23 December 2009 2:19:59.647 PM SANDIA_SPARSE_PRB FORTRAN90 version Test the routines in the SANDIA_SPARSE library. LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 5 3 9 4 17 5 33 6 65 7 129 8 257 9 513 10 1025 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 5 13 25 41 61 85 3 9 29 69 137 241 389 4 17 65 177 401 801 1457 5 33 145 441 1105 2433 4865 6 65 321 1073 2929 6993 15121 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 6 7 8 9 10 LEVEL_MAX --------- 0 1 1 1 1 1 1 13 15 17 19 21 2 85 113 145 181 221 3 389 589 849 1177 1581 4 1457 2465 3937 6001 8801 5 4865 9017 15713 26017 41265 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 1 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 201 2 20201 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 7 3 15 4 31 5 63 6 127 7 255 8 511 9 1023 10 2047 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 7 17 31 49 71 97 3 15 49 111 209 351 545 4 31 129 351 769 1471 2561 5 63 321 1023 2561 5503 10625 6 127 769 2815 7937 18943 40193 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 6 7 8 9 10 LEVEL_MAX --------- 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 545 799 1121 1519 2001 4 2561 4159 6401 9439 13441 5 10625 18943 31745 50623 77505 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 2 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 201 2 20401 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 7 3 15 4 31 5 63 6 127 7 255 8 511 9 1023 10 2047 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 7 21 37 57 81 109 3 15 73 159 289 471 713 4 31 225 597 1265 2341 3953 5 63 637 2031 4969 10363 19397 6 127 1693 6405 17945 41913 86517 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 6 7 8 9 10 LEVEL_MAX --------- 0 1 1 1 1 1 1 13 15 17 19 21 2 109 141 177 217 261 3 713 1023 1409 1879 2441 4 3953 6245 9377 13525 18881 5 19397 33559 54673 84931 126925 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 5 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 201 2 20601 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 LEVEL_MAX --------- 0 1 1 3 2 7 3 15 4 31 5 63 6 127 7 255 8 511 9 1023 10 2047 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 1 2 3 4 5 6 LEVEL_MAX --------- 0 1 1 1 1 1 1 1 3 7 10 13 16 19 2 7 29 58 95 141 196 3 15 95 255 515 906 1456 4 31 273 945 2309 4746 8722 5 63 723 3120 9065 21503 44758 6 127 1813 9484 32259 87358 204203 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 6 7 8 9 10 LEVEL_MAX --------- 0 1 1 1 1 1 1 19 22 25 28 31 2 196 260 333 415 506 3 1456 2192 3141 4330 5786 4 8722 14778 23535 35695 52041 5 44758 84708 149031 247456 392007 LEVELS_INDEX_SIZE_TEST LEVELS_INDEX_SIZE returns the number of distinct points in a sparse grid derived from a 1D rule. We are looking at rules like rule 7 Each sparse grid is of spatial dimension DIM, and is made up of product grids such that LEVEL_MIN <= LEVEL <= LEVEL_MAX. DIM: 100 LEVEL_MAX --------- 0 1 1 301 2 45551 LEVELS_INDEX_TEST LEVELS_INDEX returns all grid indexes whose level value satisfies LEVEL_MIN <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^LEVEL + 1. We are looking at rules like rule 1 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 Unique points in the grid = 5 Point Grid indices: Grid bases: 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 1.33333 2 0.666667 3 0.666667 4 0.666667 5 0.666667 Grid points: 1 0.00000 0.00000 2 -1.00000 0.00000 3 1.00000 0.00000 4 0.00000 -1.00000 5 0.00000 1.00000 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 -0.355556 2 -0.888889E-01 3 -0.888889E-01 4 -0.888889E-01 5 -0.888889E-01 6 1.06667 7 1.06667 8 0.111111 9 0.111111 10 0.111111 11 0.111111 12 1.06667 13 1.06667 Grid points: 1 0.00000 0.00000 2 -1.00000 0.00000 3 1.00000 0.00000 4 0.00000 -1.00000 5 0.00000 1.00000 6 -0.707107 0.00000 7 0.707107 0.00000 8 -1.00000 -1.00000 9 1.00000 -1.00000 10 -1.00000 1.00000 11 1.00000 1.00000 12 0.00000 -0.707107 13 0.00000 0.707107 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Unique points in the grid = 7 Grid weights: 1 -0.177636E-14 2 1.33333 3 1.33333 4 1.33333 5 1.33333 6 1.33333 7 1.33333 Grid points: 1 0.00000 0.00000 0.00000 2 -1.00000 0.00000 0.00000 3 1.00000 0.00000 0.00000 4 0.00000 -1.00000 0.00000 5 0.00000 1.00000 0.00000 6 0.00000 0.00000 -1.00000 7 0.00000 0.00000 1.00000 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 0.444444 2 0.888889 3 0.888889 4 0.888889 5 0.888889 Grid points: 1 0.00000 0.00000 2 -0.866025 0.00000 3 0.866025 0.00000 4 0.00000 -0.866025 5 0.00000 0.866025 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 2 Unique points in the grid = 17 Grid weights: 1 -1.39219 2 0.180601 3 0.180601 4 0.180601 5 0.180601 6 0.173432 7 0.796483 8 0.796483 9 0.173432 10 0.197531 11 0.197531 12 0.197531 13 0.197531 14 0.173432 15 0.796483 16 0.796483 17 0.173432 Grid points: 1 0.00000 0.00000 2 -0.781831 0.00000 3 0.781831 0.00000 4 0.00000 -0.781831 5 0.00000 0.781831 6 -0.974928 0.00000 7 -0.433884 0.00000 8 0.433884 0.00000 9 0.974928 0.00000 10 -0.781831 -0.781831 11 0.781831 -0.781831 12 -0.781831 0.781831 13 0.781831 0.781831 14 0.00000 -0.974928 15 0.00000 -0.433884 16 0.00000 0.433884 17 0.00000 0.974928 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 2 Unique points in the grid = 7 Grid weights: 1 -2.66667 2 1.77778 3 1.77778 4 1.77778 5 1.77778 6 1.77778 7 1.77778 Grid points: 1 0.00000 0.00000 0.00000 2 -0.866025 0.00000 0.00000 3 0.866025 0.00000 0.00000 4 0.00000 -0.866025 0.00000 5 0.00000 0.866025 0.00000 6 0.00000 0.00000 -0.866025 7 0.00000 0.00000 0.866025 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 3 Unique points in the grid = 5 Grid weights: 1 -1.33333 2 1.33333 3 1.33333 4 1.33333 5 1.33333 Grid points: 1 0.00000 0.00000 2 -0.707107 0.00000 3 0.707107 0.00000 4 0.00000 -0.707107 5 0.00000 0.707107 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 3 Unique points in the grid = 17 Grid weights: 1 -0.774603 2 -0.393651 3 -0.393651 4 -0.393651 5 -0.393651 6 0.355929 7 0.786928 8 0.786928 9 0.355929 10 0.444444 11 0.444444 12 0.444444 13 0.444444 14 0.355929 15 0.786928 16 0.786928 17 0.355929 Grid points: 1 0.00000 0.00000 2 -0.707107 0.00000 3 0.707107 0.00000 4 0.00000 -0.707107 5 0.00000 0.707107 6 -0.923880 0.00000 7 -0.382683 0.00000 8 0.382683 0.00000 9 0.923880 0.00000 10 -0.707107 -0.707107 11 0.707107 -0.707107 12 -0.707107 0.707107 13 0.707107 0.707107 14 0.00000 -0.923880 15 0.00000 -0.382683 16 0.00000 0.382683 17 0.00000 0.923880 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 -8.00000 2 2.66667 3 2.66667 4 2.66667 5 2.66667 6 2.66667 7 2.66667 Grid points: 1 0.00000 0.00000 0.00000 2 -0.707107 0.00000 0.00000 3 0.707107 0.00000 0.00000 4 0.00000 -0.707107 0.00000 5 0.00000 0.707107 0.00000 6 0.00000 0.00000 -0.707107 7 0.00000 0.00000 0.707107 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 4 Unique points in the grid = 5 Grid weights: 1 -0.444444 2 1.11111 3 1.11111 4 1.11111 5 1.11111 Grid points: 1 0.00000 0.00000 2 -0.774597 0.00000 3 0.774597 0.00000 4 0.00000 -0.774597 5 0.00000 0.774597 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 4 Unique points in the grid = 17 Grid weights: 1 -0.961766 2 -0.803078E-01 3 -0.803078E-01 4 -0.803078E-01 5 -0.803078E-01 6 0.209312 7 0.802795 8 0.802795 9 0.209312 10 0.308642 11 0.308642 12 0.308642 13 0.308642 14 0.209312 15 0.802795 16 0.802795 17 0.209312 Grid points: 1 0.00000 0.00000 2 -0.774597 0.00000 3 0.774597 0.00000 4 0.00000 -0.774597 5 0.00000 0.774597 6 -0.960491 0.00000 7 -0.434244 0.00000 8 0.434244 0.00000 9 0.960491 0.00000 10 -0.774597 -0.774597 11 0.774597 -0.774597 12 -0.774597 0.774597 13 0.774597 0.774597 14 0.00000 -0.960491 15 0.00000 -0.434244 16 0.00000 0.434244 17 0.00000 0.960491 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 -5.33333 2 2.22222 3 2.22222 4 2.22222 5 2.22222 6 2.22222 7 2.22222 Grid points: 1 0.00000 0.00000 0.00000 2 -0.774597 0.00000 0.00000 3 0.774597 0.00000 0.00000 4 0.00000 -0.774597 0.00000 5 0.00000 0.774597 0.00000 6 0.00000 0.00000 -0.774597 7 0.00000 0.00000 0.774597 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Unique points in the grid = 5 Grid weights: 1 -0.444444 2 1.11111 3 1.11111 4 1.11111 5 1.11111 Grid points: 1 0.00000 0.00000 2 -0.774597 0.00000 3 0.774597 0.00000 4 0.00000 -0.774597 5 0.00000 0.774597 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 5 Unique points in the grid = 21 Grid weights: 1 -1.09360 2 -0.617284 3 -0.617284 4 -0.617284 5 -0.617284 6 0.258970 7 0.559411 8 0.763660 9 0.763660 10 0.559411 11 0.258970 12 0.308642 13 0.308642 14 0.308642 15 0.308642 16 0.258970 17 0.559411 18 0.763660 19 0.763660 20 0.559411 21 0.258970 Grid points: 1 0.00000 0.00000 2 -0.774597 0.00000 3 0.774597 0.00000 4 0.00000 -0.774597 5 0.00000 0.774597 6 -0.949108 0.00000 7 -0.741531 0.00000 8 -0.405845 0.00000 9 0.405845 0.00000 10 0.741531 0.00000 11 0.949108 0.00000 12 -0.774597 -0.774597 13 0.774597 -0.774597 14 -0.774597 0.774597 15 0.774597 0.774597 16 0.00000 -0.949108 17 0.00000 -0.741531 18 0.00000 -0.405845 19 0.00000 0.405845 20 0.00000 0.741531 21 0.00000 0.949108 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 5 Unique points in the grid = 7 Grid weights: 1 -5.33333 2 2.22222 3 2.22222 4 2.22222 5 2.22222 6 2.22222 7 2.22222 Grid points: 1 0.00000 0.00000 0.00000 2 -0.774597 0.00000 0.00000 3 0.774597 0.00000 0.00000 4 0.00000 -0.774597 0.00000 5 0.00000 0.774597 0.00000 6 0.00000 0.00000 -0.774597 7 0.00000 0.00000 0.774597 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Unique points in the grid = 5 Grid weights: 1 1.04720 2 0.523599 3 0.523599 4 0.523599 5 0.523599 Grid points: 1 0.00000 0.00000 2 -1.22474 0.00000 3 1.22474 0.00000 4 0.00000 -1.22474 5 0.00000 1.22474 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 6 Unique points in the grid = 21 Grid weights: 1 0.797865E-01 2 -0.174533 3 -0.174533 4 -0.174533 5 -0.174533 6 0.172244E-02 7 0.966264E-01 8 0.754369 9 0.754369 10 0.966264E-01 11 0.172244E-02 12 0.872665E-01 13 0.872665E-01 14 0.872665E-01 15 0.872665E-01 16 0.172244E-02 17 0.966264E-01 18 0.754369 19 0.754369 20 0.966264E-01 21 0.172244E-02 Grid points: 1 0.00000 0.00000 2 -1.22474 0.00000 3 1.22474 0.00000 4 0.00000 -1.22474 5 0.00000 1.22474 6 -2.65196 0.00000 7 -1.67355 0.00000 8 -0.816288 0.00000 9 0.816288 0.00000 10 1.67355 0.00000 11 2.65196 0.00000 12 -1.22474 -1.22474 13 1.22474 -1.22474 14 -1.22474 1.22474 15 1.22474 1.22474 16 0.00000 -2.65196 17 0.00000 -1.67355 18 0.00000 -0.816288 19 0.00000 0.816288 20 0.00000 1.67355 21 0.00000 2.65196 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Unique points in the grid = 7 Grid weights: 1 -0.888178E-15 2 0.928055 3 0.928055 4 0.928055 5 0.928055 6 0.928055 7 0.928055 Grid points: 1 0.00000 0.00000 0.00000 2 -1.22474 0.00000 0.00000 3 1.22474 0.00000 0.00000 4 0.00000 -1.22474 0.00000 5 0.00000 1.22474 0.00000 6 0.00000 0.00000 -1.22474 7 0.00000 0.00000 1.22474 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Unique points in the grid = 7 Grid weights: 1 -1.00000 2 0.711093 3 0.278518 4 0.103893E-01 5 0.711093 6 0.278518 7 0.103893E-01 Grid points: 1 1.00000 1.00000 2 0.415775 1.00000 3 2.29428 1.00000 4 6.28995 1.00000 5 1.00000 0.415775 6 1.00000 2.29428 7 1.00000 6.28995 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 2 LEVEL_MIN = 1 LEVEL_MAX = 2 1D quadrature index RULE = 7 Unique points in the grid = 29 Grid weights: 1 -0.711093 2 -0.278518 3 -0.103893E-01 4 -0.711093 5 -0.278518 6 -0.103893E-01 7 0.409319 8 0.421831 9 0.147126 10 0.206335E-01 11 0.107401E-02 12 0.158655E-04 13 0.317032E-07 14 0.505653 15 0.198052 16 0.738773E-02 17 0.198052 18 0.775721E-01 19 0.289359E-02 20 0.738773E-02 21 0.289359E-02 22 0.107937E-03 23 0.409319 24 0.421831 25 0.147126 26 0.206335E-01 27 0.107401E-02 28 0.158655E-04 29 0.317032E-07 Grid points: 1 0.415775 1.00000 2 2.29428 1.00000 3 6.28995 1.00000 4 1.00000 0.415775 5 1.00000 2.29428 6 1.00000 6.28995 7 0.193044 1.00000 8 1.02666 1.00000 9 2.56788 1.00000 10 4.90035 1.00000 11 8.18215 1.00000 12 12.7342 1.00000 13 19.3957 1.00000 14 0.415775 0.415775 15 2.29428 0.415775 16 6.28995 0.415775 17 0.415775 2.29428 18 2.29428 2.29428 19 6.28995 2.29428 20 0.415775 6.28995 21 2.29428 6.28995 22 6.28995 6.28995 23 1.00000 0.193044 24 1.00000 1.02666 25 1.00000 2.56788 26 1.00000 4.90035 27 1.00000 8.18215 28 1.00000 12.7342 29 1.00000 19.3957 SPARSE_GRID_COMPUTE_TEST: SPARSE_GRID can make a sparse grid. Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Unique points in the grid = 10 Grid weights: 1 -2.00000 2 0.711093 3 0.278518 4 0.103893E-01 5 0.711093 6 0.278518 7 0.103893E-01 8 0.711093 9 0.278518 10 0.103893E-01 Grid points: 1 1.00000 1.00000 1.00000 2 0.415775 1.00000 1.00000 3 2.29428 1.00000 1.00000 4 6.28995 1.00000 1.00000 5 1.00000 0.415775 1.00000 6 1.00000 2.29428 1.00000 7 1.00000 6.28995 1.00000 8 1.00000 1.00000 0.415775 9 1.00000 1.00000 2.29428 10 1.00000 1.00000 6.28995 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.00000 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 4.00000 4.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.976996E-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.00 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 1 Unique points in the grid = 1581 Weight sum Expected sum Difference 1024.00 1024.00 0.361524E-10 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.00000 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 4.00000 4.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.444089E-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.195399E-13 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.00 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 2 Unique points in the grid = 2001 Weight sum Expected sum Difference 1024.00 1024.00 0.356977E-10 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.00000 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 4.00000 4.00000 0.355271E-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.177636E-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.198952E-12 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.00 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 3 Unique points in the grid = 2001 Weight sum Expected sum Difference 1024.00 1024.00 0.120917E-08 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.00000 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 4.00000 4.00000 0.888178E-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.234479E-12 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.00 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 4 Unique points in the grid = 2001 Weight sum Expected sum Difference 1024.00 1024.00 0.122782E-08 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 4.00000 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 4.00000 4.00000 0.888178E-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 8.00000 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 8.00000 8.00000 0.844658E-12 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1024.00 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 5 Unique points in the grid = 2441 Weight sum Expected sum Difference 1024.00 1024.00 0.154660E-08 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 3.14159 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 3 LEVEL_MAX = 4 1D quadrature index RULE = 6 Unique points in the grid = 225 Weight sum Expected sum Difference 3.14159 3.14159 0.195435E-10 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.56833 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 0 1D quadrature index RULE = 6 Unique points in the grid = 1 Weight sum Expected sum Difference 5.56833 5.56833 0.888178E-15 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.56833 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 6 Unique points in the grid = 7 Weight sum Expected sum Difference 5.56833 5.56833 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 5.56833 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 4 LEVEL_MAX = 6 1D quadrature index RULE = 6 Unique points in the grid = 6405 Weight sum Expected sum Difference 5.56833 5.56833 0.519567E-10 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 306.020 Spatial dimension DIM_NUM = 10 LEVEL_MIN = 0 LEVEL_MAX = 3 1D quadrature index RULE = 6 Unique points in the grid = 2441 Weight sum Expected sum Difference 306.020 306.020 0.810019E-10 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.00000 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 1.00000 1.00000 0.133227E-14 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.00000 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 1.00000 1.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.00000 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 1.00000 1.00000 0.00000 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.00000 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 1.00000 1.00000 0.139000E-12 SPARSE_GRID_WEIGHT_TEST: Compute the weights of a sparse grid. As a simple test, sum these weights. They should sum to exactly 1.00000 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 1.00000 1.00000 0.153055E-11 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 1.00000 2 2 0 0.00000 2 1 1 1.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.666667 4 4 0 0.00000 4 3 1 1.00000 4 2 2 0.00000 4 1 3 0.666667 4 0 4 0.00000 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.00000 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 0.00000 0 0 0 0.222045E-15 1 1 0 0.222045E-15 1 0 1 0.00000 2 2 0 0.00000 2 1 1 0.00000 2 0 2 0.111022E-15 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.111022E-15 3 0 3 0.277556E-15 4 4 0 0.00000 4 3 1 0.249800E-15 4 2 2 0.00000 4 1 3 0.277556E-15 4 0 4 0.555112E-16 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.555112E-16 5 0 5 0.666667E-01 6 6 0 0.00000 6 5 1 0.666667 6 4 2 0.00000 6 3 3 0.666667 6 2 4 0.00000 6 1 5 0.666667E-01 6 0 6 0.277556E-16 7 7 0 0.00000 7 6 1 0.00000 7 5 2 0.00000 7 4 3 0.00000 7 3 4 0.00000 7 2 5 0.00000 7 1 6 0.277556E-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 0.00000 0 0 0 0.277556E-15 1 1 0 0.277556E-15 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.111022E-15 3 3 0 0.111022E-15 3 2 1 0.111022E-15 3 1 2 0.832667E-16 3 0 3 0.00000 4 4 0 0.00000 4 3 1 0.00000 4 2 2 0.00000 4 1 3 0.277556E-15 4 0 4 0.555112E-16 5 5 0 0.111022E-15 5 4 1 0.277556E-16 5 3 2 0.277556E-16 5 2 3 0.111022E-15 5 1 4 0.277556E-16 5 0 5 0.194289E-15 6 6 0 0.00000 6 5 1 0.416334E-15 6 4 2 0.00000 6 3 3 0.208167E-15 6 2 4 0.00000 6 1 5 0.388578E-15 6 0 6 0.277556E-16 7 7 0 0.111022E-15 7 6 1 0.277556E-16 7 5 2 0.277556E-16 7 4 3 0.277556E-16 7 3 4 0.277556E-16 7 2 5 0.111022E-15 7 1 6 0.00000 7 0 7 0.749401E-15 8 8 0 0.00000 8 7 1 0.666667E-01 8 6 2 0.00000 8 5 3 0.444444 8 4 4 0.00000 8 3 5 0.666667E-01 8 2 6 0.00000 8 1 7 0.249800E-15 8 0 8 0.00000 9 9 0 0.111022E-15 9 8 1 0.00000 9 7 2 0.277556E-16 9 6 3 0.277556E-16 9 5 4 0.277556E-16 9 4 5 0.277556E-16 9 3 6 0.693889E-17 9 2 7 0.111022E-15 9 1 8 0.00000 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 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 1.00000 2 2 0 0 0.00000 2 1 1 0 1.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 1.00000 2 0 0 2 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 4 Unique points in the grid = 7 Error Total Monomial Degree Exponents 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.166533E-15 2 2 0 0 0.00000 2 1 1 0 0.166533E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.166533E-15 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.666667 4 4 0 0 0.00000 4 3 1 0 1.00000 4 2 2 0 0.00000 4 1 3 0 0.666667 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 1.00000 4 2 0 2 0.00000 4 1 1 2 1.00000 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.666667 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 1 Check up to DEGREE_MAX = 6 Unique points in the grid = 25 Error Total Monomial Degree Exponents 0.444089E-15 0 0 0 0 0.444089E-15 1 1 0 0 0.444089E-15 1 0 1 0 0.444089E-15 1 0 0 1 0.00000 2 2 0 0 0.00000 2 1 1 0 0.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.00000 2 0 0 2 0.222045E-15 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.222045E-15 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.222045E-15 3 0 0 3 0.416334E-15 4 4 0 0 0.00000 4 3 1 0 0.249800E-15 4 2 2 0 0.00000 4 1 3 0 0.277556E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 0.249800E-15 4 2 0 2 0.00000 4 1 1 2 0.249800E-15 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.277556E-15 4 0 0 4 0.111022E-15 5 5 0 0 0.00000 5 4 1 0 0.00000 5 3 2 0 0.00000 5 2 3 0 0.00000 5 1 4 0 0.111022E-15 5 0 5 0 0.00000 5 4 0 1 0.00000 5 3 1 1 0.00000 5 2 2 1 0.00000 5 1 3 1 0.00000 5 0 4 1 0.00000 5 3 0 2 0.00000 5 2 1 2 0.00000 5 1 2 2 0.00000 5 0 3 2 0.00000 5 2 0 3 0.00000 5 1 1 3 0.00000 5 0 2 3 0.00000 5 1 0 4 0.00000 5 0 1 4 0.111022E-15 5 0 0 5 0.666667E-01 6 6 0 0 0.00000 6 5 1 0 0.666667 6 4 2 0 0.00000 6 3 3 0 0.666667 6 2 4 0 0.00000 6 1 5 0 0.666667E-01 6 0 6 0 0.00000 6 5 0 1 0.00000 6 4 1 1 0.00000 6 3 2 1 0.00000 6 2 3 1 0.00000 6 1 4 1 0.00000 6 0 5 1 0.666667 6 4 0 2 0.00000 6 3 1 2 1.00000 6 2 2 2 0.00000 6 1 3 2 0.666667 6 0 4 2 0.00000 6 3 0 3 0.00000 6 2 1 3 0.00000 6 1 2 3 0.00000 6 0 3 3 0.666667 6 2 0 4 0.00000 6 1 1 4 0.666667 6 0 2 4 0.00000 6 1 0 5 0.00000 6 0 1 5 0.666667E-01 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 1.00000 2 2 0 0.00000 2 1 1 1.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 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 0.222045E-15 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.00000 2 2 0 0.00000 2 1 1 0.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.250000 4 4 0 0.00000 4 3 1 1.00000 4 2 2 0.00000 4 1 3 0.250000 4 0 4 0.00000 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.00000 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.166533E-15 2 2 0 0.138778E-16 2 1 1 0.333067E-15 2 0 2 0.305311E-15 3 3 0 0.693889E-16 3 2 1 0.832667E-16 3 1 2 0.305311E-15 3 0 3 0.832667E-15 4 4 0 0.138778E-16 4 3 1 0.335752 4 2 2 0.138778E-16 4 1 3 0.555112E-15 4 0 4 0.333067E-15 5 5 0 0.485723E-16 5 4 1 0.131839E-15 5 3 2 0.131839E-15 5 2 3 0.485723E-16 5 1 4 0.305311E-15 5 0 5 0.582867E-15 6 6 0 0.693889E-17 6 5 1 0.323286 6 4 2 0.693889E-17 6 3 3 0.323286 6 2 4 0.693889E-17 6 1 5 0.582867E-15 6 0 6 0.263678E-15 7 7 0 0.277556E-16 7 6 1 0.124900E-15 7 5 2 0.693889E-16 7 4 3 0.693889E-16 7 3 4 0.124900E-15 7 2 5 0.208167E-16 7 1 6 0.249800E-15 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 0.333067E-15 0 0 0 0.624500E-16 1 1 0 0.693889E-17 1 0 1 0.166533E-15 2 2 0 0.104083E-16 2 1 1 0.333067E-15 2 0 2 0.107553E-15 3 3 0 0.451028E-16 3 2 1 0.381639E-16 3 1 2 0.485723E-16 3 0 3 0.138778E-15 4 4 0 0.173472E-17 4 3 1 0.202300 4 2 2 0.00000 4 1 3 0.00000 4 0 4 0.693889E-16 5 5 0 0.260209E-16 5 4 1 0.641848E-16 5 3 2 0.659195E-16 5 2 3 0.242861E-16 5 1 4 0.277556E-16 5 0 5 0.00000 6 6 0 0.00000 6 5 1 0.257875 6 4 2 0.173472E-17 6 3 3 0.257875 6 2 4 0.00000 6 1 5 0.194289E-15 6 0 6 0.260209E-16 7 7 0 0.242861E-16 7 6 1 0.624500E-16 7 5 2 0.451028E-16 7 4 3 0.416334E-16 7 3 4 0.624500E-16 7 2 5 0.208167E-16 7 1 6 0.277556E-16 7 0 7 0.499600E-15 8 8 0 0.173472E-17 8 7 1 0.319132 8 6 2 0.00000 8 5 3 0.309656 8 4 4 0.173472E-17 8 3 5 0.319132 8 2 6 0.346945E-17 8 1 7 0.124900E-15 8 0 8 0.416334E-16 9 9 0 0.693889E-17 9 8 1 0.537764E-16 9 7 2 0.277556E-16 9 6 3 0.346945E-16 9 5 4 0.381639E-16 9 4 5 0.242861E-16 9 3 6 0.589806E-16 9 2 7 0.693889E-17 9 1 8 0.277556E-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 = 2 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 1.00000 2 2 0 0 0.00000 2 1 1 0 1.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 1.00000 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 0.555112E-15 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.00000 2 2 0 0 0.00000 2 1 1 0 0.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.00000 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.250000 4 4 0 0 0.00000 4 3 1 0 1.00000 4 2 2 0 0.00000 4 1 3 0 0.250000 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 1.00000 4 2 0 2 0.00000 4 1 1 2 1.00000 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.250000 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 2 Check up to DEGREE_MAX = 6 Unique points in the grid = 31 Error Total Monomial Degree Exponents 0.00000 0 0 0 0 0.222045E-15 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.333067E-15 2 2 0 0 0.277556E-16 2 1 1 0 0.333067E-15 2 0 2 0 0.277556E-16 2 1 0 1 0.277556E-16 2 0 1 1 0.499600E-15 2 0 0 2 0.721645E-15 3 3 0 0 0.138778E-15 3 2 1 0 0.166533E-15 3 1 2 0 0.610623E-15 3 0 3 0 0.138778E-15 3 2 0 1 0.00000 3 1 1 1 0.138778E-15 3 0 2 1 0.166533E-15 3 1 0 2 0.166533E-15 3 0 1 2 0.610623E-15 3 0 0 3 0.971445E-15 4 4 0 0 0.277556E-16 4 3 1 0 0.335752 4 2 2 0 0.277556E-16 4 1 3 0 0.971445E-15 4 0 4 0 0.277556E-16 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.277556E-16 4 0 3 1 0.335752 4 2 0 2 0.00000 4 1 1 2 0.335752 4 0 2 2 0.277556E-16 4 1 0 3 0.277556E-16 4 0 1 3 0.555112E-15 4 0 0 4 0.721645E-15 5 5 0 0 0.971445E-16 5 4 1 0 0.263678E-15 5 3 2 0 0.263678E-15 5 2 3 0 0.971445E-16 5 1 4 0 0.666134E-15 5 0 5 0 0.971445E-16 5 4 0 1 0.00000 5 3 1 1 0.00000 5 2 2 1 0.00000 5 1 3 1 0.971445E-16 5 0 4 1 0.263678E-15 5 3 0 2 0.00000 5 2 1 2 0.00000 5 1 2 2 0.263678E-15 5 0 3 2 0.263678E-15 5 2 0 3 0.00000 5 1 1 3 0.263678E-15 5 0 2 3 0.971445E-16 5 1 0 4 0.971445E-16 5 0 1 4 0.666134E-15 5 0 0 5 0.582867E-15 6 6 0 0 0.138778E-16 6 5 1 0 0.323286 6 4 2 0 0.138778E-16 6 3 3 0 0.323286 6 2 4 0 0.138778E-16 6 1 5 0 0.777156E-15 6 0 6 0 0.138778E-16 6 5 0 1 0.00000 6 4 1 1 0.00000 6 3 2 1 0.00000 6 2 3 1 0.00000 6 1 4 1 0.138778E-16 6 0 5 1 0.323286 6 4 0 2 0.00000 6 3 1 2 1.00000 6 2 2 2 0.00000 6 1 3 2 0.323286 6 0 4 2 0.138778E-16 6 3 0 3 0.00000 6 2 1 3 0.00000 6 1 2 3 0.138778E-16 6 0 3 3 0.323286 6 2 0 4 0.00000 6 1 1 4 0.323286 6 0 2 4 0.138778E-16 6 1 0 5 0.138778E-16 6 0 1 5 0.777156E-15 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 1.00000 2 2 0 0.00000 2 1 1 1.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 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 0.00000 0 0 0 0.111022E-15 1 1 0 0.111022E-15 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.555112E-16 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.555112E-16 3 0 3 0.166667 4 4 0 0.00000 4 3 1 1.00000 4 2 2 0.00000 4 1 3 0.166667 4 0 4 0.277556E-16 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.277556E-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 0.222045E-15 0 0 0 0.555112E-16 1 1 0 0.111022E-15 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.277556E-16 3 3 0 0.00000 3 2 1 0.277556E-16 3 1 2 0.00000 3 0 3 0.138778E-15 4 4 0 0.00000 4 3 1 0.374700E-15 4 2 2 0.00000 4 1 3 0.00000 4 0 4 0.416334E-16 5 5 0 0.138778E-16 5 4 1 0.138778E-16 5 3 2 0.138778E-16 5 2 3 0.138778E-16 5 1 4 0.555112E-16 5 0 5 0.194289E-15 6 6 0 0.00000 6 5 1 0.166667 6 4 2 0.00000 6 3 3 0.166667 6 2 4 0.00000 6 1 5 0.00000 6 0 6 0.208167E-16 7 7 0 0.693889E-17 7 6 1 0.693889E-17 7 5 2 0.693889E-17 7 4 3 0.693889E-17 7 3 4 0.693889E-17 7 2 5 0.693889E-17 7 1 6 0.277556E-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 = 3 Check up to DEGREE_MAX = 9 Unique points in the grid = 49 Error Total Monomial Degree Exponents 0.00000 0 0 0 0.152656E-15 1 1 0 0.555112E-16 1 0 1 0.00000 2 2 0 0.138778E-16 2 1 1 0.00000 2 0 2 0.145717E-15 3 3 0 0.346945E-16 3 2 1 0.277556E-16 3 1 2 0.416334E-16 3 0 3 0.138778E-15 4 4 0 0.00000 4 3 1 0.124900E-15 4 2 2 0.00000 4 1 3 0.138778E-15 4 0 4 0.142247E-15 5 5 0 0.346945E-16 5 4 1 0.138778E-16 5 3 2 0.693889E-17 5 2 3 0.693889E-17 5 1 4 0.166533E-15 5 0 5 0.388578E-15 6 6 0 0.00000 6 5 1 0.208167E-15 6 4 2 0.693889E-17 6 3 3 0.208167E-15 6 2 4 0.00000 6 1 5 0.388578E-15 6 0 6 0.171738E-15 7 7 0 0.260209E-16 7 6 1 0.173472E-16 7 5 2 0.00000 7 4 3 0.346945E-17 7 3 4 0.138778E-16 7 2 5 0.138778E-16 7 1 6 0.152656E-15 7 0 7 0.124900E-15 8 8 0 0.00000 8 7 1 0.145717E-15 8 6 2 0.00000 8 5 3 0.277778E-01 8 4 4 0.00000 8 3 5 0.00000 8 2 6 0.00000 8 1 7 0.499600E-15 8 0 8 0.184748E-15 9 9 0 0.112757E-16 9 8 1 0.520417E-17 9 7 2 0.346945E-17 9 6 3 0.693889E-17 9 5 4 0.693889E-17 9 4 5 0.693889E-17 9 3 6 0.138778E-16 9 2 7 0.138778E-16 9 1 8 0.180411E-15 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 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 1.00000 2 2 0 0 0.00000 2 1 1 0 1.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 1.00000 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 0.222045E-15 0 0 0 0 0.222045E-15 1 1 0 0 0.222045E-15 1 0 1 0 0.222045E-15 1 0 0 1 0.166533E-15 2 2 0 0 0.00000 2 1 1 0 0.166533E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.166533E-15 2 0 0 2 0.111022E-15 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.111022E-15 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.111022E-15 3 0 0 3 0.166667 4 4 0 0 0.00000 4 3 1 0 1.00000 4 2 2 0 0.00000 4 1 3 0 0.166667 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 1.00000 4 2 0 2 0.00000 4 1 1 2 1.00000 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.166667 4 0 0 4 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 5 Spatial dimension DIM_NUM = 3 LEVEL_MIN = 0 LEVEL_MAX = 2 1D quadrature index RULE = 3 Check up to DEGREE_MAX = 6 Unique points in the grid = 31 Error Total Monomial Degree Exponents 0.666134E-15 0 0 0 0 0.444089E-15 1 1 0 0 0.333067E-15 1 0 1 0 0.222045E-15 1 0 0 1 0.00000 2 2 0 0 0.00000 2 1 1 0 0.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.166533E-15 2 0 0 2 0.333067E-15 3 3 0 0 0.00000 3 2 1 0 0.555112E-16 3 1 2 0 0.555112E-16 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.555112E-16 3 1 0 2 0.555112E-16 3 0 1 2 0.222045E-15 3 0 0 3 0.138778E-15 4 4 0 0 0.00000 4 3 1 0 0.374700E-15 4 2 2 0 0.00000 4 1 3 0 0.138778E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 0.374700E-15 4 2 0 2 0.00000 4 1 1 2 0.374700E-15 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.00000 4 0 0 4 0.166533E-15 5 5 0 0 0.277556E-16 5 4 1 0 0.277556E-16 5 3 2 0 0.277556E-16 5 2 3 0 0.277556E-16 5 1 4 0 0.277556E-16 5 0 5 0 0.277556E-16 5 4 0 1 0.00000 5 3 1 1 0.00000 5 2 2 1 0.00000 5 1 3 1 0.277556E-16 5 0 4 1 0.277556E-16 5 3 0 2 0.00000 5 2 1 2 0.00000 5 1 2 2 0.277556E-16 5 0 3 2 0.277556E-16 5 2 0 3 0.00000 5 1 1 3 0.277556E-16 5 0 2 3 0.277556E-16 5 1 0 4 0.277556E-16 5 0 1 4 0.111022E-15 5 0 0 5 0.194289E-15 6 6 0 0 0.00000 6 5 1 0 0.166667 6 4 2 0 0.00000 6 3 3 0 0.166667 6 2 4 0 0.00000 6 1 5 0 0.194289E-15 6 0 6 0 0.00000 6 5 0 1 0.00000 6 4 1 1 0.00000 6 3 2 1 0.00000 6 2 3 1 0.00000 6 1 4 1 0.00000 6 0 5 1 0.166667 6 4 0 2 0.00000 6 3 1 2 1.00000 6 2 2 2 0.00000 6 1 3 2 0.166667 6 0 4 2 0.00000 6 3 0 3 0.00000 6 2 1 3 0.00000 6 1 2 3 0.00000 6 0 3 3 0.166667 6 2 0 4 0.00000 6 1 1 4 0.166667 6 0 2 4 0.00000 6 1 0 5 0.00000 6 0 1 5 0.00000 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 1.00000 2 2 0 0.00000 2 1 1 1.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.277556E-15 4 4 0 0.00000 4 3 1 1.00000 4 2 2 0.00000 4 1 3 0.277556E-15 4 0 4 0.00000 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.00000 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 0.222045E-15 0 0 0 0.277556E-16 1 1 0 0.277556E-16 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.00000 4 4 0 0.00000 4 3 1 0.499600E-15 4 2 2 0.00000 4 1 3 0.00000 4 0 4 0.00000 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.00000 5 0 5 0.00000 6 6 0 0.00000 6 5 1 0.416334E-15 6 4 2 0.00000 6 3 3 0.416334E-15 6 2 4 0.00000 6 1 5 0.00000 6 0 6 0.00000 7 7 0 0.00000 7 6 1 0.00000 7 5 2 0.00000 7 4 3 0.00000 7 3 4 0.00000 7 2 5 0.00000 7 1 6 0.00000 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 0.222045E-15 0 0 0 0.277556E-16 1 1 0 0.346945E-16 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.416334E-16 3 3 0 0.00000 3 2 1 0.693889E-17 3 1 2 0.346945E-16 3 0 3 0.138778E-15 4 4 0 0.00000 4 3 1 0.124900E-15 4 2 2 0.693889E-17 4 1 3 0.00000 4 0 4 0.693889E-17 5 5 0 0.138778E-16 5 4 1 0.00000 5 3 2 0.693889E-17 5 2 3 0.00000 5 1 4 0.693889E-16 5 0 5 0.00000 6 6 0 0.00000 6 5 1 0.00000 6 4 2 0.00000 6 3 3 0.208167E-15 6 2 4 0.00000 6 1 5 0.194289E-15 6 0 6 0.138778E-16 7 7 0 0.693889E-17 7 6 1 0.00000 7 5 2 0.00000 7 4 3 0.00000 7 3 4 0.00000 7 2 5 0.00000 7 1 6 0.138778E-16 7 0 7 0.249800E-15 8 8 0 0.00000 8 7 1 0.145717E-15 8 6 2 0.00000 8 5 3 0.173472E-15 8 4 4 0.00000 8 3 5 0.00000 8 2 6 0.00000 8 1 7 0.249800E-15 8 0 8 0.693889E-17 9 9 0 0.173472E-17 9 8 1 0.00000 9 7 2 0.00000 9 6 3 0.00000 9 5 4 0.00000 9 4 5 0.00000 9 3 6 0.00000 9 2 7 0.00000 9 1 8 0.693889E-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 = 4 Check up to DEGREE_MAX = 2 Unique points in the grid = 1 Error Total Monomial Degree Exponents 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 1.00000 2 2 0 0 0.00000 2 1 1 0 1.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 1.00000 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 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.166533E-15 2 2 0 0 0.00000 2 1 1 0 0.166533E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.166533E-15 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.277556E-15 4 4 0 0 0.00000 4 3 1 0 1.00000 4 2 2 0 0.00000 4 1 3 0 0.277556E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 1.00000 4 2 0 2 0.00000 4 1 1 2 1.00000 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.277556E-15 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 0.111022E-15 0 0 0 0 0.555112E-16 1 1 0 0 0.555112E-16 1 0 1 0 0.555112E-16 1 0 0 1 0.166533E-15 2 2 0 0 0.00000 2 1 1 0 0.166533E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.00000 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.138778E-15 4 4 0 0 0.00000 4 3 1 0 0.499600E-15 4 2 2 0 0.00000 4 1 3 0 0.138778E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 0.499600E-15 4 2 0 2 0.00000 4 1 1 2 0.499600E-15 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.00000 4 0 0 4 0.00000 5 5 0 0 0.00000 5 4 1 0 0.00000 5 3 2 0 0.00000 5 2 3 0 0.00000 5 1 4 0 0.00000 5 0 5 0 0.00000 5 4 0 1 0.00000 5 3 1 1 0.00000 5 2 2 1 0.00000 5 1 3 1 0.00000 5 0 4 1 0.00000 5 3 0 2 0.00000 5 2 1 2 0.00000 5 1 2 2 0.00000 5 0 3 2 0.00000 5 2 0 3 0.00000 5 1 1 3 0.00000 5 0 2 3 0.00000 5 1 0 4 0.00000 5 0 1 4 0.00000 5 0 0 5 0.00000 6 6 0 0 0.00000 6 5 1 0 0.416334E-15 6 4 2 0 0.00000 6 3 3 0 0.416334E-15 6 2 4 0 0.00000 6 1 5 0 0.00000 6 0 6 0 0.00000 6 5 0 1 0.00000 6 4 1 1 0.00000 6 3 2 1 0.00000 6 2 3 1 0.00000 6 1 4 1 0.00000 6 0 5 1 0.416334E-15 6 4 0 2 0.00000 6 3 1 2 1.00000 6 2 2 2 0.00000 6 1 3 2 0.416334E-15 6 0 4 2 0.00000 6 3 0 3 0.00000 6 2 1 3 0.00000 6 1 2 3 0.00000 6 0 3 3 0.416334E-15 6 2 0 4 0.00000 6 1 1 4 0.416334E-15 6 0 2 4 0.00000 6 1 0 5 0.00000 6 0 1 5 0.194289E-15 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 1.00000 2 2 0 0.00000 2 1 1 1.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.277556E-15 4 4 0 0.00000 4 3 1 1.00000 4 2 2 0.00000 4 1 3 0.277556E-15 4 0 4 0.00000 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.00000 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 0.00000 0 0 0 0.277556E-16 1 1 0 0.277556E-16 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.277556E-15 4 4 0 0.00000 4 3 1 0.499600E-15 4 2 2 0.00000 4 1 3 0.277556E-15 4 0 4 0.277556E-16 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.277556E-16 5 0 5 0.194289E-15 6 6 0 0.00000 6 5 1 0.416334E-15 6 4 2 0.00000 6 3 3 0.416334E-15 6 2 4 0.00000 6 1 5 0.00000 6 0 6 0.277556E-16 7 7 0 0.00000 7 6 1 0.00000 7 5 2 0.00000 7 4 3 0.00000 7 3 4 0.00000 7 2 5 0.00000 7 1 6 0.277556E-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 = 5 Check up to DEGREE_MAX = 9 Unique points in the grid = 73 Error Total Monomial Degree Exponents 0.999201E-15 0 0 0 0.555112E-16 1 1 0 0.277556E-16 1 0 1 0.166533E-15 2 2 0 0.00000 2 1 1 0.166533E-15 2 0 2 0.555112E-16 3 3 0 0.277556E-16 3 2 1 0.138778E-16 3 1 2 0.624500E-16 3 0 3 0.416334E-15 4 4 0 0.693889E-17 4 3 1 0.00000 4 2 2 0.138778E-16 4 1 3 0.00000 4 0 4 0.346945E-16 5 5 0 0.693889E-17 5 4 1 0.693889E-17 5 3 2 0.138778E-16 5 2 3 0.693889E-17 5 1 4 0.346945E-16 5 0 5 0.388578E-15 6 6 0 0.00000 6 5 1 0.208167E-15 6 4 2 0.693889E-17 6 3 3 0.208167E-15 6 2 4 0.693889E-17 6 1 5 0.388578E-15 6 0 6 0.208167E-16 7 7 0 0.104083E-16 7 6 1 0.00000 7 5 2 0.00000 7 4 3 0.346945E-17 7 3 4 0.138778E-16 7 2 5 0.00000 7 1 6 0.208167E-16 7 0 7 0.374700E-15 8 8 0 0.693889E-17 8 7 1 0.00000 8 6 2 0.346945E-17 8 5 3 0.00000 8 4 4 0.00000 8 3 5 0.00000 8 2 6 0.00000 8 1 7 0.124900E-15 8 0 8 0.00000 9 9 0 0.693889E-17 9 8 1 0.00000 9 7 2 0.346945E-17 9 6 3 0.346945E-17 9 5 4 0.693889E-17 9 4 5 0.00000 9 3 6 0.00000 9 2 7 0.00000 9 1 8 0.00000 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 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 1.00000 2 2 0 0 0.00000 2 1 1 0 1.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 1.00000 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 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.166533E-15 2 2 0 0 0.00000 2 1 1 0 0.166533E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.166533E-15 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.277556E-15 4 4 0 0 0.00000 4 3 1 0 1.00000 4 2 2 0 0.00000 4 1 3 0 0.277556E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 1.00000 4 2 0 2 0.00000 4 1 1 2 1.00000 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.277556E-15 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 0.111022E-15 0 0 0 0 0.555112E-16 1 1 0 0 0.555112E-16 1 0 1 0 0.555112E-16 1 0 0 1 0.166533E-15 2 2 0 0 0.00000 2 1 1 0 0.166533E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.166533E-15 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.277556E-15 4 4 0 0 0.00000 4 3 1 0 0.499600E-15 4 2 2 0 0.00000 4 1 3 0 0.277556E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 0.499600E-15 4 2 0 2 0.00000 4 1 1 2 0.499600E-15 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.277556E-15 4 0 0 4 0.555112E-16 5 5 0 0 0.00000 5 4 1 0 0.00000 5 3 2 0 0.00000 5 2 3 0 0.00000 5 1 4 0 0.555112E-16 5 0 5 0 0.00000 5 4 0 1 0.00000 5 3 1 1 0.00000 5 2 2 1 0.00000 5 1 3 1 0.00000 5 0 4 1 0.00000 5 3 0 2 0.00000 5 2 1 2 0.00000 5 1 2 2 0.00000 5 0 3 2 0.00000 5 2 0 3 0.00000 5 1 1 3 0.00000 5 0 2 3 0.00000 5 1 0 4 0.00000 5 0 1 4 0.555112E-16 5 0 0 5 0.194289E-15 6 6 0 0 0.00000 6 5 1 0 0.416334E-15 6 4 2 0 0.00000 6 3 3 0 0.416334E-15 6 2 4 0 0.00000 6 1 5 0 0.00000 6 0 6 0 0.00000 6 5 0 1 0.00000 6 4 1 1 0.00000 6 3 2 1 0.00000 6 2 3 1 0.00000 6 1 4 1 0.00000 6 0 5 1 0.416334E-15 6 4 0 2 0.00000 6 3 1 2 1.00000 6 2 2 2 0.00000 6 1 3 2 0.416334E-15 6 0 4 2 0.00000 6 3 0 3 0.00000 6 2 1 3 0.00000 6 1 2 3 0.00000 6 0 3 3 0.416334E-15 6 2 0 4 0.00000 6 1 1 4 0.416334E-15 6 0 2 4 0.00000 6 1 0 5 0.00000 6 0 1 5 0.00000 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 0.282716E-15 0 0 0 0.00000 1 1 0 0.00000 1 0 1 1.00000 2 2 0 0.00000 2 1 1 1.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 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 0.424074E-15 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.141358E-15 2 2 0 0.00000 2 1 1 0.141358E-15 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.00000 4 4 0 0.00000 4 3 1 1.00000 4 2 2 0.00000 4 1 3 0.00000 4 0 4 0.00000 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.00000 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 0.00000 0 0 0 0.277556E-16 1 1 0 0.208167E-16 1 0 1 0.424074E-15 2 2 0 0.00000 2 1 1 0.141358E-15 2 0 2 0.832667E-16 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.693889E-16 3 0 3 0.00000 4 4 0 0.00000 4 3 1 0.141358E-15 4 2 2 0.00000 4 1 3 0.00000 4 0 4 0.555112E-16 5 5 0 0.00000 5 4 1 0.00000 5 3 2 0.00000 5 2 3 0.00000 5 1 4 0.555112E-16 5 0 5 0.150782E-15 6 6 0 0.00000 6 5 1 0.188477E-15 6 4 2 0.00000 6 3 3 0.188477E-15 6 2 4 0.00000 6 1 5 0.150782E-15 6 0 6 0.444089E-15 7 7 0 0.00000 7 6 1 0.00000 7 5 2 0.00000 7 4 3 0.00000 7 3 4 0.00000 7 2 5 0.00000 7 1 6 0.444089E-15 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 0.424074E-15 0 0 0 0.555112E-16 1 1 0 0.836334E-16 1 0 1 0.141358E-15 2 2 0 0.00000 2 1 1 0.00000 2 0 2 0.832667E-16 3 3 0 0.385976E-16 3 2 1 0.00000 3 1 2 0.279672E-16 3 0 3 0.188477E-15 4 4 0 0.277556E-16 4 3 1 0.141358E-15 4 2 2 0.138778E-16 4 1 3 0.188477E-15 4 0 4 0.555112E-16 5 5 0 0.602816E-16 5 4 1 0.00000 5 3 2 0.208167E-16 5 2 3 0.277556E-16 5 1 4 0.756604E-16 5 0 5 0.452346E-15 6 6 0 0.00000 6 5 1 0.376955E-15 6 4 2 0.00000 6 3 3 0.188477E-15 6 2 4 0.00000 6 1 5 0.452346E-15 6 0 6 0.111022E-15 7 7 0 0.115359E-15 7 6 1 0.277556E-16 7 5 2 0.693889E-17 7 4 3 0.00000 7 3 4 0.555112E-16 7 2 5 0.00000 7 1 6 0.184152E-15 7 0 7 0.344644E-15 8 8 0 0.166533E-15 8 7 1 0.301564E-15 8 6 2 0.555112E-16 8 5 3 0.125652E-15 8 4 4 0.555112E-16 8 3 5 0.00000 8 2 6 0.00000 8 1 7 0.172322E-15 8 0 8 0.888178E-15 9 9 0 0.763278E-16 9 8 1 0.00000 9 7 2 0.152656E-15 9 6 3 0.00000 9 5 4 0.832667E-16 9 4 5 0.111022E-15 9 3 6 0.444089E-15 9 2 7 0.00000 9 1 8 0.930679E-15 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 0.478516E-15 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 1.00000 2 2 0 0 0.00000 2 1 1 0 1.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 1.00000 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 0.319011E-15 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.319011E-15 2 2 0 0 0.00000 2 1 1 0 0.319011E-15 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.319011E-15 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.00000 4 4 0 0 0.00000 4 3 1 0 1.00000 4 2 2 0 0.00000 4 1 3 0 0.00000 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 1.00000 4 2 0 2 0.00000 4 1 1 2 1.00000 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.212674E-15 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 0.319011E-15 0 0 0 0 0.832667E-16 1 1 0 0 0.832667E-16 1 0 1 0 0.815320E-16 1 0 0 1 0.00000 2 2 0 0 0.00000 2 1 1 0 0.00000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.159505E-15 2 0 0 2 0.555112E-16 3 3 0 0 0.00000 3 2 1 0 0.00000 3 1 2 0 0.555112E-16 3 0 3 0 0.00000 3 2 0 1 0.00000 3 1 1 1 0.00000 3 0 2 1 0.00000 3 1 0 2 0.00000 3 0 1 2 0.485723E-16 3 0 0 3 0.212674E-15 4 4 0 0 0.00000 4 3 1 0 0.159505E-15 4 2 2 0 0.00000 4 1 3 0 0.212674E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.00000 4 1 2 1 0.00000 4 0 3 1 0.159505E-15 4 2 0 2 0.00000 4 1 1 2 0.159505E-15 4 0 2 2 0.00000 4 1 0 3 0.00000 4 0 1 3 0.00000 4 0 0 4 0.111022E-15 5 5 0 0 0.00000 5 4 1 0 0.00000 5 3 2 0 0.00000 5 2 3 0 0.00000 5 1 4 0 0.111022E-15 5 0 5 0 0.00000 5 4 0 1 0.00000 5 3 1 1 0.00000 5 2 2 1 0.00000 5 1 3 1 0.00000 5 0 4 1 0.00000 5 3 0 2 0.00000 5 2 1 2 0.00000 5 1 2 2 0.00000 5 0 3 2 0.00000 5 2 0 3 0.00000 5 1 1 3 0.00000 5 0 2 3 0.00000 5 1 0 4 0.00000 5 0 1 4 0.111022E-15 5 0 0 5 0.340278E-15 6 6 0 0 0.00000 6 5 1 0 0.212674E-15 6 4 2 0 0.00000 6 3 3 0 0.212674E-15 6 2 4 0 0.00000 6 1 5 0 0.340278E-15 6 0 6 0 0.00000 6 5 0 1 0.00000 6 4 1 1 0.00000 6 3 2 1 0.00000 6 2 3 1 0.00000 6 1 4 1 0.00000 6 0 5 1 0.212674E-15 6 4 0 2 0.00000 6 3 1 2 1.00000 6 2 2 2 0.00000 6 1 3 2 0.212674E-15 6 0 4 2 0.00000 6 3 0 3 0.00000 6 2 1 3 0.00000 6 1 2 3 0.00000 6 0 3 3 0.00000 6 2 0 4 0.00000 6 1 1 4 0.00000 6 0 2 4 0.00000 6 1 0 5 0.00000 6 0 1 5 0.340278E-15 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 0.00000 0 0 0 0.00000 1 1 0 0.00000 1 0 1 0.500000 2 2 0 0.00000 2 1 1 0.500000 2 0 2 0.833333 3 3 0 0.500000 3 2 1 0.500000 3 1 2 0.833333 3 0 3 SPARSE_GRID_MONOMIAL_TEST Check the exactness of a sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. For cases where the dimension is greater than 1, many sparse grid of this level have accuracy through monomials of total degree 3 Spatial dimension DIM_NUM = 2 LEVEL_MIN = 0 LEVEL_MAX = 1 1D quadrature index RULE = 7 Check up to DEGREE_MAX = 5 Unique points in the grid = 7 Error Total Monomial Degree Exponents 0.00000 0 0 0 0.222045E-15 1 1 0 0.00000 1 0 1 0.00000 2 2 0 0.222045E-15 2 1 1 0.00000 2 0 2 0.00000 3 3 0 0.00000 3 2 1 0.00000 3 1 2 0.00000 3 0 3 0.148030E-15 4 4 0 0.00000 4 3 1 0.250000 4 2 2 0.00000 4 1 3 0.148030E-15 4 0 4 0.236848E-15 5 5 0 0.148030E-15 5 4 1 0.416667 5 3 2 0.416667 5 2 3 0.148030E-15 5 1 4 0.236848E-15 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 0.333067E-15 0 0 0 0.222045E-15 1 1 0 0.555112E-15 1 0 1 0.222045E-15 2 2 0 0.444089E-15 2 1 1 0.00000 2 0 2 0.00000 3 3 0 0.444089E-15 3 2 1 0.222045E-15 3 1 2 0.148030E-15 3 0 3 0.148030E-15 4 4 0 0.444089E-15 4 3 1 0.222045E-15 4 2 2 0.296059E-15 4 1 3 0.00000 4 0 4 0.00000 5 5 0 0.296059E-15 5 4 1 0.148030E-15 5 3 2 0.148030E-15 5 2 3 0.148030E-15 5 1 4 0.00000 5 0 5 0.473695E-15 6 6 0 0.236848E-15 6 5 1 0.148030E-15 6 4 2 0.00000 6 3 3 0.148030E-15 6 2 4 0.236848E-15 6 1 5 0.157898E-15 6 0 6 0.541366E-15 7 7 0 0.00000 7 6 1 0.236848E-15 7 5 2 0.394746E-15 7 4 3 0.394746E-15 7 3 4 0.118424E-15 7 2 5 0.315797E-15 7 1 6 0.360911E-15 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 0.111022E-14 0 0 0 0.999201E-15 1 1 0 0.111022E-14 1 0 1 0.222045E-15 2 2 0 0.133227E-14 2 1 1 0.333067E-15 2 0 2 0.296059E-15 3 3 0 0.444089E-15 3 2 1 0.888178E-15 3 1 2 0.148030E-15 3 0 3 0.296059E-15 4 4 0 0.118424E-14 4 3 1 0.111022E-15 4 2 2 0.888178E-15 4 1 3 0.296059E-15 4 0 4 0.355271E-15 5 5 0 0.296059E-15 5 4 1 0.444089E-15 5 3 2 0.592119E-15 5 2 3 0.00000 5 1 4 0.118424E-15 5 0 5 0.126319E-14 6 6 0 0.592119E-15 6 5 1 0.740149E-15 6 4 2 0.789492E-15 6 3 3 0.296059E-15 6 2 4 0.00000 6 1 5 0.631594E-15 6 0 6 0.360911E-15 7 7 0 0.157898E-15 7 6 1 0.118424E-15 7 5 2 0.986865E-15 7 4 3 0.986865E-15 7 3 4 0.00000 7 2 5 0.631594E-15 7 1 6 0.721821E-15 7 0 7 0.360911E-15 8 8 0 0.721821E-15 8 7 1 0.473695E-15 8 6 2 0.157898E-15 8 5 3 0.986865E-15 8 4 4 0.789492E-15 8 3 5 0.157898E-15 8 2 6 0.721821E-15 8 1 7 0.541366E-15 8 0 8 0.00000 9 9 0 0.360911E-15 9 8 1 0.180455E-15 9 7 2 0.842125E-15 9 6 3 0.315797E-15 9 5 4 0.315797E-15 9 4 5 0.421062E-15 9 3 6 0.541366E-15 9 2 7 0.541366E-15 9 1 8 0.481214E-15 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 0.00000 0 0 0 0 0.00000 1 1 0 0 0.00000 1 0 1 0 0.00000 1 0 0 1 0.500000 2 2 0 0 0.00000 2 1 1 0 0.500000 2 0 2 0 0.00000 2 1 0 1 0.00000 2 0 1 1 0.500000 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 0.00000 0 0 0 0 0.222045E-15 1 1 0 0 0.222045E-15 1 0 1 0 0.00000 1 0 0 1 0.00000 2 2 0 0 0.444089E-15 2 1 1 0 0.00000 2 0 2 0 0.222045E-15 2 1 0 1 0.222045E-15 2 0 1 1 0.00000 2 0 0 2 0.00000 3 3 0 0 0.00000 3 2 1 0 0.222045E-15 3 1 2 0 0.00000 3 0 3 0 0.00000 3 2 0 1 0.444089E-15 3 1 1 1 0.00000 3 0 2 1 0.222045E-15 3 1 0 2 0.00000 3 0 1 2 0.00000 3 0 0 3 0.148030E-15 4 4 0 0 0.00000 4 3 1 0 0.250000 4 2 2 0 0.148030E-15 4 1 3 0 0.148030E-15 4 0 4 0 0.00000 4 3 0 1 0.00000 4 2 1 1 0.222045E-15 4 1 2 1 0.00000 4 0 3 1 0.250000 4 2 0 2 0.222045E-15 4 1 1 2 0.250000 4 0 2 2 0.148030E-15 4 1 0 3 0.00000 4 0 1 3 0.148030E-15 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 0.222045E-15 0 0 0 0 0.122125E-14 1 1 0 0 0.666134E-15 1 0 1 0 0.111022E-15 1 0 0 1 0.222045E-15 2 2 0 0 0.111022E-14 2 1 1 0 0.222045E-15 2 0 2 0 0.122125E-14 2 1 0 1 0.666134E-15 2 0 1 1 0.222045E-15 2 0 0 2 0.296059E-15 3 3 0 0 0.00000 3 2 1 0 0.111022E-14 3 1 2 0 0.296059E-15 3 0 3 0 0.222045E-15 3 2 0 1 0.999201E-15 3 1 1 1 0.444089E-15 3 0 2 1 0.888178E-15 3 1 0 2 0.133227E-14 3 0 1 2 0.592119E-15 3 0 0 3 0.296059E-15 4 4 0 0 0.00000 4 3 1 0 0.777156E-15 4 2 2 0 0.296059E-15 4 1 3 0 0.148030E-15 4 0 4 0 0.00000 4 3 0 1 0.444089E-15 4 2 1 1 0.333067E-15 4 1 2 1 0.148030E-15 4 0 3 1 0.111022E-15 4 2 0 2 0.244249E-14 4 1 1 2 0.222045E-15 4 0 2 2 0.444089E-15 4 1 0 3 0.148030E-15 4 0 1 3 0.296059E-15 4 0 0 4 0.118424E-15 5 5 0 0 0.148030E-15 5 4 1 0 0.148030E-15 5 3 2 0 0.00000 5 2 3 0 0.148030E-15 5 1 4 0 0.118424E-15 5 0 5 0 0.296059E-15 5 4 0 1 0.444089E-15 5 3 1 1 0.00000 5 2 2 1 0.592119E-15 5 1 3 1 0.296059E-15 5 0 4 1 0.296059E-15 5 3 0 2 0.777156E-15 5 2 1 2 0.111022E-15 5 1 2 2 0.296059E-15 5 0 3 2 0.444089E-15 5 2 0 3 0.592119E-15 5 1 1 3 0.444089E-15 5 0 2 3 0.148030E-15 5 1 0 4 0.148030E-15 5 0 1 4 0.236848E-15 5 0 0 5 0.110529E-14 6 6 0 0 0.118424E-15 6 5 1 0 0.296059E-15 6 4 2 0 0.00000 6 3 3 0 0.00000 6 2 4 0 0.00000 6 1 5 0 0.00000 6 0 6 0 0.355271E-15 6 5 0 1 0.148030E-15 6 4 1 1 0.296059E-15 6 3 2 1 0.148030E-15 6 2 3 1 0.00000 6 1 4 1 0.236848E-15 6 0 5 1 0.148030E-15 6 4 0 2 0.148030E-15 6 3 1 2 0.125000 6 2 2 2 0.00000 6 1 3 2 0.148030E-15 6 0 4 2 0.00000 6 3 0 3 0.148030E-15 6 2 1 3 0.296059E-15 6 1 2 3 0.00000 6 0 3 3 0.00000 6 2 0 4 0.740149E-15 6 1 1 4 0.148030E-15 6 0 2 4 0.236848E-15 6 1 0 5 0.00000 6 0 1 5 0.789492E-15 6 0 0 6 SANDIA_SPARSE_PRB Normal end of execution. 23 December 2009 2:20:01.200 PM