16-Jan-2023 15:41:08 sandia_sparse_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sandia_sparse(). 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 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 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 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 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: 1 1 1 1 1 2 0 1 3 1 3 2 1 3 1 4 1 0 1 3 5 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: 1 4 4 1 1 2 0 4 3 1 3 8 4 3 1 4 4 0 1 3 5 4 8 1 3 6 2 4 5 1 7 6 4 5 1 8 0 0 3 3 9 8 0 3 3 10 0 8 3 3 11 8 8 3 3 12 4 2 1 5 13 4 6 1 5 14 1 4 9 1 15 3 4 9 1 16 5 4 9 1 17 7 4 9 1 18 2 0 5 3 19 6 0 5 3 20 2 8 5 3 21 6 8 5 3 22 0 2 3 5 23 8 2 3 5 24 0 6 3 5 25 8 6 3 5 26 4 1 1 9 27 4 3 1 9 28 4 5 1 9 29 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: 1 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: 1 2 2 2 1 1 1 2 0 2 2 3 1 1 3 4 2 2 3 1 1 4 2 0 2 1 3 1 5 2 4 2 1 3 1 6 2 2 0 1 1 3 7 2 2 4 1 1 3 8 1 2 2 5 1 1 9 3 2 2 5 1 1 10 0 0 2 3 3 1 11 4 0 2 3 3 1 12 0 4 2 3 3 1 13 4 4 2 3 3 1 14 2 1 2 1 5 1 15 2 3 2 1 5 1 16 0 2 0 3 1 3 17 4 2 0 3 1 3 18 0 2 4 3 1 3 19 4 2 4 3 1 3 20 2 0 0 1 3 3 21 2 4 0 1 3 3 22 2 0 4 1 3 3 23 2 4 4 1 3 3 24 2 2 1 1 1 5 25 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: 1 2 2 2 2 2 2 1 1 1 1 1 1 2 0 2 2 2 2 2 3 1 1 1 1 1 3 4 2 2 2 2 2 3 1 1 1 1 1 4 2 0 2 2 2 2 1 3 1 1 1 1 5 2 4 2 2 2 2 1 3 1 1 1 1 6 2 2 0 2 2 2 1 1 3 1 1 1 7 2 2 4 2 2 2 1 1 3 1 1 1 8 2 2 2 0 2 2 1 1 1 3 1 1 9 2 2 2 4 2 2 1 1 1 3 1 1 10 2 2 2 2 0 2 1 1 1 1 3 1 11 2 2 2 2 4 2 1 1 1 1 3 1 12 2 2 2 2 2 0 1 1 1 1 1 3 13 2 2 2 2 2 4 1 1 1 1 1 3 14 1 2 2 2 2 2 5 1 1 1 1 1 15 3 2 2 2 2 2 5 1 1 1 1 1 16 0 0 2 2 2 2 3 3 1 1 1 1 17 4 0 2 2 2 2 3 3 1 1 1 1 18 0 4 2 2 2 2 3 3 1 1 1 1 19 4 4 2 2 2 2 3 3 1 1 1 1 20 2 1 2 2 2 2 1 5 1 1 1 1 21 2 3 2 2 2 2 1 5 1 1 1 1 22 0 2 0 2 2 2 3 1 3 1 1 1 23 4 2 0 2 2 2 3 1 3 1 1 1 24 0 2 4 2 2 2 3 1 3 1 1 1 25 4 2 4 2 2 2 3 1 3 1 1 1 26 2 0 0 2 2 2 1 3 3 1 1 1 27 2 4 0 2 2 2 1 3 3 1 1 1 28 2 0 4 2 2 2 1 3 3 1 1 1 29 2 4 4 2 2 2 1 3 3 1 1 1 30 2 2 1 2 2 2 1 1 5 1 1 1 31 2 2 3 2 2 2 1 1 5 1 1 1 32 0 2 2 0 2 2 3 1 1 3 1 1 33 4 2 2 0 2 2 3 1 1 3 1 1 34 0 2 2 4 2 2 3 1 1 3 1 1 35 4 2 2 4 2 2 3 1 1 3 1 1 36 2 0 2 0 2 2 1 3 1 3 1 1 37 2 4 2 0 2 2 1 3 1 3 1 1 38 2 0 2 4 2 2 1 3 1 3 1 1 39 2 4 2 4 2 2 1 3 1 3 1 1 40 2 2 0 0 2 2 1 1 3 3 1 1 41 2 2 4 0 2 2 1 1 3 3 1 1 42 2 2 0 4 2 2 1 1 3 3 1 1 43 2 2 4 4 2 2 1 1 3 3 1 1 44 2 2 2 1 2 2 1 1 1 5 1 1 45 2 2 2 3 2 2 1 1 1 5 1 1 46 0 2 2 2 0 2 3 1 1 1 3 1 47 4 2 2 2 0 2 3 1 1 1 3 1 48 0 2 2 2 4 2 3 1 1 1 3 1 49 4 2 2 2 4 2 3 1 1 1 3 1 50 2 0 2 2 0 2 1 3 1 1 3 1 51 2 4 2 2 0 2 1 3 1 1 3 1 52 2 0 2 2 4 2 1 3 1 1 3 1 53 2 4 2 2 4 2 1 3 1 1 3 1 54 2 2 0 2 0 2 1 1 3 1 3 1 55 2 2 4 2 0 2 1 1 3 1 3 1 56 2 2 0 2 4 2 1 1 3 1 3 1 57 2 2 4 2 4 2 1 1 3 1 3 1 58 2 2 2 0 0 2 1 1 1 3 3 1 59 2 2 2 4 0 2 1 1 1 3 3 1 60 2 2 2 0 4 2 1 1 1 3 3 1 61 2 2 2 4 4 2 1 1 1 3 3 1 62 2 2 2 2 1 2 1 1 1 1 5 1 63 2 2 2 2 3 2 1 1 1 1 5 1 64 0 2 2 2 2 0 3 1 1 1 1 3 65 4 2 2 2 2 0 3 1 1 1 1 3 66 0 2 2 2 2 4 3 1 1 1 1 3 67 4 2 2 2 2 4 3 1 1 1 1 3 68 2 0 2 2 2 0 1 3 1 1 1 3 69 2 4 2 2 2 0 1 3 1 1 1 3 70 2 0 2 2 2 4 1 3 1 1 1 3 71 2 4 2 2 2 4 1 3 1 1 1 3 72 2 2 0 2 2 0 1 1 3 1 1 3 73 2 2 4 2 2 0 1 1 3 1 1 3 74 2 2 0 2 2 4 1 1 3 1 1 3 75 2 2 4 2 2 4 1 1 3 1 1 3 76 2 2 2 0 2 0 1 1 1 3 1 3 77 2 2 2 4 2 0 1 1 1 3 1 3 78 2 2 2 0 2 4 1 1 1 3 1 3 79 2 2 2 4 2 4 1 1 1 3 1 3 80 2 2 2 2 0 0 1 1 1 1 3 3 81 2 2 2 2 4 0 1 1 1 1 3 3 82 2 2 2 2 0 4 1 1 1 1 3 3 83 2 2 2 2 4 4 1 1 1 1 3 3 84 2 2 2 2 2 1 1 1 1 1 1 5 85 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: 1 2 2 1 1 2 1 2 3 1 3 3 2 3 1 4 2 1 1 3 5 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: 1 8 8 1 1 2 4 8 3 1 3 12 8 3 1 4 8 4 1 3 5 8 12 1 3 6 2 8 7 1 7 6 8 7 1 8 10 8 7 1 9 14 8 7 1 10 4 4 3 3 11 12 4 3 3 12 4 12 3 3 13 12 12 3 3 14 8 2 1 7 15 8 6 1 7 16 8 10 1 7 17 8 14 1 7 18 1 8 15 1 19 3 8 15 1 20 5 8 15 1 21 7 8 15 1 22 9 8 15 1 23 11 8 15 1 24 13 8 15 1 25 15 8 15 1 26 2 4 7 3 27 6 4 7 3 28 10 4 7 3 29 14 4 7 3 30 2 12 7 3 31 6 12 7 3 32 10 12 7 3 33 14 12 7 3 34 4 2 3 7 35 12 2 3 7 36 4 6 3 7 37 12 6 3 7 38 4 10 3 7 39 12 10 3 7 40 4 14 3 7 41 12 14 3 7 42 8 1 1 15 43 8 3 1 15 44 8 5 1 15 45 8 7 1 15 46 8 9 1 15 47 8 11 1 15 48 8 13 1 15 49 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: 1 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: 1 4 4 4 1 1 1 2 2 4 4 3 1 1 3 6 4 4 3 1 1 4 4 2 4 1 3 1 5 4 6 4 1 3 1 6 4 4 2 1 1 3 7 4 4 6 1 1 3 8 1 4 4 7 1 1 9 3 4 4 7 1 1 10 5 4 4 7 1 1 11 7 4 4 7 1 1 12 2 2 4 3 3 1 13 6 2 4 3 3 1 14 2 6 4 3 3 1 15 6 6 4 3 3 1 16 4 1 4 1 7 1 17 4 3 4 1 7 1 18 4 5 4 1 7 1 19 4 7 4 1 7 1 20 2 4 2 3 1 3 21 6 4 2 3 1 3 22 2 4 6 3 1 3 23 6 4 6 3 1 3 24 4 2 2 1 3 3 25 4 6 2 1 3 3 26 4 2 6 1 3 3 27 4 6 6 1 3 3 28 4 4 1 1 1 7 29 4 4 3 1 1 7 30 4 4 5 1 1 7 31 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: 1 4 4 4 4 4 4 1 1 1 1 1 1 2 2 4 4 4 4 4 3 1 1 1 1 1 3 6 4 4 4 4 4 3 1 1 1 1 1 4 4 2 4 4 4 4 1 3 1 1 1 1 5 4 6 4 4 4 4 1 3 1 1 1 1 6 4 4 2 4 4 4 1 1 3 1 1 1 7 4 4 6 4 4 4 1 1 3 1 1 1 8 4 4 4 2 4 4 1 1 1 3 1 1 9 4 4 4 6 4 4 1 1 1 3 1 1 10 4 4 4 4 2 4 1 1 1 1 3 1 11 4 4 4 4 6 4 1 1 1 1 3 1 12 4 4 4 4 4 2 1 1 1 1 1 3 13 4 4 4 4 4 6 1 1 1 1 1 3 14 1 4 4 4 4 4 7 1 1 1 1 1 15 3 4 4 4 4 4 7 1 1 1 1 1 16 5 4 4 4 4 4 7 1 1 1 1 1 17 7 4 4 4 4 4 7 1 1 1 1 1 18 2 2 4 4 4 4 3 3 1 1 1 1 19 6 2 4 4 4 4 3 3 1 1 1 1 20 2 6 4 4 4 4 3 3 1 1 1 1 21 6 6 4 4 4 4 3 3 1 1 1 1 22 4 1 4 4 4 4 1 7 1 1 1 1 23 4 3 4 4 4 4 1 7 1 1 1 1 24 4 5 4 4 4 4 1 7 1 1 1 1 25 4 7 4 4 4 4 1 7 1 1 1 1 26 2 4 2 4 4 4 3 1 3 1 1 1 27 6 4 2 4 4 4 3 1 3 1 1 1 28 2 4 6 4 4 4 3 1 3 1 1 1 29 6 4 6 4 4 4 3 1 3 1 1 1 30 4 2 2 4 4 4 1 3 3 1 1 1 31 4 6 2 4 4 4 1 3 3 1 1 1 32 4 2 6 4 4 4 1 3 3 1 1 1 33 4 6 6 4 4 4 1 3 3 1 1 1 34 4 4 1 4 4 4 1 1 7 1 1 1 35 4 4 3 4 4 4 1 1 7 1 1 1 36 4 4 5 4 4 4 1 1 7 1 1 1 37 4 4 7 4 4 4 1 1 7 1 1 1 38 2 4 4 2 4 4 3 1 1 3 1 1 39 6 4 4 2 4 4 3 1 1 3 1 1 40 2 4 4 6 4 4 3 1 1 3 1 1 41 6 4 4 6 4 4 3 1 1 3 1 1 42 4 2 4 2 4 4 1 3 1 3 1 1 43 4 6 4 2 4 4 1 3 1 3 1 1 44 4 2 4 6 4 4 1 3 1 3 1 1 45 4 6 4 6 4 4 1 3 1 3 1 1 46 4 4 2 2 4 4 1 1 3 3 1 1 47 4 4 6 2 4 4 1 1 3 3 1 1 48 4 4 2 6 4 4 1 1 3 3 1 1 49 4 4 6 6 4 4 1 1 3 3 1 1 50 4 4 4 1 4 4 1 1 1 7 1 1 51 4 4 4 3 4 4 1 1 1 7 1 1 52 4 4 4 5 4 4 1 1 1 7 1 1 53 4 4 4 7 4 4 1 1 1 7 1 1 54 2 4 4 4 2 4 3 1 1 1 3 1 55 6 4 4 4 2 4 3 1 1 1 3 1 56 2 4 4 4 6 4 3 1 1 1 3 1 57 6 4 4 4 6 4 3 1 1 1 3 1 58 4 2 4 4 2 4 1 3 1 1 3 1 59 4 6 4 4 2 4 1 3 1 1 3 1 60 4 2 4 4 6 4 1 3 1 1 3 1 61 4 6 4 4 6 4 1 3 1 1 3 1 62 4 4 2 4 2 4 1 1 3 1 3 1 63 4 4 6 4 2 4 1 1 3 1 3 1 64 4 4 2 4 6 4 1 1 3 1 3 1 65 4 4 6 4 6 4 1 1 3 1 3 1 66 4 4 4 2 2 4 1 1 1 3 3 1 67 4 4 4 6 2 4 1 1 1 3 3 1 68 4 4 4 2 6 4 1 1 1 3 3 1 69 4 4 4 6 6 4 1 1 1 3 3 1 70 4 4 4 4 1 4 1 1 1 1 7 1 71 4 4 4 4 3 4 1 1 1 1 7 1 72 4 4 4 4 5 4 1 1 1 1 7 1 73 4 4 4 4 7 4 1 1 1 1 7 1 74 2 4 4 4 4 2 3 1 1 1 1 3 75 6 4 4 4 4 2 3 1 1 1 1 3 76 2 4 4 4 4 6 3 1 1 1 1 3 77 6 4 4 4 4 6 3 1 1 1 1 3 78 4 2 4 4 4 2 1 3 1 1 1 3 79 4 6 4 4 4 2 1 3 1 1 1 3 80 4 2 4 4 4 6 1 3 1 1 1 3 81 4 6 4 4 4 6 1 3 1 1 1 3 82 4 4 2 4 4 2 1 1 3 1 1 3 83 4 4 6 4 4 2 1 1 3 1 1 3 84 4 4 2 4 4 6 1 1 3 1 1 3 85 4 4 6 4 4 6 1 1 3 1 1 3 86 4 4 4 2 4 2 1 1 1 3 1 3 87 4 4 4 6 4 2 1 1 1 3 1 3 88 4 4 4 2 4 6 1 1 1 3 1 3 89 4 4 4 6 4 6 1 1 1 3 1 3 90 4 4 4 4 2 2 1 1 1 1 3 3 91 4 4 4 4 6 2 1 1 1 1 3 3 92 4 4 4 4 2 6 1 1 1 1 3 3 93 4 4 4 4 6 6 1 1 1 1 3 3 94 4 4 4 4 4 1 1 1 1 1 1 7 95 4 4 4 4 4 3 1 1 1 1 1 7 96 4 4 4 4 4 5 1 1 1 1 1 7 97 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: 1 0 0 0 0 2 -1 0 1 0 3 1 0 1 0 4 0 -1 0 1 5 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: 1 0 0 0 0 2 -1 0 1 0 3 1 0 1 0 4 0 -1 0 1 5 0 1 0 1 6 -3 0 3 0 7 -2 0 3 0 8 -1 0 3 0 9 1 0 3 0 10 2 0 3 0 11 3 0 3 0 12 -1 -1 1 1 13 1 -1 1 1 14 -1 1 1 1 15 1 1 1 1 16 0 -3 0 3 17 0 -2 0 3 18 0 -1 0 3 19 0 1 0 3 20 0 2 0 3 21 0 3 0 3 22 -7 0 7 0 23 -6 0 7 0 24 -5 0 7 0 25 -4 0 7 0 26 -3 0 7 0 27 -2 0 7 0 28 -1 0 7 0 29 1 0 7 0 30 2 0 7 0 31 3 0 7 0 32 4 0 7 0 33 5 0 7 0 34 6 0 7 0 35 7 0 7 0 36 -3 -1 3 1 37 -2 -1 3 1 38 -1 -1 3 1 39 1 -1 3 1 40 2 -1 3 1 41 3 -1 3 1 42 -3 1 3 1 43 -2 1 3 1 44 -1 1 3 1 45 1 1 3 1 46 2 1 3 1 47 3 1 3 1 48 -1 -3 1 3 49 1 -3 1 3 50 -1 -2 1 3 51 1 -2 1 3 52 -1 -1 1 3 53 1 -1 1 3 54 -1 1 1 3 55 1 1 1 3 56 -1 2 1 3 57 1 2 1 3 58 -1 3 1 3 59 1 3 1 3 60 0 -7 0 7 61 0 -6 0 7 62 0 -5 0 7 63 0 -4 0 7 64 0 -3 0 7 65 0 -2 0 7 66 0 -1 0 7 67 0 1 0 7 68 0 2 0 7 69 0 3 0 7 70 0 4 0 7 71 0 5 0 7 72 0 6 0 7 73 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: 1 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: 1 0 0 0 0 0 0 2 -1 0 0 1 0 0 3 1 0 0 1 0 0 4 0 -1 0 0 1 0 5 0 1 0 0 1 0 6 0 0 -1 0 0 1 7 0 0 1 0 0 1 8 -3 0 0 3 0 0 9 -2 0 0 3 0 0 10 -1 0 0 3 0 0 11 1 0 0 3 0 0 12 2 0 0 3 0 0 13 3 0 0 3 0 0 14 -1 -1 0 1 1 0 15 1 -1 0 1 1 0 16 -1 1 0 1 1 0 17 1 1 0 1 1 0 18 0 -3 0 0 3 0 19 0 -2 0 0 3 0 20 0 -1 0 0 3 0 21 0 1 0 0 3 0 22 0 2 0 0 3 0 23 0 3 0 0 3 0 24 -1 0 -1 1 0 1 25 1 0 -1 1 0 1 26 -1 0 1 1 0 1 27 1 0 1 1 0 1 28 0 -1 -1 0 1 1 29 0 1 -1 0 1 1 30 0 -1 1 0 1 1 31 0 1 1 0 1 1 32 0 0 -3 0 0 3 33 0 0 -2 0 0 3 34 0 0 -1 0 0 3 35 0 0 1 0 0 3 36 0 0 2 0 0 3 37 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: 1 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 0 0 0 0 0 1 0 0 0 0 0 3 1 0 0 0 0 0 1 0 0 0 0 0 4 0 -1 0 0 0 0 0 1 0 0 0 0 5 0 1 0 0 0 0 0 1 0 0 0 0 6 0 0 -1 0 0 0 0 0 1 0 0 0 7 0 0 1 0 0 0 0 0 1 0 0 0 8 0 0 0 -1 0 0 0 0 0 1 0 0 9 0 0 0 1 0 0 0 0 0 1 0 0 10 0 0 0 0 -1 0 0 0 0 0 1 0 11 0 0 0 0 1 0 0 0 0 0 1 0 12 0 0 0 0 0 -1 0 0 0 0 0 1 13 0 0 0 0 0 1 0 0 0 0 0 1 14 -3 0 0 0 0 0 3 0 0 0 0 0 15 -2 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 1 0 0 0 0 0 3 0 0 0 0 0 18 2 0 0 0 0 0 3 0 0 0 0 0 19 3 0 0 0 0 0 3 0 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 1 1 0 0 0 0 1 1 0 0 0 0 24 0 -3 0 0 0 0 0 3 0 0 0 0 25 0 -2 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 1 0 0 0 0 0 3 0 0 0 0 28 0 2 0 0 0 0 0 3 0 0 0 0 29 0 3 0 0 0 0 0 3 0 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 1 0 1 0 0 0 1 0 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 1 1 0 0 0 0 1 1 0 0 0 38 0 0 -3 0 0 0 0 0 3 0 0 0 39 0 0 -2 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 1 0 0 0 0 0 3 0 0 0 42 0 0 2 0 0 0 0 0 3 0 0 0 43 0 0 3 0 0 0 0 0 3 0 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 1 0 0 1 0 0 1 0 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 1 0 1 0 0 0 1 0 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 1 1 0 0 0 0 1 1 0 0 56 0 0 0 -3 0 0 0 0 0 3 0 0 57 0 0 0 -2 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 1 0 0 0 0 0 3 0 0 60 0 0 0 2 0 0 0 0 0 3 0 0 61 0 0 0 3 0 0 0 0 0 3 0 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 1 0 0 0 1 0 1 0 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 1 0 0 1 0 0 1 0 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 1 0 1 0 0 0 1 0 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 1 1 0 0 0 0 1 1 0 78 0 0 0 0 -3 0 0 0 0 0 3 0 79 0 0 0 0 -2 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 1 0 0 0 0 0 3 0 82 0 0 0 0 2 0 0 0 0 0 3 0 83 0 0 0 0 3 0 0 0 0 0 3 0 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 1 0 0 0 0 1 1 0 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 1 0 0 0 1 0 1 0 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 1 0 0 1 0 0 1 0 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 1 0 1 0 0 0 1 0 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 1 1 0 0 0 0 1 1 104 0 0 0 0 0 -3 0 0 0 0 0 3 105 0 0 0 0 0 -2 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 1 0 0 0 0 0 3 108 0 0 0 0 0 2 0 0 0 0 0 3 109 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: 1 1 1 1 1 2 1 1 3 1 3 2 1 3 1 4 3 1 3 1 5 1 1 1 3 6 1 2 1 3 7 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: 1 1 1 7 1 2 2 1 7 1 3 3 1 7 1 4 4 1 7 1 5 5 1 7 1 6 6 1 7 1 7 7 1 7 1 8 1 1 3 3 9 2 1 3 3 10 3 1 3 3 11 1 2 3 3 12 2 2 3 3 13 3 2 3 3 14 1 3 3 3 15 2 3 3 3 16 3 3 3 3 17 1 1 1 7 18 1 2 1 7 19 1 3 1 7 20 1 4 1 7 21 1 5 1 7 22 1 6 1 7 23 1 7 1 7 24 1 1 15 1 25 2 1 15 1 26 3 1 15 1 27 4 1 15 1 28 5 1 15 1 29 6 1 15 1 30 7 1 15 1 31 8 1 15 1 32 9 1 15 1 33 10 1 15 1 34 11 1 15 1 35 12 1 15 1 36 13 1 15 1 37 14 1 15 1 38 15 1 15 1 39 1 1 7 3 40 2 1 7 3 41 3 1 7 3 42 4 1 7 3 43 5 1 7 3 44 6 1 7 3 45 7 1 7 3 46 1 2 7 3 47 2 2 7 3 48 3 2 7 3 49 4 2 7 3 50 5 2 7 3 51 6 2 7 3 52 7 2 7 3 53 1 3 7 3 54 2 3 7 3 55 3 3 7 3 56 4 3 7 3 57 5 3 7 3 58 6 3 7 3 59 7 3 7 3 60 1 1 3 7 61 2 1 3 7 62 3 1 3 7 63 1 2 3 7 64 2 2 3 7 65 3 2 3 7 66 1 3 3 7 67 2 3 3 7 68 3 3 3 7 69 1 4 3 7 70 2 4 3 7 71 3 4 3 7 72 1 5 3 7 73 2 5 3 7 74 3 5 3 7 75 1 6 3 7 76 2 6 3 7 77 3 6 3 7 78 1 7 3 7 79 2 7 3 7 80 3 7 3 7 81 1 1 1 15 82 1 2 1 15 83 1 3 1 15 84 1 4 1 15 85 1 5 1 15 86 1 6 1 15 87 1 7 1 15 88 1 8 1 15 89 1 9 1 15 90 1 10 1 15 91 1 11 1 15 92 1 12 1 15 93 1 13 1 15 94 1 14 1 15 95 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: 1 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: 1 1 1 1 1 1 1 2 1 1 1 3 1 1 3 2 1 1 3 1 1 4 3 1 1 3 1 1 5 1 1 1 1 3 1 6 1 2 1 1 3 1 7 1 3 1 1 3 1 8 1 1 1 1 1 3 9 1 1 2 1 1 3 10 1 1 3 1 1 3 11 1 1 1 7 1 1 12 2 1 1 7 1 1 13 3 1 1 7 1 1 14 4 1 1 7 1 1 15 5 1 1 7 1 1 16 6 1 1 7 1 1 17 7 1 1 7 1 1 18 1 1 1 3 3 1 19 2 1 1 3 3 1 20 3 1 1 3 3 1 21 1 2 1 3 3 1 22 2 2 1 3 3 1 23 3 2 1 3 3 1 24 1 3 1 3 3 1 25 2 3 1 3 3 1 26 3 3 1 3 3 1 27 1 1 1 1 7 1 28 1 2 1 1 7 1 29 1 3 1 1 7 1 30 1 4 1 1 7 1 31 1 5 1 1 7 1 32 1 6 1 1 7 1 33 1 7 1 1 7 1 34 1 1 1 3 1 3 35 2 1 1 3 1 3 36 3 1 1 3 1 3 37 1 1 2 3 1 3 38 2 1 2 3 1 3 39 3 1 2 3 1 3 40 1 1 3 3 1 3 41 2 1 3 3 1 3 42 3 1 3 3 1 3 43 1 1 1 1 3 3 44 1 2 1 1 3 3 45 1 3 1 1 3 3 46 1 1 2 1 3 3 47 1 2 2 1 3 3 48 1 3 2 1 3 3 49 1 1 3 1 3 3 50 1 2 3 1 3 3 51 1 3 3 1 3 3 52 1 1 1 1 1 7 53 1 1 2 1 1 7 54 1 1 3 1 1 7 55 1 1 4 1 1 7 56 1 1 5 1 1 7 57 1 1 6 1 1 7 58 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: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 1 3 2 1 1 1 1 1 3 1 1 1 1 1 4 3 1 1 1 1 1 3 1 1 1 1 1 5 1 1 1 1 1 1 1 3 1 1 1 1 6 1 2 1 1 1 1 1 3 1 1 1 1 7 1 3 1 1 1 1 1 3 1 1 1 1 8 1 1 1 1 1 1 1 1 3 1 1 1 9 1 1 2 1 1 1 1 1 3 1 1 1 10 1 1 3 1 1 1 1 1 3 1 1 1 11 1 1 1 1 1 1 1 1 1 3 1 1 12 1 1 1 2 1 1 1 1 1 3 1 1 13 1 1 1 3 1 1 1 1 1 3 1 1 14 1 1 1 1 1 1 1 1 1 1 3 1 15 1 1 1 1 2 1 1 1 1 1 3 1 16 1 1 1 1 3 1 1 1 1 1 3 1 17 1 1 1 1 1 1 1 1 1 1 1 3 18 1 1 1 1 1 2 1 1 1 1 1 3 19 1 1 1 1 1 3 1 1 1 1 1 3 20 1 1 1 1 1 1 7 1 1 1 1 1 21 2 1 1 1 1 1 7 1 1 1 1 1 22 3 1 1 1 1 1 7 1 1 1 1 1 23 4 1 1 1 1 1 7 1 1 1 1 1 24 5 1 1 1 1 1 7 1 1 1 1 1 25 6 1 1 1 1 1 7 1 1 1 1 1 26 7 1 1 1 1 1 7 1 1 1 1 1 27 1 1 1 1 1 1 3 3 1 1 1 1 28 2 1 1 1 1 1 3 3 1 1 1 1 29 3 1 1 1 1 1 3 3 1 1 1 1 30 1 2 1 1 1 1 3 3 1 1 1 1 31 2 2 1 1 1 1 3 3 1 1 1 1 32 3 2 1 1 1 1 3 3 1 1 1 1 33 1 3 1 1 1 1 3 3 1 1 1 1 34 2 3 1 1 1 1 3 3 1 1 1 1 35 3 3 1 1 1 1 3 3 1 1 1 1 36 1 1 1 1 1 1 1 7 1 1 1 1 37 1 2 1 1 1 1 1 7 1 1 1 1 38 1 3 1 1 1 1 1 7 1 1 1 1 39 1 4 1 1 1 1 1 7 1 1 1 1 40 1 5 1 1 1 1 1 7 1 1 1 1 41 1 6 1 1 1 1 1 7 1 1 1 1 42 1 7 1 1 1 1 1 7 1 1 1 1 43 1 1 1 1 1 1 3 1 3 1 1 1 44 2 1 1 1 1 1 3 1 3 1 1 1 45 3 1 1 1 1 1 3 1 3 1 1 1 46 1 1 2 1 1 1 3 1 3 1 1 1 47 2 1 2 1 1 1 3 1 3 1 1 1 48 3 1 2 1 1 1 3 1 3 1 1 1 49 1 1 3 1 1 1 3 1 3 1 1 1 50 2 1 3 1 1 1 3 1 3 1 1 1 51 3 1 3 1 1 1 3 1 3 1 1 1 52 1 1 1 1 1 1 1 3 3 1 1 1 53 1 2 1 1 1 1 1 3 3 1 1 1 54 1 3 1 1 1 1 1 3 3 1 1 1 55 1 1 2 1 1 1 1 3 3 1 1 1 56 1 2 2 1 1 1 1 3 3 1 1 1 57 1 3 2 1 1 1 1 3 3 1 1 1 58 1 1 3 1 1 1 1 3 3 1 1 1 59 1 2 3 1 1 1 1 3 3 1 1 1 60 1 3 3 1 1 1 1 3 3 1 1 1 61 1 1 1 1 1 1 1 1 7 1 1 1 62 1 1 2 1 1 1 1 1 7 1 1 1 63 1 1 3 1 1 1 1 1 7 1 1 1 64 1 1 4 1 1 1 1 1 7 1 1 1 65 1 1 5 1 1 1 1 1 7 1 1 1 66 1 1 6 1 1 1 1 1 7 1 1 1 67 1 1 7 1 1 1 1 1 7 1 1 1 68 1 1 1 1 1 1 3 1 1 3 1 1 69 2 1 1 1 1 1 3 1 1 3 1 1 70 3 1 1 1 1 1 3 1 1 3 1 1 71 1 1 1 2 1 1 3 1 1 3 1 1 72 2 1 1 2 1 1 3 1 1 3 1 1 73 3 1 1 2 1 1 3 1 1 3 1 1 74 1 1 1 3 1 1 3 1 1 3 1 1 75 2 1 1 3 1 1 3 1 1 3 1 1 76 3 1 1 3 1 1 3 1 1 3 1 1 77 1 1 1 1 1 1 1 3 1 3 1 1 78 1 2 1 1 1 1 1 3 1 3 1 1 79 1 3 1 1 1 1 1 3 1 3 1 1 80 1 1 1 2 1 1 1 3 1 3 1 1 81 1 2 1 2 1 1 1 3 1 3 1 1 82 1 3 1 2 1 1 1 3 1 3 1 1 83 1 1 1 3 1 1 1 3 1 3 1 1 84 1 2 1 3 1 1 1 3 1 3 1 1 85 1 3 1 3 1 1 1 3 1 3 1 1 86 1 1 1 1 1 1 1 1 3 3 1 1 87 1 1 2 1 1 1 1 1 3 3 1 1 88 1 1 3 1 1 1 1 1 3 3 1 1 89 1 1 1 2 1 1 1 1 3 3 1 1 90 1 1 2 2 1 1 1 1 3 3 1 1 91 1 1 3 2 1 1 1 1 3 3 1 1 92 1 1 1 3 1 1 1 1 3 3 1 1 93 1 1 2 3 1 1 1 1 3 3 1 1 94 1 1 3 3 1 1 1 1 3 3 1 1 95 1 1 1 1 1 1 1 1 1 7 1 1 96 1 1 1 2 1 1 1 1 1 7 1 1 97 1 1 1 3 1 1 1 1 1 7 1 1 98 1 1 1 4 1 1 1 1 1 7 1 1 99 1 1 1 5 1 1 1 1 1 7 1 1 100 1 1 1 6 1 1 1 1 1 7 1 1 101 1 1 1 7 1 1 1 1 1 7 1 1 102 1 1 1 1 1 1 3 1 1 1 3 1 103 2 1 1 1 1 1 3 1 1 1 3 1 104 3 1 1 1 1 1 3 1 1 1 3 1 105 1 1 1 1 2 1 3 1 1 1 3 1 106 2 1 1 1 2 1 3 1 1 1 3 1 107 3 1 1 1 2 1 3 1 1 1 3 1 108 1 1 1 1 3 1 3 1 1 1 3 1 109 2 1 1 1 3 1 3 1 1 1 3 1 110 3 1 1 1 3 1 3 1 1 1 3 1 111 1 1 1 1 1 1 1 3 1 1 3 1 112 1 2 1 1 1 1 1 3 1 1 3 1 113 1 3 1 1 1 1 1 3 1 1 3 1 114 1 1 1 1 2 1 1 3 1 1 3 1 115 1 2 1 1 2 1 1 3 1 1 3 1 116 1 3 1 1 2 1 1 3 1 1 3 1 117 1 1 1 1 3 1 1 3 1 1 3 1 118 1 2 1 1 3 1 1 3 1 1 3 1 119 1 3 1 1 3 1 1 3 1 1 3 1 120 1 1 1 1 1 1 1 1 3 1 3 1 121 1 1 2 1 1 1 1 1 3 1 3 1 122 1 1 3 1 1 1 1 1 3 1 3 1 123 1 1 1 1 2 1 1 1 3 1 3 1 124 1 1 2 1 2 1 1 1 3 1 3 1 125 1 1 3 1 2 1 1 1 3 1 3 1 126 1 1 1 1 3 1 1 1 3 1 3 1 127 1 1 2 1 3 1 1 1 3 1 3 1 128 1 1 3 1 3 1 1 1 3 1 3 1 129 1 1 1 1 1 1 1 1 1 3 3 1 130 1 1 1 2 1 1 1 1 1 3 3 1 131 1 1 1 3 1 1 1 1 1 3 3 1 132 1 1 1 1 2 1 1 1 1 3 3 1 133 1 1 1 2 2 1 1 1 1 3 3 1 134 1 1 1 3 2 1 1 1 1 3 3 1 135 1 1 1 1 3 1 1 1 1 3 3 1 136 1 1 1 2 3 1 1 1 1 3 3 1 137 1 1 1 3 3 1 1 1 1 3 3 1 138 1 1 1 1 1 1 1 1 1 1 7 1 139 1 1 1 1 2 1 1 1 1 1 7 1 140 1 1 1 1 3 1 1 1 1 1 7 1 141 1 1 1 1 4 1 1 1 1 1 7 1 142 1 1 1 1 5 1 1 1 1 1 7 1 143 1 1 1 1 6 1 1 1 1 1 7 1 144 1 1 1 1 7 1 1 1 1 1 7 1 145 1 1 1 1 1 1 3 1 1 1 1 3 146 2 1 1 1 1 1 3 1 1 1 1 3 147 3 1 1 1 1 1 3 1 1 1 1 3 148 1 1 1 1 1 2 3 1 1 1 1 3 149 2 1 1 1 1 2 3 1 1 1 1 3 150 3 1 1 1 1 2 3 1 1 1 1 3 151 1 1 1 1 1 3 3 1 1 1 1 3 152 2 1 1 1 1 3 3 1 1 1 1 3 153 3 1 1 1 1 3 3 1 1 1 1 3 154 1 1 1 1 1 1 1 3 1 1 1 3 155 1 2 1 1 1 1 1 3 1 1 1 3 156 1 3 1 1 1 1 1 3 1 1 1 3 157 1 1 1 1 1 2 1 3 1 1 1 3 158 1 2 1 1 1 2 1 3 1 1 1 3 159 1 3 1 1 1 2 1 3 1 1 1 3 160 1 1 1 1 1 3 1 3 1 1 1 3 161 1 2 1 1 1 3 1 3 1 1 1 3 162 1 3 1 1 1 3 1 3 1 1 1 3 163 1 1 1 1 1 1 1 1 3 1 1 3 164 1 1 2 1 1 1 1 1 3 1 1 3 165 1 1 3 1 1 1 1 1 3 1 1 3 166 1 1 1 1 1 2 1 1 3 1 1 3 167 1 1 2 1 1 2 1 1 3 1 1 3 168 1 1 3 1 1 2 1 1 3 1 1 3 169 1 1 1 1 1 3 1 1 3 1 1 3 170 1 1 2 1 1 3 1 1 3 1 1 3 171 1 1 3 1 1 3 1 1 3 1 1 3 172 1 1 1 1 1 1 1 1 1 3 1 3 173 1 1 1 2 1 1 1 1 1 3 1 3 174 1 1 1 3 1 1 1 1 1 3 1 3 175 1 1 1 1 1 2 1 1 1 3 1 3 176 1 1 1 2 1 2 1 1 1 3 1 3 177 1 1 1 3 1 2 1 1 1 3 1 3 178 1 1 1 1 1 3 1 1 1 3 1 3 179 1 1 1 2 1 3 1 1 1 3 1 3 180 1 1 1 3 1 3 1 1 1 3 1 3 181 1 1 1 1 1 1 1 1 1 1 3 3 182 1 1 1 1 2 1 1 1 1 1 3 3 183 1 1 1 1 3 1 1 1 1 1 3 3 184 1 1 1 1 1 2 1 1 1 1 3 3 185 1 1 1 1 2 2 1 1 1 1 3 3 186 1 1 1 1 3 2 1 1 1 1 3 3 187 1 1 1 1 1 3 1 1 1 1 3 3 188 1 1 1 1 2 3 1 1 1 1 3 3 189 1 1 1 1 3 3 1 1 1 1 3 3 190 1 1 1 1 1 1 1 1 1 1 1 7 191 1 1 1 1 1 2 1 1 1 1 1 7 192 1 1 1 1 1 3 1 1 1 1 1 7 193 1 1 1 1 1 4 1 1 1 1 1 7 194 1 1 1 1 1 5 1 1 1 1 1 7 195 1 1 1 1 1 6 1 1 1 1 1 7 196 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: 1 1.333333e+00 2 6.666667e-01 3 6.666667e-01 4 6.666667e-01 5 6.666667e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -1.000000e+00 0.000000e+00 3 1.000000e+00 0.000000e+00 4 0.000000e+00 -1.000000e+00 5 0.000000e+00 1.000000e+00 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: 1 -3.555556e-01 2 -8.888889e-02 3 -8.888889e-02 4 -8.888889e-02 5 -8.888889e-02 6 1.066667e+00 7 1.066667e+00 8 1.111111e-01 9 1.111111e-01 10 1.111111e-01 11 1.111111e-01 12 1.066667e+00 13 1.066667e+00 Grid points: 1 0.000000e+00 0.000000e+00 2 -1.000000e+00 0.000000e+00 3 1.000000e+00 0.000000e+00 4 0.000000e+00 -1.000000e+00 5 0.000000e+00 1.000000e+00 6 -7.071068e-01 0.000000e+00 7 7.071068e-01 0.000000e+00 8 -1.000000e+00 -1.000000e+00 9 1.000000e+00 -1.000000e+00 10 -1.000000e+00 1.000000e+00 11 1.000000e+00 1.000000e+00 12 0.000000e+00 -7.071068e-01 13 0.000000e+00 7.071068e-01 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: 1 -1.776357e-15 2 1.333333e+00 3 1.333333e+00 4 1.333333e+00 5 1.333333e+00 6 1.333333e+00 7 1.333333e+00 Grid points: 1 0.000000e+00 0.000000e+00 0.000000e+00 2 -1.000000e+00 0.000000e+00 0.000000e+00 3 1.000000e+00 0.000000e+00 0.000000e+00 4 0.000000e+00 -1.000000e+00 0.000000e+00 5 0.000000e+00 1.000000e+00 0.000000e+00 6 0.000000e+00 0.000000e+00 -1.000000e+00 7 0.000000e+00 0.000000e+00 1.000000e+00 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: 1 4.444444e-01 2 8.888889e-01 3 8.888889e-01 4 8.888889e-01 5 8.888889e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -8.660254e-01 0.000000e+00 3 8.660254e-01 0.000000e+00 4 0.000000e+00 -8.660254e-01 5 0.000000e+00 8.660254e-01 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: 1 -1.392189e+00 2 1.806011e-01 3 1.806011e-01 4 1.806011e-01 5 1.806011e-01 6 1.734324e-01 7 7.964831e-01 8 7.964831e-01 9 1.734324e-01 10 1.975309e-01 11 1.975309e-01 12 1.975309e-01 13 1.975309e-01 14 1.734324e-01 15 7.964831e-01 16 7.964831e-01 17 1.734324e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.818315e-01 0.000000e+00 3 7.818315e-01 0.000000e+00 4 0.000000e+00 -7.818315e-01 5 0.000000e+00 7.818315e-01 6 -9.749279e-01 0.000000e+00 7 -4.338837e-01 0.000000e+00 8 4.338837e-01 0.000000e+00 9 9.749279e-01 0.000000e+00 10 -7.818315e-01 -7.818315e-01 11 7.818315e-01 -7.818315e-01 12 -7.818315e-01 7.818315e-01 13 7.818315e-01 7.818315e-01 14 0.000000e+00 -9.749279e-01 15 0.000000e+00 -4.338837e-01 16 0.000000e+00 4.338837e-01 17 0.000000e+00 9.749279e-01 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: 1 -2.666667e+00 2 1.777778e+00 3 1.777778e+00 4 1.777778e+00 5 1.777778e+00 6 1.777778e+00 7 1.777778e+00 Grid points: 1 0.000000e+00 0.000000e+00 0.000000e+00 2 -8.660254e-01 0.000000e+00 0.000000e+00 3 8.660254e-01 0.000000e+00 0.000000e+00 4 0.000000e+00 -8.660254e-01 0.000000e+00 5 0.000000e+00 8.660254e-01 0.000000e+00 6 0.000000e+00 0.000000e+00 -8.660254e-01 7 0.000000e+00 0.000000e+00 8.660254e-01 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: 1 -1.333333e+00 2 1.333333e+00 3 1.333333e+00 4 1.333333e+00 5 1.333333e+00 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.071068e-01 0.000000e+00 3 7.071068e-01 0.000000e+00 4 0.000000e+00 -7.071068e-01 5 0.000000e+00 7.071068e-01 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: 1 -7.746032e-01 2 -3.936508e-01 3 -3.936508e-01 4 -3.936508e-01 5 -3.936508e-01 6 3.559294e-01 7 7.869278e-01 8 7.869278e-01 9 3.559294e-01 10 4.444444e-01 11 4.444444e-01 12 4.444444e-01 13 4.444444e-01 14 3.559294e-01 15 7.869278e-01 16 7.869278e-01 17 3.559294e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.071068e-01 0.000000e+00 3 7.071068e-01 0.000000e+00 4 0.000000e+00 -7.071068e-01 5 0.000000e+00 7.071068e-01 6 -9.238795e-01 0.000000e+00 7 -3.826834e-01 0.000000e+00 8 3.826834e-01 0.000000e+00 9 9.238795e-01 0.000000e+00 10 -7.071068e-01 -7.071068e-01 11 7.071068e-01 -7.071068e-01 12 -7.071068e-01 7.071068e-01 13 7.071068e-01 7.071068e-01 14 0.000000e+00 -9.238795e-01 15 0.000000e+00 -3.826834e-01 16 0.000000e+00 3.826834e-01 17 0.000000e+00 9.238795e-01 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: 1 -8.000000e+00 2 2.666667e+00 3 2.666667e+00 4 2.666667e+00 5 2.666667e+00 6 2.666667e+00 7 2.666667e+00 Grid points: 1 0.000000e+00 0.000000e+00 0.000000e+00 2 -7.071068e-01 0.000000e+00 0.000000e+00 3 7.071068e-01 0.000000e+00 0.000000e+00 4 0.000000e+00 -7.071068e-01 0.000000e+00 5 0.000000e+00 7.071068e-01 0.000000e+00 6 0.000000e+00 0.000000e+00 -7.071068e-01 7 0.000000e+00 0.000000e+00 7.071068e-01 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: 1 -4.444444e-01 2 1.111111e+00 3 1.111111e+00 4 1.111111e+00 5 1.111111e+00 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.745967e-01 0.000000e+00 3 7.745967e-01 0.000000e+00 4 0.000000e+00 -7.745967e-01 5 0.000000e+00 7.745967e-01 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: 1 -9.617659e-01 2 -8.030777e-02 3 -8.030777e-02 4 -8.030777e-02 5 -8.030777e-02 6 2.093125e-01 7 8.027948e-01 8 8.027948e-01 9 2.093125e-01 10 3.086420e-01 11 3.086420e-01 12 3.086420e-01 13 3.086420e-01 14 2.093125e-01 15 8.027948e-01 16 8.027948e-01 17 2.093125e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.745967e-01 0.000000e+00 3 7.745967e-01 0.000000e+00 4 0.000000e+00 -7.745967e-01 5 0.000000e+00 7.745967e-01 6 -9.604913e-01 0.000000e+00 7 -4.342437e-01 0.000000e+00 8 4.342437e-01 0.000000e+00 9 9.604913e-01 0.000000e+00 10 -7.745967e-01 -7.745967e-01 11 7.745967e-01 -7.745967e-01 12 -7.745967e-01 7.745967e-01 13 7.745967e-01 7.745967e-01 14 0.000000e+00 -9.604913e-01 15 0.000000e+00 -4.342437e-01 16 0.000000e+00 4.342437e-01 17 0.000000e+00 9.604913e-01 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: 1 -5.333333e+00 2 2.222222e+00 3 2.222222e+00 4 2.222222e+00 5 2.222222e+00 6 2.222222e+00 7 2.222222e+00 Grid points: 1 0.000000e+00 0.000000e+00 0.000000e+00 2 -7.745967e-01 0.000000e+00 0.000000e+00 3 7.745967e-01 0.000000e+00 0.000000e+00 4 0.000000e+00 -7.745967e-01 0.000000e+00 5 0.000000e+00 7.745967e-01 0.000000e+00 6 0.000000e+00 0.000000e+00 -7.745967e-01 7 0.000000e+00 0.000000e+00 7.745967e-01 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: 1 -4.444444e-01 2 1.111111e+00 3 1.111111e+00 4 1.111111e+00 5 1.111111e+00 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.745967e-01 0.000000e+00 3 7.745967e-01 0.000000e+00 4 0.000000e+00 -7.745967e-01 5 0.000000e+00 7.745967e-01 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: 1 -1.093595e+00 2 -6.172840e-01 3 -6.172840e-01 4 -6.172840e-01 5 -6.172840e-01 6 2.589699e-01 7 5.594108e-01 8 7.636601e-01 9 7.636601e-01 10 5.594108e-01 11 2.589699e-01 12 3.086420e-01 13 3.086420e-01 14 3.086420e-01 15 3.086420e-01 16 2.589699e-01 17 5.594108e-01 18 7.636601e-01 19 7.636601e-01 20 5.594108e-01 21 2.589699e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -7.745967e-01 0.000000e+00 3 7.745967e-01 0.000000e+00 4 0.000000e+00 -7.745967e-01 5 0.000000e+00 7.745967e-01 6 -9.491079e-01 0.000000e+00 7 -7.415312e-01 0.000000e+00 8 -4.058452e-01 0.000000e+00 9 4.058452e-01 0.000000e+00 10 7.415312e-01 0.000000e+00 11 9.491079e-01 0.000000e+00 12 -7.745967e-01 -7.745967e-01 13 7.745967e-01 -7.745967e-01 14 -7.745967e-01 7.745967e-01 15 7.745967e-01 7.745967e-01 16 0.000000e+00 -9.491079e-01 17 0.000000e+00 -7.415312e-01 18 0.000000e+00 -4.058452e-01 19 0.000000e+00 4.058452e-01 20 0.000000e+00 7.415312e-01 21 0.000000e+00 9.491079e-01 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: 1 -5.333333e+00 2 2.222222e+00 3 2.222222e+00 4 2.222222e+00 5 2.222222e+00 6 2.222222e+00 7 2.222222e+00 Grid points: 1 0.000000e+00 0.000000e+00 0.000000e+00 2 -7.745967e-01 0.000000e+00 0.000000e+00 3 7.745967e-01 0.000000e+00 0.000000e+00 4 0.000000e+00 -7.745967e-01 0.000000e+00 5 0.000000e+00 7.745967e-01 0.000000e+00 6 0.000000e+00 0.000000e+00 -7.745967e-01 7 0.000000e+00 0.000000e+00 7.745967e-01 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: 1 1.047198e+00 2 5.235988e-01 3 5.235988e-01 4 5.235988e-01 5 5.235988e-01 Grid points: 1 0.000000e+00 0.000000e+00 2 -1.224745e+00 0.000000e+00 3 1.224745e+00 0.000000e+00 4 0.000000e+00 -1.224745e+00 5 0.000000e+00 1.224745e+00 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: 1 7.978648e-02 2 -1.745329e-01 3 -1.745329e-01 4 -1.745329e-01 5 -1.745329e-01 6 1.722437e-03 7 9.662635e-02 8 7.543692e-01 9 7.543692e-01 10 9.662635e-02 11 1.722437e-03 12 8.726646e-02 13 8.726646e-02 14 8.726646e-02 15 8.726646e-02 16 1.722437e-03 17 9.662635e-02 18 7.543692e-01 19 7.543692e-01 20 9.662635e-02 21 1.722437e-03 Grid points: 1 0.000000e+00 0.000000e+00 2 -1.224745e+00 0.000000e+00 3 1.224745e+00 0.000000e+00 4 0.000000e+00 -1.224745e+00 5 0.000000e+00 1.224745e+00 6 -2.651961e+00 0.000000e+00 7 -1.673552e+00 0.000000e+00 8 -8.162879e-01 0.000000e+00 9 8.162879e-01 0.000000e+00 10 1.673552e+00 0.000000e+00 11 2.651961e+00 0.000000e+00 12 -1.224745e+00 -1.224745e+00 13 1.224745e+00 -1.224745e+00 14 -1.224745e+00 1.224745e+00 15 1.224745e+00 1.224745e+00 16 0.000000e+00 -2.651961e+00 17 0.000000e+00 -1.673552e+00 18 0.000000e+00 -8.162879e-01 19 0.000000e+00 8.162879e-01 20 0.000000e+00 1.673552e+00 21 0.000000e+00 2.651961e+00 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: 1 -8.881784e-16 2 9.280547e-01 3 9.280547e-01 4 9.280547e-01 5 9.280547e-01 6 9.280547e-01 7 9.280547e-01 Grid points: 1 0.000000e+00 0.000000e+00 0.000000e+00 2 -1.224745e+00 0.000000e+00 0.000000e+00 3 1.224745e+00 0.000000e+00 0.000000e+00 4 0.000000e+00 -1.224745e+00 0.000000e+00 5 0.000000e+00 1.224745e+00 0.000000e+00 6 0.000000e+00 0.000000e+00 -1.224745e+00 7 0.000000e+00 0.000000e+00 1.224745e+00 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: 1 -1.000000e+00 2 7.110930e-01 3 2.785177e-01 4 1.038926e-02 5 7.110930e-01 6 2.785177e-01 7 1.038926e-02 Grid points: 1 1.000000e+00 1.000000e+00 2 4.157746e-01 1.000000e+00 3 2.294280e+00 1.000000e+00 4 6.289945e+00 1.000000e+00 5 1.000000e+00 4.157746e-01 6 1.000000e+00 2.294280e+00 7 1.000000e+00 6.289945e+00 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: 1 -7.110930e-01 2 -2.785177e-01 3 -1.038926e-02 4 -7.110930e-01 5 -2.785177e-01 6 -1.038926e-02 7 4.093190e-01 8 4.218313e-01 9 1.471263e-01 10 2.063351e-02 11 1.074010e-03 12 1.586546e-05 13 3.170315e-08 14 5.056533e-01 15 1.980520e-01 16 7.387728e-03 17 1.980520e-01 18 7.757213e-02 19 2.893592e-03 20 7.387728e-03 21 2.893592e-03 22 1.079367e-04 23 4.093190e-01 24 4.218313e-01 25 1.471263e-01 26 2.063351e-02 27 1.074010e-03 28 1.586546e-05 29 3.170315e-08 Grid points: 1 4.157746e-01 1.000000e+00 2 2.294280e+00 1.000000e+00 3 6.289945e+00 1.000000e+00 4 1.000000e+00 4.157746e-01 5 1.000000e+00 2.294280e+00 6 1.000000e+00 6.289945e+00 7 1.930437e-01 1.000000e+00 8 1.026665e+00 1.000000e+00 9 2.567877e+00 1.000000e+00 10 4.900353e+00 1.000000e+00 11 8.182153e+00 1.000000e+00 12 1.273418e+01 1.000000e+00 13 1.939573e+01 1.000000e+00 14 4.157746e-01 4.157746e-01 15 2.294280e+00 4.157746e-01 16 6.289945e+00 4.157746e-01 17 4.157746e-01 2.294280e+00 18 2.294280e+00 2.294280e+00 19 6.289945e+00 2.294280e+00 20 4.157746e-01 6.289945e+00 21 2.294280e+00 6.289945e+00 22 6.289945e+00 6.289945e+00 23 1.000000e+00 1.930437e-01 24 1.000000e+00 1.026665e+00 25 1.000000e+00 2.567877e+00 26 1.000000e+00 4.900353e+00 27 1.000000e+00 8.182153e+00 28 1.000000e+00 1.273418e+01 29 1.000000e+00 1.939573e+01 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: 1 -2.000000e+00 2 7.110930e-01 3 2.785177e-01 4 1.038926e-02 5 7.110930e-01 6 2.785177e-01 7 1.038926e-02 8 7.110930e-01 9 2.785177e-01 10 1.038926e-02 Grid points: 1 1.000000e+00 1.000000e+00 1.000000e+00 2 4.157746e-01 1.000000e+00 1.000000e+00 3 2.294280e+00 1.000000e+00 1.000000e+00 4 6.289945e+00 1.000000e+00 1.000000e+00 5 1.000000e+00 4.157746e-01 1.000000e+00 6 1.000000e+00 2.294280e+00 1.000000e+00 7 1.000000e+00 6.289945e+00 1.000000e+00 8 1.000000e+00 1.000000e+00 4.157746e-01 9 1.000000e+00 1.000000e+00 2.294280e+00 10 1.000000e+00 1.000000e+00 6.289945e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.000000 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 4.000000e+00 4.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 9.769963e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.000000 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 1.024000e+03 1.024000e+03 3.615241e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.000000 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 4.000000e+00 4.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 4.440892e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 1.953993e-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.000000 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 1.024000e+03 1.024000e+03 2.114575e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.000000 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 4.000000e+00 4.000000e+00 3.552714e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 1.776357e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 1.989520e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.000000 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 1.024000e+03 1.024000e+03 1.223270e-09 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.000000 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 4.000000e+00 4.000000e+00 8.881784e-16 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 2.344791e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.000000 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 1.024000e+03 1.024000e+03 1.227818e-09 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.000000 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 4.000000e+00 4.000000e+00 8.881784e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.000000 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 8.000000e+00 8.000000e+00 8.446577e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.000000 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 1.024000e+03 1.024000e+03 1.546596e-09 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 3.141593 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 3.141593e+00 3.141593e+00 1.954970e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.568328 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 5.568328e+00 5.568328e+00 8.881784e-16 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.568328 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 5.568328e+00 5.568328e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.568328 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 5.568328e+00 5.568328e+00 5.194423e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 306.019685 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 3.060197e+02 3.060197e+02 8.100187e-11 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.000000 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 1.000000e+00 1.000000e+00 1.332268e-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.000000 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 1.000000e+00 1.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.000000 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 1.000000e+00 1.000000e+00 0.000000e+00 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.000000 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 1.000000e+00 1.000000e+00 1.389999e-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.000000 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 1.000000e+00 1.000000e+00 1.530553e-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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 6.666667e-01 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 6.666667e-01 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 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 0.000000e+00 0 0 0 3.330669e-16 1 1 0 3.330669e-16 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 2.775558e-16 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 2.775558e-16 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 2.498002e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 1.942890e-16 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 1.942890e-16 5 0 5 6.666667e-02 6 6 0 0.000000e+00 6 5 1 6.666667e-01 6 4 2 0.000000e+00 6 3 3 6.666667e-01 6 2 4 0.000000e+00 6 1 5 6.666667e-02 6 0 6 1.387779e-16 7 7 0 0.000000e+00 7 6 1 0.000000e+00 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 1.387779e-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 0.000000e+00 0 0 0 4.996004e-16 1 1 0 4.440892e-16 1 0 1 0.000000e+00 2 2 0 0.000000e+00 2 1 1 0.000000e+00 2 0 2 2.498002e-16 3 3 0 1.665335e-16 3 2 1 1.665335e-16 3 1 2 2.775558e-16 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 2.498002e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 1.804112e-16 5 5 0 1.665335e-16 5 4 1 8.326673e-17 5 3 2 8.326673e-17 5 2 3 1.665335e-16 5 1 4 1.665335e-16 5 0 5 1.942890e-16 6 6 0 0.000000e+00 6 5 1 2.081668e-16 6 4 2 0.000000e+00 6 3 3 2.081668e-16 6 2 4 0.000000e+00 6 1 5 1.942890e-16 6 0 6 1.318390e-16 7 7 0 1.665335e-16 7 6 1 6.938894e-17 7 5 2 8.326673e-17 7 4 3 8.326673e-17 7 3 4 6.938894e-17 7 2 5 1.665335e-16 7 1 6 1.665335e-16 7 0 7 0.000000e+00 8 8 0 0.000000e+00 8 7 1 6.666667e-02 8 6 2 0.000000e+00 8 5 3 4.444444e-01 8 4 4 0.000000e+00 8 3 5 6.666667e-02 8 2 6 0.000000e+00 8 1 7 0.000000e+00 8 0 8 1.075529e-16 9 9 0 1.665335e-16 9 8 1 4.857226e-17 9 7 2 8.326673e-17 9 6 3 6.938894e-17 9 5 4 6.938894e-17 9 4 5 8.326673e-17 9 3 6 4.857226e-17 9 2 7 1.665335e-16 9 1 8 8.326673e-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 = 1 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 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 1.110223e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.665335e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 6.666667e-01 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 6.666667e-01 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 6.666667e-01 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 2.220446e-16 0 0 0 0 6.661338e-16 1 1 0 0 6.661338e-16 1 0 1 0 6.661338e-16 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.665335e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 5.551115e-16 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 5.551115e-16 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 5.551115e-16 3 0 0 3 2.775558e-16 4 4 0 0 0.000000e+00 4 3 1 0 2.498002e-16 4 2 2 0 0.000000e+00 4 1 3 0 2.775558e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 2.498002e-16 4 2 0 2 0.000000e+00 4 1 1 2 2.498002e-16 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 1.387779e-16 4 0 0 4 3.885781e-16 5 5 0 0 0.000000e+00 5 4 1 0 0.000000e+00 5 3 2 0 0.000000e+00 5 2 3 0 0.000000e+00 5 1 4 0 3.885781e-16 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 0.000000e+00 5 0 4 1 0.000000e+00 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 0.000000e+00 5 2 0 3 0.000000e+00 5 1 1 3 0.000000e+00 5 0 2 3 0.000000e+00 5 1 0 4 0.000000e+00 5 0 1 4 3.885781e-16 5 0 0 5 6.666667e-02 6 6 0 0 0.000000e+00 6 5 1 0 6.666667e-01 6 4 2 0 0.000000e+00 6 3 3 0 6.666667e-01 6 2 4 0 0.000000e+00 6 1 5 0 6.666667e-02 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 0.000000e+00 6 0 5 1 6.666667e-01 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 6.666667e-01 6 0 4 2 0.000000e+00 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 0.000000e+00 6 0 3 3 6.666667e-01 6 2 0 4 0.000000e+00 6 1 1 4 6.666667e-01 6 0 2 4 0.000000e+00 6 1 0 5 0.000000e+00 6 0 1 5 6.666667e-02 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 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 2.220446e-16 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 0.000000e+00 2 2 0 0.000000e+00 2 1 1 0.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 2.500000e-01 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 2.500000e-01 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 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 0.000000e+00 0 0 0 1.110223e-16 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 1.387779e-17 2 1 1 1.665335e-16 2 0 2 3.608225e-16 3 3 0 5.551115e-17 3 2 1 8.326673e-17 3 1 2 3.608225e-16 3 0 3 5.551115e-16 4 4 0 1.387779e-17 4 3 1 3.357523e-01 4 2 2 1.387779e-17 4 1 3 5.551115e-16 4 0 4 3.885781e-16 5 5 0 5.551115e-17 5 4 1 1.595946e-16 5 3 2 1.665335e-16 5 2 3 4.857226e-17 5 1 4 3.608225e-16 5 0 5 5.828671e-16 6 6 0 0.000000e+00 6 5 1 3.232860e-01 6 4 2 6.938894e-18 6 3 3 3.232860e-01 6 2 4 0.000000e+00 6 1 5 5.828671e-16 6 0 6 3.330669e-16 7 7 0 2.775558e-17 7 6 1 1.457168e-16 7 5 2 8.326673e-17 7 4 3 9.020562e-17 7 3 4 1.387779e-16 7 2 5 2.775558e-17 7 1 6 3.053113e-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 3.330669e-16 0 0 0 7.285839e-17 1 1 0 2.775558e-17 1 0 1 1.665335e-16 2 2 0 2.081668e-17 2 1 1 1.665335e-16 2 0 2 6.938894e-17 3 3 0 6.938894e-17 3 2 1 7.285839e-17 3 1 2 2.775558e-17 3 0 3 4.163336e-16 4 4 0 5.204170e-18 4 3 1 2.023003e-01 4 2 2 3.469447e-18 4 1 3 1.387779e-16 4 0 4 6.591949e-17 5 5 0 3.469447e-17 5 4 1 6.765422e-17 5 3 2 7.632783e-17 5 2 3 3.165870e-17 5 1 4 5.551115e-17 5 0 5 1.942890e-16 6 6 0 6.938894e-18 6 5 1 2.578750e-01 6 4 2 3.469447e-18 6 3 3 2.578750e-01 6 2 4 6.722053e-18 6 1 5 3.885781e-16 6 0 6 2.949030e-17 7 7 0 1.040834e-17 7 6 1 6.245005e-17 7 5 2 4.163336e-17 7 4 3 4.336809e-17 7 3 4 6.245005e-17 7 2 5 1.756408e-17 7 1 6 2.775558e-17 7 0 7 1.249001e-16 8 8 0 8.673617e-19 8 7 1 3.191324e-01 8 6 2 2.168404e-18 8 5 3 3.096560e-01 8 4 4 0.000000e+00 8 3 5 3.191324e-01 8 2 6 3.469447e-18 8 1 7 2.498002e-16 8 0 8 1.431147e-17 9 9 0 2.081668e-17 9 8 1 4.943962e-17 9 7 2 3.122502e-17 9 6 3 3.621235e-17 9 5 4 3.122502e-17 9 4 5 2.802663e-17 9 3 6 5.204170e-17 9 2 7 1.912262e-17 9 1 8 1.387779e-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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 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 6.661338e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 0.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 0.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 0.000000e+00 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 2.500000e-01 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 2.500000e-01 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 2.500000e-01 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 2.220446e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 3.330669e-16 2 2 0 0 2.775558e-17 2 1 1 0 3.330669e-16 2 0 2 0 2.775558e-17 2 1 0 1 2.775558e-17 2 0 1 1 4.996004e-16 2 0 0 2 7.771561e-16 3 3 0 0 1.110223e-16 3 2 1 0 1.665335e-16 3 1 2 0 7.771561e-16 3 0 3 0 1.110223e-16 3 2 0 1 0.000000e+00 3 1 1 1 1.110223e-16 3 0 2 1 1.665335e-16 3 1 0 2 1.665335e-16 3 0 1 2 7.771561e-16 3 0 0 3 8.326673e-16 4 4 0 0 2.775558e-17 4 3 1 0 3.357523e-01 4 2 2 0 2.775558e-17 4 1 3 0 8.326673e-16 4 0 4 0 2.775558e-17 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 2.775558e-17 4 0 3 1 3.357523e-01 4 2 0 2 0.000000e+00 4 1 1 2 3.357523e-01 4 0 2 2 2.775558e-17 4 1 0 3 2.775558e-17 4 0 1 3 8.326673e-16 4 0 0 4 7.216450e-16 5 5 0 0 1.110223e-16 5 4 1 0 3.191891e-16 5 3 2 0 3.330669e-16 5 2 3 0 9.714451e-17 5 1 4 0 7.771561e-16 5 0 5 0 1.110223e-16 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 1.110223e-16 5 0 4 1 3.191891e-16 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 3.191891e-16 5 0 3 2 3.330669e-16 5 2 0 3 0.000000e+00 5 1 1 3 3.330669e-16 5 0 2 3 9.714451e-17 5 1 0 4 9.714451e-17 5 0 1 4 7.216450e-16 5 0 0 5 7.771561e-16 6 6 0 0 0.000000e+00 6 5 1 0 3.232860e-01 6 4 2 0 1.387779e-17 6 3 3 0 3.232860e-01 6 2 4 0 0.000000e+00 6 1 5 0 7.771561e-16 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 0.000000e+00 6 0 5 1 3.232860e-01 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 3.232860e-01 6 0 4 2 1.387779e-17 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 1.387779e-17 6 0 3 3 3.232860e-01 6 2 0 4 0.000000e+00 6 1 1 4 3.232860e-01 6 0 2 4 0.000000e+00 6 1 0 5 0.000000e+00 6 0 1 5 7.771561e-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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 1.665335e-16 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 1.665335e-16 3 0 3 1.666667e-01 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 1.666667e-01 4 0 4 1.387779e-16 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 1.387779e-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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 5.551115e-17 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 5.551115e-17 3 0 3 0.000000e+00 4 4 0 1.387779e-17 4 3 1 1.249001e-16 4 2 2 1.387779e-17 4 1 3 0.000000e+00 4 0 4 1.387779e-17 5 5 0 0.000000e+00 5 4 1 5.551115e-17 5 3 2 5.551115e-17 5 2 3 0.000000e+00 5 1 4 2.775558e-17 5 0 5 0.000000e+00 6 6 0 6.938894e-18 6 5 1 1.666667e-01 6 4 2 0.000000e+00 6 3 3 1.666667e-01 6 2 4 6.938894e-18 6 1 5 0.000000e+00 6 0 6 6.938894e-18 7 7 0 1.387779e-17 7 6 1 5.551115e-17 7 5 2 2.775558e-17 7 4 3 2.775558e-17 7 3 4 5.551115e-17 7 2 5 6.938894e-18 7 1 6 2.775558e-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 0.000000e+00 0 0 0 1.387779e-16 1 1 0 5.551115e-17 1 0 1 0.000000e+00 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 1.526557e-16 3 3 0 9.714451e-17 3 2 1 5.898060e-17 3 1 2 1.665335e-16 3 0 3 1.387779e-16 4 4 0 6.938894e-18 4 3 1 2.498002e-16 4 2 2 1.561251e-17 4 1 3 0.000000e+00 4 0 4 2.081668e-16 5 5 0 2.775558e-17 5 4 1 2.081668e-17 5 3 2 1.387779e-17 5 2 3 0.000000e+00 5 1 4 1.665335e-16 5 0 5 3.885781e-16 6 6 0 3.469447e-18 6 5 1 0.000000e+00 6 4 2 0.000000e+00 6 3 3 0.000000e+00 6 2 4 7.155734e-18 6 1 5 3.885781e-16 6 0 6 1.977585e-16 7 7 0 0.000000e+00 7 6 1 1.994932e-17 7 5 2 1.387779e-17 7 4 3 1.474515e-17 7 3 4 1.387779e-17 7 2 5 3.469447e-18 7 1 6 1.942890e-16 7 0 7 3.747003e-16 8 8 0 6.938894e-18 8 7 1 1.457168e-16 8 6 2 0.000000e+00 8 5 3 2.777778e-02 8 4 4 1.084202e-19 8 3 5 1.457168e-16 8 2 6 6.965999e-18 8 1 7 4.996004e-16 8 0 8 2.307182e-16 9 9 0 1.734723e-18 9 8 1 7.372575e-18 9 7 2 3.469447e-18 9 6 3 6.071532e-18 9 5 4 6.938894e-18 9 4 5 1.051676e-17 9 3 6 0.000000e+00 9 2 7 1.721171e-18 9 1 8 2.220446e-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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.665335e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 3.330669e-16 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 3.330669e-16 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 3.330669e-16 3 0 0 3 1.666667e-01 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 1.666667e-01 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 1.666667e-01 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 0.000000e+00 0 0 0 0 4.440892e-16 1 1 0 0 4.440892e-16 1 0 1 0 6.661338e-16 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 0.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 2.220446e-16 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 1.110223e-16 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 2.220446e-16 3 0 0 3 0.000000e+00 4 4 0 0 2.775558e-17 4 3 1 0 1.249001e-16 4 2 2 0 2.775558e-17 4 1 3 0 0.000000e+00 4 0 4 0 2.775558e-17 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 2.775558e-17 4 0 3 1 1.249001e-16 4 2 0 2 0.000000e+00 4 1 1 2 1.249001e-16 4 0 2 2 2.775558e-17 4 1 0 3 2.775558e-17 4 0 1 3 0.000000e+00 4 0 0 4 5.551115e-17 5 5 0 0 0.000000e+00 5 4 1 0 1.110223e-16 5 3 2 0 1.110223e-16 5 2 3 0 0.000000e+00 5 1 4 0 2.775558e-17 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 0.000000e+00 5 0 4 1 1.110223e-16 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 1.110223e-16 5 0 3 2 1.110223e-16 5 2 0 3 0.000000e+00 5 1 1 3 1.110223e-16 5 0 2 3 0.000000e+00 5 1 0 4 0.000000e+00 5 0 1 4 1.110223e-16 5 0 0 5 0.000000e+00 6 6 0 0 1.387779e-17 6 5 1 0 1.666667e-01 6 4 2 0 0.000000e+00 6 3 3 0 1.666667e-01 6 2 4 0 1.387779e-17 6 1 5 0 0.000000e+00 6 0 6 0 1.387779e-17 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 1.387779e-17 6 0 5 1 1.666667e-01 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 1.666667e-01 6 0 4 2 0.000000e+00 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 0.000000e+00 6 0 3 3 1.666667e-01 6 2 0 4 0.000000e+00 6 1 1 4 1.666667e-01 6 0 2 4 1.387779e-17 6 1 0 5 1.387779e-17 6 0 1 5 1.942890e-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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 1.387779e-16 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 1.387779e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 0.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 4.996004e-16 4 2 2 0.000000e+00 4 1 3 1.387779e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 1.942890e-16 6 6 0 0.000000e+00 6 5 1 4.163336e-16 6 4 2 0.000000e+00 6 3 3 4.163336e-16 6 2 4 0.000000e+00 6 1 5 0.000000e+00 6 0 6 0.000000e+00 7 7 0 0.000000e+00 7 6 1 0.000000e+00 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 0.000000e+00 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 0.000000e+00 0 0 0 2.775558e-17 1 1 0 2.775558e-17 1 0 1 0.000000e+00 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 2.775558e-17 3 3 0 1.387779e-17 3 2 1 0.000000e+00 3 1 2 2.775558e-17 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 2.498002e-16 4 2 2 0.000000e+00 4 1 3 1.387779e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 0.000000e+00 6 6 0 0.000000e+00 6 5 1 2.081668e-16 6 4 2 0.000000e+00 6 3 3 2.081668e-16 6 2 4 0.000000e+00 6 1 5 1.942890e-16 6 0 6 1.387779e-17 7 7 0 3.469447e-18 7 6 1 0.000000e+00 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 1.387779e-17 7 0 7 1.249001e-16 8 8 0 0.000000e+00 8 7 1 0.000000e+00 8 6 2 0.000000e+00 8 5 3 1.734723e-16 8 4 4 0.000000e+00 8 3 5 0.000000e+00 8 2 6 0.000000e+00 8 1 7 1.249001e-16 8 0 8 0.000000e+00 9 9 0 1.734723e-18 9 8 1 0.000000e+00 9 7 2 0.000000e+00 9 6 3 0.000000e+00 9 5 4 0.000000e+00 9 4 5 0.000000e+00 9 3 6 0.000000e+00 9 2 7 0.000000e+00 9 1 8 0.000000e+00 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.665335e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 1.387779e-16 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 1.387779e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 1.387779e-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 = 4 Check up to DEGREE_MAX = 6 Unique points in the grid = 31 Error Total Monomial Degree Exponents 2.220446e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.665335e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 0.000000e+00 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 0.000000e+00 4 4 0 0 0.000000e+00 4 3 1 0 4.996004e-16 4 2 2 0 0.000000e+00 4 1 3 0 0.000000e+00 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 4.996004e-16 4 2 0 2 0.000000e+00 4 1 1 2 4.996004e-16 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 1.387779e-16 4 0 0 4 0.000000e+00 5 5 0 0 0.000000e+00 5 4 1 0 0.000000e+00 5 3 2 0 0.000000e+00 5 2 3 0 0.000000e+00 5 1 4 0 0.000000e+00 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 0.000000e+00 5 0 4 1 0.000000e+00 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 0.000000e+00 5 2 0 3 0.000000e+00 5 1 1 3 0.000000e+00 5 0 2 3 0.000000e+00 5 1 0 4 0.000000e+00 5 0 1 4 0.000000e+00 5 0 0 5 1.942890e-16 6 6 0 0 0.000000e+00 6 5 1 0 4.163336e-16 6 4 2 0 0.000000e+00 6 3 3 0 4.163336e-16 6 2 4 0 0.000000e+00 6 1 5 0 1.942890e-16 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 0.000000e+00 6 0 5 1 4.163336e-16 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 4.163336e-16 6 0 4 2 0.000000e+00 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 0.000000e+00 6 0 3 3 4.163336e-16 6 2 0 4 0.000000e+00 6 1 1 4 4.163336e-16 6 0 2 4 0.000000e+00 6 1 0 5 0.000000e+00 6 0 1 5 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.665335e-16 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 1.387779e-16 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 1.387779e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 0.000000e+00 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 4.996004e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 0.000000e+00 6 6 0 0.000000e+00 6 5 1 4.163336e-16 6 4 2 0.000000e+00 6 3 3 4.163336e-16 6 2 4 0.000000e+00 6 1 5 0.000000e+00 6 0 6 0.000000e+00 7 7 0 0.000000e+00 7 6 1 0.000000e+00 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 0.000000e+00 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 0.000000e+00 0 0 0 2.775558e-17 1 1 0 1.387779e-17 1 0 1 0.000000e+00 2 2 0 0.000000e+00 2 1 1 1.665335e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 6.938894e-18 3 1 2 2.775558e-17 3 0 3 1.387779e-16 4 4 0 2.775558e-17 4 3 1 0.000000e+00 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 5.551115e-17 5 5 0 6.938894e-18 5 4 1 0.000000e+00 5 3 2 6.938894e-18 5 2 3 1.387779e-17 5 1 4 2.775558e-17 5 0 5 0.000000e+00 6 6 0 1.387779e-17 6 5 1 2.081668e-16 6 4 2 0.000000e+00 6 3 3 2.081668e-16 6 2 4 0.000000e+00 6 1 5 0.000000e+00 6 0 6 2.775558e-17 7 7 0 6.938894e-18 7 6 1 3.469447e-18 7 5 2 3.469447e-18 7 4 3 3.469447e-18 7 3 4 1.734723e-17 7 2 5 6.938894e-18 7 1 6 0.000000e+00 7 0 7 0.000000e+00 8 8 0 3.469447e-18 8 7 1 0.000000e+00 8 6 2 0.000000e+00 8 5 3 1.734723e-16 8 4 4 0.000000e+00 8 3 5 0.000000e+00 8 2 6 0.000000e+00 8 1 7 1.249001e-16 8 0 8 0.000000e+00 9 9 0 6.938894e-18 9 8 1 0.000000e+00 9 7 2 6.938894e-18 9 6 3 0.000000e+00 9 5 4 3.469447e-18 9 4 5 1.734723e-18 9 3 6 6.938894e-18 9 2 7 6.938894e-18 9 1 8 2.775558e-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 = 5 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.665335e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 1.387779e-16 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 1.387779e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 1.387779e-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 2.220446e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.665335e-16 2 2 0 0 0.000000e+00 2 1 1 0 0.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.665335e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 0.000000e+00 4 4 0 0 0.000000e+00 4 3 1 0 4.996004e-16 4 2 2 0 0.000000e+00 4 1 3 0 0.000000e+00 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 4.996004e-16 4 2 0 2 0.000000e+00 4 1 1 2 4.996004e-16 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 0.000000e+00 4 0 0 4 0.000000e+00 5 5 0 0 0.000000e+00 5 4 1 0 0.000000e+00 5 3 2 0 0.000000e+00 5 2 3 0 0.000000e+00 5 1 4 0 0.000000e+00 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 0.000000e+00 5 0 4 1 0.000000e+00 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 0.000000e+00 5 2 0 3 0.000000e+00 5 1 1 3 0.000000e+00 5 0 2 3 0.000000e+00 5 1 0 4 0.000000e+00 5 0 1 4 0.000000e+00 5 0 0 5 0.000000e+00 6 6 0 0 0.000000e+00 6 5 1 0 4.163336e-16 6 4 2 0 0.000000e+00 6 3 3 0 4.163336e-16 6 2 4 0 0.000000e+00 6 1 5 0 0.000000e+00 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 0.000000e+00 6 0 5 1 4.163336e-16 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 4.163336e-16 6 0 4 2 0.000000e+00 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 0.000000e+00 6 0 3 3 4.163336e-16 6 2 0 4 0.000000e+00 6 1 1 4 4.163336e-16 6 0 2 4 0.000000e+00 6 1 0 5 0.000000e+00 6 0 1 5 0.000000e+00 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 2.827160e-16 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 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 2.827160e-16 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.413580e-16 2 2 0 0.000000e+00 2 1 1 1.413580e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 1.884773e-16 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 1.884773e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.413580e-16 2 2 0 0.000000e+00 2 1 1 2.827160e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 1.413580e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 3.015637e-16 6 6 0 0.000000e+00 6 5 1 3.769546e-16 6 4 2 0.000000e+00 6 3 3 3.769546e-16 6 2 4 0.000000e+00 6 1 5 3.015637e-16 6 0 6 0.000000e+00 7 7 0 0.000000e+00 7 6 1 0.000000e+00 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 0.000000e+00 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 1.413580e-16 0 0 0 2.220446e-16 1 1 0 0.000000e+00 1 0 1 0.000000e+00 2 2 0 5.551115e-17 2 1 1 1.413580e-16 2 0 2 2.775558e-17 3 3 0 0.000000e+00 3 2 1 2.775558e-17 3 1 2 1.110223e-16 3 0 3 3.769546e-16 4 4 0 0.000000e+00 4 3 1 1.413580e-16 4 2 2 0.000000e+00 4 1 3 3.769546e-16 4 0 4 0.000000e+00 5 5 0 9.714451e-17 5 4 1 4.857226e-17 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 1.110223e-16 5 0 5 1.507819e-16 6 6 0 1.110223e-16 6 5 1 0.000000e+00 6 4 2 0.000000e+00 6 3 3 0.000000e+00 6 2 4 2.220446e-16 6 1 5 1.507819e-16 6 0 6 4.440892e-16 7 7 0 5.551115e-17 7 6 1 0.000000e+00 7 5 2 1.110223e-16 7 4 3 1.387779e-17 7 3 4 3.330669e-16 7 2 5 1.110223e-16 7 1 6 4.440892e-16 7 0 7 1.723221e-16 8 8 0 0.000000e+00 8 7 1 1.507819e-16 8 6 2 2.220446e-16 8 5 3 3.769546e-16 8 4 4 0.000000e+00 8 3 5 1.507819e-16 8 2 6 0.000000e+00 8 1 7 3.446442e-16 8 0 8 1.776357e-15 9 9 0 2.220446e-16 9 8 1 0.000000e+00 9 7 2 0.000000e+00 9 6 3 1.110223e-16 9 5 4 1.110223e-16 9 4 5 0.000000e+00 9 3 6 2.220446e-16 9 2 7 4.440892e-16 9 1 8 0.000000e+00 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 4.785162e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 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 3.190108e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 3.190108e-16 2 2 0 0 0.000000e+00 2 1 1 0 3.190108e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 3.190108e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 2.126739e-16 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 2.126739e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 0.000000e+00 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.595054e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.595054e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.595054e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 2.126739e-16 4 4 0 0 0.000000e+00 4 3 1 0 1.595054e-16 4 2 2 0 0.000000e+00 4 1 3 0 2.126739e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.595054e-16 4 2 0 2 0.000000e+00 4 1 1 2 1.595054e-16 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 0.000000e+00 4 0 0 4 0.000000e+00 5 5 0 0 0.000000e+00 5 4 1 0 0.000000e+00 5 3 2 0 0.000000e+00 5 2 3 0 0.000000e+00 5 1 4 0 0.000000e+00 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 0.000000e+00 5 0 4 1 0.000000e+00 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 0.000000e+00 5 2 0 3 0.000000e+00 5 1 1 3 0.000000e+00 5 0 2 3 0.000000e+00 5 1 0 4 0.000000e+00 5 0 1 4 0.000000e+00 5 0 0 5 3.402782e-16 6 6 0 0 0.000000e+00 6 5 1 0 4.253478e-16 6 4 2 0 0.000000e+00 6 3 3 0 4.253478e-16 6 2 4 0 0.000000e+00 6 1 5 0 3.402782e-16 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 0.000000e+00 6 0 5 1 4.253478e-16 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 4.253478e-16 6 0 4 2 0.000000e+00 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 0.000000e+00 6 0 3 3 2.126739e-16 6 2 0 4 0.000000e+00 6 1 1 4 2.126739e-16 6 0 2 4 0.000000e+00 6 1 0 5 0.000000e+00 6 0 1 5 1.701391e-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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 5.000000e-01 2 2 0 0.000000e+00 2 1 1 5.000000e-01 2 0 2 8.333333e-01 3 3 0 5.000000e-01 3 2 1 5.000000e-01 3 1 2 8.333333e-01 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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 0.000000e+00 2 2 0 2.220446e-16 2 1 1 0.000000e+00 2 0 2 1.480297e-16 3 3 0 2.220446e-16 3 2 1 2.220446e-16 3 1 2 1.480297e-16 3 0 3 1.480297e-16 4 4 0 1.480297e-16 4 3 1 2.500000e-01 4 2 2 1.480297e-16 4 1 3 1.480297e-16 4 0 4 1.184238e-16 5 5 0 1.480297e-16 5 4 1 4.166667e-01 5 3 2 4.166667e-01 5 2 3 1.480297e-16 5 1 4 2.368476e-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 4.440892e-16 0 0 0 2.220446e-16 1 1 0 1.110223e-16 1 0 1 2.220446e-16 2 2 0 1.110223e-16 2 1 1 1.110223e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 1.110223e-16 3 1 2 1.480297e-16 3 0 3 0.000000e+00 4 4 0 4.440892e-16 4 3 1 2.220446e-16 4 2 2 1.480297e-16 4 1 3 1.480297e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 2.960595e-16 5 1 4 1.184238e-16 5 0 5 1.578984e-16 6 6 0 1.184238e-16 6 5 1 2.960595e-16 6 4 2 1.973730e-16 6 3 3 2.960595e-16 6 2 4 1.184238e-16 6 1 5 0.000000e+00 6 0 6 1.804553e-16 7 7 0 1.578984e-16 7 6 1 1.184238e-16 7 5 2 0.000000e+00 7 4 3 1.973730e-16 7 3 4 1.184238e-16 7 2 5 0.000000e+00 7 1 6 1.804553e-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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 4.440892e-16 2 2 0 2.220446e-16 2 1 1 2.220446e-16 2 0 2 1.480297e-16 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 2.960595e-16 4 3 1 0.000000e+00 4 2 2 1.480297e-16 4 1 3 0.000000e+00 4 0 4 1.184238e-16 5 5 0 2.960595e-16 5 4 1 0.000000e+00 5 3 2 1.480297e-16 5 2 3 2.960595e-16 5 1 4 2.368476e-16 5 0 5 0.000000e+00 6 6 0 1.184238e-16 6 5 1 1.480297e-16 6 4 2 3.947460e-16 6 3 3 1.480297e-16 6 2 4 3.552714e-16 6 1 5 0.000000e+00 6 0 6 3.609106e-16 7 7 0 1.578984e-16 7 6 1 2.368476e-16 7 5 2 1.973730e-16 7 4 3 0.000000e+00 7 3 4 1.184238e-16 7 2 5 3.157968e-16 7 1 6 1.804553e-16 7 0 7 1.804553e-16 8 8 0 0.000000e+00 8 7 1 1.578984e-16 8 6 2 3.157968e-16 8 5 3 0.000000e+00 8 4 4 3.157968e-16 8 3 5 1.578984e-16 8 2 6 1.804553e-16 8 1 7 1.804553e-16 8 0 8 3.208094e-16 9 9 0 0.000000e+00 9 8 1 0.000000e+00 9 7 2 0.000000e+00 9 6 3 3.157968e-16 9 5 4 3.157968e-16 9 4 5 0.000000e+00 9 3 6 1.804553e-16 9 2 7 1.804553e-16 9 1 8 0.000000e+00 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 5.000000e-01 2 2 0 0 0.000000e+00 2 1 1 0 5.000000e-01 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 5.000000e-01 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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 0.000000e+00 2 2 0 0 2.220446e-16 2 1 1 0 0.000000e+00 2 0 2 0 2.220446e-16 2 1 0 1 2.220446e-16 2 0 1 1 0.000000e+00 2 0 0 2 0.000000e+00 3 3 0 0 2.220446e-16 3 2 1 0 2.220446e-16 3 1 2 0 1.480297e-16 3 0 3 0 2.220446e-16 3 2 0 1 4.440892e-16 3 1 1 1 2.220446e-16 3 0 2 1 2.220446e-16 3 1 0 2 2.220446e-16 3 0 1 2 1.480297e-16 3 0 0 3 1.480297e-16 4 4 0 0 0.000000e+00 4 3 1 0 2.500000e-01 4 2 2 0 1.480297e-16 4 1 3 0 1.480297e-16 4 0 4 0 0.000000e+00 4 3 0 1 2.220446e-16 4 2 1 1 2.220446e-16 4 1 2 1 1.480297e-16 4 0 3 1 2.500000e-01 4 2 0 2 2.220446e-16 4 1 1 2 2.500000e-01 4 0 2 2 1.480297e-16 4 1 0 3 1.480297e-16 4 0 1 3 1.480297e-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 0.000000e+00 0 0 0 0 4.440892e-16 1 1 0 0 0.000000e+00 1 0 1 0 6.661338e-16 1 0 0 1 2.220446e-16 2 2 0 0 1.110223e-16 2 1 1 0 0.000000e+00 2 0 2 0 3.330669e-16 2 1 0 1 0.000000e+00 2 0 1 1 2.220446e-16 2 0 0 2 2.960595e-16 3 3 0 0 2.220446e-16 3 2 1 0 2.220446e-16 3 1 2 0 4.440892e-16 3 0 3 0 2.220446e-16 3 2 0 1 1.110223e-16 3 1 1 1 2.220446e-16 3 0 2 1 2.220446e-16 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 0.000000e+00 4 4 0 0 1.480297e-16 4 3 1 0 0.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 1.480297e-16 4 0 4 0 0.000000e+00 4 3 0 1 3.330669e-16 4 2 1 1 1.110223e-16 4 1 2 1 0.000000e+00 4 0 3 1 0.000000e+00 4 2 0 2 2.220446e-16 4 1 1 2 2.220446e-16 4 0 2 2 1.480297e-16 4 1 0 3 2.960595e-16 4 0 1 3 1.480297e-16 4 0 0 4 0.000000e+00 5 5 0 0 2.960595e-16 5 4 1 0 1.480297e-16 5 3 2 0 0.000000e+00 5 2 3 0 1.480297e-16 5 1 4 0 4.736952e-16 5 0 5 0 2.960595e-16 5 4 0 1 0.000000e+00 5 3 1 1 2.220446e-16 5 2 2 1 0.000000e+00 5 1 3 1 1.480297e-16 5 0 4 1 0.000000e+00 5 3 0 2 4.440892e-16 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 1.480297e-16 5 2 0 3 0.000000e+00 5 1 1 3 0.000000e+00 5 0 2 3 1.480297e-16 5 1 0 4 0.000000e+00 5 0 1 4 2.368476e-16 5 0 0 5 1.578984e-16 6 6 0 0 0.000000e+00 6 5 1 0 1.480297e-16 6 4 2 0 1.973730e-16 6 3 3 0 0.000000e+00 6 2 4 0 2.368476e-16 6 1 5 0 4.736952e-16 6 0 6 0 2.368476e-16 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 1.480297e-16 6 1 4 1 3.552714e-16 6 0 5 1 2.960595e-16 6 4 0 2 2.960595e-16 6 3 1 2 1.250000e-01 6 2 2 2 1.480297e-16 6 1 3 2 1.480297e-16 6 0 4 2 1.973730e-16 6 3 0 3 1.480297e-16 6 2 1 3 1.480297e-16 6 1 2 3 0.000000e+00 6 0 3 3 0.000000e+00 6 2 0 4 2.960595e-16 6 1 1 4 0.000000e+00 6 0 2 4 1.184238e-16 6 1 0 5 0.000000e+00 6 0 1 5 3.157968e-16 6 0 0 6 sandia_sparse_test(): Normal end of execution. 16-Jan-2023 15:41:59