25 December 2011 11:04:09 AM SANDIA_SPARSE_PRB C++ version Test the SANDIA_SPARSE library. LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 5 3 9 4 17 5 33 6 65 7 129 8 257 9 513 10 1025 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 5 13 25 41 61 85 3 9 29 69 137 241 389 4 17 65 177 401 801 1457 5 33 145 441 1105 2433 4865 6 65 321 1073 2929 6993 15121 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. 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 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 201 2 20201 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 7 3 15 4 31 5 63 6 127 7 255 8 511 9 1023 10 2047 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 7 17 31 49 71 97 3 15 49 111 209 351 545 4 31 129 351 769 1471 2561 5 63 321 1023 2561 5503 10625 6 127 769 2815 7937 18943 40193 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. 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 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 201 2 20401 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 7 3 15 4 31 5 63 6 127 7 255 8 511 9 1023 10 2047 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 7 21 37 57 81 109 3 15 73 159 289 471 713 4 31 225 597 1265 2341 3953 5 63 637 2031 4969 10363 19397 6 127 1693 6405 17945 41913 86517 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. 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 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 201 2 20601 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 7 3 15 4 31 5 63 6 127 7 255 8 511 9 1023 10 2047 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 7 10 13 16 19 2 7 29 58 95 141 196 3 15 95 255 515 906 1456 4 31 273 945 2309 4746 8722 5 63 723 3120 9065 21503 44758 6 127 1813 9484 32259 87358 204203 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. 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 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 301 2 45551 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 Unique points in the grid = 5 Point Grid indices: Grid bases: 0 1 1 1 1 1 0 1 3 1 2 2 1 3 1 3 1 0 1 3 4 1 2 1 3 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 Unique points in the grid = 29 Point Grid indices: Grid bases: 0 4 4 1 1 1 0 4 3 1 2 8 4 3 1 3 4 0 1 3 4 4 8 1 3 5 2 4 5 1 6 6 4 5 1 7 0 0 3 3 8 8 0 3 3 9 0 8 3 3 10 8 8 3 3 11 4 2 1 5 12 4 6 1 5 13 1 4 9 1 14 3 4 9 1 15 5 4 9 1 16 7 4 9 1 17 2 0 5 3 18 6 0 5 3 19 2 8 5 3 20 6 8 5 3 21 0 2 3 5 22 8 2 3 5 23 0 6 3 5 24 8 6 3 5 25 4 1 1 9 26 4 3 1 9 27 4 5 1 9 28 4 7 1 9 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 Unique points in the grid = 1 Point Grid indices: Grid bases: 0 0 0 0 1 1 1 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 25 Point Grid indices: Grid bases: 0 2 2 2 1 1 1 1 0 2 2 3 1 1 2 4 2 2 3 1 1 3 2 0 2 1 3 1 4 2 4 2 1 3 1 5 2 2 0 1 1 3 6 2 2 4 1 1 3 7 1 2 2 5 1 1 8 3 2 2 5 1 1 9 0 0 2 3 3 1 10 4 0 2 3 3 1 11 0 4 2 3 3 1 12 4 4 2 3 3 1 13 2 1 2 1 5 1 14 2 3 2 1 5 1 15 0 2 0 3 1 3 16 4 2 0 3 1 3 17 0 2 4 3 1 3 18 4 2 4 3 1 3 19 2 0 0 1 3 3 20 2 4 0 1 3 3 21 2 0 4 1 3 3 22 2 4 4 1 3 3 23 2 2 1 1 1 5 24 2 2 3 1 1 5 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 1 Spatial dimension DIM_NUM = 6 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 85 Point Grid indices: Grid bases: 0 2 2 2 2 2 2 1 1 1 1 1 1 1 0 2 2 2 2 2 3 1 1 1 1 1 2 4 2 2 2 2 2 3 1 1 1 1 1 3 2 0 2 2 2 2 1 3 1 1 1 1 4 2 4 2 2 2 2 1 3 1 1 1 1 5 2 2 0 2 2 2 1 1 3 1 1 1 6 2 2 4 2 2 2 1 1 3 1 1 1 7 2 2 2 0 2 2 1 1 1 3 1 1 8 2 2 2 4 2 2 1 1 1 3 1 1 9 2 2 2 2 0 2 1 1 1 1 3 1 10 2 2 2 2 4 2 1 1 1 1 3 1 11 2 2 2 2 2 0 1 1 1 1 1 3 12 2 2 2 2 2 4 1 1 1 1 1 3 13 1 2 2 2 2 2 5 1 1 1 1 1 14 3 2 2 2 2 2 5 1 1 1 1 1 15 0 0 2 2 2 2 3 3 1 1 1 1 16 4 0 2 2 2 2 3 3 1 1 1 1 17 0 4 2 2 2 2 3 3 1 1 1 1 18 4 4 2 2 2 2 3 3 1 1 1 1 19 2 1 2 2 2 2 1 5 1 1 1 1 20 2 3 2 2 2 2 1 5 1 1 1 1 21 0 2 0 2 2 2 3 1 3 1 1 1 22 4 2 0 2 2 2 3 1 3 1 1 1 23 0 2 4 2 2 2 3 1 3 1 1 1 24 4 2 4 2 2 2 3 1 3 1 1 1 25 2 0 0 2 2 2 1 3 3 1 1 1 26 2 4 0 2 2 2 1 3 3 1 1 1 27 2 0 4 2 2 2 1 3 3 1 1 1 28 2 4 4 2 2 2 1 3 3 1 1 1 29 2 2 1 2 2 2 1 1 5 1 1 1 30 2 2 3 2 2 2 1 1 5 1 1 1 31 0 2 2 0 2 2 3 1 1 3 1 1 32 4 2 2 0 2 2 3 1 1 3 1 1 33 0 2 2 4 2 2 3 1 1 3 1 1 34 4 2 2 4 2 2 3 1 1 3 1 1 35 2 0 2 0 2 2 1 3 1 3 1 1 36 2 4 2 0 2 2 1 3 1 3 1 1 37 2 0 2 4 2 2 1 3 1 3 1 1 38 2 4 2 4 2 2 1 3 1 3 1 1 39 2 2 0 0 2 2 1 1 3 3 1 1 40 2 2 4 0 2 2 1 1 3 3 1 1 41 2 2 0 4 2 2 1 1 3 3 1 1 42 2 2 4 4 2 2 1 1 3 3 1 1 43 2 2 2 1 2 2 1 1 1 5 1 1 44 2 2 2 3 2 2 1 1 1 5 1 1 45 0 2 2 2 0 2 3 1 1 1 3 1 46 4 2 2 2 0 2 3 1 1 1 3 1 47 0 2 2 2 4 2 3 1 1 1 3 1 48 4 2 2 2 4 2 3 1 1 1 3 1 49 2 0 2 2 0 2 1 3 1 1 3 1 50 2 4 2 2 0 2 1 3 1 1 3 1 51 2 0 2 2 4 2 1 3 1 1 3 1 52 2 4 2 2 4 2 1 3 1 1 3 1 53 2 2 0 2 0 2 1 1 3 1 3 1 54 2 2 4 2 0 2 1 1 3 1 3 1 55 2 2 0 2 4 2 1 1 3 1 3 1 56 2 2 4 2 4 2 1 1 3 1 3 1 57 2 2 2 0 0 2 1 1 1 3 3 1 58 2 2 2 4 0 2 1 1 1 3 3 1 59 2 2 2 0 4 2 1 1 1 3 3 1 60 2 2 2 4 4 2 1 1 1 3 3 1 61 2 2 2 2 1 2 1 1 1 1 5 1 62 2 2 2 2 3 2 1 1 1 1 5 1 63 0 2 2 2 2 0 3 1 1 1 1 3 64 4 2 2 2 2 0 3 1 1 1 1 3 65 0 2 2 2 2 4 3 1 1 1 1 3 66 4 2 2 2 2 4 3 1 1 1 1 3 67 2 0 2 2 2 0 1 3 1 1 1 3 68 2 4 2 2 2 0 1 3 1 1 1 3 69 2 0 2 2 2 4 1 3 1 1 1 3 70 2 4 2 2 2 4 1 3 1 1 1 3 71 2 2 0 2 2 0 1 1 3 1 1 3 72 2 2 4 2 2 0 1 1 3 1 1 3 73 2 2 0 2 2 4 1 1 3 1 1 3 74 2 2 4 2 2 4 1 1 3 1 1 3 75 2 2 2 0 2 0 1 1 1 3 1 3 76 2 2 2 4 2 0 1 1 1 3 1 3 77 2 2 2 0 2 4 1 1 1 3 1 3 78 2 2 2 4 2 4 1 1 1 3 1 3 79 2 2 2 2 0 0 1 1 1 1 3 3 80 2 2 2 2 4 0 1 1 1 1 3 3 81 2 2 2 2 0 4 1 1 1 1 3 3 82 2 2 2 2 4 4 1 1 1 1 3 3 83 2 2 2 2 2 1 1 1 1 1 1 5 84 2 2 2 2 2 3 1 1 1 1 1 5 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 2 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 Unique points in the grid = 5 Point Grid indices: Grid bases: 0 2 2 1 1 1 1 2 3 1 2 3 2 3 1 3 2 1 1 3 4 2 3 1 3 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 2 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 Unique points in the grid = 49 Point Grid indices: Grid bases: 0 8 8 1 1 1 4 8 3 1 2 12 8 3 1 3 8 4 1 3 4 8 12 1 3 5 2 8 7 1 6 6 8 7 1 7 10 8 7 1 8 14 8 7 1 9 4 4 3 3 10 12 4 3 3 11 4 12 3 3 12 12 12 3 3 13 8 2 1 7 14 8 6 1 7 15 8 10 1 7 16 8 14 1 7 17 1 8 15 1 18 3 8 15 1 19 5 8 15 1 20 7 8 15 1 21 9 8 15 1 22 11 8 15 1 23 13 8 15 1 24 15 8 15 1 25 2 4 7 3 26 6 4 7 3 27 10 4 7 3 28 14 4 7 3 29 2 12 7 3 30 6 12 7 3 31 10 12 7 3 32 14 12 7 3 33 4 2 3 7 34 12 2 3 7 35 4 6 3 7 36 12 6 3 7 37 4 10 3 7 38 12 10 3 7 39 4 14 3 7 40 12 14 3 7 41 8 1 1 15 42 8 3 1 15 43 8 5 1 15 44 8 7 1 15 45 8 9 1 15 46 8 11 1 15 47 8 13 1 15 48 8 15 1 15 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 2 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 Unique points in the grid = 1 Point Grid indices: Grid bases: 0 1 1 1 1 1 1 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 2 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 31 Point Grid indices: Grid bases: 0 4 4 4 1 1 1 1 2 4 4 3 1 1 2 6 4 4 3 1 1 3 4 2 4 1 3 1 4 4 6 4 1 3 1 5 4 4 2 1 1 3 6 4 4 6 1 1 3 7 1 4 4 7 1 1 8 3 4 4 7 1 1 9 5 4 4 7 1 1 10 7 4 4 7 1 1 11 2 2 4 3 3 1 12 6 2 4 3 3 1 13 2 6 4 3 3 1 14 6 6 4 3 3 1 15 4 1 4 1 7 1 16 4 3 4 1 7 1 17 4 5 4 1 7 1 18 4 7 4 1 7 1 19 2 4 2 3 1 3 20 6 4 2 3 1 3 21 2 4 6 3 1 3 22 6 4 6 3 1 3 23 4 2 2 1 3 3 24 4 6 2 1 3 3 25 4 2 6 1 3 3 26 4 6 6 1 3 3 27 4 4 1 1 1 7 28 4 4 3 1 1 7 29 4 4 5 1 1 7 30 4 4 7 1 1 7 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 2 Spatial dimension DIM_NUM = 6 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 97 Point Grid indices: Grid bases: 0 4 4 4 4 4 4 1 1 1 1 1 1 1 2 4 4 4 4 4 3 1 1 1 1 1 2 6 4 4 4 4 4 3 1 1 1 1 1 3 4 2 4 4 4 4 1 3 1 1 1 1 4 4 6 4 4 4 4 1 3 1 1 1 1 5 4 4 2 4 4 4 1 1 3 1 1 1 6 4 4 6 4 4 4 1 1 3 1 1 1 7 4 4 4 2 4 4 1 1 1 3 1 1 8 4 4 4 6 4 4 1 1 1 3 1 1 9 4 4 4 4 2 4 1 1 1 1 3 1 10 4 4 4 4 6 4 1 1 1 1 3 1 11 4 4 4 4 4 2 1 1 1 1 1 3 12 4 4 4 4 4 6 1 1 1 1 1 3 13 1 4 4 4 4 4 7 1 1 1 1 1 14 3 4 4 4 4 4 7 1 1 1 1 1 15 5 4 4 4 4 4 7 1 1 1 1 1 16 7 4 4 4 4 4 7 1 1 1 1 1 17 2 2 4 4 4 4 3 3 1 1 1 1 18 6 2 4 4 4 4 3 3 1 1 1 1 19 2 6 4 4 4 4 3 3 1 1 1 1 20 6 6 4 4 4 4 3 3 1 1 1 1 21 4 1 4 4 4 4 1 7 1 1 1 1 22 4 3 4 4 4 4 1 7 1 1 1 1 23 4 5 4 4 4 4 1 7 1 1 1 1 24 4 7 4 4 4 4 1 7 1 1 1 1 25 2 4 2 4 4 4 3 1 3 1 1 1 26 6 4 2 4 4 4 3 1 3 1 1 1 27 2 4 6 4 4 4 3 1 3 1 1 1 28 6 4 6 4 4 4 3 1 3 1 1 1 29 4 2 2 4 4 4 1 3 3 1 1 1 30 4 6 2 4 4 4 1 3 3 1 1 1 31 4 2 6 4 4 4 1 3 3 1 1 1 32 4 6 6 4 4 4 1 3 3 1 1 1 33 4 4 1 4 4 4 1 1 7 1 1 1 34 4 4 3 4 4 4 1 1 7 1 1 1 35 4 4 5 4 4 4 1 1 7 1 1 1 36 4 4 7 4 4 4 1 1 7 1 1 1 37 2 4 4 2 4 4 3 1 1 3 1 1 38 6 4 4 2 4 4 3 1 1 3 1 1 39 2 4 4 6 4 4 3 1 1 3 1 1 40 6 4 4 6 4 4 3 1 1 3 1 1 41 4 2 4 2 4 4 1 3 1 3 1 1 42 4 6 4 2 4 4 1 3 1 3 1 1 43 4 2 4 6 4 4 1 3 1 3 1 1 44 4 6 4 6 4 4 1 3 1 3 1 1 45 4 4 2 2 4 4 1 1 3 3 1 1 46 4 4 6 2 4 4 1 1 3 3 1 1 47 4 4 2 6 4 4 1 1 3 3 1 1 48 4 4 6 6 4 4 1 1 3 3 1 1 49 4 4 4 1 4 4 1 1 1 7 1 1 50 4 4 4 3 4 4 1 1 1 7 1 1 51 4 4 4 5 4 4 1 1 1 7 1 1 52 4 4 4 7 4 4 1 1 1 7 1 1 53 2 4 4 4 2 4 3 1 1 1 3 1 54 6 4 4 4 2 4 3 1 1 1 3 1 55 2 4 4 4 6 4 3 1 1 1 3 1 56 6 4 4 4 6 4 3 1 1 1 3 1 57 4 2 4 4 2 4 1 3 1 1 3 1 58 4 6 4 4 2 4 1 3 1 1 3 1 59 4 2 4 4 6 4 1 3 1 1 3 1 60 4 6 4 4 6 4 1 3 1 1 3 1 61 4 4 2 4 2 4 1 1 3 1 3 1 62 4 4 6 4 2 4 1 1 3 1 3 1 63 4 4 2 4 6 4 1 1 3 1 3 1 64 4 4 6 4 6 4 1 1 3 1 3 1 65 4 4 4 2 2 4 1 1 1 3 3 1 66 4 4 4 6 2 4 1 1 1 3 3 1 67 4 4 4 2 6 4 1 1 1 3 3 1 68 4 4 4 6 6 4 1 1 1 3 3 1 69 4 4 4 4 1 4 1 1 1 1 7 1 70 4 4 4 4 3 4 1 1 1 1 7 1 71 4 4 4 4 5 4 1 1 1 1 7 1 72 4 4 4 4 7 4 1 1 1 1 7 1 73 2 4 4 4 4 2 3 1 1 1 1 3 74 6 4 4 4 4 2 3 1 1 1 1 3 75 2 4 4 4 4 6 3 1 1 1 1 3 76 6 4 4 4 4 6 3 1 1 1 1 3 77 4 2 4 4 4 2 1 3 1 1 1 3 78 4 6 4 4 4 2 1 3 1 1 1 3 79 4 2 4 4 4 6 1 3 1 1 1 3 80 4 6 4 4 4 6 1 3 1 1 1 3 81 4 4 2 4 4 2 1 1 3 1 1 3 82 4 4 6 4 4 2 1 1 3 1 1 3 83 4 4 2 4 4 6 1 1 3 1 1 3 84 4 4 6 4 4 6 1 1 3 1 1 3 85 4 4 4 2 4 2 1 1 1 3 1 3 86 4 4 4 6 4 2 1 1 1 3 1 3 87 4 4 4 2 4 6 1 1 1 3 1 3 88 4 4 4 6 4 6 1 1 1 3 1 3 89 4 4 4 4 2 2 1 1 1 1 3 3 90 4 4 4 4 6 2 1 1 1 1 3 3 91 4 4 4 4 2 6 1 1 1 1 3 3 92 4 4 4 4 6 6 1 1 1 1 3 3 93 4 4 4 4 4 1 1 1 1 1 1 7 94 4 4 4 4 4 3 1 1 1 1 1 7 95 4 4 4 4 4 5 1 1 1 1 1 7 96 4 4 4 4 4 7 1 1 1 1 1 7 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 Unique points in the grid = 5 Point Grid indices: Grid bases: 0 0 0 0 0 1 -1 0 1 0 2 1 0 1 0 3 0 -1 0 1 4 0 1 0 1 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 Unique points in the grid = 73 Point Grid indices: Grid bases: 0 0 0 0 0 1 -1 0 1 0 2 1 0 1 0 3 0 -1 0 1 4 0 1 0 1 5 -3 0 3 0 6 -2 0 3 0 7 -1 0 3 0 8 1 0 3 0 9 2 0 3 0 10 3 0 3 0 11 -1 -1 1 1 12 1 -1 1 1 13 -1 1 1 1 14 1 1 1 1 15 0 -3 0 3 16 0 -2 0 3 17 0 -1 0 3 18 0 1 0 3 19 0 2 0 3 20 0 3 0 3 21 -7 0 7 0 22 -6 0 7 0 23 -5 0 7 0 24 -4 0 7 0 25 -3 0 7 0 26 -2 0 7 0 27 -1 0 7 0 28 1 0 7 0 29 2 0 7 0 30 3 0 7 0 31 4 0 7 0 32 5 0 7 0 33 6 0 7 0 34 7 0 7 0 35 -3 -1 3 1 36 -2 -1 3 1 37 -1 -1 3 1 38 1 -1 3 1 39 2 -1 3 1 40 3 -1 3 1 41 -3 1 3 1 42 -2 1 3 1 43 -1 1 3 1 44 1 1 3 1 45 2 1 3 1 46 3 1 3 1 47 -1 -3 1 3 48 1 -3 1 3 49 -1 -2 1 3 50 1 -2 1 3 51 -1 -1 1 3 52 1 -1 1 3 53 -1 1 1 3 54 1 1 1 3 55 -1 2 1 3 56 1 2 1 3 57 -1 3 1 3 58 1 3 1 3 59 0 -7 0 7 60 0 -6 0 7 61 0 -5 0 7 62 0 -4 0 7 63 0 -3 0 7 64 0 -2 0 7 65 0 -1 0 7 66 0 1 0 7 67 0 2 0 7 68 0 3 0 7 69 0 4 0 7 70 0 5 0 7 71 0 6 0 7 72 0 7 0 7 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 Unique points in the grid = 1 Point Grid indices: Grid bases: 0 0 0 0 0 0 0 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 37 Point Grid indices: Grid bases: 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 2 1 0 0 1 0 0 3 0 -1 0 0 1 0 4 0 1 0 0 1 0 5 0 0 -1 0 0 1 6 0 0 1 0 0 1 7 -3 0 0 3 0 0 8 -2 0 0 3 0 0 9 -1 0 0 3 0 0 10 1 0 0 3 0 0 11 2 0 0 3 0 0 12 3 0 0 3 0 0 13 -1 -1 0 1 1 0 14 1 -1 0 1 1 0 15 -1 1 0 1 1 0 16 1 1 0 1 1 0 17 0 -3 0 0 3 0 18 0 -2 0 0 3 0 19 0 -1 0 0 3 0 20 0 1 0 0 3 0 21 0 2 0 0 3 0 22 0 3 0 0 3 0 23 -1 0 -1 1 0 1 24 1 0 -1 1 0 1 25 -1 0 1 1 0 1 26 1 0 1 1 0 1 27 0 -1 -1 0 1 1 28 0 1 -1 0 1 1 29 0 -1 1 0 1 1 30 0 1 1 0 1 1 31 0 0 -3 0 0 3 32 0 0 -2 0 0 3 33 0 0 -1 0 0 3 34 0 0 1 0 0 3 35 0 0 2 0 0 3 36 0 0 3 0 0 3 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 5 Spatial dimension DIM_NUM = 6 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 109 Point Grid indices: Grid bases: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 0 0 2 1 0 0 0 0 0 1 0 0 0 0 0 3 0 -1 0 0 0 0 0 1 0 0 0 0 4 0 1 0 0 0 0 0 1 0 0 0 0 5 0 0 -1 0 0 0 0 0 1 0 0 0 6 0 0 1 0 0 0 0 0 1 0 0 0 7 0 0 0 -1 0 0 0 0 0 1 0 0 8 0 0 0 1 0 0 0 0 0 1 0 0 9 0 0 0 0 -1 0 0 0 0 0 1 0 10 0 0 0 0 1 0 0 0 0 0 1 0 11 0 0 0 0 0 -1 0 0 0 0 0 1 12 0 0 0 0 0 1 0 0 0 0 0 1 13 -3 0 0 0 0 0 3 0 0 0 0 0 14 -2 0 0 0 0 0 3 0 0 0 0 0 15 -1 0 0 0 0 0 3 0 0 0 0 0 16 1 0 0 0 0 0 3 0 0 0 0 0 17 2 0 0 0 0 0 3 0 0 0 0 0 18 3 0 0 0 0 0 3 0 0 0 0 0 19 -1 -1 0 0 0 0 1 1 0 0 0 0 20 1 -1 0 0 0 0 1 1 0 0 0 0 21 -1 1 0 0 0 0 1 1 0 0 0 0 22 1 1 0 0 0 0 1 1 0 0 0 0 23 0 -3 0 0 0 0 0 3 0 0 0 0 24 0 -2 0 0 0 0 0 3 0 0 0 0 25 0 -1 0 0 0 0 0 3 0 0 0 0 26 0 1 0 0 0 0 0 3 0 0 0 0 27 0 2 0 0 0 0 0 3 0 0 0 0 28 0 3 0 0 0 0 0 3 0 0 0 0 29 -1 0 -1 0 0 0 1 0 1 0 0 0 30 1 0 -1 0 0 0 1 0 1 0 0 0 31 -1 0 1 0 0 0 1 0 1 0 0 0 32 1 0 1 0 0 0 1 0 1 0 0 0 33 0 -1 -1 0 0 0 0 1 1 0 0 0 34 0 1 -1 0 0 0 0 1 1 0 0 0 35 0 -1 1 0 0 0 0 1 1 0 0 0 36 0 1 1 0 0 0 0 1 1 0 0 0 37 0 0 -3 0 0 0 0 0 3 0 0 0 38 0 0 -2 0 0 0 0 0 3 0 0 0 39 0 0 -1 0 0 0 0 0 3 0 0 0 40 0 0 1 0 0 0 0 0 3 0 0 0 41 0 0 2 0 0 0 0 0 3 0 0 0 42 0 0 3 0 0 0 0 0 3 0 0 0 43 -1 0 0 -1 0 0 1 0 0 1 0 0 44 1 0 0 -1 0 0 1 0 0 1 0 0 45 -1 0 0 1 0 0 1 0 0 1 0 0 46 1 0 0 1 0 0 1 0 0 1 0 0 47 0 -1 0 -1 0 0 0 1 0 1 0 0 48 0 1 0 -1 0 0 0 1 0 1 0 0 49 0 -1 0 1 0 0 0 1 0 1 0 0 50 0 1 0 1 0 0 0 1 0 1 0 0 51 0 0 -1 -1 0 0 0 0 1 1 0 0 52 0 0 1 -1 0 0 0 0 1 1 0 0 53 0 0 -1 1 0 0 0 0 1 1 0 0 54 0 0 1 1 0 0 0 0 1 1 0 0 55 0 0 0 -3 0 0 0 0 0 3 0 0 56 0 0 0 -2 0 0 0 0 0 3 0 0 57 0 0 0 -1 0 0 0 0 0 3 0 0 58 0 0 0 1 0 0 0 0 0 3 0 0 59 0 0 0 2 0 0 0 0 0 3 0 0 60 0 0 0 3 0 0 0 0 0 3 0 0 61 -1 0 0 0 -1 0 1 0 0 0 1 0 62 1 0 0 0 -1 0 1 0 0 0 1 0 63 -1 0 0 0 1 0 1 0 0 0 1 0 64 1 0 0 0 1 0 1 0 0 0 1 0 65 0 -1 0 0 -1 0 0 1 0 0 1 0 66 0 1 0 0 -1 0 0 1 0 0 1 0 67 0 -1 0 0 1 0 0 1 0 0 1 0 68 0 1 0 0 1 0 0 1 0 0 1 0 69 0 0 -1 0 -1 0 0 0 1 0 1 0 70 0 0 1 0 -1 0 0 0 1 0 1 0 71 0 0 -1 0 1 0 0 0 1 0 1 0 72 0 0 1 0 1 0 0 0 1 0 1 0 73 0 0 0 -1 -1 0 0 0 0 1 1 0 74 0 0 0 1 -1 0 0 0 0 1 1 0 75 0 0 0 -1 1 0 0 0 0 1 1 0 76 0 0 0 1 1 0 0 0 0 1 1 0 77 0 0 0 0 -3 0 0 0 0 0 3 0 78 0 0 0 0 -2 0 0 0 0 0 3 0 79 0 0 0 0 -1 0 0 0 0 0 3 0 80 0 0 0 0 1 0 0 0 0 0 3 0 81 0 0 0 0 2 0 0 0 0 0 3 0 82 0 0 0 0 3 0 0 0 0 0 3 0 83 -1 0 0 0 0 -1 1 0 0 0 0 1 84 1 0 0 0 0 -1 1 0 0 0 0 1 85 -1 0 0 0 0 1 1 0 0 0 0 1 86 1 0 0 0 0 1 1 0 0 0 0 1 87 0 -1 0 0 0 -1 0 1 0 0 0 1 88 0 1 0 0 0 -1 0 1 0 0 0 1 89 0 -1 0 0 0 1 0 1 0 0 0 1 90 0 1 0 0 0 1 0 1 0 0 0 1 91 0 0 -1 0 0 -1 0 0 1 0 0 1 92 0 0 1 0 0 -1 0 0 1 0 0 1 93 0 0 -1 0 0 1 0 0 1 0 0 1 94 0 0 1 0 0 1 0 0 1 0 0 1 95 0 0 0 -1 0 -1 0 0 0 1 0 1 96 0 0 0 1 0 -1 0 0 0 1 0 1 97 0 0 0 -1 0 1 0 0 0 1 0 1 98 0 0 0 1 0 1 0 0 0 1 0 1 99 0 0 0 0 -1 -1 0 0 0 0 1 1 100 0 0 0 0 1 -1 0 0 0 0 1 1 101 0 0 0 0 -1 1 0 0 0 0 1 1 102 0 0 0 0 1 1 0 0 0 0 1 1 103 0 0 0 0 0 -3 0 0 0 0 0 3 104 0 0 0 0 0 -2 0 0 0 0 0 3 105 0 0 0 0 0 -1 0 0 0 0 0 3 106 0 0 0 0 0 1 0 0 0 0 0 3 107 0 0 0 0 0 2 0 0 0 0 0 3 108 0 0 0 0 0 3 0 0 0 0 0 3 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 Unique points in the grid = 7 Point Grid indices: Grid bases: 0 1 1 1 1 1 1 1 3 1 2 2 1 3 1 3 3 1 3 1 4 1 1 1 3 5 1 2 1 3 6 1 3 1 3 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 Unique points in the grid = 95 Point Grid indices: Grid bases: 0 1 1 7 1 1 2 1 7 1 2 3 1 7 1 3 4 1 7 1 4 5 1 7 1 5 6 1 7 1 6 7 1 7 1 7 1 1 3 3 8 2 1 3 3 9 3 1 3 3 10 1 2 3 3 11 2 2 3 3 12 3 2 3 3 13 1 3 3 3 14 2 3 3 3 15 3 3 3 3 16 1 1 1 7 17 1 2 1 7 18 1 3 1 7 19 1 4 1 7 20 1 5 1 7 21 1 6 1 7 22 1 7 1 7 23 1 1 15 1 24 2 1 15 1 25 3 1 15 1 26 4 1 15 1 27 5 1 15 1 28 6 1 15 1 29 7 1 15 1 30 8 1 15 1 31 9 1 15 1 32 10 1 15 1 33 11 1 15 1 34 12 1 15 1 35 13 1 15 1 36 14 1 15 1 37 15 1 15 1 38 1 1 7 3 39 2 1 7 3 40 3 1 7 3 41 4 1 7 3 42 5 1 7 3 43 6 1 7 3 44 7 1 7 3 45 1 2 7 3 46 2 2 7 3 47 3 2 7 3 48 4 2 7 3 49 5 2 7 3 50 6 2 7 3 51 7 2 7 3 52 1 3 7 3 53 2 3 7 3 54 3 3 7 3 55 4 3 7 3 56 5 3 7 3 57 6 3 7 3 58 7 3 7 3 59 1 1 3 7 60 2 1 3 7 61 3 1 3 7 62 1 2 3 7 63 2 2 3 7 64 3 2 3 7 65 1 3 3 7 66 2 3 3 7 67 3 3 3 7 68 1 4 3 7 69 2 4 3 7 70 3 4 3 7 71 1 5 3 7 72 2 5 3 7 73 3 5 3 7 74 1 6 3 7 75 2 6 3 7 76 3 6 3 7 77 1 7 3 7 78 2 7 3 7 79 3 7 3 7 80 1 1 1 15 81 1 2 1 15 82 1 3 1 15 83 1 4 1 15 84 1 5 1 15 85 1 6 1 15 86 1 7 1 15 87 1 8 1 15 88 1 9 1 15 89 1 10 1 15 90 1 11 1 15 91 1 12 1 15 92 1 13 1 15 93 1 14 1 15 94 1 15 1 15 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 7 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 Unique points in the grid = 1 Point Grid indices: Grid bases: 0 1 1 1 1 1 1 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 7 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 58 Point Grid indices: Grid bases: 0 1 1 1 1 1 1 1 1 1 1 3 1 1 2 2 1 1 3 1 1 3 3 1 1 3 1 1 4 1 1 1 1 3 1 5 1 2 1 1 3 1 6 1 3 1 1 3 1 7 1 1 1 1 1 3 8 1 1 2 1 1 3 9 1 1 3 1 1 3 10 1 1 1 7 1 1 11 2 1 1 7 1 1 12 3 1 1 7 1 1 13 4 1 1 7 1 1 14 5 1 1 7 1 1 15 6 1 1 7 1 1 16 7 1 1 7 1 1 17 1 1 1 3 3 1 18 2 1 1 3 3 1 19 3 1 1 3 3 1 20 1 2 1 3 3 1 21 2 2 1 3 3 1 22 3 2 1 3 3 1 23 1 3 1 3 3 1 24 2 3 1 3 3 1 25 3 3 1 3 3 1 26 1 1 1 1 7 1 27 1 2 1 1 7 1 28 1 3 1 1 7 1 29 1 4 1 1 7 1 30 1 5 1 1 7 1 31 1 6 1 1 7 1 32 1 7 1 1 7 1 33 1 1 1 3 1 3 34 2 1 1 3 1 3 35 3 1 1 3 1 3 36 1 1 2 3 1 3 37 2 1 2 3 1 3 38 3 1 2 3 1 3 39 1 1 3 3 1 3 40 2 1 3 3 1 3 41 3 1 3 3 1 3 42 1 1 1 1 3 3 43 1 2 1 1 3 3 44 1 3 1 1 3 3 45 1 1 2 1 3 3 46 1 2 2 1 3 3 47 1 3 2 1 3 3 48 1 1 3 1 3 3 49 1 2 3 1 3 3 50 1 3 3 1 3 3 51 1 1 1 1 1 7 52 1 1 2 1 1 7 53 1 1 3 1 1 7 54 1 1 4 1 1 7 55 1 1 5 1 1 7 56 1 1 6 1 1 7 57 1 1 7 1 1 7 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 7 Spatial dimension DIM_NUM = 6 LEVEL_MIN = 0 LEVEL_MAX = 2 Unique points in the grid = 196 Point Grid indices: Grid bases: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 2 2 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 1 1 1 4 1 1 1 1 1 1 1 3 1 1 1 1 5 1 2 1 1 1 1 1 3 1 1 1 1 6 1 3 1 1 1 1 1 3 1 1 1 1 7 1 1 1 1 1 1 1 1 3 1 1 1 8 1 1 2 1 1 1 1 1 3 1 1 1 9 1 1 3 1 1 1 1 1 3 1 1 1 10 1 1 1 1 1 1 1 1 1 3 1 1 11 1 1 1 2 1 1 1 1 1 3 1 1 12 1 1 1 3 1 1 1 1 1 3 1 1 13 1 1 1 1 1 1 1 1 1 1 3 1 14 1 1 1 1 2 1 1 1 1 1 3 1 15 1 1 1 1 3 1 1 1 1 1 3 1 16 1 1 1 1 1 1 1 1 1 1 1 3 17 1 1 1 1 1 2 1 1 1 1 1 3 18 1 1 1 1 1 3 1 1 1 1 1 3 19 1 1 1 1 1 1 7 1 1 1 1 1 20 2 1 1 1 1 1 7 1 1 1 1 1 21 3 1 1 1 1 1 7 1 1 1 1 1 22 4 1 1 1 1 1 7 1 1 1 1 1 23 5 1 1 1 1 1 7 1 1 1 1 1 24 6 1 1 1 1 1 7 1 1 1 1 1 25 7 1 1 1 1 1 7 1 1 1 1 1 26 1 1 1 1 1 1 3 3 1 1 1 1 27 2 1 1 1 1 1 3 3 1 1 1 1 28 3 1 1 1 1 1 3 3 1 1 1 1 29 1 2 1 1 1 1 3 3 1 1 1 1 30 2 2 1 1 1 1 3 3 1 1 1 1 31 3 2 1 1 1 1 3 3 1 1 1 1 32 1 3 1 1 1 1 3 3 1 1 1 1 33 2 3 1 1 1 1 3 3 1 1 1 1 34 3 3 1 1 1 1 3 3 1 1 1 1 35 1 1 1 1 1 1 1 7 1 1 1 1 36 1 2 1 1 1 1 1 7 1 1 1 1 37 1 3 1 1 1 1 1 7 1 1 1 1 38 1 4 1 1 1 1 1 7 1 1 1 1 39 1 5 1 1 1 1 1 7 1 1 1 1 40 1 6 1 1 1 1 1 7 1 1 1 1 41 1 7 1 1 1 1 1 7 1 1 1 1 42 1 1 1 1 1 1 3 1 3 1 1 1 43 2 1 1 1 1 1 3 1 3 1 1 1 44 3 1 1 1 1 1 3 1 3 1 1 1 45 1 1 2 1 1 1 3 1 3 1 1 1 46 2 1 2 1 1 1 3 1 3 1 1 1 47 3 1 2 1 1 1 3 1 3 1 1 1 48 1 1 3 1 1 1 3 1 3 1 1 1 49 2 1 3 1 1 1 3 1 3 1 1 1 50 3 1 3 1 1 1 3 1 3 1 1 1 51 1 1 1 1 1 1 1 3 3 1 1 1 52 1 2 1 1 1 1 1 3 3 1 1 1 53 1 3 1 1 1 1 1 3 3 1 1 1 54 1 1 2 1 1 1 1 3 3 1 1 1 55 1 2 2 1 1 1 1 3 3 1 1 1 56 1 3 2 1 1 1 1 3 3 1 1 1 57 1 1 3 1 1 1 1 3 3 1 1 1 58 1 2 3 1 1 1 1 3 3 1 1 1 59 1 3 3 1 1 1 1 3 3 1 1 1 60 1 1 1 1 1 1 1 1 7 1 1 1 61 1 1 2 1 1 1 1 1 7 1 1 1 62 1 1 3 1 1 1 1 1 7 1 1 1 63 1 1 4 1 1 1 1 1 7 1 1 1 64 1 1 5 1 1 1 1 1 7 1 1 1 65 1 1 6 1 1 1 1 1 7 1 1 1 66 1 1 7 1 1 1 1 1 7 1 1 1 67 1 1 1 1 1 1 3 1 1 3 1 1 68 2 1 1 1 1 1 3 1 1 3 1 1 69 3 1 1 1 1 1 3 1 1 3 1 1 70 1 1 1 2 1 1 3 1 1 3 1 1 71 2 1 1 2 1 1 3 1 1 3 1 1 72 3 1 1 2 1 1 3 1 1 3 1 1 73 1 1 1 3 1 1 3 1 1 3 1 1 74 2 1 1 3 1 1 3 1 1 3 1 1 75 3 1 1 3 1 1 3 1 1 3 1 1 76 1 1 1 1 1 1 1 3 1 3 1 1 77 1 2 1 1 1 1 1 3 1 3 1 1 78 1 3 1 1 1 1 1 3 1 3 1 1 79 1 1 1 2 1 1 1 3 1 3 1 1 80 1 2 1 2 1 1 1 3 1 3 1 1 81 1 3 1 2 1 1 1 3 1 3 1 1 82 1 1 1 3 1 1 1 3 1 3 1 1 83 1 2 1 3 1 1 1 3 1 3 1 1 84 1 3 1 3 1 1 1 3 1 3 1 1 85 1 1 1 1 1 1 1 1 3 3 1 1 86 1 1 2 1 1 1 1 1 3 3 1 1 87 1 1 3 1 1 1 1 1 3 3 1 1 88 1 1 1 2 1 1 1 1 3 3 1 1 89 1 1 2 2 1 1 1 1 3 3 1 1 90 1 1 3 2 1 1 1 1 3 3 1 1 91 1 1 1 3 1 1 1 1 3 3 1 1 92 1 1 2 3 1 1 1 1 3 3 1 1 93 1 1 3 3 1 1 1 1 3 3 1 1 94 1 1 1 1 1 1 1 1 1 7 1 1 95 1 1 1 2 1 1 1 1 1 7 1 1 96 1 1 1 3 1 1 1 1 1 7 1 1 97 1 1 1 4 1 1 1 1 1 7 1 1 98 1 1 1 5 1 1 1 1 1 7 1 1 99 1 1 1 6 1 1 1 1 1 7 1 1 100 1 1 1 7 1 1 1 1 1 7 1 1 101 1 1 1 1 1 1 3 1 1 1 3 1 102 2 1 1 1 1 1 3 1 1 1 3 1 103 3 1 1 1 1 1 3 1 1 1 3 1 104 1 1 1 1 2 1 3 1 1 1 3 1 105 2 1 1 1 2 1 3 1 1 1 3 1 106 3 1 1 1 2 1 3 1 1 1 3 1 107 1 1 1 1 3 1 3 1 1 1 3 1 108 2 1 1 1 3 1 3 1 1 1 3 1 109 3 1 1 1 3 1 3 1 1 1 3 1 110 1 1 1 1 1 1 1 3 1 1 3 1 111 1 2 1 1 1 1 1 3 1 1 3 1 112 1 3 1 1 1 1 1 3 1 1 3 1 113 1 1 1 1 2 1 1 3 1 1 3 1 114 1 2 1 1 2 1 1 3 1 1 3 1 115 1 3 1 1 2 1 1 3 1 1 3 1 116 1 1 1 1 3 1 1 3 1 1 3 1 117 1 2 1 1 3 1 1 3 1 1 3 1 118 1 3 1 1 3 1 1 3 1 1 3 1 119 1 1 1 1 1 1 1 1 3 1 3 1 120 1 1 2 1 1 1 1 1 3 1 3 1 121 1 1 3 1 1 1 1 1 3 1 3 1 122 1 1 1 1 2 1 1 1 3 1 3 1 123 1 1 2 1 2 1 1 1 3 1 3 1 124 1 1 3 1 2 1 1 1 3 1 3 1 125 1 1 1 1 3 1 1 1 3 1 3 1 126 1 1 2 1 3 1 1 1 3 1 3 1 127 1 1 3 1 3 1 1 1 3 1 3 1 128 1 1 1 1 1 1 1 1 1 3 3 1 129 1 1 1 2 1 1 1 1 1 3 3 1 130 1 1 1 3 1 1 1 1 1 3 3 1 131 1 1 1 1 2 1 1 1 1 3 3 1 132 1 1 1 2 2 1 1 1 1 3 3 1 133 1 1 1 3 2 1 1 1 1 3 3 1 134 1 1 1 1 3 1 1 1 1 3 3 1 135 1 1 1 2 3 1 1 1 1 3 3 1 136 1 1 1 3 3 1 1 1 1 3 3 1 137 1 1 1 1 1 1 1 1 1 1 7 1 138 1 1 1 1 2 1 1 1 1 1 7 1 139 1 1 1 1 3 1 1 1 1 1 7 1 140 1 1 1 1 4 1 1 1 1 1 7 1 141 1 1 1 1 5 1 1 1 1 1 7 1 142 1 1 1 1 6 1 1 1 1 1 7 1 143 1 1 1 1 7 1 1 1 1 1 7 1 144 1 1 1 1 1 1 3 1 1 1 1 3 145 2 1 1 1 1 1 3 1 1 1 1 3 146 3 1 1 1 1 1 3 1 1 1 1 3 147 1 1 1 1 1 2 3 1 1 1 1 3 148 2 1 1 1 1 2 3 1 1 1 1 3 149 3 1 1 1 1 2 3 1 1 1 1 3 150 1 1 1 1 1 3 3 1 1 1 1 3 151 2 1 1 1 1 3 3 1 1 1 1 3 152 3 1 1 1 1 3 3 1 1 1 1 3 153 1 1 1 1 1 1 1 3 1 1 1 3 154 1 2 1 1 1 1 1 3 1 1 1 3 155 1 3 1 1 1 1 1 3 1 1 1 3 156 1 1 1 1 1 2 1 3 1 1 1 3 157 1 2 1 1 1 2 1 3 1 1 1 3 158 1 3 1 1 1 2 1 3 1 1 1 3 159 1 1 1 1 1 3 1 3 1 1 1 3 160 1 2 1 1 1 3 1 3 1 1 1 3 161 1 3 1 1 1 3 1 3 1 1 1 3 162 1 1 1 1 1 1 1 1 3 1 1 3 163 1 1 2 1 1 1 1 1 3 1 1 3 164 1 1 3 1 1 1 1 1 3 1 1 3 165 1 1 1 1 1 2 1 1 3 1 1 3 166 1 1 2 1 1 2 1 1 3 1 1 3 167 1 1 3 1 1 2 1 1 3 1 1 3 168 1 1 1 1 1 3 1 1 3 1 1 3 169 1 1 2 1 1 3 1 1 3 1 1 3 170 1 1 3 1 1 3 1 1 3 1 1 3 171 1 1 1 1 1 1 1 1 1 3 1 3 172 1 1 1 2 1 1 1 1 1 3 1 3 173 1 1 1 3 1 1 1 1 1 3 1 3 174 1 1 1 1 1 2 1 1 1 3 1 3 175 1 1 1 2 1 2 1 1 1 3 1 3 176 1 1 1 3 1 2 1 1 1 3 1 3 177 1 1 1 1 1 3 1 1 1 3 1 3 178 1 1 1 2 1 3 1 1 1 3 1 3 179 1 1 1 3 1 3 1 1 1 3 1 3 180 1 1 1 1 1 1 1 1 1 1 3 3 181 1 1 1 1 2 1 1 1 1 1 3 3 182 1 1 1 1 3 1 1 1 1 1 3 3 183 1 1 1 1 1 2 1 1 1 1 3 3 184 1 1 1 1 2 2 1 1 1 1 3 3 185 1 1 1 1 3 2 1 1 1 1 3 3 186 1 1 1 1 1 3 1 1 1 1 3 3 187 1 1 1 1 2 3 1 1 1 1 3 3 188 1 1 1 1 3 3 1 1 1 1 3 3 189 1 1 1 1 1 1 1 1 1 1 1 7 190 1 1 1 1 1 2 1 1 1 1 1 7 191 1 1 1 1 1 3 1 1 1 1 1 7 192 1 1 1 1 1 4 1 1 1 1 1 7 193 1 1 1 1 1 5 1 1 1 1 1 7 194 1 1 1 1 1 6 1 1 1 1 1 7 195 1 1 1 1 1 7 1 1 1 1 1 7 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Unique points in the grid = 5 Grid weights: 0 1.33333 1 0.666667 2 0.666667 3 0.666667 4 0.666667 Grid points: 0 0 0 1 -1 0 2 1 0 3 0 -1 4 0 1 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 1 Unique points in the grid = 13 Grid weights: 0 -0.355556 1 -0.0888889 2 -0.0888889 3 -0.0888889 4 -0.0888889 5 1.06667 6 1.06667 7 0.111111 8 0.111111 9 0.111111 10 0.111111 11 1.06667 12 1.06667 Grid points: 0 0 0 1 -1 0 2 1 0 3 0 -1 4 0 1 5 -0.707107 0 6 0.707107 0 7 -1 -1 8 1 -1 9 -1 1 10 1 1 11 0 -0.707107 12 0 0.707107 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Unique points in the grid = 7 Grid weights: 0 -1.77636e-15 1 1.33333 2 1.33333 3 1.33333 4 1.33333 5 1.33333 6 1.33333 Grid points: 0 0 0 0 1 -1 0 0 2 1 0 0 3 0 -1 0 4 0 1 0 5 0 0 -1 6 0 0 1 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 2 Unique points in the grid = 5 Grid weights: 0 0.444444 1 0.888889 2 0.888889 3 0.888889 4 0.888889 Grid points: 0 0 0 1 -0.866025 0 2 0.866025 0 3 0 -0.866025 4 0 0.866025 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 2 Unique points in the grid = 17 Grid weights: 0 -1.39219 1 0.180601 2 0.180601 3 0.180601 4 0.180601 5 0.173432 6 0.796483 7 0.796483 8 0.173432 9 0.197531 10 0.197531 11 0.197531 12 0.197531 13 0.173432 14 0.796483 15 0.796483 16 0.173432 Grid points: 0 0 0 1 -0.781831 0 2 0.781831 0 3 0 -0.781831 4 0 0.781831 5 -0.974928 0 6 -0.433884 0 7 0.433884 0 8 0.974928 0 9 -0.781831 -0.781831 10 0.781831 -0.781831 11 -0.781831 0.781831 12 0.781831 0.781831 13 0 -0.974928 14 0 -0.433884 15 0 0.433884 16 0 0.974928 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 2 Unique points in the grid = 7 Grid weights: 0 -2.66667 1 1.77778 2 1.77778 3 1.77778 4 1.77778 5 1.77778 6 1.77778 Grid points: 0 0 0 0 1 -0.866025 0 0 2 0.866025 0 0 3 0 -0.866025 0 4 0 0.866025 0 5 0 0 -0.866025 6 0 0 0.866025 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 3 Unique points in the grid = 5 Grid weights: 0 -1.33333 1 1.33333 2 1.33333 3 1.33333 4 1.33333 Grid points: 0 0 0 1 -0.707107 0 2 0.707107 0 3 0 -0.707107 4 0 0.707107 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 3 Unique points in the grid = 17 Grid weights: 0 -0.774603 1 -0.393651 2 -0.393651 3 -0.393651 4 -0.393651 5 0.355929 6 0.786928 7 0.786928 8 0.355929 9 0.444444 10 0.444444 11 0.444444 12 0.444444 13 0.355929 14 0.786928 15 0.786928 16 0.355929 Grid points: 0 0 0 1 -0.707107 0 2 0.707107 0 3 0 -0.707107 4 0 0.707107 5 -0.92388 0 6 -0.382683 0 7 0.382683 0 8 0.92388 0 9 -0.707107 -0.707107 10 0.707107 -0.707107 11 -0.707107 0.707107 12 0.707107 0.707107 13 0 -0.92388 14 0 -0.382683 15 0 0.382683 16 0 0.92388 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 3 Unique points in the grid = 7 Grid weights: 0 -8 1 2.66667 2 2.66667 3 2.66667 4 2.66667 5 2.66667 6 2.66667 Grid points: 0 0 0 0 1 -0.707107 0 0 2 0.707107 0 0 3 0 -0.707107 0 4 0 0.707107 0 5 0 0 -0.707107 6 0 0 0.707107 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 4 Unique points in the grid = 5 Grid weights: 0 -0.444444 1 1.11111 2 1.11111 3 1.11111 4 1.11111 Grid points: 0 -0.960491 -0.960491 1 -0.993832 -0.960491 2 -0.888459 -0.960491 3 -0.960491 -0.993832 4 -0.960491 -0.888459 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 4 Unique points in the grid = 17 Grid weights: 0 -0.961766 1 -0.0803078 2 -0.0803078 3 -0.0803078 4 -0.0803078 5 0.209312 6 0.802795 7 0.802795 8 0.209312 9 0.308642 10 0.308642 11 0.308642 12 0.308642 13 0.209312 14 0.802795 15 0.802795 16 0.209312 Grid points: 0 -0.999873 -0.999873 1 -0.999982 -0.999873 2 -0.999599 -0.999873 3 -0.999873 -0.999982 4 -0.999873 -0.999599 5 -0.999998 -0.999873 6 -0.999944 -0.999873 7 -0.99976 -0.999873 8 -0.99938 -0.999873 9 -0.999982 -0.999982 10 -0.999599 -0.999982 11 -0.999982 -0.999599 12 -0.999599 -0.999599 13 -0.999873 -0.999998 14 -0.999873 -0.999944 15 -0.999873 -0.99976 16 -0.999873 -0.99938 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 4 Unique points in the grid = 7 Grid weights: 0 -5.33333 1 2.22222 2 2.22222 3 2.22222 4 2.22222 5 2.22222 6 2.22222 Grid points: 0 -0.960491 -0.960491 -0.960491 1 -0.993832 -0.960491 -0.960491 2 -0.888459 -0.960491 -0.960491 3 -0.960491 -0.993832 -0.960491 4 -0.960491 -0.888459 -0.960491 5 -0.960491 -0.960491 -0.993832 6 -0.960491 -0.960491 -0.888459 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Unique points in the grid = 5 Grid weights: 0 -0.444444 1 1.11111 2 1.11111 3 1.11111 4 1.11111 Grid points: 0 0 0 1 -0.774597 0 2 0.774597 0 3 0 -0.774597 4 0 0.774597 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 5 Unique points in the grid = 21 Grid weights: 0 -1.0936 1 -0.617284 2 -0.617284 3 -0.617284 4 -0.617284 5 0.25897 6 0.559411 7 0.76366 8 0.76366 9 0.559411 10 0.25897 11 0.308642 12 0.308642 13 0.308642 14 0.308642 15 0.25897 16 0.559411 17 0.76366 18 0.76366 19 0.559411 20 0.25897 Grid points: 0 0 0 1 -0.774597 0 2 0.774597 0 3 0 -0.774597 4 0 0.774597 5 -0.949108 0 6 -0.741531 0 7 -0.405845 0 8 0.405845 0 9 0.741531 0 10 0.949108 0 11 -0.774597 -0.774597 12 0.774597 -0.774597 13 -0.774597 0.774597 14 0.774597 0.774597 15 0 -0.949108 16 0 -0.741531 17 0 -0.405845 18 0 0.405845 19 0 0.741531 20 0 0.949108 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Unique points in the grid = 7 Grid weights: 0 -5.33333 1 2.22222 2 2.22222 3 2.22222 4 2.22222 5 2.22222 6 2.22222 Grid points: 0 0 0 0 1 -0.774597 0 0 2 0.774597 0 0 3 0 -0.774597 0 4 0 0.774597 0 5 0 0 -0.774597 6 0 0 0.774597 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Unique points in the grid = 5 Grid weights: 0 1.0472 1 0.523599 2 0.523599 3 0.523599 4 0.523599 Grid points: 0 0 0 1 -1.22474 0 2 1.22474 0 3 0 -1.22474 4 0 1.22474 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 6 Unique points in the grid = 21 Grid weights: 0 0.0797865 1 -0.174533 2 -0.174533 3 -0.174533 4 -0.174533 5 0.00172244 6 0.0966264 7 0.754369 8 0.754369 9 0.0966264 10 0.00172244 11 0.0872665 12 0.0872665 13 0.0872665 14 0.0872665 15 0.00172244 16 0.0966264 17 0.754369 18 0.754369 19 0.0966264 20 0.00172244 Grid points: 0 0 0 1 -1.22474 0 2 1.22474 0 3 0 -1.22474 4 0 1.22474 5 -2.65196 0 6 -1.67355 0 7 -0.816288 0 8 0.816288 0 9 1.67355 0 10 2.65196 0 11 -1.22474 -1.22474 12 1.22474 -1.22474 13 -1.22474 1.22474 14 1.22474 1.22474 15 0 -2.65196 16 0 -1.67355 17 0 -0.816288 18 0 0.816288 19 0 1.67355 20 0 2.65196 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Unique points in the grid = 7 Grid weights: 0 -8.88178e-16 1 0.928055 2 0.928055 3 0.928055 4 0.928055 5 0.928055 6 0.928055 Grid points: 0 0 0 0 1 -1.22474 0 0 2 1.22474 0 0 3 0 -1.22474 0 4 0 1.22474 0 5 0 0 -1.22474 6 0 0 1.22474 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Unique points in the grid = 7 Grid weights: 0 -1 1 0.711093 2 0.278518 3 0.0103893 4 0.711093 5 0.278518 6 0.0103893 Grid points: 0 1 1 1 0.415775 1 2 2.29428 1 3 6.28995 1 4 1 0.415775 5 1 2.29428 6 1 6.28995 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 7 Unique points in the grid = 29 Grid weights: 0 -0.711093 1 -0.278518 2 -0.0103893 3 -0.711093 4 -0.278518 5 -0.0103893 6 0.409319 7 0.421831 8 0.147126 9 0.0206335 10 0.00107401 11 1.58655e-05 12 3.17032e-08 13 0.505653 14 0.198052 15 0.00738773 16 0.198052 17 0.0775721 18 0.00289359 19 0.00738773 20 0.00289359 21 0.000107937 22 0.409319 23 0.421831 24 0.147126 25 0.0206335 26 0.00107401 27 1.58655e-05 28 3.17032e-08 Grid points: 0 0.415775 1 1 2.29428 1 2 6.28995 1 3 1 0.415775 4 1 2.29428 5 1 6.28995 6 0.193044 1 7 1.02666 1 8 2.56788 1 9 4.90035 1 10 8.18215 1 11 12.7342 1 12 19.3957 1 13 0.415775 0.415775 14 2.29428 0.415775 15 6.28995 0.415775 16 0.415775 2.29428 17 2.29428 2.29428 18 6.28995 2.29428 19 0.415775 6.28995 20 2.29428 6.28995 21 6.28995 6.28995 22 1 0.193044 23 1 1.02666 24 1 2.56788 25 1 4.90035 26 1 8.18215 27 1 12.7342 28 1 19.3957 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Unique points in the grid = 10 Grid weights: 0 -2 1 0.711093 2 0.278518 3 0.0103893 4 0.711093 5 0.278518 6 0.0103893 7 0.711093 8 0.278518 9 0.0103893 Grid points: 0 1 1 1 1 0.415775 1 1 2 2.29428 1 1 3 6.28995 1 1 4 1 0.415775 1 5 1 2.29428 1 6 1 6.28995 1 7 1 1 0.415775 8 1 1 2.29428 9 1 1 6.28995 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 1 Unique points in the grid = 65 Weight sum Expected sum Difference 4 4 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 1 Unique points in the grid = 1 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Unique points in the grid = 7 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 1 Unique points in the grid = 1073 Weight sum Expected sum Difference 8 8 9.76996e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 1 Unique points in the grid = 1581 Weight sum Expected sum Difference 1024 1024 3.63798e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 2 Unique points in the grid = 129 Weight sum Expected sum Difference 4 4 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 2 Unique points in the grid = 1 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 2 Unique points in the grid = 7 Weight sum Expected sum Difference 8 8 3.55271e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 2 Unique points in the grid = 2815 Weight sum Expected sum Difference 8 8 2.30926e-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 2 Unique points in the grid = 2001 Weight sum Expected sum Difference 1024 1024 4.26326e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 3 Unique points in the grid = 129 Weight sum Expected sum Difference 4 4 3.55271e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 3 Unique points in the grid = 1 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 3 Unique points in the grid = 7 Weight sum Expected sum Difference 8 8 1.77636e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 3 Unique points in the grid = 2815 Weight sum Expected sum Difference 8 8 1.98952e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 3 Unique points in the grid = 2001 Weight sum Expected sum Difference 1024 1024 1.2235e-09 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 4 Unique points in the grid = 129 Weight sum Expected sum Difference 4 4 8.88178e-16 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 4 Unique points in the grid = 1 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 4 Unique points in the grid = 7 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 4 Unique points in the grid = 2815 Weight sum Expected sum Difference 8 8 2.34479e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 4 Unique points in the grid = 2001 Weight sum Expected sum Difference 1024 1024 1.22782e-09 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 5 Unique points in the grid = 225 Weight sum Expected sum Difference 4 4 8.88178e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 5 Unique points in the grid = 1 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Unique points in the grid = 7 Weight sum Expected sum Difference 8 8 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 5 Unique points in the grid = 6405 Weight sum Expected sum Difference 8 8 8.44658e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 5 Unique points in the grid = 2441 Weight sum Expected sum Difference 1024 1024 1.5466e-09 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 3.14159 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 6 Unique points in the grid = 225 Weight sum Expected sum Difference 3.14159 3.14159 1.95497e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.56833 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 6 Unique points in the grid = 1 Weight sum Expected sum Difference 5.56833 5.56833 8.88178e-16 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.56833 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Unique points in the grid = 7 Weight sum Expected sum Difference 5.56833 5.56833 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.56833 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 6 Unique points in the grid = 6405 Weight sum Expected sum Difference 5.56833 5.56833 5.19442e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 306.02 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 6 Unique points in the grid = 2441 Weight sum Expected sum Difference 306.02 306.02 8.10019e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 7 Unique points in the grid = 273 Weight sum Expected sum Difference 1 1 1.33227e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 7 Unique points in the grid = 1 Weight sum Expected sum Difference 1 1 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Unique points in the grid = 10 Weight sum Expected sum Difference 1 1 0 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 7 Unique points in the grid = 9484 Weight sum Expected sum Difference 1 1 1.39e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 7 Unique points in the grid = 5786 Weight sum Expected sum Difference 1 1 1.53055e-12 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1 2 2 0 0 2 1 1 1 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 5 Unique points in the grid = 5 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 0.666667 4 4 0 0 4 3 1 1 4 2 2 0 4 1 3 0.666667 4 0 4 0 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 0 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 7 Unique points in the grid = 13 Error Total Monomial Degree Exponents 0 0 0 0 3.33067e-16 1 1 0 3.33067e-16 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 2.77556e-16 3 3 0 0 3 2 1 0 3 1 2 2.77556e-16 3 0 3 0 4 4 0 0 4 3 1 2.498e-16 4 2 2 0 4 1 3 0 4 0 4 2.498e-16 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 2.498e-16 5 0 5 0.0666667 6 6 0 0 6 5 1 0.666667 6 4 2 0 6 3 3 0.666667 6 2 4 0 6 1 5 0.0666667 6 0 6 1.52656e-16 7 7 0 0 7 6 1 0 7 5 2 0 7 4 3 0 7 3 4 0 7 2 5 0 7 1 6 1.52656e-16 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 9 Unique points in the grid = 29 Error Total Monomial Degree Exponents 1.11022e-16 0 0 0 5.55112e-16 1 1 0 6.10623e-16 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 3.88578e-16 3 3 0 1.66533e-16 3 2 1 1.66533e-16 3 1 2 4.16334e-16 3 0 3 1.38778e-16 4 4 0 0 4 3 1 2.498e-16 4 2 2 0 4 1 3 2.77556e-16 4 0 4 3.05311e-16 5 5 0 1.66533e-16 5 4 1 8.32667e-17 5 3 2 8.32667e-17 5 2 3 1.66533e-16 5 1 4 2.77556e-16 5 0 5 1.94289e-16 6 6 0 0 6 5 1 2.08167e-16 6 4 2 0 6 3 3 2.08167e-16 6 2 4 0 6 1 5 5.82867e-16 6 0 6 2.22045e-16 7 7 0 1.66533e-16 7 6 1 9.71445e-17 7 5 2 8.32667e-17 7 4 3 8.32667e-17 7 3 4 9.71445e-17 7 2 5 1.66533e-16 7 1 6 1.94289e-16 7 0 7 4.996e-16 8 8 0 0 8 7 1 0.0666667 8 6 2 0 8 5 3 0.444444 8 4 4 0 8 3 5 0.0666667 8 2 6 0 8 1 7 4.996e-16 8 0 8 1.66533e-16 9 9 0 1.66533e-16 9 8 1 5.55112e-17 9 7 2 8.32667e-17 9 6 3 9.71445e-17 9 5 4 9.71445e-17 9 4 5 8.32667e-17 9 3 6 4.85723e-17 9 2 7 1.66533e-16 9 1 8 1.38778e-16 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 2 2 0 0 0 2 1 1 0 1 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.66533e-16 2 0 0 2 0 3 3 0 0 0 3 2 1 0 0 3 1 2 0 0 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 0 3 0 0 3 0.666667 4 4 0 0 0 4 3 1 0 1 4 2 2 0 0 4 1 3 0 0.666667 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 1 4 2 0 2 0 4 1 1 2 1 4 0 2 2 0 4 1 0 3 0 4 0 1 3 0.666667 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 6 Unique points in the grid = 25 Error Total Monomial Degree Exponents 4.44089e-16 0 0 0 0 6.66134e-16 1 1 0 0 6.66134e-16 1 0 1 0 6.66134e-16 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.66533e-16 2 0 0 2 5.55112e-16 3 3 0 0 0 3 2 1 0 0 3 1 2 0 5.55112e-16 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 5.55112e-16 3 0 0 3 1.38778e-16 4 4 0 0 0 4 3 1 0 2.498e-16 4 2 2 0 0 4 1 3 0 0 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 2.498e-16 4 2 0 2 0 4 1 1 2 2.498e-16 4 0 2 2 0 4 1 0 3 0 4 0 1 3 0 4 0 0 4 4.996e-16 5 5 0 0 0 5 4 1 0 0 5 3 2 0 0 5 2 3 0 0 5 1 4 0 4.996e-16 5 0 5 0 0 5 4 0 1 0 5 3 1 1 0 5 2 2 1 0 5 1 3 1 0 5 0 4 1 0 5 3 0 2 0 5 2 1 2 0 5 1 2 2 0 5 0 3 2 0 5 2 0 3 0 5 1 1 3 0 5 0 2 3 0 5 1 0 4 0 5 0 1 4 4.996e-16 5 0 0 5 0.0666667 6 6 0 0 0 6 5 1 0 0.666667 6 4 2 0 0 6 3 3 0 0.666667 6 2 4 0 0 6 1 5 0 0.0666667 6 0 6 0 0 6 5 0 1 0 6 4 1 1 0 6 3 2 1 0 6 2 3 1 0 6 1 4 1 0 6 0 5 1 0.666667 6 4 0 2 0 6 3 1 2 1 6 2 2 2 0 6 1 3 2 0.666667 6 0 4 2 0 6 3 0 3 0 6 2 1 3 0 6 1 2 3 0 6 0 3 3 0.666667 6 2 0 4 0 6 1 1 4 0.666667 6 0 2 4 0 6 1 0 5 0 6 0 1 5 0.0666667 6 0 0 6 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1 2 2 0 0 2 1 1 1 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 5 Unique points in the grid = 5 Error Total Monomial Degree Exponents 2.22045e-16 0 0 0 2.22045e-16 1 1 0 2.22045e-16 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 2.22045e-16 3 3 0 0 3 2 1 0 3 1 2 2.22045e-16 3 0 3 0.25 4 4 0 0 4 3 1 1 4 2 2 0 4 1 3 0.25 4 0 4 1.11022e-16 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 1.11022e-16 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 7 Unique points in the grid = 17 Error Total Monomial Degree Exponents 1.11022e-16 0 0 0 3.05311e-16 1 1 0 2.22045e-16 1 0 1 3.33067e-16 2 2 0 1.38778e-17 2 1 1 3.33067e-16 2 0 2 4.30211e-16 3 3 0 4.16334e-17 3 2 1 4.16334e-17 3 1 2 4.16334e-16 3 0 3 5.55112e-16 4 4 0 1.38778e-17 4 3 1 0.335752 4 2 2 1.38778e-17 4 1 3 5.55112e-16 4 0 4 4.23273e-16 5 5 0 2.08167e-17 5 4 1 1.17961e-16 5 3 2 1.249e-16 5 2 3 2.08167e-17 5 1 4 4.16334e-16 5 0 5 5.82867e-16 6 6 0 0 6 5 1 0.323286 6 4 2 0 6 3 3 0.323286 6 2 4 0 6 1 5 5.82867e-16 6 0 6 3.40006e-16 7 7 0 1.38778e-17 7 6 1 1.17961e-16 7 5 2 6.93889e-17 7 4 3 6.245e-17 7 3 4 1.249e-16 7 2 5 1.38778e-17 7 1 6 3.60822e-16 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 9 Unique points in the grid = 49 Error Total Monomial Degree Exponents 3.33067e-16 0 0 0 3.1225e-17 1 1 0 6.245e-17 1 0 1 1.66533e-16 2 2 0 6.59195e-17 2 1 1 1.66533e-16 2 0 2 9.36751e-17 3 3 0 5.89806e-17 3 2 1 5.55112e-17 3 1 2 1.04083e-16 3 0 3 1.38778e-16 4 4 0 2.08167e-17 4 3 1 0.2023 4 2 2 2.77556e-17 4 1 3 0 4 0 4 6.41848e-17 5 5 0 5.20417e-17 5 4 1 1.04083e-16 5 3 2 1.00614e-16 5 2 3 3.81639e-17 5 1 4 8.32667e-17 5 0 5 0 6 6 0 1.38778e-17 6 5 1 0.257875 6 4 2 1.56125e-17 6 3 3 0.257875 6 2 4 1.38778e-17 6 1 5 3.88578e-16 6 0 6 3.1225e-17 7 7 0 2.77556e-17 7 6 1 1.00614e-16 7 5 2 6.41848e-17 7 4 3 5.89806e-17 7 3 4 1.04083e-16 7 2 5 2.77556e-17 7 1 6 5.55112e-17 7 0 7 2.498e-16 8 8 0 9.54098e-18 8 7 1 0.319132 8 6 2 8.67362e-18 8 5 3 0.309656 8 4 4 8.67362e-18 8 3 5 0.319132 8 2 6 1.04083e-17 8 1 7 2.498e-16 8 0 8 2.12504e-17 9 9 0 1.34441e-17 9 8 1 8.41341e-17 9 7 2 4.0766e-17 9 6 3 5.37764e-17 9 5 4 5.72459e-17 9 4 5 3.98986e-17 9 3 6 9.19403e-17 9 2 7 1.38778e-17 9 1 8 2.77556e-17 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 2 2 0 0 0 2 1 1 0 1 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 4.44089e-16 0 0 0 0 4.44089e-16 1 1 0 0 4.44089e-16 1 0 1 0 4.44089e-16 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.66533e-16 2 0 0 2 4.44089e-16 3 3 0 0 0 3 2 1 0 0 3 1 2 0 4.44089e-16 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 4.44089e-16 3 0 0 3 0.25 4 4 0 0 0 4 3 1 0 1 4 2 2 0 0 4 1 3 0 0.25 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 1 4 2 0 2 0 4 1 1 2 1 4 0 2 2 0 4 1 0 3 0 4 0 1 3 0.25 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 6 Unique points in the grid = 31 Error Total Monomial Degree Exponents 0 0 0 0 0 5.55112e-16 1 1 0 0 3.88578e-16 1 0 1 0 4.44089e-16 1 0 0 1 4.996e-16 2 2 0 0 2.77556e-17 2 1 1 0 3.33067e-16 2 0 2 0 2.77556e-17 2 1 0 1 2.77556e-17 2 0 1 1 3.33067e-16 2 0 0 2 8.88178e-16 3 3 0 0 8.32667e-17 3 2 1 0 8.32667e-17 3 1 2 0 7.49401e-16 3 0 3 0 8.32667e-17 3 2 0 1 0 3 1 1 1 8.32667e-17 3 0 2 1 8.32667e-17 3 1 0 2 8.32667e-17 3 0 1 2 7.21645e-16 3 0 0 3 8.32667e-16 4 4 0 0 2.77556e-17 4 3 1 0 0.335752 4 2 2 0 2.77556e-17 4 1 3 0 5.55112e-16 4 0 4 0 2.77556e-17 4 3 0 1 0 4 2 1 1 0 4 1 2 1 2.77556e-17 4 0 3 1 0.335752 4 2 0 2 0 4 1 1 2 0.335752 4 0 2 2 2.77556e-17 4 1 0 3 2.77556e-17 4 0 1 3 5.55112e-16 4 0 0 4 8.60423e-16 5 5 0 0 4.16334e-17 5 4 1 0 2.35922e-16 5 3 2 0 2.498e-16 5 2 3 0 4.16334e-17 5 1 4 0 7.91034e-16 5 0 5 0 4.16334e-17 5 4 0 1 0 5 3 1 1 0 5 2 2 1 0 5 1 3 1 4.16334e-17 5 0 4 1 2.35922e-16 5 3 0 2 0 5 2 1 2 0 5 1 2 2 2.35922e-16 5 0 3 2 2.498e-16 5 2 0 3 0 5 1 1 3 2.498e-16 5 0 2 3 4.16334e-17 5 1 0 4 4.16334e-17 5 0 1 4 7.77156e-16 5 0 0 5 7.77156e-16 6 6 0 0 0 6 5 1 0 0.323286 6 4 2 0 0 6 3 3 0 0.323286 6 2 4 0 0 6 1 5 0 5.82867e-16 6 0 6 0 0 6 5 0 1 0 6 4 1 1 0 6 3 2 1 0 6 2 3 1 0 6 1 4 1 0 6 0 5 1 0.323286 6 4 0 2 0 6 3 1 2 1 6 2 2 2 0 6 1 3 2 0.323286 6 0 4 2 0 6 3 0 3 0 6 2 1 3 0 6 1 2 3 0 6 0 3 3 0.323286 6 2 0 4 0 6 1 1 4 0.323286 6 0 2 4 0 6 1 0 5 0 6 0 1 5 7.77156e-16 6 0 0 6 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1 2 2 0 0 2 1 1 1 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 5 Unique points in the grid = 5 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 1.66533e-16 3 3 0 0 3 2 1 0 3 1 2 1.66533e-16 3 0 3 0.166667 4 4 0 0 4 3 1 1 4 2 2 0 4 1 3 0.166667 4 0 4 2.22045e-16 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 2.22045e-16 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 7 Unique points in the grid = 17 Error Total Monomial Degree Exponents 0 0 0 0 2.22045e-16 1 1 0 2.22045e-16 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 1.11022e-16 3 3 0 2.77556e-17 3 2 1 0 3 1 2 1.11022e-16 3 0 3 0 4 4 0 1.38778e-17 4 3 1 1.249e-16 4 2 2 1.38778e-17 4 1 3 0 4 0 4 4.16334e-17 5 5 0 0 5 4 1 5.55112e-17 5 3 2 6.93889e-17 5 2 3 1.38778e-17 5 1 4 2.77556e-17 5 0 5 1.94289e-16 6 6 0 0 6 5 1 0.166667 6 4 2 0 6 3 3 0.166667 6 2 4 0 6 1 5 0 6 0 6 6.245e-17 7 7 0 0 7 6 1 7.63278e-17 7 5 2 3.46945e-17 7 4 3 2.77556e-17 7 3 4 7.63278e-17 7 2 5 6.93889e-18 7 1 6 5.55112e-17 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 9 Unique points in the grid = 49 Error Total Monomial Degree Exponents 2.22045e-16 0 0 0 1.94289e-16 1 1 0 5.55112e-17 1 0 1 3.33067e-16 2 2 0 1.38778e-17 2 1 1 0 2 0 2 2.08167e-16 3 3 0 6.93889e-17 3 2 1 1.11022e-16 3 1 2 1.52656e-16 3 0 3 2.77556e-16 4 4 0 2.08167e-17 4 3 1 2.498e-16 4 2 2 1.38778e-17 4 1 3 2.77556e-16 4 0 4 2.01228e-16 5 5 0 2.08167e-17 5 4 1 5.55112e-17 5 3 2 4.85723e-17 5 2 3 2.77556e-17 5 1 4 2.22045e-16 5 0 5 5.82867e-16 6 6 0 3.46945e-18 6 5 1 2.08167e-16 6 4 2 1.38778e-17 6 3 3 2.08167e-16 6 2 4 6.93889e-18 6 1 5 3.88578e-16 6 0 6 1.83881e-16 7 7 0 1.04083e-17 7 6 1 4.16334e-17 7 5 2 3.46945e-18 7 4 3 6.93889e-18 7 3 4 3.46945e-17 7 2 5 6.93889e-18 7 1 6 1.52656e-16 7 0 7 3.747e-16 8 8 0 6.93889e-18 8 7 1 1.45717e-16 8 6 2 3.46945e-18 8 5 3 0.0277778 8 4 4 3.46945e-18 8 3 5 0 8 2 6 6.93889e-18 8 1 7 4.996e-16 8 0 8 2.05565e-16 9 9 0 1.21431e-17 9 8 1 2.60209e-17 9 7 2 5.20417e-18 9 6 3 1.04083e-17 9 5 4 1.04083e-17 9 4 5 0 9 3 6 2.08167e-17 9 2 7 6.93889e-18 9 1 8 2.08167e-16 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 2 2 0 0 0 2 1 1 0 1 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 2.22045e-16 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.66533e-16 2 0 0 2 3.33067e-16 3 3 0 0 0 3 2 1 0 0 3 1 2 0 3.33067e-16 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 3.33067e-16 3 0 0 3 0.166667 4 4 0 0 0 4 3 1 0 1 4 2 2 0 0 4 1 3 0 0.166667 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 1 4 2 0 2 0 4 1 1 2 1 4 0 2 2 0 4 1 0 3 0 4 0 1 3 0.166667 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 6 Unique points in the grid = 31 Error Total Monomial Degree Exponents 8.88178e-16 0 0 0 0 0 1 1 0 0 8.88178e-16 1 0 1 0 8.88178e-16 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 4.996e-16 2 0 0 2 0 3 3 0 0 5.55112e-17 3 2 1 0 0 3 1 2 0 2.22045e-16 3 0 3 0 5.55112e-17 3 2 0 1 0 3 1 1 1 5.55112e-17 3 0 2 1 0 3 1 0 2 0 3 0 1 2 4.44089e-16 3 0 0 3 0 4 4 0 0 2.77556e-17 4 3 1 0 1.249e-16 4 2 2 0 2.77556e-17 4 1 3 0 1.38778e-16 4 0 4 0 2.77556e-17 4 3 0 1 0 4 2 1 1 0 4 1 2 1 2.77556e-17 4 0 3 1 1.249e-16 4 2 0 2 0 4 1 1 2 1.249e-16 4 0 2 2 2.77556e-17 4 1 0 3 2.77556e-17 4 0 1 3 0 4 0 0 4 0 5 5 0 0 0 5 4 1 0 1.11022e-16 5 3 2 0 1.38778e-16 5 2 3 0 2.77556e-17 5 1 4 0 1.94289e-16 5 0 5 0 0 5 4 0 1 0 5 3 1 1 0 5 2 2 1 0 5 1 3 1 0 5 0 4 1 1.11022e-16 5 3 0 2 0 5 2 1 2 0 5 1 2 2 1.11022e-16 5 0 3 2 1.38778e-16 5 2 0 3 0 5 1 1 3 1.38778e-16 5 0 2 3 2.77556e-17 5 1 0 4 2.77556e-17 5 0 1 4 2.77556e-16 5 0 0 5 0 6 6 0 0 0 6 5 1 0 0.166667 6 4 2 0 0 6 3 3 0 0.166667 6 2 4 0 0 6 1 5 0 0 6 0 6 0 0 6 5 0 1 0 6 4 1 1 0 6 3 2 1 0 6 2 3 1 0 6 1 4 1 0 6 0 5 1 0.166667 6 4 0 2 0 6 3 1 2 1 6 2 2 2 0 6 1 3 2 0.166667 6 0 4 2 0 6 3 0 3 0 6 2 1 3 0 6 1 2 3 0 6 0 3 3 0.166667 6 2 0 4 0 6 1 1 4 0.166667 6 0 2 4 0 6 1 0 5 0 6 0 1 5 1.94289e-16 6 0 0 6 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 3.09839 1 1 0 3.09839 1 0 1 0.8 2 2 0 2.4 2 1 1 0.8 2 0 2 1.85903 3 3 0 1.85903 3 2 1 1.85903 3 1 2 1.85903 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 5 Unique points in the grid = 5 Error Total Monomial Degree Exponents 0 0 0 0 3.79897 1 1 0 3.79897 1 0 1 1.71094 2 2 0 3.60759 2 1 1 1.71094 2 0 2 3.4452 3 3 0 3.43212 3 2 1 3.43212 3 1 2 3.4452 3 0 3 3.11164 4 4 0 3.27099 4 3 1 6.346 4 2 2 3.27099 4 1 3 3.11164 4 0 4 3.14563 5 5 0 3.12277 5 4 1 3.11137 5 3 2 3.11137 5 2 3 3.12277 5 1 4 3.14563 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 7 Unique points in the grid = 17 Error Total Monomial Degree Exponents 2.22045e-16 0 0 0 3.99929 1 1 0 3.99929 1 0 1 1.99894 2 2 0 3.99859 2 1 1 1.99894 2 0 2 3.99788 3 3 0 3.99788 3 2 1 3.99788 3 1 2 3.99788 3 0 3 3.99647 4 4 0 3.99717 4 3 1 7.99364 4 2 2 3.99717 4 1 3 3.99647 4 0 4 3.99647 5 5 0 3.99647 5 4 1 3.99647 5 3 2 3.99647 5 2 3 3.99647 5 1 4 3.99647 5 0 5 5.99258 6 6 0 3.99576 6 5 1 13.9841 6 4 2 3.99576 6 3 3 13.9841 6 2 4 3.99576 6 1 5 5.99258 6 0 6 3.99506 7 7 0 3.99506 7 6 1 3.99506 7 5 2 3.99505 7 4 3 3.99505 7 3 4 3.99506 7 2 5 3.99506 7 1 6 3.99506 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 9 Unique points in the grid = 49 Error Total Monomial Degree Exponents 2.22045e-16 0 0 0 4e+30 1 1 0 4e+30 1 0 1 3e+60 2 2 0 4e+60 2 1 1 3e+60 2 0 2 4e+90 3 3 0 4e+90 3 2 1 4e+90 3 1 2 4e+90 3 0 3 5e+120 4 4 0 4e+120 4 3 1 9e+120 4 2 2 4e+120 4 1 3 5e+120 4 0 4 4e+150 5 5 0 4e+150 5 4 1 4e+150 5 3 2 4e+150 5 2 3 4e+150 5 1 4 4e+150 5 0 5 7e+180 6 6 0 4e+180 6 5 1 1.5e+181 6 4 2 4e+180 6 3 3 1.5e+181 6 2 4 4e+180 6 1 5 7e+180 6 0 6 4e+210 7 7 0 4e+210 7 6 1 4e+210 7 5 2 4e+210 7 4 3 4e+210 7 3 4 4e+210 7 2 5 4e+210 7 1 6 4e+210 7 0 7 9e+240 8 8 0 4e+240 8 7 1 2.1e+241 8 6 2 4e+240 8 5 3 2.5e+241 8 4 4 4e+240 8 3 5 2.1e+241 8 2 6 4e+240 8 1 7 9e+240 8 0 8 4e+270 9 9 0 4e+270 9 8 1 4e+270 9 7 2 4e+270 9 6 3 4e+270 9 5 4 4e+270 9 4 5 4e+270 9 3 6 4e+270 9 2 7 4e+270 9 1 8 4e+270 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 6.19677 1 1 0 0 6.19677 1 0 1 0 6.19677 1 0 0 1 0.8 2 2 0 0 4.8 2 1 1 0 0.8 2 0 2 0 4.8 2 1 0 1 4.8 2 0 1 1 0.8 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 0 0 0 0 0 7.59795 1 1 0 0 7.59795 1 0 1 0 7.59795 1 0 0 1 1.71094 2 2 0 0 7.21518 2 1 1 0 1.71094 2 0 2 0 7.21518 2 1 0 1 7.21518 2 0 1 1 1.71094 2 0 0 2 6.89039 3 3 0 0 6.86424 3 2 1 0 6.86424 3 1 2 0 6.89039 3 0 3 0 6.86424 3 2 0 1 6.8508 3 1 1 1 6.86424 3 0 2 1 6.86424 3 1 0 2 6.86424 3 0 1 2 6.89039 3 0 0 3 3.11164 4 4 0 0 6.54197 4 3 1 0 6.346 4 2 2 0 6.54197 4 1 3 0 3.11164 4 0 4 0 6.54197 4 3 0 1 6.51686 4 2 1 1 6.51686 4 1 2 1 6.54197 4 0 3 1 6.346 4 2 0 2 6.51686 4 1 1 2 6.346 4 0 2 2 6.54197 4 1 0 3 6.54197 4 0 1 3 3.11164 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 4 Check up to DEGREE_MAX = 6 Unique points in the grid = 31 Error Total Monomial Degree Exponents 1.11022e-16 0 0 0 0 7.99859 1 1 0 0 7.99859 1 0 1 0 7.99859 1 0 0 1 1.99894 2 2 0 0 7.99717 2 1 1 0 1.99894 2 0 2 0 7.99717 2 1 0 1 7.99717 2 0 1 1 1.99894 2 0 0 2 7.99576 3 3 0 0 7.99576 3 2 1 0 7.99576 3 1 2 0 7.99576 3 0 3 0 7.99576 3 2 0 1 7.99576 3 1 1 1 7.99576 3 0 2 1 7.99576 3 1 0 2 7.99576 3 0 1 2 7.99576 3 0 0 3 3.99647 4 4 0 0 7.99435 4 3 1 0 7.99364 4 2 2 0 7.99435 4 1 3 0 3.99647 4 0 4 0 7.99435 4 3 0 1 7.99435 4 2 1 1 7.99435 4 1 2 1 7.99435 4 0 3 1 7.99364 4 2 0 2 7.99435 4 1 1 2 7.99364 4 0 2 2 7.99435 4 1 0 3 7.99435 4 0 1 3 3.99647 4 0 0 4 7.99294 5 5 0 0 7.99293 5 4 1 0 7.99293 5 3 2 0 7.99293 5 2 3 0 7.99293 5 1 4 0 7.99294 5 0 5 0 7.99293 5 4 0 1 7.99293 5 3 1 1 7.99293 5 2 2 1 7.99293 5 1 3 1 7.99293 5 0 4 1 7.99293 5 3 0 2 7.99293 5 2 1 2 7.99293 5 1 2 2 7.99293 5 0 3 2 7.99293 5 2 0 3 7.99293 5 1 1 3 7.99293 5 0 2 3 7.99293 5 1 0 4 7.99293 5 0 1 4 7.99294 5 0 0 5 5.99258 6 6 0 0 7.99152 6 5 1 0 13.9841 6 4 2 0 7.99152 6 3 3 0 13.9841 6 2 4 0 7.99152 6 1 5 0 5.99258 6 0 6 0 7.99152 6 5 0 1 7.99152 6 4 1 1 7.99152 6 3 2 1 7.99152 6 2 3 1 7.99152 6 1 4 1 7.99152 6 0 5 1 13.9841 6 4 0 2 7.99152 6 3 1 2 25.9714 6 2 2 2 7.99152 6 1 3 2 13.9841 6 0 4 2 7.99152 6 3 0 3 7.99152 6 2 1 3 7.99152 6 1 2 3 7.99152 6 0 3 3 13.9841 6 2 0 4 7.99152 6 1 1 4 13.9841 6 0 2 4 7.99152 6 1 0 5 7.99152 6 0 1 5 5.99258 6 0 0 6 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1 2 2 0 0 2 1 1 1 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 5 Unique points in the grid = 5 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 2.77556e-16 4 4 0 0 4 3 1 1 4 2 2 0 4 1 3 2.77556e-16 4 0 4 0 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 0 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 7 Unique points in the grid = 21 Error Total Monomial Degree Exponents 0 0 0 0 2.77556e-17 1 1 0 2.77556e-17 1 0 1 1.66533e-16 2 2 0 0 2 1 1 0 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 2.77556e-16 4 4 0 0 4 3 1 4.996e-16 4 2 2 0 4 1 3 2.77556e-16 4 0 4 2.77556e-17 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 2.77556e-17 5 0 5 1.94289e-16 6 6 0 0 6 5 1 4.16334e-16 6 4 2 0 6 3 3 4.16334e-16 6 2 4 0 6 1 5 0 6 0 6 2.77556e-17 7 7 0 0 7 6 1 0 7 5 2 0 7 4 3 0 7 3 4 0 7 2 5 0 7 1 6 2.77556e-17 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 9 Unique points in the grid = 73 Error Total Monomial Degree Exponents 9.99201e-16 0 0 0 5.55112e-17 1 1 0 2.77556e-17 1 0 1 1.66533e-16 2 2 0 0 2 1 1 1.66533e-16 2 0 2 5.55112e-17 3 3 0 2.77556e-17 3 2 1 1.38778e-17 3 1 2 6.245e-17 3 0 3 4.16334e-16 4 4 0 6.93889e-18 4 3 1 0 4 2 2 1.38778e-17 4 1 3 0 4 0 4 3.46945e-17 5 5 0 6.93889e-18 5 4 1 6.93889e-18 5 3 2 1.38778e-17 5 2 3 6.93889e-18 5 1 4 3.46945e-17 5 0 5 3.88578e-16 6 6 0 0 6 5 1 2.08167e-16 6 4 2 6.93889e-18 6 3 3 2.08167e-16 6 2 4 6.93889e-18 6 1 5 3.88578e-16 6 0 6 2.08167e-17 7 7 0 1.04083e-17 7 6 1 0 7 5 2 0 7 4 3 3.46945e-18 7 3 4 1.38778e-17 7 2 5 0 7 1 6 2.08167e-17 7 0 7 3.747e-16 8 8 0 6.93889e-18 8 7 1 0 8 6 2 3.46945e-18 8 5 3 0 8 4 4 0 8 3 5 0 8 2 6 0 8 1 7 1.249e-16 8 0 8 0 9 9 0 6.93889e-18 9 8 1 0 9 7 2 3.46945e-18 9 6 3 3.46945e-18 9 5 4 6.93889e-18 9 4 5 0 9 3 6 0 9 2 7 0 9 1 8 0 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 2 2 0 0 0 2 1 1 0 1 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.66533e-16 2 0 0 2 0 3 3 0 0 0 3 2 1 0 0 3 1 2 0 0 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 0 3 0 0 3 2.77556e-16 4 4 0 0 0 4 3 1 0 1 4 2 2 0 0 4 1 3 0 2.77556e-16 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 1 4 2 0 2 0 4 1 1 2 1 4 0 2 2 0 4 1 0 3 0 4 0 1 3 2.77556e-16 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 5 Check up to DEGREE_MAX = 6 Unique points in the grid = 37 Error Total Monomial Degree Exponents 1.11022e-16 0 0 0 0 5.55112e-17 1 1 0 0 5.55112e-17 1 0 1 0 5.55112e-17 1 0 0 1 1.66533e-16 2 2 0 0 0 2 1 1 0 1.66533e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.66533e-16 2 0 0 2 0 3 3 0 0 0 3 2 1 0 0 3 1 2 0 0 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 0 3 0 0 3 2.77556e-16 4 4 0 0 0 4 3 1 0 4.996e-16 4 2 2 0 0 4 1 3 0 2.77556e-16 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 4.996e-16 4 2 0 2 0 4 1 1 2 4.996e-16 4 0 2 2 0 4 1 0 3 0 4 0 1 3 2.77556e-16 4 0 0 4 5.55112e-17 5 5 0 0 0 5 4 1 0 0 5 3 2 0 0 5 2 3 0 0 5 1 4 0 5.55112e-17 5 0 5 0 0 5 4 0 1 0 5 3 1 1 0 5 2 2 1 0 5 1 3 1 0 5 0 4 1 0 5 3 0 2 0 5 2 1 2 0 5 1 2 2 0 5 0 3 2 0 5 2 0 3 0 5 1 1 3 0 5 0 2 3 0 5 1 0 4 0 5 0 1 4 5.55112e-17 5 0 0 5 1.94289e-16 6 6 0 0 0 6 5 1 0 4.16334e-16 6 4 2 0 0 6 3 3 0 4.16334e-16 6 2 4 0 0 6 1 5 0 0 6 0 6 0 0 6 5 0 1 0 6 4 1 1 0 6 3 2 1 0 6 2 3 1 0 6 1 4 1 0 6 0 5 1 4.16334e-16 6 4 0 2 0 6 3 1 2 1 6 2 2 2 0 6 1 3 2 4.16334e-16 6 0 4 2 0 6 3 0 3 0 6 2 1 3 0 6 1 2 3 0 6 0 3 3 4.16334e-16 6 2 0 4 0 6 1 1 4 4.16334e-16 6 0 2 4 0 6 1 0 5 0 6 0 1 5 0 6 0 0 6 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 2.82716e-16 0 0 0 0 1 1 0 0 1 0 1 1 2 2 0 0 2 1 1 1 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 5 Unique points in the grid = 5 Error Total Monomial Degree Exponents 4.24074e-16 0 0 0 0 1 1 0 0 1 0 1 1.41358e-16 2 2 0 0 2 1 1 1.41358e-16 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 0 4 4 0 0 4 3 1 1 4 2 2 0 4 1 3 0 4 0 4 0 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 0 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 7 Unique points in the grid = 21 Error Total Monomial Degree Exponents 0 0 0 0 2.77556e-17 1 1 0 2.08167e-17 1 0 1 4.24074e-16 2 2 0 0 2 1 1 1.41358e-16 2 0 2 8.32667e-17 3 3 0 0 3 2 1 0 3 1 2 6.93889e-17 3 0 3 0 4 4 0 0 4 3 1 1.41358e-16 4 2 2 0 4 1 3 0 4 0 4 5.55112e-17 5 5 0 0 5 4 1 0 5 3 2 0 5 2 3 0 5 1 4 5.55112e-17 5 0 5 1.50782e-16 6 6 0 0 6 5 1 1.88477e-16 6 4 2 0 6 3 3 1.88477e-16 6 2 4 0 6 1 5 1.50782e-16 6 0 6 4.44089e-16 7 7 0 0 7 6 1 0 7 5 2 0 7 4 3 0 7 3 4 0 7 2 5 0 7 1 6 4.44089e-16 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 9 Unique points in the grid = 73 Error Total Monomial Degree Exponents 4.24074e-16 0 0 0 5.55112e-17 1 1 0 8.36334e-17 1 0 1 1.41358e-16 2 2 0 0 2 1 1 0 2 0 2 8.32667e-17 3 3 0 3.85976e-17 3 2 1 0 3 1 2 2.79672e-17 3 0 3 1.88477e-16 4 4 0 2.77556e-17 4 3 1 1.41358e-16 4 2 2 1.38778e-17 4 1 3 1.88477e-16 4 0 4 5.55112e-17 5 5 0 6.02816e-17 5 4 1 0 5 3 2 2.08167e-17 5 2 3 2.77556e-17 5 1 4 7.56604e-17 5 0 5 4.52346e-16 6 6 0 0 6 5 1 3.76955e-16 6 4 2 0 6 3 3 1.88477e-16 6 2 4 0 6 1 5 4.52346e-16 6 0 6 1.11022e-16 7 7 0 1.15359e-16 7 6 1 2.77556e-17 7 5 2 6.93889e-18 7 4 3 0 7 3 4 5.55112e-17 7 2 5 0 7 1 6 1.84152e-16 7 0 7 3.44644e-16 8 8 0 1.66533e-16 8 7 1 3.01564e-16 8 6 2 5.55112e-17 8 5 3 1.25652e-16 8 4 4 5.55112e-17 8 3 5 0 8 2 6 0 8 1 7 1.72322e-16 8 0 8 8.88178e-16 9 9 0 7.63278e-17 9 8 1 0 9 7 2 1.52656e-16 9 6 3 0 9 5 4 8.32667e-17 9 4 5 1.11022e-16 9 3 6 4.44089e-16 9 2 7 0 9 1 8 9.30679e-16 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 4.78516e-16 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 2 2 0 0 0 2 1 1 0 1 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 3.19011e-16 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 3.19011e-16 2 2 0 0 0 2 1 1 0 3.19011e-16 2 0 2 0 0 2 1 0 1 0 2 0 1 1 3.19011e-16 2 0 0 2 0 3 3 0 0 0 3 2 1 0 0 3 1 2 0 0 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 0 3 0 0 3 0 4 4 0 0 0 4 3 1 0 1 4 2 2 0 0 4 1 3 0 0 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 1 4 2 0 2 0 4 1 1 2 1 4 0 2 2 0 4 1 0 3 0 4 0 1 3 2.12674e-16 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 6 Check up to DEGREE_MAX = 6 Unique points in the grid = 37 Error Total Monomial Degree Exponents 3.19011e-16 0 0 0 0 8.32667e-17 1 1 0 0 8.32667e-17 1 0 1 0 8.1532e-17 1 0 0 1 0 2 2 0 0 0 2 1 1 0 0 2 0 2 0 0 2 1 0 1 0 2 0 1 1 1.59505e-16 2 0 0 2 5.55112e-17 3 3 0 0 0 3 2 1 0 0 3 1 2 0 5.55112e-17 3 0 3 0 0 3 2 0 1 0 3 1 1 1 0 3 0 2 1 0 3 1 0 2 0 3 0 1 2 4.85723e-17 3 0 0 3 2.12674e-16 4 4 0 0 0 4 3 1 0 1.59505e-16 4 2 2 0 0 4 1 3 0 2.12674e-16 4 0 4 0 0 4 3 0 1 0 4 2 1 1 0 4 1 2 1 0 4 0 3 1 1.59505e-16 4 2 0 2 0 4 1 1 2 1.59505e-16 4 0 2 2 0 4 1 0 3 0 4 0 1 3 0 4 0 0 4 1.11022e-16 5 5 0 0 0 5 4 1 0 0 5 3 2 0 0 5 2 3 0 0 5 1 4 0 1.11022e-16 5 0 5 0 0 5 4 0 1 0 5 3 1 1 0 5 2 2 1 0 5 1 3 1 0 5 0 4 1 0 5 3 0 2 0 5 2 1 2 0 5 1 2 2 0 5 0 3 2 0 5 2 0 3 0 5 1 1 3 0 5 0 2 3 0 5 1 0 4 0 5 0 1 4 1.11022e-16 5 0 0 5 3.40278e-16 6 6 0 0 0 6 5 1 0 2.12674e-16 6 4 2 0 0 6 3 3 0 2.12674e-16 6 2 4 0 0 6 1 5 0 3.40278e-16 6 0 6 0 0 6 5 0 1 0 6 4 1 1 0 6 3 2 1 0 6 2 3 1 0 6 1 4 1 0 6 0 5 1 2.12674e-16 6 4 0 2 0 6 3 1 2 1 6 2 2 2 0 6 1 3 2 2.12674e-16 6 0 4 2 0 6 3 0 3 0 6 2 1 3 0 6 1 2 3 0 6 0 3 3 0 6 2 0 4 0 6 1 1 4 0 6 0 2 4 0 6 1 0 5 0 6 0 1 5 3.40278e-16 6 0 0 6 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 3 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 1 1 0 0 1 0 1 0.5 2 2 0 0 2 1 1 0.5 2 0 2 0.833333 3 3 0 0.5 3 2 1 0.5 3 1 2 0.833333 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 5 Unique points in the grid = 7 Error Total Monomial Degree Exponents 0 0 0 0 2.22045e-16 1 1 0 0 1 0 1 0 2 2 0 2.22045e-16 2 1 1 0 2 0 2 0 3 3 0 0 3 2 1 0 3 1 2 0 3 0 3 1.4803e-16 4 4 0 0 4 3 1 0.25 4 2 2 0 4 1 3 1.4803e-16 4 0 4 2.36848e-16 5 5 0 1.4803e-16 5 4 1 0.416667 5 3 2 0.416667 5 2 3 1.4803e-16 5 1 4 2.36848e-16 5 0 5 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 7 Unique points in the grid = 29 Error Total Monomial Degree Exponents 3.33067e-16 0 0 0 2.22045e-16 1 1 0 5.55112e-16 1 0 1 2.22045e-16 2 2 0 4.44089e-16 2 1 1 0 2 0 2 0 3 3 0 4.44089e-16 3 2 1 2.22045e-16 3 1 2 1.4803e-16 3 0 3 1.4803e-16 4 4 0 4.44089e-16 4 3 1 2.22045e-16 4 2 2 2.96059e-16 4 1 3 0 4 0 4 0 5 5 0 2.96059e-16 5 4 1 1.4803e-16 5 3 2 1.4803e-16 5 2 3 1.4803e-16 5 1 4 0 5 0 5 4.73695e-16 6 6 0 2.36848e-16 6 5 1 1.4803e-16 6 4 2 0 6 3 3 1.4803e-16 6 2 4 2.36848e-16 6 1 5 1.57898e-16 6 0 6 5.41366e-16 7 7 0 0 7 6 1 2.36848e-16 7 5 2 3.94746e-16 7 4 3 3.94746e-16 7 3 4 1.18424e-16 7 2 5 3.15797e-16 7 1 6 3.60911e-16 7 0 7 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 7 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 2 LEVEL_MAX = 3 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 9 Unique points in the grid = 95 Error Total Monomial Degree Exponents 1.11022e-15 0 0 0 9.99201e-16 1 1 0 1.11022e-15 1 0 1 2.22045e-16 2 2 0 1.33227e-15 2 1 1 3.33067e-16 2 0 2 2.96059e-16 3 3 0 4.44089e-16 3 2 1 8.88178e-16 3 1 2 1.4803e-16 3 0 3 2.96059e-16 4 4 0 1.18424e-15 4 3 1 1.11022e-16 4 2 2 8.88178e-16 4 1 3 2.96059e-16 4 0 4 3.55271e-16 5 5 0 2.96059e-16 5 4 1 4.44089e-16 5 3 2 5.92119e-16 5 2 3 0 5 1 4 1.18424e-16 5 0 5 1.26319e-15 6 6 0 5.92119e-16 6 5 1 7.40149e-16 6 4 2 7.89492e-16 6 3 3 2.96059e-16 6 2 4 0 6 1 5 6.31594e-16 6 0 6 3.60911e-16 7 7 0 1.57898e-16 7 6 1 1.18424e-16 7 5 2 9.86865e-16 7 4 3 9.86865e-16 7 3 4 0 7 2 5 6.31594e-16 7 1 6 7.21821e-16 7 0 7 3.60911e-16 8 8 0 7.21821e-16 8 7 1 4.73695e-16 8 6 2 1.57898e-16 8 5 3 9.86865e-16 8 4 4 7.89492e-16 8 3 5 1.57898e-16 8 2 6 7.21821e-16 8 1 7 5.41366e-16 8 0 8 0 9 9 0 3.60911e-16 9 8 1 1.80455e-16 9 7 2 8.42125e-16 9 6 3 3.15797e-16 9 5 4 3.15797e-16 9 4 5 4.21062e-16 9 3 6 5.41366e-16 9 2 7 5.41366e-16 9 1 8 4.81214e-16 9 0 9 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 1 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0.5 2 2 0 0 0 2 1 1 0 0.5 2 0 2 0 0 2 1 0 1 0 2 0 1 1 0.5 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 4 Unique points in the grid = 10 Error Total Monomial Degree Exponents 0 0 0 0 0 2.22045e-16 1 1 0 0 2.22045e-16 1 0 1 0 0 1 0 0 1 0 2 2 0 0 4.44089e-16 2 1 1 0 0 2 0 2 0 2.22045e-16 2 1 0 1 2.22045e-16 2 0 1 1 0 2 0 0 2 0 3 3 0 0 0 3 2 1 0 2.22045e-16 3 1 2 0 0 3 0 3 0 0 3 2 0 1 4.44089e-16 3 1 1 1 0 3 0 2 1 2.22045e-16 3 1 0 2 0 3 0 1 2 0 3 0 0 3 1.4803e-16 4 4 0 0 0 4 3 1 0 0.25 4 2 2 0 1.4803e-16 4 1 3 0 1.4803e-16 4 0 4 0 0 4 3 0 1 0 4 2 1 1 2.22045e-16 4 1 2 1 0 4 0 3 1 0.25 4 2 0 2 2.22045e-16 4 1 1 2 0.25 4 0 2 2 1.4803e-16 4 1 0 3 0 4 0 1 3 1.4803e-16 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 6 Unique points in the grid = 58 Error Total Monomial Degree Exponents 2.22045e-16 0 0 0 0 1.22125e-15 1 1 0 0 6.66134e-16 1 0 1 0 1.11022e-16 1 0 0 1 2.22045e-16 2 2 0 0 1.11022e-15 2 1 1 0 2.22045e-16 2 0 2 0 1.22125e-15 2 1 0 1 6.66134e-16 2 0 1 1 2.22045e-16 2 0 0 2 2.96059e-16 3 3 0 0 0 3 2 1 0 1.11022e-15 3 1 2 0 2.96059e-16 3 0 3 0 2.22045e-16 3 2 0 1 9.99201e-16 3 1 1 1 4.44089e-16 3 0 2 1 8.88178e-16 3 1 0 2 1.33227e-15 3 0 1 2 5.92119e-16 3 0 0 3 2.96059e-16 4 4 0 0 0 4 3 1 0 7.77156e-16 4 2 2 0 2.96059e-16 4 1 3 0 1.4803e-16 4 0 4 0 0 4 3 0 1 4.44089e-16 4 2 1 1 3.33067e-16 4 1 2 1 1.4803e-16 4 0 3 1 1.11022e-16 4 2 0 2 2.44249e-15 4 1 1 2 2.22045e-16 4 0 2 2 4.44089e-16 4 1 0 3 1.4803e-16 4 0 1 3 2.96059e-16 4 0 0 4 1.18424e-16 5 5 0 0 1.4803e-16 5 4 1 0 1.4803e-16 5 3 2 0 0 5 2 3 0 1.4803e-16 5 1 4 0 1.18424e-16 5 0 5 0 2.96059e-16 5 4 0 1 4.44089e-16 5 3 1 1 0 5 2 2 1 5.92119e-16 5 1 3 1 2.96059e-16 5 0 4 1 2.96059e-16 5 3 0 2 7.77156e-16 5 2 1 2 1.11022e-16 5 1 2 2 2.96059e-16 5 0 3 2 4.44089e-16 5 2 0 3 5.92119e-16 5 1 1 3 4.44089e-16 5 0 2 3 1.4803e-16 5 1 0 4 1.4803e-16 5 0 1 4 2.36848e-16 5 0 0 5 1.10529e-15 6 6 0 0 1.18424e-16 6 5 1 0 2.96059e-16 6 4 2 0 0 6 3 3 0 0 6 2 4 0 0 6 1 5 0 0 6 0 6 0 3.55271e-16 6 5 0 1 1.4803e-16 6 4 1 1 2.96059e-16 6 3 2 1 1.4803e-16 6 2 3 1 0 6 1 4 1 2.36848e-16 6 0 5 1 1.4803e-16 6 4 0 2 1.4803e-16 6 3 1 2 0.125 6 2 2 2 0 6 1 3 2 1.4803e-16 6 0 4 2 0 6 3 0 3 1.4803e-16 6 2 1 3 2.96059e-16 6 1 2 3 0 6 0 3 3 0 6 2 0 4 7.40149e-16 6 1 1 4 1.4803e-16 6 0 2 4 2.36848e-16 6 1 0 5 0 6 0 1 5 7.89492e-16 6 0 0 6 SANDIA_SPARSE_PRB Normal end of execution. 25 December 2011 11:04:09 AM