cvt_test 23-Jun-2005 14:43:43 CVT_TEST Test the MATLAB CVT routines. TEST01 CVT computes a Centroidal Voronoi Tessellation. Step SEED L2-Change Energy 0 123456789 1 29242052 8.750651e-001 3.276376e-002 2 396524255 2.609642e-001 2.216674e-002 3 1804077568 2.008713e-001 2.058524e-002 4 58279807 1.406907e-001 1.936336e-002 5 890554932 1.189042e-001 1.891450e-002 6 214536894 8.826162e-002 1.856249e-002 7 1592773222 1.060953e-001 1.862238e-002 8 1874550474 9.275847e-002 1.809659e-002 9 2041615702 8.200714e-002 1.807659e-002 10 2056573688 8.889546e-002 1.805882e-002 11 1522461057 7.281421e-002 1.757247e-002 12 1338654111 7.634906e-002 1.775264e-002 13 758290347 7.814315e-002 1.756194e-002 14 1895558656 6.781088e-002 1.765224e-002 15 553115540 5.992204e-002 1.717670e-002 16 1150573110 5.737923e-002 1.744758e-002 17 1130930562 7.406204e-002 1.740633e-002 18 1398936087 6.288661e-002 1.724678e-002 19 1351174075 6.205747e-002 1.708413e-002 20 1271270653 5.276311e-002 1.742168e-002 21 383674773 6.573860e-002 1.729273e-002 22 533903734 5.604229e-002 1.736796e-002 23 412527942 5.748708e-002 1.697922e-002 24 498761874 6.100875e-002 1.711036e-002 25 1767322623 6.250668e-002 1.724441e-002 26 8802113 5.064649e-002 1.718507e-002 27 337656644 3.957797e-002 1.700340e-002 28 982491412 4.262760e-002 1.705205e-002 29 1661195312 4.706045e-002 1.710081e-002 30 1727223671 4.940814e-002 1.701330e-002 31 1934076831 4.405288e-002 1.715150e-002 32 286968437 5.782067e-002 1.713457e-002 33 1651892980 4.404639e-002 1.732191e-002 34 1093660108 5.341884e-002 1.729031e-002 35 1312296485 4.763206e-002 1.701236e-002 36 1505118054 4.162846e-002 1.730844e-002 37 1225827697 4.305559e-002 1.731370e-002 38 2103031061 4.450023e-002 1.699073e-002 39 237994259 4.330992e-002 1.714678e-002 40 308344071 4.032513e-002 1.713117e-002 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 = 0.040325 CVT ENERGY = 0.017131 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.161617 0.875273 2 0.822332 0.807007 3 0.506747 0.499076 4 0.495419 0.158325 5 0.169318 0.622788 6 0.168737 0.369471 7 0.491355 0.829847 8 0.818655 0.148630 9 0.826369 0.474470 10 0.156155 0.116276 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 8.750651e-001 3.276376e-002 2 396524255 2.609642e-001 2.216674e-002 3 1804077568 2.008713e-001 2.058524e-002 4 58279807 1.406907e-001 1.936336e-002 5 890554932 1.189042e-001 1.891450e-002 6 214536894 8.826162e-002 1.856249e-002 7 1592773222 1.060953e-001 1.862238e-002 8 1874550474 9.275847e-002 1.809659e-002 9 2041615702 8.200714e-002 1.807659e-002 10 2056573688 8.889546e-002 1.805882e-002 11 1522461057 7.281421e-002 1.757247e-002 12 1338654111 7.634906e-002 1.775264e-002 13 758290347 7.814315e-002 1.756194e-002 14 1895558656 6.781088e-002 1.765224e-002 15 553115540 5.992204e-002 1.717670e-002 16 1150573110 5.737923e-002 1.744758e-002 17 1130930562 7.406204e-002 1.740633e-002 18 1398936087 6.288661e-002 1.724678e-002 19 1351174075 6.205747e-002 1.708413e-002 20 1271270653 5.276311e-002 1.742168e-002 21 383674773 6.573860e-002 1.729273e-002 22 533903734 5.604229e-002 1.736796e-002 23 412527942 5.748708e-002 1.697922e-002 24 498761874 6.100875e-002 1.711036e-002 25 1767322623 6.250668e-002 1.724441e-002 26 8802113 5.064649e-002 1.718507e-002 27 337656644 3.957797e-002 1.700340e-002 28 982491412 4.262760e-002 1.705205e-002 29 1661195312 4.706045e-002 1.710081e-002 30 1727223671 4.940814e-002 1.701330e-002 31 1934076831 4.405288e-002 1.715150e-002 32 286968437 5.782067e-002 1.713457e-002 33 1651892980 4.404639e-002 1.732191e-002 34 1093660108 5.341884e-002 1.729031e-002 35 1312296485 4.763206e-002 1.701236e-002 36 1505118054 4.162846e-002 1.730844e-002 37 1225827697 4.305559e-002 1.731370e-002 38 2103031061 4.450023e-002 1.699073e-002 39 237994259 4.330992e-002 1.714678e-002 40 308344071 4.032513e-002 1.713117e-002 41 878651545 3.662467e-002 1.695317e-002 42 336554041 4.426567e-002 1.698276e-002 43 69693939 3.543783e-002 1.727123e-002 44 107597223 4.639095e-002 1.709561e-002 45 284388055 5.541087e-002 1.710023e-002 46 821532605 4.085533e-002 1.707003e-002 47 1912444717 4.889515e-002 1.692758e-002 48 2139238658 6.006373e-002 1.712748e-002 49 1514249906 4.088142e-002 1.725307e-002 50 765384573 4.109666e-002 1.711792e-002 51 599511796 4.934493e-002 1.708779e-002 52 1929718247 5.377928e-002 1.708299e-002 53 1495267469 5.617983e-002 1.715989e-002 54 346287018 4.155170e-002 1.715133e-002 55 972591208 4.473538e-002 1.727822e-002 56 1170908305 3.928691e-002 1.691868e-002 57 2101087755 4.024282e-002 1.693326e-002 58 1585775448 3.732618e-002 1.705376e-002 59 1719007417 4.450185e-002 1.716412e-002 60 47014704 3.365549e-002 1.697284e-002 61 325311895 5.005553e-002 1.733538e-002 62 2114713435 4.251727e-002 1.694349e-002 63 469955390 4.349006e-002 1.725484e-002 64 2044044375 4.757866e-002 1.696824e-002 65 1902665122 3.643203e-002 1.709281e-002 66 999386148 3.971669e-002 1.702121e-002 67 1762727540 4.226257e-002 1.688462e-002 68 886787757 3.980963e-002 1.685617e-002 69 1442441010 4.121842e-002 1.705991e-002 70 766630007 4.927807e-002 1.702703e-002 71 473489672 2.963025e-002 1.704086e-002 72 1247561645 2.978381e-002 1.723712e-002 73 1093781229 4.780580e-002 1.720395e-002 74 1723735430 3.973502e-002 1.698903e-002 75 1100723884 5.235798e-002 1.705164e-002 76 -2171060 4.068897e-002 1.702001e-002 77 1556984304 4.162888e-002 1.707826e-002 78 1035291506 2.793159e-002 1.690123e-002 79 158213521 3.553712e-002 1.717651e-002 80 1863192335 3.713071e-002 1.707477e-002 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 = 0.037131 CVT ENERGY = 0.017075 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.157237 0.876880 2 0.826100 0.804395 3 0.504892 0.507378 4 0.505312 0.159902 5 0.167928 0.624010 6 0.172834 0.369433 7 0.500579 0.835640 8 0.828362 0.141327 9 0.827018 0.470060 10 0.152134 0.119033 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 8.716792e-001 3.272498e-002 2 720688506 2.682286e-001 2.220734e-002 3 681172 1.816211e-001 2.037109e-002 4 539098006 1.389885e-001 1.945498e-002 5 1544551628 1.098299e-001 1.900087e-002 6 1039137261 9.273402e-002 1.869618e-002 7 1856120581 8.289752e-002 1.847912e-002 8 1398888834 7.996241e-002 1.825700e-002 9 777275849 7.617674e-002 1.808130e-002 10 193908656 6.915847e-002 1.791773e-002 11 594766309 6.094354e-002 1.778546e-002 12 1528604881 5.545327e-002 1.764046e-002 13 2135424592 4.822723e-002 1.755802e-002 14 843278689 4.491970e-002 1.746526e-002 15 1298034490 3.873339e-002 1.744345e-002 16 1774985135 3.618128e-002 1.738798e-002 17 58892340 3.332873e-002 1.737112e-002 18 497310354 3.240704e-002 1.734887e-002 19 1555340604 3.208623e-002 1.729661e-002 20 573219264 3.009223e-002 1.728692e-002 21 769258892 3.022026e-002 1.726087e-002 22 1733894875 2.888727e-002 1.722763e-002 23 1708504563 2.972674e-002 1.720549e-002 24 332981687 3.058986e-002 1.716935e-002 25 871833470 2.581835e-002 1.716571e-002 26 491107991 2.689939e-002 1.713338e-002 27 64836647 2.333585e-002 1.713100e-002 28 954805664 2.145404e-002 1.709417e-002 29 1033236242 2.188305e-002 1.710706e-002 30 1875753496 1.991521e-002 1.709303e-002 31 932903206 1.752856e-002 1.708793e-002 32 900419333 1.708026e-002 1.706888e-002 33 898406847 1.581799e-002 1.705240e-002 34 957321340 1.464574e-002 1.703462e-002 35 1879036371 1.440386e-002 1.703330e-002 36 550745514 1.210331e-002 1.704180e-002 37 1822412817 1.035026e-002 1.704000e-002 38 1926341691 1.168482e-002 1.704444e-002 39 578466603 1.334758e-002 1.702410e-002 40 1767869167 1.016693e-002 1.701699e-002 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 = 0.010167 CVT ENERGY = 0.017017 SAMPLE = "uniform". Samples SAMPLE_NUM = 1000000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.156681 0.841575 2 0.817925 0.820511 3 0.615333 0.490160 4 0.491625 0.144074 5 0.111511 0.525429 6 0.353314 0.454954 7 0.479455 0.817469 8 0.822849 0.147148 9 0.870060 0.484831 10 0.149031 0.163101 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-001 3.430968e-002 2 29252052 2.888033e-001 2.282189e-002 3 29262052 1.974512e-001 2.062846e-002 4 29272052 1.476514e-001 1.963103e-002 5 29282052 1.148220e-001 1.907463e-002 6 29292052 9.127902e-002 1.874133e-002 7 29302052 8.814468e-002 1.849141e-002 8 29312052 8.344492e-002 1.828899e-002 9 29322052 7.647994e-002 1.808564e-002 10 29332052 6.948106e-002 1.789580e-002 11 29342052 6.306380e-002 1.774081e-002 12 29352052 5.847443e-002 1.762864e-002 13 29362052 4.677373e-002 1.753371e-002 14 29372052 4.396146e-002 1.747286e-002 15 29382052 3.813456e-002 1.740788e-002 16 29392052 3.616533e-002 1.736855e-002 17 29402052 3.381555e-002 1.733500e-002 18 29412052 3.476403e-002 1.731187e-002 19 29422052 3.702363e-002 1.726369e-002 20 29432052 3.328745e-002 1.723462e-002 21 29442052 3.385829e-002 1.719071e-002 22 29452052 3.460954e-002 1.717196e-002 23 29462052 2.921509e-002 1.713844e-002 24 29472052 2.497847e-002 1.710849e-002 25 29482052 2.358221e-002 1.710810e-002 26 29492052 2.082782e-002 1.708139e-002 27 29502052 1.632158e-002 1.708099e-002 28 29512052 1.476770e-002 1.707363e-002 29 29522052 9.591279e-003 1.707075e-002 30 29532052 9.655906e-003 1.707477e-002 31 29542052 1.030772e-002 1.706052e-002 32 29552052 9.225189e-003 1.706924e-002 33 29562052 8.555069e-003 1.706484e-002 34 29572052 4.625623e-003 1.706492e-002 35 29582052 7.783681e-003 1.705902e-002 36 29592052 8.045066e-003 1.706966e-002 37 29602052 5.328606e-003 1.706026e-002 38 29612052 7.622415e-003 1.706037e-002 39 29622052 6.566532e-003 1.706765e-002 40 29632052 6.010474e-003 1.706022e-002 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-016 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-001 3.431461e-002 2 29252052 2.892032e-001 2.279972e-002 3 29262052 1.918026e-001 2.061519e-002 4 29272052 1.519455e-001 1.963421e-002 5 29282052 1.144193e-001 1.906037e-002 6 29292052 9.534331e-002 1.872229e-002 7 29302052 8.829268e-002 1.847698e-002 8 29312052 8.070677e-002 1.825203e-002 9 29322052 7.409990e-002 1.804674e-002 10 29332052 6.938704e-002 1.786818e-002 11 29342052 6.170323e-002 1.771854e-002 12 29352052 5.403396e-002 1.760233e-002 13 29362052 4.934897e-002 1.751475e-002 14 29372052 4.532478e-002 1.744495e-002 15 29382052 4.101362e-002 1.738793e-002 16 29392052 4.044914e-002 1.734228e-002 17 29402052 3.637345e-002 1.729942e-002 18 29412052 3.861727e-002 1.725911e-002 19 29422052 3.370598e-002 1.721950e-002 20 29432052 3.483218e-002 1.718451e-002 21 29442052 3.251232e-002 1.715196e-002 22 29452052 2.966154e-002 1.712444e-002 23 29462052 2.582977e-002 1.710406e-002 24 29472052 1.913016e-002 1.708930e-002 25 29482052 1.638868e-002 1.708010e-002 26 29492052 1.661196e-002 1.707340e-002 27 29502052 1.016219e-002 1.706805e-002 28 29512052 8.696092e-003 1.706600e-002 29 29522052 7.117985e-003 1.706440e-002 30 29532052 9.338862e-003 1.706308e-002 31 29542052 9.987398e-003 1.706103e-002 32 29552052 8.432421e-003 1.705865e-002 33 29562052 5.676761e-003 1.705701e-002 34 29572052 4.963830e-003 1.705621e-002 35 29582052 3.160306e-003 1.705559e-002 36 29592052 1.989504e-003 1.705537e-002 37 29602052 1.630449e-003 1.705527e-002 38 29612052 2.122019e-003 1.705518e-002 39 29622052 1.263761e-003 1.705506e-002 40 29632052 1.968808e-003 1.705497e-002 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-016 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-001 3.428456e-002 2 29262052 2.890669e-001 2.311355e-002 3 29282052 2.052209e-001 2.095145e-002 4 29302052 1.820873e-001 1.989450e-002 5 29322052 1.172862e-001 1.879609e-002 6 29342052 1.126308e-001 1.891532e-002 7 29362052 9.064141e-002 1.839330e-002 8 29382052 9.143136e-002 1.843294e-002 9 29402052 9.117416e-002 1.822150e-002 10 29422052 7.720665e-002 1.781066e-002 11 29442052 7.766472e-002 1.770020e-002 12 29462052 8.200340e-002 1.773921e-002 13 29482052 5.883988e-002 1.754118e-002 14 29502052 6.553229e-002 1.749210e-002 15 29522052 5.241684e-002 1.743168e-002 16 29542052 6.368244e-002 1.751685e-002 17 29562052 5.916366e-002 1.716028e-002 18 29582052 5.671385e-002 1.730267e-002 19 29602052 5.567801e-002 1.727420e-002 20 29622052 5.022993e-002 1.722940e-002 21 29642052 4.722392e-002 1.709615e-002 22 29662052 6.657957e-002 1.723994e-002 23 29682052 4.123598e-002 1.732766e-002 24 29702052 5.558140e-002 1.706064e-002 25 29722052 4.471303e-002 1.702303e-002 26 29742052 4.747281e-002 1.696746e-002 27 29762052 4.166321e-002 1.701241e-002 28 29782052 4.843750e-002 1.721260e-002 29 29802052 4.352783e-002 1.714878e-002 30 29822052 4.421980e-002 1.704587e-002 31 29842052 2.912240e-002 1.696139e-002 32 29862052 3.707058e-002 1.720390e-002 33 29882052 4.085668e-002 1.712078e-002 34 29902052 3.143790e-002 1.708710e-002 35 29922052 3.718887e-002 1.713939e-002 36 29942052 4.222188e-002 1.713623e-002 37 29962052 2.928820e-002 1.717802e-002 38 29982052 4.233868e-002 1.720043e-002 39 30002052 4.199406e-002 1.713269e-002 40 30022052 3.843131e-002 1.686286e-002 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-016 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 6.618348e-001 3.020279e-002 2 1703739660 2.393778e-001 2.159678e-002 3 1956211282 1.728722e-001 1.977954e-002 4 703763026 1.477480e-001 1.904857e-002 5 878628297 1.242256e-001 1.837518e-002 6 1552444705 1.183565e-001 1.831115e-002 7 390357255 7.773102e-002 1.815621e-002 8 689833854 9.744738e-002 1.777799e-002 9 1751610365 7.603008e-002 1.764050e-002 10 852519522 8.867829e-002 1.761498e-002 11 309030697 7.488369e-002 1.736344e-002 12 1316592958 6.536068e-002 1.733102e-002 13 1105896658 6.545267e-002 1.732142e-002 14 1045195875 5.441104e-002 1.741615e-002 15 1897548003 5.397559e-002 1.701219e-002 16 1870465968 5.166525e-002 1.719132e-002 17 789370021 4.400651e-002 1.714917e-002 18 444524362 4.097082e-002 1.707983e-002 19 689805975 4.423105e-002 1.715245e-002 20 1558080092 6.023978e-002 1.723386e-002 21 1381530061 5.465153e-002 1.711654e-002 22 157511124 6.117060e-002 1.698560e-002 23 16143349 5.527407e-002 1.715977e-002 24 1155157008 3.675023e-002 1.696913e-002 25 25788210 5.788942e-002 1.726403e-002 26 1456770040 5.369305e-002 1.705579e-002 27 922599524 4.692073e-002 1.712929e-002 28 910060503 3.581060e-002 1.703201e-002 29 1036849277 4.030670e-002 1.700100e-002 30 1558644233 4.574589e-002 1.693597e-002 31 192063102 4.788970e-002 1.711121e-002 32 61275996 4.316024e-002 1.684337e-002 33 1575049278 4.300156e-002 1.714174e-002 34 339755903 4.144211e-002 1.707172e-002 35 1360647670 4.349234e-002 1.700490e-002 36 1802859403 3.111482e-002 1.698581e-002 37 2066534888 4.738526e-002 1.684565e-002 38 101044121 3.882129e-002 1.698109e-002 39 340723523 5.405427e-002 1.709808e-002 40 1321862545 4.685620e-002 1.704878e-002 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 = 0.046856 CVT ENERGY = 0.017049 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.495575 0.876794 2 0.491651 0.621154 3 0.148501 0.166523 4 0.494463 0.104830 5 0.479606 0.356519 6 0.832452 0.153836 7 0.826677 0.476616 8 0.828796 0.810716 9 0.151437 0.829226 10 0.151545 0.503779 TEST08 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1 with a different batch size. Step SEED L2-Change Energy 0 123456789 1 29242052 8.750651e-001 3.276376e-002 2 396524255 2.609642e-001 2.216674e-002 3 1804077568 2.008713e-001 2.058524e-002 4 58279807 1.406907e-001 1.936336e-002 5 890554932 1.189042e-001 1.891450e-002 6 214536894 8.826162e-002 1.856249e-002 7 1592773222 1.060953e-001 1.862238e-002 8 1874550474 9.275847e-002 1.809659e-002 9 2041615702 8.200714e-002 1.807659e-002 10 2056573688 8.889546e-002 1.805882e-002 11 1522461057 7.281421e-002 1.757247e-002 12 1338654111 7.634906e-002 1.775264e-002 13 758290347 7.814315e-002 1.756194e-002 14 1895558656 6.781088e-002 1.765224e-002 15 553115540 5.992204e-002 1.717670e-002 16 1150573110 5.737923e-002 1.744758e-002 17 1130930562 7.406204e-002 1.740633e-002 18 1398936087 6.288661e-002 1.724678e-002 19 1351174075 6.205747e-002 1.708413e-002 20 1271270653 5.276311e-002 1.742168e-002 21 383674773 6.573860e-002 1.729273e-002 22 533903734 5.604229e-002 1.736796e-002 23 412527942 5.748708e-002 1.697922e-002 24 498761874 6.100875e-002 1.711036e-002 25 1767322623 6.250668e-002 1.724441e-002 26 8802113 5.064649e-002 1.718507e-002 27 337656644 3.957797e-002 1.700340e-002 28 982491412 4.262760e-002 1.705205e-002 29 1661195312 4.706045e-002 1.710081e-002 30 1727223671 4.940814e-002 1.701330e-002 31 1934076831 4.405288e-002 1.715150e-002 32 286968437 5.782067e-002 1.713457e-002 33 1651892980 4.404639e-002 1.732191e-002 34 1093660108 5.341884e-002 1.729031e-002 35 1312296485 4.763206e-002 1.701236e-002 36 1505118054 4.162846e-002 1.730844e-002 37 1225827697 4.305559e-002 1.731370e-002 38 2103031061 4.450023e-002 1.699073e-002 39 237994259 4.330992e-002 1.714678e-002 40 308344071 4.032513e-002 1.713117e-002 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 = 0.040325 CVT ENERGY = 0.017131 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 5 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.161617 0.875273 2 0.822332 0.807007 3 0.506747 0.499076 4 0.495419 0.158325 5 0.169318 0.622788 6 0.168737 0.369471 7 0.491355 0.829847 8 0.818655 0.148630 9 0.826369 0.474470 10 0.156155 0.116276 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 8.750651e-001 3.276376e-002 2 29242052 2.718337e-001 2.204795e-002 3 29242052 1.822155e-001 2.014078e-002 4 29242052 1.355055e-001 1.932008e-002 5 29242052 1.078421e-001 1.883798e-002 6 29242052 9.185518e-002 1.851405e-002 7 29242052 8.377314e-002 1.826355e-002 8 29242052 7.956481e-002 1.803453e-002 9 29242052 6.900681e-002 1.784278e-002 10 29242052 5.608884e-002 1.770761e-002 11 29242052 4.782260e-002 1.761752e-002 12 29242052 4.522978e-002 1.754666e-002 13 29242052 4.007811e-002 1.748766e-002 14 29242052 3.456237e-002 1.744088e-002 15 29242052 3.606397e-002 1.740411e-002 16 29242052 3.235594e-002 1.737101e-002 17 29242052 3.301457e-002 1.734446e-002 18 29242052 3.200902e-002 1.731920e-002 19 29242052 3.271542e-002 1.729275e-002 20 29242052 2.975714e-002 1.726712e-002 21 29242052 2.945157e-002 1.724235e-002 22 29242052 2.935247e-002 1.721814e-002 23 29242052 3.187776e-002 1.719355e-002 24 29242052 2.874269e-002 1.716791e-002 25 29242052 2.842234e-002 1.714510e-002 26 29242052 2.950041e-002 1.712313e-002 27 29242052 2.271821e-002 1.710246e-002 28 29242052 1.815665e-002 1.708902e-002 29 29242052 1.979173e-002 1.707989e-002 30 29242052 1.654707e-002 1.706994e-002 31 29242052 1.677337e-002 1.706161e-002 32 29242052 1.345810e-002 1.705391e-002 33 29242052 9.762254e-003 1.704933e-002 34 29242052 9.673194e-003 1.704655e-002 35 29242052 8.278705e-003 1.704420e-002 36 29242052 6.875151e-003 1.704220e-002 37 29242052 6.056211e-003 1.704081e-002 38 29242052 4.384212e-003 1.703983e-002 39 29242052 3.744155e-003 1.703918e-002 40 29242052 3.729613e-003 1.703886e-002 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 = 0.003730 CVT ENERGY = 0.017039 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.159834 0.872585 2 0.819608 0.815427 3 0.514900 0.495826 4 0.499417 0.163613 5 0.168480 0.618821 6 0.176366 0.363826 7 0.504824 0.825883 8 0.820640 0.150126 9 0.841449 0.478793 10 0.154544 0.118775 TEST10 CVT computes a Centroidal Voronoi Tessellation. Compute 100 points in 3D. Step SEED L2-Change Energy 0 123456789 1 162518201 5.506854e+000 1.871594e-002 2 914652320 2.441502e+000 1.394324e-002 3 1182014520 1.712422e+000 1.323708e-002 4 734877640 1.389684e+000 1.271289e-002 5 1808590614 1.356385e+000 1.253323e-002 6 1376754667 1.268260e+000 1.235384e-002 7 39225810 1.292775e+000 1.222609e-002 8 1835665933 1.271860e+000 1.214565e-002 9 683368702 1.408191e+000 1.204733e-002 10 1192180323 1.203009e+000 1.187836e-002 11 1451564322 1.250120e+000 1.196630e-002 12 1525473369 1.129494e+000 1.182734e-002 13 1258784351 1.205712e+000 1.197831e-002 14 1939780355 1.229284e+000 1.196397e-002 15 1792150340 1.164692e+000 1.192898e-002 16 1077745899 1.170247e+000 1.175706e-002 17 1381981537 1.157098e+000 1.178390e-002 18 -11611923 1.073726e+000 1.183158e-002 19 733709902 1.140534e+000 1.169525e-002 20 1511987296 1.160646e+000 1.176203e-002 21 1849799130 1.104036e+000 1.171766e-002 22 1011187751 1.148054e+000 1.171969e-002 23 430762708 1.197869e+000 1.172928e-002 24 2076182163 1.191890e+000 1.178565e-002 25 662061697 1.182773e+000 1.175147e-002 26 253385434 1.150449e+000 1.175804e-002 27 836175832 1.258748e+000 1.167537e-002 28 529591688 1.102764e+000 1.174625e-002 29 154633765 1.116018e+000 1.162597e-002 30 778723351 1.145724e+000 1.171346e-002 31 1341651177 1.129715e+000 1.171753e-002 32 11115418 1.087813e+000 1.172714e-002 33 181250519 1.127499e+000 1.170092e-002 34 628655915 1.221128e+000 1.163178e-002 35 1574892130 1.148458e+000 1.174751e-002 36 1853258335 1.186026e+000 1.171188e-002 37 1106992749 1.150877e+000 1.157754e-002 38 2113411425 1.176883e+000 1.175095e-002 39 1552081075 1.206624e+000 1.178396e-002 40 921807728 1.114772e+000 1.166904e-002 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 = 1.114772 CVT ENERGY = 0.011669 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 First 10 generators (rows) Row: 1 2 3 Col 1 0.349426 0.912282 0.858230 2 0.453845 0.358798 0.067403 3 0.356210 0.121954 0.096372 4 0.692816 0.083540 0.620456 5 0.489219 0.753974 0.876433 6 0.086148 0.898242 0.487951 7 0.080776 0.100601 0.886353 8 0.857875 0.078377 0.100646 9 0.320329 0.891333 0.092330 10 0.498837 0.888310 0.256171 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 2.325195e-001 1.057705e-002 2 1328042058 2.504329e-001 1.106292e-002 3 1539989115 2.414177e-001 1.061145e-002 4 200382020 2.169692e-001 1.017049e-002 5 1958948863 2.166539e-001 1.003383e-002 6 691823909 2.206829e-001 1.063538e-002 7 655816003 2.168696e-001 1.082497e-002 8 450926852 2.454723e-001 1.059215e-002 9 1273398721 2.436313e-001 1.051969e-002 10 1462772409 2.462108e-001 1.023362e-002 11 1371189933 2.540012e-001 1.100644e-002 12 845524934 2.243916e-001 1.057445e-002 13 2013025619 2.169231e-001 1.064950e-002 14 1021685265 2.525485e-001 1.059082e-002 15 204970068 2.507859e-001 1.073098e-002 16 778034624 2.039930e-001 1.036695e-002 17 1938972586 2.293342e-001 1.070233e-002 18 1519833303 2.257621e-001 1.041891e-002 19 2077270047 1.890817e-001 1.037506e-002 20 1923497586 1.614823e-001 1.045228e-002 21 167698528 1.922310e-001 1.033922e-002 22 1655479938 2.076201e-001 1.029532e-002 23 475051709 1.779442e-001 1.017218e-002 24 83696007 2.149779e-001 1.024439e-002 25 1805594913 2.139327e-001 1.040388e-002 26 508154254 1.791649e-001 1.028451e-002 27 1861070898 1.928729e-001 1.057329e-002 28 1661633678 1.969875e-001 1.039508e-002 29 914834335 1.933329e-001 1.034672e-002 30 715643788 1.835640e-001 1.061701e-002 31 810642687 2.262798e-001 1.049725e-002 32 471503978 2.610075e-001 1.061374e-002 33 1019331795 2.563652e-001 1.093625e-002 34 2118751796 2.155559e-001 1.089520e-002 35 1168375939 2.548189e-001 1.087471e-002 36 26482542 2.451323e-001 1.028439e-002 37 2056065863 2.112410e-001 1.071121e-002 38 414064984 2.120556e-001 1.048878e-002 39 1342855162 1.844429e-001 1.025593e-002 40 444956424 2.228278e-001 1.005441e-002 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 = 0.222828 CVT ENERGY = 0.010054 SAMPLE = "uniform". Samples SAMPLE_NUM = 1000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 2.220446e-016 Generators (rows): Row: 1 2 Col 1 0.105670 0.123979 2 0.121099 0.402157 3 0.106924 0.640159 4 0.132602 0.892757 5 0.354508 0.116088 6 0.364220 0.305155 7 0.365729 0.568932 8 0.377942 0.865642 9 0.602325 0.122063 10 0.602441 0.367667 11 0.619698 0.625539 12 0.620221 0.878282 13 0.869419 0.099672 14 0.864519 0.346083 15 0.857674 0.578286 16 0.858781 0.844710 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+000 1.141464e-002 2 123456789 2.107204e+000 7.337538e-003 3 123456789 1.390811e+000 6.520322e-003 4 123456789 1.104628e+000 6.093849e-003 5 123456789 9.516608e-001 5.953929e-003 6 123456789 9.835673e-001 5.812519e-003 7 123456789 9.443679e-001 5.773479e-003 8 123456789 8.153409e-001 5.656700e-003 9 123456789 9.033686e-001 5.516524e-003 10 123456789 8.654526e-001 5.543751e-003 11 123456789 9.105516e-001 5.604885e-003 12 123456789 8.803876e-001 5.488901e-003 13 123456789 7.429956e-001 5.444156e-003 14 123456789 7.600265e-001 5.381034e-003 15 123456789 7.530610e-001 5.438527e-003 16 123456789 8.417234e-001 5.358096e-003 17 123456789 7.584886e-001 5.371615e-003 18 123456789 6.705096e-001 5.348151e-003 19 123456789 7.357281e-001 5.324630e-003 20 123456789 7.171119e-001 5.371430e-003 21 123456789 7.557667e-001 5.319414e-003 22 123456789 8.199987e-001 5.317007e-003 23 123456789 7.567854e-001 5.346751e-003 24 123456789 7.573236e-001 5.331317e-003 25 123456789 6.958045e-001 5.325241e-003 26 123456789 7.468962e-001 5.332247e-003 27 123456789 7.442739e-001 5.319888e-003 28 123456789 6.748831e-001 5.270517e-003 29 123456789 7.152752e-001 5.298039e-003 30 123456789 7.371427e-001 5.309481e-003 31 123456789 7.423177e-001 5.291492e-003 32 123456789 7.268626e-001 5.261994e-003 33 123456789 7.147667e-001 5.271737e-003 34 123456789 7.036994e-001 5.205256e-003 35 123456789 7.909858e-001 5.241560e-003 36 123456789 7.829487e-001 5.255926e-003 37 123456789 7.314960e-001 5.256254e-003 38 123456789 7.529876e-001 5.235219e-003 39 123456789 6.845993e-001 5.184304e-003 40 123456789 7.376803e-001 5.270458e-003 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-016 CVT_TEST Normal end of execution. 23-Jun-2005 15:16:59