17-Jan-2023 07:47:23 sparse_grid_hermite_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sparse_grid_hermite(). sparse_grid_hermite_test01 SPARSE_GRID_HERM_SIZE returns the number of distinct points in a Gauss-Hermite sparse grid. Note that, unlike most sparse grids, a sparse grid based on Gauss-Hermite points is almost entirely NOT nested. Hence the point counts should be much higher than for a grid of the same level, but using rules such as Fejer2 or Gauss-Patterson or Newton-Cotes-Open. Each sparse grid is of spatial dimension DIM, and is made up of all product grids of levels up to LEVEL_MAX. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 7 22 37 57 81 3 15 75 161 289 471 4 31 224 608 1268 2341 5 63 613 2070 4994 10367 6 127 1578 6507 18076 41957 7 255 3887 19215 61107 157877 8 511 9268 53986 195256 559192 9 1023 21561 145700 595164 1881838 10 2047 49214 380501 1743184 6061126 sparse_grid_hermite_test01 SPARSE_GRID_HERM_SIZE returns the number of distinct points in a Gauss-Hermite sparse grid. Note that, unlike most sparse grids, a sparse grid based on Gauss-Hermite points is almost entirely NOT nested. Hence the point counts should be much higher than for a grid of the same level, but using rules such as Fejer2 or Gauss-Patterson or Newton-Cotes-Open. Each sparse grid is of spatial dimension DIM, and is made up of all product grids of levels up to 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 6 86522 163213 287409 479233 764365 7 357221 731957 1388737 2478511 4208385 8 1382908 3067766 6253544 11916685 21493065 9 5069006 12137652 26516244 53833091 102935845 10 17726108 45689730 106724648 230380259 466201790 sparse_grid_hermite_test01 SPARSE_GRID_HERM_SIZE returns the number of distinct points in a Gauss-Hermite sparse grid. Note that, unlike most sparse grids, a sparse grid based on Gauss-Hermite points is almost entirely NOT nested. Hence the point counts should be much higher than for a grid of the same level, but using rules such as Fejer2 or Gauss-Patterson or Newton-Cotes-Open. Each sparse grid is of spatial dimension DIM, and is made up of all product grids of levels up to LEVEL_MAX. DIM: 100 LEVEL_MAX 0 1 1 201 2 20601 sparse_grid_hermite_test02: SPARSE_GRID_HERM_INDEX returns abstract indexes for the points that make up a Gauss-Hermite sparse grid. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 75 Grid index/base: 1 -3 0 3 0 2 -2 0 3 0 3 -1 0 3 0 4 0 0 3 0 5 1 0 3 0 6 2 0 3 0 7 3 0 3 0 8 -1 -1 1 1 9 0 -1 1 1 10 1 -1 1 1 11 -1 0 1 1 12 0 0 1 1 13 1 0 1 1 14 -1 1 1 1 15 0 1 1 1 16 1 1 1 1 17 0 -3 0 3 18 0 -2 0 3 19 0 -1 0 3 20 0 0 0 3 21 0 1 0 3 22 0 2 0 3 23 0 3 0 3 24 -7 0 7 0 25 -6 0 7 0 26 -5 0 7 0 27 -4 0 7 0 28 -3 0 7 0 29 -2 0 7 0 30 -1 0 7 0 31 1 0 7 0 32 2 0 7 0 33 3 0 7 0 34 4 0 7 0 35 5 0 7 0 36 6 0 7 0 37 7 0 7 0 38 -3 -1 3 1 39 -2 -1 3 1 40 -1 -1 3 1 41 1 -1 3 1 42 2 -1 3 1 43 3 -1 3 1 44 -3 1 3 1 45 -2 1 3 1 46 -1 1 3 1 47 1 1 3 1 48 2 1 3 1 49 3 1 3 1 50 -1 -3 1 3 51 1 -3 1 3 52 -1 -2 1 3 53 1 -2 1 3 54 -1 -1 1 3 55 1 -1 1 3 56 -1 1 1 3 57 1 1 1 3 58 -1 2 1 3 59 1 2 1 3 60 -1 3 1 3 61 1 3 1 3 62 0 -7 0 7 63 0 -6 0 7 64 0 -5 0 7 65 0 -4 0 7 66 0 -3 0 7 67 0 -2 0 7 68 0 -1 0 7 69 0 1 0 7 70 0 2 0 7 71 0 3 0 7 72 0 4 0 7 73 0 5 0 7 74 0 6 0 7 75 0 7 0 7 sparse_grid_hermite_test02: SPARSE_GRID_HERM_INDEX returns abstract indexes for the points that make up a Gauss-Hermite sparse grid. LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 224 Grid index/base: 1 -7 0 7 0 2 -6 0 7 0 3 -5 0 7 0 4 -4 0 7 0 5 -3 0 7 0 6 -2 0 7 0 7 -1 0 7 0 8 0 0 7 0 9 1 0 7 0 10 2 0 7 0 11 3 0 7 0 12 4 0 7 0 13 5 0 7 0 14 6 0 7 0 15 7 0 7 0 16 -3 -1 3 1 17 -2 -1 3 1 18 -1 -1 3 1 19 0 -1 3 1 20 1 -1 3 1 21 2 -1 3 1 22 3 -1 3 1 23 -3 0 3 1 24 -2 0 3 1 25 -1 0 3 1 26 0 0 3 1 27 1 0 3 1 28 2 0 3 1 29 3 0 3 1 30 -3 1 3 1 31 -2 1 3 1 32 -1 1 3 1 33 0 1 3 1 34 1 1 3 1 35 2 1 3 1 36 3 1 3 1 37 -1 -3 1 3 38 0 -3 1 3 39 1 -3 1 3 40 -1 -2 1 3 41 0 -2 1 3 42 1 -2 1 3 43 -1 -1 1 3 44 0 -1 1 3 45 1 -1 1 3 46 -1 0 1 3 47 0 0 1 3 48 1 0 1 3 49 -1 1 1 3 50 0 1 1 3 51 1 1 1 3 52 -1 2 1 3 53 0 2 1 3 54 1 2 1 3 55 -1 3 1 3 56 0 3 1 3 57 1 3 1 3 58 0 -7 0 7 59 0 -6 0 7 60 0 -5 0 7 61 0 -4 0 7 62 0 -3 0 7 63 0 -2 0 7 64 0 -1 0 7 65 0 0 0 7 66 0 1 0 7 67 0 2 0 7 68 0 3 0 7 69 0 4 0 7 70 0 5 0 7 71 0 6 0 7 72 0 7 0 7 73 -15 0 15 0 74 -14 0 15 0 75 -13 0 15 0 76 -12 0 15 0 77 -11 0 15 0 78 -10 0 15 0 79 -9 0 15 0 80 -8 0 15 0 81 -7 0 15 0 82 -6 0 15 0 83 -5 0 15 0 84 -4 0 15 0 85 -3 0 15 0 86 -2 0 15 0 87 -1 0 15 0 88 1 0 15 0 89 2 0 15 0 90 3 0 15 0 91 4 0 15 0 92 5 0 15 0 93 6 0 15 0 94 7 0 15 0 95 8 0 15 0 96 9 0 15 0 97 10 0 15 0 98 11 0 15 0 99 12 0 15 0 100 13 0 15 0 101 14 0 15 0 102 15 0 15 0 103 -7 -1 7 1 104 -6 -1 7 1 105 -5 -1 7 1 106 -4 -1 7 1 107 -3 -1 7 1 108 -2 -1 7 1 109 -1 -1 7 1 110 1 -1 7 1 111 2 -1 7 1 112 3 -1 7 1 113 4 -1 7 1 114 5 -1 7 1 115 6 -1 7 1 116 7 -1 7 1 117 -7 1 7 1 118 -6 1 7 1 119 -5 1 7 1 120 -4 1 7 1 121 -3 1 7 1 122 -2 1 7 1 123 -1 1 7 1 124 1 1 7 1 125 2 1 7 1 126 3 1 7 1 127 4 1 7 1 128 5 1 7 1 129 6 1 7 1 130 7 1 7 1 131 -3 -3 3 3 132 -2 -3 3 3 133 -1 -3 3 3 134 1 -3 3 3 135 2 -3 3 3 136 3 -3 3 3 137 -3 -2 3 3 138 -2 -2 3 3 139 -1 -2 3 3 140 1 -2 3 3 141 2 -2 3 3 142 3 -2 3 3 143 -3 -1 3 3 144 -2 -1 3 3 145 -1 -1 3 3 146 1 -1 3 3 147 2 -1 3 3 148 3 -1 3 3 149 -3 1 3 3 150 -2 1 3 3 151 -1 1 3 3 152 1 1 3 3 153 2 1 3 3 154 3 1 3 3 155 -3 2 3 3 156 -2 2 3 3 157 -1 2 3 3 158 1 2 3 3 159 2 2 3 3 160 3 2 3 3 161 -3 3 3 3 162 -2 3 3 3 163 -1 3 3 3 164 1 3 3 3 165 2 3 3 3 166 3 3 3 3 167 -1 -7 1 7 168 1 -7 1 7 169 -1 -6 1 7 170 1 -6 1 7 171 -1 -5 1 7 172 1 -5 1 7 173 -1 -4 1 7 174 1 -4 1 7 175 -1 -3 1 7 176 1 -3 1 7 177 -1 -2 1 7 178 1 -2 1 7 179 -1 -1 1 7 180 1 -1 1 7 181 -1 1 1 7 182 1 1 1 7 183 -1 2 1 7 184 1 2 1 7 185 -1 3 1 7 186 1 3 1 7 187 -1 4 1 7 188 1 4 1 7 189 -1 5 1 7 190 1 5 1 7 191 -1 6 1 7 192 1 6 1 7 193 -1 7 1 7 194 1 7 1 7 195 0 -15 0 15 196 0 -14 0 15 197 0 -13 0 15 198 0 -12 0 15 199 0 -11 0 15 200 0 -10 0 15 201 0 -9 0 15 202 0 -8 0 15 203 0 -7 0 15 204 0 -6 0 15 205 0 -5 0 15 206 0 -4 0 15 207 0 -3 0 15 208 0 -2 0 15 209 0 -1 0 15 210 0 1 0 15 211 0 2 0 15 212 0 3 0 15 213 0 4 0 15 214 0 5 0 15 215 0 6 0 15 216 0 7 0 15 217 0 8 0 15 218 0 9 0 15 219 0 10 0 15 220 0 11 0 15 221 0 12 0 15 222 0 13 0 15 223 0 14 0 15 224 0 15 0 15 sparse_grid_hermite_test02: SPARSE_GRID_HERM_INDEX returns abstract indexes for the points that make up a Gauss-Hermite sparse grid. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 1 Grid index/base: 1 0 0 0 0 0 0 sparse_grid_hermite_test02: SPARSE_GRID_HERM_INDEX returns abstract indexes for the points that make up a Gauss-Hermite sparse grid. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 37 Grid index/base: 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 sparse_grid_hermite_test02: SPARSE_GRID_HERM_INDEX returns abstract indexes for the points that make up a Gauss-Hermite sparse grid. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 6 Number of unique points in the grid = 109 Grid index/base: 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 sparse_grid_hermite_test03: SPARSE_GRID_HERM makes a sparse Gauss-Hermite grid. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 1 Grid weights: 1 3.141593 Grid points: 1 0.000000 0.000000 sparse_grid_hermite_test03: SPARSE_GRID_HERM makes a sparse Gauss-Hermite grid. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 75 Grid weights: 1 -0.000574 2 -0.032209 3 -0.251456 4 2.478402 5 -0.251456 6 -0.032209 7 -0.000574 8 -0.087266 9 -0.109706 10 -0.087266 11 -0.109706 12 -1.396263 13 -0.109706 14 -0.087266 15 -0.109706 16 -0.087266 17 -0.000574 18 -0.032209 19 -0.251456 20 -1.436157 21 -0.251456 22 -0.032209 23 -0.000574 24 0.000000 25 0.000002 26 0.000177 27 0.004924 28 0.054556 29 0.280914 30 0.730302 31 0.730302 32 0.280914 33 0.054556 34 0.004924 35 0.000177 36 0.000002 37 0.000000 38 0.000287 39 0.016104 40 0.125728 41 0.125728 42 0.016104 43 0.000287 44 0.000287 45 0.016104 46 0.125728 47 0.125728 48 0.016104 49 0.000287 50 0.000287 51 0.000287 52 0.016104 53 0.016104 54 0.125728 55 0.125728 56 0.125728 57 0.125728 58 0.016104 59 0.016104 60 0.000287 61 0.000287 62 0.000000 63 0.000002 64 0.000177 65 0.004924 66 0.054556 67 0.280914 68 0.730302 69 0.730302 70 0.280914 71 0.054556 72 0.004924 73 0.000177 74 0.000002 75 0.000000 Grid points: 1 -2.651961 0.000000 2 -1.673552 0.000000 3 -0.816288 0.000000 4 0.000000 0.000000 5 0.816288 0.000000 6 1.673552 0.000000 7 2.651961 0.000000 8 -1.224745 -1.224745 9 0.000000 -1.224745 10 1.224745 -1.224745 11 -1.224745 0.000000 12 0.000000 0.000000 13 1.224745 0.000000 14 -1.224745 1.224745 15 0.000000 1.224745 16 1.224745 1.224745 17 0.000000 -2.651961 18 0.000000 -1.673552 19 0.000000 -0.816288 20 0.000000 0.000000 21 0.000000 0.816288 22 0.000000 1.673552 23 0.000000 2.651961 24 -4.499991 0.000000 25 -3.669950 0.000000 26 -2.967167 0.000000 27 -2.325732 0.000000 28 -1.719993 0.000000 29 -1.136116 0.000000 30 -0.565070 0.000000 31 0.565070 0.000000 32 1.136116 0.000000 33 1.719993 0.000000 34 2.325732 0.000000 35 2.967167 0.000000 36 3.669950 0.000000 37 4.499991 0.000000 38 -2.651961 -1.224745 39 -1.673552 -1.224745 40 -0.816288 -1.224745 41 0.816288 -1.224745 42 1.673552 -1.224745 43 2.651961 -1.224745 44 -2.651961 1.224745 45 -1.673552 1.224745 46 -0.816288 1.224745 47 0.816288 1.224745 48 1.673552 1.224745 49 2.651961 1.224745 50 -1.224745 -2.651961 51 1.224745 -2.651961 52 -1.224745 -1.673552 53 1.224745 -1.673552 54 -1.224745 -0.816288 55 1.224745 -0.816288 56 -1.224745 0.816288 57 1.224745 0.816288 58 -1.224745 1.673552 59 1.224745 1.673552 60 -1.224745 2.651961 61 1.224745 2.651961 62 0.000000 -4.499991 63 0.000000 -3.669950 64 0.000000 -2.967167 65 0.000000 -2.325732 66 0.000000 -1.719993 67 0.000000 -1.136116 68 0.000000 -0.565070 69 0.000000 0.565070 70 0.000000 1.136116 71 0.000000 1.719993 72 0.000000 2.325732 73 0.000000 2.967167 74 0.000000 3.669950 75 0.000000 4.499991 sparse_grid_hermite_test03: SPARSE_GRID_HERM makes a sparse Gauss-Hermite grid. LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 224 Grid weights: 1 -0.000000 2 -0.000001 3 -0.000059 4 -0.001641 5 -0.018185 6 -0.093638 7 -0.243434 8 2.392808 9 -0.243434 10 -0.093638 11 -0.018185 12 -0.001641 13 -0.000059 14 -0.000001 15 -0.000000 16 -0.000287 17 -0.016104 18 -0.125728 19 -0.072719 20 -0.125728 21 -0.016104 22 -0.000287 23 -0.000361 24 -0.020246 25 -0.158058 26 -0.957438 27 -0.158058 28 -0.020246 29 -0.000361 30 -0.000287 31 -0.016104 32 -0.125728 33 -0.072719 34 -0.125728 35 -0.016104 36 -0.000287 37 -0.000287 38 -0.000361 39 -0.000287 40 -0.016104 41 -0.020246 42 -0.016104 43 -0.125728 44 -0.158058 45 -0.125728 46 -0.072719 47 -0.957438 48 -0.072719 49 -0.125728 50 -0.158058 51 -0.125728 52 -0.016104 53 -0.020246 54 -0.016104 55 -0.000287 56 -0.000361 57 -0.000287 58 -0.000000 59 -0.000001 60 -0.000059 61 -0.001641 62 -0.018185 63 -0.093638 64 -0.243434 65 -0.999842 66 -0.243434 67 -0.093638 68 -0.018185 69 -0.001641 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149 0.000414 150 0.023202 151 0.181142 152 0.181142 153 0.023202 154 0.000414 155 0.000053 156 0.002972 157 0.023202 158 0.023202 159 0.002972 160 0.000053 161 0.000001 162 0.000053 163 0.000414 164 0.000414 165 0.000053 166 0.000001 167 0.000000 168 0.000000 169 0.000000 170 0.000000 171 0.000030 172 0.000030 173 0.000821 174 0.000821 175 0.009093 176 0.009093 177 0.046819 178 0.046819 179 0.121717 180 0.121717 181 0.121717 182 0.121717 183 0.046819 184 0.046819 185 0.009093 186 0.009093 187 0.000821 188 0.000821 189 0.000030 190 0.000030 191 0.000000 192 0.000000 193 0.000000 194 0.000000 195 0.000000 196 0.000000 197 0.000000 198 0.000000 199 0.000000 200 0.000000 201 0.000001 202 0.000019 203 0.000247 204 0.002187 205 0.013263 206 0.056448 207 0.171428 208 0.375996 209 0.600459 210 0.600459 211 0.375996 212 0.171428 213 0.056448 214 0.013263 215 0.002187 216 0.000247 217 0.000019 218 0.000001 219 0.000000 220 0.000000 221 0.000000 222 0.000000 223 0.000000 224 0.000000 Grid points: 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0.000000 94 2.831680 0.000000 95 3.260321 0.000000 96 3.700743 0.000000 97 4.156272 0.000000 98 4.631560 0.000000 99 5.133596 0.000000 100 5.673961 0.000000 101 6.275079 0.000000 102 6.995680 0.000000 103 -4.499991 -1.224745 104 -3.669950 -1.224745 105 -2.967167 -1.224745 106 -2.325732 -1.224745 107 -1.719993 -1.224745 108 -1.136116 -1.224745 109 -0.565070 -1.224745 110 0.565070 -1.224745 111 1.136116 -1.224745 112 1.719993 -1.224745 113 2.325732 -1.224745 114 2.967167 -1.224745 115 3.669950 -1.224745 116 4.499991 -1.224745 117 -4.499991 1.224745 118 -3.669950 1.224745 119 -2.967167 1.224745 120 -2.325732 1.224745 121 -1.719993 1.224745 122 -1.136116 1.224745 123 -0.565070 1.224745 124 0.565070 1.224745 125 1.136116 1.224745 126 1.719993 1.224745 127 2.325732 1.224745 128 2.967167 1.224745 129 3.669950 1.224745 130 4.499991 1.224745 131 -2.651961 -2.651961 132 -1.673552 -2.651961 133 -0.816288 -2.651961 134 0.816288 -2.651961 135 1.673552 -2.651961 136 2.651961 -2.651961 137 -2.651961 -1.673552 138 -1.673552 -1.673552 139 -0.816288 -1.673552 140 0.816288 -1.673552 141 1.673552 -1.673552 142 2.651961 -1.673552 143 -2.651961 -0.816288 144 -1.673552 -0.816288 145 -0.816288 -0.816288 146 0.816288 -0.816288 147 1.673552 -0.816288 148 2.651961 -0.816288 149 -2.651961 0.816288 150 -1.673552 0.816288 151 -0.816288 0.816288 152 0.816288 0.816288 153 1.673552 0.816288 154 2.651961 0.816288 155 -2.651961 1.673552 156 -1.673552 1.673552 157 -0.816288 1.673552 158 0.816288 1.673552 159 1.673552 1.673552 160 2.651961 1.673552 161 -2.651961 2.651961 162 -1.673552 2.651961 163 -0.816288 2.651961 164 0.816288 2.651961 165 1.673552 2.651961 166 2.651961 2.651961 167 -1.224745 -4.499991 168 1.224745 -4.499991 169 -1.224745 -3.669950 170 1.224745 -3.669950 171 -1.224745 -2.967167 172 1.224745 -2.967167 173 -1.224745 -2.325732 174 1.224745 -2.325732 175 -1.224745 -1.719993 176 1.224745 -1.719993 177 -1.224745 -1.136116 178 1.224745 -1.136116 179 -1.224745 -0.565070 180 1.224745 -0.565070 181 -1.224745 0.565070 182 1.224745 0.565070 183 -1.224745 1.136116 184 1.224745 1.136116 185 -1.224745 1.719993 186 1.224745 1.719993 187 -1.224745 2.325732 188 1.224745 2.325732 189 -1.224745 2.967167 190 1.224745 2.967167 191 -1.224745 3.669950 192 1.224745 3.669950 193 -1.224745 4.499991 194 1.224745 4.499991 195 0.000000 -6.995680 196 0.000000 -6.275079 197 0.000000 -5.673961 198 0.000000 -5.133596 199 0.000000 -4.631560 200 0.000000 -4.156272 201 0.000000 -3.700743 202 0.000000 -3.260321 203 0.000000 -2.831680 204 0.000000 -2.412318 205 0.000000 -2.000259 206 0.000000 -1.593886 207 0.000000 -1.191827 208 0.000000 -0.792877 209 0.000000 -0.395943 210 0.000000 0.395943 211 0.000000 0.792877 212 0.000000 1.191827 213 0.000000 1.593886 214 0.000000 2.000259 215 0.000000 2.412318 216 0.000000 2.831680 217 0.000000 3.260321 218 0.000000 3.700743 219 0.000000 4.156272 220 0.000000 4.631560 221 0.000000 5.133596 222 0.000000 5.673961 223 0.000000 6.275079 224 0.000000 6.995680 sparse_grid_hermite_test03: SPARSE_GRID_HERM makes a sparse Gauss-Hermite grid. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 1 Grid weights: 1 5.568328 Grid points: 1 0.000000 0.000000 0.000000 sparse_grid_hermite_test03: SPARSE_GRID_HERM makes a sparse Gauss-Hermite grid. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 37 Grid weights: 1 -1.643983 2 -0.618703 3 -0.618703 4 -0.618703 5 -0.618703 6 -0.618703 7 -0.618703 8 0.003053 9 0.171266 10 1.337085 11 1.337085 12 0.171266 13 0.003053 14 0.154676 15 0.154676 16 0.154676 17 0.154676 18 0.003053 19 0.171266 20 1.337085 21 1.337085 22 0.171266 23 0.003053 24 0.154676 25 0.154676 26 0.154676 27 0.154676 28 0.154676 29 0.154676 30 0.154676 31 0.154676 32 0.003053 33 0.171266 34 1.337085 35 1.337085 36 0.171266 37 0.003053 Grid points: 1 0.000000 0.000000 0.000000 2 -1.224745 0.000000 0.000000 3 1.224745 0.000000 0.000000 4 0.000000 -1.224745 0.000000 5 0.000000 1.224745 0.000000 6 0.000000 0.000000 -1.224745 7 0.000000 0.000000 1.224745 8 -2.651961 0.000000 0.000000 9 -1.673552 0.000000 0.000000 10 -0.816288 0.000000 0.000000 11 0.816288 0.000000 0.000000 12 1.673552 0.000000 0.000000 13 2.651961 0.000000 0.000000 14 -1.224745 -1.224745 0.000000 15 1.224745 -1.224745 0.000000 16 -1.224745 1.224745 0.000000 17 1.224745 1.224745 0.000000 18 0.000000 -2.651961 0.000000 19 0.000000 -1.673552 0.000000 20 0.000000 -0.816288 0.000000 21 0.000000 0.816288 0.000000 22 0.000000 1.673552 0.000000 23 0.000000 2.651961 0.000000 24 -1.224745 0.000000 -1.224745 25 1.224745 0.000000 -1.224745 26 -1.224745 0.000000 1.224745 27 1.224745 0.000000 1.224745 28 0.000000 -1.224745 -1.224745 29 0.000000 1.224745 -1.224745 30 0.000000 -1.224745 1.224745 31 0.000000 1.224745 1.224745 32 0.000000 0.000000 -2.651961 33 0.000000 0.000000 -1.673552 34 0.000000 0.000000 -0.816288 35 0.000000 0.000000 0.816288 36 0.000000 0.000000 1.673552 37 0.000000 0.000000 2.651961 sparse_grid_hermite_test04: Compute the weights of a Gauss-Hermite sparse grid. As a simple test, sum these weights. They should sum to sqrt(pi^DIM_NUM). LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 224 Weight sum Exact sum Difference 3.141593e+00 3.141593e+00 1.955058e-11 sparse_grid_hermite_test04: Compute the weights of a Gauss-Hermite sparse grid. As a simple test, sum these weights. They should sum to sqrt(pi^DIM_NUM). LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 1 Weight sum Exact sum Difference 5.568328e+00 5.568328e+00 8.881784e-16 sparse_grid_hermite_test04: Compute the weights of a Gauss-Hermite sparse grid. As a simple test, sum these weights. They should sum to sqrt(pi^DIM_NUM). LEVEL_MIN = 0 LEVEL_MAX = 1 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 7 Weight sum Exact sum Difference 5.568328e+00 5.568328e+00 0.000000e+00 sparse_grid_hermite_test04: Compute the weights of a Gauss-Hermite sparse grid. As a simple test, sum these weights. They should sum to sqrt(pi^DIM_NUM). LEVEL_MIN = 4 LEVEL_MAX = 6 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 6507 Weight sum Exact sum Difference 5.568328e+00 5.568328e+00 5.197975e-11 sparse_grid_hermite_test04: Compute the weights of a Gauss-Hermite sparse grid. As a simple test, sum these weights. They should sum to sqrt(pi^DIM_NUM). LEVEL_MIN = 0 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 10 Number of unique points in the grid = 2441 Weight sum Exact sum Difference 3.060197e+02 3.060197e+02 8.100187e-11 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 2 The maximum total degree to check is DEGREE_MAX = 3 Number of unique points in the grid = 1 Error Total Monomial Degree Exponents 2.827160e-16 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.000000e+00 2 2 0 0.000000e+00 2 1 1 1.000000e+00 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 0 LEVEL_MAX = 1 Spatial dimension DIM_NUM = 2 The maximum total degree to check is DEGREE_MAX = 5 Number of unique points in the grid = 5 Error Total Monomial Degree Exponents 2.827160e-16 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.413580e-16 2 2 0 0.000000e+00 2 1 1 1.413580e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 1.884773e-16 4 4 0 0.000000e+00 4 3 1 1.000000e+00 4 2 2 0.000000e+00 4 1 3 1.884773e-16 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 1 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 2 The maximum total degree to check is DEGREE_MAX = 7 Number of unique points in the grid = 22 Error Total Monomial Degree Exponents 2.827160e-16 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 1.413580e-16 2 2 0 0.000000e+00 2 1 1 2.827160e-16 2 0 2 0.000000e+00 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 1.413580e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 0.000000e+00 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 3.015637e-16 6 6 0 0.000000e+00 6 5 1 3.769546e-16 6 4 2 0.000000e+00 6 3 3 3.769546e-16 6 2 4 0.000000e+00 6 1 5 3.015637e-16 6 0 6 0.000000e+00 7 7 0 0.000000e+00 7 6 1 0.000000e+00 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 0.000000e+00 7 0 7 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 The maximum total degree to check is DEGREE_MAX = 9 Number of unique points in the grid = 75 Error Total Monomial Degree Exponents 1.413580e-16 0 0 0 1.110223e-16 1 1 0 0.000000e+00 1 0 1 0.000000e+00 2 2 0 5.551115e-17 2 1 1 0.000000e+00 2 0 2 1.110223e-16 3 3 0 1.387779e-17 3 2 1 0.000000e+00 3 1 2 5.551115e-17 3 0 3 1.884773e-16 4 4 0 0.000000e+00 4 3 1 0.000000e+00 4 2 2 0.000000e+00 4 1 3 1.884773e-16 4 0 4 1.942890e-16 5 5 0 5.551115e-17 5 4 1 5.551115e-17 5 3 2 4.163336e-17 5 2 3 5.551115e-17 5 1 4 1.110223e-16 5 0 5 0.000000e+00 6 6 0 1.110223e-16 6 5 1 0.000000e+00 6 4 2 5.551115e-17 6 3 3 0.000000e+00 6 2 4 0.000000e+00 6 1 5 1.507819e-16 6 0 6 0.000000e+00 7 7 0 1.110223e-16 7 6 1 2.775558e-17 7 5 2 8.326673e-17 7 4 3 5.551115e-17 7 3 4 0.000000e+00 7 2 5 1.110223e-16 7 1 6 0.000000e+00 7 0 7 1.723221e-16 8 8 0 0.000000e+00 8 7 1 0.000000e+00 8 6 2 1.110223e-16 8 5 3 3.769546e-16 8 4 4 0.000000e+00 8 3 5 1.507819e-16 8 2 6 1.110223e-16 8 1 7 5.169663e-16 8 0 8 1.776357e-15 9 9 0 8.881784e-16 9 8 1 5.551115e-17 9 7 2 0.000000e+00 9 6 3 5.551115e-17 9 5 4 2.775558e-17 9 4 5 0.000000e+00 9 3 6 1.110223e-16 9 2 7 0.000000e+00 9 1 8 1.776357e-15 9 0 9 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 The maximum total degree to check is DEGREE_MAX = 11 Number of unique points in the grid = 224 Error Total Monomial Degree Exponents 6.223427e-12 0 0 0 1.110223e-16 1 1 0 2.220446e-16 1 0 1 3.111713e-12 2 2 0 0.000000e+00 2 1 1 3.111713e-12 2 0 2 1.110223e-16 3 3 0 2.775558e-17 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 3.111949e-12 4 4 0 5.551115e-17 4 3 1 1.413580e-16 4 2 2 1.110223e-16 4 1 3 3.111949e-12 4 0 4 2.775558e-16 5 5 0 0.000000e+00 5 4 1 5.551115e-17 5 3 2 0.000000e+00 5 2 3 1.110223e-16 5 1 4 1.110223e-16 5 0 5 3.111987e-12 6 6 0 0.000000e+00 6 5 1 0.000000e+00 6 4 2 0.000000e+00 6 3 3 1.884773e-16 6 2 4 0.000000e+00 6 1 5 3.111836e-12 6 0 6 0.000000e+00 7 7 0 4.440892e-16 7 6 1 5.551115e-17 7 5 2 1.110223e-16 7 4 3 1.110223e-16 7 3 4 1.110223e-16 7 2 5 0.000000e+00 7 1 6 6.661338e-16 7 0 7 3.112310e-12 8 8 0 4.440892e-16 8 7 1 0.000000e+00 8 6 2 0.000000e+00 8 5 3 1.256515e-16 8 4 4 1.110223e-16 8 3 5 0.000000e+00 8 2 6 0.000000e+00 8 1 7 3.112310e-12 8 0 8 1.776357e-15 9 9 0 8.881784e-16 9 8 1 5.551115e-16 9 7 2 0.000000e+00 9 6 3 4.440892e-16 9 5 4 2.220446e-16 9 4 5 0.000000e+00 9 3 6 2.220446e-16 9 2 7 0.000000e+00 9 1 8 0.000000e+00 9 0 9 3.112367e-12 10 10 0 8.881784e-16 10 9 1 5.169663e-16 10 8 2 0.000000e+00 10 7 3 2.010425e-16 10 6 4 2.220446e-16 10 5 5 2.010425e-16 10 4 6 0.000000e+00 10 3 7 5.169663e-16 10 2 8 0.000000e+00 10 1 9 3.112214e-12 10 010 3.552714e-15 11 11 0 5.329071e-15 11 10 1 1.332268e-15 11 9 2 0.000000e+00 11 8 3 1.110223e-15 11 7 4 4.440892e-16 11 6 5 0.000000e+00 11 5 6 0.000000e+00 11 4 7 8.881784e-16 11 3 8 3.330669e-16 11 2 9 1.776357e-15 11 110 1.776357e-14 11 011 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 4 LEVEL_MAX = 5 Spatial dimension DIM_NUM = 2 The maximum total degree to check is DEGREE_MAX = 13 Number of unique points in the grid = 613 Error Total Monomial Degree Exponents 6.224133e-12 0 0 0 5.551115e-17 1 1 0 2.775558e-17 1 0 1 6.224133e-12 2 2 0 2.775558e-17 2 1 1 6.223992e-12 2 0 2 0.000000e+00 3 3 0 4.163336e-17 3 2 1 2.775558e-17 3 1 2 8.326673e-17 3 0 3 6.223898e-12 4 4 0 1.110223e-16 4 3 1 6.224275e-12 4 2 2 1.110223e-16 4 1 3 6.224086e-12 4 0 4 5.551115e-16 5 5 0 1.942890e-16 5 4 1 5.551115e-17 5 3 2 1.110223e-16 5 2 3 1.665335e-16 5 1 4 1.110223e-16 5 0 5 4.978968e-12 6 6 0 1.665335e-16 6 5 1 6.224275e-12 6 4 2 1.942890e-16 6 3 3 6.224275e-12 6 2 4 1.110223e-16 6 1 5 4.978817e-12 6 0 6 1.221245e-15 7 7 0 2.220446e-16 7 6 1 1.110223e-16 7 5 2 2.775558e-17 7 4 3 1.110223e-16 7 3 4 1.110223e-16 7 2 5 0.000000e+00 7 1 6 1.110223e-16 7 0 7 3.911884e-12 8 8 0 2.220446e-16 8 7 1 4.979269e-12 8 6 2 5.551115e-17 8 5 3 6.224526e-12 8 4 4 4.440892e-16 8 3 5 4.979269e-12 8 2 6 7.771561e-16 8 1 7 3.911884e-12 8 0 8 2.220446e-15 9 9 0 4.440892e-16 9 8 1 5.551115e-17 9 7 2 2.220446e-16 9 6 3 0.000000e+00 9 5 4 0.000000e+00 9 4 5 2.775558e-16 9 3 6 2.220446e-16 9 2 7 1.332268e-15 9 1 8 4.440892e-16 9 0 9 3.378586e-12 10 10 0 8.881784e-16 10 9 1 3.912229e-12 10 8 2 0.000000e+00 10 7 3 4.979420e-12 10 6 4 2.220446e-16 10 5 5 4.979621e-12 10 4 6 4.440892e-16 10 3 7 3.912229e-12 10 2 8 1.332268e-15 10 1 9 3.378279e-12 10 010 1.776357e-15 11 11 0 7.105427e-15 11 10 1 6.661338e-16 11 9 2 0.000000e+00 11 8 3 1.110223e-16 11 7 4 6.661338e-16 11 6 5 3.330669e-16 11 5 6 4.440892e-16 11 4 7 5.551115e-16 11 3 8 4.440892e-16 11 2 9 1.776357e-15 11 110 1.065814e-14 11 011 3.184485e-12 12 12 0 0.000000e+00 12 11 1 3.378739e-12 12 10 2 0.000000e+00 12 9 3 3.912631e-12 12 8 4 1.332268e-15 12 7 5 3.734565e-12 12 6 6 3.330669e-16 12 5 7 3.912631e-12 12 4 8 7.549517e-15 12 3 9 3.378892e-12 12 210 7.105427e-15 12 111 3.184151e-12 12 012 2.842171e-14 13 13 0 1.421085e-14 13 12 1 8.881784e-15 13 11 2 7.105427e-15 13 10 3 1.776357e-15 13 9 4 8.881784e-16 13 8 5 1.776357e-15 13 7 6 8.881784e-16 13 6 7 1.776357e-15 13 5 8 8.881784e-16 13 4 9 3.552714e-15 13 310 1.243450e-14 13 211 0.000000e+00 13 112 2.842171e-14 13 013 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 The maximum total degree to check is DEGREE_MAX = 2 Number of unique points in the grid = 1 Error Total Monomial Degree Exponents 4.785162e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.000000e+00 2 2 0 0 0.000000e+00 2 1 1 0 1.000000e+00 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.000000e+00 2 0 0 2 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 0 LEVEL_MAX = 1 Spatial dimension DIM_NUM = 3 The maximum total degree to check is DEGREE_MAX = 4 Number of unique points in the grid = 7 Error Total Monomial Degree Exponents 3.190108e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 3.190108e-16 2 2 0 0 0.000000e+00 2 1 1 0 3.190108e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 3.190108e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 2.126739e-16 4 4 0 0 0.000000e+00 4 3 1 0 1.000000e+00 4 2 2 0 0.000000e+00 4 1 3 0 2.126739e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.000000e+00 4 2 0 2 0.000000e+00 4 1 1 2 1.000000e+00 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 0.000000e+00 4 0 0 4 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 The maximum total degree to check is DEGREE_MAX = 6 Number of unique points in the grid = 37 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.595054e-16 2 2 0 0 0.000000e+00 2 1 1 0 1.595054e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 1.595054e-16 2 0 0 2 0.000000e+00 3 3 0 0 0.000000e+00 3 2 1 0 0.000000e+00 3 1 2 0 0.000000e+00 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 0.000000e+00 3 0 2 1 0.000000e+00 3 1 0 2 0.000000e+00 3 0 1 2 0.000000e+00 3 0 0 3 2.126739e-16 4 4 0 0 0.000000e+00 4 3 1 0 1.595054e-16 4 2 2 0 0.000000e+00 4 1 3 0 2.126739e-16 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 0.000000e+00 4 0 3 1 1.595054e-16 4 2 0 2 0.000000e+00 4 1 1 2 1.595054e-16 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 0.000000e+00 4 0 0 4 0.000000e+00 5 5 0 0 0.000000e+00 5 4 1 0 0.000000e+00 5 3 2 0 0.000000e+00 5 2 3 0 0.000000e+00 5 1 4 0 0.000000e+00 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 0.000000e+00 5 0 4 1 0.000000e+00 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 0.000000e+00 5 2 0 3 0.000000e+00 5 1 1 3 0.000000e+00 5 0 2 3 0.000000e+00 5 1 0 4 0.000000e+00 5 0 1 4 0.000000e+00 5 0 0 5 3.402782e-16 6 6 0 0 0.000000e+00 6 5 1 0 4.253478e-16 6 4 2 0 0.000000e+00 6 3 3 0 4.253478e-16 6 2 4 0 0.000000e+00 6 1 5 0 3.402782e-16 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 0.000000e+00 6 0 5 1 4.253478e-16 6 4 0 2 0.000000e+00 6 3 1 2 1.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 4.253478e-16 6 0 4 2 0.000000e+00 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 0.000000e+00 6 0 3 3 2.126739e-16 6 2 0 4 0.000000e+00 6 1 1 4 2.126739e-16 6 0 2 4 0.000000e+00 6 1 0 5 0.000000e+00 6 0 1 5 1.701391e-16 6 0 0 6 sparse_grid_hermite_test05 Check the exactness of a Gauss-Hermite sparse grid quadrature rule, applied to all monomials of orders 0 to DEGREE_MAX. LEVEL_MIN = 1 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 3 The maximum total degree to check is DEGREE_MAX = 8 Number of unique points in the grid = 161 Error Total Monomial Degree Exponents 6.380216e-16 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 1.595054e-16 2 2 0 0 5.551115e-17 2 1 1 0 1.595054e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 4.785162e-16 2 0 0 2 1.110223e-16 3 3 0 0 1.110223e-16 3 2 1 0 2.775558e-17 3 1 2 0 1.110223e-16 3 0 3 0 0.000000e+00 3 2 0 1 0.000000e+00 3 1 1 1 3.330669e-16 3 0 2 1 8.326673e-17 3 1 0 2 1.110223e-16 3 0 1 2 2.220446e-16 3 0 0 3 0.000000e+00 4 4 0 0 2.220446e-16 4 3 1 0 3.190108e-16 4 2 2 0 1.110223e-16 4 1 3 0 0.000000e+00 4 0 4 0 0.000000e+00 4 3 0 1 0.000000e+00 4 2 1 1 0.000000e+00 4 1 2 1 2.220446e-16 4 0 3 1 4.785162e-16 4 2 0 2 0.000000e+00 4 1 1 2 4.785162e-16 4 0 2 2 5.551115e-17 4 1 0 3 2.775558e-17 4 0 1 3 2.126739e-16 4 0 0 4 2.220446e-16 5 5 0 0 0.000000e+00 5 4 1 0 5.551115e-17 5 3 2 0 5.551115e-17 5 2 3 0 1.110223e-16 5 1 4 0 0.000000e+00 5 0 5 0 0.000000e+00 5 4 0 1 0.000000e+00 5 3 1 1 0.000000e+00 5 2 2 1 0.000000e+00 5 1 3 1 2.220446e-16 5 0 4 1 6.938894e-17 5 3 0 2 0.000000e+00 5 2 1 2 0.000000e+00 5 1 2 2 0.000000e+00 5 0 3 2 5.551115e-17 5 2 0 3 0.000000e+00 5 1 1 3 1.110223e-16 5 0 2 3 0.000000e+00 5 1 0 4 1.665335e-16 5 0 1 4 4.440892e-16 5 0 0 5 0.000000e+00 6 6 0 0 1.110223e-16 6 5 1 0 0.000000e+00 6 4 2 0 5.551115e-17 6 3 3 0 0.000000e+00 6 2 4 0 0.000000e+00 6 1 5 0 0.000000e+00 6 0 6 0 0.000000e+00 6 5 0 1 0.000000e+00 6 4 1 1 0.000000e+00 6 3 2 1 0.000000e+00 6 2 3 1 0.000000e+00 6 1 4 1 4.440892e-16 6 0 5 1 4.253478e-16 6 4 0 2 0.000000e+00 6 3 1 2 0.000000e+00 6 2 2 2 0.000000e+00 6 1 3 2 2.126739e-16 6 0 4 2 1.110223e-16 6 3 0 3 0.000000e+00 6 2 1 3 0.000000e+00 6 1 2 3 1.110223e-16 6 0 3 3 2.126739e-16 6 2 0 4 0.000000e+00 6 1 1 4 2.126739e-16 6 0 2 4 0.000000e+00 6 1 0 5 2.220446e-16 6 0 1 5 0.000000e+00 6 0 0 6 1.776357e-15 7 7 0 0 4.440892e-16 7 6 1 0 1.110223e-16 7 5 2 0 1.110223e-16 7 4 3 0 0.000000e+00 7 3 4 0 2.220446e-16 7 2 5 0 1.110223e-16 7 1 6 0 1.776357e-15 7 0 7 0 0.000000e+00 7 6 0 1 0.000000e+00 7 5 1 1 0.000000e+00 7 4 2 1 0.000000e+00 7 3 3 1 0.000000e+00 7 2 4 1 0.000000e+00 7 1 5 1 0.000000e+00 7 0 6 1 1.110223e-16 7 5 0 2 0.000000e+00 7 4 1 2 0.000000e+00 7 3 2 2 0.000000e+00 7 2 3 2 0.000000e+00 7 1 4 2 0.000000e+00 7 0 5 2 2.220446e-16 7 4 0 3 0.000000e+00 7 3 1 3 0.000000e+00 7 2 2 3 0.000000e+00 7 1 3 3 0.000000e+00 7 0 4 3 2.498002e-16 7 3 0 4 0.000000e+00 7 2 1 4 0.000000e+00 7 1 2 4 5.551115e-17 7 0 3 4 2.220446e-16 7 2 0 5 0.000000e+00 7 1 1 5 5.551115e-17 7 0 2 5 0.000000e+00 7 1 0 6 0.000000e+00 7 0 1 6 4.440892e-16 7 0 0 7 1.944447e-16 8 8 0 0 4.440892e-16 8 7 1 0 3.402782e-16 8 6 2 0 2.775558e-16 8 5 3 0 1.417826e-16 8 4 4 0 4.440892e-16 8 3 5 0 3.402782e-16 8 2 6 0 0.000000e+00 8 1 7 0 1.944447e-16 8 0 8 0 0.000000e+00 8 7 0 1 0.000000e+00 8 6 1 1 0.000000e+00 8 5 2 1 0.000000e+00 8 4 3 1 0.000000e+00 8 3 4 1 0.000000e+00 8 2 5 1 0.000000e+00 8 1 6 1 4.440892e-16 8 0 7 1 3.402782e-16 8 6 0 2 0.000000e+00 8 5 1 2 6.380216e-16 8 4 2 2 0.000000e+00 8 3 3 2 6.380216e-16 8 2 4 2 0.000000e+00 8 1 5 2 3.402782e-16 8 0 6 2 0.000000e+00 8 5 0 3 0.000000e+00 8 4 1 3 0.000000e+00 8 3 2 3 0.000000e+00 8 2 3 3 0.000000e+00 8 1 4 3 1.110223e-16 8 0 5 3 1.417826e-16 8 4 0 4 0.000000e+00 8 3 1 4 2.126739e-16 8 2 2 4 0.000000e+00 8 1 3 4 1.417826e-16 8 0 4 4 1.110223e-16 8 3 0 5 0.000000e+00 8 2 1 5 0.000000e+00 8 1 2 5 1.942890e-16 8 0 3 5 3.402782e-16 8 2 0 6 0.000000e+00 8 1 1 6 1.701391e-16 8 0 2 6 2.220446e-16 8 1 0 7 2.220446e-16 8 0 1 7 3.888894e-16 8 0 0 8 sparse_grid_hermite_test06: SPARSE_GRID_HERM makes a sparse Gauss-Hermite grid. Write the data to a set of quadrature files. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 R data written to "gh_d2_level3_r.txt". W data written to "gh_d2_level3_w.txt". X data written to "gh_d2_level3_x.txt", sparse_grid_hermite_test(): Normal end of execution. 17-Jan-2023 07:47:27