06 November 2009 02:35:56 PM SPARSE_GRID_GL_PRB C++ version Test the routines in the SPARSE_GRID_GL library. TEST01 SPARSE_GRID_GL_SIZE returns the number of distinct points in a Gauss-Legendre sparse grid. Note that, unlike most sparse grids, a sparse grid based on Gauss-Legendre 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 6 LEVEL_MAX 0 1 1 1 1 1 1 1 3 5 7 9 11 13 2 7 22 37 57 81 109 3 15 75 161 289 471 713 4 31 224 608 1268 2341 3953 5 63 613 2070 4994 10367 19397 6 127 1578 6507 18076 41957 86522 TEST01 SPARSE_GRID_GL_SIZE returns the number of distinct points in a Gauss-Legendre sparse grid. Note that, unlike most sparse grids, a sparse grid based on Gauss-Legendre 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 TEST01 SPARSE_GRID_GL_SIZE returns the number of distinct points in a Gauss-Legendre sparse grid. Note that, unlike most sparse grids, a sparse grid based on Gauss-Legendre 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_GL_INDEX returns abstract indices for the points that make up a Gauss-Legendre 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_GL_INDEX returns abstract indices for the points that make up a Gauss-Legendre 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_GL_INDEX returns abstract indices for the points that make up a Gauss-Legendre 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_GL_INDEX returns abstract indices for the points that make up a Gauss-Legendre 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_GL_INDEX returns abstract indices for the points that make up a Gauss-Legendre 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_GL makes a sparse Gauss-Legendre grid. LEVEL_MIN = 2 LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 75 Grid weights: 0 -0.143872 1 -0.310784 2 -0.424256 3 0.717433 4 -0.424256 5 -0.310784 6 -0.143872 7 -0.308642 8 -0.261628 9 -0.308642 10 -0.261628 11 -0.790123 12 -0.261628 13 -0.308642 14 -0.261628 15 -0.308642 16 -0.143872 17 -0.310784 18 -0.424256 19 -0.835918 20 -0.424256 21 -0.310784 22 -0.143872 23 0.061506 24 0.140732 25 0.214318 26 0.279141 27 0.332538 28 0.372322 29 0.396863 30 0.396863 31 0.372322 32 0.332538 33 0.279141 34 0.214318 35 0.140732 36 0.061506 37 0.071936 38 0.155392 39 0.212128 40 0.212128 41 0.155392 42 0.071936 43 0.071936 44 0.155392 45 0.212128 46 0.212128 47 0.155392 48 0.071936 49 0.071936 50 0.071936 51 0.155392 52 0.155392 53 0.212128 54 0.212128 55 0.212128 56 0.212128 57 0.155392 58 0.155392 59 0.071936 60 0.071936 61 0.061506 62 0.140732 63 0.214318 64 0.279141 65 0.332538 66 0.372322 67 0.396863 68 0.396863 69 0.372322 70 0.332538 71 0.279141 72 0.214318 73 0.140732 74 0.061506 Grid points: 0 -0.949108 0.000000 1 -0.741531 0.000000 2 -0.405845 0.000000 3 0.000000 0.000000 4 0.405845 0.000000 5 0.741531 0.000000 6 0.949108 0.000000 7 -0.774597 -0.774597 8 0.000000 -0.774597 9 0.774597 -0.774597 10 -0.774597 0.000000 11 0.000000 0.000000 12 0.774597 0.000000 13 -0.774597 0.774597 14 0.000000 0.774597 15 0.774597 0.774597 16 0.000000 -0.949108 17 0.000000 -0.741531 18 0.000000 -0.405845 19 0.000000 0.000000 20 0.000000 0.405845 21 0.000000 0.741531 22 0.000000 0.949108 23 -0.987993 0.000000 24 -0.937273 0.000000 25 -0.848207 0.000000 26 -0.724418 0.000000 27 -0.570972 0.000000 28 -0.394151 0.000000 29 -0.201194 0.000000 30 0.201194 0.000000 31 0.394151 0.000000 32 0.570972 0.000000 33 0.724418 0.000000 34 0.848207 0.000000 35 0.937273 0.000000 36 0.987993 0.000000 37 -0.949108 -0.774597 38 -0.741531 -0.774597 39 -0.405845 -0.774597 40 0.405845 -0.774597 41 0.741531 -0.774597 42 0.949108 -0.774597 43 -0.949108 0.774597 44 -0.741531 0.774597 45 -0.405845 0.774597 46 0.405845 0.774597 47 0.741531 0.774597 48 0.949108 0.774597 49 -0.774597 -0.949108 50 0.774597 -0.949108 51 -0.774597 -0.741531 52 0.774597 -0.741531 53 -0.774597 -0.405845 54 0.774597 -0.405845 55 -0.774597 0.405845 56 0.774597 0.405845 57 -0.774597 0.741531 58 0.774597 0.741531 59 -0.774597 0.949108 60 0.774597 0.949108 61 0.000000 -0.987993 62 0.000000 -0.937273 63 0.000000 -0.848207 64 0.000000 -0.724418 65 0.000000 -0.570972 66 0.000000 -0.394151 67 0.000000 -0.201194 68 0.000000 0.201194 69 0.000000 0.394151 70 0.000000 0.570972 71 0.000000 0.724418 72 0.000000 0.848207 73 0.000000 0.937273 74 0.000000 0.987993 TEST03: SPARSE_GRID_GL makes a sparse Gauss-Legendre grid. LEVEL_MIN = 3 LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 224 Grid weights: 0 -0.034170 1 -0.078184 2 -0.119066 3 -0.155079 4 -0.184744 5 -0.206846 6 -0.220479 7 0.528555 8 -0.220479 9 -0.206846 10 -0.184744 11 -0.155079 12 -0.119066 13 -0.078184 14 -0.034170 15 -0.071936 16 -0.155392 17 -0.212128 18 -0.119656 19 -0.212128 20 -0.155392 21 -0.071936 22 -0.060978 23 -0.131722 24 -0.179815 25 -0.371519 26 -0.179815 27 -0.131722 28 -0.060978 29 -0.071936 30 -0.155392 31 -0.212128 32 -0.119656 33 -0.212128 34 -0.155392 35 -0.071936 36 -0.071936 37 -0.060978 38 -0.071936 39 -0.155392 40 -0.131722 41 -0.155392 42 -0.212128 43 -0.179815 44 -0.212128 45 -0.119656 46 -0.371519 47 -0.119656 48 -0.212128 49 -0.179815 50 -0.212128 51 -0.155392 52 -0.131722 53 -0.155392 54 -0.071936 55 -0.060978 56 -0.071936 57 -0.034170 58 -0.078184 59 -0.119066 60 -0.155079 61 -0.184744 62 -0.206846 63 -0.220479 64 -0.405156 65 -0.220479 66 -0.206846 67 -0.184744 68 -0.155079 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0.000000 93 0.642707 0.000000 94 0.715777 0.000000 95 0.781733 0.000000 96 0.839920 0.000000 97 0.889760 0.000000 98 0.930757 0.000000 99 0.962504 0.000000 100 0.984686 0.000000 101 0.997087 0.000000 102 -0.987993 -0.774597 103 -0.937273 -0.774597 104 -0.848207 -0.774597 105 -0.724418 -0.774597 106 -0.570972 -0.774597 107 -0.394151 -0.774597 108 -0.201194 -0.774597 109 0.201194 -0.774597 110 0.394151 -0.774597 111 0.570972 -0.774597 112 0.724418 -0.774597 113 0.848207 -0.774597 114 0.937273 -0.774597 115 0.987993 -0.774597 116 -0.987993 0.774597 117 -0.937273 0.774597 118 -0.848207 0.774597 119 -0.724418 0.774597 120 -0.570972 0.774597 121 -0.394151 0.774597 122 -0.201194 0.774597 123 0.201194 0.774597 124 0.394151 0.774597 125 0.570972 0.774597 126 0.724418 0.774597 127 0.848207 0.774597 128 0.937273 0.774597 129 0.987993 0.774597 130 -0.949108 -0.949108 131 -0.741531 -0.949108 132 -0.405845 -0.949108 133 0.405845 -0.949108 134 0.741531 -0.949108 135 0.949108 -0.949108 136 -0.949108 -0.741531 137 -0.741531 -0.741531 138 -0.405845 -0.741531 139 0.405845 -0.741531 140 0.741531 -0.741531 141 0.949108 -0.741531 142 -0.949108 -0.405845 143 -0.741531 -0.405845 144 -0.405845 -0.405845 145 0.405845 -0.405845 146 0.741531 -0.405845 147 0.949108 -0.405845 148 -0.949108 0.405845 149 -0.741531 0.405845 150 -0.405845 0.405845 151 0.405845 0.405845 152 0.741531 0.405845 153 0.949108 0.405845 154 -0.949108 0.741531 155 -0.741531 0.741531 156 -0.405845 0.741531 157 0.405845 0.741531 158 0.741531 0.741531 159 0.949108 0.741531 160 -0.949108 0.949108 161 -0.741531 0.949108 162 -0.405845 0.949108 163 0.405845 0.949108 164 0.741531 0.949108 165 0.949108 0.949108 166 -0.774597 -0.987993 167 0.774597 -0.987993 168 -0.774597 -0.937273 169 0.774597 -0.937273 170 -0.774597 -0.848207 171 0.774597 -0.848207 172 -0.774597 -0.724418 173 0.774597 -0.724418 174 -0.774597 -0.570972 175 0.774597 -0.570972 176 -0.774597 -0.394151 177 0.774597 -0.394151 178 -0.774597 -0.201194 179 0.774597 -0.201194 180 -0.774597 0.201194 181 0.774597 0.201194 182 -0.774597 0.394151 183 0.774597 0.394151 184 -0.774597 0.570972 185 0.774597 0.570972 186 -0.774597 0.724418 187 0.774597 0.724418 188 -0.774597 0.848207 189 0.774597 0.848207 190 -0.774597 0.937273 191 0.774597 0.937273 192 -0.774597 0.987993 193 0.774597 0.987993 194 0.000000 -0.997087 195 0.000000 -0.984686 196 0.000000 -0.962504 197 0.000000 -0.930757 198 0.000000 -0.889760 199 0.000000 -0.839920 200 0.000000 -0.781733 201 0.000000 -0.715777 202 0.000000 -0.642707 203 0.000000 -0.563249 204 0.000000 -0.478194 205 0.000000 -0.388386 206 0.000000 -0.294718 207 0.000000 -0.198121 208 0.000000 -0.099555 209 0.000000 0.099555 210 0.000000 0.198121 211 0.000000 0.294718 212 0.000000 0.388386 213 0.000000 0.478194 214 0.000000 0.563249 215 0.000000 0.642707 216 0.000000 0.715777 217 0.000000 0.781733 218 0.000000 0.839920 219 0.000000 0.889760 220 0.000000 0.930757 221 0.000000 0.962504 222 0.000000 0.984686 223 0.000000 0.997087 TEST03: SPARSE_GRID_GL makes a sparse Gauss-Legendre grid. LEVEL_MIN = 0 LEVEL_MAX = 0 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 1 Grid weights: 0 8.000000 Grid points: 0 0.000000 0.000000 0.000000 TEST03: SPARSE_GRID_GL makes a sparse Gauss-Legendre grid. LEVEL_MIN = 0 LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 37 Grid weights: 0 -3.577082 1 -2.469136 2 -2.469136 3 -2.469136 4 -2.469136 5 -2.469136 6 -2.469136 7 0.517940 8 1.118822 9 1.527320 10 1.527320 11 1.118822 12 0.517940 13 0.617284 14 0.617284 15 0.617284 16 0.617284 17 0.517940 18 1.118822 19 1.527320 20 1.527320 21 1.118822 22 0.517940 23 0.617284 24 0.617284 25 0.617284 26 0.617284 27 0.617284 28 0.617284 29 0.617284 30 0.617284 31 0.517940 32 1.118822 33 1.527320 34 1.527320 35 1.118822 36 0.517940 Grid points: 0 0.000000 0.000000 0.000000 1 -0.774597 0.000000 0.000000 2 0.774597 0.000000 0.000000 3 0.000000 -0.774597 0.000000 4 0.000000 0.774597 0.000000 5 0.000000 0.000000 -0.774597 6 0.000000 0.000000 0.774597 7 -0.949108 0.000000 0.000000 8 -0.741531 0.000000 0.000000 9 -0.405845 0.000000 0.000000 10 0.405845 0.000000 0.000000 11 0.741531 0.000000 0.000000 12 0.949108 0.000000 0.000000 13 -0.774597 -0.774597 0.000000 14 0.774597 -0.774597 0.000000 15 -0.774597 0.774597 0.000000 16 0.774597 0.774597 0.000000 17 0.000000 -0.949108 0.000000 18 0.000000 -0.741531 0.000000 19 0.000000 -0.405845 0.000000 20 0.000000 0.405845 0.000000 21 0.000000 0.741531 0.000000 22 0.000000 0.949108 0.000000 23 -0.774597 0.000000 -0.774597 24 0.774597 0.000000 -0.774597 25 -0.774597 0.000000 0.774597 26 0.774597 0.000000 0.774597 27 0.000000 -0.774597 -0.774597 28 0.000000 0.774597 -0.774597 29 0.000000 -0.774597 0.774597 30 0.000000 0.774597 0.774597 31 0.000000 0.000000 -0.949108 32 0.000000 0.000000 -0.741531 33 0.000000 0.000000 -0.405845 34 0.000000 0.000000 0.405845 35 0.000000 0.000000 0.741531 36 0.000000 0.000000 0.949108 TEST04: Compute the weights of a Gauss-Legendre sparse grid . As a simple test, sum these weights. They should sum to exactly 2^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 4.000000e+00 4.000000e+00 7.105427e-15 TEST04: Compute the weights of a Gauss-Legendre sparse grid . As a simple test, sum these weights. They should sum to exactly 2^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 8.000000e+00 8.000000e+00 0.000000e+00 TEST04: Compute the weights of a Gauss-Legendre sparse grid . As a simple test, sum these weights. They should sum to exactly 2^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 8.000000e+00 8.000000e+00 0.000000e+00 TEST04: Compute the weights of a Gauss-Legendre sparse grid . As a simple test, sum these weights. They should sum to exactly 2^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 8.000000e+00 8.000000e+00 8.020251e-13 TEST04: Compute the weights of a Gauss-Legendre sparse grid . As a simple test, sum these weights. They should sum to exactly 2^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 1.024000e+03 1.024000e+03 1.546596e-09 TEST05 Check the exactness of a Gauss-Legendre 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 0.0e+00 0 0 0 0.0e+00 1 1 0 0.0e+00 1 0 1 2.5e-01 2 2 0 0.0e+00 2 1 1 2.5e-01 2 0 2 5.0e-01 3 3 0 2.5e-01 3 2 1 2.5e-01 3 1 2 5.0e-01 3 0 3 TEST05 Check the exactness of a Gauss-Legendre 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 0.0e+00 0 0 0 0.0e+00 1 1 0 0.0e+00 1 0 1 2.2e-16 2 2 0 0.0e+00 2 1 1 2.2e-16 2 0 2 0.0e+00 3 3 0 2.2e-16 3 2 1 2.2e-16 3 1 2 0.0e+00 3 0 3 0.0e+00 4 4 0 0.0e+00 4 3 1 6.2e-02 4 2 2 0.0e+00 4 1 3 0.0e+00 4 0 4 2.2e-16 5 5 0 0.0e+00 5 4 1 1.2e-01 5 3 2 1.2e-01 5 2 3 0.0e+00 5 1 4 4.4e-16 5 0 5 TEST05 Check the exactness of a Gauss-Legendre 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 = 10 Number of unique points in the grid = 22 Error Total Monomial Degree Exponents 1.1e-16 0 0 0 0.0e+00 1 1 0 2.2e-16 1 0 1 0.0e+00 2 2 0 1.1e-16 2 1 1 2.2e-16 2 0 2 1.1e-16 3 3 0 0.0e+00 3 2 1 2.2e-16 3 1 2 0.0e+00 3 0 3 1.1e-16 4 4 0 2.2e-16 4 3 1 0.0e+00 4 2 2 2.2e-16 4 1 3 1.1e-16 4 0 4 3.3e-16 5 5 0 1.1e-16 5 4 1 2.2e-16 5 3 2 0.0e+00 5 2 3 1.1e-16 5 1 4 2.2e-16 5 0 5 0.0e+00 6 6 0 0.0e+00 6 5 1 0.0e+00 6 4 2 0.0e+00 6 3 3 0.0e+00 6 2 4 2.2e-16 6 1 5 2.2e-16 6 0 6 1.1e-16 7 7 0 0.0e+00 7 6 1 2.2e-16 7 5 2 0.0e+00 7 4 3 0.0e+00 7 3 4 2.2e-16 7 2 5 2.2e-16 7 1 6 0.0e+00 7 0 7 2.2e-16 8 8 0 0.0e+00 8 7 1 6.3e-04 8 6 2 2.2e-16 8 5 3 0.0e+00 8 4 4 2.2e-16 8 3 5 6.2e-04 8 2 6 0.0e+00 8 1 7 0.0e+00 8 0 8 0.0e+00 9 9 0 2.2e-16 9 8 1 2.5e-03 9 7 2 1.2e-03 9 6 3 2.2e-16 9 5 4 4.4e-16 9 4 5 1.2e-03 9 3 6 2.5e-03 9 2 7 0.0e+00 9 1 8 2.2e-16 9 0 9 4.4e-16 10 10 0 1.1e-16 10 9 1 6.0e-03 10 8 2 5.0e-03 10 7 3 1.7e-03 10 6 4 2.2e-16 10 5 5 1.7e-03 10 4 6 5.0e-03 10 3 7 6.0e-03 10 2 8 2.2e-16 10 1 9 3.3e-16 10 0 10 TEST05 Check the exactness of a Gauss-Legendre 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 = 14 Number of unique points in the grid = 75 Error Total Monomial Degree Exponents 7.8e-16 0 0 0 0.0e+00 1 1 0 1.1e-16 1 0 1 2.2e-16 2 2 0 2.2e-16 2 1 1 4.4e-16 2 0 2 2.2e-16 3 3 0 2.2e-16 3 2 1 4.4e-16 3 1 2 0.0e+00 3 0 3 4.4e-16 4 4 0 2.2e-16 4 3 1 2.2e-16 4 2 2 0.0e+00 4 1 3 4.4e-16 4 0 4 4.4e-16 5 5 0 1.1e-16 5 4 1 2.2e-16 5 3 2 0.0e+00 5 2 3 2.2e-16 5 1 4 4.4e-16 5 0 5 2.2e-16 6 6 0 5.6e-16 6 5 1 6.7e-16 6 4 2 1.1e-16 6 3 3 0.0e+00 6 2 4 2.2e-16 6 1 5 6.7e-16 6 0 6 8.9e-16 7 7 0 0.0e+00 7 6 1 4.4e-16 7 5 2 4.4e-16 7 4 3 1.1e-16 7 3 4 4.4e-16 7 2 5 2.2e-16 7 1 6 2.2e-16 7 0 7 6.7e-16 8 8 0 0.0e+00 8 7 1 0.0e+00 8 6 2 3.3e-16 8 5 3 2.2e-16 8 4 4 3.3e-16 8 3 5 4.4e-16 8 2 6 0.0e+00 8 1 7 1.1e-16 8 0 8 2.2e-16 9 9 0 4.4e-16 9 8 1 4.4e-16 9 7 2 6.7e-16 9 6 3 2.2e-16 9 5 4 6.7e-16 9 4 5 0.0e+00 9 3 6 0.0e+00 9 2 7 2.2e-16 9 1 8 4.4e-16 9 0 9 0.0e+00 10 10 0 0.0e+00 10 9 1 2.2e-16 10 8 2 7.8e-16 10 7 3 1.1e-16 10 6 4 6.7e-16 10 5 5 3.3e-16 10 4 6 6.7e-16 10 3 7 6.7e-16 10 2 8 4.4e-16 10 1 9 0.0e+00 10 0 10 3.3e-16 11 11 0 4.4e-16 11 10 1 0.0e+00 11 9 2 6.7e-16 11 8 3 2.2e-16 11 7 4 1.1e-16 11 6 5 0.0e+00 11 5 6 7.8e-16 11 4 7 1.1e-16 11 3 8 2.2e-16 11 2 9 2.2e-16 11 1 10 0.0e+00 11 0 11 4.4e-16 12 12 0 8.9e-16 12 11 1 1.1e-16 12 10 2 1.1e-16 12 9 3 2.2e-16 12 8 4 2.2e-16 12 7 5 6.3e-06 12 6 6 4.4e-16 12 5 7 2.2e-16 12 4 8 2.2e-16 12 3 9 6.7e-16 12 2 10 3.3e-16 12 1 11 4.4e-16 12 0 12 2.2e-16 13 13 0 4.4e-16 13 12 1 2.2e-16 13 11 2 3.3e-16 13 10 3 0.0e+00 13 9 4 5.6e-16 13 8 5 2.5e-05 13 7 6 2.5e-05 13 6 7 8.9e-16 13 5 8 3.3e-16 13 4 9 3.3e-16 13 3 10 4.4e-16 13 2 11 2.2e-16 13 1 12 4.4e-16 13 0 13 0.0e+00 14 14 0 6.7e-16 14 13 1 2.2e-16 14 12 2 2.2e-16 14 11 3 3.3e-16 14 10 4 4.4e-16 14 9 5 6.0e-05 14 8 6 1.0e-04 14 7 7 6.0e-05 14 6 8 4.4e-16 14 5 9 5.6e-16 14 4 10 2.2e-16 14 3 11 2.2e-16 14 2 12 0.0e+00 14 1 13 0.0e+00 14 0 14 TEST05 Check the exactness of a Gauss-Legendre 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 1.8e-15 0 0 0 6.7e-16 1 1 0 4.4e-16 1 0 1 0.0e+00 2 2 0 1.3e-15 2 1 1 1.3e-15 2 0 2 1.2e-15 3 3 0 0.0e+00 3 2 1 2.2e-16 3 1 2 2.2e-16 3 0 3 5.6e-16 4 4 0 5.6e-16 4 3 1 1.1e-15 4 2 2 2.2e-16 4 1 3 1.1e-16 4 0 4 0.0e+00 5 5 0 2.2e-16 5 4 1 8.9e-16 5 3 2 3.3e-16 5 2 3 6.7e-16 5 1 4 0.0e+00 5 0 5 2.2e-16 6 6 0 2.2e-16 6 5 1 2.2e-16 6 4 2 4.4e-16 6 3 3 0.0e+00 6 2 4 6.7e-16 6 1 5 1.6e-15 6 0 6 2.2e-16 7 7 0 1.2e-15 7 6 1 0.0e+00 7 5 2 0.0e+00 7 4 3 4.4e-16 7 3 4 1.1e-16 7 2 5 0.0e+00 7 1 6 1.3e-15 7 0 7 3.3e-16 8 8 0 1.1e-15 8 7 1 0.0e+00 8 6 2 8.9e-16 8 5 3 4.4e-16 8 4 4 8.9e-16 8 3 5 1.1e-16 8 2 6 8.9e-16 8 1 7 6.7e-16 8 0 8 1.1e-16 9 9 0 4.4e-16 9 8 1 8.9e-16 9 7 2 0.0e+00 9 6 3 1.3e-15 9 5 4 1.3e-15 9 4 5 1.6e-15 9 3 6 2.2e-16 9 2 7 2.2e-16 9 1 8 1.1e-16 9 0 9 1.1e-15 10 10 0 4.4e-16 10 9 1 3.3e-16 10 8 2 7.8e-16 10 7 3 4.4e-16 10 6 4 2.2e-16 10 5 5 2.2e-16 10 4 6 2.2e-16 10 3 7 6.7e-16 10 2 8 8.9e-16 10 1 9 6.7e-16 10 0 10 5.6e-16 11 11 0 8.9e-16 11 10 1 6.7e-16 11 9 2 6.7e-16 11 8 3 5.6e-16 11 7 4 4.4e-16 11 6 5 4.4e-16 11 5 6 1.1e-15 11 4 7 2.2e-16 11 3 8 1.3e-15 11 2 9 2.2e-16 11 1 10 2.2e-16 11 0 11 4.4e-16 12 12 0 2.2e-16 12 11 1 2.2e-16 12 10 2 4.4e-16 12 9 3 8.9e-16 12 8 4 4.4e-16 12 7 5 1.6e-15 12 6 6 2.2e-15 12 5 7 0.0e+00 12 4 8 5.6e-16 12 3 9 6.7e-16 12 2 10 4.4e-16 12 1 11 2.0e-15 12 0 12 2.2e-16 13 13 0 6.7e-16 13 12 1 3.3e-16 13 11 2 8.9e-16 13 10 3 6.7e-16 13 9 4 8.9e-16 13 8 5 1.8e-15 13 7 6 0.0e+00 13 6 7 7.8e-16 13 5 8 0.0e+00 13 4 9 2.2e-16 13 3 10 5.6e-16 13 2 11 4.4e-16 13 1 12 0.0e+00 13 0 13 1.0e-15 14 14 0 4.4e-16 14 13 1 8.9e-16 14 12 2 1.1e-15 14 11 3 5.6e-16 14 10 4 2.2e-16 14 9 5 4.4e-16 14 8 6 1.1e-15 14 7 7 4.4e-16 14 6 8 4.4e-16 14 5 9 2.2e-16 14 4 10 1.3e-15 14 3 11 1.1e-15 14 2 12 1.1e-15 14 1 13 2.2e-15 14 0 14 2.2e-16 15 15 0 4.4e-16 15 14 1 4.4e-16 15 13 2 4.4e-16 15 12 3 1.0e-15 15 11 4 4.4e-16 15 10 5 4.4e-16 15 9 6 2.2e-16 15 8 7 0.0e+00 15 7 8 2.2e-16 15 6 9 1.1e-15 15 5 10 8.9e-16 15 4 11 6.7e-16 15 3 12 6.7e-16 15 2 13 6.7e-16 15 1 14 1.7e-15 15 0 15 2.2e-16 16 16 0 4.4e-16 16 15 1 2.2e-16 16 14 2 2.2e-16 16 13 3 2.2e-16 16 12 4 2.2e-16 16 11 5 1.1e-15 16 10 6 0.0e+00 16 9 7 3.3e-16 16 8 8 2.2e-16 16 7 9 1.9e-15 16 6 10 1.1e-15 16 5 11 1.1e-15 16 4 12 1.2e-15 16 3 13 3.3e-16 16 2 14 1.0e-15 16 1 15 1.2e-15 16 0 16 1.7e-15 17 17 0 4.4e-16 17 16 1 8.9e-16 17 15 2 1.0e-15 17 14 3 0.0e+00 17 13 4 7.8e-16 17 12 5 4.4e-16 17 11 6 4.4e-16 17 10 7 0.0e+00 17 9 8 8.9e-16 17 8 9 2.2e-16 17 7 10 1.0e-15 17 6 11 2.2e-16 17 5 12 2.2e-16 17 4 13 1.2e-15 17 3 14 3.3e-16 17 2 15 4.4e-16 17 1 16 1.0e-15 17 0 17 4.4e-16 18 18 0 2.2e-16 18 17 1 1.1e-15 18 16 2 4.4e-16 18 15 3 0.0e+00 18 14 4 6.7e-16 18 13 5 8.9e-16 18 12 6 6.7e-16 18 11 7 2.2e-16 18 10 8 6.7e-16 18 9 9 1.2e-15 18 8 10 4.4e-16 18 7 11 4.4e-16 18 6 12 4.4e-16 18 5 13 6.7e-16 18 4 14 6.7e-16 18 3 15 6.7e-16 18 2 16 3.3e-16 18 1 17 1.3e-15 18 0 18 2.2e-16 19 19 0 1.1e-15 19 18 1 1.3e-15 19 17 2 1.2e-15 19 16 3 6.7e-16 19 15 4 0.0e+00 19 14 5 1.6e-15 19 13 6 1.3e-15 19 12 7 7.8e-16 19 11 8 7.8e-16 19 10 9 4.4e-16 19 9 10 1.8e-15 19 8 11 6.7e-16 19 7 12 8.9e-16 19 6 13 1.1e-15 19 5 14 8.9e-16 19 4 15 3.3e-16 19 3 16 3.3e-16 19 2 17 2.2e-16 19 1 18 4.4e-16 19 0 19 1.1e-15 20 20 0 2.2e-16 20 19 1 1.0e-15 20 18 2 6.7e-16 20 17 3 2.2e-16 20 16 4 8.9e-16 20 15 5 2.1e-10 20 14 6 1.6e-15 20 13 7 1.6e-15 20 12 8 4.4e-16 20 11 9 8.9e-16 20 10 10 6.7e-16 20 9 11 4.4e-16 20 8 12 4.4e-16 20 7 13 2.1e-10 20 6 14 8.9e-16 20 5 15 8.9e-16 20 4 16 1.1e-16 20 3 17 0.0e+00 20 2 18 6.7e-16 20 1 19 1.4e-15 20 0 20 1.7e-15 21 21 0 7.8e-16 21 20 1 8.9e-16 21 19 2 5.6e-16 21 18 3 2.4e-15 21 17 4 4.4e-16 21 16 5 1.7e-09 21 15 6 8.5e-10 21 14 7 6.7e-16 21 13 8 4.4e-16 21 12 9 4.4e-16 21 11 10 2.2e-16 21 10 11 2.2e-16 21 9 12 2.2e-16 21 8 13 8.5e-10 21 7 14 1.7e-09 21 6 15 2.2e-16 21 5 16 7.8e-16 21 4 17 2.2e-16 21 3 18 2.2e-16 21 2 19 1.1e-16 21 1 20 6.7e-16 21 0 21 8.9e-16 22 22 0 4.4e-16 22 21 1 2.2e-16 22 20 2 0.0e+00 22 19 3 1.1e-15 22 18 4 5.6e-16 22 17 5 7.4e-09 22 16 6 6.8e-09 22 15 7 2.0e-09 22 14 8 8.9e-16 22 13 9 6.7e-16 22 12 10 1.1e-16 22 11 11 1.1e-15 22 10 12 4.4e-16 22 9 13 2.0e-09 22 8 14 6.8e-09 22 7 15 7.4e-09 22 6 16 0.0e+00 22 5 17 2.2e-16 22 4 18 8.9e-16 22 3 19 2.2e-16 22 2 20 1.1e-16 22 1 21 6.7e-16 22 0 22 TEST05 Check the exactness of a Gauss-Legendre 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 = 32 Number of unique points in the grid = 613 Error Total Monomial Degree Exponents 2.6e-15 0 0 0 2.9e-15 1 1 0 3.1e-15 1 0 1 1.6e-15 2 2 0 1.1e-15 2 1 1 3.6e-15 2 0 2 1.1e-15 3 3 0 1.3e-15 3 2 1 1.3e-15 3 1 2 3.1e-15 3 0 3 0.0e+00 4 4 0 2.2e-16 4 3 1 5.6e-16 4 2 2 4.4e-15 4 1 3 1.6e-15 4 0 4 1.6e-15 5 5 0 4.4e-16 5 4 1 1.0e-15 5 3 2 1.2e-15 5 2 3 3.4e-15 5 1 4 5.1e-15 5 0 5 2.7e-15 6 6 0 3.3e-16 6 5 1 2.3e-15 6 4 2 1.0e-15 6 3 3 2.7e-15 6 2 4 4.6e-15 6 1 5 4.0e-15 6 0 6 7.8e-16 7 7 0 1.6e-15 7 6 1 2.2e-16 7 5 2 1.7e-15 7 4 3 1.3e-15 7 3 4 2.9e-15 7 2 5 4.4e-16 7 1 6 2.7e-15 7 0 7 3.3e-15 8 8 0 1.6e-15 8 7 1 1.9e-15 8 6 2 3.8e-15 8 5 3 2.8e-15 8 4 4 2.0e-15 8 3 5 1.3e-15 8 2 6 1.1e-16 8 1 7 1.6e-15 8 0 8 3.6e-15 9 9 0 1.2e-15 9 8 1 1.9e-15 9 7 2 2.2e-16 9 6 3 6.7e-16 9 5 4 4.4e-16 9 4 5 2.0e-15 9 3 6 3.1e-15 9 2 7 6.7e-16 9 1 8 2.1e-15 9 0 9 1.1e-16 10 10 0 3.9e-15 10 9 1 1.3e-15 10 8 2 6.7e-16 10 7 3 6.7e-16 10 6 4 5.6e-16 10 5 5 2.4e-15 10 4 6 0.0e+00 10 3 7 1.3e-15 10 2 8 8.9e-16 10 1 9 1.1e-16 10 0 10 1.7e-15 11 11 0 1.6e-15 11 10 1 1.8e-15 11 9 2 7.8e-16 11 8 3 1.1e-15 11 7 4 3.8e-15 11 6 5 2.4e-15 11 5 6 3.0e-15 11 4 7 2.1e-15 11 3 8 2.3e-15 11 2 9 4.4e-16 11 1 10 6.0e-15 11 0 11 3.4e-15 12 12 0 2.7e-15 12 11 1 2.2e-15 12 10 2 3.3e-15 12 9 3 1.1e-15 12 8 4 1.8e-15 12 7 5 1.1e-15 12 6 6 6.7e-16 12 5 7 4.4e-16 12 4 8 1.1e-16 12 3 9 2.1e-15 12 2 10 1.1e-15 12 1 11 0.0e+00 12 0 12 1.3e-15 13 13 0 2.3e-15 13 12 1 3.3e-15 13 11 2 2.6e-15 13 10 3 3.8e-15 13 9 4 3.3e-15 13 8 5 1.0e-15 13 7 6 8.9e-16 13 6 7 4.4e-15 13 5 8 1.2e-15 13 4 9 2.9e-15 13 3 10 1.3e-15 13 2 11 0.0e+00 13 1 12 2.2e-16 13 0 13 1.6e-15 14 14 0 1.0e-15 14 13 1 2.6e-15 14 12 2 6.7e-16 14 11 3 1.1e-15 14 10 4 4.4e-16 14 9 5 6.7e-16 14 8 6 3.1e-15 14 7 7 6.7e-16 14 6 8 4.4e-16 14 5 9 2.2e-16 14 4 10 1.2e-15 14 3 11 2.6e-15 14 2 12 2.4e-15 14 1 13 3.8e-15 14 0 14 2.2e-16 15 15 0 4.4e-16 15 14 1 1.3e-15 15 13 2 3.6e-15 15 12 3 1.6e-15 15 11 4 2.2e-16 15 10 5 1.1e-15 15 9 6 3.1e-15 15 8 7 2.6e-15 15 7 8 0.0e+00 15 6 9 4.4e-16 15 5 10 2.2e-16 15 4 11 3.1e-15 15 3 12 4.4e-16 15 2 13 1.3e-15 15 1 14 1.3e-15 15 0 15 2.0e-15 16 16 0 0.0e+00 16 15 1 2.2e-15 16 14 2 4.4e-16 16 13 3 1.2e-15 16 12 4 3.3e-15 16 11 5 1.3e-15 16 10 6 7.8e-16 16 9 7 8.9e-16 16 8 8 2.3e-15 16 7 9 3.1e-15 16 6 10 1.1e-15 16 5 11 2.4e-15 16 4 12 2.2e-16 16 3 13 1.6e-15 16 2 14 0.0e+00 16 1 15 1.8e-15 16 0 16 6.7e-16 17 17 0 2.0e-15 17 16 1 2.7e-15 17 15 2 0.0e+00 17 14 3 8.9e-16 17 13 4 2.6e-15 17 12 5 1.3e-15 17 11 6 4.2e-15 17 10 7 1.3e-15 17 9 8 1.3e-15 17 8 9 1.8e-15 17 7 10 3.3e-15 17 6 11 4.4e-15 17 5 12 2.9e-15 17 4 13 6.7e-16 17 3 14 2.2e-16 17 2 15 4.1e-15 17 1 16 1.7e-15 17 0 17 0.0e+00 18 18 0 1.3e-15 18 17 1 0.0e+00 18 16 2 2.1e-15 18 15 3 8.9e-16 18 14 4 3.8e-15 18 13 5 1.6e-15 18 12 6 2.4e-15 18 11 7 1.1e-15 18 10 8 4.4e-16 18 9 9 4.4e-16 18 8 10 1.8e-15 18 7 11 3.7e-15 18 6 12 2.2e-16 18 5 13 4.4e-16 18 4 14 8.9e-16 18 3 15 1.1e-15 18 2 16 3.1e-15 18 1 17 2.2e-16 18 0 18 4.1e-15 19 19 0 1.9e-15 19 18 1 1.8e-15 19 17 2 1.2e-15 19 16 3 2.2e-16 19 15 4 1.3e-15 19 14 5 1.1e-15 19 13 6 1.6e-15 19 12 7 2.2e-15 19 11 8 1.6e-15 19 10 9 2.2e-16 19 9 10 1.8e-15 19 8 11 2.2e-16 19 7 12 2.4e-15 19 6 13 2.2e-16 19 5 14 2.9e-15 19 4 15 6.7e-16 19 3 16 2.2e-16 19 2 17 2.2e-15 19 1 18 4.4e-16 19 0 19 1.8e-15 20 20 0 2.3e-15 20 19 1 1.0e-15 20 18 2 2.6e-15 20 17 3 2.2e-16 20 16 4 8.9e-16 20 15 5 8.9e-16 20 14 6 2.0e-15 20 13 7 5.6e-16 20 12 8 2.6e-15 20 11 9 2.0e-15 20 10 10 2.3e-15 20 9 11 2.2e-16 20 8 12 5.1e-15 20 7 13 8.9e-16 20 6 14 1.3e-15 20 5 15 4.3e-15 20 4 16 1.1e-15 20 3 17 6.7e-16 20 2 18 1.1e-15 20 1 19 8.9e-16 20 0 20 3.7e-15 21 21 0 8.9e-16 21 20 1 1.1e-15 21 19 2 1.1e-15 21 18 3 2.4e-15 21 17 4 2.2e-16 21 16 5 2.2e-15 21 15 6 3.6e-15 21 14 7 1.3e-15 21 13 8 1.6e-15 21 12 9 8.9e-16 21 11 10 6.7e-16 21 10 11 4.4e-15 21 9 12 2.2e-15 21 8 13 6.7e-16 21 7 14 2.8e-15 21 6 15 8.9e-16 21 5 16 2.4e-15 21 4 17 2.6e-15 21 3 18 2.2e-16 21 2 19 1.9e-15 21 1 20 2.1e-15 21 0 21 2.2e-16 22 22 0 1.7e-15 22 21 1 4.6e-15 22 20 2 7.8e-16 22 19 3 8.9e-16 22 18 4 8.9e-16 22 17 5 1.2e-15 22 16 6 1.4e-15 22 15 7 1.9e-15 22 14 8 7.8e-16 22 13 9 1.3e-15 22 12 10 4.6e-15 22 11 11 6.7e-16 22 10 12 2.2e-15 22 9 13 1.6e-15 22 8 14 4.2e-15 22 7 15 2.0e-15 22 6 16 3.0e-15 22 5 17 1.3e-15 22 4 18 3.8e-15 22 3 19 4.4e-16 22 2 20 1.6e-15 22 1 21 8.9e-16 22 0 22 1.7e-15 23 23 0 6.7e-16 23 22 1 8.9e-16 23 21 2 4.4e-16 23 20 3 2.6e-15 23 19 4 2.2e-16 23 18 5 2.4e-15 23 17 6 4.4e-16 23 16 7 3.3e-15 23 15 8 8.9e-16 23 14 9 2.2e-15 23 13 10 1.1e-15 23 12 11 7.8e-16 23 11 12 1.8e-15 23 10 13 1.8e-15 23 9 14 1.1e-15 23 8 15 2.1e-15 23 7 16 1.6e-15 23 6 17 1.8e-15 23 5 18 3.4e-15 23 4 19 1.8e-15 23 3 20 3.3e-16 23 2 21 4.4e-16 23 1 22 8.9e-16 23 0 23 8.9e-16 24 24 0 2.9e-15 24 23 1 2.2e-16 24 22 2 4.4e-16 24 21 3 7.8e-16 24 20 4 8.9e-16 24 19 5 1.1e-15 24 18 6 6.7e-16 24 17 7 8.9e-16 24 16 8 2.9e-15 24 15 9 6.7e-16 24 14 10 1.9e-15 24 13 11 2.2e-16 24 12 12 1.1e-15 24 11 13 1.3e-15 24 10 14 1.3e-15 24 9 15 2.4e-15 24 8 16 1.3e-15 24 7 17 6.7e-16 24 6 18 3.1e-15 24 5 19 2.2e-16 24 4 20 2.2e-15 24 3 21 1.0e-15 24 2 22 1.3e-15 24 1 23 8.9e-16 24 0 24 3.2e-15 25 25 0 6.7e-16 25 24 1 5.6e-16 25 23 2 3.3e-16 25 22 3 5.6e-16 25 21 4 4.4e-16 25 20 5 1.9e-15 25 19 6 6.7e-16 25 18 7 6.7e-16 25 17 8 2.2e-16 25 16 9 6.7e-16 25 15 10 4.4e-16 25 14 11 4.4e-16 25 13 12 2.2e-16 25 12 13 3.1e-15 25 11 14 2.0e-15 25 10 15 1.8e-15 25 9 16 1.8e-15 25 8 17 1.8e-15 25 7 18 6.7e-16 25 6 19 2.2e-16 25 5 20 5.6e-16 25 4 21 1.3e-15 25 3 22 7.8e-16 25 2 23 1.8e-15 25 1 24 2.2e-16 25 0 25 5.6e-16 26 26 0 1.1e-15 26 25 1 2.6e-15 26 24 2 2.2e-15 26 23 3 2.0e-15 26 22 4 1.1e-15 26 21 5 1.8e-15 26 20 6 0.0e+00 26 19 7 1.0e-15 26 18 8 3.3e-16 26 17 9 3.3e-16 26 16 10 1.1e-15 26 15 11 2.0e-15 26 14 12 1.3e-15 26 13 13 1.2e-15 26 12 14 1.1e-15 26 11 15 1.1e-15 26 10 16 1.1e-16 26 9 17 4.4e-16 26 8 18 2.2e-15 26 7 19 2.9e-15 26 6 20 3.3e-16 26 5 21 2.2e-15 26 4 22 1.8e-15 26 3 23 2.2e-16 26 2 24 1.4e-15 26 1 25 3.1e-15 26 0 26 4.4e-16 27 27 0 6.7e-16 27 26 1 1.1e-15 27 25 2 1.0e-15 27 24 3 1.6e-15 27 23 4 6.7e-16 27 22 5 1.3e-15 27 21 6 6.7e-16 27 20 7 1.1e-15 27 19 8 2.0e-15 27 18 9 4.4e-16 27 17 10 3.1e-15 27 16 11 2.2e-16 27 15 12 4.4e-16 27 14 13 1.6e-15 27 13 14 2.1e-15 27 12 15 6.7e-16 27 11 16 3.3e-16 27 10 17 1.8e-15 27 9 18 1.2e-15 27 8 19 7.8e-16 27 7 20 4.4e-16 27 6 21 1.1e-16 27 5 22 1.2e-15 27 4 23 1.6e-15 27 3 24 1.3e-15 27 2 25 2.7e-15 27 1 26 0.0e+00 27 0 27 3.1e-15 28 28 0 1.0e-15 28 27 1 0.0e+00 28 26 2 1.7e-15 28 25 3 1.1e-15 28 24 4 1.1e-15 28 23 5 4.4e-16 28 22 6 6.7e-16 28 21 7 4.4e-16 28 20 8 6.7e-16 28 19 9 2.2e-16 28 18 10 1.6e-15 28 17 11 2.2e-16 28 16 12 2.4e-15 28 15 13 1.1e-14 28 14 14 8.9e-16 28 13 15 0.0e+00 28 12 16 3.8e-15 28 11 17 7.8e-16 28 10 18 4.4e-16 28 9 19 2.2e-15 28 8 20 3.0e-15 28 7 21 4.4e-16 28 6 22 2.6e-15 28 5 23 0.0e+00 28 4 24 6.7e-16 28 3 25 2.2e-16 28 2 26 2.0e-15 28 1 27 2.9e-15 28 0 28 1.3e-15 29 29 0 1.3e-15 29 28 1 2.2e-16 29 27 2 1.1e-15 29 26 3 4.4e-16 29 25 4 1.8e-15 29 24 5 3.3e-16 29 23 6 6.7e-16 29 22 7 6.7e-16 29 21 8 1.1e-15 29 20 9 7.8e-16 29 19 10 1.0e-15 29 18 11 8.9e-16 29 17 12 3.1e-15 29 16 13 5.8e-14 29 15 14 5.6e-14 29 14 15 1.1e-15 29 13 16 7.8e-16 29 12 17 0.0e+00 29 11 18 1.8e-15 29 10 19 7.8e-16 29 9 20 1.6e-15 29 8 21 2.0e-15 29 7 22 2.2e-16 29 6 23 2.4e-15 29 5 24 8.9e-16 29 4 25 1.6e-15 29 3 26 1.3e-15 29 2 27 4.4e-16 29 1 28 2.9e-15 29 0 29 1.1e-15 30 30 0 8.9e-16 30 29 1 1.2e-15 30 28 2 4.4e-16 30 27 3 8.9e-16 30 26 4 8.9e-16 30 25 5 7.8e-16 30 24 6 6.7e-16 30 23 7 1.6e-15 30 22 8 4.4e-16 30 21 9 2.4e-15 30 20 10 8.9e-16 30 19 11 6.7e-16 30 18 12 3.3e-15 30 17 13 2.5e-13 30 16 14 4.6e-13 30 15 15 2.5e-13 30 14 16 1.1e-15 30 13 17 1.3e-15 30 12 18 0.0e+00 30 11 19 1.6e-15 30 10 20 1.1e-15 30 9 21 1.6e-15 30 8 22 2.0e-15 30 7 23 1.1e-16 30 6 24 2.6e-15 30 5 25 8.9e-16 30 4 26 8.9e-16 30 3 27 1.7e-15 30 2 28 1.2e-15 30 1 29 1.8e-15 30 0 30 2.0e-15 31 31 0 2.2e-16 31 30 1 2.2e-16 31 29 2 2.8e-15 31 28 3 8.9e-16 31 27 4 1.1e-15 31 26 5 4.4e-16 31 25 6 5.6e-16 31 24 7 1.6e-15 31 23 8 8.9e-16 31 22 9 4.4e-16 31 21 10 2.9e-15 31 20 11 7.8e-16 31 19 12 1.1e-15 31 18 13 8.0e-13 31 17 14 2.0e-12 31 16 15 2.0e-12 31 15 16 8.0e-13 31 14 17 1.2e-15 31 13 18 8.9e-16 31 12 19 1.8e-15 31 11 20 1.8e-15 31 10 21 1.6e-15 31 9 22 5.6e-16 31 8 23 3.3e-16 31 7 24 4.4e-16 31 6 25 5.6e-16 31 5 26 4.4e-16 31 4 27 6.7e-16 31 3 28 1.2e-15 31 2 29 1.6e-15 31 1 30 1.3e-15 31 0 31 1.0e-15 32 32 0 1.1e-15 32 31 1 0.0e+00 32 30 2 2.2e-16 32 29 3 4.4e-16 32 28 4 0.0e+00 32 27 5 1.8e-15 32 26 6 4.4e-16 32 25 7 8.9e-16 32 24 8 6.7e-16 32 23 9 4.4e-16 32 22 10 1.1e-15 32 21 11 1.0e-15 32 20 12 4.4e-16 32 19 13 2.1e-12 32 18 14 6.4e-12 32 17 15 8.9e-12 32 16 16 6.4e-12 32 15 17 2.1e-12 32 14 18 1.3e-15 32 13 19 1.1e-15 32 12 20 1.3e-15 32 11 21 8.9e-16 32 10 22 6.7e-16 32 9 23 2.3e-15 32 8 24 2.1e-15 32 7 25 4.4e-16 32 6 26 3.3e-16 32 5 27 1.3e-15 32 4 28 1.3e-15 32 3 29 0.0e+00 32 2 30 3.3e-16 32 1 31 2.2e-16 32 0 32 TEST05 Check the exactness of a Gauss-Legendre 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 0.0e+00 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 2.5e-01 2 2 0 0 0.0e+00 2 1 1 0 2.5e-01 2 0 2 0 0.0e+00 2 1 0 1 0.0e+00 2 0 1 1 2.5e-01 2 0 0 2 TEST05 Check the exactness of a Gauss-Legendre 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 0.0e+00 0 0 0 0 1.1e-16 1 1 0 0 0.0e+00 1 0 1 0 0.0e+00 1 0 0 1 2.2e-16 2 2 0 0 1.1e-16 2 1 1 0 2.2e-16 2 0 2 0 0.0e+00 2 1 0 1 0.0e+00 2 0 1 1 2.2e-16 2 0 0 2 0.0e+00 3 3 0 0 2.2e-16 3 2 1 0 2.2e-16 3 1 2 0 0.0e+00 3 0 3 0 2.2e-16 3 2 0 1 0.0e+00 3 1 1 1 2.2e-16 3 0 2 1 2.2e-16 3 1 0 2 2.2e-16 3 0 1 2 0.0e+00 3 0 0 3 0.0e+00 4 4 0 0 0.0e+00 4 3 1 0 6.2e-02 4 2 2 0 0.0e+00 4 1 3 0 0.0e+00 4 0 4 0 0.0e+00 4 3 0 1 2.2e-16 4 2 1 1 2.2e-16 4 1 2 1 0.0e+00 4 0 3 1 6.2e-02 4 2 0 2 2.2e-16 4 1 1 2 6.2e-02 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-Legendre 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 1.1e-16 0 0 0 0 5.6e-16 1 1 0 0 2.2e-16 1 0 1 0 1.1e-16 1 0 0 1 3.3e-16 2 2 0 0 6.7e-16 2 1 1 0 0.0e+00 2 0 2 0 4.4e-16 2 1 0 1 2.2e-16 2 0 1 1 2.2e-16 2 0 0 2 2.2e-16 3 3 0 0 3.3e-16 3 2 1 0 0.0e+00 3 1 2 0 2.2e-16 3 0 3 0 3.3e-16 3 2 0 1 6.7e-16 3 1 1 1 0.0e+00 3 0 2 1 2.2e-16 3 1 0 2 2.2e-16 3 0 1 2 0.0e+00 3 0 0 3 2.2e-16 4 4 0 0 2.2e-16 4 3 1 0 2.2e-16 4 2 2 0 5.6e-16 4 1 3 0 2.2e-16 4 0 4 0 2.2e-16 4 3 0 1 3.3e-16 4 2 1 1 0.0e+00 4 1 2 1 0.0e+00 4 0 3 1 5.6e-16 4 2 0 2 2.2e-16 4 1 1 2 0.0e+00 4 0 2 2 2.2e-16 4 1 0 3 2.2e-16 4 0 1 3 1.1e-16 4 0 0 4 2.2e-16 5 5 0 0 2.2e-16 5 4 1 0 0.0e+00 5 3 2 0 2.2e-16 5 2 3 0 1.1e-16 5 1 4 0 3.3e-16 5 0 5 0 1.1e-16 5 4 0 1 0.0e+00 5 3 1 1 0.0e+00 5 2 2 1 5.6e-16 5 1 3 1 1.1e-16 5 0 4 1 2.2e-16 5 3 0 2 5.6e-16 5 2 1 2 2.2e-16 5 1 2 2 2.2e-16 5 0 3 2 2.2e-16 5 2 0 3 4.4e-16 5 1 1 3 2.2e-16 5 0 2 3 0.0e+00 5 1 0 4 2.2e-16 5 0 1 4 2.2e-16 5 0 0 5 4.4e-16 6 6 0 0 5.6e-16 6 5 1 0 2.2e-16 6 4 2 0 0.0e+00 6 3 3 0 0.0e+00 6 2 4 0 3.3e-16 6 1 5 0 2.2e-16 6 0 6 0 2.2e-16 6 5 0 1 1.1e-16 6 4 1 1 2.2e-16 6 3 2 1 3.3e-16 6 2 3 1 1.1e-16 6 1 4 1 3.3e-16 6 0 5 1 2.2e-16 6 4 0 2 0.0e+00 6 3 1 2 1.6e-02 6 2 2 2 2.2e-16 6 1 3 2 2.2e-16 6 0 4 2 0.0e+00 6 3 0 3 5.6e-16 6 2 1 3 5.6e-16 6 1 2 3 0.0e+00 6 0 3 3 2.2e-16 6 2 0 4 1.1e-16 6 1 1 4 4.4e-16 6 0 2 4 5.6e-16 6 1 0 5 3.3e-16 6 0 1 5 4.4e-16 6 0 0 6 TEST05 Check the exactness of a Gauss-Legendre 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 = 12 Number of unique points in the grid = 161 Error Total Monomial Degree Exponents 2.4e-15 0 0 0 0 2.4e-15 1 1 0 0 1.2e-15 1 0 1 0 2.1e-15 1 0 0 1 0.0e+00 2 2 0 0 6.7e-16 2 1 1 0 1.1e-15 2 0 2 0 1.2e-15 2 1 0 1 4.4e-16 2 0 1 1 5.8e-15 2 0 0 2 2.2e-15 3 3 0 0 4.4e-16 3 2 1 0 1.0e-15 3 1 2 0 2.7e-15 3 0 3 0 1.3e-15 3 2 0 1 0.0e+00 3 1 1 1 5.6e-16 3 0 2 1 2.2e-15 3 1 0 2 1.1e-15 3 0 1 2 6.9e-15 3 0 0 3 1.1e-16 4 4 0 0 1.1e-15 4 3 1 0 1.9e-15 4 2 2 0 1.6e-15 4 1 3 0 1.1e-16 4 0 4 0 2.2e-15 4 3 0 1 6.7e-16 4 2 1 1 2.2e-15 4 1 2 1 2.2e-15 4 0 3 1 1.2e-15 4 2 0 2 1.7e-15 4 1 1 2 2.2e-16 4 0 2 2 1.1e-16 4 1 0 3 6.7e-16 4 0 1 3 3.4e-15 4 0 0 4 1.0e-15 5 5 0 0 5.6e-16 5 4 1 0 2.2e-16 5 3 2 0 1.3e-15 5 2 3 0 2.2e-16 5 1 4 0 1.2e-15 5 0 5 0 4.4e-16 5 4 0 1 6.7e-16 5 3 1 1 2.6e-15 5 2 2 1 2.2e-16 5 1 3 1 2.2e-16 5 0 4 1 2.2e-15 5 3 0 2 1.0e-15 5 2 1 2 2.8e-15 5 1 2 2 1.3e-15 5 0 3 2 2.2e-16 5 2 0 3 1.7e-15 5 1 1 3 1.6e-15 5 0 2 3 2.3e-15 5 1 0 4 2.4e-15 5 0 1 4 3.0e-15 5 0 0 5 1.0e-15 6 6 0 0 2.0e-15 6 5 1 0 1.0e-15 6 4 2 0 2.2e-16 6 3 3 0 0.0e+00 6 2 4 0 2.2e-15 6 1 5 0 7.8e-16 6 0 6 0 6.7e-16 6 5 0 1 1.6e-15 6 4 1 1 2.2e-16 6 3 2 1 4.4e-16 6 2 3 1 1.1e-16 6 1 4 1 2.2e-16 6 0 5 1 2.2e-16 6 4 0 2 5.6e-16 6 3 1 2 1.7e-15 6 2 2 2 6.7e-16 6 1 3 2 1.4e-15 6 0 4 2 1.1e-16 6 3 0 3 5.6e-16 6 2 1 3 5.6e-16 6 1 2 3 4.4e-16 6 0 3 3 2.2e-16 6 2 0 4 1.7e-15 6 1 1 4 2.2e-16 6 0 2 4 5.6e-16 6 1 0 5 2.6e-15 6 0 1 5 3.1e-15 6 0 0 6 8.9e-16 7 7 0 0 0.0e+00 7 6 1 0 2.1e-15 7 5 2 0 1.3e-15 7 4 3 0 1.9e-15 7 3 4 0 7.8e-16 7 2 5 0 4.4e-16 7 1 6 0 5.6e-16 7 0 7 0 1.6e-15 7 6 0 1 1.3e-15 7 5 1 1 8.9e-16 7 4 2 1 0.0e+00 7 3 3 1 0.0e+00 7 2 4 1 1.0e-15 7 1 5 1 7.8e-16 7 0 6 1 3.3e-16 7 5 0 2 8.9e-16 7 4 1 2 3.3e-16 7 3 2 2 8.9e-16 7 2 3 2 1.4e-15 7 1 4 2 1.1e-16 7 0 5 2 2.2e-16 7 4 0 3 1.2e-15 7 3 1 3 1.1e-15 7 2 2 3 3.3e-16 7 1 3 3 1.0e-15 7 0 4 3 1.2e-15 7 3 0 4 1.3e-15 7 2 1 4 6.7e-16 7 1 2 4 1.8e-15 7 0 3 4 8.9e-16 7 2 0 5 1.6e-15 7 1 1 5 6.7e-16 7 0 2 5 7.8e-16 7 1 0 6 1.6e-15 7 0 1 6 2.2e-16 7 0 0 7 8.9e-16 8 8 0 0 6.7e-16 8 7 1 0 2.0e-15 8 6 2 0 1.0e-15 8 5 3 0 5.6e-16 8 4 4 0 5.6e-16 8 3 5 0 6.7e-16 8 2 6 0 4.4e-16 8 1 7 0 1.3e-15 8 0 8 0 3.3e-16 8 7 0 1 2.2e-16 8 6 1 1 0.0e+00 8 5 2 1 0.0e+00 8 4 3 1 2.2e-16 8 3 4 1 8.9e-16 8 2 5 1 2.2e-16 8 1 6 1 1.3e-15 8 0 7 1 1.2e-15 8 6 0 2 8.9e-16 8 5 1 2 2.2e-16 8 4 2 2 0.0e+00 8 3 3 2 6.7e-16 8 2 4 2 2.2e-16 8 1 5 2 3.3e-16 8 0 6 2 0.0e+00 8 5 0 3 2.2e-16 8 4 1 3 0.0e+00 8 3 2 3 4.4e-16 8 2 3 3 6.7e-16 8 1 4 3 8.9e-16 8 0 5 3 2.2e-16 8 4 0 4 4.4e-16 8 3 1 4 4.4e-16 8 2 2 4 1.0e-15 8 1 3 4 5.6e-16 8 0 4 4 1.0e-15 8 3 0 5 1.1e-15 8 2 1 5 4.4e-16 8 1 2 5 2.2e-16 8 0 3 5 5.6e-16 8 2 0 6 2.2e-16 8 1 1 6 1.0e-15 8 0 2 6 3.3e-16 8 1 0 7 2.2e-16 8 0 1 7 3.3e-15 8 0 0 8 0.0e+00 9 9 0 0 5.6e-16 9 8 1 0 0.0e+00 9 7 2 0 4.4e-16 9 6 3 0 8.9e-16 9 5 4 0 1.3e-15 9 4 5 0 1.0e-15 9 3 6 0 4.4e-16 9 2 7 0 6.7e-16 9 1 8 0 2.2e-15 9 0 9 0 0.0e+00 9 8 0 1 3.3e-16 9 7 1 1 1.1e-15 9 6 2 1 2.2e-16 9 5 3 1 0.0e+00 9 4 4 1 0.0e+00 9 3 5 1 1.1e-16 9 2 6 1 3.3e-16 9 1 7 1 1.1e-15 9 0 8 1 2.2e-16 9 7 0 2 2.2e-16 9 6 1 2 2.2e-16 9 5 2 2 0.0e+00 9 4 3 2 4.4e-16 9 3 4 2 2.2e-16 9 2 5 2 6.7e-16 9 1 6 2 1.9e-15 9 0 7 2 7.8e-16 9 6 0 3 6.7e-16 9 5 1 3 6.7e-16 9 4 2 3 2.2e-16 9 3 3 3 2.2e-16 9 2 4 3 0.0e+00 9 1 5 3 2.2e-16 9 0 6 3 6.7e-16 9 5 0 4 2.2e-16 9 4 1 4 8.9e-16 9 3 2 4 4.4e-16 9 2 3 4 4.4e-16 9 1 4 4 1.4e-15 9 0 5 4 8.9e-16 9 4 0 5 6.7e-16 9 3 1 5 0.0e+00 9 2 2 5 8.9e-16 9 1 3 5 1.2e-15 9 0 4 5 1.2e-15 9 3 0 6 1.6e-15 9 2 1 6 2.7e-15 9 1 2 6 1.0e-15 9 0 3 6 2.2e-16 9 2 0 7 8.9e-16 9 1 1 7 0.0e+00 9 0 2 7 2.4e-15 9 1 0 8 3.3e-15 9 0 1 8 5.6e-16 9 0 0 9 4.4e-16 10 10 0 0 1.1e-15 10 9 1 0 1.3e-15 10 8 2 0 1.3e-15 10 7 3 0 5.6e-16 10 6 4 0 1.6e-15 10 5 5 0 1.1e-16 10 4 6 0 1.8e-15 10 3 7 0 6.7e-16 10 2 8 0 1.3e-15 10 1 9 0 7.8e-16 10 0 10 0 4.4e-16 10 9 0 1 0.0e+00 10 8 1 1 2.2e-16 10 7 2 1 4.4e-16 10 6 3 1 4.4e-16 10 5 4 1 2.2e-16 10 4 5 1 1.3e-15 10 3 6 1 4.4e-16 10 2 7 1 8.9e-16 10 1 8 1 1.0e-15 10 0 9 1 8.9e-16 10 8 0 2 3.3e-16 10 7 1 2 1.6e-04 10 6 2 2 0.0e+00 10 5 3 2 4.4e-16 10 4 4 2 0.0e+00 10 3 5 2 1.6e-04 10 2 6 2 5.6e-16 10 1 7 2 1.8e-15 10 0 8 2 6.7e-16 10 7 0 3 4.4e-16 10 6 1 3 8.9e-16 10 5 2 3 1.1e-16 10 4 3 3 1.1e-15 10 3 4 3 1.1e-16 10 2 5 3 1.1e-15 10 1 6 3 2.2e-16 10 0 7 3 1.8e-15 10 6 0 4 2.2e-16 10 5 1 4 8.9e-16 10 4 2 4 1.1e-15 10 3 3 4 1.3e-15 10 2 4 4 4.4e-16 10 1 5 4 1.3e-15 10 0 6 4 3.3e-16 10 5 0 5 1.9e-15 10 4 1 5 3.3e-16 10 3 2 5 1.1e-16 10 2 3 5 2.1e-15 10 1 4 5 1.7e-15 10 0 5 5 1.2e-15 10 4 0 6 2.0e-15 10 3 1 6 1.6e-04 10 2 2 6 5.6e-16 10 1 3 6 1.0e-15 10 0 4 6 6.7e-16 10 3 0 7 2.2e-15 10 2 1 7 2.2e-15 10 1 2 7 0.0e+00 10 0 3 7 8.9e-16 10 2 0 8 6.7e-16 10 1 1 8 2.2e-15 10 0 2 8 1.8e-15 10 1 0 9 2.3e-15 10 0 1 9 1.6e-15 10 0 0 10 2.2e-16 11 11 0 0 0.0e+00 11 10 1 0 6.7e-16 11 9 2 0 6.7e-16 11 8 3 0 8.9e-16 11 7 4 0 3.3e-16 11 6 5 0 0.0e+00 11 5 6 0 8.9e-16 11 4 7 0 1.2e-15 11 3 8 0 2.2e-16 11 2 9 0 8.9e-16 11 1 10 0 6.7e-16 11 0 11 0 1.1e-15 11 10 0 1 2.2e-16 11 9 1 1 0.0e+00 11 8 2 1 1.1e-15 11 7 3 1 4.4e-16 11 6 4 1 4.4e-16 11 5 5 1 6.7e-16 11 4 6 1 4.4e-16 11 3 7 1 0.0e+00 11 2 8 1 7.8e-16 11 1 9 1 4.4e-16 11 0 10 1 8.9e-16 11 9 0 2 1.3e-15 11 8 1 2 6.2e-04 11 7 2 2 3.1e-04 11 6 3 2 4.4e-16 11 5 4 2 4.4e-16 11 4 5 2 3.1e-04 11 3 6 2 6.2e-04 11 2 7 2 2.2e-16 11 1 8 2 2.2e-16 11 0 9 2 1.1e-15 11 8 0 3 8.9e-16 11 7 1 3 3.1e-04 11 6 2 3 0.0e+00 11 5 3 3 6.7e-16 11 4 4 3 0.0e+00 11 3 5 3 3.1e-04 11 2 6 3 1.2e-15 11 1 7 3 8.9e-16 11 0 8 3 1.6e-15 11 7 0 4 8.9e-16 11 6 1 4 8.9e-16 11 5 2 4 2.2e-16 11 4 3 4 1.6e-15 11 3 4 4 2.2e-16 11 2 5 4 3.3e-16 11 1 6 4 4.4e-16 11 0 7 4 1.1e-16 11 6 0 5 4.4e-16 11 5 1 5 2.2e-16 11 4 2 5 2.0e-15 11 3 3 5 2.2e-16 11 2 4 5 0.0e+00 11 1 5 5 6.7e-16 11 0 6 5 8.9e-16 11 5 0 6 3.3e-16 11 4 1 6 3.1e-04 11 3 2 6 3.1e-04 11 2 3 6 4.4e-16 11 1 4 6 1.1e-15 11 0 5 6 4.4e-16 11 4 0 7 1.1e-16 11 3 1 7 6.3e-04 11 2 2 7 4.4e-16 11 1 3 7 8.9e-16 11 0 4 7 1.1e-15 11 3 0 8 3.3e-16 11 2 1 8 2.2e-16 11 1 2 8 1.8e-15 11 0 3 8 2.2e-16 11 2 0 9 3.8e-15 11 1 1 9 2.2e-16 11 0 2 9 8.9e-16 11 1 0 10 1.8e-15 11 0 1 10 4.4e-16 11 0 0 11 2.2e-15 12 12 0 0 0.0e+00 12 11 1 0 2.2e-16 12 10 2 0 0.0e+00 12 9 3 0 2.2e-16 12 8 4 0 0.0e+00 12 7 5 0 6.2e-06 12 6 6 0 8.9e-16 12 5 7 0 6.7e-16 12 4 8 0 1.3e-15 12 3 9 0 4.4e-16 12 2 10 0 6.7e-16 12 1 11 0 6.7e-16 12 0 12 0 4.4e-16 12 11 0 1 1.2e-15 12 10 1 1 2.2e-16 12 9 2 1 8.9e-16 12 8 3 1 2.2e-16 12 7 4 1 2.2e-16 12 6 5 1 1.1e-15 12 5 6 1 2.2e-16 12 4 7 1 1.1e-16 12 3 8 1 6.7e-16 12 2 9 1 2.2e-16 12 1 10 1 4.4e-16 12 0 11 1 1.1e-16 12 10 0 2 0.0e+00 12 9 1 2 1.5e-03 12 8 2 2 1.3e-03 12 7 3 2 4.3e-04 12 6 4 2 6.7e-16 12 5 5 2 4.3e-04 12 4 6 2 1.2e-03 12 3 7 2 1.5e-03 12 2 8 2 0.0e+00 12 1 9 2 4.4e-16 12 0 10 2 4.4e-16 12 9 0 3 1.1e-16 12 8 1 3 1.2e-03 12 7 2 3 6.3e-04 12 6 3 3 8.9e-16 12 5 4 3 0.0e+00 12 4 5 3 6.3e-04 12 3 6 3 1.2e-03 12 2 7 3 2.1e-15 12 1 8 3 6.7e-16 12 0 9 3 2.2e-16 12 8 0 4 8.9e-16 12 7 1 4 4.3e-04 12 6 2 4 4.4e-16 12 5 3 4 0.0e+00 12 4 4 4 0.0e+00 12 3 5 4 4.3e-04 12 2 6 4 1.1e-15 12 1 7 4 3.3e-16 12 0 8 4 0.0e+00 12 7 0 5 1.1e-16 12 6 1 5 1.1e-15 12 5 2 5 2.2e-16 12 4 3 5 4.4e-16 12 3 4 5 6.7e-16 12 2 5 5 1.1e-15 12 1 6 5 8.9e-16 12 0 7 5 6.2e-06 12 6 0 6 4.4e-16 12 5 1 6 4.3e-04 12 4 2 6 6.3e-04 12 3 3 6 4.3e-04 12 2 4 6 1.6e-15 12 1 5 6 6.2e-06 12 0 6 6 0.0e+00 12 5 0 7 2.2e-16 12 4 1 7 1.2e-03 12 3 2 7 1.2e-03 12 2 3 7 8.9e-16 12 1 4 7 8.9e-16 12 0 5 7 3.3e-16 12 4 0 8 2.2e-16 12 3 1 8 1.5e-03 12 2 2 8 6.7e-16 12 1 3 8 0.0e+00 12 0 4 8 7.8e-16 12 3 0 9 2.2e-16 12 2 1 9 2.2e-16 12 1 2 9 1.3e-15 12 0 3 9 8.9e-16 12 2 0 10 3.1e-15 12 1 1 10 1.6e-15 12 0 2 10 0.0e+00 12 1 0 11 0.0e+00 12 0 1 11 1.8e-15 12 0 0 12 TEST06: Call SPARSE_GRID_GL to make a sparse Gauss-Legendre 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 "gl_d2_level3_r.txt". W data written to "gl_d2_level3_w.txt". X data written to "gl_d2_level3_x.txt". SPARSE_GRID_GL_PRB Normal end of execution. 06 November 2009 02:35:56 PM