>> cvt_test 15-Sep-2010 16:45:58 CVT_TEST MATLAB version Test the CVT library. TEST01 CVT computes a Centroidal Voronoi Tessellation. Step SEED L2-Change Energy 0 123456789 1 29242052 8.940030e-01 3.419919e-02 2 396524255 2.824564e-01 2.276680e-02 3 1804077568 2.161568e-01 2.085658e-02 4 58279807 1.477493e-01 1.944282e-02 5 890554932 1.283413e-01 1.897176e-02 6 214536894 8.960171e-02 1.859560e-02 7 1592773222 1.102347e-01 1.856606e-02 8 1874550474 9.236769e-02 1.809569e-02 9 2041615702 8.441385e-02 1.808610e-02 10 2056573688 8.941519e-02 1.799344e-02 11 1522461057 7.935737e-02 1.749078e-02 12 1338654111 7.809860e-02 1.765559e-02 13 758290347 7.983841e-02 1.748531e-02 14 1895558656 7.256098e-02 1.755883e-02 15 553115540 6.471175e-02 1.704020e-02 16 1150573110 6.936469e-02 1.735544e-02 17 1130930562 6.793165e-02 1.723610e-02 18 1398936087 6.767943e-02 1.716154e-02 19 1351174075 5.539154e-02 1.701183e-02 20 1271270653 4.531095e-02 1.730400e-02 21 383674773 5.249361e-02 1.718908e-02 22 533903734 4.559622e-02 1.732207e-02 23 412527942 5.393337e-02 1.691134e-02 24 498761874 5.427016e-02 1.708939e-02 25 1767322623 5.896687e-02 1.723658e-02 26 8802113 4.038236e-02 1.714110e-02 27 337656644 3.540781e-02 1.698687e-02 28 982491412 4.621968e-02 1.706182e-02 29 1661195312 4.106082e-02 1.710234e-02 30 1727223671 3.703044e-02 1.700439e-02 31 1934076831 4.225577e-02 1.715442e-02 32 286968437 5.523915e-02 1.705179e-02 33 1651892980 3.350856e-02 1.735319e-02 34 1093660108 4.375073e-02 1.724619e-02 35 1312296485 4.994957e-02 1.708435e-02 36 1505118054 4.485278e-02 1.728073e-02 37 1225827697 4.655303e-02 1.731938e-02 38 2103031061 4.545167e-02 1.702508e-02 39 237994259 4.522406e-02 1.706157e-02 40 308344071 4.859585e-02 1.719588e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 878651545 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.048596 CVT ENERGY = 0.017196 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.177221 0.881571 2 0.837556 0.827059 3 0.515287 0.501840 4 0.507924 0.167342 5 0.179980 0.630281 6 0.175928 0.375518 7 0.512095 0.837544 8 0.830500 0.167848 9 0.832437 0.495910 10 0.168871 0.121883 TEST02 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with twice the number of iterations. Step SEED L2-Change Energy 0 123456789 1 29242052 8.940030e-01 3.419919e-02 2 396524255 2.824564e-01 2.276680e-02 3 1804077568 2.161568e-01 2.085658e-02 4 58279807 1.477493e-01 1.944282e-02 5 890554932 1.283413e-01 1.897176e-02 6 214536894 8.960171e-02 1.859560e-02 7 1592773222 1.102347e-01 1.856606e-02 8 1874550474 9.236769e-02 1.809569e-02 9 2041615702 8.441385e-02 1.808610e-02 10 2056573688 8.941519e-02 1.799344e-02 11 1522461057 7.935737e-02 1.749078e-02 12 1338654111 7.809860e-02 1.765559e-02 13 758290347 7.983841e-02 1.748531e-02 14 1895558656 7.256098e-02 1.755883e-02 15 553115540 6.471175e-02 1.704020e-02 16 1150573110 6.936469e-02 1.735544e-02 17 1130930562 6.793165e-02 1.723610e-02 18 1398936087 6.767943e-02 1.716154e-02 19 1351174075 5.539154e-02 1.701183e-02 20 1271270653 4.531095e-02 1.730400e-02 21 383674773 5.249361e-02 1.718908e-02 22 533903734 4.559622e-02 1.732207e-02 23 412527942 5.393337e-02 1.691134e-02 24 498761874 5.427016e-02 1.708939e-02 25 1767322623 5.896687e-02 1.723658e-02 26 8802113 4.038236e-02 1.714110e-02 27 337656644 3.540781e-02 1.698687e-02 28 982491412 4.621968e-02 1.706182e-02 29 1661195312 4.106082e-02 1.710234e-02 30 1727223671 3.703044e-02 1.700439e-02 31 1934076831 4.225577e-02 1.715442e-02 32 286968437 5.523915e-02 1.705179e-02 33 1651892980 3.350856e-02 1.735319e-02 34 1093660108 4.375073e-02 1.724619e-02 35 1312296485 4.994957e-02 1.708435e-02 36 1505118054 4.485278e-02 1.728073e-02 37 1225827697 4.655303e-02 1.731938e-02 38 2103031061 4.545167e-02 1.702508e-02 39 237994259 4.522406e-02 1.706157e-02 40 308344071 4.859585e-02 1.719588e-02 41 878651545 3.844885e-02 1.695578e-02 42 336554041 4.468017e-02 1.697407e-02 43 69693939 4.060311e-02 1.723996e-02 44 107597223 4.553827e-02 1.705553e-02 45 284388055 4.572381e-02 1.703035e-02 46 821532605 3.424931e-02 1.702883e-02 47 1912444717 4.307396e-02 1.686906e-02 48 2139238658 6.195016e-02 1.710381e-02 49 1514249906 4.436381e-02 1.724285e-02 50 765384573 4.729302e-02 1.716729e-02 51 599511796 4.764413e-02 1.704197e-02 52 1929718247 5.285149e-02 1.698549e-02 53 1495267469 5.833490e-02 1.716230e-02 54 346287018 3.520815e-02 1.714239e-02 55 972591208 4.014540e-02 1.729200e-02 56 1170908305 3.406724e-02 1.692684e-02 57 2101087755 4.640373e-02 1.694084e-02 58 1585775448 4.353077e-02 1.698973e-02 59 1719007417 4.996372e-02 1.717167e-02 60 47014704 3.399011e-02 1.691075e-02 61 325311895 4.891706e-02 1.726361e-02 62 2114713435 4.210414e-02 1.694687e-02 63 469955390 4.263634e-02 1.727774e-02 64 2044044375 4.262928e-02 1.691800e-02 65 1902665122 4.286735e-02 1.710209e-02 66 999386148 4.877387e-02 1.708765e-02 67 1762727540 4.407321e-02 1.687130e-02 68 886787757 4.126693e-02 1.687553e-02 69 1442441010 4.463893e-02 1.705500e-02 70 766630007 4.516911e-02 1.698350e-02 71 473489672 2.847137e-02 1.706662e-02 72 1247561645 2.183333e-02 1.720890e-02 73 1093781229 4.481614e-02 1.716669e-02 74 1723735430 4.187755e-02 1.694455e-02 75 1100723884 5.382599e-02 1.702761e-02 76 2145312587 4.457394e-02 1.697304e-02 77 1556984304 3.822007e-02 1.706768e-02 78 1035291506 3.793730e-02 1.689759e-02 79 158213521 4.307693e-02 1.717601e-02 80 1863192335 4.090684e-02 1.705547e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 343175222 INIT = "uniform". Max iterations IT_MAX = 80 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 80 Difference IT_DIFF = 0.040907 CVT ENERGY = 0.017055 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.165613 0.881070 2 0.839858 0.824262 3 0.517269 0.510056 4 0.512253 0.168433 5 0.182060 0.631697 6 0.183971 0.377948 7 0.510910 0.847692 8 0.834976 0.161121 9 0.838384 0.491932 10 0.161762 0.123829 TEST03 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with 100 times the sample points. Step SEED L2-Change Energy 0 123456789 1 29242052 8.913408e-01 3.427722e-02 2 720688506 2.899146e-01 2.282247e-02 3 681172 1.966161e-01 2.066091e-02 4 539098006 1.483810e-01 1.959439e-02 5 1544551628 1.158508e-01 1.907183e-02 6 1039137261 9.553126e-02 1.872795e-02 7 1856120581 8.479768e-02 1.849771e-02 8 1398888834 8.138543e-02 1.825954e-02 9 777275849 7.677487e-02 1.806973e-02 10 193908656 6.807580e-02 1.790546e-02 11 594766309 6.122291e-02 1.776560e-02 12 1528604881 5.485180e-02 1.761663e-02 13 2135424592 4.751630e-02 1.753671e-02 14 843278689 4.424457e-02 1.744323e-02 15 1298034490 3.953020e-02 1.741580e-02 16 1774985135 3.826706e-02 1.736084e-02 17 58892340 3.810730e-02 1.733416e-02 18 497310354 3.674388e-02 1.730645e-02 19 1555340604 3.692684e-02 1.724446e-02 20 573219264 3.494405e-02 1.721390e-02 21 769258892 3.424142e-02 1.716842e-02 22 1733894875 3.094262e-02 1.714554e-02 23 1708504563 3.016228e-02 1.711642e-02 24 332981687 2.322157e-02 1.710182e-02 25 871833470 1.929512e-02 1.708972e-02 26 491107991 1.656731e-02 1.707194e-02 27 64836647 1.345582e-02 1.707821e-02 28 954805664 1.228480e-02 1.706402e-02 29 1033236242 1.062872e-02 1.706546e-02 30 1875753496 8.639504e-03 1.706424e-02 31 932903206 7.300899e-03 1.707585e-02 32 900419333 8.076311e-03 1.706751e-02 33 898406847 6.742500e-03 1.706172e-02 34 957321340 5.520445e-03 1.705488e-02 35 1879036371 5.687185e-03 1.705364e-02 36 550745514 5.706912e-03 1.706150e-02 37 1822412817 4.147936e-03 1.706943e-02 38 1926341691 4.574800e-03 1.707544e-02 39 578466603 4.366183e-03 1.704648e-02 40 1767869167 4.876352e-03 1.705146e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 1282315487 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.004876 CVT ENERGY = 0.017051 SAMPLE = "uniform". Samples SAMPLE_NUM = 1000000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.168348 0.878131 2 0.835356 0.834497 3 0.522646 0.495763 4 0.504354 0.163497 5 0.182525 0.627963 6 0.181252 0.374070 7 0.507305 0.832846 8 0.833868 0.168015 9 0.843060 0.503669 10 0.166970 0.122596 TEST04 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with Halton sampling. Step SEED L2-Change Energy 0 123456789 1 29242052 8.912165e-01 3.430968e-02 2 29252052 2.888033e-01 2.282189e-02 3 29262052 1.974512e-01 2.062846e-02 4 29272052 1.476514e-01 1.963103e-02 5 29282052 1.148220e-01 1.907463e-02 6 29292052 9.127902e-02 1.874133e-02 7 29302052 8.814468e-02 1.849141e-02 8 29312052 8.344492e-02 1.828899e-02 9 29322052 7.647994e-02 1.808564e-02 10 29332052 6.948106e-02 1.789580e-02 11 29342052 6.306380e-02 1.774081e-02 12 29352052 5.847443e-02 1.762864e-02 13 29362052 4.677373e-02 1.753371e-02 14 29372052 4.396146e-02 1.747286e-02 15 29382052 3.813456e-02 1.740788e-02 16 29392052 3.616533e-02 1.736855e-02 17 29402052 3.381555e-02 1.733500e-02 18 29412052 3.476403e-02 1.731187e-02 19 29422052 3.702363e-02 1.726369e-02 20 29432052 3.328745e-02 1.723462e-02 21 29442052 3.385829e-02 1.719071e-02 22 29452052 3.460954e-02 1.717196e-02 23 29462052 2.921509e-02 1.713844e-02 24 29472052 2.497847e-02 1.710849e-02 25 29482052 2.358221e-02 1.710810e-02 26 29492052 2.082782e-02 1.708139e-02 27 29502052 1.632158e-02 1.708099e-02 28 29512052 1.476770e-02 1.707363e-02 29 29522052 9.591279e-03 1.707075e-02 30 29532052 9.655906e-03 1.707477e-02 31 29542052 1.030772e-02 1.706052e-02 32 29552052 9.225189e-03 1.706924e-02 33 29562052 8.555069e-03 1.706484e-02 34 29572052 4.625623e-03 1.706492e-02 35 29582052 7.783681e-03 1.705902e-02 36 29592052 8.045066e-03 1.706966e-02 37 29602052 5.328606e-03 1.706026e-02 38 29612052 7.622415e-03 1.706037e-02 39 29622052 6.566532e-03 1.706765e-02 40 29632052 6.010474e-03 1.706022e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 29642052 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.006010 CVT ENERGY = 0.017060 SAMPLE = "halton". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.168423 0.877673 2 0.834415 0.834500 3 0.523113 0.496708 4 0.504477 0.164092 5 0.181816 0.627303 6 0.181405 0.374130 7 0.506539 0.833295 8 0.833916 0.167607 9 0.843147 0.502631 10 0.167289 0.122778 TEST05 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with grid sampling. Step SEED L2-Change Energy 0 123456789 1 29242052 8.930608e-01 3.431461e-02 2 29252052 2.892032e-01 2.279972e-02 3 29262052 1.918026e-01 2.061519e-02 4 29272052 1.519455e-01 1.963421e-02 5 29282052 1.144193e-01 1.906037e-02 6 29292052 9.534331e-02 1.872229e-02 7 29302052 8.829268e-02 1.847698e-02 8 29312052 8.070677e-02 1.825203e-02 9 29322052 7.409990e-02 1.804674e-02 10 29332052 6.938704e-02 1.786818e-02 11 29342052 6.170323e-02 1.771854e-02 12 29352052 5.403396e-02 1.760233e-02 13 29362052 4.934897e-02 1.751475e-02 14 29372052 4.532478e-02 1.744495e-02 15 29382052 4.101362e-02 1.738793e-02 16 29392052 4.044914e-02 1.734228e-02 17 29402052 3.637345e-02 1.729942e-02 18 29412052 3.861727e-02 1.725911e-02 19 29422052 3.370598e-02 1.721950e-02 20 29432052 3.483218e-02 1.718451e-02 21 29442052 3.251232e-02 1.715196e-02 22 29452052 2.966154e-02 1.712444e-02 23 29462052 2.582977e-02 1.710406e-02 24 29472052 1.913016e-02 1.708930e-02 25 29482052 1.638868e-02 1.708010e-02 26 29492052 1.661196e-02 1.707340e-02 27 29502052 1.016219e-02 1.706805e-02 28 29512052 8.696092e-03 1.706600e-02 29 29522052 7.117985e-03 1.706440e-02 30 29532052 9.338862e-03 1.706308e-02 31 29542052 9.987398e-03 1.706103e-02 32 29552052 8.432421e-03 1.705865e-02 33 29562052 5.676761e-03 1.705701e-02 34 29572052 4.963830e-03 1.705621e-02 35 29582052 3.160306e-03 1.705559e-02 36 29592052 1.989504e-03 1.705537e-02 37 29602052 1.630449e-03 1.705527e-02 38 29612052 2.122019e-03 1.705518e-02 39 29622052 1.263761e-03 1.705506e-02 40 29632052 1.968808e-03 1.705497e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 29642052 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.001969 CVT ENERGY = 0.017055 SAMPLE = "grid". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.168405 0.877954 2 0.835000 0.835000 3 0.521436 0.496652 4 0.505149 0.163885 5 0.181755 0.627263 6 0.181448 0.372936 7 0.506241 0.833254 8 0.834008 0.168066 9 0.841564 0.503507 10 0.167071 0.122429 TEST06 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with MATLAB RANDOM sampling. Step SEED L2-Change Energy 0 123456789 1 29242052 8.942821e-01 3.428456e-02 2 29262052 2.890669e-01 2.311355e-02 3 29282052 2.052209e-01 2.095145e-02 4 29302052 1.820873e-01 1.989450e-02 5 29322052 1.172862e-01 1.879609e-02 6 29342052 1.126308e-01 1.891532e-02 7 29362052 9.064141e-02 1.839330e-02 8 29382052 9.143136e-02 1.843294e-02 9 29402052 9.117416e-02 1.822150e-02 10 29422052 7.720665e-02 1.781066e-02 11 29442052 7.766472e-02 1.770020e-02 12 29462052 8.200340e-02 1.773921e-02 13 29482052 5.883988e-02 1.754118e-02 14 29502052 6.553229e-02 1.749210e-02 15 29522052 5.241684e-02 1.743168e-02 16 29542052 6.368244e-02 1.751685e-02 17 29562052 5.916366e-02 1.716028e-02 18 29582052 5.671385e-02 1.730267e-02 19 29602052 5.567801e-02 1.727420e-02 20 29622052 5.022993e-02 1.722940e-02 21 29642052 4.722392e-02 1.709615e-02 22 29662052 6.657957e-02 1.723994e-02 23 29682052 4.123598e-02 1.732766e-02 24 29702052 5.558140e-02 1.706064e-02 25 29722052 4.471303e-02 1.702303e-02 26 29742052 4.747281e-02 1.696746e-02 27 29762052 4.166321e-02 1.701241e-02 28 29782052 4.843750e-02 1.721260e-02 29 29802052 4.352783e-02 1.714878e-02 30 29822052 4.421980e-02 1.704587e-02 31 29842052 2.912240e-02 1.696139e-02 32 29862052 3.707058e-02 1.720390e-02 33 29882052 4.085668e-02 1.712078e-02 34 29902052 3.143790e-02 1.708710e-02 35 29922052 3.718887e-02 1.713939e-02 36 29942052 4.222188e-02 1.713623e-02 37 29962052 2.928820e-02 1.717802e-02 38 29982052 4.233868e-02 1.720043e-02 39 30002052 4.199406e-02 1.713269e-02 40 30022052 3.843131e-02 1.686286e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 30042052 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.038431 CVT ENERGY = 0.016863 SAMPLE = "random". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.171547 0.875920 2 0.832488 0.833830 3 0.515246 0.497006 4 0.508561 0.162343 5 0.177609 0.623484 6 0.180645 0.371402 7 0.503120 0.834720 8 0.837449 0.165328 9 0.843049 0.502728 10 0.171055 0.118861 TEST07 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with a different seed. Step SEED L2-Change Energy 0 987654321 1 1525819924 7.796175e-01 3.758641e-02 2 1703739660 3.351238e-01 2.350118e-02 3 1956211282 2.635870e-01 2.055678e-02 4 703763026 2.088297e-01 1.903517e-02 5 878628297 1.556444e-01 1.823368e-02 6 1552444705 1.311147e-01 1.798070e-02 7 390357255 1.003401e-01 1.755814e-02 8 689833854 8.107797e-02 1.719840e-02 9 1751610365 5.904053e-02 1.722485e-02 10 852519522 6.120446e-02 1.725488e-02 11 309030697 4.985190e-02 1.694212e-02 12 1316592958 5.670540e-02 1.700507e-02 13 1105896658 4.020915e-02 1.708643e-02 14 1045195875 4.752924e-02 1.725639e-02 15 1897548003 4.603104e-02 1.689033e-02 16 1870465968 6.637207e-02 1.709418e-02 17 789370021 5.405032e-02 1.711052e-02 18 444524362 4.301032e-02 1.719858e-02 19 689805975 4.161760e-02 1.712896e-02 20 1558080092 4.843414e-02 1.715244e-02 21 1381530061 4.880506e-02 1.718080e-02 22 157511124 5.487486e-02 1.712880e-02 23 16143349 4.057497e-02 1.715880e-02 24 1155157008 5.315483e-02 1.713450e-02 25 25788210 4.865867e-02 1.706973e-02 26 1456770040 4.805390e-02 1.705930e-02 27 922599524 4.530867e-02 1.716236e-02 28 910060503 2.875686e-02 1.705300e-02 29 1036849277 4.327169e-02 1.692548e-02 30 1558644233 5.245716e-02 1.703658e-02 31 192063102 4.608843e-02 1.733458e-02 32 61275996 5.122495e-02 1.683920e-02 33 1575049278 4.458096e-02 1.709934e-02 34 339755903 3.826457e-02 1.716370e-02 35 1360647670 3.528694e-02 1.696463e-02 36 1802859403 4.528272e-02 1.691861e-02 37 2066534888 4.964161e-02 1.698488e-02 38 101044121 4.990540e-02 1.696783e-02 39 340723523 5.483375e-02 1.731701e-02 40 1321862545 4.869287e-02 1.714118e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 987654321 Current SEED = 1047111519 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.048693 CVT ENERGY = 0.017141 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.833068 0.836707 2 0.499362 0.522698 3 0.122098 0.170059 4 0.499436 0.846036 5 0.374483 0.183824 6 0.881976 0.180629 7 0.628776 0.179369 8 0.835690 0.513866 9 0.160909 0.834702 10 0.167995 0.510114 TEST08 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1 with a different batch size. Step SEED L2-Change Energy 0 123456789 1 29242052 8.940030e-01 3.419919e-02 2 396524255 2.824564e-01 2.276680e-02 3 1804077568 2.161568e-01 2.085658e-02 4 58279807 1.477493e-01 1.944282e-02 5 890554932 1.283413e-01 1.897176e-02 6 214536894 8.960171e-02 1.859560e-02 7 1592773222 1.102347e-01 1.856606e-02 8 1874550474 9.236769e-02 1.809569e-02 9 2041615702 8.441385e-02 1.808610e-02 10 2056573688 8.941519e-02 1.799344e-02 11 1522461057 7.935737e-02 1.749078e-02 12 1338654111 7.809860e-02 1.765559e-02 13 758290347 7.983841e-02 1.748531e-02 14 1895558656 7.256098e-02 1.755883e-02 15 553115540 6.471175e-02 1.704020e-02 16 1150573110 6.936469e-02 1.735544e-02 17 1130930562 6.793165e-02 1.723610e-02 18 1398936087 6.767943e-02 1.716154e-02 19 1351174075 5.539154e-02 1.701183e-02 20 1271270653 4.531095e-02 1.730400e-02 21 383674773 5.249361e-02 1.718908e-02 22 533903734 4.559622e-02 1.732207e-02 23 412527942 5.393337e-02 1.691134e-02 24 498761874 5.427016e-02 1.708939e-02 25 1767322623 5.896687e-02 1.723658e-02 26 8802113 4.038236e-02 1.714110e-02 27 337656644 3.540781e-02 1.698687e-02 28 982491412 4.621968e-02 1.706182e-02 29 1661195312 4.106082e-02 1.710234e-02 30 1727223671 3.703044e-02 1.700439e-02 31 1934076831 4.225577e-02 1.715442e-02 32 286968437 5.523915e-02 1.705179e-02 33 1651892980 3.350856e-02 1.735319e-02 34 1093660108 4.375073e-02 1.724619e-02 35 1312296485 4.994957e-02 1.708435e-02 36 1505118054 4.485278e-02 1.728073e-02 37 1225827697 4.655303e-02 1.731938e-02 38 2103031061 4.545167e-02 1.702508e-02 39 237994259 4.522406e-02 1.706157e-02 40 308344071 4.859585e-02 1.719588e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 878651545 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.048596 CVT ENERGY = 0.017196 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 5 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.177221 0.881571 2 0.837556 0.827059 3 0.515287 0.501840 4 0.507924 0.167342 5 0.179980 0.630281 6 0.175928 0.375518 7 0.512095 0.837544 8 0.830500 0.167848 9 0.832437 0.495910 10 0.168871 0.121883 TEST09 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with IT_FIXED = IT_MAX. Step SEED L2-Change Energy 0 123456789 1 29242052 8.940030e-01 3.419919e-02 2 29242052 2.905377e-01 2.258389e-02 3 29242052 1.928897e-01 2.038812e-02 4 29242052 1.449446e-01 1.943296e-02 5 29242052 1.096676e-01 1.888354e-02 6 29242052 9.457551e-02 1.855182e-02 7 29242052 8.886678e-02 1.828003e-02 8 29242052 7.941881e-02 1.804106e-02 9 29242052 6.275176e-02 1.785324e-02 10 29242052 5.411818e-02 1.772358e-02 11 29242052 5.191310e-02 1.762342e-02 12 29242052 4.457332e-02 1.753857e-02 13 29242052 4.239263e-02 1.747594e-02 14 29242052 4.006855e-02 1.742342e-02 15 29242052 3.286887e-02 1.738146e-02 16 29242052 3.527045e-02 1.735150e-02 17 29242052 3.582355e-02 1.731609e-02 18 29242052 3.053959e-02 1.728136e-02 19 29242052 3.232267e-02 1.725463e-02 20 29242052 2.967783e-02 1.722908e-02 21 29242052 3.352317e-02 1.720566e-02 22 29242052 3.454501e-02 1.717819e-02 23 29242052 3.407151e-02 1.714551e-02 24 29242052 3.508484e-02 1.711502e-02 25 29242052 3.120479e-02 1.708352e-02 26 29242052 3.268436e-02 1.705598e-02 27 29242052 3.084701e-02 1.702912e-02 28 29242052 2.202042e-02 1.701011e-02 29 29242052 1.562952e-02 1.700021e-02 30 29242052 1.351930e-02 1.699423e-02 31 29242052 1.281832e-02 1.698994e-02 32 29242052 1.164994e-02 1.698628e-02 33 29242052 7.430306e-03 1.698376e-02 34 29242052 6.130237e-03 1.698252e-02 35 29242052 3.278178e-03 1.698179e-02 36 29242052 2.161963e-03 1.698157e-02 37 29242052 1.969353e-03 1.698143e-02 38 29242052 1.955736e-03 1.698129e-02 39 29242052 6.618640e-04 1.698121e-02 40 29242052 3.402353e-04 1.698119e-02 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 396524255 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 40 Iterations IT_NUM = 40 Difference IT_DIFF = 0.000340 CVT ENERGY = 0.016981 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.172088 0.875224 2 0.835165 0.835221 3 0.523955 0.505164 4 0.506095 0.170500 5 0.178812 0.623009 6 0.184022 0.368130 7 0.521193 0.838361 8 0.830412 0.174849 9 0.849083 0.502440 10 0.161318 0.121970 TEST10 CVT computes a Centroidal Voronoi Tessellation. Compute 100 points in 3D. Step SEED L2-Change Energy 0 123456789 1 162518201 5.575870e+00 1.902781e-02 2 914652320 2.499326e+00 1.409272e-02 3 1182014520 1.785880e+00 1.327612e-02 4 734877640 1.459265e+00 1.277620e-02 5 1808590614 1.322214e+00 1.256995e-02 6 1376754667 1.324828e+00 1.238134e-02 7 39225810 1.252932e+00 1.231566e-02 8 1835665933 1.288687e+00 1.217790e-02 9 683368702 1.357117e+00 1.209061e-02 10 1192180323 1.208342e+00 1.199915e-02 11 1451564322 1.190380e+00 1.203512e-02 12 1525473369 1.200796e+00 1.194158e-02 13 1258784351 1.242336e+00 1.198181e-02 14 1939780355 1.218808e+00 1.193385e-02 15 1792150340 1.182092e+00 1.187771e-02 16 1077745899 1.218703e+00 1.176960e-02 17 1381981537 1.121576e+00 1.181378e-02 18 2135871724 1.117898e+00 1.181264e-02 19 733709902 1.186048e+00 1.174697e-02 20 1511987296 1.229241e+00 1.181401e-02 21 1849799130 1.139685e+00 1.171938e-02 22 1011187751 1.108465e+00 1.174391e-02 23 430762708 1.167053e+00 1.175587e-02 24 2076182163 1.171884e+00 1.174956e-02 25 662061697 1.168754e+00 1.176785e-02 26 253385434 1.195502e+00 1.175095e-02 27 836175832 1.218574e+00 1.171252e-02 28 529591688 1.113094e+00 1.166449e-02 29 154633765 1.067318e+00 1.166396e-02 30 778723351 1.130392e+00 1.173306e-02 31 1341651177 1.045801e+00 1.172539e-02 32 11115418 1.134116e+00 1.176387e-02 33 181250519 1.177633e+00 1.171090e-02 34 628655915 1.205566e+00 1.166837e-02 35 1574892130 1.065888e+00 1.170441e-02 36 1853258335 1.185683e+00 1.182104e-02 37 1106992749 1.244701e+00 1.162287e-02 38 2113411425 1.117243e+00 1.170310e-02 39 1552081075 1.190594e+00 1.172673e-02 40 921807728 1.110091e+00 1.173446e-02 Dimension DIM_NUM = 3 Number of points N = 100 Initial SEED = 123456789 Current SEED = 1707197995 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 1.110091 CVT ENERGY = 0.011734 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 First 10 generators (rows) Row: 1 2 3 Col 1 0.351377 0.914543 0.887342 2 0.442049 0.326834 0.076620 3 0.344176 0.126858 0.097061 4 0.708074 0.130770 0.625162 5 0.486658 0.738148 0.867735 6 0.121716 0.915644 0.382635 7 0.094466 0.107437 0.894845 8 0.864948 0.084260 0.103335 9 0.345125 0.917712 0.092081 10 0.383596 0.912549 0.303727 TEST11 CVT computes a Centroidal Voronoi Tessellation. In this test, we initialize the generators to grid points; this is an unstable CVT solution. Initial generators (rows): Row: 1 2 Col 1 0.125000 0.125000 2 0.125000 0.375000 3 0.125000 0.625000 4 0.125000 0.875000 5 0.375000 0.125000 6 0.375000 0.375000 7 0.375000 0.625000 8 0.375000 0.875000 9 0.625000 0.125000 10 0.625000 0.375000 11 0.625000 0.625000 12 0.625000 0.875000 13 0.875000 0.125000 14 0.875000 0.375000 15 0.875000 0.625000 16 0.875000 0.875000 Step SEED L2-Change Energy 0 123456789 1 123456789 1.846758e-01 1.046450e-02 2 1328042058 2.223203e-01 1.099211e-02 3 1539989115 2.017935e-01 1.055967e-02 4 200382020 2.019205e-01 1.022654e-02 5 1958948863 2.136785e-01 1.006036e-02 6 691823909 2.030401e-01 1.055548e-02 7 655816003 2.150778e-01 1.087898e-02 8 450926852 2.551839e-01 1.069016e-02 9 1273398721 2.291458e-01 1.059367e-02 10 1462772409 2.688908e-01 1.042150e-02 11 1371189933 2.484409e-01 1.109275e-02 12 845524934 2.308120e-01 1.037710e-02 13 2013025619 2.308340e-01 1.055465e-02 14 1021685265 2.435475e-01 1.064356e-02 15 204970068 2.349632e-01 1.075167e-02 16 778034624 2.209265e-01 1.044326e-02 17 1938972586 2.148351e-01 1.073079e-02 18 1519833303 2.360563e-01 1.031291e-02 19 2077270047 2.046226e-01 1.049077e-02 20 1923497586 1.473442e-01 1.042380e-02 21 167698528 2.287529e-01 1.041837e-02 22 1655479938 2.039566e-01 1.037653e-02 23 475051709 2.050943e-01 1.011748e-02 24 83696007 1.934074e-01 1.018402e-02 25 1805594913 2.064952e-01 1.029340e-02 26 508154254 2.019340e-01 1.029345e-02 27 1861070898 2.117487e-01 1.066078e-02 28 1661633678 1.860818e-01 1.039315e-02 29 914834335 2.034757e-01 1.035821e-02 30 715643788 1.793350e-01 1.058339e-02 31 810642687 1.928330e-01 1.039021e-02 32 471503978 2.311628e-01 1.054492e-02 33 1019331795 2.539997e-01 1.084180e-02 34 2118751796 2.065268e-01 1.093321e-02 35 1168375939 2.217469e-01 1.084197e-02 36 26482542 2.292148e-01 1.033325e-02 37 2056065863 2.021717e-01 1.081766e-02 38 414064984 2.378344e-01 1.047139e-02 39 1342855162 1.653391e-01 1.021044e-02 40 444956424 2.028198e-01 1.003404e-02 Dimension DIM_NUM = 2 Number of points N = 16 Initial SEED = 123456789 Current SEED = 2115448041 INIT = "user initialization". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.202820 CVT ENERGY = 0.010034 SAMPLE = "uniform". Samples SAMPLE_NUM = 1000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 2 Col 1 0.124407 0.131737 2 0.131095 0.399531 3 0.117560 0.641729 4 0.137583 0.894953 5 0.360939 0.113240 6 0.377630 0.310748 7 0.369431 0.567716 8 0.383183 0.864456 9 0.604839 0.137584 10 0.607581 0.387287 11 0.623353 0.630739 12 0.623385 0.882404 13 0.872884 0.117162 14 0.867112 0.360631 15 0.866551 0.602682 16 0.864296 0.865609 TEST12 The "random" initialization option calls the system random number generator. There is some question about whether this works correctly. The test is as follows: CVT call #1: DIM_NUM = 2 N = 10 INIT = -1 IT_MAX = 0 SEED = 100000 Print output values of SEED and R #1. CVT call #2: (jump SEED) DIM_NUM = 2 N = 10 INIT = -1 IT_MAX = 0 SEED = 200000 Print output values of SEED and R #2. CVT call #3: (restore SEED) DIM_NUM = 2 N = 10 INIT = -1 IT_MAX = 0 SEED = 100000 Print output values of SEED and R #3. We expect: * the values R #1 and R #2 will differ; AND * the values R #1 and R #3 will agree. Step SEED L2-Change Energy 0 100000 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 100000 Current SEED = 100020 INIT = "random". Max iterations IT_MAX = 0 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 0 Difference IT_DIFF = 0.000000 CVT ENERGY = 0.000000 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.000000 R #1: Row: 1 2 Col 1 0.607040 0.388734 2 0.736869 0.936127 3 0.509642 0.742189 4 0.168957 0.573648 5 0.834113 0.919096 6 0.710314 0.366077 7 0.817605 0.295455 8 0.219698 0.374558 9 0.669632 0.623522 10 0.453915 0.201599 Step SEED L2-Change Energy 0 200000 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 200000 Current SEED = 200020 INIT = "random". Max iterations IT_MAX = 0 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 0 Difference IT_DIFF = 0.000000 CVT ENERGY = 0.000000 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.000000 R #2: Row: 1 2 Col 1 0.911544 0.624686 2 0.065045 0.847961 3 0.561485 0.074612 4 0.970223 0.007740 5 0.724464 0.075234 6 0.286489 0.970275 7 0.127589 0.054476 8 0.201144 0.833360 9 0.637503 0.255879 10 0.718892 0.978478 Step SEED L2-Change Energy 0 100000 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 100000 Current SEED = 100020 INIT = "random". Max iterations IT_MAX = 0 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 0 Difference IT_DIFF = 0.000000 CVT ENERGY = 0.000000 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.000000 R #3: Row: 1 2 Col 1 0.607040 0.388734 2 0.736869 0.936127 3 0.509642 0.742189 4 0.168957 0.573648 5 0.834113 0.919096 6 0.710314 0.366077 7 0.817605 0.295455 8 0.219698 0.374558 9 0.669632 0.623522 10 0.453915 0.201599 TEST13 CVT computes a Centroidal Voronoi Tessellation. In this example, we call the "USER" routine, which allows the user to define the geometry and density implicitly, by returning sample points. Step SEED L2-Change Energy 0 123456789 1 123456789 4.538819e+00 1.141464e-02 2 123456789 2.107204e+00 7.337538e-03 3 123456789 1.390811e+00 6.520322e-03 4 123456789 1.104628e+00 6.093849e-03 5 123456789 9.516608e-01 5.953929e-03 6 123456789 9.835673e-01 5.812519e-03 7 123456789 9.443679e-01 5.773479e-03 8 123456789 8.153409e-01 5.656700e-03 9 123456789 9.033686e-01 5.516524e-03 10 123456789 8.654526e-01 5.543751e-03 11 123456789 9.105516e-01 5.604885e-03 12 123456789 8.803876e-01 5.488901e-03 13 123456789 7.429956e-01 5.444156e-03 14 123456789 7.600265e-01 5.381034e-03 15 123456789 7.530610e-01 5.438527e-03 16 123456789 8.417234e-01 5.358096e-03 17 123456789 7.584886e-01 5.371615e-03 18 123456789 6.705096e-01 5.348151e-03 19 123456789 7.357281e-01 5.324630e-03 20 123456789 7.171119e-01 5.371430e-03 21 123456789 7.557667e-01 5.319414e-03 22 123456789 8.199987e-01 5.317007e-03 23 123456789 7.567854e-01 5.346751e-03 24 123456789 7.573236e-01 5.331317e-03 25 123456789 6.958045e-01 5.325241e-03 26 123456789 7.468962e-01 5.332247e-03 27 123456789 7.442739e-01 5.319888e-03 28 123456789 6.748831e-01 5.270517e-03 29 123456789 7.152752e-01 5.298039e-03 30 123456789 7.371427e-01 5.309481e-03 31 123456789 7.423177e-01 5.291492e-03 32 123456789 7.268626e-01 5.261994e-03 33 123456789 7.147667e-01 5.271737e-03 34 123456789 7.036994e-01 5.205256e-03 35 123456789 7.909858e-01 5.241560e-03 36 123456789 7.829487e-01 5.255926e-03 37 123456789 7.314960e-01 5.256254e-03 38 123456789 7.529876e-01 5.235219e-03 39 123456789 6.845993e-01 5.184304e-03 40 123456789 7.376803e-01 5.270458e-03 Dimension DIM_NUM = 2 Number of points N = 100 Initial SEED = 123456789 Current SEED = 123456789 INIT = "user". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.737680 CVT ENERGY = 0.005270 SAMPLE = "user". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-16 TEST14 Generate a CVT in the interval [0,1] using 10 points. Exact answer: { 0.05, 0.15, 0.25, ..., 0.85, 0.95 } It turns out that, for a fixed number of points N, a 1D problem will converge much more slowly than for cases where the dimension is higher. Step SEED L2-Change Energy 0 123456789 1 123456799 1.250022e-01 1.303420e-03 2 123556799 3.908669e-02 9.925026e-04 3 123656799 2.737870e-02 9.517483e-04 4 123756799 2.245662e-02 9.268205e-04 5 123856799 2.015785e-02 9.093786e-04 6 123956799 1.832158e-02 8.964860e-04 7 124056799 1.654812e-02 8.864917e-04 8 124156799 1.498411e-02 8.786222e-04 9 124256799 1.363182e-02 8.721971e-04 10 124356799 1.248702e-02 8.669341e-04 11 124456799 1.136181e-02 8.625954e-04 12 124556799 1.047609e-02 8.589924e-04 13 124656799 9.554732e-03 8.559217e-04 14 124756799 8.763032e-03 8.533784e-04 15 124856799 8.057027e-03 8.512271e-04 16 124956799 7.383212e-03 8.493883e-04 17 125056799 6.768040e-03 8.478003e-04 18 125156799 6.210961e-03 8.464473e-04 19 125256799 5.777144e-03 8.452876e-04 20 125356799 5.302729e-03 8.442842e-04 21 125456799 4.952723e-03 8.433845e-04 22 125556799 4.670162e-03 8.425910e-04 23 125656799 4.374807e-03 8.419192e-04 24 125756799 4.100081e-03 8.413197e-04 25 125856799 3.886931e-03 8.407341e-04 26 125956799 3.655124e-03 8.402640e-04 27 126056799 3.522817e-03 8.398102e-04 28 126156799 3.389440e-03 8.394389e-04 29 126256799 3.289946e-03 8.390438e-04 30 126356799 3.143722e-03 8.387148e-04 31 126456799 3.090476e-03 8.384022e-04 32 126556799 3.043284e-03 8.381342e-04 33 126656799 2.932533e-03 8.378375e-04 34 126756799 2.863065e-03 8.376068e-04 35 126856799 2.792944e-03 8.373739e-04 36 126956799 2.724767e-03 8.371712e-04 37 127056799 2.636882e-03 8.369637e-04 38 127156799 2.598011e-03 8.367734e-04 39 127256799 2.525722e-03 8.365920e-04 40 127356799 2.505656e-03 8.364541e-04 41 127456799 2.379554e-03 8.362630e-04 42 127556799 2.326656e-03 8.361264e-04 43 127656799 2.311140e-03 8.359830e-04 44 127756799 2.249890e-03 8.358702e-04 45 127856799 2.157387e-03 8.357223e-04 46 127956799 2.143078e-03 8.356128e-04 47 128056799 2.090141e-03 8.354966e-04 48 128156799 2.007892e-03 8.354062e-04 49 128256799 1.959262e-03 8.352826e-04 50 128356799 1.955939e-03 8.351997e-04 Dimension DIM_NUM = 1 Number of points N = 10 Initial SEED = 123456789 Current SEED = 128456799 INIT = "uniform". Max iterations IT_MAX = 50 IT_FIXED (fixed samples) = 1 Iterations IT_NUM = 50 Difference IT_DIFF = 0.001956 CVT ENERGY = 0.000835 SAMPLE = "uniform". Samples SAMPLE_NUM = 100000 Sampling BATCH size = 10000 EPSILON (unit roundoff) = 2.220446e-16 Generators (rows): Row: 1 Col 1 0.051979 2 0.155713 3 0.258814 4 0.360964 5 0.461964 6 0.561764 7 0.660443 8 0.758169 9 0.855189 10 0.951780 CVT_TEST Normal end of execution. 15-Sep-2010 17:31:47 >>