e-01,
1813 7.1569028908444327e-03);
1814 process_point_3(2.0413933387602909e-01,
1815 5.8379737830214440e-01,
1816 1.5453486150960340e-02);
1830 b_point_permutations.push_back({centroid});
1831 b_weights.push_back(9.7135796282798836e-02);
1832 process_point_1(4.4729513394452691e-02,
1833 2.5577675658698031e-02);
1834 process_point_1(4.8968251919873762e-01,
1835 3.1334700227139071e-02);
1836 process_point_1(4.3708959149293664e-01,
1837 7.7827541004774278e-02);
1838 process_point_1(1.8820353561903275e-01,
1839 7.9647738927210249e-02);
1840 process_point_3(3.6838412054736258e-02,
1841 2.2196298916076568e-01,
1842 4.3283539377289376e-02);
1847 b_point_permutations.push_back({centroid});
1848 b_weights.push_back(8.1743329146285973e-02);
1849 process_point_1(3.2055373216943517e-02,
1850 1.3352968813149567e-02);
1851 process_point_1(1.4216110105656438e-01,
1852 4.5957963604744731e-02);
1853 process_point_3(2.8367665339938453e-02,
1854 1.6370173373718250e-01,
1855 2.5297757707288385e-02);
1856 process_point_3(2.9619889488729734e-02,
1857 3.6914678182781102e-01,
1858 3.4184648162959429e-02);
1859 process_point_3(1.4813288578382056e-01,
1860 3.2181299528883545e-01,
1861 6.3904906396424044e-02);
1868 b_point_permutations.push_back({centroid});
1869 b_weights.push_back(5.8010548912480253e-02);
1870 process_point_1(6.1981697552226933e-10,
1871 6.4319281759256394e-05);
1872 process_point_1(1.6077453539526160e-01,
1873 2.3173338462425461e-02);
1874 process_point_1(3.2227652182142102e-01,
1875 2.9562912335429289e-02);
1876 process_point_1(4.5108918345413578e-02,
1877 8.0639799796161822e-03);
1878 process_point_2(1.1229654600437609e-01,
1879 3.8134080103702457e-02);
1880 process_point_3(4.5887144875245922e-01,
1881 2.5545792330413102e-03,
1882 8.3844221982985519e-03);
1883 process_point_3(3.3775870685338598e-02,
1884 7.1835032644207453e-01,
1885 1.0234559352745330e-02);
1886 process_point_3(1.8364136980992790e-01,
1887 3.4415910578175279e-02,
1888 2.0524915967988139e-02);
1893 b_point_permutations.push_back({centroid});
1894 b_weights.push_back(4.7399773556020743e-02);
1895 process_point_1(3.1225006869518868e-01,
1896 2.6937059992268701e-02);
1897 process_point_1(1.1430965385734609e-01,
1898 9.8691597167933822e-03);
1899 process_point_3(4.1043073921896539e-01,
1900 1.6548602561961109e-01,
1901 1.1393881220195230e-02);
1902 process_point_3(6.1380088247906528e-03,
1903 9.4298876734520487e-01,
1904 3.6194434433925362e-04);
1905 process_point_3(1.2105018114558939e-01,
1906 4.7719037990428043e-01,
1907 2.5739731980456069e-02);
1908 process_point_3(3.2779468216442620e-02,
1909 5.9425626948000698e-01,
1910 1.0135871679755789e-02);
1911 process_point_3(3.2485281564823047e-02,
1912 8.0117728465834437e-01,
1913 6.5761472770359038e-03);
1914 process_point_3(1.7497934218393901e-01,
1915 6.2807184547536599e-01,
1916 1.2907035798861989e-02);
1929 b_point_permutations.push_back({centroid});
1930 b_weights.push_back(8.5761179732224219e-02);
1931 process_point_1(2.8485417614371900e-02, 1.0431870512894697e-02);
1932 process_point_1(4.9589190096589092e-01, 1.6606273054585369e-02);
1933 process_point_1(1.0263548271224643e-01, 3.8630759237019321e-02);
1934 process_point_1(4.3846592676435220e-01, 6.7316154079468296e-02);
1935 process_point_1(2.1021995670317828e-01, 7.0515684111716576e-02);
1936 process_point_3(7.3254276860644785e-03,
1937 1.4932478865208237e-01,
1938 1.0290289572953278e-02);
1939 process_point_3(4.6010500165429957e-02,
1940 2.8958112563770588e-01,
1941 4.0332476640500554e-02);
1946 process_point_1(2.4646363436335583e-02, 7.9316425099736389e-03);
1947 process_point_1(4.8820375094554153e-01, 2.4266838081452032e-02);
1948 process_point_1(1.0925782765935427e-01, 2.8486052068877544e-02);
1949 process_point_1(4.4011164865859309e-01, 4.9918334928060942e-02);
1950 process_point_1(2.7146250701492608e-01, 6.2541213195902765e-02);
1951 process_point_3(2.1382490256170616e-02,
1952 1.2727971723358933e-01,
1953 1.5083677576511438e-02);
1954 process_point_3(2.3034156355267121e-02,
1955 2.9165567973834094e-01,
1956 2.1783585038607559e-02);
1957 process_point_3(1.1629601967792658e-01,
1958 2.5545422863851736e-01,
1959 4.3227363659414209e-02);
1968 b_point_permutations.push_back({centroid});
1969 b_weights.push_back(6.7960036586831640e-02);
1970 process_point_1(2.1509681108843159e-02, 6.0523371035391717e-03);
1971 process_point_1(4.8907694645253935e-01, 2.3994401928894731e-02);
1972 process_point_1(4.2694141425980042e-01, 5.5601967530453329e-02);
1973 process_point_1(2.2137228629183292e-01, 5.8278485119199981e-02);
1974 process_point_3(5.1263891023823893e-03,
1975 2.7251581777342970e-01,
1976 9.5906810035432631e-03);
1977 process_point_3(2.4370186901093827e-02,
1978 1.1092204280346341e-01,
1979 1.4965401105165668e-02);
1980 process_point_3(8.7895483032197297e-02,
1981 1.6359740106785048e-01,
1982 2.4179039811593819e-02);
1983 process_point_3(6.8012243554206653e-02,
1984 3.0844176089211778e-01,
1985 3.4641276140848373e-02);
1990 process_point_1(1.9390961248701044e-02, 4.9234036024000819e-03);
1991 process_point_1(6.1799883090872587e-02, 1.4433699669776668e-02);
1992 process_point_1(4.8896391036217862e-01, 2.1883581369428889e-02);
1993 process_point_1(4.1764471934045394e-01, 3.2788353544125348e-02);
1994 process_point_1(1.7720553241254344e-01, 4.2162588736993016e-02);
1995 process_point_1(2.7347752830883865e-01, 5.1774104507291585e-02);
1996 process_point_3(1.2683309328720416e-03,
1997 1.1897449769695684e-01,
1998 5.0102288385006719e-03);
1999 process_point_3(1.4646950055654417e-02,
2000 2.9837288213625779e-01,
2001 1.4436308113533840e-02);
2002 process_point_3(5.7124757403647919e-02,
2003 1.7226668782135557e-01,
2004 2.4665753212563674e-02);
2005 process_point_3(9.2916249356971847e-02,
2006 3.3686145979634496e-01,
2007 3.8571510787060684e-02);
2015 for (
unsigned int permutation_n = 0; permutation_n < b_weights.size();
2018 for (
const std::array<double, dim + 1> &b_point :
2019 b_point_permutations[permutation_n])
2021 const double volume = (dim == 2 ? 1.0 / 2.0 : 1.0 / 6.0);
2022 this->
weights.emplace_back(volume * b_weights[permutation_n]);
2024 for (
int d = 0; d < dim; ++d)
2025 c_point[d] = b_point[d];