15 January 2023 02:32:44 PM SPARSE_GRID_HERMITE_TEST C++ version Test the SPARSE_GRID_HERMITE library. TEST01 SPARSE_GRID_HERMITE_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 Fejer1 or Fejer2 or Gauss-Patterson or Newton-Cotes-Open or Newton-Cotes-Open-Half. 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 TEST01 SPARSE_GRID_HERMITE_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 Fejer1 or Fejer2 or Gauss-Patterson or Newton-Cotes-Open or Newton-Cotes-Open-Half. 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 TEST01 SPARSE_GRID_HERMITE_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 Fejer1 or Fejer2 or Gauss-Patterson or Newton-Cotes-Open or Newton-Cotes-Open-Half. 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 TEST02: SPARSE_GRID_HERMITE_INDEX returns abstract indices 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: 0 -3 0 3 0 1 -2 0 3 0 2 -1 0 3 0 3 0 0 3 0 4 1 0 3 0 5 2 0 3 0 6 3 0 3 0 7 -1 -1 1 1 8 0 -1 1 1 9 1 -1 1 1 10 -1 0 1 1 11 0 0 1 1 12 1 0 1 1 13 -1 1 1 1 14 0 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 0 0 3 20 0 1 0 3 21 0 2 0 3 22 0 3 0 3 23 -7 0 7 0 24 -6 0 7 0 25 -5 0 7 0 26 -4 0 7 0 27 -3 0 7 0 28 -2 0 7 0 29 -1 0 7 0 30 1 0 7 0 31 2 0 7 0 32 3 0 7 0 33 4 0 7 0 34 5 0 7 0 35 6 0 7 0 36 7 0 7 0 37 -3 -1 3 1 38 -2 -1 3 1 39 -1 -1 3 1 40 1 -1 3 1 41 2 -1 3 1 42 3 -1 3 1 43 -3 1 3 1 44 -2 1 3 1 45 -1 1 3 1 46 1 1 3 1 47 2 1 3 1 48 3 1 3 1 49 -1 -3 1 3 50 1 -3 1 3 51 -1 -2 1 3 52 1 -2 1 3 53 -1 -1 1 3 54 1 -1 1 3 55 -1 1 1 3 56 1 1 1 3 57 -1 2 1 3 58 1 2 1 3 59 -1 3 1 3 60 1 3 1 3 61 0 -7 0 7 62 0 -6 0 7 63 0 -5 0 7 64 0 -4 0 7 65 0 -3 0 7 66 0 -2 0 7 67 0 -1 0 7 68 0 1 0 7 69 0 2 0 7 70 0 3 0 7 71 0 4 0 7 72 0 5 0 7 73 0 6 0 7 74 0 7 0 7 TEST02: SPARSE_GRID_HERMITE_INDEX returns abstract indices 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: 0 -7 0 7 0 1 -6 0 7 0 2 -5 0 7 0 3 -4 0 7 0 4 -3 0 7 0 5 -2 0 7 0 6 -1 0 7 0 7 0 0 7 0 8 1 0 7 0 9 2 0 7 0 10 3 0 7 0 11 4 0 7 0 12 5 0 7 0 13 6 0 7 0 14 7 0 7 0 15 -3 -1 3 1 16 -2 -1 3 1 17 -1 -1 3 1 18 0 -1 3 1 19 1 -1 3 1 20 2 -1 3 1 21 3 -1 3 1 22 -3 0 3 1 23 -2 0 3 1 24 -1 0 3 1 25 0 0 3 1 26 1 0 3 1 27 2 0 3 1 28 3 0 3 1 29 -3 1 3 1 30 -2 1 3 1 31 -1 1 3 1 32 0 1 3 1 33 1 1 3 1 34 2 1 3 1 35 3 1 3 1 36 -1 -3 1 3 37 0 -3 1 3 38 1 -3 1 3 39 -1 -2 1 3 40 0 -2 1 3 41 1 -2 1 3 42 -1 -1 1 3 43 0 -1 1 3 44 1 -1 1 3 45 -1 0 1 3 46 0 0 1 3 47 1 0 1 3 48 -1 1 1 3 49 0 1 1 3 50 1 1 1 3 51 -1 2 1 3 52 0 2 1 3 53 1 2 1 3 54 -1 3 1 3 55 0 3 1 3 56 1 3 1 3 57 0 -7 0 7 58 0 -6 0 7 59 0 -5 0 7 60 0 -4 0 7 61 0 -3 0 7 62 0 -2 0 7 63 0 -1 0 7 64 0 0 0 7 65 0 1 0 7 66 0 2 0 7 67 0 3 0 7 68 0 4 0 7 69 0 5 0 7 70 0 6 0 7 71 0 7 0 7 72 -15 0 15 0 73 -14 0 15 0 74 -13 0 15 0 75 -12 0 15 0 76 -11 0 15 0 77 -10 0 15 0 78 -9 0 15 0 79 -8 0 15 0 80 -7 0 15 0 81 -6 0 15 0 82 -5 0 15 0 83 -4 0 15 0 84 -3 0 15 0 85 -2 0 15 0 86 -1 0 15 0 87 1 0 15 0 88 2 0 15 0 89 3 0 15 0 90 4 0 15 0 91 5 0 15 0 92 6 0 15 0 93 7 0 15 0 94 8 0 15 0 95 9 0 15 0 96 10 0 15 0 97 11 0 15 0 98 12 0 15 0 99 13 0 15 0 100 14 0 15 0 101 15 0 15 0 102 -7 -1 7 1 103 -6 -1 7 1 104 -5 -1 7 1 105 -4 -1 7 1 106 -3 -1 7 1 107 -2 -1 7 1 108 -1 -1 7 1 109 1 -1 7 1 110 2 -1 7 1 111 3 -1 7 1 112 4 -1 7 1 113 5 -1 7 1 114 6 -1 7 1 115 7 -1 7 1 116 -7 1 7 1 117 -6 1 7 1 118 -5 1 7 1 119 -4 1 7 1 120 -3 1 7 1 121 -2 1 7 1 122 -1 1 7 1 123 1 1 7 1 124 2 1 7 1 125 3 1 7 1 126 4 1 7 1 127 5 1 7 1 128 6 1 7 1 129 7 1 7 1 130 -3 -3 3 3 131 -2 -3 3 3 132 -1 -3 3 3 133 1 -3 3 3 134 2 -3 3 3 135 3 -3 3 3 136 -3 -2 3 3 137 -2 -2 3 3 138 -1 -2 3 3 139 1 -2 3 3 140 2 -2 3 3 141 3 -2 3 3 142 -3 -1 3 3 143 -2 -1 3 3 144 -1 -1 3 3 145 1 -1 3 3 146 2 -1 3 3 147 3 -1 3 3 148 -3 1 3 3 149 -2 1 3 3 150 -1 1 3 3 151 1 1 3 3 152 2 1 3 3 153 3 1 3 3 154 -3 2 3 3 155 -2 2 3 3 156 -1 2 3 3 157 1 2 3 3 158 2 2 3 3 159 3 2 3 3 160 -3 3 3 3 161 -2 3 3 3 162 -1 3 3 3 163 1 3 3 3 164 2 3 3 3 165 3 3 3 3 166 -1 -7 1 7 167 1 -7 1 7 168 -1 -6 1 7 169 1 -6 1 7 170 -1 -5 1 7 171 1 -5 1 7 172 -1 -4 1 7 173 1 -4 1 7 174 -1 -3 1 7 175 1 -3 1 7 176 -1 -2 1 7 177 1 -2 1 7 178 -1 -1 1 7 179 1 -1 1 7 180 -1 1 1 7 181 1 1 1 7 182 -1 2 1 7 183 1 2 1 7 184 -1 3 1 7 185 1 3 1 7 186 -1 4 1 7 187 1 4 1 7 188 -1 5 1 7 189 1 5 1 7 190 -1 6 1 7 191 1 6 1 7 192 -1 7 1 7 193 1 7 1 7 194 0 -15 0 15 195 0 -14 0 15 196 0 -13 0 15 197 0 -12 0 15 198 0 -11 0 15 199 0 -10 0 15 200 0 -9 0 15 201 0 -8 0 15 202 0 -7 0 15 203 0 -6 0 15 204 0 -5 0 15 205 0 -4 0 15 206 0 -3 0 15 207 0 -2 0 15 208 0 -1 0 15 209 0 1 0 15 210 0 2 0 15 211 0 3 0 15 212 0 4 0 15 213 0 5 0 15 214 0 6 0 15 215 0 7 0 15 216 0 8 0 15 217 0 9 0 15 218 0 10 0 15 219 0 11 0 15 220 0 12 0 15 221 0 13 0 15 222 0 14 0 15 223 0 15 0 15 TEST02: SPARSE_GRID_HERMITE_INDEX returns abstract indices 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: 0 0 0 0 0 0 0 TEST02: SPARSE_GRID_HERMITE_INDEX returns abstract indices 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: 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 2 1 0 0 1 0 0 3 0 -1 0 0 1 0 4 0 1 0 0 1 0 5 0 0 -1 0 0 1 6 0 0 1 0 0 1 7 -3 0 0 3 0 0 8 -2 0 0 3 0 0 9 -1 0 0 3 0 0 10 1 0 0 3 0 0 11 2 0 0 3 0 0 12 3 0 0 3 0 0 13 -1 -1 0 1 1 0 14 1 -1 0 1 1 0 15 -1 1 0 1 1 0 16 1 1 0 1 1 0 17 0 -3 0 0 3 0 18 0 -2 0 0 3 0 19 0 -1 0 0 3 0 20 0 1 0 0 3 0 21 0 2 0 0 3 0 22 0 3 0 0 3 0 23 -1 0 -1 1 0 1 24 1 0 -1 1 0 1 25 -1 0 1 1 0 1 26 1 0 1 1 0 1 27 0 -1 -1 0 1 1 28 0 1 -1 0 1 1 29 0 -1 1 0 1 1 30 0 1 1 0 1 1 31 0 0 -3 0 0 3 32 0 0 -2 0 0 3 33 0 0 -1 0 0 3 34 0 0 1 0 0 3 35 0 0 2 0 0 3 36 0 0 3 0 0 3 TEST02: SPARSE_GRID_HERMITE_INDEX returns abstract indices 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: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 0 0 2 1 0 0 0 0 0 1 0 0 0 0 0 3 0 -1 0 0 0 0 0 1 0 0 0 0 4 0 1 0 0 0 0 0 1 0 0 0 0 5 0 0 -1 0 0 0 0 0 1 0 0 0 6 0 0 1 0 0 0 0 0 1 0 0 0 7 0 0 0 -1 0 0 0 0 0 1 0 0 8 0 0 0 1 0 0 0 0 0 1 0 0 9 0 0 0 0 -1 0 0 0 0 0 1 0 10 0 0 0 0 1 0 0 0 0 0 1 0 11 0 0 0 0 0 -1 0 0 0 0 0 1 12 0 0 0 0 0 1 0 0 0 0 0 1 13 -3 0 0 0 0 0 3 0 0 0 0 0 14 -2 0 0 0 0 0 3 0 0 0 0 0 15 -1 0 0 0 0 0 3 0 0 0 0 0 16 1 0 0 0 0 0 3 0 0 0 0 0 17 2 0 0 0 0 0 3 0 0 0 0 0 18 3 0 0 0 0 0 3 0 0 0 0 0 19 -1 -1 0 0 0 0 1 1 0 0 0 0 20 1 -1 0 0 0 0 1 1 0 0 0 0 21 -1 1 0 0 0 0 1 1 0 0 0 0 22 1 1 0 0 0 0 1 1 0 0 0 0 23 0 -3 0 0 0 0 0 3 0 0 0 0 24 0 -2 0 0 0 0 0 3 0 0 0 0 25 0 -1 0 0 0 0 0 3 0 0 0 0 26 0 1 0 0 0 0 0 3 0 0 0 0 27 0 2 0 0 0 0 0 3 0 0 0 0 28 0 3 0 0 0 0 0 3 0 0 0 0 29 -1 0 -1 0 0 0 1 0 1 0 0 0 30 1 0 -1 0 0 0 1 0 1 0 0 0 31 -1 0 1 0 0 0 1 0 1 0 0 0 32 1 0 1 0 0 0 1 0 1 0 0 0 33 0 -1 -1 0 0 0 0 1 1 0 0 0 34 0 1 -1 0 0 0 0 1 1 0 0 0 35 0 -1 1 0 0 0 0 1 1 0 0 0 36 0 1 1 0 0 0 0 1 1 0 0 0 37 0 0 -3 0 0 0 0 0 3 0 0 0 38 0 0 -2 0 0 0 0 0 3 0 0 0 39 0 0 -1 0 0 0 0 0 3 0 0 0 40 0 0 1 0 0 0 0 0 3 0 0 0 41 0 0 2 0 0 0 0 0 3 0 0 0 42 0 0 3 0 0 0 0 0 3 0 0 0 43 -1 0 0 -1 0 0 1 0 0 1 0 0 44 1 0 0 -1 0 0 1 0 0 1 0 0 45 -1 0 0 1 0 0 1 0 0 1 0 0 46 1 0 0 1 0 0 1 0 0 1 0 0 47 0 -1 0 -1 0 0 0 1 0 1 0 0 48 0 1 0 -1 0 0 0 1 0 1 0 0 49 0 -1 0 1 0 0 0 1 0 1 0 0 50 0 1 0 1 0 0 0 1 0 1 0 0 51 0 0 -1 -1 0 0 0 0 1 1 0 0 52 0 0 1 -1 0 0 0 0 1 1 0 0 53 0 0 -1 1 0 0 0 0 1 1 0 0 54 0 0 1 1 0 0 0 0 1 1 0 0 55 0 0 0 -3 0 0 0 0 0 3 0 0 56 0 0 0 -2 0 0 0 0 0 3 0 0 57 0 0 0 -1 0 0 0 0 0 3 0 0 58 0 0 0 1 0 0 0 0 0 3 0 0 59 0 0 0 2 0 0 0 0 0 3 0 0 60 0 0 0 3 0 0 0 0 0 3 0 0 61 -1 0 0 0 -1 0 1 0 0 0 1 0 62 1 0 0 0 -1 0 1 0 0 0 1 0 63 -1 0 0 0 1 0 1 0 0 0 1 0 64 1 0 0 0 1 0 1 0 0 0 1 0 65 0 -1 0 0 -1 0 0 1 0 0 1 0 66 0 1 0 0 -1 0 0 1 0 0 1 0 67 0 -1 0 0 1 0 0 1 0 0 1 0 68 0 1 0 0 1 0 0 1 0 0 1 0 69 0 0 -1 0 -1 0 0 0 1 0 1 0 70 0 0 1 0 -1 0 0 0 1 0 1 0 71 0 0 -1 0 1 0 0 0 1 0 1 0 72 0 0 1 0 1 0 0 0 1 0 1 0 73 0 0 0 -1 -1 0 0 0 0 1 1 0 74 0 0 0 1 -1 0 0 0 0 1 1 0 75 0 0 0 -1 1 0 0 0 0 1 1 0 76 0 0 0 1 1 0 0 0 0 1 1 0 77 0 0 0 0 -3 0 0 0 0 0 3 0 78 0 0 0 0 -2 0 0 0 0 0 3 0 79 0 0 0 0 -1 0 0 0 0 0 3 0 80 0 0 0 0 1 0 0 0 0 0 3 0 81 0 0 0 0 2 0 0 0 0 0 3 0 82 0 0 0 0 3 0 0 0 0 0 3 0 83 -1 0 0 0 0 -1 1 0 0 0 0 1 84 1 0 0 0 0 -1 1 0 0 0 0 1 85 -1 0 0 0 0 1 1 0 0 0 0 1 86 1 0 0 0 0 1 1 0 0 0 0 1 87 0 -1 0 0 0 -1 0 1 0 0 0 1 88 0 1 0 0 0 -1 0 1 0 0 0 1 89 0 -1 0 0 0 1 0 1 0 0 0 1 90 0 1 0 0 0 1 0 1 0 0 0 1 91 0 0 -1 0 0 -1 0 0 1 0 0 1 92 0 0 1 0 0 -1 0 0 1 0 0 1 93 0 0 -1 0 0 1 0 0 1 0 0 1 94 0 0 1 0 0 1 0 0 1 0 0 1 95 0 0 0 -1 0 -1 0 0 0 1 0 1 96 0 0 0 1 0 -1 0 0 0 1 0 1 97 0 0 0 -1 0 1 0 0 0 1 0 1 98 0 0 0 1 0 1 0 0 0 1 0 1 99 0 0 0 0 -1 -1 0 0 0 0 1 1 100 0 0 0 0 1 -1 0 0 0 0 1 1 101 0 0 0 0 -1 1 0 0 0 0 1 1 102 0 0 0 0 1 1 0 0 0 0 1 1 103 0 0 0 0 0 -3 0 0 0 0 0 3 104 0 0 0 0 0 -2 0 0 0 0 0 3 105 0 0 0 0 0 -1 0 0 0 0 0 3 106 0 0 0 0 0 1 0 0 0 0 0 3 107 0 0 0 0 0 2 0 0 0 0 0 3 108 0 0 0 0 0 3 0 0 0 0 0 3 TEST03: SPARSE_GRID_HERMITE 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: 0 3.141593 Grid points: 0 0.000000 0.000000 TEST03: SPARSE_GRID_HERMITE 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: 0 -0.000574 1 -0.032209 2 -0.251456 3 2.478402 4 -0.251456 5 -0.032209 6 -0.000574 7 -0.087266 8 -0.109706 9 -0.087266 10 -0.109706 11 -1.396263 12 -0.109706 13 -0.087266 14 -0.109706 15 -0.087266 16 -0.000574 17 -0.032209 18 -0.251456 19 -1.436157 20 -0.251456 21 -0.032209 22 -0.000574 23 0.000000 24 0.000002 25 0.000177 26 0.004924 27 0.054556 28 0.280914 29 0.730302 30 0.730302 31 0.280914 32 0.054556 33 0.004924 34 0.000177 35 0.000002 36 0.000000 37 0.000287 38 0.016104 39 0.125728 40 0.125728 41 0.016104 42 0.000287 43 0.000287 44 0.016104 45 0.125728 46 0.125728 47 0.016104 48 0.000287 49 0.000287 50 0.000287 51 0.016104 52 0.016104 53 0.125728 54 0.125728 55 0.125728 56 0.125728 57 0.016104 58 0.016104 59 0.000287 60 0.000287 61 0.000000 62 0.000002 63 0.000177 64 0.004924 65 0.054556 66 0.280914 67 0.730302 68 0.730302 69 0.280914 70 0.054556 71 0.004924 72 0.000177 73 0.000002 74 0.000000 Grid points: 0 -2.651961 0.000000 1 -1.673552 0.000000 2 -0.816288 0.000000 3 0.000000 0.000000 4 0.816288 0.000000 5 1.673552 0.000000 6 2.651961 0.000000 7 -1.224745 -1.224745 8 0.000000 -1.224745 9 1.224745 -1.224745 10 -1.224745 0.000000 11 0.000000 0.000000 12 1.224745 0.000000 13 -1.224745 1.224745 14 0.000000 1.224745 15 1.224745 1.224745 16 0.000000 -2.651961 17 0.000000 -1.673552 18 0.000000 -0.816288 19 0.000000 0.000000 20 0.000000 0.816288 21 0.000000 1.673552 22 0.000000 2.651961 23 -4.499991 0.000000 24 -3.669950 0.000000 25 -2.967167 0.000000 26 -2.325732 0.000000 27 -1.719993 0.000000 28 -1.136116 0.000000 29 -0.565070 0.000000 30 0.565070 0.000000 31 1.136116 0.000000 32 1.719993 0.000000 33 2.325732 0.000000 34 2.967167 0.000000 35 3.669950 0.000000 36 4.499991 0.000000 37 -2.651961 -1.224745 38 -1.673552 -1.224745 39 -0.816288 -1.224745 40 0.816288 -1.224745 41 1.673552 -1.224745 42 2.651961 -1.224745 43 -2.651961 1.224745 44 -1.673552 1.224745 45 -0.816288 1.224745 46 0.816288 1.224745 47 1.673552 1.224745 48 2.651961 1.224745 49 -1.224745 -2.651961 50 1.224745 -2.651961 51 -1.224745 -1.673552 52 1.224745 -1.673552 53 -1.224745 -0.816288 54 1.224745 -0.816288 55 -1.224745 0.816288 56 1.224745 0.816288 57 -1.224745 1.673552 58 1.224745 1.673552 59 -1.224745 2.651961 60 1.224745 2.651961 61 0.000000 -4.499991 62 0.000000 -3.669950 63 0.000000 -2.967167 64 0.000000 -2.325732 65 0.000000 -1.719993 66 0.000000 -1.136116 67 0.000000 -0.565070 68 0.000000 0.565070 69 0.000000 1.136116 70 0.000000 1.719993 71 0.000000 2.325732 72 0.000000 2.967167 73 0.000000 3.669950 74 0.000000 4.499991 TEST03: SPARSE_GRID_HERMITE 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: 0 -0.000000 1 -0.000001 2 -0.000059 3 -0.001641 4 -0.018185 5 -0.093638 6 -0.243434 7 2.392808 8 -0.243434 9 -0.093638 10 -0.018185 11 -0.001641 12 -0.000059 13 -0.000001 14 -0.000000 15 -0.000287 16 -0.016104 17 -0.125728 18 -0.072719 19 -0.125728 20 -0.016104 21 -0.000287 22 -0.000361 23 -0.020246 24 -0.158058 25 -0.957438 26 -0.158058 27 -0.020246 28 -0.000361 29 -0.000287 30 -0.016104 31 -0.125728 32 -0.072719 33 -0.125728 34 -0.016104 35 -0.000287 36 -0.000287 37 -0.000361 38 -0.000287 39 -0.016104 40 -0.020246 41 -0.016104 42 -0.125728 43 -0.158058 44 -0.125728 45 -0.072719 46 -0.957438 47 -0.072719 48 -0.125728 49 -0.158058 50 -0.125728 51 -0.016104 52 -0.020246 53 -0.016104 54 -0.000287 55 -0.000361 56 -0.000287 57 -0.000000 58 -0.000001 59 -0.000059 60 -0.001641 61 -0.018185 62 -0.093638 63 -0.243434 64 -0.999842 65 -0.243434 66 -0.093638 67 -0.018185 68 -0.001641 69 -0.000059 70 -0.000001 71 -0.000000 72 0.000000 73 0.000000 74 0.000000 75 0.000000 76 0.000000 77 0.000000 78 0.000001 79 0.000019 80 0.000247 81 0.002187 82 0.013263 83 0.056448 84 0.171428 85 0.375996 86 0.600459 87 0.600459 88 0.375996 89 0.171428 90 0.056448 91 0.013263 92 0.002187 93 0.000247 94 0.000019 95 0.000001 96 0.000000 97 0.000000 98 0.000000 99 0.000000 100 0.000000 101 0.000000 102 0.000000 103 0.000000 104 0.000030 105 0.000821 106 0.009093 107 0.046819 108 0.121717 109 0.121717 110 0.046819 111 0.009093 112 0.000821 113 0.000030 114 0.000000 115 0.000000 116 0.000000 117 0.000000 118 0.000030 119 0.000821 120 0.009093 121 0.046819 122 0.121717 123 0.121717 124 0.046819 125 0.009093 126 0.000821 127 0.000030 128 0.000000 129 0.000000 130 0.000001 131 0.000053 132 0.000414 133 0.000414 134 0.000053 135 0.000001 136 0.000053 137 0.002972 138 0.023202 139 0.023202 140 0.002972 141 0.000053 142 0.000414 143 0.023202 144 0.181142 145 0.181142 146 0.023202 147 0.000414 148 0.000414 149 0.023202 150 0.181142 151 0.181142 152 0.023202 153 0.000414 154 0.000053 155 0.002972 156 0.023202 157 0.023202 158 0.002972 159 0.000053 160 0.000001 161 0.000053 162 0.000414 163 0.000414 164 0.000053 165 0.000001 166 0.000000 167 0.000000 168 0.000000 169 0.000000 170 0.000030 171 0.000030 172 0.000821 173 0.000821 174 0.009093 175 0.009093 176 0.046819 177 0.046819 178 0.121717 179 0.121717 180 0.121717 181 0.121717 182 0.046819 183 0.046819 184 0.009093 185 0.009093 186 0.000821 187 0.000821 188 0.000030 189 0.000030 190 0.000000 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 0.000001 201 0.000019 202 0.000247 203 0.002187 204 0.013263 205 0.056448 206 0.171428 207 0.375996 208 0.600459 209 0.600459 210 0.375996 211 0.171428 212 0.056448 213 0.013263 214 0.002187 215 0.000247 216 0.000019 217 0.000001 218 0.000000 219 0.000000 220 0.000000 221 0.000000 222 0.000000 223 0.000000 Grid points: 0 -4.499991 0.000000 1 -3.669950 0.000000 2 -2.967167 0.000000 3 -2.325732 0.000000 4 -1.719993 0.000000 5 -1.136116 0.000000 6 -0.565070 0.000000 7 0.000000 0.000000 8 0.565070 0.000000 9 1.136116 0.000000 10 1.719993 0.000000 11 2.325732 0.000000 12 2.967167 0.000000 13 3.669950 0.000000 14 4.499991 0.000000 15 -2.651961 -1.224745 16 -1.673552 -1.224745 17 -0.816288 -1.224745 18 0.000000 -1.224745 19 0.816288 -1.224745 20 1.673552 -1.224745 21 2.651961 -1.224745 22 -2.651961 0.000000 23 -1.673552 0.000000 24 -0.816288 0.000000 25 0.000000 0.000000 26 0.816288 0.000000 27 1.673552 0.000000 28 2.651961 0.000000 29 -2.651961 1.224745 30 -1.673552 1.224745 31 -0.816288 1.224745 32 0.000000 1.224745 33 0.816288 1.224745 34 1.673552 1.224745 35 2.651961 1.224745 36 -1.224745 -2.651961 37 0.000000 -2.651961 38 1.224745 -2.651961 39 -1.224745 -1.673552 40 0.000000 -1.673552 41 1.224745 -1.673552 42 -1.224745 -0.816288 43 0.000000 -0.816288 44 1.224745 -0.816288 45 -1.224745 0.000000 46 0.000000 0.000000 47 1.224745 0.000000 48 -1.224745 0.816288 49 0.000000 0.816288 50 1.224745 0.816288 51 -1.224745 1.673552 52 0.000000 1.673552 53 1.224745 1.673552 54 -1.224745 2.651961 55 0.000000 2.651961 56 1.224745 2.651961 57 0.000000 -4.499991 58 0.000000 -3.669950 59 0.000000 -2.967167 60 0.000000 -2.325732 61 0.000000 -1.719993 62 0.000000 -1.136116 63 0.000000 -0.565070 64 0.000000 0.000000 65 0.000000 0.565070 66 0.000000 1.136116 67 0.000000 1.719993 68 0.000000 2.325732 69 0.000000 2.967167 70 0.000000 3.669950 71 0.000000 4.499991 72 -6.995680 0.000000 73 -6.275079 0.000000 74 -5.673961 0.000000 75 -5.133596 0.000000 76 -4.631560 0.000000 77 -4.156272 0.000000 78 -3.700743 0.000000 79 -3.260321 0.000000 80 -2.831680 0.000000 81 -2.412318 0.000000 82 -2.000259 0.000000 83 -1.593886 0.000000 84 -1.191827 0.000000 85 -0.792877 0.000000 86 -0.395943 0.000000 87 0.395943 0.000000 88 0.792877 0.000000 89 1.191827 0.000000 90 1.593886 0.000000 91 2.000259 0.000000 92 2.412318 0.000000 93 2.831680 0.000000 94 3.260321 0.000000 95 3.700743 0.000000 96 4.156272 0.000000 97 4.631560 0.000000 98 5.133596 0.000000 99 5.673961 0.000000 100 6.275079 0.000000 101 6.995680 0.000000 102 -4.499991 -1.224745 103 -3.669950 -1.224745 104 -2.967167 -1.224745 105 -2.325732 -1.224745 106 -1.719993 -1.224745 107 -1.136116 -1.224745 108 -0.565070 -1.224745 109 0.565070 -1.224745 110 1.136116 -1.224745 111 1.719993 -1.224745 112 2.325732 -1.224745 113 2.967167 -1.224745 114 3.669950 -1.224745 115 4.499991 -1.224745 116 -4.499991 1.224745 117 -3.669950 1.224745 118 -2.967167 1.224745 119 -2.325732 1.224745 120 -1.719993 1.224745 121 -1.136116 1.224745 122 -0.565070 1.224745 123 0.565070 1.224745 124 1.136116 1.224745 125 1.719993 1.224745 126 2.325732 1.224745 127 2.967167 1.224745 128 3.669950 1.224745 129 4.499991 1.224745 130 -2.651961 -2.651961 131 -1.673552 -2.651961 132 -0.816288 -2.651961 133 0.816288 -2.651961 134 1.673552 -2.651961 135 2.651961 -2.651961 136 -2.651961 -1.673552 137 -1.673552 -1.673552 138 -0.816288 -1.673552 139 0.816288 -1.673552 140 1.673552 -1.673552 141 2.651961 -1.673552 142 -2.651961 -0.816288 143 -1.673552 -0.816288 144 -0.816288 -0.816288 145 0.816288 -0.816288 146 1.673552 -0.816288 147 2.651961 -0.816288 148 -2.651961 0.816288 149 -1.673552 0.816288 150 -0.816288 0.816288 151 0.816288 0.816288 152 1.673552 0.816288 153 2.651961 0.816288 154 -2.651961 1.673552 155 -1.673552 1.673552 156 -0.816288 1.673552 157 0.816288 1.673552 158 1.673552 1.673552 159 2.651961 1.673552 160 -2.651961 2.651961 161 -1.673552 2.651961 162 -0.816288 2.651961 163 0.816288 2.651961 164 1.673552 2.651961 165 2.651961 2.651961 166 -1.224745 -4.499991 167 1.224745 -4.499991 168 -1.224745 -3.669950 169 1.224745 -3.669950 170 -1.224745 -2.967167 171 1.224745 -2.967167 172 -1.224745 -2.325732 173 1.224745 -2.325732 174 -1.224745 -1.719993 175 1.224745 -1.719993 176 -1.224745 -1.136116 177 1.224745 -1.136116 178 -1.224745 -0.565070 179 1.224745 -0.565070 180 -1.224745 0.565070 181 1.224745 0.565070 182 -1.224745 1.136116 183 1.224745 1.136116 184 -1.224745 1.719993 185 1.224745 1.719993 186 -1.224745 2.325732 187 1.224745 2.325732 188 -1.224745 2.967167 189 1.224745 2.967167 190 -1.224745 3.669950 191 1.224745 3.669950 192 -1.224745 4.499991 193 1.224745 4.499991 194 0.000000 -6.995680 195 0.000000 -6.275079 196 0.000000 -5.673961 197 0.000000 -5.133596 198 0.000000 -4.631560 199 0.000000 -4.156272 200 0.000000 -3.700743 201 0.000000 -3.260321 202 0.000000 -2.831680 203 0.000000 -2.412318 204 0.000000 -2.000259 205 0.000000 -1.593886 206 0.000000 -1.191827 207 0.000000 -0.792877 208 0.000000 -0.395943 209 0.000000 0.395943 210 0.000000 0.792877 211 0.000000 1.191827 212 0.000000 1.593886 213 0.000000 2.000259 214 0.000000 2.412318 215 0.000000 2.831680 216 0.000000 3.260321 217 0.000000 3.700743 218 0.000000 4.156272 219 0.000000 4.631560 220 0.000000 5.133596 221 0.000000 5.673961 222 0.000000 6.275079 223 0.000000 6.995680 TEST03: SPARSE_GRID_HERMITE 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: 0 5.568328 Grid points: 0 0.000000 0.000000 0.000000 TEST03: SPARSE_GRID_HERMITE 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: 0 -1.643983 1 -0.618703 2 -0.618703 3 -0.618703 4 -0.618703 5 -0.618703 6 -0.618703 7 0.003053 8 0.171266 9 1.337085 10 1.337085 11 0.171266 12 0.003053 13 0.154676 14 0.154676 15 0.154676 16 0.154676 17 0.003053 18 0.171266 19 1.337085 20 1.337085 21 0.171266 22 0.003053 23 0.154676 24 0.154676 25 0.154676 26 0.154676 27 0.154676 28 0.154676 29 0.154676 30 0.154676 31 0.003053 32 0.171266 33 1.337085 34 1.337085 35 0.171266 36 0.003053 Grid points: 0 0.000000 0.000000 0.000000 1 -1.224745 0.000000 0.000000 2 1.224745 0.000000 0.000000 3 0.000000 -1.224745 0.000000 4 0.000000 1.224745 0.000000 5 0.000000 0.000000 -1.224745 6 0.000000 0.000000 1.224745 7 -2.651961 0.000000 0.000000 8 -1.673552 0.000000 0.000000 9 -0.816288 0.000000 0.000000 10 0.816288 0.000000 0.000000 11 1.673552 0.000000 0.000000 12 2.651961 0.000000 0.000000 13 -1.224745 -1.224745 0.000000 14 1.224745 -1.224745 0.000000 15 -1.224745 1.224745 0.000000 16 1.224745 1.224745 0.000000 17 0.000000 -2.651961 0.000000 18 0.000000 -1.673552 0.000000 19 0.000000 -0.816288 0.000000 20 0.000000 0.816288 0.000000 21 0.000000 1.673552 0.000000 22 0.000000 2.651961 0.000000 23 -1.224745 0.000000 -1.224745 24 1.224745 0.000000 -1.224745 25 -1.224745 0.000000 1.224745 26 1.224745 0.000000 1.224745 27 0.000000 -1.224745 -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 0.000000 -2.651961 32 0.000000 0.000000 -1.673552 33 0.000000 0.000000 -0.816288 34 0.000000 0.000000 0.816288 35 0.000000 0.000000 1.673552 36 0.000000 0.000000 2.651961 TEST04: Compute the weights of a Gauss-Hermite sparse grid . As a simple test, sum these weights. They should sum to exactly 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 TEST04: Compute the weights of a Gauss-Hermite sparse grid . As a simple test, sum these weights. They should sum to exactly 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 TEST04: Compute the weights of a Gauss-Hermite sparse grid . As a simple test, sum these weights. They should sum to exactly 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 TEST04: Compute the weights of a Gauss-Hermite sparse grid . As a simple test, sum these weights. They should sum to exactly 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 TEST04: Compute the weights of a Gauss-Hermite sparse grid . As a simple test, sum these weights. They should sum to exactly 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 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 be checked is DEGREE_MAX = 3 Number of unique points in the grid = 1 Error Total Monomial Degree Exponents 2.8e-16 0 0 0 0.0e+00 1 1 0 0.0e+00 1 0 1 1.0e+00 2 2 0 0.0e+00 2 1 1 1.0e+00 2 0 2 0.0e+00 3 3 0 0.0e+00 3 2 1 0.0e+00 3 1 2 0.0e+00 3 0 3 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 be checked is DEGREE_MAX = 5 Number of unique points in the grid = 5 Error Total Monomial Degree Exponents 4.2e-16 0 0 0 0.0e+00 1 1 0 0.0e+00 1 0 1 1.4e-16 2 2 0 0.0e+00 2 1 1 1.4e-16 2 0 2 0.0e+00 3 3 0 0.0e+00 3 2 1 0.0e+00 3 1 2 0.0e+00 3 0 3 1.9e-16 4 4 0 0.0e+00 4 3 1 1.0e+00 4 2 2 0.0e+00 4 1 3 1.9e-16 4 0 4 0.0e+00 5 5 0 0.0e+00 5 4 1 0.0e+00 5 3 2 0.0e+00 5 2 3 0.0e+00 5 1 4 0.0e+00 5 0 5 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 be checked is DEGREE_MAX = 7 Number of unique points in the grid = 22 Error Total Monomial Degree Exponents 0.0e+00 0 0 0 2.8e-17 1 1 0 2.1e-17 1 0 1 4.2e-16 2 2 0 0.0e+00 2 1 1 1.4e-16 2 0 2 8.3e-17 3 3 0 0.0e+00 3 2 1 0.0e+00 3 1 2 6.9e-17 3 0 3 1.9e-16 4 4 0 0.0e+00 4 3 1 1.4e-16 4 2 2 0.0e+00 4 1 3 0.0e+00 4 0 4 2.8e-17 5 5 0 0.0e+00 5 4 1 0.0e+00 5 3 2 0.0e+00 5 2 3 0.0e+00 5 1 4 2.8e-17 5 0 5 3.0e-16 6 6 0 0.0e+00 6 5 1 3.8e-16 6 4 2 0.0e+00 6 3 3 3.8e-16 6 2 4 0.0e+00 6 1 5 3.0e-16 6 0 6 4.4e-16 7 7 0 0.0e+00 7 6 1 0.0e+00 7 5 2 0.0e+00 7 4 3 0.0e+00 7 3 4 0.0e+00 7 2 5 0.0e+00 7 1 6 4.4e-16 7 0 7 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 be checked is DEGREE_MAX = 9 Number of unique points in the grid = 75 Error Total Monomial Degree Exponents 1.4e-16 0 0 0 5.6e-17 1 1 0 8.4e-17 1 0 1 0.0e+00 2 2 0 0.0e+00 2 1 1 0.0e+00 2 0 2 8.3e-17 3 3 0 3.9e-17 3 2 1 0.0e+00 3 1 2 2.8e-17 3 0 3 3.8e-16 4 4 0 2.8e-17 4 3 1 1.4e-16 4 2 2 1.4e-17 4 1 3 1.9e-16 4 0 4 5.6e-17 5 5 0 2.4e-17 5 4 1 0.0e+00 5 3 2 2.1e-17 5 2 3 0.0e+00 5 1 4 6.9e-17 5 0 5 6.0e-16 6 6 0 0.0e+00 6 5 1 1.9e-16 6 4 2 0.0e+00 6 3 3 0.0e+00 6 2 4 5.6e-17 6 1 5 3.0e-16 6 0 6 2.2e-16 7 7 0 6.1e-17 7 6 1 5.6e-17 7 5 2 1.4e-17 7 4 3 2.8e-17 7 3 4 1.4e-16 7 2 5 0.0e+00 7 1 6 1.3e-16 7 0 7 1.7e-16 8 8 0 1.7e-16 8 7 1 3.0e-16 8 6 2 2.8e-17 8 5 3 6.3e-16 8 4 4 5.6e-17 8 3 5 0.0e+00 8 2 6 0.0e+00 8 1 7 1.7e-16 8 0 8 6.7e-16 9 9 0 1.3e-16 9 8 1 0.0e+00 9 7 2 6.2e-17 9 6 3 0.0e+00 9 5 4 2.8e-17 9 4 5 0.0e+00 9 3 6 0.0e+00 9 2 7 0.0e+00 9 1 8 7.6e-16 9 0 9 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 be checked is DEGREE_MAX = 22 Number of unique points in the grid = 224 Error Total Monomial Degree Exponents 6.2e-12 0 0 0 1.4e-16 1 1 0 1.1e-16 1 0 1 3.1e-12 2 2 0 2.8e-17 2 1 1 3.1e-12 2 0 2 5.6e-17 3 3 0 4.1e-17 3 2 1 1.4e-17 3 1 2 1.7e-16 3 0 3 3.1e-12 4 4 0 2.8e-17 4 3 1 1.4e-16 4 2 2 1.4e-17 4 1 3 3.1e-12 4 0 4 5.6e-17 5 5 0 2.1e-18 5 4 1 1.4e-17 5 3 2 1.8e-17 5 2 3 2.8e-17 5 1 4 3.1e-17 5 0 5 3.1e-12 6 6 0 2.8e-17 6 5 1 7.5e-16 6 4 2 2.8e-17 6 3 3 7.5e-16 6 2 4 2.8e-17 6 1 5 3.1e-12 6 0 6 2.2e-16 7 7 0 1.5e-16 7 6 1 1.4e-16 7 5 2 6.2e-17 7 4 3 5.6e-17 7 3 4 5.8e-17 7 2 5 0.0e+00 7 1 6 1.3e-16 7 0 7 3.1e-12 8 8 0 2.8e-16 8 7 1 1.4e-15 8 6 2 2.8e-17 8 5 3 6.3e-16 8 4 4 5.6e-17 8 3 5 1.4e-15 8 2 6 1.1e-16 8 1 7 3.1e-12 8 0 8 0.0e+00 9 9 0 1.3e-16 9 8 1 1.4e-16 9 7 2 1.7e-16 9 6 3 2.8e-17 9 5 4 2.0e-17 9 4 5 0.0e+00 9 3 6 7.4e-16 9 2 7 1.1e-16 9 1 8 3.9e-16 9 0 9 3.1e-12 10 10 0 8.9e-16 10 9 1 3.4e-16 10 8 2 0.0e+00 10 7 3 0.0e+00 10 6 4 2.2e-16 10 5 5 8.0e-16 10 4 6 0.0e+00 10 3 7 1.7e-16 10 2 8 0.0e+00 10 1 9 3.1e-12 10 0 10 3.6e-15 11 11 0 4.2e-16 11 10 1 3.3e-16 11 9 2 9.3e-18 11 8 3 1.7e-16 11 7 4 5.4e-16 11 6 5 0.0e+00 11 5 6 2.1e-17 11 4 7 2.2e-16 11 3 8 7.4e-16 11 2 9 0.0e+00 11 1 10 1.2e-14 11 0 11 3.1e-12 12 12 0 0.0e+00 12 11 1 4.6e-16 12 10 2 8.9e-16 12 9 3 2.3e-16 12 8 4 2.2e-16 12 7 5 9.7e-16 12 6 6 2.2e-16 12 5 7 4.6e-16 12 4 8 4.4e-16 12 3 9 6.1e-16 12 2 10 1.8e-15 12 1 11 3.1e-12 12 0 12 5.7e-14 13 13 0 1.5e-14 13 12 1 3.6e-15 13 11 2 3.1e-16 13 10 3 8.9e-16 13 9 4 7.3e-16 13 8 5 2.2e-16 13 7 6 8.4e-16 13 6 7 0.0e+00 13 5 8 2.3e-15 13 4 9 8.9e-16 13 3 10 3.0e-15 13 2 11 0.0e+00 13 1 12 6.0e-14 13 0 13 3.1e-12 14 14 0 1.4e-14 14 13 1 1.4e-15 14 12 2 7.0e-15 14 11 3 8.2e-16 14 10 4 8.9e-16 14 9 5 1.8e-16 14 8 6 4.4e-16 14 7 7 1.8e-16 14 6 8 0.0e+00 14 5 9 1.0e-15 14 4 10 0.0e+00 14 3 11 4.5e-16 14 2 12 1.4e-14 14 1 13 3.1e-12 14 0 14 3.4e-13 15 15 0 1.2e-13 15 14 1 1.5e-14 15 13 2 2.1e-14 15 12 3 3.6e-15 15 11 4 8.8e-15 15 10 5 2.2e-15 15 9 6 4.6e-16 15 8 7 2.2e-15 15 7 8 3.3e-15 15 6 9 0.0e+00 15 5 10 2.6e-15 15 4 11 7.1e-15 15 3 12 5.1e-15 15 2 13 0.0e+00 15 1 14 4.0e-13 15 0 15 3.1e-12 16 16 0 0.0e+00 16 15 1 1.5e-15 16 14 2 4.3e-14 16 13 3 3.0e-16 16 12 4 2.7e-15 16 11 5 3.3e-16 16 10 6 8.9e-16 16 9 7 4.2e-16 16 8 8 1.8e-15 16 7 9 0.0e+00 16 6 10 0.0e+00 16 5 11 5.9e-16 16 4 12 4.3e-14 16 3 13 1.1e-15 16 2 14 5.7e-14 16 1 15 3.1e-12 16 0 16 7.4e-12 17 17 0 2.7e-13 17 16 1 1.1e-13 17 15 2 1.3e-14 17 14 3 3.0e-14 17 13 4 1.4e-14 17 12 5 7.1e-15 17 11 6 8.4e-15 17 10 7 8.9e-15 17 9 8 6.1e-16 17 8 9 0.0e+00 17 7 10 2.0e-14 17 6 11 7.1e-15 17 5 12 1.5e-14 17 4 13 2.8e-14 17 3 14 1.1e-13 17 2 15 0.0e+00 17 1 16 6.8e-12 17 0 17 3.1e-12 18 18 0 0.0e+00 18 17 1 2.9e-16 18 16 2 0.0e+00 18 15 3 3.7e-16 18 14 4 2.8e-14 18 13 5 7.1e-16 18 12 6 7.1e-15 18 11 7 7.5e-16 18 10 8 7.1e-15 18 9 9 5.6e-16 18 8 10 2.1e-14 18 7 11 3.6e-16 18 6 12 0.0e+00 18 5 13 9.1e-16 18 4 14 0.0e+00 18 3 15 2.9e-16 18 2 16 0.0e+00 18 1 17 3.1e-12 18 0 18 7.3e-12 19 19 0 4.9e-12 19 18 1 9.1e-13 19 17 2 4.2e-14 19 16 3 2.3e-13 19 15 4 2.8e-14 19 14 5 0.0e+00 19 13 6 1.0e-13 19 12 7 1.4e-14 19 11 8 9.8e-14 19 10 9 0.0e+00 19 9 10 6.2e-15 19 8 11 1.4e-14 19 7 12 1.7e-13 19 6 13 5.7e-14 19 5 14 2.1e-13 19 4 15 0.0e+00 19 3 16 3.7e-12 19 2 17 1.8e-12 19 1 18 8.4e-12 19 0 19 3.1e-12 20 20 0 7.3e-12 20 19 1 2.8e-16 20 18 2 4.5e-13 20 17 3 7.8e-16 20 16 4 2.3e-13 20 15 5 1.5e-02 20 14 6 0.0e+00 20 13 7 1.1e-15 20 12 8 5.7e-14 20 11 9 8.3e-16 20 10 10 0.0e+00 20 9 11 4.1e-16 20 8 12 5.7e-14 20 7 13 1.5e-02 20 6 14 2.3e-13 20 5 15 1.2e-15 20 4 16 9.1e-13 20 3 17 1.4e-16 20 2 18 7.3e-12 20 1 19 3.1e-12 20 0 20 1.7e-10 21 21 0 4.1e-12 21 20 1 3.6e-12 21 19 2 5.5e-12 21 18 3 9.1e-13 21 17 4 1.4e-12 21 16 5 4.5e-13 21 15 6 2.3e-13 21 14 7 1.1e-13 21 13 8 2.2e-13 21 12 9 0.0e+00 21 11 10 4.8e-13 21 10 11 1.1e-13 21 9 12 5.3e-13 21 8 13 2.3e-13 21 7 14 3.6e-13 21 6 15 0.0e+00 21 5 16 3.3e-12 21 4 17 0.0e+00 21 3 18 1.2e-11 21 2 19 0.0e+00 21 1 20 2.7e-10 21 0 21 3.1e-12 22 22 0 5.8e-11 22 21 1 9.3e-16 22 20 2 3.6e-12 22 19 3 1.8e-16 22 18 4 1.8e-12 22 17 5 5.7e-02 22 16 6 2.3e-13 22 15 7 2.8e-02 22 14 8 2.3e-13 22 13 9 1.1e-15 22 12 10 0.0e+00 22 11 11 0.0e+00 22 10 12 2.3e-13 22 9 13 2.8e-02 22 8 14 0.0e+00 22 7 15 5.7e-02 22 6 16 0.0e+00 22 5 17 7.3e-16 22 4 18 0.0e+00 22 3 19 5.8e-16 22 2 20 5.8e-11 22 1 21 3.1e-12 22 0 22 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 be checked is DEGREE_MAX = 11 Number of unique points in the grid = 224 Error Total Monomial Degree Exponents 6.2e-12 0 0 0 1.4e-16 1 1 0 1.1e-16 1 0 1 3.1e-12 2 2 0 2.8e-17 2 1 1 3.1e-12 2 0 2 5.6e-17 3 3 0 4.1e-17 3 2 1 1.4e-17 3 1 2 1.7e-16 3 0 3 3.1e-12 4 4 0 2.8e-17 4 3 1 1.4e-16 4 2 2 1.4e-17 4 1 3 3.1e-12 4 0 4 5.6e-17 5 5 0 2.1e-18 5 4 1 1.4e-17 5 3 2 1.8e-17 5 2 3 2.8e-17 5 1 4 3.1e-17 5 0 5 3.1e-12 6 6 0 2.8e-17 6 5 1 7.5e-16 6 4 2 2.8e-17 6 3 3 7.5e-16 6 2 4 2.8e-17 6 1 5 3.1e-12 6 0 6 2.2e-16 7 7 0 1.5e-16 7 6 1 1.4e-16 7 5 2 6.2e-17 7 4 3 5.6e-17 7 3 4 5.8e-17 7 2 5 0.0e+00 7 1 6 1.3e-16 7 0 7 3.1e-12 8 8 0 2.8e-16 8 7 1 1.4e-15 8 6 2 2.8e-17 8 5 3 6.3e-16 8 4 4 5.6e-17 8 3 5 1.4e-15 8 2 6 1.1e-16 8 1 7 3.1e-12 8 0 8 0.0e+00 9 9 0 1.3e-16 9 8 1 1.4e-16 9 7 2 1.7e-16 9 6 3 2.8e-17 9 5 4 2.0e-17 9 4 5 0.0e+00 9 3 6 7.4e-16 9 2 7 1.1e-16 9 1 8 3.9e-16 9 0 9 3.1e-12 10 10 0 8.9e-16 10 9 1 3.4e-16 10 8 2 0.0e+00 10 7 3 0.0e+00 10 6 4 2.2e-16 10 5 5 8.0e-16 10 4 6 0.0e+00 10 3 7 1.7e-16 10 2 8 0.0e+00 10 1 9 3.1e-12 10 0 10 3.6e-15 11 11 0 4.2e-16 11 10 1 3.3e-16 11 9 2 9.3e-18 11 8 3 1.7e-16 11 7 4 5.4e-16 11 6 5 0.0e+00 11 5 6 2.1e-17 11 4 7 2.2e-16 11 3 8 7.4e-16 11 2 9 0.0e+00 11 1 10 1.2e-14 11 0 11 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 be checked is DEGREE_MAX = 2 Number of unique points in the grid = 1 Error Total Monomial Degree Exponents 4.8e-16 0 0 0 0 0.0e+00 1 1 0 0 0.0e+00 1 0 1 0 0.0e+00 1 0 0 1 1.0e+00 2 2 0 0 0.0e+00 2 1 1 0 1.0e+00 2 0 2 0 0.0e+00 2 1 0 1 0.0e+00 2 0 1 1 1.0e+00 2 0 0 2 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 be checked is DEGREE_MAX = 4 Number of unique points in the grid = 7 Error Total Monomial Degree Exponents 3.2e-16 0 0 0 0 0.0e+00 1 1 0 0 0.0e+00 1 0 1 0 0.0e+00 1 0 0 1 3.2e-16 2 2 0 0 0.0e+00 2 1 1 0 3.2e-16 2 0 2 0 0.0e+00 2 1 0 1 0.0e+00 2 0 1 1 3.2e-16 2 0 0 2 0.0e+00 3 3 0 0 0.0e+00 3 2 1 0 0.0e+00 3 1 2 0 0.0e+00 3 0 3 0 0.0e+00 3 2 0 1 0.0e+00 3 1 1 1 0.0e+00 3 0 2 1 0.0e+00 3 1 0 2 0.0e+00 3 0 1 2 0.0e+00 3 0 0 3 2.1e-16 4 4 0 0 0.0e+00 4 3 1 0 1.0e+00 4 2 2 0 0.0e+00 4 1 3 0 2.1e-16 4 0 4 0 0.0e+00 4 3 0 1 0.0e+00 4 2 1 1 0.0e+00 4 1 2 1 0.0e+00 4 0 3 1 1.0e+00 4 2 0 2 0.0e+00 4 1 1 2 1.0e+00 4 0 2 2 0.0e+00 4 1 0 3 0.0e+00 4 0 1 3 0.0e+00 4 0 0 4 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 be checked is DEGREE_MAX = 6 Number of unique points in the grid = 37 Error Total Monomial Degree Exponents 3.2e-16 0 0 0 0 8.3e-17 1 1 0 0 8.3e-17 1 0 1 0 8.2e-17 1 0 0 1 0.0e+00 2 2 0 0 0.0e+00 2 1 1 0 0.0e+00 2 0 2 0 0.0e+00 2 1 0 1 0.0e+00 2 0 1 1 1.6e-16 2 0 0 2 5.6e-17 3 3 0 0 0.0e+00 3 2 1 0 0.0e+00 3 1 2 0 5.6e-17 3 0 3 0 0.0e+00 3 2 0 1 0.0e+00 3 1 1 1 0.0e+00 3 0 2 1 0.0e+00 3 1 0 2 0.0e+00 3 0 1 2 4.9e-17 3 0 0 3 2.1e-16 4 4 0 0 0.0e+00 4 3 1 0 1.6e-16 4 2 2 0 0.0e+00 4 1 3 0 2.1e-16 4 0 4 0 0.0e+00 4 3 0 1 0.0e+00 4 2 1 1 0.0e+00 4 1 2 1 0.0e+00 4 0 3 1 1.6e-16 4 2 0 2 0.0e+00 4 1 1 2 1.6e-16 4 0 2 2 0.0e+00 4 1 0 3 0.0e+00 4 0 1 3 0.0e+00 4 0 0 4 5.6e-17 5 5 0 0 0.0e+00 5 4 1 0 0.0e+00 5 3 2 0 0.0e+00 5 2 3 0 0.0e+00 5 1 4 0 5.6e-17 5 0 5 0 0.0e+00 5 4 0 1 0.0e+00 5 3 1 1 0.0e+00 5 2 2 1 0.0e+00 5 1 3 1 0.0e+00 5 0 4 1 0.0e+00 5 3 0 2 0.0e+00 5 2 1 2 0.0e+00 5 1 2 2 0.0e+00 5 0 3 2 0.0e+00 5 2 0 3 0.0e+00 5 1 1 3 0.0e+00 5 0 2 3 0.0e+00 5 1 0 4 0.0e+00 5 0 1 4 5.6e-17 5 0 0 5 3.4e-16 6 6 0 0 0.0e+00 6 5 1 0 4.3e-16 6 4 2 0 0.0e+00 6 3 3 0 4.3e-16 6 2 4 0 0.0e+00 6 1 5 0 3.4e-16 6 0 6 0 0.0e+00 6 5 0 1 0.0e+00 6 4 1 1 0.0e+00 6 3 2 1 0.0e+00 6 2 3 1 0.0e+00 6 1 4 1 0.0e+00 6 0 5 1 4.3e-16 6 4 0 2 0.0e+00 6 3 1 2 1.0e+00 6 2 2 2 0.0e+00 6 1 3 2 4.3e-16 6 0 4 2 0.0e+00 6 3 0 3 0.0e+00 6 2 1 3 0.0e+00 6 1 2 3 0.0e+00 6 0 3 3 2.1e-16 6 2 0 4 0.0e+00 6 1 1 4 2.1e-16 6 0 2 4 0.0e+00 6 1 0 5 0.0e+00 6 0 1 5 1.7e-16 6 0 0 6 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 be checked is DEGREE_MAX = 8 Number of unique points in the grid = 161 Error Total Monomial Degree Exponents 1.6e-16 0 0 0 0 5.6e-17 1 1 0 0 5.6e-17 1 0 1 0 1.6e-16 1 0 0 1 0.0e+00 2 2 0 0 2.8e-17 2 1 1 0 3.2e-16 2 0 2 0 2.8e-17 2 1 0 1 2.8e-17 2 0 1 1 1.3e-15 2 0 0 2 1.1e-16 3 3 0 0 1.4e-17 3 2 1 0 2.8e-17 3 1 2 0 1.1e-16 3 0 3 0 4.3e-17 3 2 0 1 0.0e+00 3 1 1 1 4.3e-17 3 0 2 1 0.0e+00 3 1 0 2 0.0e+00 3 0 1 2 2.3e-16 3 0 0 3 2.1e-16 4 4 0 0 0.0e+00 4 3 1 0 1.6e-16 4 2 2 0 2.8e-17 4 1 3 0 8.5e-16 4 0 4 0 0.0e+00 4 3 0 1 0.0e+00 4 2 1 1 0.0e+00 4 1 2 1 0.0e+00 4 0 3 1 1.6e-16 4 2 0 2 0.0e+00 4 1 1 2 3.2e-16 4 0 2 2 0.0e+00 4 1 0 3 2.8e-17 4 0 1 3 4.3e-16 4 0 0 4 1.1e-16 5 5 0 0 2.5e-16 5 4 1 0 0.0e+00 5 3 2 0 8.3e-17 5 2 3 0 0.0e+00 5 1 4 0 1.1e-16 5 0 5 0 1.2e-16 5 4 0 1 0.0e+00 5 3 1 1 0.0e+00 5 2 2 1 0.0e+00 5 1 3 1 1.2e-16 5 0 4 1 0.0e+00 5 3 0 2 0.0e+00 5 2 1 2 0.0e+00 5 1 2 2 0.0e+00 5 0 3 2 1.4e-16 5 2 0 3 0.0e+00 5 1 1 3 2.8e-17 5 0 2 3 0.0e+00 5 1 0 4 0.0e+00 5 0 1 4 1.1e-16 5 0 0 5 5.1e-16 6 6 0 0 1.1e-16 6 5 1 0 8.5e-16 6 4 2 0 2.8e-17 6 3 3 0 2.1e-16 6 2 4 0 0.0e+00 6 1 5 0 1.7e-16 6 0 6 0 0.0e+00 6 5 0 1 0.0e+00 6 4 1 1 0.0e+00 6 3 2 1 0.0e+00 6 2 3 1 0.0e+00 6 1 4 1 0.0e+00 6 0 5 1 0.0e+00 6 4 0 2 0.0e+00 6 3 1 2 0.0e+00 6 2 2 2 0.0e+00 6 1 3 2 4.3e-16 6 0 4 2 2.8e-17 6 3 0 3 0.0e+00 6 2 1 3 0.0e+00 6 1 2 3 2.8e-17 6 0 3 3 0.0e+00 6 2 0 4 0.0e+00 6 1 1 4 4.3e-16 6 0 2 4 0.0e+00 6 1 0 5 0.0e+00 6 0 1 5 0.0e+00 6 0 0 6 4.4e-16 7 7 0 0 1.9e-16 7 6 1 0 0.0e+00 7 5 2 0 2.8e-17 7 4 3 0 5.6e-17 7 3 4 0 5.6e-17 7 2 5 0 0.0e+00 7 1 6 0 4.4e-16 7 0 7 0 4.2e-16 7 6 0 1 0.0e+00 7 5 1 1 2.8e-17 7 4 2 1 0.0e+00 7 3 3 1 2.8e-17 7 2 4 1 0.0e+00 7 1 5 1 4.2e-16 7 0 6 1 5.6e-17 7 5 0 2 0.0e+00 7 4 1 2 0.0e+00 7 3 2 2 0.0e+00 7 2 3 2 0.0e+00 7 1 4 2 5.6e-17 7 0 5 2 2.5e-16 7 4 0 3 0.0e+00 7 3 1 3 2.8e-17 7 2 2 3 0.0e+00 7 1 3 3 2.5e-16 7 0 4 3 5.6e-17 7 3 0 4 0.0e+00 7 2 1 4 0.0e+00 7 1 2 4 5.6e-17 7 0 3 4 5.6e-17 7 2 0 5 0.0e+00 7 1 1 5 1.7e-16 7 0 2 5 0.0e+00 7 1 0 6 0.0e+00 7 0 1 6 4.1e-16 7 0 0 7 0.0e+00 8 8 0 0 0.0e+00 8 7 1 0 1.7e-16 8 6 2 0 0.0e+00 8 5 3 0 4.3e-16 8 4 4 0 1.1e-16 8 3 5 0 0.0e+00 8 2 6 0 2.2e-16 8 1 7 0 1.9e-16 8 0 8 0 0.0e+00 8 7 0 1 0.0e+00 8 6 1 1 0.0e+00 8 5 2 1 0.0e+00 8 4 3 1 0.0e+00 8 3 4 1 0.0e+00 8 2 5 1 0.0e+00 8 1 6 1 0.0e+00 8 0 7 1 6.8e-16 8 6 0 2 0.0e+00 8 5 1 2 6.4e-16 8 4 2 2 0.0e+00 8 3 3 2 6.4e-16 8 2 4 2 0.0e+00 8 1 5 2 3.4e-16 8 0 6 2 5.6e-17 8 5 0 3 0.0e+00 8 4 1 3 0.0e+00 8 3 2 3 0.0e+00 8 2 3 3 0.0e+00 8 1 4 3 5.6e-17 8 0 5 3 4.3e-16 8 4 0 4 0.0e+00 8 3 1 4 0.0e+00 8 2 2 4 0.0e+00 8 1 3 4 4.3e-16 8 0 4 4 1.1e-16 8 3 0 5 0.0e+00 8 2 1 5 0.0e+00 8 1 2 5 1.1e-16 8 0 3 5 3.4e-16 8 2 0 6 0.0e+00 8 1 1 6 3.4e-16 8 0 2 6 0.0e+00 8 1 0 7 2.2e-16 8 0 1 7 5.8e-16 8 0 0 8 TEST06: Call SPARSE_GRID_HERMITE to make 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. 15 January 2023 02:32:44 PM