Fri Jun 27 10:30:49 2025 test_int_2d_test(): python version: 3.10.12 numpy version: 1.26.4 Test test_int_2d(). test_int_2d_test01(): Use a Monte Carlo rule. Repeatedly multiply the number of points by 16. Problem Points Approx Error 1 1 1.953559e+00 3.086249e-01 1 4 1.480443e+00 1.644914e-01 1 16 1.266535e+00 3.783990e-01 1 64 1.721821e+00 7.688724e-02 1 256 1.760885e+00 1.159510e-01 1 1024 1.729750e+00 8.481547e-02 1 4096 1.635884e+00 9.050345e-03 1 16384 1.666693e+00 2.175874e-02 1 65536 1.636625e+00 8.308918e-03 1 262144 1.647149e+00 2.215086e-03 1 1048576 1.642701e+00 2.232987e-03 1 4194304 1.643640e+00 1.293688e-03 1 Exact 1.644934e+00 2 1 5.066571e+00 7.113990e-01 2 4 4.026998e+00 3.281746e-01 2 16 4.232902e+00 1.222698e-01 2 64 4.286285e+00 6.888725e-02 2 256 4.322039e+00 3.313318e-02 2 1024 4.357911e+00 2.738798e-03 2 4096 4.361936e+00 6.763678e-03 2 16384 4.355130e+00 4.172381e-05 2 65536 4.353714e+00 1.458221e-03 2 262144 4.355251e+00 7.889174e-05 2 1048576 4.356121e+00 9.489673e-04 2 4194304 4.355605e+00 4.324804e-04 2 Exact 4.355172e+00 3 1 2.630943e+00 4.932518e-01 3 4 3.314263e+00 1.900690e-01 3 16 3.024795e+00 9.939897e-02 3 64 2.960511e+00 1.636834e-01 3 256 3.202465e+00 7.827095e-02 3 1024 3.097683e+00 2.651095e-02 3 4096 3.138541e+00 1.434689e-02 3 16384 3.142140e+00 1.794523e-02 3 65536 3.129885e+00 5.691034e-03 3 262144 3.125664e+00 1.469412e-03 3 1048576 3.124425e+00 2.302743e-04 3 4194304 3.123893e+00 3.011150e-04 3 Exact 3.124194e+00 4 1 1.876331e+00 7.026765e-01 4 4 3.346679e+00 7.676714e-01 4 16 3.154025e+00 5.750171e-01 4 64 2.634432e+00 5.542410e-02 4 256 2.484069e+00 9.493837e-02 4 1024 2.598014e+00 1.900668e-02 4 4096 2.572080e+00 6.927716e-03 4 16384 2.571135e+00 7.872593e-03 4 65536 2.577462e+00 1.545884e-03 4 262144 2.580504e+00 1.496680e-03 4 1048576 2.579355e+00 3.469926e-04 4 4194304 2.579665e+00 6.577681e-04 4 Exact 2.579008e+00 5 1 1.759905e-01 2.684540e-01 5 4 5.068986e-01 6.245419e-02 5 16 4.558163e-01 1.137183e-02 5 64 4.669113e-01 2.246688e-02 5 256 4.480714e-01 3.626963e-03 5 1024 4.400785e-01 4.365986e-03 5 4096 4.404389e-01 4.005550e-03 5 16384 4.434955e-01 9.489092e-04 5 65536 4.430062e-01 1.438265e-03 5 262144 4.450225e-01 5.780533e-04 5 1048576 4.443889e-01 5.553124e-05 5 4194304 4.442557e-01 1.887314e-04 5 Exact 4.444444e-01 6 1 9.724296e-01 8.905866e-01 6 4 1.491242e+00 3.717746e-01 6 16 2.252168e+00 3.891518e-01 6 64 1.764012e+00 9.900438e-02 6 256 1.842893e+00 2.012349e-02 6 1024 1.833705e+00 2.931130e-02 6 4096 1.887796e+00 2.477944e-02 6 16384 1.867311e+00 4.294961e-03 6 65536 1.864309e+00 1.293223e-03 6 262144 1.866929e+00 3.912530e-03 6 1048576 1.861940e+00 1.076065e-03 6 4194304 1.863225e+00 2.091579e-04 6 Exact 1.863016e+00 7 1 2.898895e-01 2.434439e-01 7 4 4.401313e-01 9.320203e-02 7 16 5.765879e-01 4.325453e-02 7 64 5.574954e-01 2.416206e-02 7 256 5.250308e-01 8.302550e-03 7 1024 5.366147e-01 3.281392e-03 7 4096 5.378981e-01 4.564722e-03 7 16384 5.336748e-01 3.414537e-04 7 65536 5.352211e-01 1.887731e-03 7 262144 5.331774e-01 1.559403e-04 7 1048576 5.331808e-01 1.525777e-04 7 4194304 5.329567e-01 3.766453e-04 7 Exact 5.333333e-01 8 1 2.730850e-02 2.639547e+00 8 4 3.084048e+00 4.171922e-01 8 16 3.429089e+00 7.622334e-01 8 64 3.708759e+00 1.041903e+00 8 256 2.185394e+00 4.814615e-01 8 1024 2.792068e+00 1.252119e-01 8 4096 2.751897e+00 8.504161e-02 8 16384 2.614789e+00 5.206721e-02 8 65536 2.682992e+00 1.613602e-02 8 262144 2.652190e+00 1.466616e-02 8 1048576 2.664319e+00 2.537061e-03 8 4194304 2.667270e+00 4.139660e-04 8 Exact 2.666856e+00 test_int_2d_test02(): Apply a product of composite midpoint rules. Repeatedly multiply the number of points by 16. Problem Points Approx Error 1 1 1.000000e+00 6.449341e-01 1 4 7.500000e-01 8.949341e-01 1 16 1.343527e+00 3.014073e-01 1 64 1.590788e+00 5.414642e-02 1 256 1.667261e+00 2.232670e-02 1 1024 1.680119e+00 3.518519e-02 1 4096 1.674151e+00 2.921696e-02 1 16384 1.665206e+00 2.027230e-02 1 65536 1.657852e+00 1.291835e-02 1 262144 1.652769e+00 7.834720e-03 1 1048576 1.649535e+00 4.600470e-03 1 4194304 1.647574e+00 2.640431e-03 1 Exact 1.644934e+00 2 1 0.000000e+00 4.355172e+00 2 4 0.000000e+00 4.355172e+00 2 16 3.127551e+00 1.227621e+00 2 64 4.096851e+00 2.583213e-01 2 256 4.346757e+00 8.415383e-03 2 1024 4.391165e+00 3.599237e-02 2 4096 4.386563e+00 3.139088e-02 2 16384 4.375366e+00 2.019388e-02 2 65536 4.366795e+00 1.162241e-02 2 262144 4.361505e+00 6.333313e-03 2 1048576 4.358519e+00 3.346768e-03 2 4194304 4.356908e+00 1.735912e-03 2 Exact 4.355172e+00 3 1 2.000000e+00 1.124194e+00 3 4 1.914214e+00 1.209981e+00 3 16 2.827139e+00 2.970555e-01 3 64 3.092188e+00 3.200663e-02 3 256 3.148324e+00 2.412970e-02 3 1024 3.149788e+00 2.559341e-02 3 4096 3.141548e+00 1.735339e-02 3 16384 3.134415e+00 1.022095e-02 3 65536 3.129832e+00 5.638014e-03 3 262144 3.127195e+00 3.000606e-03 3 1048576 3.125758e+00 1.563225e-03 3 4194304 3.124998e+00 8.035293e-04 3 Exact 3.124194e+00 4 1 1.632993e+00 9.460144e-01 4 4 1.615355e+00 9.636525e-01 4 16 2.364570e+00 2.144375e-01 4 64 2.571164e+00 7.843694e-03 4 256 2.608881e+00 2.987356e-02 4 1024 2.605227e+00 2.621954e-02 4 4096 2.595889e+00 1.688174e-02 4 16384 2.588719e+00 9.711836e-03 4 65536 2.584296e+00 5.288189e-03 4 262144 2.581800e+00 2.792406e-03 4 1048576 2.580455e+00 1.447466e-03 4 4194304 2.579749e+00 7.415562e-04 4 Exact 2.579008e+00 5 1 0.000000e+00 4.444444e-01 5 4 2.500000e-01 1.944444e-01 5 16 3.581564e-01 8.628802e-02 5 64 4.054576e-01 3.898689e-02 5 256 4.264989e-01 1.794552e-02 5 1024 4.360404e-01 8.404061e-03 5 4096 4.404494e-01 3.995075e-03 5 16384 4.425217e-01 1.922765e-03 5 65536 4.435099e-01 9.345166e-04 5 262144 4.439868e-01 4.576464e-04 5 1048576 4.442190e-01 2.253953e-04 5 4194304 4.443330e-01 1.114781e-04 5 Exact 4.444444e-01 6 1 7.000000e+00 5.136984e+00 6 4 7.000000e+00 5.136984e+00 6 16 3.500000e+00 1.636984e+00 6 64 2.579082e+00 7.160654e-01 6 256 2.193750e+00 3.307338e-01 6 1024 2.022820e+00 1.598034e-01 6 4096 1.941561e+00 7.854505e-02 6 16384 1.901951e+00 3.893520e-02 6 65536 1.882398e+00 1.938216e-02 6 262144 1.872687e+00 9.670648e-03 6 1048576 1.867846e+00 4.830108e-03 6 4194304 1.865430e+00 2.413738e-03 6 Exact 1.863016e+00 7 1 0.000000e+00 5.333333e-01 7 4 5.000000e-01 3.333333e-02 7 16 5.456305e-01 1.229716e-02 7 64 5.480304e-01 1.469708e-02 7 256 5.434938e-01 1.016045e-02 7 1024 5.393772e-01 6.043857e-03 7 4096 5.366916e-01 3.358220e-03 7 16384 5.351308e-01 1.797451e-03 7 65536 5.342739e-01 9.405232e-04 7 262144 5.338184e-01 4.850465e-04 7 1048576 5.335811e-01 2.477555e-04 7 4194304 5.334591e-01 1.257294e-04 7 Exact 5.333333e-01 8 1 1.034984e-06 2.666855e+00 8 4 8.458460e-01 1.821010e+00 8 16 1.604593e+00 1.062263e+00 8 64 2.298461e+00 3.683947e-01 8 256 2.502902e+00 1.639538e-01 8 1024 2.589564e+00 7.729163e-02 8 4096 2.629342e+00 3.751346e-02 8 16384 2.648378e+00 1.847806e-02 8 65536 2.657686e+00 9.169893e-03 8 262144 2.662288e+00 4.567727e-03 8 1048576 2.664576e+00 2.279566e-03 8 4194304 2.665717e+00 1.138710e-03 8 Exact 2.666856e+00 test_int_2d_test03(): Use a product of Gauss-Legendre rules. The 1D rules essentially double in order. Problem Points Approx Error 1 1 1.33333 0.311601 1 9 1.58123 0.0637073 1 49 1.63077 0.0141646 1 225 1.6416 0.00333146 1 961 1.64413 0.000807489 1 3969 1.64474 0.000198756 1 16129 1.64488 4.93032e-05 1 65025 1.64492 1.22778e-05 1 Exact 1.64493 2 1 4 0.355172 2 9 4.30864 0.0465302 2 49 4.3499 0.00526763 2 225 4.35456 0.000611658 2 961 4.3551 7.33017e-05 2 3969 4.35516 8.96068e-06 2 16129 4.35517 1.10734e-06 2 65025 4.35517 1.37619e-07 2 Exact 4.35517 3 1 2.82843 0.295767 3 9 3.10384 0.020355 3 49 3.12224 0.00195471 3 225 3.12398 0.000218752 3 961 3.12417 2.59885e-05 3 3969 3.12419 3.17026e-06 3 16129 3.12419 3.91572e-07 3 65025 3.12419 4.86577e-08 3 Exact 3.12419 4 1 2.3094 0.269606 4 9 2.55776 0.0212471 4 49 2.57694 0.00206741 4 225 2.57878 0.000231912 4 961 2.57898 2.75674e-05 4 3969 2.579 3.36332e-06 4 16129 2.57901 4.15432e-07 4 65025 2.57901 5.1623e-08 4 Exact 2.57901 5 1 0.5 0.0555556 5 9 0.447801 0.00335694 5 49 0.444773 0.000328619 5 225 0.444481 3.69473e-05 5 961 0.444449 4.39436e-06 5 3969 0.444445 5.36199e-07 5 16129 0.444445 6.62327e-08 5 65025 0.444444 8.23038e-09 5 Exact 0.444444 6 1 1 0.863016 6 9 2.06173 0.198712 6 49 1.8629 0.000113944 6 225 1.86838 0.00536441 6 961 1.86276 0.000251951 6 3969 1.86315 0.000137089 6 16129 1.863 1.22869e-05 6 65025 1.86302 5.37063e-06 6 Exact 1.86302 7 1 0 0.533333 7 9 0.443145 0.0901887 7 49 0.504725 0.0286088 7 225 0.523695 0.00963804 7 961 0.530005 0.00332792 7 3969 0.53217 0.00116284 7 16129 0.532925 0.00040872 7 65025 0.533189 0.000144081 7 Exact 0.533333 8 1 0.277725 2.38913 8 9 1.91043 0.756428 8 49 2.6705 0.00364122 8 225 2.66686 1.41248e-10 8 961 2.66686 8.88178e-16 8 3969 2.66686 0 8 16129 2.66686 1.33227e-15 8 65025 2.66686 1.33227e-15 8 Exact 2.66686 test_int_2d_test(): Normal end of execution. Fri Jun 27 10:30:54 2025