>> sparse_grid_mixed_size_table ( ) 05-Mar-2011 14:31:07 SPARSE_GRID_MIXED_SIZE_TABLE makes point count tables. MATLAB version SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. Here we report the total number of polynomials of degree DEGREE or less in the given DIM dimensional space. (This is essentially Pascal's triangle.) DIM: 1 2 3 4 5 DEGREE 1 2 3 4 5 6 2 3 6 10 15 21 3 4 10 20 35 56 4 5 15 35 70 126 5 6 21 56 126 252 6 7 28 84 210 462 7 8 36 120 330 792 8 9 45 165 495 1287 9 10 55 220 715 2002 10 11 66 286 1001 3003 11 12 78 364 1365 4368 12 13 91 455 1820 6188 13 14 105 560 2380 8568 14 15 120 680 3060 11628 15 16 136 816 3876 15504 05-Mar-2011 14:31:07 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. Here we report the total number of polynomials of degree DEGREE or less in the given DIM dimensional space. (This is essentially Pascal's triangle.) DIM: 6 7 8 9 10 DEGREE 1 7 8 9 10 11 2 28 36 45 55 66 3 84 120 165 220 286 4 210 330 495 715 1001 5 462 792 1287 2002 3003 6 924 1716 3003 5005 8008 7 1716 3432 6435 11440 19448 8 3003 6435 12870 24310 43758 9 5005 11440 24310 48620 92378 10 8008 19448 43758 92378 184756 11 12376 31824 75582 167960 352716 05-Mar-2011 14:31:07 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 1 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:31:14 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 1 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:31:33 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 1 ALPHA parameter is 0.000000 BETA parameter is 0.000000 DIM: 100 LEVEL_MAX 0 1 1 201 2 20201 05-Mar-2011 14:31:36 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 3 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:31:50 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 3 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:32:16 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 11 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:32:17 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 11 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:32:36 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 13 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:32:36 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 13 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 05-Mar-2011 14:32:50 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 16 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 15 97 303 705 1391 5 15 161 687 1985 4623 05-Mar-2011 14:32:51 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 16 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 2465 4047 6273 9295 13281 5 9377 17263 29569 47887 74145 05-Mar-2011 14:33:17 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 17 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 7 25 63 129 231 4 9 41 129 321 681 5 11 61 231 681 1683 6 13 85 377 1289 3653 7 15 113 575 2241 7183 05-Mar-2011 14:33:22 SPARSE_GRID_MIXED_SIZE_TABULATE SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a sparse grid. We use the same rule in all dimensions, and count the points for a range of dimensions and levels. 1D rule index is 17 ALPHA parameter is 0.000000 BETA parameter is 0.000000 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 3 377 575 833 1159 1561 4 1289 2241 3649 5641 8361 5 3653 7183 13073 22363 36365 05-Mar-2011 14:33:40 SPARSE_GRID_MIXED_SIZE_TABLE: Normal end of execution. 05-Mar-2011 14:33:40 >>