20-Jun-2023 12:04:42 sparse_grid_hw_test(): MATLAB/Octave version 5.2.0 Test sparse_grid_hw(). cce_test(): cce_order() + cc(): Clenshaw Curtis Exponential quadrature over [0,1]: Exact integral is 0.19146246 Level Nodes Estimate Error 1 1 0.19333 0.0097753 2 3 0.19147 5.6817e-05 3 5 0.19146 3.9596e-08 4 9 0.19146 6.5235e-15 5 17 0.19146 1.4497e-16 6 33 0.19146 2.8993e-16 7 65 0.19146 1.4497e-16 8 129 0.19146 2.8993e-16 9 257 0.19146 1.4497e-16 10 513 0.19146 4.349e-16 cce_sparse_test(): cce() creates a sparse grid: Sparse Clenshaw-Curtis Exponential sparse grid. Exact integral is 6.61967e-08 D Level Nodes SG error MC error 10 1 1 0.10217 0.11517 10 2 21 0.0039099 0.026319 10 3 221 6.4537e-05 0.0079425 10 4 1581 1.2369e-07 0.0029239 10 5 8801 1.0089e-08 0.0012371 10 6 41265 8.7633e-11 0.0005562 10 7 171425 3.568e-12 0.00027246 ccl_test(): ccl_order() + cc() Clenshaw Curtis Linear (CCL) quadrature over [0,1]: Exact integral is 0.19146246 Level Nodes Estimate Error 1 1 0.19333 0.0097753 2 3 0.19147 5.6817e-05 3 5 0.19146 3.9596e-08 4 7 0.19146 1.1782e-11 5 9 0.19146 6.5235e-15 6 11 0.19146 1.4497e-16 7 13 0.19146 1.4497e-16 8 15 0.19146 1.4497e-16 9 17 0.19146 1.4497e-16 10 19 0.19146 1.4497e-16 ccl_sparse_test(): ccl() builds a sparse grid: Clenshaw-Curtis Linear sparse grid. Exact integral is 6.61967e-08 D Level Nodes SG error MC error 10 1 1 0.10217 0.12139 10 2 21 0.0039099 0.025147 10 3 221 6.4537e-05 0.007903 10 4 1581 1.2382e-07 0.0029612 10 5 8761 1.0078e-08 0.0012548 10 6 40425 8.7383e-11 0.00057262 10 7 162385 3.9295e-12 0.0002784 ccs_test(): ccs_order() + cc(): Clenshaw Curtis Slow quadrature over [0,1]: Exact integral is 0.19146246 Level Nodes Estimate Error 1 1 0.19333 0.0097753 2 3 0.19147 5.6817e-05 3 5 0.19146 3.9596e-08 4 9 0.19146 6.5235e-15 5 9 0.19146 6.5235e-15 6 17 0.19146 1.4497e-16 7 17 0.19146 1.4497e-16 8 17 0.19146 1.4497e-16 9 17 0.19146 1.4497e-16 10 33 0.19146 2.8993e-16 ccs_sparse_test(): ccs() builds a sparse grid: Clenshaw-Curtis Slow sparse grid. Exact integral is 6.61967e-08 D Level Nodes SG error MC error 10 1 1 0.10217 0.11619 10 2 21 0.0039099 0.026241 10 3 221 6.4537e-05 0.0076836 10 4 1581 1.2369e-07 0.0029459 10 5 8721 1.0089e-08 0.0012386 10 6 39665 8.8015e-11 0.00055534 10 7 155105 3.3849e-12 0.00029312 get_seq_test(): get_seq() returns all D-dimensional vectors that sum to NORM. D = 3 NORM = 6 1: 4 1 1 2: 3 2 1 3: 3 1 2 4: 2 3 1 5: 2 2 2 6: 2 1 3 7: 1 4 1 8: 1 3 2 9: 1 2 3 10: 1 1 4 glo_test(): glo_order() + gqu2(): Gauss-Legender Odd quadrature over [0,1]: Exact integral is 0.19146246 Level Nodes Estimate Error 1 1 0.19333 0.0097753 2 3 0.19146 9.4658e-08 3 3 0.19146 9.4658e-08 4 5 0.19146 2.5442e-13 5 5 0.19146 2.5442e-13 6 7 0.19146 4.349e-16 7 7 0.19146 4.349e-16 8 9 0.19146 1.4497e-16 9 9 0.19146 1.4497e-16 10 11 0.19146 1.4497e-16 glo_sparse_test(): glo() builds a sparse grid: Gauss-Legendre Odd sparse grid. Exact integral is 6.61967e-08 D Level Nodes SG error MC error 10 1 1 0.10217 0.11906 10 2 21 0.004529 0.025602 10 3 201 0.00011892 0.0082596 10 4 1201 2.0958e-06 0.0033488 10 5 5281 2.6834e-08 0.0015628 10 6 19165 2.6782e-10 0.00085302 10 7 61285 8.997e-14 0.00046317 gqn_test(): gqn() builds a sparse grid. Gauss-Hermite quadrature over (-oo,+oo): Exact integral is 1.35453 Level Nodes Estimate Error 1 1 1 0.26174 2 2 1.4142 0.044062 3 3 1.3333 0.015649 4 4 1.364 0.0069593 5 5 1.3497 0.0035798 gqn_sparse_test(): gqn() builds a sparse grid: Gauss quadrature, Hermite weight over (-oo,+oo). Exact integral is 1.35453 D Level Nodes SG estimate MC estimate SG error MC error 5 1 1 1 1.3536 0.26174 0.30953 5 2 11 1.4142 1.3535 0.044062 0.090852 5 3 61 1.3333 1.3539 0.015649 0.036584 5 4 241 1.364 1.3548 0.0069593 0.018717 5 5 781 1.3497 1.3549 0.0035798 0.010594 5 6 2203 1.3572 1.3545 0.0019877 0.0061962 5 7 5593 1.3529 1.3541 0.0011805 0.0041168 5 8 13073 1.3555 1.3546 0.00073084 0.0026586 gqu_test(): gqu() builds a sparse grid. Gauss-Legendre quadrature over [0,1]: Exact integral is 0.19146246 Level Nodes Estimate Error 1 1 0.19333 0.0097753 2 2 0.19146 3.7965e-05 3 3 0.19146 9.4658e-08 4 4 0.19146 1.7425e-10 5 5 0.19146 2.5442e-13 gqu_sparse_test(): gqu() builds a sparse grid: Sparse Gaussian unweighted quadrature over [0,1]. Exact integral is 4.92608e-05 D Level Nodes SG error MC error 6 1 1 0.060104 0.088252 6 2 13 0.0017103 0.024388 6 3 85 3.129e-05 0.0098632 6 4 389 4.1665e-07 0.0045875 6 5 1433 4.3251e-09 0.0023755 6 6 4541 3.6497e-11 0.0013572 6 7 12841 1.8696e-12 0.00079473 6 8 33193 9.1876e-13 0.00048545 6 9 79729 4.2994e-12 0.00032469 6 10 180077 7.0046e-12 0.00021399 kpn_test(): kpn() builds a sparse grid. Kronrod-Patterson-Hermite quadrature over (-oo,+oo): Exact integral is 1.35453 Level Nodes Estimate Error 1 1 1 0.26174 2 3 1.3333 0.015649 3 3 1.3333 0.015649 4 7 1.346 0.0063033 5 9 1.355 0.00032265 kpn_sparse_test(): kpn() builds a sparse grid: Sparse nested, Hermite weight over (-oo,+oo). Exact integral is 1.35453 D Level Nodes SG estimate MC estimate SG error MC error 5 1 1 1 1.35 0.26174 0.30247 5 2 11 1.3333 1.3552 0.015649 0.090281 5 3 51 1.3333 1.3534 0.015649 0.040962 5 4 151 1.346 1.3556 0.0063033 0.025242 5 5 401 1.355 1.3536 0.00032265 0.015432 5 6 993 1.355 1.3543 0.00032265 0.0096509 5 7 2033 1.355 1.3547 0.00032265 0.0066857 5 8 3793 1.355 1.3547 0.00032265 0.0048409 kpu_test(): kpu() builds a sparse grid. Kronrod-Patterson quadrature over [0,1]: Exact integral is 0.19146246 Level Nodes Estimate Error 1 1 0.19333 0.0097753 2 3 0.19146 9.4658e-08 3 3 0.19146 9.4658e-08 4 7 0.19146 4.349e-16 5 7 0.19146 4.349e-16 kpu_sparse_test(): kpu() builds a sparse grid: Sparse nested, unweighted quadrature over [0,1]. Exact integral is 6.61967e-08 D Level Nodes SG error MC error 10 2 21 0.004529 0.026325 10 3 201 0.00011892 0.0082657 10 4 1201 2.0959e-06 0.0034221 nwspgr_size_test(): nwspgr_size() returns the size of a sparse grid, based on: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Kronrod-Patterson, [0,1], Dim 2, Level 3 Symmetric Full 21 Compressed 9 Kronrod-Patterson, (-oo,+oo), Dim 2, Level 3 Symmetric Full 21 Compressed 9 Gauss-Legendre, [0,1], Dim 2, Level 3 Symmetric Full 14 Compressed 13 Gauss Hermite, (-oo,+oo), [0,1], Dim 2, Level 3 Symmetric Full 14 Compressed 13 Clenshaw Curtis, [-1,+1], [0,1], Dim 2, Level 3 Unsymmetric Full 25 Compressed 13 Dimension / Level table for Clenshaw Curtis Exponential (CCE) Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 1 1 1 1 1 1 1 1 1 1 2: 3 5 7 9 11 13 15 17 19 21 3: 5 13 25 41 61 85 113 145 181 221 4: 9 29 69 137 241 389 589 849 1177 1581 5: 17 65 177 401 801 1457 2465 3937 6001 8801 6: 33 145 441 1105 2433 4865 9017 15713 26017 41265 Dimension / Level table for Clenshaw Curtis Exponential (CCE) Uncompressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 1 1 1 1 1 1 1 1 1 1 2: 3 7 10 13 16 19 22 25 28 31 3: 5 25 52 87 131 184 246 317 397 486 4: 9 67 195 411 746 1228 1884 2741 3826 5166 5: 17 161 609 1573 3376 6430 11222 18319 28369 42101 6: 33 371 1710 5257 13083 28426 55868 101575 173548 281867 Dimension / Level table for Gauss-Legendre Linear (GLL) Compressed Dim: 1 2 3 4 5 6 Level: 1: 1 1 1 1 1 1 2: 2 5 7 9 11 13 3: 3 13 25 41 61 85 4: 4 29 69 137 241 389 5: 5 53 165 385 781 1433 6: 6 89 351 953 2203 4541 7: 7 137 681 2145 5593 12841 8: 8 201 1233 4481 13073 33193 9: 9 281 2097 8785 28553 79729 10: 10 381 3407 16345 58923 180077 11: 11 501 5297 29033 115813 385901 Dimension / Level table for Gauss-Legendre-Odd (GLO) Compressed Dim: 1 2 3 4 5 6 Level: 1: 1 1 1 1 1 1 2: 3 5 7 9 11 13 3: 3 9 19 33 51 73 4: 5 17 39 81 151 257 5: 5 33 87 193 391 737 6: 7 45 153 409 933 1925 7: 7 81 273 777 1973 4509 8: 9 97 465 1481 4013 9837 9: 9 161 705 2537 7693 20445 10: 11 181 1175 4369 13983 40025 11: 11 281 1595 7129 24983 75917 nwspgr_time_test(): Compute the time required for NWSPGR to determine a sparse grid, based on either: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Dimension / Level Time table, CC Exponential Uncompressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000718 0.000609 0.000645 0.000676 0.000708 0.000748 0.000801 0.000860 0.000914 0.000967 2: 0.000832 0.001410 0.001816 0.002348 0.002981 0.003745 0.004613 0.005582 0.006670 0.007846 3: 0.001144 0.002441 0.004540 0.007035 0.010635 0.015477 0.021533 0.029218 0.038550 0.049709 4: 0.002073 0.004483 0.010236 0.019986 0.035228 0.058292 0.090923 0.135957 0.195339 0.272526 5: 0.004650 0.009168 0.023858 0.055448 0.113765 0.212882 0.370270 0.609667 0.955972 1.440632 6: 0.013473 0.022376 0.058503 0.153710 0.359660 0.762425 1.480490 2.699928 4.649726 7.673604 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001264 0.001127 0.001167 0.001199 0.001246 0.001308 0.001361 0.001414 0.001469 0.001524 2: 0.009245 0.010605 0.012124 0.013732 0.015509 0.017336 0.019293 0.021380 0.023553 0.025929 3: 0.062960 0.078394 0.096127 0.116372 0.139268 0.165158 0.194047 0.226509 0.261701 0.300654 4: 0.370592 0.491545 0.640325 0.819170 1.036004 1.289309 1.587933 1.932877 2.331602 2.796431 5: 2.099479 2.975306 4.128551 5.599066 7.484639 9.879521 12.874843 16.708058 21.547047 27.672508 Dimension / Level Time table for CC Linear Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000733 0.000613 0.000638 0.000682 0.000748 0.000799 0.000842 0.000863 0.000910 0.000970 2: 0.000821 0.001404 0.001819 0.002369 0.003119 0.003829 0.004608 0.005575 0.006675 0.007891 3: 0.001148 0.002478 0.004550 0.007056 0.010660 0.015486 0.021557 0.029208 0.038610 0.049832 4: 0.001797 0.004169 0.009913 0.019616 0.034816 0.057776 0.090477 0.135498 0.194962 0.272132 5: 0.002651 0.006736 0.020824 0.051528 0.108690 0.206394 0.363066 0.599848 0.944241 1.422798 6: 0.004031 0.010517 0.041992 0.128531 0.321678 0.703893 1.399554 2.576995 4.487434 7.436066 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001265 0.001128 0.001155 0.001208 0.001254 0.001303 0.001362 0.001411 0.001465 0.001523 2: 0.009242 0.010653 0.012132 0.013706 0.015483 0.017311 0.019264 0.021329 0.023520 0.025839 3: 0.063017 0.078426 0.096290 0.116431 0.139267 0.165002 0.194468 0.226045 0.261453 0.300277 4: 0.368930 0.490922 0.639092 0.818946 1.033440 1.289262 1.586984 1.932547 2.333723 2.791975 5: 2.080411 2.954100 4.099297 5.568535 7.450218 9.826249 12.812794 16.660455 21.560154 27.556867 Dimension / Level Time table for CC Slow Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000736 0.000631 0.000648 0.000687 0.000744 0.000792 0.000842 0.000858 0.000911 0.000966 2: 0.000818 0.001410 0.001833 0.002399 0.003070 0.003810 0.004609 0.005597 0.006678 0.007888 3: 0.001165 0.002468 0.004559 0.007072 0.010707 0.015494 0.021531 0.029193 0.038509 0.049708 4: 0.002087 0.004495 0.010281 0.019996 0.035227 0.058275 0.090929 0.136132 0.195577 0.272520 5: 0.002943 0.007327 0.021885 0.053327 0.111539 0.210319 0.368247 0.607009 0.951413 1.434816 6: 0.005613 0.012891 0.046866 0.138997 0.341772 0.738259 1.451028 2.656652 4.591572 7.555457 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001271 0.001141 0.001165 0.001201 0.001251 0.001302 0.001353 0.001407 0.001470 0.001523 2: 0.009240 0.010642 0.012129 0.013760 0.015480 0.017289 0.019283 0.021368 0.023561 0.025805 3: 0.063055 0.078443 0.096052 0.116371 0.139518 0.165268 0.193950 0.226654 0.261706 0.300355 4: 0.370092 0.492161 0.640858 0.819612 1.036436 1.287946 1.587715 1.934193 2.332293 2.790593 5: 2.093254 2.970705 4.120789 5.593545 7.481395 9.884960 12.927701 16.718039 21.647559 27.755441 Dimension / Level Time table for Gauss-Hermite Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000823 0.000691 0.000728 0.000793 0.000875 0.000974 0.001003 0.001058 0.001139 0.001220 2: 0.000680 0.001355 0.001893 0.002579 0.003450 0.004564 0.005648 0.006968 0.008431 0.010064 3: 0.000701 0.001906 0.004042 0.006865 0.011123 0.016865 0.024343 0.034081 0.046205 0.060902 4: 0.000821 0.002695 0.007423 0.016036 0.030330 0.053023 0.086843 0.135137 0.202472 0.291045 5: 0.000948 0.003635 0.013016 0.033879 0.074228 0.145866 0.266283 0.456500 0.745361 1.165817 6: 0.001094 0.004917 0.021536 0.066471 0.165783 0.363654 0.731089 1.373965 2.431575 4.116438 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001523 0.001419 0.001467 0.001531 0.001602 0.001687 0.001762 0.001854 0.001928 0.001998 2: 0.011819 0.013778 0.015805 0.018153 0.020418 0.022952 0.025661 0.028430 0.031538 0.034643 3: 0.078611 0.099432 0.123718 0.151842 0.183721 0.219964 0.260491 0.305787 0.356061 0.411794 4: 0.407721 0.556171 0.741991 0.971563 1.252173 1.588315 1.988153 2.461577 3.018438 3.655570 5: 1.762755 2.580653 3.683985 5.139052 7.022478 9.441502 12.472417 16.273623 21.006066 26.744109 Dimension / Level Time table for Gauss-Legendre Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000761 0.000658 0.000690 0.000759 0.000842 0.000967 0.001027 0.001070 0.001134 0.001215 2: 0.000663 0.001348 0.001893 0.002597 0.003454 0.004583 0.005652 0.006961 0.008422 0.010049 3: 0.000693 0.001916 0.004058 0.006854 0.011122 0.016893 0.024393 0.034032 0.046163 0.060963 4: 0.000834 0.002683 0.007425 0.016052 0.030352 0.052920 0.086775 0.135254 0.202025 0.291691 5: 0.000940 0.003633 0.013026 0.033840 0.074065 0.146103 0.266366 0.456991 0.745582 1.167435 6: 0.001086 0.004936 0.021541 0.066326 0.165739 0.363767 0.731245 1.372076 2.434356 4.116930 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001514 0.001419 0.001483 0.001549 0.001614 0.001691 0.001767 0.001845 0.001948 0.001993 2: 0.011842 0.013803 0.015894 0.018032 0.020420 0.022968 0.025652 0.028504 0.031524 0.034630 3: 0.078711 0.099460 0.123835 0.151867 0.183753 0.219801 0.260609 0.305818 0.356042 0.412450 4: 0.407911 0.556483 0.743102 0.973633 1.251479 1.588067 1.990114 2.461454 3.014349 3.656464 5: 1.762508 2.581758 3.683241 5.136173 7.026328 9.438765 12.473847 16.275911 20.981108 26.749336 Dimension / Level Time table, KP, (-oo,+oo) Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000793 0.000656 0.000703 0.000763 0.000836 0.000936 0.001007 0.001061 0.001135 0.001212 2: 0.000682 0.001390 0.001959 0.002680 0.003547 0.004669 0.005765 0.007076 0.008581 0.010208 3: 0.000692 0.001955 0.004100 0.006957 0.011207 0.017117 0.024658 0.034560 0.046709 0.061548 4: 0.000891 0.002723 0.007453 0.015891 0.029697 0.051774 0.084529 0.131527 0.196444 0.283404 5: 0.000996 0.003858 0.013219 0.033629 0.071960 0.139052 0.250142 0.425636 0.690676 1.077329 6: 0.001132 0.005061 0.021495 0.065207 0.159222 0.341371 0.671385 1.237676 2.162438 3.615415 Dimension / Level Time table for KP on [0,1] Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000903 0.000722 0.000749 0.000816 0.000891 0.001012 0.001076 0.001132 0.001197 0.001271 2: 0.000819 0.001524 0.002081 0.002792 0.003677 0.004781 0.005909 0.007226 0.008705 0.010327 3: 0.000880 0.002148 0.004308 0.007174 0.011487 0.017313 0.024869 0.034684 0.046839 0.061760 4: 0.001154 0.003004 0.007727 0.016141 0.030066 0.052145 0.084831 0.131764 0.196683 0.283355 5: 0.001321 0.004106 0.013374 0.033558 0.071846 0.138553 0.249588 0.425091 0.689518 1.075099 6: 0.001547 0.005084 0.020783 0.063291 0.155207 0.334075 0.659429 1.221236 2.140224 3.583258 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001605 0.001486 0.001527 0.001594 0.001677 0.001739 0.001817 0.001909 0.001990 0.002071 2: 0.012151 0.014100 0.016180 0.018450 0.020797 0.023364 0.026016 0.028880 0.031891 0.035036 3: 0.079593 0.100421 0.124880 0.152764 0.184864 0.221371 0.262076 0.307568 0.358080 0.413493 4: 0.396618 0.542628 0.723226 0.948076 1.221815 1.551098 1.943891 2.403439 2.949877 3.574681 5: 1.621996 2.376013 3.392605 4.730636 6.468936 8.719986 11.598606 15.368218 19.816945 25.262725 nwspgr_test(): nwspgr() generates a sparse grid, based on either: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Kronrod-Patterson, [0,1], Dim 2, Level 3 1: 0.0771605 * f(0.112702,0.112702) 2: 0.123457 * f(0.112702,0.5) 3: 0.0771605 * f(0.112702,0.887298) 4: 0.123457 * f(0.5,0.112702) 5: 0.197531 * f(0.5,0.5) 6: 0.123457 * f(0.5,0.887298) 7: 0.0771605 * f(0.887298,0.112702) 8: 0.123457 * f(0.887298,0.5) 9: 0.0771605 * f(0.887298,0.887298) Kronrod-Patterson, (-oo,+oo), Dim 2, Level 3 1: 0.0277778 * f(-1.73205,-1.73205) 2: 0.111111 * f(-1.73205,0) 3: 0.0277778 * f(-1.73205,1.73205) 4: 0.111111 * f(0,-1.73205) 5: 0.444444 * f(0,0) 6: 0.111111 * f(0,1.73205) 7: 0.0277778 * f(1.73205,-1.73205) 8: 0.111111 * f(1.73205,0) 9: 0.0277778 * f(1.73205,1.73205) Gauss-Legendre, [0,1], Dim 2, Level 3 1: 0.277778 * f(0.112702,0.5) 2: 0.25 * f(0.211325,0.211325) 3: -0.5 * f(0.211325,0.5) 4: 0.25 * f(0.211325,0.788675) 5: 0.277778 * f(0.5,0.112702) 6: -0.5 * f(0.5,0.211325) 7: 0.888889 * f(0.5,0.5) 8: -0.5 * f(0.5,0.788675) 9: 0.277778 * f(0.5,0.887298) 10: 0.25 * f(0.788675,0.211325) 11: -0.5 * f(0.788675,0.5) 12: 0.25 * f(0.788675,0.788675) 13: 0.277778 * f(0.887298,0.5) Gauss Hermite, (-oo,+oo), Dim 2, Level 3 1: 0.166667 * f(-1.73205,0) 2: 0.25 * f(-1,-1) 3: -0.5 * f(-1,0) 4: 0.25 * f(-1,1) 5: 0.166667 * f(0,-1.73205) 6: -0.5 * f(0,-1) 7: 1.33333 * f(0,0) 8: -0.5 * f(0,1) 9: 0.166667 * f(0,1.73205) 10: 0.25 * f(1,-1) 11: -0.5 * f(1,0) 12: 0.25 * f(1,1) 13: 0.166667 * f(1.73205,0) Clenshaw Curtis Exponential, [-1,+1], Dim 2, Level 3 1: 0.0277778 * f(0,0) 2: -0.0222222 * f(0,0.5) 3: 0.0277778 * f(0,1) 4: 0.266667 * f(0.146447,0.5) 5: -0.0222222 * f(0.5,0) 6: 0.266667 * f(0.5,0.146447) 7: -0.0888889 * f(0.5,0.5) 8: 0.266667 * f(0.5,0.853553) 9: -0.0222222 * f(0.5,1) 10: 0.266667 * f(0.853553,0.5) 11: 0.0277778 * f(1,0) 12: -0.0222222 * f(1,0.5) 13: 0.0277778 * f(1,1) order_report(): For each family of rules, report: L, the level index, RP, the required polynomial precision, AP, the actual polynomial precision, O, the rule order (number of points). GLO family Gauss-Legendre Odd quadrature, uniform weight, [-1,+1] L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 9 5 5 9 9 5 6 11 13 7 7 13 13 7 8 15 17 9 9 17 17 9 10 19 21 11 11 21 21 11 12 23 25 13 13 25 25 13 14 27 29 15 15 29 29 15 16 31 33 17 17 33 33 17 18 35 37 19 19 37 37 19 20 39 41 21 21 41 41 21 22 43 45 23 23 45 45 23 24 47 49 25 25 49 49 25 GQN family Gauss quadrature, exponential weight, (-oo,+oo) L RP AP O 1 1 1 1 2 3 3 2 3 5 5 3 4 7 7 4 5 9 9 5 6 11 11 6 7 13 13 7 8 15 15 8 9 17 17 9 10 19 19 10 11 21 21 11 12 23 23 12 13 25 25 13 14 27 27 14 15 29 29 15 16 31 31 16 17 33 33 17 18 35 35 18 19 37 37 19 20 39 39 20 21 41 41 21 22 43 43 22 23 45 45 23 24 47 47 24 25 49 49 25 GQU family Gauss quadrature, unit weight, [0,1] L RP AP O 1 1 1 1 2 3 3 2 3 5 5 3 4 7 7 4 5 9 9 5 6 11 11 6 7 13 13 7 8 15 15 8 9 17 17 9 10 19 19 10 11 21 21 11 12 23 23 12 13 25 25 13 14 27 27 14 15 29 29 15 16 31 31 16 17 33 33 17 18 35 35 18 19 37 37 19 20 39 39 20 21 41 41 21 22 43 43 22 23 45 45 23 24 47 47 24 25 49 49 25 KPN family Gauss-Kronrod-Patterson quadrature, exponential weight, (-oo,+oo) L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 7 7 5 9 15 9 6 11 15 9 7 13 15 9 8 15 15 9 9 17 17 17 10 19 29 19 11 21 29 19 12 23 29 19 13 25 29 19 14 27 29 19 15 29 29 19 16 31 31 31 17 33 33 33 18 35 51 35 19 37 51 35 20 39 51 35 21 41 51 35 22 43 51 35 23 45 51 35 24 47 51 35 25 49 51 35 KPU family Gauss-Kronrod-Patterson quadrature, unit weight, [0,1] L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 11 7 5 9 11 7 6 11 11 7 7 13 23 15 8 15 23 15 9 17 23 15 10 19 23 15 11 21 23 15 12 23 23 15 13 25 47 31 14 27 47 31 15 29 47 31 16 31 47 31 17 33 47 31 18 35 47 31 19 37 47 31 20 39 47 31 21 41 47 31 22 43 47 31 23 45 47 31 24 47 47 31 25 49 95 63 symmetric_sparse_size_test(): Given a symmetric sparse grid rule represented only by the points with positive values, determine the total number of points in the grid. For dimension DIM, we report R, the number of points in the positive orthant, and R2, the total number of points. DIM R R2 5 6 11 5 21 61 3 23 69 tensor_product_test(): Given a sequence of 1D quadrature rules, construct the tensor product rule. A 1D rule over [-1,+1]: 1: 1 * f(-1) 2: 1 * f(1) A 2D rule over [-1,+1] x [2.0,3.0]: 1: 0.25 * f(-1,2) 2: 0.5 * f(-1,2.5) 3: 0.25 * f(-1,3) 4: 0.25 * f(1,2) 5: 0.5 * f(1,2.5) 6: 0.25 * f(1,3) A 3D rule over [-1,+1] x [2.0,3.0] x [10.0,15.0]: 1: 0.625 * f(-1,2,10) 2: 0.625 * f(-1,2,15) 3: 1.25 * f(-1,2.5,10) 4: 1.25 * f(-1,2.5,15) 5: 0.625 * f(-1,3,10) 6: 0.625 * f(-1,3,15) 7: 0.625 * f(1,2,10) 8: 0.625 * f(1,2,15) 9: 1.25 * f(1,2.5,10) 10: 1.25 * f(1,2.5,15) 11: 0.625 * f(1,3,10) 12: 0.625 * f(1,3,15) sparse_grid_hw_test(): Normal end of execution. 20-Jun-2023 12:32:07