15 January 2010 01:54:24 PM SPARSE_GRID_OPEN_PRB C++ version Test the routines in the SPARSE_GRID_OPEN library. TEST01 SPARSE_GRID_OFN_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from open fully nested quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is complete nesting, that is, a sparse grid of a given level includes ALL the points on grids of lower levels. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 7 17 31 49 71 3 15 49 111 209 351 4 31 129 351 769 1471 5 63 321 1023 2561 5503 6 127 769 2815 7937 18943 7 255 1793 7423 23297 61183 8 511 4097 18943 65537 187903 9 1023 9217 47103 178177 553983 10 2047 20481 114687 471041 1579007 TEST01 SPARSE_GRID_OFN_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from open fully nested quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is complete nesting, that is, a sparse grid of a given level includes ALL the points on grids of lower levels. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 545 799 1121 1519 2001 4 2561 4159 6401 9439 13441 5 10625 18943 31745 50623 77505 6 40193 78079 141569 242815 397825 7 141569 297727 580865 1066495 1862145 8 471041 1066495 2228225 4361215 8085505 9 1496065 3629055 8085505 16807935 32978945 10 4571137 11829247 28000257 61616127 127574017 TEST011 SPARSE_GRID_ONN_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from open non nested quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is no nesting. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 7 10 13 16 2 5 25 52 87 131 3 7 63 189 403 736 4 9 129 543 1461 3206 5 11 231 1320 4433 11583 6 13 377 2834 11739 36218 7 15 575 5531 27911 100893 8 17 833 10013 60809 255663 9 19 1159 17062 123253 598538 10 21 1561 27664 235135 1310165 TEST011 SPARSE_GRID_ONN_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from open non nested quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is no nesting. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 19 22 25 28 31 2 184 246 317 397 486 3 1216 1870 2725 3808 5146 4 6190 10900 17903 27847 41461 5 25954 52074 96055 165844 271467 6 93535 212738 439019 838915 1506232 7 298357 765313 1760035 3711040 7290952 8 860455 2476883 6323269 14666470 31453182 9 2279829 7329934 20693565 52638759 122920642 10 5618754 20087574 62483217 173788146 440815035 TEST012 SPARSE_GRID_OWN_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from open weakly nested quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is weak nesting, that is, 0.0 is the only point any two rules have in common. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 5 17 31 49 71 3 7 45 105 201 341 4 9 97 297 681 1341 5 11 181 735 2001 4543 6 13 305 1631 5257 13683 7 15 477 3305 12609 37433 8 17 705 6209 28017 94473 9 19 997 10951 58297 222563 10 21 1361 18319 114561 493935 TEST012 SPARSE_GRID_OWN_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from open weakly nested quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is weak nesting, that is, 0.0 is the only point any two rules have in common. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 533 785 1105 1501 1981 4 2381 3921 6097 9061 12981 5 9113 16703 28577 46303 71785 6 30869 62735 117713 207355 347005 7 94601 212481 436033 833017 1501545 8 266489 659585 1476673 3053065 5916505 9 698373 1899663 4629457 10338603 21503085 10 1718697 5124927 13566753 32667567 72810297 TEST013 SPARSE_GRID_F2S_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from Fejer Type 2 Slow quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is complete nesting, that is, a sparse grid of a given level includes ALL the points on grids of lower levels. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 7 17 31 49 71 3 7 33 87 177 311 4 15 65 207 513 1071 5 15 97 399 1217 3023 6 15 161 751 2625 7503 7 15 161 1135 4929 16463 8 31 257 1759 8705 33183 9 31 321 2335 13697 60703 10 31 449 3679 21889 105887 TEST013 SPARSE_GRID_F2S_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from Fejer Type 2 Slow quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is complete nesting, that is, a sparse grid of a given level includes ALL the points on grids of lower levels. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 97 127 161 199 241 3 497 743 1057 1447 1921 4 1985 3375 5377 8143 11841 5 6497 12559 22401 37519 59745 6 18401 40111 79745 147343 256545 7 46049 112815 249217 506767 963105 8 104705 286303 699393 1559839 3227905 9 217281 663071 1787649 4362783 9809985 10 421185 1423327 4217601 11231007 27377857 TEST015 SPARSE_GRID_GPS_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from Gauss-Patterson-Slow quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is complete nesting, that is, a sparse grid of a given level includes ALL the points on grids of lower levels. DIM: 1 2 3 4 5 LEVEL_MAX 0 1 1 1 1 1 1 3 5 7 9 11 2 3 9 19 33 51 3 7 17 39 81 151 4 7 33 87 193 391 5 7 33 135 385 903 6 15 65 207 641 1743 7 15 97 399 1217 3343 8 15 97 495 1985 6223 9 15 161 751 2881 10063 10 15 161 1135 4929 17103 TEST015 SPARSE_GRID_GPS_SIZE returns the number of distinct points in a sparse grid made up of all product grids formed from Gauss-Patterson-Slow quadrature rules. The sparse grid is the sum of all product grids of order LEVEL, with 0 <= LEVEL <= LEVEL_MAX. LEVEL is the sum of the levels of the 1D rules, the order of the 1D rule is 2^(LEVEL+1) - 1, the region is [-1,1]^DIM_NUM. For this kind of rule, there is complete nesting, that is, a sparse grid of a given level includes ALL the points on grids of lower levels. DIM: 6 7 8 9 10 LEVEL_MAX 0 1 1 1 1 1 1 13 15 17 19 21 2 73 99 129 163 201 3 257 407 609 871 1201 4 737 1303 2177 3463 5281 5 1889 3655 6657 11527 19105 6 4161 8975 17921 33679 60225 7 8481 19855 43137 87823 169185 8 16929 42031 97153 211087 434145 9 30689 83247 206465 477327 1041185 10 53729 154927 411265 1014159 2347809 TEST02: LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. LEVEL_MAX = 2 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 17 Grid index: 0 4 4 1 2 4 2 6 4 3 4 2 4 4 6 5 1 4 6 3 4 7 5 4 8 7 4 9 2 2 10 6 2 11 2 6 12 6 6 13 4 1 14 4 3 15 4 5 16 4 7 TEST02: LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 49 Grid index: 0 8 8 1 4 8 2 12 8 3 8 4 4 8 12 5 2 8 6 6 8 7 10 8 8 14 8 9 4 4 10 12 4 11 4 12 12 12 12 13 8 2 14 8 6 15 8 10 16 8 14 17 1 8 18 3 8 19 5 8 20 7 8 21 9 8 22 11 8 23 13 8 24 15 8 25 2 4 26 6 4 27 10 4 28 14 4 29 2 12 30 6 12 31 10 12 32 14 12 33 4 2 34 12 2 35 4 6 36 12 6 37 4 10 38 12 10 39 4 14 40 12 14 41 8 1 42 8 3 43 8 5 44 8 7 45 8 9 46 8 11 47 8 13 48 8 15 TEST02: LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 129 Grid index: 0 16 16 1 8 16 2 24 16 3 16 8 4 16 24 5 4 16 6 12 16 7 20 16 8 28 16 9 8 8 10 24 8 11 8 24 12 24 24 13 16 4 14 16 12 15 16 20 16 16 28 17 2 16 18 6 16 19 10 16 20 14 16 21 18 16 22 22 16 23 26 16 24 30 16 25 4 8 26 12 8 27 20 8 28 28 8 29 4 24 30 12 24 31 20 24 32 28 24 33 8 4 34 24 4 35 8 12 36 24 12 37 8 20 38 24 20 39 8 28 40 24 28 41 16 2 42 16 6 43 16 10 44 16 14 45 16 18 46 16 22 47 16 26 48 16 30 49 1 16 50 3 16 51 5 16 52 7 16 53 9 16 54 11 16 55 13 16 56 15 16 57 17 16 58 19 16 59 21 16 60 23 16 61 25 16 62 27 16 63 29 16 64 31 16 65 2 8 66 6 8 67 10 8 68 14 8 69 18 8 70 22 8 71 26 8 72 30 8 73 2 24 74 6 24 75 10 24 76 14 24 77 18 24 78 22 24 79 26 24 80 30 24 81 4 4 82 12 4 83 20 4 84 28 4 85 4 12 86 12 12 87 20 12 88 28 12 89 4 20 90 12 20 91 20 20 92 28 20 93 4 28 94 12 28 95 20 28 96 28 28 97 8 2 98 24 2 99 8 6 100 24 6 101 8 10 102 24 10 103 8 14 104 24 14 105 8 18 106 24 18 107 8 22 108 24 22 109 8 26 110 24 26 111 8 30 112 24 30 113 16 1 114 16 3 115 16 5 116 16 7 117 16 9 118 16 11 119 16 13 120 16 15 121 16 17 122 16 19 123 16 21 124 16 23 125 16 25 126 16 27 127 16 29 128 16 31 TEST02: LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. LEVEL_MAX = 2 Spatial dimension DIM_NUM = 3 Number of unique points in the grid = 31 Grid index: 0 4 4 4 1 2 4 4 2 6 4 4 3 4 2 4 4 4 6 4 5 4 4 2 6 4 4 6 7 1 4 4 8 3 4 4 9 5 4 4 10 7 4 4 11 2 2 4 12 6 2 4 13 2 6 4 14 6 6 4 15 4 1 4 16 4 3 4 17 4 5 4 18 4 7 4 19 2 4 2 20 6 4 2 21 2 4 6 22 6 4 6 23 4 2 2 24 4 6 2 25 4 2 6 26 4 6 6 27 4 4 1 28 4 4 3 29 4 4 5 30 4 4 7 TEST02: LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. LEVEL_MAX = 2 Spatial dimension DIM_NUM = 6 Number of unique points in the grid = 97 Grid index: 0 4 4 4 4 4 4 1 2 4 4 4 4 4 2 6 4 4 4 4 4 3 4 2 4 4 4 4 4 4 6 4 4 4 4 5 4 4 2 4 4 4 6 4 4 6 4 4 4 7 4 4 4 2 4 4 8 4 4 4 6 4 4 9 4 4 4 4 2 4 10 4 4 4 4 6 4 11 4 4 4 4 4 2 12 4 4 4 4 4 6 13 1 4 4 4 4 4 14 3 4 4 4 4 4 15 5 4 4 4 4 4 16 7 4 4 4 4 4 17 2 2 4 4 4 4 18 6 2 4 4 4 4 19 2 6 4 4 4 4 20 6 6 4 4 4 4 21 4 1 4 4 4 4 22 4 3 4 4 4 4 23 4 5 4 4 4 4 24 4 7 4 4 4 4 25 2 4 2 4 4 4 26 6 4 2 4 4 4 27 2 4 6 4 4 4 28 6 4 6 4 4 4 29 4 2 2 4 4 4 30 4 6 2 4 4 4 31 4 2 6 4 4 4 32 4 6 6 4 4 4 33 4 4 1 4 4 4 34 4 4 3 4 4 4 35 4 4 5 4 4 4 36 4 4 7 4 4 4 37 2 4 4 2 4 4 38 6 4 4 2 4 4 39 2 4 4 6 4 4 40 6 4 4 6 4 4 41 4 2 4 2 4 4 42 4 6 4 2 4 4 43 4 2 4 6 4 4 44 4 6 4 6 4 4 45 4 4 2 2 4 4 46 4 4 6 2 4 4 47 4 4 2 6 4 4 48 4 4 6 6 4 4 49 4 4 4 1 4 4 50 4 4 4 3 4 4 51 4 4 4 5 4 4 52 4 4 4 7 4 4 53 2 4 4 4 2 4 54 6 4 4 4 2 4 55 2 4 4 4 6 4 56 6 4 4 4 6 4 57 4 2 4 4 2 4 58 4 6 4 4 2 4 59 4 2 4 4 6 4 60 4 6 4 4 6 4 61 4 4 2 4 2 4 62 4 4 6 4 2 4 63 4 4 2 4 6 4 64 4 4 6 4 6 4 65 4 4 4 2 2 4 66 4 4 4 6 2 4 67 4 4 4 2 6 4 68 4 4 4 6 6 4 69 4 4 4 4 1 4 70 4 4 4 4 3 4 71 4 4 4 4 5 4 72 4 4 4 4 7 4 73 2 4 4 4 4 2 74 6 4 4 4 4 2 75 2 4 4 4 4 6 76 6 4 4 4 4 6 77 4 2 4 4 4 2 78 4 6 4 4 4 2 79 4 2 4 4 4 6 80 4 6 4 4 4 6 81 4 4 2 4 4 2 82 4 4 6 4 4 2 83 4 4 2 4 4 6 84 4 4 6 4 4 6 85 4 4 4 2 4 2 86 4 4 4 6 4 2 87 4 4 4 2 4 6 88 4 4 4 6 4 6 89 4 4 4 4 2 2 90 4 4 4 4 6 2 91 4 4 4 4 2 6 92 4 4 4 4 6 6 93 4 4 4 4 4 1 94 4 4 4 4 4 3 95 4 4 4 4 4 5 96 4 4 4 4 4 7 TEST04: Make a sparse Fejer Type 2 grid. LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. Now we demonstrate how to convert grid indices into physical grid points. In this case, we want points on [-1,+1]^DIM_NUM. LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 49 Grid index: 0 8 8 1 4 8 2 12 8 3 8 4 4 8 12 5 2 8 6 6 8 7 10 8 8 14 8 9 4 4 10 12 4 11 4 12 12 12 12 13 8 2 14 8 6 15 8 10 16 8 14 17 1 8 18 3 8 19 5 8 20 7 8 21 9 8 22 11 8 23 13 8 24 15 8 25 2 4 26 6 4 27 10 4 28 14 4 29 2 12 30 6 12 31 10 12 32 14 12 33 4 2 34 12 2 35 4 6 36 12 6 37 4 10 38 12 10 39 4 14 40 12 14 41 8 1 42 8 3 43 8 5 44 8 7 45 8 9 46 8 11 47 8 13 48 8 15 Grid points: 0 6.12323e-17 6.12323e-17 1 -0.707107 6.12323e-17 2 0.707107 6.12323e-17 3 6.12323e-17 -0.707107 4 6.12323e-17 0.707107 5 -0.92388 6.12323e-17 6 -0.382683 6.12323e-17 7 0.382683 6.12323e-17 8 0.92388 6.12323e-17 9 -0.707107 -0.707107 10 0.707107 -0.707107 11 -0.707107 0.707107 12 0.707107 0.707107 13 6.12323e-17 -0.92388 14 6.12323e-17 -0.382683 15 6.12323e-17 0.382683 16 6.12323e-17 0.92388 17 -0.980785 6.12323e-17 18 -0.83147 6.12323e-17 19 -0.55557 6.12323e-17 20 -0.19509 6.12323e-17 21 0.19509 6.12323e-17 22 0.55557 6.12323e-17 23 0.83147 6.12323e-17 24 0.980785 6.12323e-17 25 -0.92388 -0.707107 26 -0.382683 -0.707107 27 0.382683 -0.707107 28 0.92388 -0.707107 29 -0.92388 0.707107 30 -0.382683 0.707107 31 0.382683 0.707107 32 0.92388 0.707107 33 -0.707107 -0.92388 34 0.707107 -0.92388 35 -0.707107 -0.382683 36 0.707107 -0.382683 37 -0.707107 0.382683 38 0.707107 0.382683 39 -0.707107 0.92388 40 0.707107 0.92388 41 6.12323e-17 -0.980785 42 6.12323e-17 -0.83147 43 6.12323e-17 -0.55557 44 6.12323e-17 -0.19509 45 6.12323e-17 0.19509 46 6.12323e-17 0.55557 47 6.12323e-17 0.83147 48 6.12323e-17 0.980785 TEST05: Make a sparse Gauss Patterson grid. LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. Now we demonstrate how to convert grid indices into physical grid points. In this case, we want points on [-1,+1]^DIM_NUM. LEVEL_MAX = 3 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 49 Grid index: 0 8 8 1 4 8 2 12 8 3 8 4 4 8 12 5 2 8 6 6 8 7 10 8 8 14 8 9 4 4 10 12 4 11 4 12 12 12 12 13 8 2 14 8 6 15 8 10 16 8 14 17 1 8 18 3 8 19 5 8 20 7 8 21 9 8 22 11 8 23 13 8 24 15 8 25 2 4 26 6 4 27 10 4 28 14 4 29 2 12 30 6 12 31 10 12 32 14 12 33 4 2 34 12 2 35 4 6 36 12 6 37 4 10 38 12 10 39 4 14 40 12 14 41 8 1 42 8 3 43 8 5 44 8 7 45 8 9 46 8 11 47 8 13 48 8 15 Grid points: 0 0 0 1 -0.774597 0 2 0.774597 0 3 0 -0.774597 4 0 0.774597 5 -0.960491 0 6 -0.434244 0 7 0.434244 0 8 0.960491 0 9 -0.774597 -0.774597 10 0.774597 -0.774597 11 -0.774597 0.774597 12 0.774597 0.774597 13 0 -0.960491 14 0 -0.434244 15 0 0.434244 16 0 0.960491 17 -0.993832 0 18 -0.888459 0 19 -0.621103 0 20 -0.223387 0 21 0.223387 0 22 0.621103 0 23 0.888459 0 24 0.993832 0 25 -0.960491 -0.774597 26 -0.434244 -0.774597 27 0.434244 -0.774597 28 0.960491 -0.774597 29 -0.960491 0.774597 30 -0.434244 0.774597 31 0.434244 0.774597 32 0.960491 0.774597 33 -0.774597 -0.960491 34 0.774597 -0.960491 35 -0.774597 -0.434244 36 0.774597 -0.434244 37 -0.774597 0.434244 38 0.774597 0.434244 39 -0.774597 0.960491 40 0.774597 0.960491 41 0 -0.993832 42 0 -0.888459 43 0 -0.621103 44 0 -0.223387 45 0 0.223387 46 0 0.621103 47 0 0.888459 48 0 0.993832 TEST06: Make a sparse Newton Cotes Open grid. LEVELS_OPEN_INDEX returns all grid indexes whose level value satisfies 0 <= LEVEL <= LEVEL_MAX. Here, LEVEL is the sum of the levels of the 1D rules, and the order of the rule is 2^(LEVEL+1) - 1. Now we demonstrate how to convert grid indices into physical grid points. In this case, we want points on [0,+1]^DIM_NUM. LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 129 Grid index: 0 16 16 1 8 16 2 24 16 3 16 8 4 16 24 5 4 16 6 12 16 7 20 16 8 28 16 9 8 8 10 24 8 11 8 24 12 24 24 13 16 4 14 16 12 15 16 20 16 16 28 17 2 16 18 6 16 19 10 16 20 14 16 21 18 16 22 22 16 23 26 16 24 30 16 25 4 8 26 12 8 27 20 8 28 28 8 29 4 24 30 12 24 31 20 24 32 28 24 33 8 4 34 24 4 35 8 12 36 24 12 37 8 20 38 24 20 39 8 28 40 24 28 41 16 2 42 16 6 43 16 10 44 16 14 45 16 18 46 16 22 47 16 26 48 16 30 49 1 16 50 3 16 51 5 16 52 7 16 53 9 16 54 11 16 55 13 16 56 15 16 57 17 16 58 19 16 59 21 16 60 23 16 61 25 16 62 27 16 63 29 16 64 31 16 65 2 8 66 6 8 67 10 8 68 14 8 69 18 8 70 22 8 71 26 8 72 30 8 73 2 24 74 6 24 75 10 24 76 14 24 77 18 24 78 22 24 79 26 24 80 30 24 81 4 4 82 12 4 83 20 4 84 28 4 85 4 12 86 12 12 87 20 12 88 28 12 89 4 20 90 12 20 91 20 20 92 28 20 93 4 28 94 12 28 95 20 28 96 28 28 97 8 2 98 24 2 99 8 6 100 24 6 101 8 10 102 24 10 103 8 14 104 24 14 105 8 18 106 24 18 107 8 22 108 24 22 109 8 26 110 24 26 111 8 30 112 24 30 113 16 1 114 16 3 115 16 5 116 16 7 117 16 9 118 16 11 119 16 13 120 16 15 121 16 17 122 16 19 123 16 21 124 16 23 125 16 25 126 16 27 127 16 29 128 16 31 Grid points: 0 0 0 1 -0.5 0 2 0.5 0 3 0 -0.5 4 0 0.5 5 -0.75 0 6 -0.25 0 7 0.25 0 8 0.75 0 9 -0.5 -0.5 10 0.5 -0.5 11 -0.5 0.5 12 0.5 0.5 13 0 -0.75 14 0 -0.25 15 0 0.25 16 0 0.75 17 -0.875 0 18 -0.625 0 19 -0.375 0 20 -0.125 0 21 0.125 0 22 0.375 0 23 0.625 0 24 0.875 0 25 -0.75 -0.5 26 -0.25 -0.5 27 0.25 -0.5 28 0.75 -0.5 29 -0.75 0.5 30 -0.25 0.5 31 0.25 0.5 32 0.75 0.5 33 -0.5 -0.75 34 0.5 -0.75 35 -0.5 -0.25 36 0.5 -0.25 37 -0.5 0.25 38 0.5 0.25 39 -0.5 0.75 40 0.5 0.75 41 0 -0.875 42 0 -0.625 43 0 -0.375 44 0 -0.125 45 0 0.125 46 0 0.375 47 0 0.625 48 0 0.875 49 -0.9375 0 50 -0.8125 0 51 -0.6875 0 52 -0.5625 0 53 -0.4375 0 54 -0.3125 0 55 -0.1875 0 56 -0.0625 0 57 0.0625 0 58 0.1875 0 59 0.3125 0 60 0.4375 0 61 0.5625 0 62 0.6875 0 63 0.8125 0 64 0.9375 0 65 -0.875 -0.5 66 -0.625 -0.5 67 -0.375 -0.5 68 -0.125 -0.5 69 0.125 -0.5 70 0.375 -0.5 71 0.625 -0.5 72 0.875 -0.5 73 -0.875 0.5 74 -0.625 0.5 75 -0.375 0.5 76 -0.125 0.5 77 0.125 0.5 78 0.375 0.5 79 0.625 0.5 80 0.875 0.5 81 -0.75 -0.75 82 -0.25 -0.75 83 0.25 -0.75 84 0.75 -0.75 85 -0.75 -0.25 86 -0.25 -0.25 87 0.25 -0.25 88 0.75 -0.25 89 -0.75 0.25 90 -0.25 0.25 91 0.25 0.25 92 0.75 0.25 93 -0.75 0.75 94 -0.25 0.75 95 0.25 0.75 96 0.75 0.75 97 -0.5 -0.875 98 0.5 -0.875 99 -0.5 -0.625 100 0.5 -0.625 101 -0.5 -0.375 102 0.5 -0.375 103 -0.5 -0.125 104 0.5 -0.125 105 -0.5 0.125 106 0.5 0.125 107 -0.5 0.375 108 0.5 0.375 109 -0.5 0.625 110 0.5 0.625 111 -0.5 0.875 112 0.5 0.875 113 0 -0.9375 114 0 -0.8125 115 0 -0.6875 116 0 -0.5625 117 0 -0.4375 118 0 -0.3125 119 0 -0.1875 120 0 -0.0625 121 0 0.0625 122 0 0.1875 123 0 0.3125 124 0 0.4375 125 0 0.5625 126 0 0.6875 127 0 0.8125 128 0 0.9375 TEST08: Make sparse grids and write to files. LEVEL_MAX = 4 Spatial dimension DIM_NUM = 2 Number of unique points in the grid = 129 Grid index: 0 16 16 1 8 16 2 24 16 3 16 8 4 16 24 5 4 16 6 12 16 7 20 16 8 28 16 9 8 8 10 24 8 11 8 24 12 24 24 13 16 4 14 16 12 15 16 20 16 16 28 17 2 16 18 6 16 19 10 16 20 14 16 21 18 16 22 22 16 23 26 16 24 30 16 25 4 8 26 12 8 27 20 8 28 28 8 29 4 24 30 12 24 31 20 24 32 28 24 33 8 4 34 24 4 35 8 12 36 24 12 37 8 20 38 24 20 39 8 28 40 24 28 41 16 2 42 16 6 43 16 10 44 16 14 45 16 18 46 16 22 47 16 26 48 16 30 49 1 16 50 3 16 51 5 16 52 7 16 53 9 16 54 11 16 55 13 16 56 15 16 57 17 16 58 19 16 59 21 16 60 23 16 61 25 16 62 27 16 63 29 16 64 31 16 65 2 8 66 6 8 67 10 8 68 14 8 69 18 8 70 22 8 71 26 8 72 30 8 73 2 24 74 6 24 75 10 24 76 14 24 77 18 24 78 22 24 79 26 24 80 30 24 81 4 4 82 12 4 83 20 4 84 28 4 85 4 12 86 12 12 87 20 12 88 28 12 89 4 20 90 12 20 91 20 20 92 28 20 93 4 28 94 12 28 95 20 28 96 28 28 97 8 2 98 24 2 99 8 6 100 24 6 101 8 10 102 24 10 103 8 14 104 24 14 105 8 18 106 24 18 107 8 22 108 24 22 109 8 26 110 24 26 111 8 30 112 24 30 113 16 1 114 16 3 115 16 5 116 16 7 117 16 9 118 16 11 119 16 13 120 16 15 121 16 17 122 16 19 123 16 21 124 16 23 125 16 25 126 16 27 127 16 29 128 16 31 Wrote file "f2_d2_level4.txt". Wrote file "gp_d2_level4.txt". Wrote file "nco_d2_level4.txt". SPARSE_GRID_OPEN_PRB Normal end of execution. 15 January 2010 01:54:25 PM