sparse_grid_hw_test 20-Mar-2019 15:30:47 sparse_grid_hw_test MATLAB version 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 2.8993e-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 0.11625 10 2 21 0.0039099 0.025543 10 3 221 6.4537e-05 0.007713 10 4 1581 1.2369e-07 0.0028344 10 5 8801 1.0089e-08 0.0012467 10 6 41265 8.7957e-11 0.00057202 10 7 171425 2.893e-12 0.000278 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 2.8993e-16 10 19 0.19146 1.4497e-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 0.11461 10 2 21 0.0039099 0.025431 10 3 221 6.4537e-05 0.0079728 10 4 1581 1.2382e-07 0.0028939 10 5 8761 1.0077e-08 0.0012431 10 6 40425 8.7689e-11 0.00055171 10 7 162385 4.3717e-12 0.00029157 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 2.8993e-16 7 17 0.19146 2.8993e-16 8 17 0.19146 2.8993e-16 9 17 0.19146 2.8993e-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 0.11608 10 2 21 0.0039099 0.024506 10 3 221 6.4537e-05 0.0079737 10 4 1581 1.2369e-07 0.0029371 10 5 8721 1.0089e-08 0.0012744 10 6 39665 8.7894e-11 0.00057122 10 7 155105 3.1329e-12 0.00029176 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 0.11641 10 2 21 0.004529 0.025752 10 3 201 0.00011892 0.00805 10 4 1201 2.0958e-06 0.0033803 10 5 5281 2.6833e-08 0.0016261 10 6 19165 2.6744e-10 0.00084658 10 7 61285 4.4785e-13 0.0004744 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 1.334 0.26174 0.29638 5 2 11 1.4142 1.3517 0.044062 0.088846 5 3 61 1.3333 1.3539 0.015649 0.037634 5 4 241 1.364 1.3549 0.0069593 0.019448 5 5 781 1.3497 1.3543 0.0035798 0.011052 5 6 2203 1.3572 1.3548 0.0019877 0.006507 5 7 5593 1.3529 1.3545 0.0011805 0.0038926 5 8 13073 1.3555 1.3545 0.00073084 0.0025455 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 0.090211 6 2 13 0.0017103 0.024463 6 3 85 3.129e-05 0.0095623 6 4 389 4.1665e-07 0.0045827 6 5 1433 4.3251e-09 0.0023813 6 6 4541 3.6632e-11 0.0013456 6 7 12841 2.3977e-13 0.00081054 6 8 33193 2.3206e-13 0.00048802 6 9 79729 6.2823e-13 0.00030505 6 10 180077 1.0324e-11 0.00021885 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 1.3507 0.26174 0.29415 5 2 11 1.3333 1.3545 0.015649 0.093427 5 3 51 1.3333 1.3555 0.015649 0.042176 5 4 151 1.346 1.3556 0.0063033 0.024381 5 5 401 1.355 1.3555 0.00032265 0.014918 5 6 993 1.355 1.355 0.00032265 0.0096011 5 7 2033 1.355 1.3548 0.00032265 0.0065457 5 8 3793 1.355 1.3546 0.00032265 0.0047045 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 0.025955 10 3 201 0.00011892 0.0081977 10 4 1201 2.0959e-06 0.0033263 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: 0.000556 0.000321 0.000192 0.000137 0.000125 0.000130 0.000138 0.000147 0.000158 0.000167 2: 0.000221 0.000270 0.000326 0.000386 0.000493 0.000627 0.000871 0.001096 0.001208 0.001438 3: 0.000219 0.000321 0.000753 0.001083 0.001724 0.002349 0.003362 0.005182 0.007355 0.008085 4: 0.000288 0.000560 0.001366 0.002712 0.004397 0.007197 0.011328 0.017385 0.026300 0.034341 5: 0.000286 0.000872 0.003120 0.005507 0.009131 0.018636 0.032362 0.058877 0.091113 0.136708 6: 0.000410 0.001269 0.003734 0.009346 0.023176 0.045942 0.091072 0.177740 0.319827 0.618931 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001993 0.000362 0.000230 0.000218 0.000228 0.000240 0.000245 0.000245 0.000258 0.000265 2: 0.001691 0.002003 0.002657 0.002961 0.003117 0.003417 0.003690 0.004163 0.004365 0.004805 3: 0.010865 0.013186 0.015902 0.019206 0.023463 0.028144 0.032478 0.037942 0.044186 0.050859 4: 0.051879 0.070303 0.090615 0.116146 0.144661 0.195608 0.245505 0.306635 0.369910 0.449106 5: 0.221366 0.333982 0.492355 0.671318 0.967814 1.302434 1.747611 2.151822 2.840314 3.864393 Dimension / Level Time table for CC Linear Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.007502 0.000349 0.000136 0.000135 0.000116 0.000122 0.000131 0.000139 0.000146 0.000154 2: 0.000143 0.000245 0.000289 0.000453 0.000814 0.001304 0.001457 0.001331 0.001374 0.002223 3: 0.000275 0.000397 0.001172 0.001402 0.002130 0.003319 0.003461 0.004801 0.006460 0.008420 4: 0.000237 0.000715 0.001416 0.003151 0.004230 0.006835 0.011320 0.016469 0.027668 0.036567 5: 0.000279 0.000823 0.002546 0.005401 0.010179 0.018926 0.034247 0.056662 0.096713 0.148032 6: 0.000604 0.001359 0.004435 0.010634 0.023268 0.048179 0.094899 0.186061 0.332644 0.599756 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001836 0.000350 0.000223 0.000281 0.000267 0.000243 0.000245 0.000260 0.000248 0.000308 2: 0.001940 0.002102 0.002287 0.003409 0.003451 0.003925 0.005072 0.005103 0.005645 0.005136 3: 0.011613 0.013066 0.016091 0.020617 0.025175 0.030926 0.034591 0.040079 0.050756 0.049022 4: 0.051385 0.073757 0.095589 0.124162 0.150986 0.175858 0.221461 0.305326 0.383477 0.464853 5: 0.204404 0.303559 0.499237 0.657210 0.868180 1.330723 1.781895 2.409522 3.013648 3.948132 Dimension / Level Time table for CC Slow Compressed Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.007668 0.000421 0.000349 0.000192 0.000148 0.000137 0.000143 0.000150 0.000174 0.000248 2: 0.000200 0.000563 0.000378 0.000498 0.000539 0.000902 0.000916 0.001257 0.001329 0.002063 3: 0.000296 0.000428 0.000810 0.001121 0.001925 0.002542 0.003594 0.005013 0.006702 0.008868 4: 0.000287 0.000721 0.001694 0.002845 0.004688 0.007514 0.012193 0.018635 0.026638 0.037349 5: 0.000346 0.000824 0.002238 0.006446 0.010624 0.020184 0.037667 0.066136 0.102089 0.157089 6: 0.000672 0.001075 0.003432 0.009557 0.024254 0.052831 0.103211 0.202213 0.351269 0.645030 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.001937 0.000379 0.000244 0.000230 0.000226 0.000227 0.000351 0.000312 0.000292 0.000289 2: 0.001801 0.002020 0.002879 0.003309 0.003440 0.003788 0.004118 0.004293 0.004702 0.005505 3: 0.012783 0.013992 0.016906 0.021020 0.024925 0.027080 0.035049 0.041370 0.048512 0.057298 4: 0.058022 0.076246 0.098278 0.119959 0.159557 0.199376 0.253403 0.313497 0.376595 0.464502 5: 0.225411 0.334103 0.484751 0.667674 0.940775 1.300555 1.819961 2.448191 3.241428 4.114172 Dimension / Level Time table for Gauss-Hermite Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.007744 0.000371 0.000156 0.000122 0.000122 0.000134 0.000146 0.000148 0.000154 0.000171 2: 0.000178 0.000256 0.000279 0.000372 0.000454 0.000569 0.000708 0.001224 0.001294 0.001551 3: 0.000218 0.000307 0.000616 0.001067 0.001566 0.002341 0.003427 0.006447 0.006051 0.007995 4: 0.000312 0.000419 0.001174 0.002568 0.004428 0.006712 0.009965 0.014372 0.022996 0.033114 5: 0.000274 0.000582 0.001786 0.004402 0.008522 0.015873 0.028409 0.046095 0.075333 0.109873 6: 0.000508 0.000777 0.002430 0.006441 0.016496 0.031387 0.063733 0.117954 0.207108 0.339788 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000950 0.000381 0.000243 0.000241 0.000263 0.000273 0.000246 0.000281 0.000276 0.000245 2: 0.001977 0.001771 0.001848 0.002205 0.002566 0.004970 0.004628 0.004236 0.005054 0.004961 3: 0.010781 0.012355 0.014655 0.017804 0.023025 0.027392 0.031870 0.037561 0.041802 0.047166 4: 0.041829 0.057963 0.077862 0.102345 0.126457 0.165656 0.210921 0.272834 0.305246 0.391861 5: 0.171280 0.238350 0.347383 0.497797 0.684338 0.940542 1.136459 1.692920 2.287558 2.941254 Dimension / Level Time table for Gauss-Legendre Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.002499 0.000344 0.000141 0.000140 0.000111 0.000120 0.000131 0.000138 0.000163 0.000208 2: 0.000159 0.000288 0.000379 0.000455 0.000577 0.000747 0.000773 0.001017 0.001037 0.001482 3: 0.000270 0.000318 0.000641 0.000960 0.001384 0.002123 0.003097 0.004805 0.006392 0.007675 4: 0.000243 0.000413 0.001113 0.002484 0.004323 0.006656 0.009972 0.015603 0.023371 0.032028 5: 0.000287 0.000490 0.001601 0.004092 0.008273 0.015554 0.026518 0.045487 0.071604 0.111587 6: 0.000392 0.000682 0.002335 0.006496 0.017444 0.034137 0.064020 0.121101 0.214938 0.362195 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000958 0.000398 0.000302 0.000358 0.000274 0.000281 0.000263 0.000262 0.000444 0.000325 2: 0.001585 0.002116 0.002136 0.002948 0.002769 0.003392 0.003979 0.005418 0.004533 0.005022 3: 0.011370 0.012296 0.015102 0.017849 0.022645 0.026911 0.029139 0.034738 0.041106 0.045366 4: 0.040614 0.053287 0.070950 0.091321 0.117869 0.149542 0.209278 0.266751 0.335636 0.409547 5: 0.171283 0.250427 0.357161 0.503938 0.682989 0.925593 1.263748 1.684539 2.141598 2.974599 Dimension / Level Time table, KP, (-oo,+oo) Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.001856 0.000369 0.000155 0.000121 0.000118 0.000124 0.000135 0.000144 0.000152 0.000162 2: 0.000151 0.000266 0.000322 0.000374 0.000481 0.000609 0.000789 0.001098 0.001729 0.001671 3: 0.000276 0.000380 0.000616 0.000926 0.001614 0.002946 0.003599 0.004883 0.005755 0.007590 4: 0.000326 0.000655 0.001428 0.002652 0.004613 0.006604 0.010635 0.015974 0.022796 0.031846 5: 0.000291 0.000708 0.001924 0.004154 0.008325 0.015252 0.027445 0.047135 0.083203 0.152050 6: 0.000429 0.000722 0.002247 0.006299 0.016274 0.063755 0.066520 0.188199 0.261637 0.370472 Dimension / Level Time table for KP on [0,1] Dim: 1 2 3 4 5 6 7 8 9 10 Level: 1: 0.001092 0.000486 0.000247 0.000154 0.000128 0.000128 0.000138 0.000149 0.000152 0.000165 2: 0.000230 0.000316 0.000362 0.000393 0.000484 0.000607 0.000801 0.000961 0.001346 0.002275 3: 0.000231 0.000323 0.001288 0.001010 0.001756 0.005689 0.004793 0.005399 0.007797 0.008417 4: 0.001792 0.001585 0.002675 0.002475 0.004195 0.006772 0.010585 0.015567 0.022561 0.031892 5: 0.000286 0.000660 0.001758 0.003956 0.008436 0.015843 0.026832 0.045886 0.074067 0.170421 6: 0.000442 0.000591 0.002249 0.006712 0.016878 0.033727 0.109298 0.195877 0.215806 0.393404 Dim: 11 12 13 14 15 16 17 18 19 20 Level: 1: 0.000944 0.000354 0.000245 0.000345 0.000271 0.000247 0.000243 0.000249 0.000390 0.000314 2: 0.001622 0.001861 0.002139 0.002960 0.002900 0.003332 0.003557 0.004290 0.004990 0.004850 3: 0.011493 0.012497 0.015031 0.018100 0.022218 0.026574 0.031390 0.036640 0.043098 0.049925 4: 0.047263 0.077532 0.135850 0.108565 0.135755 0.171693 0.213410 0.264870 0.328353 0.399138 5: 0.173874 0.253615 0.487204 0.571731 0.714789 0.984377 1.294947 1.694948 2.558892 3.248633 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-Mar-2019 15:34:31 diary off