17-Jan-2023 07:59:24 sparse_grid_total_poly_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sparse_grid_total_poly(). RULE_TEST Compute and display points and weights of a rule. Rule is Clenshaw Curtis Closed Order = 1 1 0.000000 2.000000 Order = 2 1 -1.000000 1.000000 2 1.000000 1.000000 Order = 3 1 -1.000000 0.333333 2 0.000000 1.333333 3 1.000000 0.333333 Order = 4 1 -1.000000 0.111111 2 -0.500000 0.888889 3 0.500000 0.888889 4 1.000000 0.111111 Order = 5 1 -1.000000 0.066667 2 -0.707107 0.533333 3 0.000000 0.800000 4 0.707107 0.533333 5 1.000000 0.066667 Order = 6 1 -1.000000 0.040000 2 -0.809017 0.360743 3 -0.309017 0.599257 4 0.309017 0.599257 5 0.809017 0.360743 6 1.000000 0.040000 Order = 7 1 -1.000000 0.028571 2 -0.866025 0.253968 3 -0.500000 0.457143 4 0.000000 0.520635 5 0.500000 0.457143 6 0.866025 0.253968 7 1.000000 0.028571 Order = 8 1 -1.000000 0.020408 2 -0.900969 0.190141 3 -0.623490 0.352242 4 -0.222521 0.437208 5 0.222521 0.437208 6 0.623490 0.352242 7 0.900969 0.190141 8 1.000000 0.020408 RULE_TEST Compute and display points and weights of a rule. Rule is Clenshaw Curtis Closed Nested Order = 1 1 0.000000 2.000000 Order = 2 1 0.000000 2.000000 2 1.000000 -0.000000 Order = 3 1 0.000000 1.333333 2 1.000000 0.333333 3 -1.000000 0.333333 Order = 4 1 0.000000 1.333333 2 1.000000 0.333333 3 -1.000000 0.333333 4 0.707107 -0.000000 Order = 5 1 0.000000 0.800000 2 1.000000 0.066667 3 -1.000000 0.066667 4 0.707107 0.533333 5 -0.707107 0.533333 Order = 6 1 0.000000 0.800000 2 1.000000 0.066667 3 -1.000000 0.066667 4 0.707107 0.533333 5 -0.707107 0.533333 6 0.923880 0.000000 Order = 7 1 0.000000 0.692250 2 1.000000 0.247641 3 -1.000000 0.082705 4 0.707107 0.694592 5 -0.707107 0.461337 6 0.923880 -0.304762 7 -0.382683 0.126237 Order = 8 1 0.000000 0.539869 2 1.000000 0.088982 3 -1.000000 0.088982 4 0.707107 0.425584 5 -0.707107 0.425584 6 0.923880 -0.000000 7 -0.382683 0.215499 8 0.382683 0.215499 RULE_TEST Compute and display points and weights of a rule. Rule is Clenshaw Curtis Open Order = 1 1 0.000000 2.000000 Order = 2 1 -0.707107 1.000000 2 0.707107 1.000000 Order = 3 1 -0.866025 0.444444 2 0.000000 1.111111 3 0.866025 0.444444 Order = 4 1 -0.923880 0.264298 2 -0.382683 0.735702 3 0.382683 0.735702 4 0.923880 0.264298 Order = 5 1 -0.951057 0.167781 2 -0.587785 0.525552 3 0.000000 0.613333 4 0.587785 0.525552 5 0.951057 0.167781 Order = 6 1 -0.965926 0.118661 2 -0.707107 0.377778 3 -0.258819 0.503561 4 0.258819 0.503561 5 0.707107 0.377778 6 0.965926 0.118661 Order = 7 1 -0.974928 0.086716 2 -0.781831 0.287831 3 -0.433884 0.398242 4 0.000000 0.454422 5 0.433884 0.398242 6 0.781831 0.287831 7 0.974928 0.086716 Order = 8 1 -0.980785 0.066983 2 -0.831470 0.222988 3 -0.555570 0.324153 4 -0.195090 0.385877 5 0.195090 0.385877 6 0.555570 0.324153 7 0.831470 0.222988 8 0.980785 0.066983 RULE_TEST Compute and display points and weights of a rule. Rule is Clenshaw Curtis Open Nested Order = 1 1 0.000000 2.000000 Order = 2 1 0.000000 2.000000 2 0.707107 -0.000000 Order = 3 1 0.000000 0.666667 2 0.707107 0.666667 3 -0.707107 0.666667 Order = 4 1 0.000000 0.666667 2 0.707107 0.666667 3 -0.707107 0.666667 4 0.923880 -0.000000 Order = 5 1 0.000000 1.043790 2 0.707107 0.384464 3 -0.707107 0.792660 4 0.923880 0.156210 5 -0.382683 -0.377124 Order = 6 1 0.000000 1.577124 2 0.707107 0.855228 3 -0.707107 0.855228 4 0.923880 -0.000000 5 -0.382683 -0.643790 6 0.382683 -0.643790 Order = 7 1 0.000000 0.361905 2 0.707107 0.247619 3 -0.707107 0.247619 4 0.923880 0.177965 5 -0.382683 0.393464 6 0.382683 0.393464 7 -0.923880 0.177965 Order = 8 1 0.000000 0.361905 2 0.707107 0.247619 3 -0.707107 0.247619 4 0.923880 0.177965 5 -0.382683 0.393464 6 0.382683 0.393464 7 -0.923880 0.177965 8 0.980785 0.000000 RULE_TEST Compute and display points and weights of a rule. Rule is Clenshaw Curtis Open Half Order = 1 1 0.000000 2.000000 Order = 2 1 0.707107 1.000000 2 -0.707107 1.000000 Order = 3 1 0.866025 0.444444 2 0.000000 1.111111 3 -0.866025 0.444444 Order = 4 1 0.923880 0.264298 2 0.382683 0.735702 3 -0.382683 0.735702 4 -0.923880 0.264298 Order = 5 1 0.951057 0.167781 2 0.587785 0.525552 3 0.000000 0.613333 4 -0.587785 0.525552 5 -0.951057 0.167781 Order = 6 1 0.965926 0.118661 2 0.707107 0.377778 3 0.258819 0.503561 4 -0.258819 0.503561 5 -0.707107 0.377778 6 -0.965926 0.118661 Order = 7 1 0.974928 0.086716 2 0.781831 0.287831 3 0.433884 0.398242 4 0.000000 0.454422 5 -0.433884 0.398242 6 -0.781831 0.287831 7 -0.974928 0.086716 Order = 8 1 0.980785 0.066983 2 0.831470 0.222988 3 0.555570 0.324153 4 0.195090 0.385877 5 -0.195090 0.385877 6 -0.555570 0.324153 7 -0.831470 0.222988 8 -0.980785 0.066983 RULE_TEST Compute and display points and weights of a rule. Rule is Clenshaw Curtis Open Half Nested Order = 1 1 0.000000 2.000000 Order = 2 1 0.000000 2.000000 2 0.866025 -0.000000 Order = 3 1 0.000000 1.111111 2 0.866025 0.444444 3 -0.866025 0.444444 Order = 4 1 0.000000 0.909357 2 0.781831 0.545321 3 -0.781831 0.545321 4 0.974928 -0.000000 Order = 5 1 0.000000 0.880324 2 0.781831 0.571479 3 -0.781831 0.535276 4 0.974928 -0.016112 5 -0.433884 0.029033 Order = 6 1 0.000000 0.844121 2 0.781831 0.530805 3 -0.781831 0.530805 4 0.974928 -0.000000 5 -0.433884 0.047135 6 0.433884 0.047135 Order = 7 1 0.000000 0.454422 2 0.781831 0.287831 3 -0.781831 0.287831 4 0.974928 0.086716 5 -0.433884 0.398242 6 0.433884 0.398242 7 -0.974928 0.086716 Order = 8 1 0.000000 0.420641 2 0.743145 0.282422 3 -0.743145 0.282422 4 0.951057 0.126434 5 -0.406737 0.380823 6 0.406737 0.380823 7 -0.951057 0.126434 8 0.994522 -0.000000 RULE_TEST Compute and display points and weights of a rule. Rule is Newton Cotes Closed Order = 1 1 0.000000 2.000000 Order = 2 1 -1.000000 1.000000 2 1.000000 1.000000 Order = 3 1 -1.000000 0.333333 2 0.000000 1.333333 3 1.000000 0.333333 Order = 4 1 -1.000000 0.250000 2 -0.333333 0.750000 3 0.333333 0.750000 4 1.000000 0.250000 Order = 5 1 -1.000000 0.155556 2 -0.500000 0.711111 3 0.000000 0.266667 4 0.500000 0.711111 5 1.000000 0.155556 Order = 6 1 -1.000000 0.131944 2 -0.600000 0.520833 3 -0.200000 0.347222 4 0.200000 0.347222 5 0.600000 0.520833 6 1.000000 0.131944 Order = 7 1 -1.000000 0.097619 2 -0.666667 0.514286 3 -0.333333 0.064286 4 0.000000 0.647619 5 0.333333 0.064286 6 0.666667 0.514286 7 1.000000 0.097619 Order = 8 1 -1.000000 0.086921 2 -0.714286 0.414005 3 -0.428571 0.153125 4 -0.142857 0.345949 5 0.142857 0.345949 6 0.428571 0.153125 7 0.714286 0.414005 8 1.000000 0.086921 RULE_TEST Compute and display points and weights of a rule. Rule is Newton Cotes Closed Nested Order = 1 1 0.000000 2.000000 Order = 2 1 0.000000 2.000000 2 -1.000000 0.000000 Order = 3 1 0.000000 1.333333 2 -1.000000 0.333333 3 1.000000 0.333333 Order = 4 1 0.000000 1.333333 2 -1.000000 0.333333 3 1.000000 0.333333 4 -0.500000 0.000000 Order = 5 1 0.000000 0.266667 2 -1.000000 0.155556 3 1.000000 0.155556 4 -0.500000 0.711111 5 0.500000 0.711111 Order = 6 1 0.000000 0.266667 2 -1.000000 0.155556 3 1.000000 0.155556 4 -0.500000 0.711111 5 0.500000 0.711111 6 -0.750000 0.000000 Order = 7 1 0.000000 1.282540 2 -1.000000 0.053968 3 1.000000 0.131368 4 -0.500000 0.033862 5 0.500000 1.117460 6 -0.750000 0.464399 7 0.250000 -1.083598 Order = 8 1 0.000000 3.314286 2 -1.000000 0.121693 3 1.000000 0.121693 4 -0.500000 1.388360 5 0.500000 1.388360 6 -0.750000 0.000000 7 0.250000 -2.167196 8 -0.250000 -2.167196 RULE_TEST Compute and display points and weights of a rule. Rule is Newton Cotes Open Order = 1 1 0.000000 2.000000 Order = 2 1 -0.333333 1.000000 2 0.333333 1.000000 Order = 3 1 -0.500000 1.333333 2 0.000000 -0.666667 3 0.500000 1.333333 Order = 4 1 -0.600000 0.916667 2 -0.200000 0.083333 3 0.200000 0.083333 4 0.600000 0.916667 Order = 5 1 -0.666667 1.100000 2 -0.333333 -1.400000 3 0.000000 2.600000 4 0.333333 -1.400000 5 0.666667 1.100000 Order = 6 1 -0.714286 0.848611 2 -0.428571 -0.629167 3 -0.142857 0.780556 4 0.142857 0.780556 5 0.428571 -0.629167 6 0.714286 0.848611 Order = 7 1 -0.750000 0.973545 2 -0.500000 -2.019048 3 -0.250000 4.647619 4 0.000000 -5.204233 5 0.250000 4.647619 6 0.500000 -2.019048 7 0.750000 0.973545 Order = 8 1 -0.777778 0.797768 2 -0.555556 -1.251339 3 -0.333333 2.217411 4 -0.111111 -0.763839 5 0.111111 -0.763839 6 0.333333 2.217411 7 0.555556 -1.251339 8 0.777778 0.797768 RULE_TEST Compute and display points and weights of a rule. Rule is Newton Cotes Open Nested Order = 1 1 0.000000 2.000000 Order = 2 1 0.000000 2.000000 2 -0.500000 0.000000 Order = 3 1 0.000000 -0.666667 2 -0.500000 1.333333 3 0.500000 1.333333 Order = 4 1 0.000000 -0.666667 2 -0.500000 1.333333 3 0.500000 1.333333 4 -0.750000 0.000000 Order = 5 1 0.000000 4.311111 2 -0.500000 -1.155556 3 0.500000 2.826667 4 -0.750000 0.995556 5 0.250000 -4.977778 Order = 6 1 0.000000 14.266667 2 -0.500000 3.822222 3 0.500000 3.822222 4 -0.750000 -0.000000 5 0.250000 -9.955556 6 -0.250000 -9.955556 Order = 7 1 0.000000 -5.204233 2 -0.500000 -2.019048 3 0.500000 -2.019048 4 -0.750000 0.973545 5 0.250000 4.647619 6 -0.250000 4.647619 7 0.750000 0.973545 Order = 8 1 0.000000 -5.204233 2 -0.500000 -2.019048 3 0.500000 -2.019048 4 -0.750000 0.973545 5 0.250000 4.647619 6 -0.250000 4.647619 7 0.750000 0.973545 8 -0.875000 0.000000 RULE_TEST Compute and display points and weights of a rule. Rule is Newton Cotes Open Half Order = 1 1 0.000000 2.000000 Order = 2 1 -0.500000 1.000000 2 0.500000 1.000000 Order = 3 1 -0.666667 0.750000 2 0.000000 0.500000 3 0.666667 0.750000 Order = 4 1 -0.750000 0.541667 2 -0.250000 0.458333 3 0.250000 0.458333 4 0.750000 0.541667 Order = 5 1 -0.800000 0.477431 2 -0.400000 0.173611 3 0.000000 0.697917 4 0.400000 0.173611 5 0.800000 0.477431 Order = 6 1 -0.833333 0.385938 2 -0.500000 0.217187 3 -0.166667 0.396875 4 0.166667 0.396875 5 0.500000 0.217187 6 0.833333 0.385938 Order = 7 1 -0.857143 0.358001 2 -0.571429 0.012760 3 -0.285714 0.810286 4 0.000000 -0.362095 5 0.285714 0.810286 6 0.571429 0.012760 7 0.857143 0.358001 Order = 8 1 -0.875000 0.305501 2 -0.625000 0.073711 3 -0.375000 0.487528 4 -0.125000 0.133260 5 0.125000 0.133260 6 0.375000 0.487528 7 0.625000 0.073711 8 0.875000 0.305501 RULE_TEST Compute and display points and weights of a rule. Rule is Newton Cotes Open Half Nested Order = 1 1 0.000000 2.000000 Order = 2 1 0.000000 2.000000 2 -0.666667 0.000000 Order = 3 1 0.000000 0.500000 2 -0.666667 0.750000 3 0.666667 0.750000 Order = 4 1 0.000000 -0.041667 2 -0.571429 1.020833 3 0.571429 1.020833 4 -0.857143 0.000000 Order = 5 1 0.000000 2.238194 2 -0.571429 -0.119097 3 0.571429 1.704792 4 -0.857143 0.455972 5 0.285714 -2.279861 Order = 6 1 0.000000 6.797917 2 -0.571429 2.160764 3 0.571429 2.160764 4 -0.857143 0.000000 5 0.285714 -4.559722 6 -0.285714 -4.559722 Order = 7 1 0.000000 -0.362095 2 -0.571429 0.012760 3 0.571429 0.012760 4 -0.857143 0.358001 5 0.285714 0.810286 6 -0.285714 0.810286 7 0.857143 0.358001 Order = 8 1 0.000000 -2.069446 2 -0.533333 -0.732553 3 0.533333 -0.732553 4 -0.800000 0.606304 5 0.266667 2.160972 6 -0.266667 2.160972 7 0.800000 0.606304 8 -0.933333 0.000000 POINT_QUALITY_TEST Determine the "point quality" of nested quadrature rules based on dyadic fractions and on Clenshaw-Curtis points. The "point quality" of a quadrature rule is the maximum absolute value of the Lagrange factor over the interval. Nested Nested Nested N CCC CCC CCO CCO CCOH CCOH 1 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 2 1.0000e+00 2.0000e+00 5.0000e-01 1.7071e+00 5.0000e-01 1.8660e+00 3 3.8489e-01 3.8489e-01 2.5000e-01 5.0000e-01 2.5000e-01 2.5000e-01 4 2.4999e-01 5.0944e-01 1.2500e-01 9.6194e-01 1.2500e-01 7.6773e-01 5 1.1606e-01 1.1606e-01 6.2500e-02 5.9382e-01 6.2500e-02 4.3463e-01 6 6.2497e-02 1.5125e-01 3.1250e-02 8.2107e-01 3.1250e-02 6.2320e-01 7 3.0213e-02 5.0017e-02 1.5625e-02 6.2500e-02 1.5625e-02 1.5625e-02 8 1.5623e-02 6.4264e-02 7.8125e-03 1.2380e-01 7.8125e-03 7.1168e-02 9 7.6640e-03 7.6640e-03 3.9063e-03 9.9647e-02 3.9063e-03 5.6371e-02 10 3.9056e-03 9.9805e-03 1.9531e-03 1.5501e-01 1.9531e-03 8.9506e-02 11 1.9293e-03 5.0084e-03 9.7656e-04 2.6124e-02 9.7656e-04 1.1991e-02 12 9.7632e-04 6.9433e-03 4.8828e-04 4.7845e-02 4.8828e-04 2.2376e-02 13 4.8412e-04 1.1029e-03 2.4414e-04 2.1264e-02 2.4414e-04 9.2239e-03 14 2.4406e-04 1.5320e-03 1.2207e-04 2.5412e-02 1.2207e-04 1.1142e-02 15 1.2129e-04 4.2984e-04 6.1035e-05 4.8828e-04 6.1035e-05 6.1035e-05 16 6.1007e-05 5.0337e-04 3.0518e-05 9.7421e-04 3.0518e-05 4.0077e-04 17 3.0370e-05 3.0370e-05 1.5259e-05 8.7872e-04 1.5259e-05 3.6023e-04 18 1.5250e-05 3.9469e-05 7.6294e-06 1.4362e-03 7.6294e-06 5.9487e-04 19 7.5998e-06 2.3086e-05 3.8147e-06 3.2600e-04 3.8147e-06 1.2446e-04 20 3.8119e-06 3.2521e-05 1.9073e-06 6.1350e-04 1.9073e-06 2.3620e-04 21 1.9015e-06 4.9145e-06 9.5367e-07 3.2430e-04 9.5367e-07 1.2157e-04 22 9.5283e-07 8.0059e-06 4.7684e-07 4.1844e-04 4.7684e-07 1.5797e-04 23 4.7550e-07 3.8790e-06 2.3842e-07 1.8018e-05 2.3842e-07 5.0428e-06 24 2.3816e-07 4.8340e-06 1.1921e-07 3.5260e-05 1.1921e-07 9.9245e-06 25 1.1893e-07 2.6721e-07 5.9605e-08 2.5024e-05 5.9605e-08 6.9535e-06 26 5.9530e-08 4.2546e-07 2.9802e-08 3.6821e-05 2.9802e-08 1.0328e-05 27 2.9714e-08 2.4176e-07 1.4901e-08 4.3478e-06 1.4901e-08 1.0555e-06 28 1.4879e-08 3.2763e-07 7.4506e-09 7.7086e-06 7.4506e-09 1.8901e-06 29 7.4284e-09 4.0064e-08 3.7253e-09 2.8183e-06 3.7253e-09 6.5895e-07 30 3.7190e-09 5.6422e-08 1.8626e-09 3.0946e-06 1.8626e-09 7.2562e-07 31 1.8573e-09 1.3647e-08 9.3132e-10 1.4901e-08 9.3132e-10 9.3132e-10 32 9.2952e-10 1.4547e-08 4.6566e-10 2.9784e-08 4.6566e-10 8.7234e-09 POINT_QUALITY_TEST Determine the "point quality" of nested quadrature rules based on dyadic fractions and on Clenshaw-Curtis points. The "point quality" of a quadrature rule is the maximum absolute value of the Lagrange factor over the interval. Nested Nested Nested N NCC NCC NCO NCO NCOH NCOH 1 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 2 1.0000e+00 2.0000e+00 8.8889e-01 1.5000e+00 7.5000e-01 1.6667e+00 3 3.8489e-01 3.8489e-01 7.5000e-01 7.5000e-01 5.5556e-01 5.5556e-01 4 1.9752e-01 4.3213e-01 6.1440e-01 1.3125e+00 4.1016e-01 1.2507e+00 5 1.1348e-01 1.1348e-01 4.9383e-01 9.8438e-01 3.0240e-01 8.9338e-01 6 6.9219e-02 1.7921e-01 3.9167e-01 1.2305e+00 2.2280e-01 1.1486e+00 7 4.3821e-02 1.0776e-01 3.0762e-01 3.0762e-01 1.6409e-01 1.6409e-01 8 2.8447e-02 1.2083e-01 2.3978e-01 5.7678e-01 1.2082e-01 4.6261e-01 9 1.8801e-02 1.8801e-02 1.8579e-01 5.0468e-01 8.8946e-02 4.0093e-01 10 1.2598e-02 3.3865e-02 1.4326e-01 6.9394e-01 6.5473e-02 5.6130e-01 11 8.5307e-03 2.7257e-02 1.1003e-01 2.6023e-01 4.8190e-02 1.8710e-01 12 5.8251e-03 3.5673e-02 8.4213e-02 4.2287e-01 3.5468e-02 3.1183e-01 13 4.0052e-03 1.1247e-02 6.4270e-02 2.6429e-01 2.6103e-02 1.8710e-01 14 2.7709e-03 1.7663e-02 4.8927e-02 2.9733e-01 1.9210e-02 2.1205e-01 15 1.9250e-03 1.0132e-02 3.7166e-02 3.7166e-02 1.4136e-02 1.4136e-02 16 1.3444e-03 1.0912e-02 2.8178e-02 7.2010e-02 1.0403e-02 4.8522e-02 17 9.4270e-04 9.4270e-04 2.1328e-02 6.7509e-02 7.6552e-03 4.5391e-02 18 6.6117e-04 1.7963e-03 1.6118e-02 9.7044e-02 5.6331e-03 6.5891e-02 19 4.6699e-04 1.6264e-03 1.2165e-02 4.2457e-02 4.1451e-03 2.7632e-02 20 3.2892e-04 2.2858e-03 9.1694e-03 7.1646e-02 3.0501e-03 4.7241e-02 21 2.3362e-04 9.3526e-04 6.9039e-03 4.9257e-02 2.2444e-03 3.2002e-02 22 1.6564e-04 1.5520e-03 5.1929e-03 5.8492e-02 1.6515e-03 3.8196e-02 23 1.1738e-04 1.0235e-03 3.9023e-03 1.0967e-02 1.2152e-03 6.1606e-03 24 8.3864e-05 1.1866e-03 2.9300e-03 1.9878e-02 8.9416e-04 1.1328e-02 25 5.9820e-05 1.9355e-04 2.1982e-03 1.6151e-02 6.5793e-04 9.1352e-03 26 4.2605e-05 3.4616e-04 1.6479e-03 2.1198e-02 4.8411e-04 1.2082e-02 27 3.0353e-05 2.7293e-04 1.2346e-03 6.6245e-03 3.5621e-04 3.5077e-03 28 2.1815e-05 3.5234e-04 9.2435e-04 1.0351e-02 2.6210e-04 5.5444e-03 29 1.5660e-05 1.0304e-04 6.9166e-04 5.8223e-03 1.9285e-04 3.0405e-03 30 1.1230e-05 1.5894e-04 5.1726e-04 6.1862e-03 1.4190e-04 3.2366e-03 31 8.0451e-06 8.6220e-05 3.8664e-04 3.8664e-04 1.0441e-04 1.0441e-04 32 5.7577e-06 8.9881e-05 2.8886e-04 7.6119e-04 7.6822e-05 4.3098e-04 WEIGHT_QUALITY_TEST Determine the "weight quality" of nested quadrature rules based on dyadic fractions and on Clenshaw-Curtis points. The "quality" of a quadrature rule is the sum the absolute value of the weights. Nested Nested Nested CCC CCC CCO CCO CCOH CCOH N Quality Quality Quality Quality Quality Quality 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 1 1 4 1 1 1 1 1 1 5 1 1 1 1.377 1 1.016 6 1 1 1 2.288 1 1 7 1 1.305 1 1 1 1 8 1 1 1 1 1 1 9 1 1 1 1.212 1 1.004 10 1 1 1 1.532 1 1.029 11 1 1.04 1 1.204 1 1.008 12 1 1.031 1 2.077 1 1.008 13 1 1.057 1 1.93 1 1.019 14 1 1.036 1 4.685 1 1 15 1 1.503 1 1 1 1 16 1 1 1 1 1 1 17 1 1 1 1.114 1 1.001 18 1 1 1 1.394 1 1.013 19 1 1.009 1 1.127 1 1.004 20 1 1.009 1 1.951 1 1.027 21 1 1.009 1 1.635 1 1.018 22 1 1.039 1 4.345 1 1.059 23 1 1.033 1 1.133 1 1.003 24 1 1.043 1 1.73 1 1.006 25 1 1.013 1 2.327 1 1.019 26 1 1.043 1 7.227 1 1.072 27 1 1.127 1 1.624 1 1.01 28 1 1.205 1 5.714 1 1.011 29 1 1.099 0.9999 3.594 1 1.024 30 1 1.149 0.9998 9.417 0.9998 1 31 1 1.63 1 1 1.001 1 32 1 1 0.9988 1 0.9982 1 WEIGHT_QUALITY_TEST Determine the "weight quality" of nested quadrature rules based on dyadic fractions and on Clenshaw-Curtis points. The "quality" of a quadrature rule is the sum the absolute value of the weights. Nested Nested Nested NCC NCC NCO NCO NCOH NCOH N Quality Quality Quality Quality Quality Quality 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1.667 1.667 1 1 4 1 1 1 1.667 1 1.042 5 1 1 3.8 7.133 1 3.399 6 1 1 2.258 20.91 1 10.12 7 1 2.084 10.24 10.24 1.362 1.362 8 1 5.334 5.03 10.24 1 4.535 9 1.451 1.451 30.44 75.26 3.433 29.55 10 1 1.451 14.06 289.5 1.728 113.9 11 3.065 8.442 96.08 187.4 9.87 59.19 12 1.589 32.22 40.74 516.1 4.205 170.7 13 7.532 19.57 315.7 1085 30.22 310.9 14 3.247 56.68 125.6 5110 12.3 1477 15 20.34 106.4 1068 1068 96.31 96.31 16 8.348 476.7 400.1 1068 36.63 382.7 17 58.46 58.46 3687 1.333e+04 316 4529 18 22.22 58.46 1311 4.68e+04 114.2 1.591e+04 19 175.5 671.2 1.294e+04 3.727e+04 1060 1.163e+04 20 63.25 2427 4390 9.674e+04 364.6 3.044e+04 21 544.2 1848 4.604e+04 2.736e+05 3617 8.216e+04 22 186.4 4955 1.495e+04 1.572e+06 1191 4.659e+05 23 1732 1.34e+04 1.655e+05 3.583e+05 1.252e+04 8.445e+04 24 567.4 7.517e+04 5.167e+04 7.508e+05 3961 1.843e+05 25 5626 1.515e+04 6.005e+05 4.767e+06 4.389e+04 1.118e+06 26 1770 3.263e+04 1.806e+05 2.098e+07 1.337e+04 4.855e+06 27 1.86e+04 1.986e+05 2.195e+06 9.685e+06 1.554e+05 1.973e+06 28 5634 8.762e+05 6.38e+05 2.925e+07 4.569e+04 6.021e+06 29 6.24e+04 3.761e+05 8.075e+06 4.31e+07 5.548e+05 8.238e+06 30 1.825e+04 1.163e+06 2.273e+06 2.974e+08 1.579e+05 5.696e+07 31 2.12e+05 1.645e+06 2.988e+07 2.988e+07 1.996e+06 1.996e+06 32 6e+04 1.104e+07 8.158e+06 2.988e+07 5.509e+05 9.014e+06 sparse_grid_total_poly_test(): Normal end of execution. 17-Jan-2023 07:59:25