16 May 2012 9:00:00.496 AM SPARSE_GRID_HERMITE_PRB FORTRAN90 version Test the SPARSE_GRID_HERMITE library. TEST01 SPARSE_GRID_HERMITE_SIZE_TOTAL returns the number of points in a Gauss-Hermite sparse grid. 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 0 0 0 0 0 1 3 7 10 13 16 2 7 29 58 95 141 3 15 95 255 515 906 4 31 273 945 2309 4746 5 63 723 3120 9065 21503 6 127 1813 9484 32259 87358 7 255 4375 27109 106455 325943 8 511 10265 73915 330985 1135893 9 1023 23579 194190 980797 3743358 10 2047 53277 495198 2793943 11775507 TEST01 SPARSE_GRID_HERMITE_SIZE_TOTAL returns the number of points in a Gauss-Hermite sparse grid. 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 2047 53277 495198 2793943 11775507 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 TEST01 SPARSE_GRID_HERMITE_SIZE_TOTAL returns the number of points in a Gauss-Hermite sparse grid. 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 8 1 301 2 45551 TEST02 SPARSE_GRID_HERMITE_SIZE returns the number of distinct points in a Gauss-Hermite sparse grid. 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 21 37 57 81 3 15 73 159 289 471 4 31 221 597 1265 2341 5 63 609 2031 4969 10363 6 127 1573 6397 17945 41913 7 255 3881 18943 60577 157583 8 511 9261 53365 193441 557693 9 1023 21553 144351 589625 1875443 10 2047 49205 377661 1727625 6037137 TEST02 SPARSE_GRID_HERMITE_SIZE returns the number of distinct points in a Gauss-Hermite sparse grid. 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 TEST02 SPARSE_GRID_HERMITE_SIZE returns the number of distinct points in a Gauss-Hermite sparse grid. 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 TEST03: SPARSE_GRID_HERMITE_INDEX returns abstract indices for the points that make up a Hermite sparse grid. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of points in the grid = 95 Number of unique points in the grid = 73 Sparse grid unique index: 1 5 2 10 3 23 4 37 5 51 6 64 7 69 8 14 9 33 10 56 11 16 12 37 13 58 14 18 15 41 16 60 17 29 18 32 19 35 20 37 21 39 22 42 23 45 24 1 25 2 26 3 27 7 28 8 29 21 30 25 31 37 32 49 33 53 34 66 35 67 36 71 37 72 38 73 39 4 40 9 41 22 42 33 43 50 44 63 45 68 46 5 47 10 48 23 49 37 50 51 51 64 52 69 53 6 54 11 55 24 56 41 57 52 58 65 59 70 60 12 61 29 62 54 63 13 64 32 65 55 66 15 67 35 68 57 69 16 70 37 71 58 72 17 73 39 74 59 75 19 76 42 77 61 78 20 79 45 80 62 81 26 82 27 83 28 84 30 85 31 86 34 87 36 88 37 89 38 90 40 91 43 92 44 93 46 94 47 95 48 Sparse grid index/order: 1 1 1 15 1 2 2 1 15 1 3 3 1 15 1 4 1 1 7 3 5 1 2 7 3 6 1 3 7 3 7 4 1 15 1 8 5 1 15 1 9 2 1 7 3 10 2 2 7 3 11 2 3 7 3 12 1 1 3 7 13 1 2 3 7 14 1 1 3 3 15 1 3 3 7 16 1 4 3 7 17 1 5 3 7 18 1 3 3 3 19 1 6 3 7 20 1 7 3 7 21 6 1 15 1 22 3 1 7 3 23 3 2 7 3 24 3 3 7 3 25 7 1 15 1 26 1 1 1 15 27 1 2 1 15 28 1 3 1 15 29 2 1 3 7 30 1 4 1 15 31 1 5 1 15 32 2 2 3 7 33 4 1 7 3 34 1 6 1 15 35 2 3 3 7 36 1 7 1 15 37 1 8 1 15 38 1 9 1 15 39 2 5 3 7 40 1 10 1 15 41 4 3 7 3 42 2 6 3 7 43 1 11 1 15 44 1 12 1 15 45 2 7 3 7 46 1 13 1 15 47 1 14 1 15 48 1 15 1 15 49 9 1 15 1 50 5 1 7 3 51 5 2 7 3 52 5 3 7 3 53 10 1 15 1 54 3 1 3 7 55 3 2 3 7 56 3 1 3 3 57 3 3 3 7 58 3 4 3 7 59 3 5 3 7 60 3 3 3 3 61 3 6 3 7 62 3 7 3 7 63 6 1 7 3 64 6 2 7 3 65 6 3 7 3 66 11 1 15 1 67 12 1 15 1 68 7 1 7 3 69 7 2 7 3 70 7 3 7 3 71 13 1 15 1 72 14 1 15 1 73 15 1 15 1 TEST03: SPARSE_GRID_HERMITE_INDEX returns abstract indices for the points that make up a Hermite sparse grid. LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of points in the grid = 273 Number of unique points in the grid = 221 Sparse grid unique index: 1 7 2 12 3 16 4 30 5 34 6 69 7 82 8 111 9 140 10 153 11 188 12 192 13 206 14 210 15 215 16 21 17 38 18 73 19 104 20 145 21 180 22 197 23 23 24 40 25 75 26 111 27 147 28 182 29 199 30 25 31 42 32 77 33 118 34 149 35 184 36 201 37 49 38 97 39 159 40 52 41 102 42 162 43 54 44 107 45 164 46 56 47 111 48 166 49 58 50 115 51 168 52 60 53 120 54 170 55 63 56 125 57 173 58 90 59 93 60 95 61 99 62 101 63 106 64 109 65 111 66 113 67 116 68 121 69 123 70 127 71 129 72 132 73 1 74 2 75 3 76 4 77 5 78 9 79 10 80 14 81 18 82 28 83 32 84 45 85 67 86 80 87 84 88 111 89 138 90 142 91 155 92 177 93 190 94 194 95 204 96 208 97 212 98 213 99 217 100 218 101 219 102 220 103 221 104 6 105 11 106 15 107 29 108 33 109 68 110 81 111 104 112 139 113 152 114 187 115 191 116 205 117 209 118 214 119 7 120 12 121 16 122 30 123 34 124 69 125 82 126 111 127 140 128 153 129 188 130 192 131 206 132 210 133 215 134 8 135 13 136 17 137 31 138 35 139 70 140 83 141 118 142 141 143 154 144 189 145 193 146 207 147 211 148 216 149 19 150 36 151 71 152 97 153 143 154 178 155 195 156 20 157 37 158 72 159 102 160 144 161 179 162 196 163 22 164 39 165 74 166 107 167 146 168 181 169 198 170 23 171 40 172 75 173 111 174 147 175 182 176 199 177 24 178 41 179 76 180 115 181 148 182 183 183 200 184 26 185 43 186 78 187 120 188 150 189 185 190 202 191 27 192 44 193 79 194 125 195 151 196 186 197 203 198 46 199 90 200 156 201 47 202 93 203 157 204 48 205 95 206 158 207 50 208 99 209 160 210 51 211 101 212 161 213 53 214 106 215 163 216 55 217 109 218 165 219 56 220 111 221 166 222 57 223 113 224 167 225 59 226 116 227 169 228 61 229 121 230 171 231 62 232 123 233 172 234 64 235 127 236 174 237 65 238 129 239 175 240 66 241 132 242 176 243 85 244 86 245 87 246 88 247 89 248 91 249 92 250 94 251 96 252 98 253 100 254 103 255 105 256 108 257 110 258 111 259 112 260 114 261 117 262 119 263 122 264 124 265 126 266 128 267 130 268 131 269 133 270 134 271 135 272 136 273 137 Sparse grid index/order: 1 1 1 31 1 2 2 1 31 1 3 3 1 31 1 4 4 1 31 1 5 5 1 31 1 6 1 1 15 3 7 1 2 15 3 8 1 3 15 3 9 6 1 31 1 10 7 1 31 1 11 2 1 15 3 12 2 2 15 3 13 2 3 15 3 14 8 1 31 1 15 3 1 15 3 16 3 2 15 3 17 3 3 15 3 18 9 1 31 1 19 1 1 7 7 20 1 2 7 7 21 1 1 7 3 22 1 3 7 7 23 1 4 7 7 24 1 5 7 7 25 1 3 7 3 26 1 6 7 7 27 1 7 7 7 28 10 1 31 1 29 4 1 15 3 30 4 2 15 3 31 4 3 15 3 32 11 1 31 1 33 5 1 15 3 34 5 2 15 3 35 5 3 15 3 36 2 1 7 7 37 2 2 7 7 38 2 1 7 3 39 2 3 7 7 40 2 4 7 7 41 2 5 7 7 42 2 3 7 3 43 2 6 7 7 44 2 7 7 7 45 12 1 31 1 46 1 1 3 15 47 1 2 3 15 48 1 3 3 15 49 1 1 3 7 50 1 4 3 15 51 1 5 3 15 52 1 2 3 7 53 1 6 3 15 54 1 3 3 7 55 1 7 3 15 56 1 8 3 15 57 1 9 3 15 58 1 5 3 7 59 1 10 3 15 60 1 6 3 7 61 1 11 3 15 62 1 12 3 15 63 1 7 3 7 64 1 13 3 15 65 1 14 3 15 66 1 15 3 15 67 13 1 31 1 68 6 1 15 3 69 6 2 15 3 70 6 3 15 3 71 3 1 7 7 72 3 2 7 7 73 3 1 7 3 74 3 3 7 7 75 3 4 7 7 76 3 5 7 7 77 3 3 7 3 78 3 6 7 7 79 3 7 7 7 80 14 1 31 1 81 7 1 15 3 82 7 2 15 3 83 7 3 15 3 84 15 1 31 1 85 1 1 1 31 86 1 2 1 31 87 1 3 1 31 88 1 4 1 31 89 1 5 1 31 90 2 1 3 15 91 1 6 1 31 92 1 7 1 31 93 2 2 3 15 94 1 8 1 31 95 2 3 3 15 96 1 9 1 31 97 4 1 7 7 98 1 10 1 31 99 2 4 3 15 100 1 11 1 31 101 2 5 3 15 102 4 2 7 7 103 1 12 1 31 104 8 1 15 3 105 1 13 1 31 106 2 6 3 15 107 4 3 7 7 108 1 14 1 31 109 2 7 3 15 110 1 15 1 31 111 1 16 1 31 112 1 17 1 31 113 2 9 3 15 114 1 18 1 31 115 4 5 7 7 116 2 10 3 15 117 1 19 1 31 118 8 3 15 3 119 1 20 1 31 120 4 6 7 7 121 2 11 3 15 122 1 21 1 31 123 2 12 3 15 124 1 22 1 31 125 4 7 7 7 126 1 23 1 31 127 2 13 3 15 128 1 24 1 31 129 2 14 3 15 130 1 25 1 31 131 1 26 1 31 132 2 15 3 15 133 1 27 1 31 134 1 28 1 31 135 1 29 1 31 136 1 30 1 31 137 1 31 1 31 138 17 1 31 1 139 9 1 15 3 140 9 2 15 3 141 9 3 15 3 142 18 1 31 1 143 5 1 7 7 144 5 2 7 7 145 5 1 7 3 146 5 3 7 7 147 5 4 7 7 148 5 5 7 7 149 5 3 7 3 150 5 6 7 7 151 5 7 7 7 152 10 1 15 3 153 10 2 15 3 154 10 3 15 3 155 19 1 31 1 156 3 1 3 15 157 3 2 3 15 158 3 3 3 15 159 3 1 3 7 160 3 4 3 15 161 3 5 3 15 162 3 2 3 7 163 3 6 3 15 164 3 3 3 7 165 3 7 3 15 166 3 8 3 15 167 3 9 3 15 168 3 5 3 7 169 3 10 3 15 170 3 6 3 7 171 3 11 3 15 172 3 12 3 15 173 3 7 3 7 174 3 13 3 15 175 3 14 3 15 176 3 15 3 15 177 20 1 31 1 178 6 1 7 7 179 6 2 7 7 180 6 1 7 3 181 6 3 7 7 182 6 4 7 7 183 6 5 7 7 184 6 3 7 3 185 6 6 7 7 186 6 7 7 7 187 11 1 15 3 188 11 2 15 3 189 11 3 15 3 190 21 1 31 1 191 12 1 15 3 192 12 2 15 3 193 12 3 15 3 194 22 1 31 1 195 7 1 7 7 196 7 2 7 7 197 7 1 7 3 198 7 3 7 7 199 7 4 7 7 200 7 5 7 7 201 7 3 7 3 202 7 6 7 7 203 7 7 7 7 204 23 1 31 1 205 13 1 15 3 206 13 2 15 3 207 13 3 15 3 208 24 1 31 1 209 14 1 15 3 210 14 2 15 3 211 14 3 15 3 212 25 1 31 1 213 26 1 31 1 214 15 1 15 3 215 15 2 15 3 216 15 3 15 3 217 27 1 31 1 218 28 1 31 1 219 29 1 31 1 220 30 1 31 1 221 31 1 31 1 TEST03: SPARSE_GRID_HERMITE_INDEX returns abstract indices for the points that make up a Hermite sparse grid. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 Number of points in the grid = 273 Number of unique points in the grid = 1 Sparse grid unique index: 1 1 2 12 3 16 4 30 5 34 6 69 7 82 8 111 9 140 10 153 11 188 12 192 13 206 14 210 15 215 16 21 17 38 18 73 19 104 20 145 21 180 22 197 23 23 24 40 25 75 26 111 27 147 28 182 29 199 30 25 31 42 32 77 33 118 34 149 35 184 36 201 37 49 38 97 39 159 40 52 41 102 42 162 43 54 44 107 45 164 46 56 47 111 48 166 49 58 50 115 51 168 52 60 53 120 54 170 55 63 56 125 57 173 58 90 59 93 60 95 61 99 62 101 63 106 64 109 65 111 66 113 67 116 68 121 69 123 70 127 71 129 72 132 73 1 74 2 75 3 76 4 77 5 78 9 79 10 80 14 81 18 82 28 83 32 84 45 85 67 86 80 87 84 88 111 89 138 90 142 91 155 92 177 93 190 94 194 95 204 96 208 97 212 98 213 99 217 100 218 101 219 102 220 103 221 104 6 105 11 106 15 107 29 108 33 109 68 110 81 111 104 112 139 113 152 114 187 115 191 116 205 117 209 118 214 119 7 120 12 121 16 122 30 123 34 124 69 125 82 126 111 127 140 128 153 129 188 130 192 131 206 132 210 133 215 134 8 135 13 136 17 137 31 138 35 139 70 140 83 141 118 142 141 143 154 144 189 145 193 146 207 147 211 148 216 149 19 150 36 151 71 152 97 153 143 154 178 155 195 156 20 157 37 158 72 159 102 160 144 161 179 162 196 163 22 164 39 165 74 166 107 167 146 168 181 169 198 170 23 171 40 172 75 173 111 174 147 175 182 176 199 177 24 178 41 179 76 180 115 181 148 182 183 183 200 184 26 185 43 186 78 187 120 188 150 189 185 190 202 191 27 192 44 193 79 194 125 195 151 196 186 197 203 198 46 199 90 200 156 201 47 202 93 203 157 204 48 205 95 206 158 207 50 208 99 209 160 210 51 211 101 212 161 213 53 214 106 215 163 216 55 217 109 218 165 219 56 220 111 221 166 222 57 223 113 224 167 225 59 226 116 227 169 228 61 229 121 230 171 231 62 232 123 233 172 234 64 235 127 236 174 237 65 238 129 239 175 240 66 241 132 242 176 243 85 244 86 245 87 246 88 247 89 248 91 249 92 250 94 251 96 252 98 253 100 254 103 255 105 256 108 257 110 258 111 259 112 260 114 261 117 262 119 263 122 264 124 265 126 266 128 267 130 268 131 269 133 270 134 271 135 272 136 273 137 Sparse grid index/order: 1 1 1 1 1 1 1 TEST03: SPARSE_GRID_HERMITE_INDEX returns abstract indices for the points that make up a Hermite sparse grid. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 Number of points in the grid = 58 Number of unique points in the grid = 37 Sparse grid unique index: 1 19 2 5 3 19 4 33 5 12 6 19 7 26 8 17 9 19 10 21 11 1 12 2 13 8 14 19 15 30 16 36 17 37 18 3 19 12 20 31 21 5 22 19 23 33 24 7 25 26 26 35 27 9 28 10 29 14 30 19 31 24 32 28 33 29 34 4 35 17 36 32 37 5 38 19 39 33 40 6 41 21 42 34 43 11 44 17 45 25 46 12 47 19 48 26 49 13 50 21 51 27 52 15 53 16 54 18 55 19 56 20 57 22 58 23 Sparse grid index/order: 1 1 1 1 7 1 1 2 2 1 1 7 1 1 3 1 1 1 3 3 1 4 1 1 1 3 1 3 5 1 1 2 3 1 3 6 1 1 3 3 1 3 7 1 3 1 3 3 1 8 3 1 1 7 1 1 9 1 1 1 1 7 1 10 1 2 1 1 7 1 11 1 1 1 1 3 3 12 1 1 2 1 3 3 13 1 1 3 1 3 3 14 1 3 1 1 7 1 15 1 1 1 1 1 7 16 1 1 2 1 1 7 17 1 2 1 1 3 3 18 1 1 3 1 1 7 19 1 1 4 1 1 7 20 1 1 5 1 1 7 21 1 2 3 1 3 3 22 1 1 6 1 1 7 23 1 1 7 1 1 7 24 1 5 1 1 7 1 25 1 3 1 1 3 3 26 1 3 2 1 3 3 27 1 3 3 1 3 3 28 1 6 1 1 7 1 29 1 7 1 1 7 1 30 5 1 1 7 1 1 31 3 1 1 3 3 1 32 3 1 1 3 1 3 33 3 1 2 3 1 3 34 3 1 3 3 1 3 35 3 3 1 3 3 1 36 6 1 1 7 1 1 37 7 1 1 7 1 1 TEST03: SPARSE_GRID_HERMITE_INDEX returns abstract indices for the points that make up a Hermite sparse grid. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 6 Number of points in the grid = 196 Number of unique points in the grid = 109 Sparse grid unique index: 1 55 2 8 3 55 4 102 5 21 6 55 7 89 8 32 9 55 10 78 11 41 12 55 13 69 14 48 15 55 16 62 17 53 18 55 19 57 20 1 21 2 22 14 23 55 24 96 25 108 26 109 27 3 28 21 29 97 30 8 31 55 32 102 33 13 34 89 35 107 36 15 37 16 38 26 39 55 40 84 41 94 42 95 43 4 44 32 45 98 46 8 47 55 48 102 49 12 50 78 51 106 52 17 53 32 54 85 55 21 56 55 57 89 58 25 59 78 60 93 61 27 62 28 63 36 64 55 65 74 66 82 67 83 68 5 69 41 70 99 71 8 72 55 73 102 74 11 75 69 76 105 77 18 78 41 79 86 80 21 81 55 82 89 83 24 84 69 85 92 86 29 87 41 88 75 89 32 90 55 91 78 92 35 93 69 94 81 95 37 96 38 97 44 98 55 99 66 100 72 101 73 102 6 103 48 104 100 105 8 106 55 107 102 108 10 109 62 110 104 111 19 112 48 113 87 114 21 115 55 116 89 117 23 118 62 119 91 120 30 121 48 122 76 123 32 124 55 125 78 126 34 127 62 128 80 129 39 130 48 131 67 132 41 133 55 134 69 135 43 136 62 137 71 138 45 139 46 140 50 141 55 142 60 143 64 144 65 145 7 146 53 147 101 148 8 149 55 150 102 151 9 152 57 153 103 154 20 155 53 156 88 157 21 158 55 159 89 160 22 161 57 162 90 163 31 164 53 165 77 166 32 167 55 168 78 169 33 170 57 171 79 172 40 173 53 174 68 175 41 176 55 177 69 178 42 179 57 180 70 181 47 182 53 183 61 184 48 185 55 186 62 187 49 188 57 189 63 190 51 191 52 192 54 193 55 194 56 195 58 196 59 Sparse grid index/order: 1 1 1 1 1 1 1 7 1 1 1 1 1 2 2 1 1 1 1 1 7 1 1 1 1 1 3 1 1 1 1 1 1 3 3 1 1 1 1 4 1 1 1 1 1 1 3 1 3 1 1 1 5 1 1 1 1 1 1 3 1 1 3 1 1 6 1 1 1 1 1 1 3 1 1 1 3 1 7 1 1 1 1 1 1 3 1 1 1 1 3 8 1 1 1 1 1 2 3 1 1 1 1 3 9 1 1 1 1 1 3 3 1 1 1 1 3 10 1 1 1 1 3 1 3 1 1 1 3 1 11 1 1 1 3 1 1 3 1 1 3 1 1 12 1 1 3 1 1 1 3 1 3 1 1 1 13 1 3 1 1 1 1 3 3 1 1 1 1 14 3 1 1 1 1 1 7 1 1 1 1 1 15 1 1 1 1 1 1 1 7 1 1 1 1 16 1 2 1 1 1 1 1 7 1 1 1 1 17 1 1 1 1 1 1 1 3 3 1 1 1 18 1 1 1 1 1 1 1 3 1 3 1 1 19 1 1 1 1 1 1 1 3 1 1 3 1 20 1 1 1 1 1 1 1 3 1 1 1 3 21 1 1 1 1 1 2 1 3 1 1 1 3 22 1 1 1 1 1 3 1 3 1 1 1 3 23 1 1 1 1 3 1 1 3 1 1 3 1 24 1 1 1 3 1 1 1 3 1 3 1 1 25 1 1 3 1 1 1 1 3 3 1 1 1 26 1 3 1 1 1 1 1 7 1 1 1 1 27 1 1 1 1 1 1 1 1 7 1 1 1 28 1 1 2 1 1 1 1 1 7 1 1 1 29 1 1 1 1 1 1 1 1 3 3 1 1 30 1 1 1 1 1 1 1 1 3 1 3 1 31 1 1 1 1 1 1 1 1 3 1 1 3 32 1 1 1 1 1 2 1 1 3 1 1 3 33 1 1 1 1 1 3 1 1 3 1 1 3 34 1 1 1 1 3 1 1 1 3 1 3 1 35 1 1 1 3 1 1 1 1 3 3 1 1 36 1 1 3 1 1 1 1 1 7 1 1 1 37 1 1 1 1 1 1 1 1 1 7 1 1 38 1 1 1 2 1 1 1 1 1 7 1 1 39 1 1 1 1 1 1 1 1 1 3 3 1 40 1 1 1 1 1 1 1 1 1 3 1 3 41 1 1 1 1 1 2 1 1 1 3 1 3 42 1 1 1 1 1 3 1 1 1 3 1 3 43 1 1 1 1 3 1 1 1 1 3 3 1 44 1 1 1 3 1 1 1 1 1 7 1 1 45 1 1 1 1 1 1 1 1 1 1 7 1 46 1 1 1 1 2 1 1 1 1 1 7 1 47 1 1 1 1 1 1 1 1 1 1 3 3 48 1 1 1 1 1 2 1 1 1 1 3 3 49 1 1 1 1 1 3 1 1 1 1 3 3 50 1 1 1 1 3 1 1 1 1 1 7 1 51 1 1 1 1 1 1 1 1 1 1 1 7 52 1 1 1 1 1 2 1 1 1 1 1 7 53 1 1 1 1 2 1 1 1 1 1 3 3 54 1 1 1 1 1 3 1 1 1 1 1 7 55 1 1 1 1 1 4 1 1 1 1 1 7 56 1 1 1 1 1 5 1 1 1 1 1 7 57 1 1 1 1 2 3 1 1 1 1 3 3 58 1 1 1 1 1 6 1 1 1 1 1 7 59 1 1 1 1 1 7 1 1 1 1 1 7 60 1 1 1 1 5 1 1 1 1 1 7 1 61 1 1 1 1 3 1 1 1 1 1 3 3 62 1 1 1 1 3 2 1 1 1 1 3 3 63 1 1 1 1 3 3 1 1 1 1 3 3 64 1 1 1 1 6 1 1 1 1 1 7 1 65 1 1 1 1 7 1 1 1 1 1 7 1 66 1 1 1 5 1 1 1 1 1 7 1 1 67 1 1 1 3 1 1 1 1 1 3 3 1 68 1 1 1 3 1 1 1 1 1 3 1 3 69 1 1 1 3 1 2 1 1 1 3 1 3 70 1 1 1 3 1 3 1 1 1 3 1 3 71 1 1 1 3 3 1 1 1 1 3 3 1 72 1 1 1 6 1 1 1 1 1 7 1 1 73 1 1 1 7 1 1 1 1 1 7 1 1 74 1 1 5 1 1 1 1 1 7 1 1 1 75 1 1 3 1 1 1 1 1 3 3 1 1 76 1 1 3 1 1 1 1 1 3 1 3 1 77 1 1 3 1 1 1 1 1 3 1 1 3 78 1 1 3 1 1 2 1 1 3 1 1 3 79 1 1 3 1 1 3 1 1 3 1 1 3 80 1 1 3 1 3 1 1 1 3 1 3 1 81 1 1 3 3 1 1 1 1 3 3 1 1 82 1 1 6 1 1 1 1 1 7 1 1 1 83 1 1 7 1 1 1 1 1 7 1 1 1 84 1 5 1 1 1 1 1 7 1 1 1 1 85 1 3 1 1 1 1 1 3 3 1 1 1 86 1 3 1 1 1 1 1 3 1 3 1 1 87 1 3 1 1 1 1 1 3 1 1 3 1 88 1 3 1 1 1 1 1 3 1 1 1 3 89 1 3 1 1 1 2 1 3 1 1 1 3 90 1 3 1 1 1 3 1 3 1 1 1 3 91 1 3 1 1 3 1 1 3 1 1 3 1 92 1 3 1 3 1 1 1 3 1 3 1 1 93 1 3 3 1 1 1 1 3 3 1 1 1 94 1 6 1 1 1 1 1 7 1 1 1 1 95 1 7 1 1 1 1 1 7 1 1 1 1 96 5 1 1 1 1 1 7 1 1 1 1 1 97 3 1 1 1 1 1 3 3 1 1 1 1 98 3 1 1 1 1 1 3 1 3 1 1 1 99 3 1 1 1 1 1 3 1 1 3 1 1 100 3 1 1 1 1 1 3 1 1 1 3 1 101 3 1 1 1 1 1 3 1 1 1 1 3 102 3 1 1 1 1 2 3 1 1 1 1 3 103 3 1 1 1 1 3 3 1 1 1 1 3 104 3 1 1 1 3 1 3 1 1 1 3 1 105 3 1 1 3 1 1 3 1 1 3 1 1 106 3 1 3 1 1 1 3 1 3 1 1 1 107 3 3 1 1 1 1 3 3 1 1 1 1 108 6 1 1 1 1 1 7 1 1 1 1 1 109 7 1 1 1 1 1 7 1 1 1 1 1 TEST04: SPARSE_GRID_HERMITE computes Hermite sparse grid points and weights. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 2 Number of points in the grid = 196 Number of unique points in the grid = 1 Grid weights: 1 3.141593 Grid points: 1 0.000000 0.000000 TEST04: SPARSE_GRID_HERMITE computes Hermite sparse grid points and weights. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of points in the grid = 95 Number of unique points in the grid = 73 Grid weights: 1 0.000000 2 0.000002 3 0.000177 4 0.000287 5 -0.000574 6 0.000287 7 0.004924 8 0.054556 9 0.016104 10 -0.032209 11 0.016104 12 0.000287 13 0.016104 14 -0.087266 15 0.125728 16 -0.109706 17 0.125728 18 -0.087266 19 0.016104 20 0.000287 21 0.280914 22 0.125728 23 -0.251456 24 0.125728 25 0.730302 26 0.000000 27 0.000002 28 0.000177 29 -0.000574 30 0.004924 31 0.054556 32 -0.032209 33 -0.109706 34 0.280914 35 -0.251456 36 0.730302 37 -0.354018 38 0.730302 39 -0.251456 40 0.280914 41 -0.109706 42 -0.032209 43 0.054556 44 0.004924 45 -0.000574 46 0.000177 47 0.000002 48 0.000000 49 0.730302 50 0.125728 51 -0.251456 52 0.125728 53 0.280914 54 0.000287 55 0.016104 56 -0.087266 57 0.125728 58 -0.109706 59 0.125728 60 -0.087266 61 0.016104 62 0.000287 63 0.016104 64 -0.032209 65 0.016104 66 0.054556 67 0.004924 68 0.000287 69 -0.000574 70 0.000287 71 0.000177 72 0.000002 73 0.000000 Grid points: 1 -4.499991 0.000000 2 -3.669950 0.000000 3 -2.967167 0.000000 4 -2.651961 -1.224745 5 -2.651961 0.000000 6 -2.651961 1.224745 7 -2.325732 0.000000 8 -1.719993 0.000000 9 -1.673552 -1.224745 10 -1.673552 0.000000 11 -1.673552 1.224745 12 -1.224745 -2.651961 13 -1.224745 -1.673552 14 -1.224745 -1.224745 15 -1.224745 -0.816288 16 -1.224745 0.000000 17 -1.224745 0.816288 18 -1.224745 1.224745 19 -1.224745 1.673552 20 -1.224745 2.651961 21 -1.136116 0.000000 22 -0.816288 -1.224745 23 -0.816288 0.000000 24 -0.816288 1.224745 25 -0.565070 0.000000 26 0.000000 -4.499991 27 0.000000 -3.669950 28 0.000000 -2.967167 29 0.000000 -2.651961 30 0.000000 -2.325732 31 0.000000 -1.719993 32 0.000000 -1.673552 33 0.000000 -1.224745 34 0.000000 -1.136116 35 0.000000 -0.816288 36 0.000000 -0.565070 37 0.000000 0.000000 38 0.000000 0.565070 39 0.000000 0.816288 40 0.000000 1.136116 41 0.000000 1.224745 42 0.000000 1.673552 43 0.000000 1.719993 44 0.000000 2.325732 45 0.000000 2.651961 46 0.000000 2.967167 47 0.000000 3.669950 48 0.000000 4.499991 49 0.565070 0.000000 50 0.816288 -1.224745 51 0.816288 0.000000 52 0.816288 1.224745 53 1.136116 0.000000 54 1.224745 -2.651961 55 1.224745 -1.673552 56 1.224745 -1.224745 57 1.224745 -0.816288 58 1.224745 0.000000 59 1.224745 0.816288 60 1.224745 1.224745 61 1.224745 1.673552 62 1.224745 2.651961 63 1.673552 -1.224745 64 1.673552 0.000000 65 1.673552 1.224745 66 1.719993 0.000000 67 2.325732 0.000000 68 2.651961 -1.224745 69 2.651961 0.000000 70 2.651961 1.224745 71 2.967167 0.000000 72 3.669950 0.000000 73 4.499991 0.000000 TEST04: SPARSE_GRID_HERMITE computes Hermite sparse grid points and weights. LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of points in the grid = 273 Number of unique points in the grid = 221 Grid weights: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 -0.000000 8 0.000000 9 0.000000 10 0.000001 11 0.000000 12 -0.000001 13 0.000000 14 0.000019 15 0.000030 16 -0.000059 17 0.000030 18 0.000247 19 0.000001 20 0.000053 21 -0.000287 22 0.000414 23 -0.000361 24 0.000414 25 -0.000287 26 0.000053 27 0.000001 28 0.002187 29 0.000821 30 -0.001641 31 0.000821 32 0.013263 33 0.009093 34 -0.018185 35 0.009093 36 0.000053 37 0.002972 38 -0.016104 39 0.023202 40 -0.020246 41 0.023202 42 -0.016104 43 0.002972 44 0.000053 45 0.056448 46 0.000000 47 0.000000 48 0.000030 49 -0.000287 50 0.000821 51 0.009093 52 -0.016104 53 0.046819 54 -0.125728 55 0.121717 56 -0.072719 57 0.121717 58 -0.125728 59 0.046819 60 -0.016104 61 0.009093 62 0.000821 63 -0.000287 64 0.000030 65 0.000000 66 0.000000 67 0.171428 68 0.046819 69 -0.093638 70 0.046819 71 0.000414 72 0.023202 73 -0.125728 74 0.181142 75 -0.158058 76 0.181142 77 -0.125728 78 0.023202 79 0.000414 80 0.375996 81 0.121717 82 -0.243434 83 0.121717 84 0.600459 85 0.000000 86 0.000000 87 0.000000 88 0.000000 89 0.000000 90 -0.000000 91 0.000000 92 0.000001 93 -0.000001 94 0.000019 95 -0.000059 96 0.000247 97 -0.000361 98 0.002187 99 -0.001641 100 0.013263 101 -0.018185 102 -0.020246 103 0.056448 104 -0.072719 105 0.171428 106 -0.093638 107 -0.158058 108 0.375996 109 -0.243434 110 0.600459 111 -0.521909 112 0.600459 113 -0.243434 114 0.375996 115 -0.158058 116 -0.093638 117 0.171428 118 -0.072719 119 0.056448 120 -0.020246 121 -0.018185 122 0.013263 123 -0.001641 124 0.002187 125 -0.000361 126 0.000247 127 -0.000059 128 0.000019 129 -0.000001 130 0.000001 131 0.000000 132 -0.000000 133 0.000000 134 0.000000 135 0.000000 136 0.000000 137 0.000000 138 0.600459 139 0.121717 140 -0.243434 141 0.121717 142 0.375996 143 0.000414 144 0.023202 145 -0.125728 146 0.181142 147 -0.158058 148 0.181142 149 -0.125728 150 0.023202 151 0.000414 152 0.046819 153 -0.093638 154 0.046819 155 0.171428 156 0.000000 157 0.000000 158 0.000030 159 -0.000287 160 0.000821 161 0.009093 162 -0.016104 163 0.046819 164 -0.125728 165 0.121717 166 -0.072719 167 0.121717 168 -0.125728 169 0.046819 170 -0.016104 171 0.009093 172 0.000821 173 -0.000287 174 0.000030 175 0.000000 176 0.000000 177 0.056448 178 0.000053 179 0.002972 180 -0.016104 181 0.023202 182 -0.020246 183 0.023202 184 -0.016104 185 0.002972 186 0.000053 187 0.009093 188 -0.018185 189 0.009093 190 0.013263 191 0.000821 192 -0.001641 193 0.000821 194 0.002187 195 0.000001 196 0.000053 197 -0.000287 198 0.000414 199 -0.000361 200 0.000414 201 -0.000287 202 0.000053 203 0.000001 204 0.000247 205 0.000030 206 -0.000059 207 0.000030 208 0.000019 209 0.000000 210 -0.000001 211 0.000000 212 0.000001 213 0.000000 214 0.000000 215 -0.000000 216 0.000000 217 0.000000 218 0.000000 219 0.000000 220 0.000000 221 0.000000 Grid points: 1 -6.995680 0.000000 2 -6.275079 0.000000 3 -5.673961 0.000000 4 -5.133596 0.000000 5 -4.631560 0.000000 6 -4.499991 -1.224745 7 -4.499991 0.000000 8 -4.499991 1.224745 9 -4.156272 0.000000 10 -3.700743 0.000000 11 -3.669950 -1.224745 12 -3.669950 0.000000 13 -3.669950 1.224745 14 -3.260321 0.000000 15 -2.967167 -1.224745 16 -2.967167 0.000000 17 -2.967167 1.224745 18 -2.831680 0.000000 19 -2.651961 -2.651961 20 -2.651961 -1.673552 21 -2.651961 -1.224745 22 -2.651961 -0.816288 23 -2.651961 0.000000 24 -2.651961 0.816288 25 -2.651961 1.224745 26 -2.651961 1.673552 27 -2.651961 2.651961 28 -2.412318 0.000000 29 -2.325732 -1.224745 30 -2.325732 0.000000 31 -2.325732 1.224745 32 -2.000259 0.000000 33 -1.719993 -1.224745 34 -1.719993 0.000000 35 -1.719993 1.224745 36 -1.673552 -2.651961 37 -1.673552 -1.673552 38 -1.673552 -1.224745 39 -1.673552 -0.816288 40 -1.673552 0.000000 41 -1.673552 0.816288 42 -1.673552 1.224745 43 -1.673552 1.673552 44 -1.673552 2.651961 45 -1.593886 0.000000 46 -1.224745 -4.499991 47 -1.224745 -3.669950 48 -1.224745 -2.967167 49 -1.224745 -2.651961 50 -1.224745 -2.325732 51 -1.224745 -1.719993 52 -1.224745 -1.673552 53 -1.224745 -1.136116 54 -1.224745 -0.816288 55 -1.224745 -0.565070 56 -1.224745 0.000000 57 -1.224745 0.565070 58 -1.224745 0.816288 59 -1.224745 1.136116 60 -1.224745 1.673552 61 -1.224745 1.719993 62 -1.224745 2.325732 63 -1.224745 2.651961 64 -1.224745 2.967167 65 -1.224745 3.669950 66 -1.224745 4.499991 67 -1.191827 0.000000 68 -1.136116 -1.224745 69 -1.136116 0.000000 70 -1.136116 1.224745 71 -0.816288 -2.651961 72 -0.816288 -1.673552 73 -0.816288 -1.224745 74 -0.816288 -0.816288 75 -0.816288 0.000000 76 -0.816288 0.816288 77 -0.816288 1.224745 78 -0.816288 1.673552 79 -0.816288 2.651961 80 -0.792877 0.000000 81 -0.565070 -1.224745 82 -0.565070 0.000000 83 -0.565070 1.224745 84 -0.395943 0.000000 85 0.000000 -6.995680 86 0.000000 -6.275079 87 0.000000 -5.673961 88 0.000000 -5.133596 89 0.000000 -4.631560 90 0.000000 -4.499991 91 0.000000 -4.156272 92 0.000000 -3.700743 93 0.000000 -3.669950 94 0.000000 -3.260321 95 0.000000 -2.967167 96 0.000000 -2.831680 97 0.000000 -2.651961 98 0.000000 -2.412318 99 0.000000 -2.325732 100 0.000000 -2.000259 101 0.000000 -1.719993 102 0.000000 -1.673552 103 0.000000 -1.593886 104 0.000000 -1.224745 105 0.000000 -1.191827 106 0.000000 -1.136116 107 0.000000 -0.816288 108 0.000000 -0.792877 109 0.000000 -0.565070 110 0.000000 -0.395943 111 0.000000 0.000000 112 0.000000 0.395943 113 0.000000 0.565070 114 0.000000 0.792877 115 0.000000 0.816288 116 0.000000 1.136116 117 0.000000 1.191827 118 0.000000 1.224745 119 0.000000 1.593886 120 0.000000 1.673552 121 0.000000 1.719993 122 0.000000 2.000259 123 0.000000 2.325732 124 0.000000 2.412318 125 0.000000 2.651961 126 0.000000 2.831680 127 0.000000 2.967167 128 0.000000 3.260321 129 0.000000 3.669950 130 0.000000 3.700743 131 0.000000 4.156272 132 0.000000 4.499991 133 0.000000 4.631560 134 0.000000 5.133596 135 0.000000 5.673961 136 0.000000 6.275079 137 0.000000 6.995680 138 0.395943 0.000000 139 0.565070 -1.224745 140 0.565070 0.000000 141 0.565070 1.224745 142 0.792877 0.000000 143 0.816288 -2.651961 144 0.816288 -1.673552 145 0.816288 -1.224745 146 0.816288 -0.816288 147 0.816288 0.000000 148 0.816288 0.816288 149 0.816288 1.224745 150 0.816288 1.673552 151 0.816288 2.651961 152 1.136116 -1.224745 153 1.136116 0.000000 154 1.136116 1.224745 155 1.191827 0.000000 156 1.224745 -4.499991 157 1.224745 -3.669950 158 1.224745 -2.967167 159 1.224745 -2.651961 160 1.224745 -2.325732 161 1.224745 -1.719993 162 1.224745 -1.673552 163 1.224745 -1.136116 164 1.224745 -0.816288 165 1.224745 -0.565070 166 1.224745 0.000000 167 1.224745 0.565070 168 1.224745 0.816288 169 1.224745 1.136116 170 1.224745 1.673552 171 1.224745 1.719993 172 1.224745 2.325732 173 1.224745 2.651961 174 1.224745 2.967167 175 1.224745 3.669950 176 1.224745 4.499991 177 1.593886 0.000000 178 1.673552 -2.651961 179 1.673552 -1.673552 180 1.673552 -1.224745 181 1.673552 -0.816288 182 1.673552 0.000000 183 1.673552 0.816288 184 1.673552 1.224745 185 1.673552 1.673552 186 1.673552 2.651961 187 1.719993 -1.224745 188 1.719993 0.000000 189 1.719993 1.224745 190 2.000259 0.000000 191 2.325732 -1.224745 192 2.325732 0.000000 193 2.325732 1.224745 194 2.412318 0.000000 195 2.651961 -2.651961 196 2.651961 -1.673552 197 2.651961 -1.224745 198 2.651961 -0.816288 199 2.651961 0.000000 200 2.651961 0.816288 201 2.651961 1.224745 202 2.651961 1.673552 203 2.651961 2.651961 204 2.831680 0.000000 205 2.967167 -1.224745 206 2.967167 0.000000 207 2.967167 1.224745 208 3.260321 0.000000 209 3.669950 -1.224745 210 3.669950 0.000000 211 3.669950 1.224745 212 3.700743 0.000000 213 4.156272 0.000000 214 4.499991 -1.224745 215 4.499991 0.000000 216 4.499991 1.224745 217 4.631560 0.000000 218 5.133596 0.000000 219 5.673961 0.000000 220 6.275079 0.000000 221 6.995680 0.000000 TEST04: SPARSE_GRID_HERMITE computes Hermite sparse grid points and weights. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 Number of points in the grid = 273 Number of unique points in the grid = 1 Grid weights: 1 5.568328 Grid points: 1 0.000000 0.000000 0.000000 TEST04: SPARSE_GRID_HERMITE computes Hermite sparse grid points and weights. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 Number of points in the grid = 58 Number of unique points in the grid = 37 Grid weights: 1 0.003053 2 0.171266 3 0.154676 4 0.154676 5 -0.618703 6 0.154676 7 0.154676 8 1.337085 9 0.003053 10 0.171266 11 0.154676 12 -0.618703 13 0.154676 14 1.337085 15 0.003053 16 0.171266 17 -0.618703 18 1.337085 19 -1.643983 20 1.337085 21 -0.618703 22 0.171266 23 0.003053 24 1.337085 25 0.154676 26 -0.618703 27 0.154676 28 0.171266 29 0.003053 30 1.337085 31 0.154676 32 0.154676 33 -0.618703 34 0.154676 35 0.154676 36 0.171266 37 0.003053 Grid points: 1 -2.651961 0.000000 0.000000 2 -1.673552 0.000000 0.000000 3 -1.224745 -1.224745 0.000000 4 -1.224745 0.000000 -1.224745 5 -1.224745 0.000000 0.000000 6 -1.224745 0.000000 1.224745 7 -1.224745 1.224745 0.000000 8 -0.816288 0.000000 0.000000 9 0.000000 -2.651961 0.000000 10 0.000000 -1.673552 0.000000 11 0.000000 -1.224745 -1.224745 12 0.000000 -1.224745 0.000000 13 0.000000 -1.224745 1.224745 14 0.000000 -0.816288 0.000000 15 0.000000 0.000000 -2.651961 16 0.000000 0.000000 -1.673552 17 0.000000 0.000000 -1.224745 18 0.000000 0.000000 -0.816288 19 0.000000 0.000000 0.000000 20 0.000000 0.000000 0.816288 21 0.000000 0.000000 1.224745 22 0.000000 0.000000 1.673552 23 0.000000 0.000000 2.651961 24 0.000000 0.816288 0.000000 25 0.000000 1.224745 -1.224745 26 0.000000 1.224745 0.000000 27 0.000000 1.224745 1.224745 28 0.000000 1.673552 0.000000 29 0.000000 2.651961 0.000000 30 0.816288 0.000000 0.000000 31 1.224745 -1.224745 0.000000 32 1.224745 0.000000 -1.224745 33 1.224745 0.000000 0.000000 34 1.224745 0.000000 1.224745 35 1.224745 1.224745 0.000000 36 1.673552 0.000000 0.000000 37 2.651961 0.000000 0.000000 TEST05: 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 points in the grid = 273 Number of unique points in the grid = 221 Weight sum Exact sum Difference 3.14159 3.14159 0.310862E-14 TEST05: 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 points in the grid = 273 Number of unique points in the grid = 1 Weight sum Exact sum Difference 5.56833 5.56833 0.888178E-15 TEST05: 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 points in the grid = 10 Number of unique points in the grid = 7 Weight sum Exact sum Difference 5.56833 5.56833 0.888178E-15 TEST05: 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 points in the grid = 9484 Number of unique points in the grid = 6397 Weight sum Exact sum Difference 5.56833 5.56833 0.177636E-14 TEST05: 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 points in the grid = 5786 Number of unique points in the grid = 2441 Weight sum Exact sum Difference 306.020 306.020 0.492832E-10 TEST06 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 points in the grid = -1 Number of unique points in the grid = 1 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 3.14159 3.14159 0.282716E-15 0 0 0 0.00000 0.00000 0.00000 1 1 0 0.00000 0.00000 0.00000 1 0 1 1.57080 0.00000 1.00000 2 2 0 0.00000 0.00000 0.00000 2 1 1 1.57080 0.00000 1.00000 2 0 2 0.00000 0.00000 0.00000 3 3 0 0.00000 0.00000 0.00000 3 2 1 0.00000 0.00000 0.00000 3 1 2 0.00000 0.00000 0.00000 3 0 3 TEST06 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 points in the grid = 7 Number of unique points in the grid = 5 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 3.14159 3.14159 0.141358E-15 0 0 0 0.00000 0.222045E-15 0.222045E-15 1 1 0 0.00000 0.222045E-15 0.222045E-15 1 0 1 1.57080 1.57080 0.155494E-14 2 2 0 0.00000 0.00000 0.00000 2 1 1 1.57080 1.57080 0.155494E-14 2 0 2 0.00000 0.444089E-15 0.444089E-15 3 3 0 0.00000 0.00000 0.00000 3 2 1 0.00000 0.00000 0.00000 3 1 2 0.00000 0.444089E-15 0.444089E-15 3 0 3 2.35619 2.35619 0.188477E-14 4 4 0 0.00000 0.00000 0.00000 4 3 1 0.785398 0.00000 1.00000 4 2 2 0.00000 0.00000 0.00000 4 1 3 2.35619 2.35619 0.188477E-14 4 0 4 0.00000 0.444089E-15 0.444089E-15 5 5 0 0.00000 0.00000 0.00000 5 4 1 0.00000 0.00000 0.00000 5 3 2 0.00000 0.00000 0.00000 5 2 3 0.00000 0.00000 0.00000 5 1 4 0.00000 0.444089E-15 0.444089E-15 5 0 5 TEST06 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 = 8 Number of points in the grid = 29 Number of unique points in the grid = 21 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 3.14159 3.14159 0.183765E-14 0 0 0 0.00000 0.868229E-15 0.868229E-15 1 1 0 0.00000 0.832667E-15 0.832667E-15 1 0 1 1.57080 1.57080 0.848148E-15 2 2 0 0.00000 0.277556E-16 0.277556E-16 2 1 1 1.57080 1.57080 0.848148E-15 2 0 2 0.00000 0.978384E-15 0.978384E-15 3 3 0 0.00000 0.194289E-15 0.194289E-15 3 2 1 0.00000 0.166533E-15 0.166533E-15 3 1 2 0.00000 0.113798E-14 0.113798E-14 3 0 3 2.35619 2.35619 0.753909E-15 4 4 0 0.00000 0.555112E-16 0.555112E-16 4 3 1 0.785398 0.785398 0.268580E-14 4 2 2 0.00000 0.555112E-16 0.555112E-16 4 1 3 2.35619 2.35619 0.113086E-14 4 0 4 0.00000 0.327516E-14 0.327516E-14 5 5 0 0.00000 0.277556E-15 0.277556E-15 5 4 1 0.00000 0.277556E-15 0.277556E-15 5 3 2 0.00000 0.277556E-15 0.277556E-15 5 2 3 0.00000 0.277556E-15 0.277556E-15 5 1 4 0.00000 0.344169E-14 0.344169E-14 5 0 5 5.89049 5.89049 0.135704E-14 6 6 0 0.00000 0.00000 0.00000 6 5 1 1.17810 1.17810 0.339259E-14 6 4 2 0.00000 0.00000 0.00000 6 3 3 1.17810 1.17810 0.339259E-14 6 2 4 0.00000 0.00000 0.00000 6 1 5 5.89049 5.89049 0.135704E-14 6 0 6 0.00000 0.106581E-13 0.106581E-13 7 7 0 0.00000 0.388578E-15 0.388578E-15 7 6 1 0.00000 0.444089E-15 0.444089E-15 7 5 2 0.00000 0.388578E-15 0.388578E-15 7 4 3 0.00000 0.444089E-15 0.444089E-15 7 3 4 0.00000 0.388578E-15 0.388578E-15 7 2 5 0.00000 0.444089E-15 0.444089E-15 7 1 6 0.00000 0.117684E-13 0.117684E-13 7 0 7 20.6167 20.6167 0.120625E-14 8 8 0 0.00000 0.555112E-16 0.555112E-16 8 7 1 2.94524 1.76715 0.400000 8 6 2 0.00000 0.111022E-15 0.111022E-15 8 5 3 1.76715 1.76715 0.389520E-14 8 4 4 0.00000 0.111022E-15 0.111022E-15 8 3 5 2.94524 1.76715 0.400000 8 2 6 0.00000 0.555112E-16 0.555112E-16 8 1 7 20.6167 20.6167 0.103393E-14 8 0 8 TEST06 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 = 10 Number of points in the grid = 95 Number of unique points in the grid = 73 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 3.14159 3.14159 0.00000 0 0 0 0.00000 -0.325454E-16 0.325454E-16 1 1 0 0.00000 -0.117799E-15 0.117799E-15 1 0 1 1.57080 1.57080 0.169630E-14 2 2 0 0.00000 -0.480302E-16 0.480302E-16 2 1 1 1.57080 1.57080 0.183765E-14 2 0 2 0.00000 -0.387690E-15 0.387690E-15 3 3 0 0.00000 0.404191E-15 0.404191E-15 3 2 1 0.00000 0.339789E-15 0.339789E-15 3 1 2 0.00000 -0.370906E-15 0.370906E-15 3 0 3 2.35619 2.35619 0.169630E-14 4 4 0 0.00000 -0.234188E-16 0.234188E-16 4 3 1 0.785398 0.785398 0.127222E-14 4 2 2 0.00000 -0.199493E-16 0.199493E-16 4 1 3 2.35619 2.35619 0.150782E-14 4 0 4 0.00000 -0.217055E-14 0.217055E-14 5 5 0 0.00000 0.732053E-15 0.732053E-15 5 4 1 0.00000 0.563785E-15 0.563785E-15 5 3 2 0.00000 0.585035E-15 0.585035E-15 5 2 3 0.00000 0.740510E-15 0.740510E-15 5 1 4 0.00000 -0.246981E-14 0.246981E-14 5 0 5 5.89049 5.89049 0.301564E-15 6 6 0 0.00000 -0.346945E-16 0.346945E-16 6 5 1 1.17810 1.17810 0.150782E-14 6 4 2 0.00000 0.607153E-16 0.607153E-16 6 3 3 1.17810 1.17810 0.150782E-14 6 2 4 0.00000 -0.819657E-16 0.819657E-16 6 1 5 5.89049 5.89049 0.00000 6 0 6 0.00000 -0.723983E-14 0.723983E-14 7 7 0 0.00000 0.123512E-14 0.123512E-14 7 6 1 0.00000 0.161676E-14 0.161676E-14 7 5 2 0.00000 0.846545E-15 0.846545E-15 7 4 3 0.00000 0.832667E-15 0.832667E-15 7 3 4 0.00000 0.177896E-14 0.177896E-14 7 2 5 0.00000 0.940654E-15 0.940654E-15 7 1 6 0.00000 -0.556434E-14 0.556434E-14 7 0 7 20.6167 20.6167 0.172322E-14 8 8 0 0.00000 -0.277556E-15 0.277556E-15 8 7 1 2.94524 2.94524 0.211095E-14 8 6 2 0.00000 -0.693889E-16 0.693889E-16 8 5 3 1.76715 1.76715 0.163347E-14 8 4 4 0.00000 -0.102349E-15 0.102349E-15 8 3 5 2.94524 2.94524 0.226173E-14 8 2 6 0.00000 -0.150487E-15 0.150487E-15 8 1 7 20.6167 20.6167 0.172322E-14 8 0 8 0.00000 0.168147E-13 0.168147E-13 9 9 0 0.00000 0.355271E-14 0.355271E-14 9 8 1 0.00000 0.599520E-14 0.599520E-14 9 7 2 0.00000 0.188738E-14 0.188738E-14 9 6 3 0.00000 0.245637E-14 0.245637E-14 9 5 4 0.00000 0.251882E-14 0.251882E-14 9 4 5 0.00000 0.235575E-14 0.235575E-14 9 3 6 0.00000 0.572112E-14 0.572112E-14 9 2 7 0.00000 0.386453E-14 0.386453E-14 9 1 8 0.00000 0.118388E-13 0.118388E-13 9 0 9 92.7752 92.7752 0.199128E-14 10 10 0 0.00000 0.00000 0.00000 10 9 1 10.3084 10.3084 0.206787E-14 10 8 2 0.00000 -0.166533E-15 0.166533E-15 10 7 3 4.41786 4.41786 0.261355E-14 10 6 4 0.00000 -0.277556E-15 0.277556E-15 10 5 5 4.41786 4.41786 0.221147E-14 10 4 6 0.00000 -0.430211E-15 0.430211E-15 10 3 7 10.3084 10.3084 0.224019E-14 10 2 8 0.00000 -0.774554E-15 0.774554E-15 10 1 9 92.7752 92.7752 0.199128E-14 10 0 10 TEST06 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 = 13 Number of points in the grid = 273 Number of unique points in the grid = 221 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 3.14159 3.14159 0.113086E-14 0 0 0 0.00000 -0.575842E-15 0.575842E-15 1 1 0 0.00000 -0.437896E-15 0.437896E-15 1 0 1 1.57080 1.57080 0.141358E-15 2 2 0 0.00000 0.601796E-17 0.601796E-17 2 1 1 1.57080 1.57080 0.282716E-15 2 0 2 0.00000 -0.109540E-14 0.109540E-14 3 3 0 0.00000 -0.921546E-16 0.921546E-16 3 2 1 0.00000 -0.141575E-15 0.141575E-15 3 1 2 0.00000 -0.120617E-14 0.120617E-14 3 0 3 2.35619 2.35619 0.565432E-15 4 4 0 0.00000 -0.352298E-16 0.352298E-16 4 3 1 0.785398 0.785398 0.169630E-14 4 2 2 0.00000 -0.282151E-16 0.282151E-16 4 1 3 2.35619 2.35619 0.942387E-15 4 0 4 0.00000 -0.280060E-14 0.280060E-14 5 5 0 0.00000 -0.158253E-15 0.158253E-15 5 4 1 0.00000 -0.393497E-15 0.393497E-15 5 3 2 0.00000 -0.235158E-15 0.235158E-15 5 2 3 0.00000 -0.175754E-15 0.175754E-15 5 1 4 0.00000 -0.304647E-14 0.304647E-14 5 0 5 5.89049 5.89049 0.603127E-15 6 6 0 0.00000 0.109396E-15 0.109396E-15 6 5 1 1.17810 1.17810 0.565432E-15 6 4 2 0.00000 -0.765277E-16 0.765277E-16 6 3 3 1.17810 1.17810 0.131934E-14 6 2 4 0.00000 0.124604E-15 0.124604E-15 6 1 5 5.89049 5.89049 0.150782E-15 6 0 6 0.00000 -0.102677E-13 0.102677E-13 7 7 0 0.00000 0.500145E-15 0.500145E-15 7 6 1 0.00000 -0.923184E-15 0.923184E-15 7 5 2 0.00000 -0.286175E-15 0.286175E-15 7 4 3 0.00000 -0.605931E-15 0.605931E-15 7 3 4 0.00000 -0.134332E-14 0.134332E-14 7 2 5 0.00000 0.884490E-15 0.884490E-15 7 1 6 0.00000 -0.114898E-13 0.114898E-13 7 0 7 20.6167 20.6167 0.206787E-14 8 8 0 0.00000 0.348693E-15 0.348693E-15 8 7 1 2.94524 2.94524 0.00000 8 6 2 0.00000 -0.330597E-17 0.330597E-17 8 5 3 1.76715 1.76715 0.100521E-14 8 4 4 0.00000 0.984727E-16 0.984727E-16 8 3 5 2.94524 2.94524 0.00000 8 2 6 0.00000 0.200579E-15 0.200579E-15 8 1 7 20.6167 20.6167 0.155090E-14 8 0 8 0.00000 -0.579216E-13 0.579216E-13 9 9 0 0.00000 0.358746E-14 0.358746E-14 9 8 1 0.00000 -0.316535E-14 0.316535E-14 9 7 2 0.00000 0.174126E-15 0.174126E-15 9 6 3 0.00000 -0.220557E-14 0.220557E-14 9 5 4 0.00000 -0.210847E-14 0.210847E-14 9 4 5 0.00000 0.912533E-16 0.912533E-16 9 3 6 0.00000 -0.333521E-14 0.333521E-14 9 2 7 0.00000 0.610431E-14 0.610431E-14 9 1 8 0.00000 -0.515125E-13 0.515125E-13 9 0 9 92.7752 92.7752 0.352303E-14 10 10 0 0.00000 0.798244E-15 0.798244E-15 10 9 1 10.3084 10.3084 0.861611E-15 10 8 2 0.00000 0.294056E-15 0.294056E-15 10 7 3 4.41786 4.41786 0.201042E-15 10 6 4 0.00000 0.142043E-16 0.142043E-16 10 5 5 4.41786 4.41786 0.402085E-15 10 4 6 0.00000 0.490954E-15 0.490954E-15 10 3 7 10.3084 10.3084 0.137858E-14 10 2 8 0.00000 0.113484E-14 0.113484E-14 10 1 9 92.7752 92.7752 0.275715E-14 10 0 10 0.00000 -0.178991E-12 0.178991E-12 11 11 0 0.00000 0.196243E-13 0.196243E-13 11 10 1 0.00000 0.990852E-15 0.990852E-15 11 9 2 0.00000 0.455893E-14 0.455893E-14 11 8 3 0.00000 -0.389363E-14 0.389363E-14 11 7 4 0.00000 -0.970573E-15 0.970573E-15 11 6 5 0.00000 -0.502354E-15 0.502354E-15 11 5 6 0.00000 -0.479637E-14 0.479637E-14 11 4 7 0.00000 0.498985E-14 0.498985E-14 11 3 8 0.00000 0.639182E-14 0.639182E-14 11 2 9 0.00000 0.209165E-13 0.209165E-13 11 1 10 0.00000 -0.204538E-12 0.204538E-12 11 0 11 510.263 510.263 0.445601E-14 12 12 0 0.00000 -0.143809E-14 0.143809E-14 12 11 1 46.3876 46.3876 0.137858E-14 12 10 2 0.00000 0.104116E-14 0.104116E-14 12 9 3 15.4625 15.4625 0.919051E-15 12 8 4 0.00000 0.336563E-15 0.336563E-15 12 7 5 11.0447 11.0447 0.160834E-15 12 6 6 0.00000 0.455386E-16 0.455386E-16 12 5 7 15.4625 15.4625 0.804170E-15 12 4 8 0.00000 0.161333E-14 0.161333E-14 12 3 9 46.3876 46.3876 0.137858E-14 12 2 10 0.00000 -0.222001E-14 0.222001E-14 12 1 11 510.263 510.263 0.334200E-14 12 0 12 0.00000 0.620956E-13 0.620956E-13 13 13 0 0.00000 0.132803E-12 0.132803E-12 13 12 1 0.00000 0.167935E-12 0.167935E-12 13 11 2 0.00000 0.249818E-13 0.249818E-13 13 10 3 0.00000 0.135783E-13 0.135783E-13 13 9 4 0.00000 0.106721E-13 0.106721E-13 13 8 5 0.00000 0.734266E-14 0.734266E-14 13 7 6 0.00000 0.115360E-14 0.115360E-14 13 6 7 0.00000 0.947543E-14 0.947543E-14 13 5 8 0.00000 0.113869E-13 0.113869E-13 13 4 9 0.00000 0.223476E-13 0.223476E-13 13 3 10 0.00000 0.156487E-12 0.156487E-12 13 2 11 0.00000 0.124093E-12 0.124093E-12 13 1 12 0.00000 -0.560660E-13 0.560660E-13 13 0 13 TEST06 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 be checked is DEGREE_MAX = 13 Number of points in the grid = 723 Number of unique points in the grid = 609 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 3.14159 3.14159 0.183765E-14 0 0 0 0.00000 -0.176536E-15 0.176536E-15 1 1 0 0.00000 0.113904E-15 0.113904E-15 1 0 1 1.57080 1.57080 0.155494E-14 2 2 0 0.00000 0.231780E-16 0.231780E-16 2 1 1 1.57080 1.57080 0.989506E-15 2 0 2 0.00000 -0.164211E-14 0.164211E-14 3 3 0 0.00000 -0.303713E-15 0.303713E-15 3 2 1 0.00000 -0.439376E-15 0.439376E-15 3 1 2 0.00000 -0.122877E-14 0.122877E-14 3 0 3 2.35619 2.35619 0.282716E-14 4 4 0 0.00000 0.259585E-16 0.259585E-16 4 3 1 0.785398 0.785398 0.113086E-14 4 2 2 0.00000 0.349060E-16 0.349060E-16 4 1 3 2.35619 2.35619 0.942387E-15 4 0 4 0.00000 -0.196581E-14 0.196581E-14 5 5 0 0.00000 -0.448913E-15 0.448913E-15 5 4 1 0.00000 -0.644272E-15 0.644272E-15 5 3 2 0.00000 -0.652928E-15 0.652928E-15 5 2 3 0.00000 -0.443766E-15 0.443766E-15 5 1 4 0.00000 -0.271667E-14 0.271667E-14 5 0 5 5.89049 5.89049 0.331720E-14 6 6 0 0.00000 -0.592743E-16 0.592743E-16 6 5 1 1.17810 1.17810 0.376955E-15 6 4 2 0.00000 0.260161E-16 0.260161E-16 6 3 3 1.17810 1.17810 0.376955E-15 6 2 4 0.00000 -0.700096E-16 0.700096E-16 6 1 5 5.89049 5.89049 0.301564E-14 6 0 6 0.00000 -0.216757E-14 0.216757E-14 7 7 0 0.00000 -0.821425E-15 0.821425E-15 7 6 1 0.00000 -0.163005E-14 0.163005E-14 7 5 2 0.00000 -0.106026E-14 0.106026E-14 7 4 3 0.00000 -0.109445E-14 0.109445E-14 7 3 4 0.00000 -0.169087E-14 0.169087E-14 7 2 5 0.00000 -0.109773E-14 0.109773E-14 7 1 6 0.00000 -0.593276E-15 0.593276E-15 7 0 7 20.6167 20.6167 0.396341E-14 8 8 0 0.00000 -0.110938E-15 0.110938E-15 8 7 1 2.94524 2.94524 0.150782E-14 8 6 2 0.00000 -0.135843E-15 0.135843E-15 8 5 3 1.76715 1.76715 0.150782E-14 8 4 4 0.00000 -0.142436E-15 0.142436E-15 8 3 5 2.94524 2.94524 0.00000 8 2 6 0.00000 -0.896749E-16 0.896749E-16 8 1 7 20.6167 20.6167 0.448038E-14 8 0 8 0.00000 0.361235E-13 0.361235E-13 9 9 0 0.00000 -0.217240E-14 0.217240E-14 9 8 1 0.00000 -0.573672E-14 0.573672E-14 9 7 2 0.00000 -0.211580E-14 0.211580E-14 9 6 3 0.00000 -0.188078E-14 0.188078E-14 9 5 4 0.00000 -0.246637E-14 0.246637E-14 9 4 5 0.00000 -0.173141E-14 0.173141E-14 9 3 6 0.00000 -0.522005E-14 0.522005E-14 9 2 7 0.00000 -0.207217E-14 0.207217E-14 9 1 8 0.00000 0.387035E-13 0.387035E-13 9 0 9 92.7752 92.7752 0.566748E-14 10 10 0 0.00000 -0.533115E-15 0.533115E-15 10 9 1 10.3084 10.3084 0.189554E-14 10 8 2 0.00000 -0.897850E-17 0.897850E-17 10 7 3 4.41786 4.41786 0.804170E-15 10 6 4 0.00000 0.358452E-16 0.358452E-16 10 5 5 4.41786 4.41786 0.321668E-14 10 4 6 0.00000 -0.175910E-15 0.175910E-15 10 3 7 10.3084 10.3084 0.344644E-14 10 2 8 0.00000 -0.468455E-15 0.468455E-15 10 1 9 92.7752 92.7752 0.536113E-14 10 0 10 0.00000 0.422537E-12 0.422537E-12 11 11 0 0.00000 -0.412853E-14 0.412853E-14 11 10 1 0.00000 -0.155217E-13 0.155217E-13 11 9 2 0.00000 -0.487750E-14 0.487750E-14 11 8 3 0.00000 -0.785653E-14 0.785653E-14 11 7 4 0.00000 -0.561286E-14 0.561286E-14 11 6 5 0.00000 -0.592132E-14 0.592132E-14 11 5 6 0.00000 -0.845845E-14 0.845845E-14 11 4 7 0.00000 -0.161478E-14 0.161478E-14 11 3 8 0.00000 -0.246621E-13 0.246621E-13 11 2 9 0.00000 -0.414205E-15 0.414205E-15 11 1 10 0.00000 0.416093E-12 0.416093E-12 11 0 11 510.263 510.263 0.445601E-14 12 12 0 0.00000 -0.335905E-14 0.335905E-14 12 11 1 46.3876 46.3876 0.382938E-14 12 10 2 0.00000 -0.699119E-15 0.699119E-15 12 9 3 15.4625 15.4625 0.241251E-14 12 8 4 0.00000 0.496904E-16 0.496904E-16 12 7 5 11.0447 11.0447 0.241251E-14 12 6 6 0.00000 0.263383E-15 0.263383E-15 12 5 7 15.4625 15.4625 0.275715E-14 12 4 8 0.00000 -0.189944E-14 0.189944E-14 12 3 9 46.3876 46.3876 0.260398E-14 12 2 10 0.00000 0.154936E-15 0.154936E-15 12 1 11 510.263 510.263 0.434461E-14 12 0 12 0.00000 0.344106E-11 0.344106E-11 13 13 0 0.00000 -0.207593E-13 0.207593E-13 13 12 1 0.00000 -0.931172E-13 0.931172E-13 13 11 2 0.00000 -0.177829E-13 0.177829E-13 13 10 3 0.00000 -0.358659E-13 0.358659E-13 13 9 4 0.00000 -0.183454E-13 0.183454E-13 13 8 5 0.00000 -0.237836E-13 0.237836E-13 13 7 6 0.00000 -0.145811E-13 0.145811E-13 13 6 7 0.00000 -0.218251E-13 0.218251E-13 13 5 8 0.00000 -0.368389E-13 0.368389E-13 13 4 9 0.00000 -0.187867E-13 0.187867E-13 13 3 10 0.00000 -0.102520E-12 0.102520E-12 13 2 11 0.00000 -0.578033E-13 0.578033E-13 13 1 12 0.00000 0.320941E-11 0.320941E-11 13 0 13 TEST06 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 points in the grid = 723 Number of unique points in the grid = 1 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 5.56833 5.56833 0.478516E-15 0 0 0 0 0.00000 0.00000 0.00000 1 1 0 0 0.00000 0.00000 0.00000 1 0 1 0 0.00000 0.00000 0.00000 1 0 0 1 2.78416 0.00000 1.00000 2 2 0 0 0.00000 0.00000 0.00000 2 1 1 0 2.78416 0.00000 1.00000 2 0 2 0 0.00000 0.00000 0.00000 2 1 0 1 0.00000 0.00000 0.00000 2 0 1 1 2.78416 0.00000 1.00000 2 0 0 2 TEST06 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 = 9 Number of points in the grid = 10 Number of unique points in the grid = 7 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 5.56833 5.56833 0.159505E-15 0 0 0 0 0.00000 0.444089E-15 0.444089E-15 1 1 0 0 0.00000 0.444089E-15 0.444089E-15 1 0 1 0 0.00000 0.888178E-15 0.888178E-15 1 0 0 1 2.78416 2.78416 0.175456E-14 2 2 0 0 0.00000 0.00000 0.00000 2 1 1 0 2.78416 2.78416 0.175456E-14 2 0 2 0 0.00000 0.00000 0.00000 2 1 0 1 0.00000 0.00000 0.00000 2 0 1 1 2.78416 2.78416 0.175456E-14 2 0 0 2 0.00000 0.666134E-15 0.666134E-15 3 3 0 0 0.00000 0.00000 0.00000 3 2 1 0 0.00000 0.00000 0.00000 3 1 2 0 0.00000 0.666134E-15 0.666134E-15 3 0 3 0 0.00000 0.00000 0.00000 3 2 0 1 0.00000 0.00000 0.00000 3 1 1 1 0.00000 0.00000 0.00000 3 0 2 1 0.00000 0.00000 0.00000 3 1 0 2 0.00000 0.00000 0.00000 3 0 1 2 0.00000 0.111022E-14 0.111022E-14 3 0 0 3 4.17625 4.17625 0.212674E-14 4 4 0 0 0.00000 0.00000 0.00000 4 3 1 0 1.39208 0.00000 1.00000 4 2 2 0 0.00000 0.00000 0.00000 4 1 3 0 4.17625 4.17625 0.212674E-14 4 0 4 0 0.00000 0.00000 0.00000 4 3 0 1 0.00000 0.00000 0.00000 4 2 1 1 0.00000 0.00000 0.00000 4 1 2 1 0.00000 0.00000 0.00000 4 0 3 1 1.39208 0.00000 1.00000 4 2 0 2 0.00000 0.00000 0.00000 4 1 1 2 1.39208 0.00000 1.00000 4 0 2 2 0.00000 0.00000 0.00000 4 1 0 3 0.00000 0.00000 0.00000 4 0 1 3 4.17625 4.17625 0.233941E-14 4 0 0 4 0.00000 0.888178E-15 0.888178E-15 5 5 0 0 0.00000 0.00000 0.00000 5 4 1 0 0.00000 0.00000 0.00000 5 3 2 0 0.00000 0.00000 0.00000 5 2 3 0 0.00000 0.00000 0.00000 5 1 4 0 0.00000 0.888178E-15 0.888178E-15 5 0 5 0 0.00000 0.00000 0.00000 5 4 0 1 0.00000 0.00000 0.00000 5 3 1 1 0.00000 0.00000 0.00000 5 2 2 1 0.00000 0.00000 0.00000 5 1 3 1 0.00000 0.00000 0.00000 5 0 4 1 0.00000 0.00000 0.00000 5 3 0 2 0.00000 0.00000 0.00000 5 2 1 2 0.00000 0.00000 0.00000 5 1 2 2 0.00000 0.00000 0.00000 5 0 3 2 0.00000 0.00000 0.00000 5 2 0 3 0.00000 0.00000 0.00000 5 1 1 3 0.00000 0.00000 0.00000 5 0 2 3 0.00000 0.00000 0.00000 5 1 0 4 0.00000 0.00000 0.00000 5 0 1 4 0.00000 0.177636E-14 0.177636E-14 5 0 0 5 10.4406 6.26437 0.400000 6 6 0 0 0.00000 0.00000 0.00000 6 5 1 0 2.08812 0.00000 1.00000 6 4 2 0 0.00000 0.00000 0.00000 6 3 3 0 2.08812 0.00000 1.00000 6 2 4 0 0.00000 0.00000 0.00000 6 1 5 0 10.4406 6.26437 0.400000 6 0 6 0 0.00000 0.00000 0.00000 6 5 0 1 0.00000 0.00000 0.00000 6 4 1 1 0.00000 0.00000 0.00000 6 3 2 1 0.00000 0.00000 0.00000 6 2 3 1 0.00000 0.00000 0.00000 6 1 4 1 0.00000 0.00000 0.00000 6 0 5 1 2.08812 0.00000 1.00000 6 4 0 2 0.00000 0.00000 0.00000 6 3 1 2 0.696041 0.00000 1.00000 6 2 2 2 0.00000 0.00000 0.00000 6 1 3 2 2.08812 0.00000 1.00000 6 0 4 2 0.00000 0.00000 0.00000 6 3 0 3 0.00000 0.00000 0.00000 6 2 1 3 0.00000 0.00000 0.00000 6 1 2 3 0.00000 0.00000 0.00000 6 0 3 3 2.08812 0.00000 1.00000 6 2 0 4 0.00000 0.00000 0.00000 6 1 1 4 2.08812 0.00000 1.00000 6 0 2 4 0.00000 0.00000 0.00000 6 1 0 5 0.00000 0.00000 0.00000 6 0 1 5 10.4406 6.26437 0.400000 6 0 0 6 0.00000 0.177636E-14 0.177636E-14 7 7 0 0 0.00000 0.00000 0.00000 7 6 1 0 0.00000 0.00000 0.00000 7 5 2 0 0.00000 0.00000 0.00000 7 4 3 0 0.00000 0.00000 0.00000 7 3 4 0 0.00000 0.00000 0.00000 7 2 5 0 0.00000 0.00000 0.00000 7 1 6 0 0.00000 0.177636E-14 0.177636E-14 7 0 7 0 0.00000 0.00000 0.00000 7 6 0 1 0.00000 0.00000 0.00000 7 5 1 1 0.00000 0.00000 0.00000 7 4 2 1 0.00000 0.00000 0.00000 7 3 3 1 0.00000 0.00000 0.00000 7 2 4 1 0.00000 0.00000 0.00000 7 1 5 1 0.00000 0.00000 0.00000 7 0 6 1 0.00000 0.00000 0.00000 7 5 0 2 0.00000 0.00000 0.00000 7 4 1 2 0.00000 0.00000 0.00000 7 3 2 2 0.00000 0.00000 0.00000 7 2 3 2 0.00000 0.00000 0.00000 7 1 4 2 0.00000 0.00000 0.00000 7 0 5 2 0.00000 0.00000 0.00000 7 4 0 3 0.00000 0.00000 0.00000 7 3 1 3 0.00000 0.00000 0.00000 7 2 2 3 0.00000 0.00000 0.00000 7 1 3 3 0.00000 0.00000 0.00000 7 0 4 3 0.00000 0.00000 0.00000 7 3 0 4 0.00000 0.00000 0.00000 7 2 1 4 0.00000 0.00000 0.00000 7 1 2 4 0.00000 0.00000 0.00000 7 0 3 4 0.00000 0.00000 0.00000 7 2 0 5 0.00000 0.00000 0.00000 7 1 1 5 0.00000 0.00000 0.00000 7 0 2 5 0.00000 0.00000 0.00000 7 1 0 6 0.00000 0.00000 0.00000 7 0 1 6 0.00000 0.266454E-14 0.266454E-14 7 0 0 7 36.5422 9.39655 0.742857 8 8 0 0 0.00000 0.00000 0.00000 8 7 1 0 5.22031 0.00000 1.00000 8 6 2 0 0.00000 0.00000 0.00000 8 5 3 0 3.13218 0.00000 1.00000 8 4 4 0 0.00000 0.00000 0.00000 8 3 5 0 5.22031 0.00000 1.00000 8 2 6 0 0.00000 0.00000 0.00000 8 1 7 0 36.5422 9.39655 0.742857 8 0 8 0 0.00000 0.00000 0.00000 8 7 0 1 0.00000 0.00000 0.00000 8 6 1 1 0.00000 0.00000 0.00000 8 5 2 1 0.00000 0.00000 0.00000 8 4 3 1 0.00000 0.00000 0.00000 8 3 4 1 0.00000 0.00000 0.00000 8 2 5 1 0.00000 0.00000 0.00000 8 1 6 1 0.00000 0.00000 0.00000 8 0 7 1 5.22031 0.00000 1.00000 8 6 0 2 0.00000 0.00000 0.00000 8 5 1 2 1.04406 0.00000 1.00000 8 4 2 2 0.00000 0.00000 0.00000 8 3 3 2 1.04406 0.00000 1.00000 8 2 4 2 0.00000 0.00000 0.00000 8 1 5 2 5.22031 0.00000 1.00000 8 0 6 2 0.00000 0.00000 0.00000 8 5 0 3 0.00000 0.00000 0.00000 8 4 1 3 0.00000 0.00000 0.00000 8 3 2 3 0.00000 0.00000 0.00000 8 2 3 3 0.00000 0.00000 0.00000 8 1 4 3 0.00000 0.00000 0.00000 8 0 5 3 3.13218 0.00000 1.00000 8 4 0 4 0.00000 0.00000 0.00000 8 3 1 4 1.04406 0.00000 1.00000 8 2 2 4 0.00000 0.00000 0.00000 8 1 3 4 3.13218 0.00000 1.00000 8 0 4 4 0.00000 0.00000 0.00000 8 3 0 5 0.00000 0.00000 0.00000 8 2 1 5 0.00000 0.00000 0.00000 8 1 2 5 0.00000 0.00000 0.00000 8 0 3 5 5.22031 0.00000 1.00000 8 2 0 6 0.00000 0.00000 0.00000 8 1 1 6 5.22031 0.00000 1.00000 8 0 2 6 0.00000 0.00000 0.00000 8 1 0 7 0.00000 0.00000 0.00000 8 0 1 7 36.5422 9.39655 0.742857 8 0 0 8 0.00000 0.177636E-14 0.177636E-14 9 9 0 0 0.00000 0.00000 0.00000 9 8 1 0 0.00000 0.00000 0.00000 9 7 2 0 0.00000 0.00000 0.00000 9 6 3 0 0.00000 0.00000 0.00000 9 5 4 0 0.00000 0.00000 0.00000 9 4 5 0 0.00000 0.00000 0.00000 9 3 6 0 0.00000 0.00000 0.00000 9 2 7 0 0.00000 0.00000 0.00000 9 1 8 0 0.00000 0.177636E-14 0.177636E-14 9 0 9 0 0.00000 0.00000 0.00000 9 8 0 1 0.00000 0.00000 0.00000 9 7 1 1 0.00000 0.00000 0.00000 9 6 2 1 0.00000 0.00000 0.00000 9 5 3 1 0.00000 0.00000 0.00000 9 4 4 1 0.00000 0.00000 0.00000 9 3 5 1 0.00000 0.00000 0.00000 9 2 6 1 0.00000 0.00000 0.00000 9 1 7 1 0.00000 0.00000 0.00000 9 0 8 1 0.00000 0.00000 0.00000 9 7 0 2 0.00000 0.00000 0.00000 9 6 1 2 0.00000 0.00000 0.00000 9 5 2 2 0.00000 0.00000 0.00000 9 4 3 2 0.00000 0.00000 0.00000 9 3 4 2 0.00000 0.00000 0.00000 9 2 5 2 0.00000 0.00000 0.00000 9 1 6 2 0.00000 0.00000 0.00000 9 0 7 2 0.00000 0.00000 0.00000 9 6 0 3 0.00000 0.00000 0.00000 9 5 1 3 0.00000 0.00000 0.00000 9 4 2 3 0.00000 0.00000 0.00000 9 3 3 3 0.00000 0.00000 0.00000 9 2 4 3 0.00000 0.00000 0.00000 9 1 5 3 0.00000 0.00000 0.00000 9 0 6 3 0.00000 0.00000 0.00000 9 5 0 4 0.00000 0.00000 0.00000 9 4 1 4 0.00000 0.00000 0.00000 9 3 2 4 0.00000 0.00000 0.00000 9 2 3 4 0.00000 0.00000 0.00000 9 1 4 4 0.00000 0.00000 0.00000 9 0 5 4 0.00000 0.00000 0.00000 9 4 0 5 0.00000 0.00000 0.00000 9 3 1 5 0.00000 0.00000 0.00000 9 2 2 5 0.00000 0.00000 0.00000 9 1 3 5 0.00000 0.00000 0.00000 9 0 4 5 0.00000 0.00000 0.00000 9 3 0 6 0.00000 0.00000 0.00000 9 2 1 6 0.00000 0.00000 0.00000 9 1 2 6 0.00000 0.00000 0.00000 9 0 3 6 0.00000 0.00000 0.00000 9 2 0 7 0.00000 0.00000 0.00000 9 1 1 7 0.00000 0.00000 0.00000 9 0 2 7 0.00000 0.00000 0.00000 9 1 0 8 0.00000 0.00000 0.00000 9 0 1 8 0.00000 0.355271E-14 0.355271E-14 9 0 0 9 TEST06 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 = 9 Number of points in the grid = 58 Number of unique points in the grid = 37 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 5.56833 5.56833 0.255209E-14 0 0 0 0 0.00000 0.164105E-14 0.164105E-14 1 1 0 0 0.00000 0.169309E-14 0.169309E-14 1 0 1 0 0.00000 0.136002E-14 0.136002E-14 1 0 0 1 2.78416 2.78416 0.638022E-15 2 2 0 0 0.00000 0.277556E-16 0.277556E-16 2 1 1 0 2.78416 2.78416 0.797527E-15 2 0 2 0 0.00000 0.00000 0.00000 2 1 0 1 0.00000 0.00000 0.00000 2 0 1 1 2.78416 2.78416 0.797527E-15 2 0 0 2 0.00000 0.231065E-14 0.231065E-14 3 3 0 0 0.00000 0.333067E-15 0.333067E-15 3 2 1 0 0.00000 0.277556E-15 0.277556E-15 3 1 2 0 0.00000 0.260902E-14 0.260902E-14 3 0 3 0 0.00000 0.333067E-15 0.333067E-15 3 2 0 1 0.00000 0.00000 0.00000 3 1 1 1 0.00000 0.333067E-15 0.333067E-15 3 0 2 1 0.00000 0.166533E-15 0.166533E-15 3 1 0 2 0.00000 0.166533E-15 0.166533E-15 3 0 1 2 0.00000 0.155431E-14 0.155431E-14 3 0 0 3 4.17625 4.17625 0.638022E-15 4 4 0 0 0.00000 -0.555112E-16 0.555112E-16 4 3 1 0 1.39208 1.39208 0.303060E-14 4 2 2 0 0.00000 -0.555112E-16 0.555112E-16 4 1 3 0 4.17625 4.17625 0.850696E-15 4 0 4 0 0.00000 -0.555112E-16 0.555112E-16 4 3 0 1 0.00000 0.00000 0.00000 4 2 1 1 0.00000 0.00000 0.00000 4 1 2 1 0.00000 -0.555112E-16 0.555112E-16 4 0 3 1 1.39208 1.39208 0.303060E-14 4 2 0 2 0.00000 0.00000 0.00000 4 1 1 2 1.39208 1.39208 0.303060E-14 4 0 2 2 0.00000 -0.555112E-16 0.555112E-16 4 1 0 3 0.00000 -0.555112E-16 0.555112E-16 4 0 1 3 4.17625 4.17625 0.127604E-14 4 0 0 4 0.00000 0.610623E-14 0.610623E-14 5 5 0 0 0.00000 0.444089E-15 0.444089E-15 5 4 1 0 0.00000 0.444089E-15 0.444089E-15 5 3 2 0 0.00000 0.444089E-15 0.444089E-15 5 2 3 0 0.00000 0.444089E-15 0.444089E-15 5 1 4 0 0.00000 0.632827E-14 0.632827E-14 5 0 5 0 0.00000 0.444089E-15 0.444089E-15 5 4 0 1 0.00000 0.00000 0.00000 5 3 1 1 0.00000 0.00000 0.00000 5 2 2 1 0.00000 0.00000 0.00000 5 1 3 1 0.00000 0.444089E-15 0.444089E-15 5 0 4 1 0.00000 0.333067E-15 0.333067E-15 5 3 0 2 0.00000 0.00000 0.00000 5 2 1 2 0.00000 0.00000 0.00000 5 1 2 2 0.00000 0.333067E-15 0.333067E-15 5 0 3 2 0.00000 0.444089E-15 0.444089E-15 5 2 0 3 0.00000 0.00000 0.00000 5 1 1 3 0.00000 0.444089E-15 0.444089E-15 5 0 2 3 0.00000 0.333067E-15 0.333067E-15 5 1 0 4 0.00000 0.333067E-15 0.333067E-15 5 0 1 4 0.00000 0.521805E-14 0.521805E-14 5 0 0 5 10.4406 10.4406 0.136111E-14 6 6 0 0 0.00000 0.111022E-15 0.111022E-15 6 5 1 0 2.08812 2.08812 0.340278E-14 6 4 2 0 0.00000 0.111022E-15 0.111022E-15 6 3 3 0 2.08812 2.08812 0.340278E-14 6 2 4 0 0.00000 0.111022E-15 0.111022E-15 6 1 5 0 10.4406 10.4406 0.136111E-14 6 0 6 0 0.00000 0.111022E-15 0.111022E-15 6 5 0 1 0.00000 0.00000 0.00000 6 4 1 1 0.00000 0.00000 0.00000 6 3 2 1 0.00000 0.00000 0.00000 6 2 3 1 0.00000 0.00000 0.00000 6 1 4 1 0.00000 0.111022E-15 0.111022E-15 6 0 5 1 2.08812 2.08812 0.340278E-14 6 4 0 2 0.00000 0.00000 0.00000 6 3 1 2 0.696041 0.00000 1.00000 6 2 2 2 0.00000 0.00000 0.00000 6 1 3 2 2.08812 2.08812 0.340278E-14 6 0 4 2 0.00000 0.111022E-15 0.111022E-15 6 3 0 3 0.00000 0.00000 0.00000 6 2 1 3 0.00000 0.00000 0.00000 6 1 2 3 0.00000 0.111022E-15 0.111022E-15 6 0 3 3 2.08812 2.08812 0.361546E-14 6 2 0 4 0.00000 0.00000 0.00000 6 1 1 4 2.08812 2.08812 0.361546E-14 6 0 2 4 0.00000 0.111022E-15 0.111022E-15 6 1 0 5 0.00000 0.111022E-15 0.111022E-15 6 0 1 5 10.4406 10.4406 0.136111E-14 6 0 0 6 0.00000 0.226485E-13 0.226485E-13 7 7 0 0 0.00000 0.666134E-15 0.666134E-15 7 6 1 0 0.00000 0.777156E-15 0.777156E-15 7 5 2 0 0.00000 0.666134E-15 0.666134E-15 7 4 3 0 0.00000 0.777156E-15 0.777156E-15 7 3 4 0 0.00000 0.666134E-15 0.666134E-15 7 2 5 0 0.00000 0.777156E-15 0.777156E-15 7 1 6 0 0.00000 0.212053E-13 0.212053E-13 7 0 7 0 0.00000 0.666134E-15 0.666134E-15 7 6 0 1 0.00000 0.00000 0.00000 7 5 1 1 0.00000 0.00000 0.00000 7 4 2 1 0.00000 0.00000 0.00000 7 3 3 1 0.00000 0.00000 0.00000 7 2 4 1 0.00000 0.00000 0.00000 7 1 5 1 0.00000 0.666134E-15 0.666134E-15 7 0 6 1 0.00000 0.555112E-15 0.555112E-15 7 5 0 2 0.00000 0.00000 0.00000 7 4 1 2 0.00000 0.00000 0.00000 7 3 2 2 0.00000 0.00000 0.00000 7 2 3 2 0.00000 0.00000 0.00000 7 1 4 2 0.00000 0.555112E-15 0.555112E-15 7 0 5 2 0.00000 0.666134E-15 0.666134E-15 7 4 0 3 0.00000 0.00000 0.00000 7 3 1 3 0.00000 0.00000 0.00000 7 2 2 3 0.00000 0.00000 0.00000 7 1 3 3 0.00000 0.666134E-15 0.666134E-15 7 0 4 3 0.00000 0.555112E-15 0.555112E-15 7 3 0 4 0.00000 0.00000 0.00000 7 2 1 4 0.00000 0.00000 0.00000 7 1 2 4 0.00000 0.555112E-15 0.555112E-15 7 0 3 4 0.00000 0.666134E-15 0.666134E-15 7 2 0 5 0.00000 0.00000 0.00000 7 1 1 5 0.00000 0.666134E-15 0.666134E-15 7 0 2 5 0.00000 0.555112E-15 0.555112E-15 7 1 0 6 0.00000 0.555112E-15 0.555112E-15 7 0 1 6 0.00000 0.179856E-13 0.179856E-13 7 0 0 7 36.5422 36.5422 0.116667E-14 8 8 0 0 0.00000 0.00000 0.00000 8 7 1 0 5.22031 3.13218 0.400000 8 6 2 0 0.00000 0.00000 0.00000 8 5 3 0 3.13218 3.13218 0.411169E-14 8 4 4 0 0.00000 0.00000 0.00000 8 3 5 0 5.22031 3.13218 0.400000 8 2 6 0 0.00000 0.00000 0.00000 8 1 7 0 36.5422 36.5422 0.972223E-15 8 0 8 0 0.00000 0.00000 0.00000 8 7 0 1 0.00000 0.00000 0.00000 8 6 1 1 0.00000 0.00000 0.00000 8 5 2 1 0.00000 0.00000 0.00000 8 4 3 1 0.00000 0.00000 0.00000 8 3 4 1 0.00000 0.00000 0.00000 8 2 5 1 0.00000 0.00000 0.00000 8 1 6 1 0.00000 0.00000 0.00000 8 0 7 1 5.22031 3.13218 0.400000 8 6 0 2 0.00000 0.00000 0.00000 8 5 1 2 1.04406 0.00000 1.00000 8 4 2 2 0.00000 0.00000 0.00000 8 3 3 2 1.04406 0.00000 1.00000 8 2 4 2 0.00000 0.00000 0.00000 8 1 5 2 5.22031 3.13218 0.400000 8 0 6 2 0.00000 0.00000 0.00000 8 5 0 3 0.00000 0.00000 0.00000 8 4 1 3 0.00000 0.00000 0.00000 8 3 2 3 0.00000 0.00000 0.00000 8 2 3 3 0.00000 0.00000 0.00000 8 1 4 3 0.00000 0.00000 0.00000 8 0 5 3 3.13218 3.13218 0.411169E-14 8 4 0 4 0.00000 0.00000 0.00000 8 3 1 4 1.04406 0.00000 1.00000 8 2 2 4 0.00000 0.00000 0.00000 8 1 3 4 3.13218 3.13218 0.411169E-14 8 0 4 4 0.00000 0.00000 0.00000 8 3 0 5 0.00000 0.00000 0.00000 8 2 1 5 0.00000 0.00000 0.00000 8 1 2 5 0.00000 0.00000 0.00000 8 0 3 5 5.22031 3.13218 0.400000 8 2 0 6 0.00000 0.00000 0.00000 8 1 1 6 5.22031 3.13218 0.400000 8 0 2 6 0.00000 0.00000 0.00000 8 1 0 7 0.00000 0.00000 0.00000 8 0 1 7 36.5422 36.5422 0.972223E-15 8 0 0 8 0.00000 0.888178E-13 0.888178E-13 9 9 0 0 0.00000 0.999201E-15 0.999201E-15 9 8 1 0 0.00000 0.888178E-15 0.888178E-15 9 7 2 0 0.00000 0.999201E-15 0.999201E-15 9 6 3 0 0.00000 0.111022E-14 0.111022E-14 9 5 4 0 0.00000 0.999201E-15 0.999201E-15 9 4 5 0 0.00000 0.888178E-15 0.888178E-15 9 3 6 0 0.00000 0.999201E-15 0.999201E-15 9 2 7 0 0.00000 0.888178E-15 0.888178E-15 9 1 8 0 0.00000 0.892619E-13 0.892619E-13 9 0 9 0 0.00000 0.111022E-14 0.111022E-14 9 8 0 1 0.00000 0.00000 0.00000 9 7 1 1 0.00000 0.00000 0.00000 9 6 2 1 0.00000 0.00000 0.00000 9 5 3 1 0.00000 0.00000 0.00000 9 4 4 1 0.00000 0.00000 0.00000 9 3 5 1 0.00000 0.00000 0.00000 9 2 6 1 0.00000 0.00000 0.00000 9 1 7 1 0.00000 0.111022E-14 0.111022E-14 9 0 8 1 0.00000 0.555112E-15 0.555112E-15 9 7 0 2 0.00000 0.00000 0.00000 9 6 1 2 0.00000 0.00000 0.00000 9 5 2 2 0.00000 0.00000 0.00000 9 4 3 2 0.00000 0.00000 0.00000 9 3 4 2 0.00000 0.00000 0.00000 9 2 5 2 0.00000 0.00000 0.00000 9 1 6 2 0.00000 0.555112E-15 0.555112E-15 9 0 7 2 0.00000 0.111022E-14 0.111022E-14 9 6 0 3 0.00000 0.00000 0.00000 9 5 1 3 0.00000 0.00000 0.00000 9 4 2 3 0.00000 0.00000 0.00000 9 3 3 3 0.00000 0.00000 0.00000 9 2 4 3 0.00000 0.00000 0.00000 9 1 5 3 0.00000 0.111022E-14 0.111022E-14 9 0 6 3 0.00000 0.777156E-15 0.777156E-15 9 5 0 4 0.00000 0.00000 0.00000 9 4 1 4 0.00000 0.00000 0.00000 9 3 2 4 0.00000 0.00000 0.00000 9 2 3 4 0.00000 0.00000 0.00000 9 1 4 4 0.00000 0.777156E-15 0.777156E-15 9 0 5 4 0.00000 0.111022E-14 0.111022E-14 9 4 0 5 0.00000 0.00000 0.00000 9 3 1 5 0.00000 0.00000 0.00000 9 2 2 5 0.00000 0.00000 0.00000 9 1 3 5 0.00000 0.111022E-14 0.111022E-14 9 0 4 5 0.00000 0.555112E-15 0.555112E-15 9 3 0 6 0.00000 0.00000 0.00000 9 2 1 6 0.00000 0.00000 0.00000 9 1 2 6 0.00000 0.555112E-15 0.555112E-15 9 0 3 6 0.00000 0.111022E-14 0.111022E-14 9 2 0 7 0.00000 0.00000 0.00000 9 1 1 7 0.00000 0.111022E-14 0.111022E-14 9 0 2 7 0.00000 0.555112E-15 0.555112E-15 9 1 0 8 0.00000 0.555112E-15 0.555112E-15 9 0 1 8 0.00000 0.899281E-13 0.899281E-13 9 0 0 9 TEST06 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 = 9 Number of points in the grid = 255 Number of unique points in the grid = 159 Exact Estimate Error Total Monomial Degree Exponents -------------- -------------- -------------- -- -------------------- 5.56833 5.56833 0.111654E-14 0 0 0 0 0.00000 -0.118655E-15 0.118655E-15 1 1 0 0 0.00000 0.737257E-17 0.737257E-17 1 0 1 0 0.00000 0.281893E-16 0.281893E-16 1 0 0 1 2.78416 2.78416 0.239258E-14 2 2 0 0 0.00000 0.105168E-15 0.105168E-15 2 1 1 0 2.78416 2.78416 0.239258E-14 2 0 2 0 0.00000 -0.585469E-17 0.585469E-17 2 1 0 1 0.00000 0.00000 0.00000 2 0 1 1 2.78416 2.78416 0.287110E-14 2 0 0 2 0.00000 -0.584762E-15 0.584762E-15 3 3 0 0 0.00000 0.779758E-15 0.779758E-15 3 2 1 0 0.00000 0.784529E-15 0.784529E-15 3 1 2 0 0.00000 -0.408853E-15 0.408853E-15 3 0 3 0 0.00000 0.682614E-15 0.682614E-15 3 2 0 1 0.00000 0.138778E-16 0.138778E-16 3 1 1 1 0.00000 0.700828E-15 0.700828E-15 3 0 2 1 0.00000 0.645751E-15 0.645751E-15 3 1 0 2 0.00000 0.832667E-15 0.832667E-15 3 0 1 2 0.00000 -0.116519E-14 0.116519E-14 3 0 0 3 4.17625 4.17625 0.212674E-14 4 4 0 0 0.00000 0.641848E-16 0.641848E-16 4 3 1 0 1.39208 1.39208 0.143555E-14 4 2 2 0 0.00000 0.711237E-16 0.711237E-16 4 1 3 0 4.17625 4.17625 0.212674E-14 4 0 4 0 0.00000 -0.102349E-15 0.102349E-15 4 3 0 1 0.00000 0.00000 0.00000 4 2 1 1 0.00000 0.00000 0.00000 4 1 2 1 0.00000 -0.832667E-16 0.832667E-16 4 0 3 1 1.39208 1.39208 0.143555E-14 4 2 0 2 0.00000 0.00000 0.00000 4 1 1 2 1.39208 1.39208 0.143555E-14 4 0 2 2 0.00000 0.294903E-16 0.294903E-16 4 1 0 3 0.00000 -0.117961E-15 0.117961E-15 4 0 1 3 4.17625 4.17625 0.276476E-14 4 0 0 4 0.00000 -0.467295E-14 0.467295E-14 5 5 0 0 0.00000 0.123859E-14 0.123859E-14 5 4 1 0 0.00000 0.971445E-15 0.971445E-15 5 3 2 0 0.00000 0.105905E-14 0.105905E-14 5 2 3 0 0.00000 0.131188E-14 0.131188E-14 5 1 4 0 0.00000 -0.392655E-14 0.392655E-14 5 0 5 0 0.00000 0.107206E-14 0.107206E-14 5 4 0 1 0.00000 -0.138778E-16 0.138778E-16 5 3 1 1 0.00000 0.152656E-15 0.152656E-15 5 2 2 1 0.00000 -0.138778E-16 0.138778E-16 5 1 3 1 0.00000 0.104083E-14 0.104083E-14 5 0 4 1 0.00000 0.105471E-14 0.105471E-14 5 3 0 2 0.00000 0.152656E-15 0.152656E-15 5 2 1 2 0.00000 0.124900E-15 0.124900E-15 5 1 2 2 0.00000 0.120737E-14 0.120737E-14 5 0 3 2 0.00000 0.892515E-15 0.892515E-15 5 2 0 3 0.00000 -0.138778E-16 0.138778E-16 5 1 1 3 0.00000 0.943690E-15 0.943690E-15 5 0 2 3 0.00000 0.129801E-14 0.129801E-14 5 1 0 4 0.00000 0.120737E-14 0.120737E-14 5 0 1 4 0.00000 -0.485636E-14 0.485636E-14 5 0 0 5 10.4406 10.4406 0.00000 6 6 0 0 0.00000 0.111022E-15 0.111022E-15 6 5 1 0 2.08812 2.08812 0.127604E-14 6 4 2 0 0.00000 0.260209E-15 0.260209E-15 6 3 3 0 2.08812 2.08812 0.170139E-14 6 2 4 0 0.00000 0.196457E-15 0.196457E-15 6 1 5 0 10.4406 10.4406 0.340278E-15 6 0 6 0 0.00000 0.277556E-15 0.277556E-15 6 5 0 1 0.00000 0.00000 0.00000 6 4 1 1 0.00000 0.00000 0.00000 6 3 2 1 0.00000 0.00000 0.00000 6 2 3 1 0.00000 0.00000 0.00000 6 1 4 1 0.00000 0.319189E-15 0.319189E-15 6 0 5 1 2.08812 2.08812 0.148872E-14 6 4 0 2 0.00000 -0.138778E-16 0.138778E-16 6 3 1 2 0.696041 0.696041 0.430665E-14 6 2 2 2 0.00000 -0.138778E-16 0.138778E-16 6 1 3 2 2.08812 2.08812 0.148872E-14 6 0 4 2 0.00000 0.936751E-16 0.936751E-16 6 3 0 3 0.00000 0.00000 0.00000 6 2 1 3 0.00000 0.00000 0.00000 6 1 2 3 0.00000 0.166533E-15 0.166533E-15 6 0 3 3 2.08812 2.08812 0.212674E-14 6 2 0 4 0.00000 -0.138778E-16 0.138778E-16 6 1 1 4 2.08812 2.08812 0.170139E-14 6 0 2 4 0.00000 0.196457E-15 0.196457E-15 6 1 0 5 0.00000 0.124900E-15 0.124900E-15 6 0 1 5 10.4406 10.4406 0.850696E-15 6 0 0 6 0.00000 -0.777216E-14 0.777216E-14 7 7 0 0 0.00000 0.235922E-14 0.235922E-14 7 6 1 0 0.00000 0.374700E-14 0.374700E-14 7 5 2 0 0.00000 0.169309E-14 0.169309E-14 7 4 3 0 0.00000 0.165146E-14 0.165146E-14 7 3 4 0 0.00000 0.325261E-14 0.325261E-14 7 2 5 0 0.00000 0.238438E-14 0.238438E-14 7 1 6 0 0.00000 -0.102960E-13 0.102960E-13 7 0 7 0 0.00000 0.202616E-14 0.202616E-14 7 6 0 1 0.00000 0.138778E-16 0.138778E-16 7 5 1 1 0.00000 0.235922E-15 0.235922E-15 7 4 2 1 0.00000 0.138778E-16 0.138778E-16 7 3 3 1 0.00000 0.235922E-15 0.235922E-15 7 2 4 1 0.00000 0.138778E-16 0.138778E-16 7 1 5 1 0.00000 0.215106E-14 0.215106E-14 7 0 6 1 0.00000 0.385803E-14 0.385803E-14 7 5 0 2 0.00000 0.235922E-15 0.235922E-15 7 4 1 2 0.00000 0.235922E-15 0.235922E-15 7 3 2 2 0.00000 0.235922E-15 0.235922E-15 7 2 3 2 0.00000 0.235922E-15 0.235922E-15 7 1 4 2 0.00000 0.353884E-14 0.353884E-14 7 0 5 2 0.00000 0.147105E-14 0.147105E-14 7 4 0 3 0.00000 0.138778E-16 0.138778E-16 7 3 1 3 0.00000 0.235922E-15 0.235922E-15 7 2 2 3 0.00000 0.138778E-16 0.138778E-16 7 1 3 3 0.00000 0.126288E-14 0.126288E-14 7 0 4 3 0.00000 0.154043E-14 0.154043E-14 7 3 0 4 0.00000 0.235922E-15 0.235922E-15 7 2 1 4 0.00000 0.235922E-15 0.235922E-15 7 1 2 4 0.00000 0.179023E-14 0.179023E-14 7 0 3 4 0.00000 0.308607E-14 0.308607E-14 7 2 0 5 0.00000 0.138778E-16 0.138778E-16 7 1 1 5 0.00000 0.301148E-14 0.301148E-14 7 0 2 5 0.00000 0.291173E-14 0.291173E-14 7 1 0 6 0.00000 0.242861E-14 0.242861E-14 7 0 1 6 0.00000 -0.101295E-13 0.101295E-13 7 0 0 7 36.5422 36.5422 0.213889E-14 8 8 0 0 0.00000 -0.111022E-15 0.111022E-15 8 7 1 0 5.22031 5.22031 0.238195E-14 8 6 2 0 0.00000 -0.138778E-15 0.138778E-15 8 5 3 0 3.13218 3.13218 0.198496E-14 8 4 4 0 0.00000 -0.381639E-16 0.381639E-16 8 3 5 0 5.22031 5.22031 0.238195E-14 8 2 6 0 0.00000 -0.440620E-15 0.440620E-15 8 1 7 0 36.5422 36.5422 0.194445E-14 8 0 8 0 0.00000 -0.111022E-15 0.111022E-15 8 7 0 1 0.00000 0.00000 0.00000 8 6 1 1 0.00000 0.00000 0.00000 8 5 2 1 0.00000 0.00000 0.00000 8 4 3 1 0.00000 0.00000 0.00000 8 3 4 1 0.00000 0.00000 0.00000 8 2 5 1 0.00000 0.00000 0.00000 8 1 6 1 0.00000 -0.832667E-16 0.832667E-16 8 0 7 1 5.22031 5.22031 0.221181E-14 8 6 0 2 0.00000 -0.277556E-16 0.277556E-16 8 5 1 2 1.04406 1.04406 0.467883E-14 8 4 2 2 0.00000 -0.277556E-16 0.277556E-16 8 3 3 2 1.04406 1.04406 0.467883E-14 8 2 4 2 0.00000 -0.277556E-16 0.277556E-16 8 1 5 2 5.22031 5.22031 0.238195E-14 8 0 6 2 0.00000 0.194289E-15 0.194289E-15 8 5 0 3 0.00000 0.00000 0.00000 8 4 1 3 0.00000 0.00000 0.00000 8 3 2 3 0.00000 0.00000 0.00000 8 2 3 3 0.00000 0.00000 0.00000 8 1 4 3 0.00000 0.111022E-15 0.111022E-15 8 0 5 3 3.13218 3.13218 0.212674E-14 8 4 0 4 0.00000 0.277556E-16 0.277556E-16 8 3 1 4 1.04406 1.04406 0.489150E-14 8 2 2 4 0.00000 0.277556E-16 0.277556E-16 8 1 3 4 3.13218 3.13218 0.198496E-14 8 0 4 4 0.00000 0.173472E-16 0.173472E-16 8 3 0 5 0.00000 0.00000 0.00000 8 2 1 5 0.00000 0.00000 0.00000 8 1 2 5 0.00000 0.00000 0.00000 8 0 3 5 5.22031 5.22031 0.221181E-14 8 2 0 6 0.00000 0.277556E-16 0.277556E-16 8 1 1 6 5.22031 5.22031 0.221181E-14 8 0 2 6 0.00000 0.170003E-15 0.170003E-15 8 1 0 7 0.00000 0.333067E-15 0.333067E-15 8 0 1 7 36.5422 36.5422 0.155556E-14 8 0 0 8 0.00000 0.194463E-13 0.194463E-13 9 9 0 0 0.00000 0.666134E-14 0.666134E-14 9 8 1 0 0.00000 0.113243E-13 0.113243E-13 9 7 2 0 0.00000 0.377476E-14 0.377476E-14 9 6 3 0 0.00000 0.380251E-14 0.380251E-14 9 5 4 0 0.00000 0.437150E-14 0.437150E-14 9 4 5 0 0.00000 0.354577E-14 0.354577E-14 9 3 6 0 0.00000 0.100007E-13 0.100007E-13 9 2 7 0 0.00000 0.680272E-14 0.680272E-14 9 1 8 0 0.00000 0.272022E-13 0.272022E-13 9 0 9 0 0.00000 0.666134E-14 0.666134E-14 9 8 0 1 0.00000 0.00000 0.00000 9 7 1 1 0.00000 0.333067E-15 0.333067E-15 9 6 2 1 0.00000 0.00000 0.00000 9 5 3 1 0.00000 0.333067E-15 0.333067E-15 9 4 4 1 0.00000 0.00000 0.00000 9 3 5 1 0.00000 0.333067E-15 0.333067E-15 9 2 6 1 0.00000 0.00000 0.00000 9 1 7 1 0.00000 0.638378E-14 0.638378E-14 9 0 8 1 0.00000 0.122125E-13 0.122125E-13 9 7 0 2 0.00000 0.360822E-15 0.360822E-15 9 6 1 2 0.00000 0.360822E-15 0.360822E-15 9 5 2 2 0.00000 0.360822E-15 0.360822E-15 9 4 3 2 0.00000 0.360822E-15 0.360822E-15 9 3 4 2 0.00000 0.360822E-15 0.360822E-15 9 2 5 2 0.00000 0.360822E-15 0.360822E-15 9 1 6 2 0.00000 0.105749E-13 0.105749E-13 9 0 7 2 0.00000 0.288658E-14 0.288658E-14 9 6 0 3 0.00000 0.00000 0.00000 9 5 1 3 0.00000 0.333067E-15 0.333067E-15 9 4 2 3 0.00000 0.00000 0.00000 9 3 3 3 0.00000 0.333067E-15 0.333067E-15 9 2 4 3 0.00000 0.00000 0.00000 9 1 5 3 0.00000 0.305311E-14 0.305311E-14 9 0 6 3 0.00000 0.380251E-14 0.380251E-14 9 5 0 4 0.00000 0.305311E-15 0.305311E-15 9 4 1 4 0.00000 0.305311E-15 0.305311E-15 9 3 2 4 0.00000 0.305311E-15 0.305311E-15 9 2 3 4 0.00000 0.305311E-15 0.305311E-15 9 1 4 4 0.00000 0.396905E-14 0.396905E-14 9 0 5 4 0.00000 0.403844E-14 0.403844E-14 9 4 0 5 0.00000 0.00000 0.00000 9 3 1 5 0.00000 0.333067E-15 0.333067E-15 9 2 2 5 0.00000 0.00000 0.00000 9 1 3 5 0.00000 0.408007E-14 0.408007E-14 9 0 4 5 0.00000 0.332373E-14 0.332373E-14 9 3 0 6 0.00000 0.360822E-15 0.360822E-15 9 2 1 6 0.00000 0.360822E-15 0.360822E-15 9 1 2 6 0.00000 0.324740E-14 0.324740E-14 9 0 3 6 0.00000 0.994517E-14 0.994517E-14 9 2 0 7 0.00000 0.00000 0.00000 9 1 1 7 0.00000 0.954792E-14 0.954792E-14 9 0 2 7 0.00000 0.674721E-14 0.674721E-14 9 1 0 8 0.00000 0.768829E-14 0.768829E-14 9 0 1 8 0.00000 0.219286E-13 0.219286E-13 9 0 0 9 TEST07: Call SPARSE_GRID_HERMITE_WRITE to write sparse grid data to a set of files. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of points in the grid = 95 Number of unique points in the grid = 73 SPARSE_GRID_HERMITE_WRITE: Wrote the R file = "test07_r.txt". Wrote the W file = "test07_w.txt". Wrote the X file = "test07_x.txt". SPARSE_GRID_HERMITE_PRB Normal end of execution. 16 May 2012 9:03:52.434 AM