08-Jan-2022 09:42:15 sparse_grid_hw_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 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 6.3785e-15 5 17 0.19146 1.4497e-16 6 33 0.19146 1.4497e-16 7 65 0.19146 1.4497e-16 8 129 0.19146 1.4497e-16 9 257 0.19146 1.4497e-16 10 513 0.19146 1.4497e-16 CCE_SPARSE_TEST: CCE 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 0.1173 10 2 21 0.0039099 0.024833 10 3 221 6.4537e-05 0.0077693 10 4 1581 1.2369e-07 0.0029185 10 5 8801 1.0089e-08 0.0012351 10 6 41265 8.7957e-11 0.00056764 10 7 171425 2.893e-12 0.00028452 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 1.1783e-11 5 9 0.19146 6.3785e-15 6 11 0.19146 4.349e-16 7 13 0.19146 1.4497e-16 8 15 0.19146 2.8993e-16 9 17 0.19146 1.4497e-16 10 19 0.19146 2.8993e-16 CCL_SPARSE_TEST: CCL 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 0.11576 10 2 21 0.0039099 0.02549 10 3 221 6.4537e-05 0.0078388 10 4 1581 1.2382e-07 0.0029942 10 5 8761 1.0077e-08 0.0012961 10 6 40425 8.7689e-11 0.0005933 10 7 162385 4.3717e-12 0.00027422 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 6.3785e-15 5 9 0.19146 6.3785e-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 1.4497e-16 CCS_SPARSE_TEST: CCS 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 0.1111 10 2 21 0.0039099 0.026057 10 3 221 6.4537e-05 0.0077926 10 4 1581 1.2369e-07 0.002923 10 5 8721 1.0089e-08 0.0012648 10 6 39665 8.7894e-11 0.00055953 10 7 155105 3.1329e-12 0.00028877 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 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 0.1145 10 2 21 0.004529 0.025444 10 3 201 0.00011892 0.0081979 10 4 1201 2.0958e-06 0.0031948 10 5 5281 2.6833e-08 0.0016254 10 6 19165 2.6744e-10 0.00081675 10 7 61285 4.4785e-13 0.00048893 GQN_TEST: 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 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 1.3614 0.26174 0.30746 5 2 11 1.4142 1.3527 0.044062 0.092878 5 3 61 1.3333 1.3523 0.015649 0.038364 5 4 241 1.364 1.3554 0.0069593 0.020268 5 5 781 1.3497 1.3541 0.0035798 0.011089 5 6 2203 1.3572 1.3548 0.0019877 0.006419 5 7 5593 1.3529 1.3546 0.0011805 0.0040398 5 8 13073 1.3555 1.3545 0.00073084 0.0025742 GQU_TEST: 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 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 0.090713 6 2 13 0.0017103 0.025411 6 3 85 3.129e-05 0.0094788 6 4 389 4.1665e-07 0.0044172 6 5 1433 4.3251e-09 0.0023863 6 6 4541 3.6632e-11 0.0013505 6 7 12841 2.3977e-13 0.00082453 6 8 33193 2.3206e-13 0.00049563 6 9 79729 6.2823e-13 0.00031924 6 10 180077 1.0324e-11 0.00020242 KPN_TEST: 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 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 1.3562 0.26174 0.29141 5 2 11 1.3333 1.3536 0.015649 0.089061 5 3 51 1.3333 1.3562 0.015649 0.042474 5 4 151 1.346 1.3551 0.0063033 0.02421 5 5 401 1.355 1.3554 0.00032265 0.015158 5 6 993 1.355 1.3548 0.00032265 0.0095619 5 7 2033 1.355 1.3549 0.00032265 0.0070375 5 8 3793 1.355 1.3547 0.00032265 0.004909 KPU_TEST: 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 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 0.026069 10 3 201 0.00011892 0.0081957 10 4 1201 2.0959e-06 0.003363 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: 0.002202 0.000171 0.000155 0.000137 0.000309 0.000117 0.000113 0.000116 0.000123 0.000130 2: 0.003179 0.000362 0.000439 0.000374 0.000401 0.000494 0.000628 0.000760 0.000935 0.001137 3: 0.000429 0.000313 0.000554 0.000798 0.001267 0.001827 0.002638 0.003594 0.004851 0.006394 4: 0.000232 0.000382 0.000862 0.001807 0.003481 0.005714 0.008869 0.013220 0.019035 0.027054 5: 0.000210 0.000446 0.001410 0.003634 0.007681 0.014615 0.025811 0.044099 0.070877 0.111883 6: 0.000338 0.000717 0.002596 0.007632 0.018097 0.038498 0.077155 0.144111 0.255105 0.427276 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000346 0.000192 0.000189 0.000193 0.000352 0.000181 0.000179 0.000182 0.000188 0.000194 2: 0.001351 0.001473 0.001555 0.001784 0.002000 0.002220 0.002467 0.002746 0.003024 0.003337 3: 0.007523 0.009383 0.011681 0.014271 0.017196 0.020826 0.024377 0.028295 0.034285 0.037950 4: 0.037314 0.050608 0.066942 0.087603 0.112041 0.141800 0.179301 0.218320 0.270426 0.326535 5: 0.165115 0.241767 0.339288 0.477915 0.661442 0.903110 1.229256 1.621202 2.095768 2.767558 Dimension / Level Time table for CC Linear Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000230 0.000145 0.000128 0.000130 0.000293 0.000115 0.000110 0.000115 0.000120 0.000129 2: 0.000227 0.000306 0.000350 0.000296 0.000369 0.000469 0.000590 0.000719 0.000867 0.001000 3: 0.000234 0.000240 0.000445 0.000755 0.001142 0.001713 0.002439 0.003341 0.004424 0.005797 4: 0.000137 0.000303 0.000779 0.001638 0.003133 0.005239 0.008401 0.012854 0.018871 0.026863 5: 0.000267 0.000465 0.001519 0.003877 0.007666 0.014511 0.025765 0.043396 0.070115 0.108574 6: 0.000308 0.000605 0.002592 0.007503 0.017352 0.037253 0.074115 0.139828 0.246425 0.418937 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000316 0.000193 0.000187 0.000193 0.000348 0.000180 0.000185 0.000183 0.000188 0.000195 2: 0.001322 0.001474 0.001556 0.001755 0.002009 0.002208 0.002477 0.002735 0.003023 0.003391 3: 0.007628 0.009443 0.011625 0.014261 0.017194 0.020532 0.024087 0.028340 0.032871 0.037868 4: 0.037568 0.050790 0.066910 0.087347 0.111895 0.141352 0.176757 0.218357 0.268244 0.325187 5: 0.163660 0.240088 0.339093 0.479178 0.656865 0.916409 1.210430 1.614337 2.120739 2.730732 Dimension / Level Time table for CC Slow Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000228 0.000139 0.000129 0.000132 0.000289 0.000112 0.000109 0.000115 0.000128 0.000128 2: 0.000230 0.000307 0.000349 0.000296 0.000372 0.000469 0.000587 0.000719 0.000869 0.001000 3: 0.000233 0.000242 0.000442 0.000722 0.001174 0.001708 0.002448 0.003346 0.004423 0.005794 4: 0.000137 0.000306 0.000779 0.001685 0.003067 0.005263 0.008369 0.012904 0.018861 0.027099 5: 0.000197 0.000420 0.001370 0.003550 0.007516 0.014353 0.025674 0.043673 0.070205 0.108541 6: 0.000312 0.000808 0.002559 0.007652 0.018731 0.040770 0.076581 0.139961 0.247984 0.421001 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000327 0.000192 0.000188 0.000193 0.000339 0.000180 0.000179 0.000182 0.000189 0.000195 2: 0.001319 0.001481 0.001546 0.001751 0.001999 0.002209 0.002497 0.002738 0.003051 0.003320 3: 0.007527 0.009397 0.011620 0.014248 0.017159 0.022775 0.024633 0.028388 0.032845 0.037806 4: 0.037324 0.052674 0.069803 0.087357 0.112243 0.141661 0.177289 0.219021 0.267232 0.326113 5: 0.164187 0.239874 0.342888 0.475934 0.654423 0.896394 1.218949 1.608439 2.101300 2.758903 Dimension / Level Time table for Gauss-Hermite Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000983 0.000145 0.000130 0.000137 0.000279 0.000110 0.000108 0.000114 0.000119 0.000127 2: 0.002108 0.000300 0.000360 0.000279 0.000353 0.000443 0.000554 0.000678 0.000840 0.001013 3: 0.001558 0.000257 0.000408 0.000634 0.001011 0.001495 0.002155 0.002982 0.003963 0.005155 4: 0.000733 0.000257 0.000636 0.001324 0.002456 0.004254 0.006821 0.010582 0.015525 0.022938 5: 0.000214 0.000326 0.001033 0.002599 0.005598 0.010622 0.018973 0.032195 0.051412 0.080386 6: 0.000236 0.000476 0.001560 0.005050 0.011640 0.023921 0.046546 0.086513 0.150527 0.250998 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000313 0.000193 0.000187 0.000192 0.000344 0.000180 0.000178 0.000183 0.000188 0.000256 2: 0.001235 0.001507 0.001571 0.001736 0.002035 0.002200 0.002490 0.002713 0.003040 0.003383 3: 0.006989 0.008741 0.010872 0.013214 0.015999 0.018941 0.021833 0.025510 0.029742 0.034226 4: 0.030827 0.041926 0.055635 0.072664 0.093392 0.118439 0.147577 0.183628 0.229447 0.273224 5: 0.119301 0.173950 0.248486 0.346702 0.477238 0.649771 0.871734 1.153766 1.521890 1.986984 Dimension / Level Time table for Gauss-Legendre Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000223 0.000153 0.000142 0.000149 0.000334 0.000122 0.000121 0.000126 0.000135 0.000143 2: 0.000227 0.000335 0.000364 0.000307 0.000383 0.000493 0.000598 0.000732 0.000890 0.001058 3: 0.000247 0.000225 0.000415 0.000695 0.001057 0.001569 0.002195 0.003060 0.004062 0.005250 4: 0.000105 0.000246 0.000625 0.001515 0.002740 0.004347 0.006863 0.010499 0.015663 0.023542 5: 0.000187 0.000313 0.001106 0.002584 0.005653 0.010651 0.019108 0.032020 0.051374 0.079779 6: 0.000186 0.000387 0.001517 0.004603 0.011129 0.023855 0.046535 0.085360 0.149717 0.251543 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000314 0.000193 0.000188 0.000192 0.000343 0.000180 0.000178 0.000183 0.000197 0.000198 2: 0.001236 0.001411 0.001475 0.001699 0.001988 0.002131 0.002364 0.002633 0.002910 0.003203 3: 0.006690 0.008375 0.010364 0.012746 0.015282 0.018254 0.021746 0.025466 0.030472 0.034376 4: 0.031017 0.042029 0.055721 0.084671 0.098811 0.120605 0.147999 0.183292 0.224693 0.285767 5: 0.128027 0.180906 0.258771 0.362349 0.480200 0.648363 0.866011 1.151010 1.509002 1.980621 Dimension / Level Time table, KP, (-oo,+oo) Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000221 0.000167 0.000147 0.000152 0.000344 0.000130 0.000173 0.000134 0.000139 0.000149 2: 0.000260 0.000361 0.000434 0.000359 0.000439 0.000553 0.000697 0.000836 0.000982 0.001161 3: 0.000310 0.000263 0.000466 0.000755 0.001208 0.001756 0.002500 0.003372 0.004534 0.005791 4: 0.000125 0.000251 0.000682 0.001438 0.002710 0.004634 0.007436 0.011460 0.017204 0.024305 5: 0.000144 0.000304 0.001028 0.002714 0.005932 0.011473 0.020509 0.035218 0.056220 0.089049 6: 0.000238 0.000512 0.001536 0.004811 0.011900 0.025536 0.050418 0.093747 0.164957 0.277064 Dimension / Level Time table for KP on [0,1] Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.000247 0.000166 0.000143 0.000128 0.000273 0.000108 0.000107 0.000110 0.000117 0.000124 2: 0.000226 0.000309 0.000345 0.000301 0.000365 0.000461 0.000573 0.000702 0.000843 0.001011 3: 0.000221 0.000230 0.000415 0.000674 0.001074 0.001604 0.002278 0.003176 0.004309 0.005587 4: 0.000145 0.000458 0.000685 0.001424 0.002658 0.004646 0.007428 0.011471 0.017072 0.024202 5: 0.000156 0.000321 0.001052 0.002719 0.005946 0.011431 0.020838 0.034788 0.056337 0.087235 6: 0.000198 0.000387 0.001555 0.004758 0.011854 0.025466 0.050268 0.093231 0.164159 0.276743 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000362 0.000197 0.000189 0.000195 0.000349 0.000182 0.000180 0.000282 0.000198 0.000204 2: 0.001441 0.001653 0.001631 0.001789 0.002047 0.002248 0.002499 0.002777 0.003064 0.003393 3: 0.007203 0.009082 0.011212 0.013757 0.016667 0.019780 0.023554 0.027535 0.032072 0.037113 4: 0.034875 0.046800 0.061311 0.079571 0.102126 0.129693 0.162723 0.201253 0.245756 0.298903 5: 0.131842 0.192938 0.273263 0.383483 0.526771 0.715145 0.958576 1.268417 1.665987 2.189329 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. 08-Jan-2022 09:45:43