25 April 2014 05:11:30 PM SPARSE_COUNT_PRB C++ version Test the SPARSE_COUNT library. TEST01 CC_SE_SIZE returns the number of distinct points in a sparse grid made from * CC_SE, Clenshaw Curtis Slow Exponential Growth family. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 5 13 25 41 61 3 9 29 69 137 241 4 9 49 153 369 761 5 17 81 297 849 2033 6 17 129 545 1777 4833 7 17 161 881 3377 10433 8 17 225 1361 5953 20753 9 33 257 1953 9857 38593 10 33 385 2721 15361 67425 TEST01 CC_SE_SIZE returns the number of distinct points in a sparse grid made from * CC_SE, Clenshaw Curtis Slow Exponential Growth family. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 85 113 145 181 221 3 389 589 849 1177 1581 4 1409 2409 3873 5929 8721 5 4289 8233 14689 24721 39665 6 11473 24529 48289 88945 155105 7 27697 65537 141601 284209 536705 8 61345 159953 377729 823057 1677665 9 126401 361665 930049 2192865 4810625 10 244289 765089 2136577 5436321 12803073 TEST02 CFN_E_SIZE returns the number of distinct points in a CFN_E sparse grid made from any closed fully nested family of 1D quadrature rules with exponential growth, including: * CC_E, the Clenshaw Curtis Exponential Growth family; * NCC_E, the Newton Cotes Closed Exponential Growth family. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 5 13 25 41 61 3 9 29 69 137 241 4 17 65 177 401 801 5 33 145 441 1105 2433 6 65 321 1073 2929 6993 7 129 705 2561 7537 19313 8 257 1537 6017 18945 51713 9 513 3329 13953 46721 135073 10 1025 7169 32001 113409 345665 TEST02 CFN_E_SIZE returns the number of distinct points in a CFN_E sparse grid made from any closed fully nested family of 1D quadrature rules with exponential growth, including: * CC_E, the Clenshaw Curtis Exponential Growth family; * NCC_E, the Newton Cotes Closed Exponential Growth family. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 85 113 145 181 221 3 389 589 849 1177 1581 4 1457 2465 3937 6001 8801 5 4865 9017 15713 26017 41265 6 15121 30241 56737 100897 171425 7 44689 95441 190881 361249 652065 8 127105 287745 609025 1218049 2320385 9 350657 836769 1863937 3918273 7836545 10 943553 2362881 5515265 12133761 25370753 TEST03 F2_SE_SIZE returns the number of distinct points in a sparse grid made from * F2_SE, Fejer Type 2 Slow Exponential Growth family. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 7 17 31 49 71 3 7 33 87 177 311 4 15 65 207 513 1071 5 15 97 399 1217 3023 6 15 161 751 2625 7503 7 15 161 1135 4929 16463 8 31 257 1759 8705 33183 9 31 321 2335 13697 60703 10 31 449 3679 21889 105887 TEST03 F2_SE_SIZE returns the number of distinct points in a sparse grid made from * F2_SE, Fejer Type 2 Slow Exponential Growth family. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 497 743 1057 1447 1921 4 1985 3375 5377 8143 11841 5 6497 12559 22401 37519 59745 6 18401 40111 79745 147343 256545 7 46049 112815 249217 506767 963105 8 104705 286303 699393 1559839 3227905 9 217281 663071 1787649 4362783 9809985 10 421185 1423327 4217601 11231007 27377857 TEST04 GP_SE_SIZE returns the number of distinct points in a sparse grid made from * GP_SE, Gauss Patterson Slow Exponential Growth family. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 3 9 19 33 51 3 7 17 39 81 151 4 7 33 87 193 391 5 7 33 135 385 903 6 15 65 207 641 1743 7 15 97 399 1217 3343 8 15 97 495 1985 6223 9 15 161 751 2881 10063 10 15 161 1135 4929 17103 TEST04 GP_SE_SIZE returns the number of distinct points in a sparse grid made from * GP_SE, Gauss Patterson Slow Exponential Growth family. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 73 99 129 163 201 3 257 407 609 871 1201 4 737 1303 2177 3463 5281 5 1889 3655 6657 11527 19105 6 4161 8975 17921 33679 60225 7 8481 19855 43137 87823 169185 8 16929 42031 97153 211087 434145 9 30689 83247 206465 477327 1041185 10 53729 154927 411265 1014159 2347809 TEST05 OFN_E_SIZE returns the number of distinct points in an OFN_E sparse grid made from product grids formed from open fully nested quadrature rules with Exponential Growth, including * F2_E, the Fejer Type 2 Exponential Growth Family; * GP_E, the Gauss Patterson Exponential Growth Family; * NCO_E, the Newton Cotes Open Exponential Growth Family. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 7 17 31 49 71 3 15 49 111 209 351 4 31 129 351 769 1471 5 63 321 1023 2561 5503 6 127 769 2815 7937 18943 7 255 1793 7423 23297 61183 8 511 4097 18943 65537 187903 9 1023 9217 47103 178177 553983 10 2047 20481 114687 471041 1579007 TEST05 OFN_E_SIZE returns the number of distinct points in an OFN_E sparse grid made from product grids formed from open fully nested quadrature rules with Exponential Growth, including * F2_E, the Fejer Type 2 Exponential Growth Family; * GP_E, the Gauss Patterson Exponential Growth Family; * NCO_E, the Newton Cotes Open Exponential Growth Family. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 545 799 1121 1519 2001 4 2561 4159 6401 9439 13441 5 10625 18943 31745 50623 77505 6 40193 78079 141569 242815 397825 7 141569 297727 580865 1066495 1862145 8 471041 1066495 2228225 4361215 8085505 9 1496065 3629055 8085505 16807935 32978945 10 4571137 11829247 28000257 61616127 127574017 TEST06 ONN_E_SIZE returns the number of distinct points in an ONN_E sparse grid made from product grids formed from open non-nested quadrature rules with exponential growth, including: * LG_E, the Gauss Laguerre Exponential Growth Family; * GJ_E, the Gauss Jacobi Exponential Growth Family; * GLG_E, the Generalized Gauss Laguerre Exponential Growth Family * GW_E, any Golub Welsch Exponential Growth Family; DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 7 10 13 16 2 7 29 58 95 141 3 15 95 255 515 906 4 31 273 945 2309 4746 5 63 723 3120 9065 21503 6 127 1813 9484 32259 87358 7 255 4375 27109 106455 325943 8 511 10265 73915 330985 1135893 9 1023 23579 194190 980797 3743358 10 2047 53277 495198 2793943 11775507 TEST06 ONN_E_SIZE returns the number of distinct points in an ONN_E sparse grid made from product grids formed from open non-nested quadrature rules with exponential growth, including: * LG_E, the Gauss Laguerre Exponential Growth Family; * GJ_E, the Gauss Jacobi Exponential Growth Family; * GLG_E, the Generalized Gauss Laguerre Exponential Growth Family * GW_E, any Golub Welsch Exponential Growth Family; DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 19 22 25 28 31 2 196 260 333 415 506 3 1456 2192 3141 4330 5786 4 8722 14778 23535 35695 52041 5 44758 84708 149031 247456 392007 6 204203 428772 828795 1499773 2571712 7 849161 1966079 4154403 8158810 15089932 8 3275735 8316605 19122245 40599130 80725502 9 11876081 32894998 81953165 187432959 399429602 10 40869038 122928088 330545025 811645950 1848483779 TEST07 ONN_L_SIZE returns the number of distinct points in an ONN_L sparse grid made from product grids formed from open non-nested quadrature rules with linear growth, including: * LG_L, the Gauss Laguerre Linear Growth Family; * GJ_L, the Gauss Jacobi Linear Growth Family; * GLG_L, the Generalized Gauss Laguerre Linear Growth Family; * GW_L, any Golub Welsch Linear Growth Family; DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 7 10 13 16 2 5 25 52 87 131 3 7 63 189 403 736 4 9 129 543 1461 3206 5 11 231 1320 4433 11583 6 13 377 2834 11739 36218 7 15 575 5531 27911 100893 8 17 833 10013 60809 255663 9 19 1159 17062 123253 598538 10 21 1561 27664 235135 1310165 TEST07 ONN_L_SIZE returns the number of distinct points in an ONN_L sparse grid made from product grids formed from open non-nested quadrature rules with linear growth, including: * LG_L, the Gauss Laguerre Linear Growth Family; * GJ_L, the Gauss Jacobi Linear Growth Family; * GLG_L, the Generalized Gauss Laguerre Linear Growth Family; * GW_L, any Golub Welsch Linear Growth Family; DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 19 22 25 28 31 2 184 246 317 397 486 3 1216 1870 2725 3808 5146 4 6190 10900 17903 27847 41461 5 25954 52074 96055 165844 271467 6 93535 212738 439019 838915 1506232 7 298357 765313 1760035 3711040 7290952 8 860455 2476883 6323269 14666470 31453182 9 2279829 7329934 20693565 52638759 122920642 10 5618754 20087574 62483217 173788146 440815035 TEST08 OWN_E_SIZE returns the number of distinct points in an OWN_E sparse grid made from product grids formed from open weakly nested quadrature rules with exponential growth, including: * GGH_E, the Generalized Gauss-Hermite Exponential Growth Family; * GH_E, the Gauss-Hermite Exponential Growth Family; * LG_E, the Gauss-Legendre Exponential Growth Family; DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 7 21 37 57 81 3 15 73 159 289 471 4 31 221 597 1265 2341 5 63 609 2031 4969 10363 6 127 1573 6397 17945 41913 7 255 3881 18943 60577 157583 8 511 9261 53365 193441 557693 9 1023 21553 144351 589625 1875443 10 2047 49205 377661 1727625 6037137 TEST08 OWN_E_SIZE returns the number of distinct points in an OWN_E sparse grid made from product grids formed from open weakly nested quadrature rules with exponential growth, including: * GGH_E, the Generalized Gauss-Hermite Exponential Growth Family; * GH_E, the Gauss-Hermite Exponential Growth Family; * LG_E, the Gauss-Legendre Exponential Growth Family; DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 109 141 177 217 261 3 713 1023 1409 1879 2441 4 3953 6245 9377 13525 18881 5 19397 33559 54673 84931 126925 6 86517 163213 287409 479233 764365 7 357153 731951 1388737 2478511 4208385 8 1382361 3067669 6253537 11916685 21493065 9 5065693 12136743 26516113 53833083 102935845 10 17709469 45683389 106723249 230380089 466201781 TEST09 OWN_L_SIZE returns the number of distinct points in an OWN_L sparse grid made from product grids formed from open weakly nested quadrature rules with linear growth, including: * GGH_L, the Generalized Gauss-Hermite Linear Growth Family; * GH_L, the Gauss-Hermite Linear Growth Family; * LG_L, the Gauss-Legendre Linear Growth Family; DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 5 17 31 49 71 3 7 45 105 201 341 4 9 97 297 681 1341 5 11 181 735 2001 4543 6 13 305 1631 5257 13683 7 15 477 3305 12609 37433 8 17 705 6209 28017 94473 9 19 997 10951 58297 222563 10 21 1361 18319 114561 493935 TEST09 OWN_L_SIZE returns the number of distinct points in an OWN_L sparse grid made from product grids formed from open weakly nested quadrature rules with linear growth, including: * GGH_L, the Generalized Gauss-Hermite Linear Growth Family; * GH_L, the Gauss-Hermite Linear Growth Family; * LG_L, the Gauss-Legendre Linear Growth Family; DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 533 785 1105 1501 1981 4 2381 3921 6097 9061 12981 5 9113 16703 28577 46303 71785 6 30869 62735 117713 207355 347005 7 94601 212481 436033 833017 1501545 8 266489 659585 1476673 3053065 5916505 9 698373 1899663 4629457 10338603 21503085 10 1718697 5124927 13566753 32667567 72810297 TEST10 OWN_O_SIZE returns the number of distinct points in an OWN_O sparse grid made from product grids formed from open weakly nested quadrature rules with odd growth, including: * GGH_L, the Generalized Gauss-Hermite Odd Growth Family; * GH_L, the Gauss-Hermite Odd Growth Family; * LG_L, the Gauss-Legendre Odd Growth Family; DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 3 9 19 33 51 3 5 17 39 81 151 4 5 29 87 193 391 5 7 41 153 409 933 6 7 65 265 777 1973 7 9 81 457 1481 4013 8 9 121 649 2521 7693 9 11 141 1127 4353 13983 10 11 201 1379 6985 24951 TEST10 OWN_O_SIZE returns the number of distinct points in an OWN_O sparse grid made from product grids formed from open weakly nested quadrature rules with odd growth, including: * GGH_L, the Generalized Gauss-Hermite Odd Growth Family; * GH_L, the Gauss-Hermite Odd Growth Family; * LG_L, the Gauss-Legendre Odd Growth Family; DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 73 99 129 163 201 3 257 407 609 871 1201 4 737 1303 2177 3463 5281 5 1925 3697 6705 11581 19165 6 4509 9465 18577 34525 61285 7 9837 22249 46993 93637 177525 8 20445 49465 111313 235909 474885 9 40025 103967 249377 560415 1192425 10 75917 209051 531569 1263567 2835589 SPARSE_COUNT_PRB Normal end of execution. 25 April 2014 05:11:31 PM