17-Jan-2023 06:00:59 sparse_grid_gl_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sparse_grid_gl(). sparse_grid_gl_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 sparse_grid_gl_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 sparse_grid_gl_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 sparse_grid_gl_test02: SPARSE_GRID_GL_INDEX returns abstract indexes 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: 1 -3 0 3 0 2 -2 0 3 0 3 -1 0 3 0 4 0 0 3 0 5 1 0 3 0 6 2 0 3 0 7 3 0 3 0 8 -1 -1 1 1 9 0 -1 1 1 10 1 -1 1 1 11 -1 0 1 1 12 0 0 1 1 13 1 0 1 1 14 -1 1 1 1 15 0 1 1 1 16 1 1 1 1 17 0 -3 0 3 18 0 -2 0 3 19 0 -1 0 3 20 0 0 0 3 21 0 1 0 3 22 0 2 0 3 23 0 3 0 3 24 -7 0 7 0 25 -6 0 7 0 26 -5 0 7 0 27 -4 0 7 0 28 -3 0 7 0 29 -2 0 7 0 30 -1 0 7 0 31 1 0 7 0 32 2 0 7 0 33 3 0 7 0 34 4 0 7 0 35 5 0 7 0 36 6 0 7 0 37 7 0 7 0 38 -3 -1 3 1 39 -2 -1 3 1 40 -1 -1 3 1 41 1 -1 3 1 42 2 -1 3 1 43 3 -1 3 1 44 -3 1 3 1 45 -2 1 3 1 46 -1 1 3 1 47 1 1 3 1 48 2 1 3 1 49 3 1 3 1 50 -1 -3 1 3 51 1 -3 1 3 52 -1 -2 1 3 53 1 -2 1 3 54 -1 -1 1 3 55 1 -1 1 3 56 -1 1 1 3 57 1 1 1 3 58 -1 2 1 3 59 1 2 1 3 60 -1 3 1 3 61 1 3 1 3 62 0 -7 0 7 63 0 -6 0 7 64 0 -5 0 7 65 0 -4 0 7 66 0 -3 0 7 67 0 -2 0 7 68 0 -1 0 7 69 0 1 0 7 70 0 2 0 7 71 0 3 0 7 72 0 4 0 7 73 0 5 0 7 74 0 6 0 7 75 0 7 0 7 sparse_grid_gl_test02: SPARSE_GRID_GL_INDEX returns abstract indexes 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: 1 -7 0 7 0 2 -6 0 7 0 3 -5 0 7 0 4 -4 0 7 0 5 -3 0 7 0 6 -2 0 7 0 7 -1 0 7 0 8 0 0 7 0 9 1 0 7 0 10 2 0 7 0 11 3 0 7 0 12 4 0 7 0 13 5 0 7 0 14 6 0 7 0 15 7 0 7 0 16 -3 -1 3 1 17 -2 -1 3 1 18 -1 -1 3 1 19 0 -1 3 1 20 1 -1 3 1 21 2 -1 3 1 22 3 -1 3 1 23 -3 0 3 1 24 -2 0 3 1 25 -1 0 3 1 26 0 0 3 1 27 1 0 3 1 28 2 0 3 1 29 3 0 3 1 30 -3 1 3 1 31 -2 1 3 1 32 -1 1 3 1 33 0 1 3 1 34 1 1 3 1 35 2 1 3 1 36 3 1 3 1 37 -1 -3 1 3 38 0 -3 1 3 39 1 -3 1 3 40 -1 -2 1 3 41 0 -2 1 3 42 1 -2 1 3 43 -1 -1 1 3 44 0 -1 1 3 45 1 -1 1 3 46 -1 0 1 3 47 0 0 1 3 48 1 0 1 3 49 -1 1 1 3 50 0 1 1 3 51 1 1 1 3 52 -1 2 1 3 53 0 2 1 3 54 1 2 1 3 55 -1 3 1 3 56 0 3 1 3 57 1 3 1 3 58 0 -7 0 7 59 0 -6 0 7 60 0 -5 0 7 61 0 -4 0 7 62 0 -3 0 7 63 0 -2 0 7 64 0 -1 0 7 65 0 0 0 7 66 0 1 0 7 67 0 2 0 7 68 0 3 0 7 69 0 4 0 7 70 0 5 0 7 71 0 6 0 7 72 0 7 0 7 73 -15 0 15 0 74 -14 0 15 0 75 -13 0 15 0 76 -12 0 15 0 77 -11 0 15 0 78 -10 0 15 0 79 -9 0 15 0 80 -8 0 15 0 81 -7 0 15 0 82 -6 0 15 0 83 -5 0 15 0 84 -4 0 15 0 85 -3 0 15 0 86 -2 0 15 0 87 -1 0 15 0 88 1 0 15 0 89 2 0 15 0 90 3 0 15 0 91 4 0 15 0 92 5 0 15 0 93 6 0 15 0 94 7 0 15 0 95 8 0 15 0 96 9 0 15 0 97 10 0 15 0 98 11 0 15 0 99 12 0 15 0 100 13 0 15 0 101 14 0 15 0 102 15 0 15 0 103 -7 -1 7 1 104 -6 -1 7 1 105 -5 -1 7 1 106 -4 -1 7 1 107 -3 -1 7 1 108 -2 -1 7 1 109 -1 -1 7 1 110 1 -1 7 1 111 2 -1 7 1 112 3 -1 7 1 113 4 -1 7 1 114 5 -1 7 1 115 6 -1 7 1 116 7 -1 7 1 117 -7 1 7 1 118 -6 1 7 1 119 -5 1 7 1 120 -4 1 7 1 121 -3 1 7 1 122 -2 1 7 1 123 -1 1 7 1 124 1 1 7 1 125 2 1 7 1 126 3 1 7 1 127 4 1 7 1 128 5 1 7 1 129 6 1 7 1 130 7 1 7 1 131 -3 -3 3 3 132 -2 -3 3 3 133 -1 -3 3 3 134 1 -3 3 3 135 2 -3 3 3 136 3 -3 3 3 137 -3 -2 3 3 138 -2 -2 3 3 139 -1 -2 3 3 140 1 -2 3 3 141 2 -2 3 3 142 3 -2 3 3 143 -3 -1 3 3 144 -2 -1 3 3 145 -1 -1 3 3 146 1 -1 3 3 147 2 -1 3 3 148 3 -1 3 3 149 -3 1 3 3 150 -2 1 3 3 151 -1 1 3 3 152 1 1 3 3 153 2 1 3 3 154 3 1 3 3 155 -3 2 3 3 156 -2 2 3 3 157 -1 2 3 3 158 1 2 3 3 159 2 2 3 3 160 3 2 3 3 161 -3 3 3 3 162 -2 3 3 3 163 -1 3 3 3 164 1 3 3 3 165 2 3 3 3 166 3 3 3 3 167 -1 -7 1 7 168 1 -7 1 7 169 -1 -6 1 7 170 1 -6 1 7 171 -1 -5 1 7 172 1 -5 1 7 173 -1 -4 1 7 174 1 -4 1 7 175 -1 -3 1 7 176 1 -3 1 7 177 -1 -2 1 7 178 1 -2 1 7 179 -1 -1 1 7 180 1 -1 1 7 181 -1 1 1 7 182 1 1 1 7 183 -1 2 1 7 184 1 2 1 7 185 -1 3 1 7 186 1 3 1 7 187 -1 4 1 7 188 1 4 1 7 189 -1 5 1 7 190 1 5 1 7 191 -1 6 1 7 192 1 6 1 7 193 -1 7 1 7 194 1 7 1 7 195 0 -15 0 15 196 0 -14 0 15 197 0 -13 0 15 198 0 -12 0 15 199 0 -11 0 15 200 0 -10 0 15 201 0 -9 0 15 202 0 -8 0 15 203 0 -7 0 15 204 0 -6 0 15 205 0 -5 0 15 206 0 -4 0 15 207 0 -3 0 15 208 0 -2 0 15 209 0 -1 0 15 210 0 1 0 15 211 0 2 0 15 212 0 3 0 15 213 0 4 0 15 214 0 5 0 15 215 0 6 0 15 216 0 7 0 15 217 0 8 0 15 218 0 9 0 15 219 0 10 0 15 220 0 11 0 15 221 0 12 0 15 222 0 13 0 15 223 0 14 0 15 224 0 15 0 15 sparse_grid_gl_test02: SPARSE_GRID_GL_INDEX returns abstract indexes 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: 1 0 0 0 0 0 0 sparse_grid_gl_test02: SPARSE_GRID_GL_INDEX returns abstract indexes 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: 1 0 0 0 0 0 0 2 -1 0 0 1 0 0 3 1 0 0 1 0 0 4 0 -1 0 0 1 0 5 0 1 0 0 1 0 6 0 0 -1 0 0 1 7 0 0 1 0 0 1 8 -3 0 0 3 0 0 9 -2 0 0 3 0 0 10 -1 0 0 3 0 0 11 1 0 0 3 0 0 12 2 0 0 3 0 0 13 3 0 0 3 0 0 14 -1 -1 0 1 1 0 15 1 -1 0 1 1 0 16 -1 1 0 1 1 0 17 1 1 0 1 1 0 18 0 -3 0 0 3 0 19 0 -2 0 0 3 0 20 0 -1 0 0 3 0 21 0 1 0 0 3 0 22 0 2 0 0 3 0 23 0 3 0 0 3 0 24 -1 0 -1 1 0 1 25 1 0 -1 1 0 1 26 -1 0 1 1 0 1 27 1 0 1 1 0 1 28 0 -1 -1 0 1 1 29 0 1 -1 0 1 1 30 0 -1 1 0 1 1 31 0 1 1 0 1 1 32 0 0 -3 0 0 3 33 0 0 -2 0 0 3 34 0 0 -1 0 0 3 35 0 0 1 0 0 3 36 0 0 2 0 0 3 37 0 0 3 0 0 3 sparse_grid_gl_test02: SPARSE_GRID_GL_INDEX returns abstract indexes 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: 1 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 0 0 0 0 0 1 0 0 0 0 0 3 1 0 0 0 0 0 1 0 0 0 0 0 4 0 -1 0 0 0 0 0 1 0 0 0 0 5 0 1 0 0 0 0 0 1 0 0 0 0 6 0 0 -1 0 0 0 0 0 1 0 0 0 7 0 0 1 0 0 0 0 0 1 0 0 0 8 0 0 0 -1 0 0 0 0 0 1 0 0 9 0 0 0 1 0 0 0 0 0 1 0 0 10 0 0 0 0 -1 0 0 0 0 0 1 0 11 0 0 0 0 1 0 0 0 0 0 1 0 12 0 0 0 0 0 -1 0 0 0 0 0 1 13 0 0 0 0 0 1 0 0 0 0 0 1 14 -3 0 0 0 0 0 3 0 0 0 0 0 15 -2 0 0 0 0 0 3 0 0 0 0 0 16 -1 0 0 0 0 0 3 0 0 0 0 0 17 1 0 0 0 0 0 3 0 0 0 0 0 18 2 0 0 0 0 0 3 0 0 0 0 0 19 3 0 0 0 0 0 3 0 0 0 0 0 20 -1 -1 0 0 0 0 1 1 0 0 0 0 21 1 -1 0 0 0 0 1 1 0 0 0 0 22 -1 1 0 0 0 0 1 1 0 0 0 0 23 1 1 0 0 0 0 1 1 0 0 0 0 24 0 -3 0 0 0 0 0 3 0 0 0 0 25 0 -2 0 0 0 0 0 3 0 0 0 0 26 0 -1 0 0 0 0 0 3 0 0 0 0 27 0 1 0 0 0 0 0 3 0 0 0 0 28 0 2 0 0 0 0 0 3 0 0 0 0 29 0 3 0 0 0 0 0 3 0 0 0 0 30 -1 0 -1 0 0 0 1 0 1 0 0 0 31 1 0 -1 0 0 0 1 0 1 0 0 0 32 -1 0 1 0 0 0 1 0 1 0 0 0 33 1 0 1 0 0 0 1 0 1 0 0 0 34 0 -1 -1 0 0 0 0 1 1 0 0 0 35 0 1 -1 0 0 0 0 1 1 0 0 0 36 0 -1 1 0 0 0 0 1 1 0 0 0 37 0 1 1 0 0 0 0 1 1 0 0 0 38 0 0 -3 0 0 0 0 0 3 0 0 0 39 0 0 -2 0 0 0 0 0 3 0 0 0 40 0 0 -1 0 0 0 0 0 3 0 0 0 41 0 0 1 0 0 0 0 0 3 0 0 0 42 0 0 2 0 0 0 0 0 3 0 0 0 43 0 0 3 0 0 0 0 0 3 0 0 0 44 -1 0 0 -1 0 0 1 0 0 1 0 0 45 1 0 0 -1 0 0 1 0 0 1 0 0 46 -1 0 0 1 0 0 1 0 0 1 0 0 47 1 0 0 1 0 0 1 0 0 1 0 0 48 0 -1 0 -1 0 0 0 1 0 1 0 0 49 0 1 0 -1 0 0 0 1 0 1 0 0 50 0 -1 0 1 0 0 0 1 0 1 0 0 51 0 1 0 1 0 0 0 1 0 1 0 0 52 0 0 -1 -1 0 0 0 0 1 1 0 0 53 0 0 1 -1 0 0 0 0 1 1 0 0 54 0 0 -1 1 0 0 0 0 1 1 0 0 55 0 0 1 1 0 0 0 0 1 1 0 0 56 0 0 0 -3 0 0 0 0 0 3 0 0 57 0 0 0 -2 0 0 0 0 0 3 0 0 58 0 0 0 -1 0 0 0 0 0 3 0 0 59 0 0 0 1 0 0 0 0 0 3 0 0 60 0 0 0 2 0 0 0 0 0 3 0 0 61 0 0 0 3 0 0 0 0 0 3 0 0 62 -1 0 0 0 -1 0 1 0 0 0 1 0 63 1 0 0 0 -1 0 1 0 0 0 1 0 64 -1 0 0 0 1 0 1 0 0 0 1 0 65 1 0 0 0 1 0 1 0 0 0 1 0 66 0 -1 0 0 -1 0 0 1 0 0 1 0 67 0 1 0 0 -1 0 0 1 0 0 1 0 68 0 -1 0 0 1 0 0 1 0 0 1 0 69 0 1 0 0 1 0 0 1 0 0 1 0 70 0 0 -1 0 -1 0 0 0 1 0 1 0 71 0 0 1 0 -1 0 0 0 1 0 1 0 72 0 0 -1 0 1 0 0 0 1 0 1 0 73 0 0 1 0 1 0 0 0 1 0 1 0 74 0 0 0 -1 -1 0 0 0 0 1 1 0 75 0 0 0 1 -1 0 0 0 0 1 1 0 76 0 0 0 -1 1 0 0 0 0 1 1 0 77 0 0 0 1 1 0 0 0 0 1 1 0 78 0 0 0 0 -3 0 0 0 0 0 3 0 79 0 0 0 0 -2 0 0 0 0 0 3 0 80 0 0 0 0 -1 0 0 0 0 0 3 0 81 0 0 0 0 1 0 0 0 0 0 3 0 82 0 0 0 0 2 0 0 0 0 0 3 0 83 0 0 0 0 3 0 0 0 0 0 3 0 84 -1 0 0 0 0 -1 1 0 0 0 0 1 85 1 0 0 0 0 -1 1 0 0 0 0 1 86 -1 0 0 0 0 1 1 0 0 0 0 1 87 1 0 0 0 0 1 1 0 0 0 0 1 88 0 -1 0 0 0 -1 0 1 0 0 0 1 89 0 1 0 0 0 -1 0 1 0 0 0 1 90 0 -1 0 0 0 1 0 1 0 0 0 1 91 0 1 0 0 0 1 0 1 0 0 0 1 92 0 0 -1 0 0 -1 0 0 1 0 0 1 93 0 0 1 0 0 -1 0 0 1 0 0 1 94 0 0 -1 0 0 1 0 0 1 0 0 1 95 0 0 1 0 0 1 0 0 1 0 0 1 96 0 0 0 -1 0 -1 0 0 0 1 0 1 97 0 0 0 1 0 -1 0 0 0 1 0 1 98 0 0 0 -1 0 1 0 0 0 1 0 1 99 0 0 0 1 0 1 0 0 0 1 0 1 100 0 0 0 0 -1 -1 0 0 0 0 1 1 101 0 0 0 0 1 -1 0 0 0 0 1 1 102 0 0 0 0 -1 1 0 0 0 0 1 1 103 0 0 0 0 1 1 0 0 0 0 1 1 104 0 0 0 0 0 -3 0 0 0 0 0 3 105 0 0 0 0 0 -2 0 0 0 0 0 3 106 0 0 0 0 0 -1 0 0 0 0 0 3 107 0 0 0 0 0 1 0 0 0 0 0 3 108 0 0 0 0 0 2 0 0 0 0 0 3 109 0 0 0 0 0 3 0 0 0 0 0 3 sparse_grid_gl_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: 1 -0.143872 2 -0.310784 3 -0.424256 4 0.717433 5 -0.424256 6 -0.310784 7 -0.143872 8 -0.308642 9 -0.261628 10 -0.308642 11 -0.261628 12 -0.790123 13 -0.261628 14 -0.308642 15 -0.261628 16 -0.308642 17 -0.143872 18 -0.310784 19 -0.424256 20 -0.835918 21 -0.424256 22 -0.310784 23 -0.143872 24 0.061506 25 0.140732 26 0.214318 27 0.279141 28 0.332538 29 0.372322 30 0.396863 31 0.396863 32 0.372322 33 0.332538 34 0.279141 35 0.214318 36 0.140732 37 0.061506 38 0.071936 39 0.155392 40 0.212128 41 0.212128 42 0.155392 43 0.071936 44 0.071936 45 0.155392 46 0.212128 47 0.212128 48 0.155392 49 0.071936 50 0.071936 51 0.071936 52 0.155392 53 0.155392 54 0.212128 55 0.212128 56 0.212128 57 0.212128 58 0.155392 59 0.155392 60 0.071936 61 0.071936 62 0.061506 63 0.140732 64 0.214318 65 0.279141 66 0.332538 67 0.372322 68 0.396863 69 0.396863 70 0.372322 71 0.332538 72 0.279141 73 0.214318 74 0.140732 75 0.061506 Grid points: 1 -0.949108 0.000000 2 -0.741531 0.000000 3 -0.405845 0.000000 4 0.000000 0.000000 5 0.405845 0.000000 6 0.741531 0.000000 7 0.949108 0.000000 8 -0.774597 -0.774597 9 0.000000 -0.774597 10 0.774597 -0.774597 11 -0.774597 0.000000 12 0.000000 0.000000 13 0.774597 0.000000 14 -0.774597 0.774597 15 0.000000 0.774597 16 0.774597 0.774597 17 0.000000 -0.949108 18 0.000000 -0.741531 19 0.000000 -0.405845 20 0.000000 0.000000 21 0.000000 0.405845 22 0.000000 0.741531 23 0.000000 0.949108 24 -0.987993 0.000000 25 -0.937273 0.000000 26 -0.848207 0.000000 27 -0.724418 0.000000 28 -0.570972 0.000000 29 -0.394151 0.000000 30 -0.201194 0.000000 31 0.201194 0.000000 32 0.394151 0.000000 33 0.570972 0.000000 34 0.724418 0.000000 35 0.848207 0.000000 36 0.937273 0.000000 37 0.987993 0.000000 38 -0.949108 -0.774597 39 -0.741531 -0.774597 40 -0.405845 -0.774597 41 0.405845 -0.774597 42 0.741531 -0.774597 43 0.949108 -0.774597 44 -0.949108 0.774597 45 -0.741531 0.774597 46 -0.405845 0.774597 47 0.405845 0.774597 48 0.741531 0.774597 49 0.949108 0.774597 50 -0.774597 -0.949108 51 0.774597 -0.949108 52 -0.774597 -0.741531 53 0.774597 -0.741531 54 -0.774597 -0.405845 55 0.774597 -0.405845 56 -0.774597 0.405845 57 0.774597 0.405845 58 -0.774597 0.741531 59 0.774597 0.741531 60 -0.774597 0.949108 61 0.774597 0.949108 62 0.000000 -0.987993 63 0.000000 -0.937273 64 0.000000 -0.848207 65 0.000000 -0.724418 66 0.000000 -0.570972 67 0.000000 -0.394151 68 0.000000 -0.201194 69 0.000000 0.201194 70 0.000000 0.394151 71 0.000000 0.570972 72 0.000000 0.724418 73 0.000000 0.848207 74 0.000000 0.937273 75 0.000000 0.987993 sparse_grid_gl_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: 1 -0.034170 2 -0.078184 3 -0.119066 4 -0.155079 5 -0.184744 6 -0.206846 7 -0.220479 8 0.528555 9 -0.220479 10 -0.206846 11 -0.184744 12 -0.155079 13 -0.119066 14 -0.078184 15 -0.034170 16 -0.071936 17 -0.155392 18 -0.212128 19 -0.119656 20 -0.212128 21 -0.155392 22 -0.071936 23 -0.060978 24 -0.131722 25 -0.179815 26 -0.371519 27 -0.179815 28 -0.131722 29 -0.060978 30 -0.071936 31 -0.155392 32 -0.212128 33 -0.119656 34 -0.212128 35 -0.155392 36 -0.071936 37 -0.071936 38 -0.060978 39 -0.071936 40 -0.155392 41 -0.131722 42 -0.155392 43 -0.212128 44 -0.179815 45 -0.212128 46 -0.119656 47 -0.371519 48 -0.119656 49 -0.212128 50 -0.179815 51 -0.212128 52 -0.155392 53 -0.131722 54 -0.155392 55 -0.071936 56 -0.060978 57 -0.071936 58 -0.034170 59 -0.078184 60 -0.119066 61 -0.155079 62 -0.184744 63 -0.206846 64 -0.220479 65 -0.405156 66 -0.220479 67 -0.206846 68 -0.184744 69 -0.155079 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149 0.049441 150 0.106800 151 0.145794 152 0.145794 153 0.106800 154 0.049441 155 0.036218 156 0.078235 157 0.106800 158 0.106800 159 0.078235 160 0.036218 161 0.016766 162 0.036218 163 0.049441 164 0.049441 165 0.036218 166 0.016766 167 0.017085 168 0.017085 169 0.039092 170 0.039092 171 0.059533 172 0.059533 173 0.077539 174 0.077539 175 0.092372 176 0.092372 177 0.103423 178 0.103423 179 0.110240 180 0.110240 181 0.110240 182 0.110240 183 0.103423 184 0.103423 185 0.092372 186 0.092372 187 0.077539 188 0.077539 189 0.059533 190 0.059533 191 0.039092 192 0.039092 193 0.017085 194 0.017085 195 0.014942 196 0.034637 197 0.054018 198 0.072865 199 0.090987 200 0.108206 201 0.124350 202 0.139257 203 0.152781 204 0.164786 205 0.175153 206 0.183780 207 0.190580 208 0.195487 209 0.198450 210 0.198450 211 0.195487 212 0.190580 213 0.183780 214 0.175153 215 0.164786 216 0.152781 217 0.139257 218 0.124350 219 0.108206 220 0.090987 221 0.072865 222 0.054018 223 0.034637 224 0.014942 Grid points: 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-0.741531 138 -0.741531 -0.741531 139 -0.405845 -0.741531 140 0.405845 -0.741531 141 0.741531 -0.741531 142 0.949108 -0.741531 143 -0.949108 -0.405845 144 -0.741531 -0.405845 145 -0.405845 -0.405845 146 0.405845 -0.405845 147 0.741531 -0.405845 148 0.949108 -0.405845 149 -0.949108 0.405845 150 -0.741531 0.405845 151 -0.405845 0.405845 152 0.405845 0.405845 153 0.741531 0.405845 154 0.949108 0.405845 155 -0.949108 0.741531 156 -0.741531 0.741531 157 -0.405845 0.741531 158 0.405845 0.741531 159 0.741531 0.741531 160 0.949108 0.741531 161 -0.949108 0.949108 162 -0.741531 0.949108 163 -0.405845 0.949108 164 0.405845 0.949108 165 0.741531 0.949108 166 0.949108 0.949108 167 -0.774597 -0.987993 168 0.774597 -0.987993 169 -0.774597 -0.937273 170 0.774597 -0.937273 171 -0.774597 -0.848207 172 0.774597 -0.848207 173 -0.774597 -0.724418 174 0.774597 -0.724418 175 -0.774597 -0.570972 176 0.774597 -0.570972 177 -0.774597 -0.394151 178 0.774597 -0.394151 179 -0.774597 -0.201194 180 0.774597 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sparse_grid_gl_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: 1 8.000000 Grid points: 1 0.000000 0.000000 0.000000 sparse_grid_gl_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: 1 -3.577082 2 -2.469136 3 -2.469136 4 -2.469136 5 -2.469136 6 -2.469136 7 -2.469136 8 0.517940 9 1.118822 10 1.527320 11 1.527320 12 1.118822 13 0.517940 14 0.617284 15 0.617284 16 0.617284 17 0.617284 18 0.517940 19 1.118822 20 1.527320 21 1.527320 22 1.118822 23 0.517940 24 0.617284 25 0.617284 26 0.617284 27 0.617284 28 0.617284 29 0.617284 30 0.617284 31 0.617284 32 0.517940 33 1.118822 34 1.527320 35 1.527320 36 1.118822 37 0.517940 Grid points: 1 0.000000 0.000000 0.000000 2 -0.774597 0.000000 0.000000 3 0.774597 0.000000 0.000000 4 0.000000 -0.774597 0.000000 5 0.000000 0.774597 0.000000 6 0.000000 0.000000 -0.774597 7 0.000000 0.000000 0.774597 8 -0.949108 0.000000 0.000000 9 -0.741531 0.000000 0.000000 10 -0.405845 0.000000 0.000000 11 0.405845 0.000000 0.000000 12 0.741531 0.000000 0.000000 13 0.949108 0.000000 0.000000 14 -0.774597 -0.774597 0.000000 15 0.774597 -0.774597 0.000000 16 -0.774597 0.774597 0.000000 17 0.774597 0.774597 0.000000 18 0.000000 -0.949108 0.000000 19 0.000000 -0.741531 0.000000 20 0.000000 -0.405845 0.000000 21 0.000000 0.405845 0.000000 22 0.000000 0.741531 0.000000 23 0.000000 0.949108 0.000000 24 -0.774597 0.000000 -0.774597 25 0.774597 0.000000 -0.774597 26 -0.774597 0.000000 0.774597 27 0.774597 0.000000 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 0.774597 0.774597 32 0.000000 0.000000 -0.949108 33 0.000000 0.000000 -0.741531 34 0.000000 0.000000 -0.405845 35 0.000000 0.000000 0.405845 36 0.000000 0.000000 0.741531 37 0.000000 0.000000 0.949108 sparse_grid_gl_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 sparse_grid_gl_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 sparse_grid_gl_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 sparse_grid_gl_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 sparse_grid_gl_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 sparse_grid_gl_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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 2.500000e-01 2 2 0 0.000000e+00 2 1 1 2.500000e-01 2 0 2 5.000000e-01 3 3 0 2.500000e-01 3 2 1 2.500000e-01 3 1 2 5.000000e-01 3 0 3 sparse_grid_gl_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 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 2.220446e-16 2 2 0 0.000000e+00 2 1 1 2.220446e-16 2 0 2 0.000000e+00 3 3 0 2.220446e-16 3 2 1 2.220446e-16 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 6.250000e-02 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 2.220446e-16 5 5 0 0.000000e+00 5 4 1 1.250000e-01 5 3 2 1.250000e-01 5 2 3 0.000000e+00 5 1 4 2.220446e-16 5 0 5 sparse_grid_gl_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 = 7 Number of unique points in the grid = 22 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 0.000000e+00 1 1 0 1.110223e-16 1 0 1 0.000000e+00 2 2 0 1.110223e-16 2 1 1 0.000000e+00 2 0 2 1.110223e-16 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 2.220446e-16 3 0 3 1.110223e-16 4 4 0 2.220446e-16 4 3 1 0.000000e+00 4 2 2 2.220446e-16 4 1 3 2.220446e-16 4 0 4 2.220446e-16 5 5 0 1.110223e-16 5 4 1 2.220446e-16 5 3 2 2.220446e-16 5 2 3 2.220446e-16 5 1 4 0.000000e+00 5 0 5 0.000000e+00 6 6 0 2.220446e-16 6 5 1 2.220446e-16 6 4 2 1.110223e-16 6 3 3 2.220446e-16 6 2 4 0.000000e+00 6 1 5 0.000000e+00 6 0 6 3.330669e-16 7 7 0 2.220446e-16 7 6 1 0.000000e+00 7 5 2 2.220446e-16 7 4 3 1.110223e-16 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 2.220446e-16 7 0 7 sparse_grid_gl_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 = 9 Number of unique points in the grid = 75 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 2.220446e-16 2 2 0 0.000000e+00 2 1 1 2.220446e-16 2 0 2 0.000000e+00 3 3 0 2.220446e-16 3 2 1 2.220446e-16 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 2.220446e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 0.000000e+00 5 5 0 0.000000e+00 5 4 1 2.220446e-16 5 3 2 0.000000e+00 5 2 3 1.110223e-16 5 1 4 2.220446e-16 5 0 5 0.000000e+00 6 6 0 2.220446e-16 6 5 1 2.220446e-16 6 4 2 2.220446e-16 6 3 3 0.000000e+00 6 2 4 2.220446e-16 6 1 5 0.000000e+00 6 0 6 4.440892e-16 7 7 0 0.000000e+00 7 6 1 0.000000e+00 7 5 2 1.110223e-16 7 4 3 0.000000e+00 7 3 4 0.000000e+00 7 2 5 0.000000e+00 7 1 6 0.000000e+00 7 0 7 2.220446e-16 8 8 0 0.000000e+00 8 7 1 0.000000e+00 8 6 2 2.220446e-16 8 5 3 0.000000e+00 8 4 4 0.000000e+00 8 3 5 1.110223e-16 8 2 6 2.220446e-16 8 1 7 2.220446e-16 8 0 8 2.220446e-16 9 9 0 0.000000e+00 9 8 1 2.220446e-16 9 7 2 0.000000e+00 9 6 3 0.000000e+00 9 5 4 0.000000e+00 9 4 5 0.000000e+00 9 3 6 2.220446e-16 9 2 7 0.000000e+00 9 1 8 2.220446e-16 9 0 9 sparse_grid_gl_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 = 11 Number of unique points in the grid = 224 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 2.220446e-16 1 1 0 0.000000e+00 1 0 1 2.220446e-16 2 2 0 0.000000e+00 2 1 1 2.220446e-16 2 0 2 0.000000e+00 3 3 0 2.220446e-16 3 2 1 2.220446e-16 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 0.000000e+00 4 3 1 2.220446e-16 4 2 2 0.000000e+00 4 1 3 1.110223e-16 4 0 4 2.220446e-16 5 5 0 0.000000e+00 5 4 1 2.220446e-16 5 3 2 2.220446e-16 5 2 3 0.000000e+00 5 1 4 0.000000e+00 5 0 5 0.000000e+00 6 6 0 2.220446e-16 6 5 1 2.220446e-16 6 4 2 2.220446e-16 6 3 3 2.220446e-16 6 2 4 2.220446e-16 6 1 5 2.220446e-16 6 0 6 0.000000e+00 7 7 0 0.000000e+00 7 6 1 2.220446e-16 7 5 2 2.220446e-16 7 4 3 0.000000e+00 7 3 4 2.220446e-16 7 2 5 0.000000e+00 7 1 6 1.110223e-16 7 0 7 0.000000e+00 8 8 0 2.220446e-16 8 7 1 2.220446e-16 8 6 2 2.220446e-16 8 5 3 2.220446e-16 8 4 4 2.220446e-16 8 3 5 0.000000e+00 8 2 6 2.220446e-16 8 1 7 0.000000e+00 8 0 8 0.000000e+00 9 9 0 0.000000e+00 9 8 1 2.220446e-16 9 7 2 2.220446e-16 9 6 3 2.220446e-16 9 5 4 2.220446e-16 9 4 5 0.000000e+00 9 3 6 2.220446e-16 9 2 7 2.220446e-16 9 1 8 0.000000e+00 9 0 9 0.000000e+00 10 10 0 0.000000e+00 10 9 1 2.220446e-16 10 8 2 1.110223e-16 10 7 3 0.000000e+00 10 6 4 1.110223e-16 10 5 5 2.220446e-16 10 4 6 2.220446e-16 10 3 7 2.220446e-16 10 2 8 2.220446e-16 10 1 9 0.000000e+00 10 010 2.220446e-16 11 11 0 2.220446e-16 11 10 1 2.220446e-16 11 9 2 2.220446e-16 11 8 3 0.000000e+00 11 7 4 2.220446e-16 11 6 5 2.220446e-16 11 5 6 0.000000e+00 11 4 7 2.220446e-16 11 3 8 2.220446e-16 11 2 9 0.000000e+00 11 110 2.220446e-16 11 011 sparse_grid_gl_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 = 13 Number of unique points in the grid = 613 Error Total Monomial Degree Exponents 0.000000e+00 0 0 0 0.000000e+00 1 1 0 0.000000e+00 1 0 1 2.220446e-16 2 2 0 2.220446e-16 2 1 1 0.000000e+00 2 0 2 2.220446e-16 3 3 0 0.000000e+00 3 2 1 0.000000e+00 3 1 2 0.000000e+00 3 0 3 0.000000e+00 4 4 0 1.110223e-16 4 3 1 2.220446e-16 4 2 2 0.000000e+00 4 1 3 0.000000e+00 4 0 4 4.440892e-16 5 5 0 2.220446e-16 5 4 1 2.220446e-16 5 3 2 0.000000e+00 5 2 3 0.000000e+00 5 1 4 2.220446e-16 5 0 5 0.000000e+00 6 6 0 0.000000e+00 6 5 1 2.220446e-16 6 4 2 0.000000e+00 6 3 3 2.220446e-16 6 2 4 2.220446e-16 6 1 5 0.000000e+00 6 0 6 2.220446e-16 7 7 0 0.000000e+00 7 6 1 4.440892e-16 7 5 2 0.000000e+00 7 4 3 0.000000e+00 7 3 4 2.220446e-16 7 2 5 2.220446e-16 7 1 6 2.220446e-16 7 0 7 2.220446e-16 8 8 0 0.000000e+00 8 7 1 1.110223e-16 8 6 2 2.220446e-16 8 5 3 2.220446e-16 8 4 4 2.220446e-16 8 3 5 2.220446e-16 8 2 6 0.000000e+00 8 1 7 2.220446e-16 8 0 8 2.220446e-16 9 9 0 0.000000e+00 9 8 1 2.220446e-16 9 7 2 4.440892e-16 9 6 3 2.220446e-16 9 5 4 0.000000e+00 9 4 5 0.000000e+00 9 3 6 0.000000e+00 9 2 7 0.000000e+00 9 1 8 1.110223e-16 9 0 9 1.110223e-16 10 10 0 0.000000e+00 10 9 1 3.330669e-16 10 8 2 0.000000e+00 10 7 3 2.220446e-16 10 6 4 0.000000e+00 10 5 5 2.220446e-16 10 4 6 0.000000e+00 10 3 7 2.220446e-16 10 2 8 1.110223e-16 10 1 9 0.000000e+00 10 010 2.220446e-16 11 11 0 0.000000e+00 11 10 1 2.220446e-16 11 9 2 4.440892e-16 11 8 3 2.220446e-16 11 7 4 2.220446e-16 11 6 5 2.220446e-16 11 5 6 0.000000e+00 11 4 7 2.220446e-16 11 3 8 0.000000e+00 11 2 9 0.000000e+00 11 110 0.000000e+00 11 011 3.330669e-16 12 12 0 2.220446e-16 12 11 1 0.000000e+00 12 10 2 2.220446e-16 12 9 3 2.220446e-16 12 8 4 2.220446e-16 12 7 5 2.220446e-16 12 6 6 2.220446e-16 12 5 7 2.220446e-16 12 4 8 0.000000e+00 12 3 9 2.220446e-16 12 210 2.220446e-16 12 111 2.220446e-16 12 012 2.220446e-16 13 13 0 0.000000e+00 13 12 1 2.220446e-16 13 11 2 0.000000e+00 13 10 3 0.000000e+00 13 9 4 0.000000e+00 13 8 5 4.440892e-16 13 7 6 0.000000e+00 13 6 7 2.220446e-16 13 5 8 2.220446e-16 13 4 9 0.000000e+00 13 310 2.220446e-16 13 211 3.330669e-16 13 112 4.440892e-16 13 013 sparse_grid_gl_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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 2.500000e-01 2 2 0 0 0.000000e+00 2 1 1 0 2.500000e-01 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 2.500000e-01 2 0 0 2 sparse_grid_gl_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 0.000000e+00 0 0 0 0 0.000000e+00 1 1 0 0 0.000000e+00 1 0 1 0 0.000000e+00 1 0 0 1 2.220446e-16 2 2 0 0 0.000000e+00 2 1 1 0 2.220446e-16 2 0 2 0 0.000000e+00 2 1 0 1 0.000000e+00 2 0 1 1 2.220446e-16 2 0 0 2 0.000000e+00 3 3 0 0 2.220446e-16 3 2 1 0 2.220446e-16 3 1 2 0 0.000000e+00 3 0 3 0 2.220446e-16 3 2 0 1 0.000000e+00 3 1 1 1 2.220446e-16 3 0 2 1 2.220446e-16 3 1 0 2 2.220446e-16 3 0 1 2 0.000000e+00 3 0 0 3 2.220446e-16 4 4 0 0 0.000000e+00 4 3 1 0 6.250000e-02 4 2 2 0 0.000000e+00 4 1 3 0 0.000000e+00 4 0 4 0 0.000000e+00 4 3 0 1 2.220446e-16 4 2 1 1 2.220446e-16 4 1 2 1 0.000000e+00 4 0 3 1 6.250000e-02 4 2 0 2 2.220446e-16 4 1 1 2 6.250000e-02 4 0 2 2 0.000000e+00 4 1 0 3 0.000000e+00 4 0 1 3 0.000000e+00 4 0 0 4 sparse_grid_gl_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 2.220446e-16 0 0 0 0 2.220446e-16 1 1 0 0 2.220446e-16 1 0 1 0 2.220446e-16 1 0 0 1 2.220446e-16 2 2 0 0 2.220446e-16 2 1 1 0 4.440892e-16 2 0 2 0 2.220446e-16 2 1 0 1 2.220446e-16 2 0 1 1 2.220446e-16 2 0 0 2 2.220446e-16 3 3 0 0 0.000000e+00 3 2 1 0 4.440892e-16 3 1 2 0 1.110223e-16 3 0 3 0 2.220446e-16 3 2 0 1 2.220446e-16 3 1 1 1 4.440892e-16 3 0 2 1 2.220446e-16 3 1 0 2 2.220446e-16 3 0 1 2 0.000000e+00 3 0 0 3 2.220446e-16 4 4 0 0 3.330669e-16 4 3 1 0 0.000000e+00 4 2 2 0 1.110223e-16 4 1 3 0 2.220446e-16 4 0 4 0 3.330669e-16 4 3 0 1 0.000000e+00 4 2 1 1 4.440892e-16 4 1 2 1 2.220446e-16 4 0 3 1 0.000000e+00 4 2 0 2 2.220446e-16 4 1 1 2 4.440892e-16 4 0 2 2 1.110223e-16 4 1 0 3 1.110223e-16 4 0 1 3 2.220446e-16 4 0 0 4 2.220446e-16 5 5 0 0 2.220446e-16 5 4 1 0 0.000000e+00 5 3 2 0 0.000000e+00 5 2 3 0 1.110223e-16 5 1 4 0 4.440892e-16 5 0 5 0 4.440892e-16 5 4 0 1 3.330669e-16 5 3 1 1 0.000000e+00 5 2 2 1 2.220446e-16 5 1 3 1 2.220446e-16 5 0 4 1 2.220446e-16 5 3 0 2 2.220446e-16 5 2 1 2 4.440892e-16 5 1 2 2 2.220446e-16 5 0 3 2 2.220446e-16 5 2 0 3 2.220446e-16 5 1 1 3 2.220446e-16 5 0 2 3 0.000000e+00 5 1 0 4 2.220446e-16 5 0 1 4 4.440892e-16 5 0 0 5 2.220446e-16 6 6 0 0 2.220446e-16 6 5 1 0 2.220446e-16 6 4 2 0 0.000000e+00 6 3 3 0 2.220446e-16 6 2 4 0 2.220446e-16 6 1 5 0 2.220446e-16 6 0 6 0 0.000000e+00 6 5 0 1 4.440892e-16 6 4 1 1 2.220446e-16 6 3 2 1 0.000000e+00 6 2 3 1 1.110223e-16 6 1 4 1 2.220446e-16 6 0 5 1 4.440892e-16 6 4 0 2 2.220446e-16 6 3 1 2 1.562500e-02 6 2 2 2 2.220446e-16 6 1 3 2 0.000000e+00 6 0 4 2 1.110223e-16 6 3 0 3 3.330669e-16 6 2 1 3 3.330669e-16 6 1 2 3 0.000000e+00 6 0 3 3 2.220446e-16 6 2 0 4 1.110223e-16 6 1 1 4 2.220446e-16 6 0 2 4 2.220446e-16 6 1 0 5 4.440892e-16 6 0 1 5 0.000000e+00 6 0 0 6 sparse_grid_gl_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 = 8 Number of unique points in the grid = 161 Error Total Monomial Degree Exponents 7.771561e-16 0 0 0 0 1.221245e-15 1 1 0 0 1.110223e-15 1 0 1 0 8.881784e-16 1 0 0 1 8.881784e-16 2 2 0 0 1.110223e-15 2 1 1 0 9.992007e-16 2 0 2 0 1.110223e-15 2 1 0 1 6.661338e-16 2 0 1 1 8.881784e-16 2 0 0 2 7.771561e-16 3 3 0 0 8.881784e-16 3 2 1 0 8.881784e-16 3 1 2 0 3.330669e-16 3 0 3 0 5.551115e-16 3 2 0 1 9.992007e-16 3 1 1 1 5.551115e-16 3 0 2 1 6.661338e-16 3 1 0 2 5.551115e-16 3 0 1 2 3.330669e-16 3 0 0 3 2.220446e-16 4 4 0 0 6.661338e-16 4 3 1 0 6.661338e-16 4 2 2 0 2.220446e-16 4 1 3 0 5.551115e-16 4 0 4 0 2.220446e-16 4 3 0 1 8.881784e-16 4 2 1 1 6.661338e-16 4 1 2 1 2.220446e-16 4 0 3 1 5.551115e-16 4 2 0 2 5.551115e-16 4 1 1 2 5.551115e-16 4 0 2 2 4.440892e-16 4 1 0 3 4.440892e-16 4 0 1 3 6.661338e-16 4 0 0 4 2.220446e-16 5 5 0 0 4.440892e-16 5 4 1 0 3.330669e-16 5 3 2 0 2.220446e-16 5 2 3 0 5.551115e-16 5 1 4 0 2.220446e-16 5 0 5 0 2.220446e-16 5 4 0 1 4.440892e-16 5 3 1 1 7.771561e-16 5 2 2 1 4.440892e-16 5 1 3 1 5.551115e-16 5 0 4 1 2.220446e-16 5 3 0 2 2.220446e-16 5 2 1 2 6.661338e-16 5 1 2 2 0.000000e+00 5 0 3 2 5.551115e-16 5 2 0 3 2.220446e-16 5 1 1 3 2.220446e-16 5 0 2 3 0.000000e+00 5 1 0 4 2.220446e-16 5 0 1 4 2.220446e-16 5 0 0 5 2.220446e-16 6 6 0 0 0.000000e+00 6 5 1 0 2.220446e-16 6 4 2 0 4.440892e-16 6 3 3 0 2.220446e-16 6 2 4 0 0.000000e+00 6 1 5 0 0.000000e+00 6 0 6 0 3.330669e-16 6 5 0 1 2.220446e-16 6 4 1 1 3.330669e-16 6 3 2 1 2.220446e-16 6 2 3 1 4.440892e-16 6 1 4 1 3.330669e-16 6 0 5 1 6.661338e-16 6 4 0 2 2.220446e-16 6 3 1 2 3.330669e-16 6 2 2 2 2.220446e-16 6 1 3 2 2.220446e-16 6 0 4 2 4.440892e-16 6 3 0 3 2.220446e-16 6 2 1 3 3.330669e-16 6 1 2 3 1.110223e-16 6 0 3 3 2.220446e-16 6 2 0 4 4.440892e-16 6 1 1 4 2.220446e-16 6 0 2 4 2.220446e-16 6 1 0 5 3.330669e-16 6 0 1 5 4.440892e-16 6 0 0 6 0.000000e+00 7 7 0 0 4.440892e-16 7 6 1 0 0.000000e+00 7 5 2 0 2.220446e-16 7 4 3 0 2.220446e-16 7 3 4 0 0.000000e+00 7 2 5 0 0.000000e+00 7 1 6 0 4.440892e-16 7 0 7 0 0.000000e+00 7 6 0 1 2.220446e-16 7 5 1 1 4.440892e-16 7 4 2 1 4.440892e-16 7 3 3 1 2.220446e-16 7 2 4 1 2.220446e-16 7 1 5 1 0.000000e+00 7 0 6 1 1.110223e-16 7 5 0 2 4.440892e-16 7 4 1 2 0.000000e+00 7 3 2 2 1.110223e-16 7 2 3 2 2.220446e-16 7 1 4 2 2.220446e-16 7 0 5 2 2.220446e-16 7 4 0 3 3.330669e-16 7 3 1 3 1.110223e-16 7 2 2 3 4.440892e-16 7 1 3 3 0.000000e+00 7 0 4 3 2.220446e-16 7 3 0 4 2.220446e-16 7 2 1 4 2.220446e-16 7 1 2 4 5.551115e-16 7 0 3 4 2.220446e-16 7 2 0 5 2.220446e-16 7 1 1 5 0.000000e+00 7 0 2 5 0.000000e+00 7 1 0 6 4.440892e-16 7 0 1 6 0.000000e+00 7 0 0 7 2.220446e-16 8 8 0 0 2.220446e-16 8 7 1 0 0.000000e+00 8 6 2 0 2.220446e-16 8 5 3 0 3.330669e-16 8 4 4 0 3.330669e-16 8 3 5 0 2.220446e-16 8 2 6 0 0.000000e+00 8 1 7 0 2.220446e-16 8 0 8 0 2.220446e-16 8 7 0 1 0.000000e+00 8 6 1 1 2.220446e-16 8 5 2 1 2.220446e-16 8 4 3 1 2.220446e-16 8 3 4 1 1.110223e-16 8 2 5 1 0.000000e+00 8 1 6 1 4.440892e-16 8 0 7 1 0.000000e+00 8 6 0 2 2.220446e-16 8 5 1 2 3.330669e-16 8 4 2 2 0.000000e+00 8 3 3 2 1.110223e-16 8 2 4 2 2.220446e-16 8 1 5 2 2.220446e-16 8 0 6 2 2.220446e-16 8 5 0 3 0.000000e+00 8 4 1 3 2.220446e-16 8 3 2 3 0.000000e+00 8 2 3 3 1.110223e-16 8 1 4 3 2.220446e-16 8 0 5 3 2.220446e-16 8 4 0 4 2.220446e-16 8 3 1 4 1.110223e-16 8 2 2 4 0.000000e+00 8 1 3 4 2.220446e-16 8 0 4 4 0.000000e+00 8 3 0 5 0.000000e+00 8 2 1 5 0.000000e+00 8 1 2 5 0.000000e+00 8 0 3 5 4.440892e-16 8 2 0 6 0.000000e+00 8 1 1 6 0.000000e+00 8 0 2 6 0.000000e+00 8 1 0 7 2.220446e-16 8 0 1 7 2.220446e-16 8 0 0 8 sparse_grid_gl_test06: SPARSE_GRID_GL makes 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_test(): Normal end of execution. 17-Jan-2023 06:01:02