December 4 2002 10:36:21.399 AM CVT_SIZE_PRB A sample problem for the probabilistic sized Centroidal Voronoi Tesselation algorithm. Given a region in 2D, the problem is to determine GENERATORS, a set of points which define a division of the region into Voronoid cells, which are also CENTROIDS of the Voronoi cells, and which have a certain SIZE. Geometry parameters: ------------------- The spatial dimension is DIM_NUM = 2 The minimum corner of the bounding box is: 0.0000 0.0000 The maximum corner of the bounding box is: 10.0000 10.0000 CVT Algorithm parameters: ------------------------- The number of Voronoi cells to generate: 11 Number of iterations to determine CVT: 1 Number of sampling points: 5500 Voronoi cell generators are initialized by RANDOM_NUMBER. The desired CVT cell volumes and initial weights are: 1 0.488520E-01 0.935974E-02 2 0.977040E-01 0.132367E-01 3 0.195408 0.187195E-01 4 0.390816 0.264733E-01 5 0.781632 0.374389E-01 6 1.56326 0.529467E-01 7 3.12653 0.748779E-01 8 6.25305 0.105893 9 12.5061 0.149756 10 25.0122 0.211787 11 50.0244 0.299512 Nearest Neighbor Search parameters: ----------------------------------- The nearest neighbor search is not speeded up. The nearest neighbor search is done by exhaustion. Miscellaneous parameters: ------------------------ Generator and moment output files WILL be written. RANDOM_INITIALIZE Initialize RANDOM_NUMBER with arbitrary SEED = 635924994 Initializing the cell generators. Carry out the CVT iteration. Area iteration 1 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.935974E-02 2 0.977040E-01 0.909091E-01 0.132367E-01 3 0.195408 0.109091 0.187195E-01 4 0.390816 0.454545 0.264733E-01 5 0.781632 0.527273 0.374389E-01 6 1.56326 1.98182 0.529467E-01 7 3.12653 3.25455 0.748779E-01 8 6.25305 7.85455 0.105893 9 12.5061 12.2545 0.149756 10 25.0122 22.8727 0.211787 11 50.0244 50.6000 0.299512 Area discrepancy = 5.57474 Area iteration 2 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.116483E-01 2 0.977040E-01 0.545455E-01 0.136622E-01 3 0.195408 0.127273 0.232966E-01 4 0.390816 0.454545 0.244397E-01 5 0.781632 1.09091 0.453833E-01 6 1.56326 1.18182 0.468179E-01 7 3.12653 2.20000 0.730683E-01 8 6.25305 6.60000 0.940684E-01 9 12.5061 14.3818 0.150621 10 25.0122 26.6364 0.220498 11 50.0244 47.2727 0.296496 Area discrepancy = 8.43963 Area iteration 3 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.143703E-01 2 0.977040E-01 0.254545 0.168548E-01 3 0.195408 0.672727 0.284899E-01 4 0.390816 0.309091 0.223659E-01 5 0.781632 1.01818 0.379138E-01 6 1.56326 2.56364 0.531431E-01 7 3.12653 3.29091 0.859691E-01 8 6.25305 5.72727 0.903674E-01 9 12.5061 12.3455 0.138622 10 25.0122 25.2909 0.210881 11 50.0244 48.5273 0.301022 Area discrepancy = 4.62833 Area iteration 4 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.183912E-01 2 0.977040E-01 0.727273E-01 0.106913E-01 3 0.195408 0.127273 0.157208E-01 4 0.390816 0.418182 0.257491E-01 5 0.781632 0.890909 0.340109E-01 6 1.56326 1.43636 0.424881E-01 7 3.12653 2.78182 0.857923E-01 8 6.25305 5.98182 0.966755E-01 9 12.5061 12.2182 0.142848 10 25.0122 25.6909 0.214716 11 50.0244 50.3818 0.312917 Area discrepancy = 2.34546 Area iteration 5 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.226734E-01 2 0.977040E-01 0.127273 0.122218E-01 3 0.195408 0.200000 0.192121E-01 4 0.390816 0.472727 0.245507E-01 5 0.781632 0.600000 0.314195E-01 6 1.56326 1.49091 0.437168E-01 7 3.12653 2.60000 0.897041E-01 8 6.25305 6.41818 0.974862E-01 9 12.5061 13.2727 0.142537 10 25.0122 24.4000 0.208953 11 50.0244 50.4182 0.307525 Area discrepancy = 2.88316 Area iteration 6 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.363636E-01 0.280106E-01 2 0.977040E-01 0.727273E-01 0.105833E-01 3 0.195408 0.181818 0.187684E-01 4 0.390816 0.363636 0.220618E-01 5 0.781632 1.05455 0.354423E-01 6 1.56326 1.43636 0.442420E-01 7 3.12653 3.25455 0.972194E-01 8 6.25305 6.50909 0.950997E-01 9 12.5061 11.5455 0.136743 10 25.0122 24.4182 0.209086 11 50.0244 51.1273 0.302743 Area discrepancy = 3.51963 Area iteration 7 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.127273 0.322847E-01 2 0.977040E-01 0.727273E-01 0.121981E-01 3 0.195408 0.272727 0.193484E-01 4 0.390816 0.309091 0.227435E-01 5 0.781632 0.618182 0.303428E-01 6 1.56326 1.38182 0.458970E-01 7 3.12653 3.63636 0.947555E-01 8 6.25305 6.14545 0.926896E-01 9 12.5061 12.3818 0.141523 10 25.0122 24.8182 0.210431 11 50.0244 50.2364 0.297786 Area discrepancy = 1.75503 Area iteration 8 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.201829E-01 2 0.977040E-01 0.145455 0.142664E-01 3 0.195408 0.236364 0.165259E-01 4 0.390816 0.309091 0.258056E-01 5 0.781632 0.818182 0.344280E-01 6 1.56326 1.94545 0.492594E-01 7 3.12653 2.61818 0.886575E-01 8 6.25305 6.63636 0.943438E-01 9 12.5061 12.6909 0.143519 10 25.0122 25.5636 0.213164 11 50.0244 49.0364 0.299847 Area discrepancy = 3.25397 Area iteration 9 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.545455E-01 0.251429E-01 2 0.977040E-01 0.909091E-01 0.116527E-01 3 0.195408 0.145455 0.149751E-01 4 0.390816 0.672727 0.289188E-01 5 0.781632 1.12727 0.335359E-01 6 1.56326 1.80000 0.440065E-01 7 3.12653 4.03636 0.965536E-01 8 6.25305 6.25455 0.912676E-01 9 12.5061 11.7091 0.141986 10 25.0122 24.4545 0.210137 11 50.0244 49.6545 0.301824 Area discrepancy = 3.56262 Area iteration 10 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.727273E-01 0.242147E-01 2 0.977040E-01 0.127273 0.122937E-01 3 0.195408 0.254545 0.176635E-01 4 0.390816 0.436364 0.224310E-01 5 0.781632 0.418182 0.284183E-01 6 1.56326 1.40000 0.417348E-01 7 3.12653 2.87273 0.864782E-01 8 6.25305 5.89091 0.928681E-01 9 12.5061 13.5636 0.149330 10 25.0122 25.8000 0.216272 11 50.0244 49.1636 0.308296 Area discrepancy = 4.00689 Area iteration 11 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.363636E-01 0.198427E-01 2 0.977040E-01 0.545455E-01 0.107696E-01 3 0.195408 0.200000 0.154738E-01 4 0.390816 0.254545 0.212246E-01 5 0.781632 0.709091 0.355172E-01 6 1.56326 1.07273 0.440941E-01 7 3.12653 2.54545 0.902029E-01 8 6.25305 6.50909 0.956647E-01 9 12.5061 12.4000 0.143367 10 25.0122 24.1636 0.212910 11 50.0244 52.0545 0.310933 Area discrepancy = 4.58150 Area iteration 12 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.727273E-01 0.223788E-01 2 0.977040E-01 0.200000 0.130990E-01 3 0.195408 0.127273 0.148827E-01 4 0.390816 0.454545 0.255901E-01 5 0.781632 0.854545 0.362841E-01 6 1.56326 2.45455 0.517940E-01 7 3.12653 3.21818 0.972740E-01 8 6.25305 5.58182 0.912358E-01 9 12.5061 12.2364 0.140097 10 25.0122 25.8364 0.210775 11 50.0244 48.9636 0.296590 Area discrepancy = 4.13981 Area iteration 13 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.163636 0.185838E-01 2 0.977040E-01 0.545455E-01 0.927651E-02 3 0.195408 0.218182 0.186848E-01 4 0.390816 0.327273 0.240421E-01 5 0.781632 0.981818 0.351605E-01 6 1.56326 1.30909 0.418808E-01 7 3.12653 3.76364 0.971465E-01 8 6.25305 6.87273 0.978426E-01 9 12.5061 13.0727 0.143505 10 25.0122 24.8909 0.210128 11 50.0244 48.3455 0.303749 Area discrepancy = 4.32230 Area iteration 14 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.103118E-01 2 0.977040E-01 0.363636E-01 0.117759E-01 3 0.195408 0.200000 0.179577E-01 4 0.390816 0.345455 0.266811E-01 5 0.781632 0.600000 0.318596E-01 6 1.56326 1.85455 0.464778E-01 7 3.12653 2.92727 0.899194E-01 8 6.25305 5.29091 0.947783E-01 9 12.5061 12.0727 0.142543 10 25.0122 24.3636 0.213914 11 50.0244 52.3091 0.313782 Area discrepancy = 5.16108 Area iteration 15 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.00000 0.126691E-01 2 0.977040E-01 0.727273E-01 0.144679E-01 3 0.195408 0.309091 0.174465E-01 4 0.390816 0.454545 0.278931E-01 5 0.781632 0.745455 0.357411E-01 6 1.56326 1.40000 0.419416E-01 7 3.12653 3.09091 0.913388E-01 8 6.25305 7.40000 0.101273 9 12.5061 12.4000 0.142596 10 25.0122 25.8545 0.213033 11 50.0244 48.2727 0.301601 Area discrepancy = 4.33338 Area iteration 16 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.909091E-01 0.158685E-01 2 0.977040E-01 0.290909 0.168032E-01 3 0.195408 0.727273E-01 0.139000E-01 4 0.390816 0.454545 0.259163E-01 5 0.781632 0.781818 0.366722E-01 6 1.56326 1.45455 0.444094E-01 7 3.12653 3.07273 0.920496E-01 8 6.25305 5.81818 0.932827E-01 9 12.5061 11.4909 0.143494 10 25.0122 23.5818 0.209958 11 50.0244 52.8909 0.307646 Area discrepancy = 6.33132 Area iteration 17 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.545455E-01 0.116306E-01 2 0.977040E-01 0.363636E-01 0.973639E-02 3 0.195408 0.163636 0.173721E-01 4 0.390816 0.381818 0.240269E-01 5 0.781632 0.909091 0.366617E-01 6 1.56326 1.41818 0.460316E-01 7 3.12653 3.10909 0.928366E-01 8 6.25305 7.45455 0.966900E-01 9 12.5061 13.4182 0.149674 10 25.0122 26.3091 0.216196 11 50.0244 46.7455 0.299144 Area discrepancy = 7.08720 Area iteration 18 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.363636E-01 0.110599E-01 2 0.977040E-01 0.909091E-01 0.122292E-01 3 0.195408 0.272727 0.190754E-01 4 0.390816 0.272727 0.244256E-01 5 0.781632 0.854545 0.341585E-01 6 1.56326 1.50909 0.485619E-01 7 3.12653 3.32727 0.935455E-01 8 6.25305 6.14545 0.889828E-01 9 12.5061 11.5818 0.145195 10 25.0122 24.0727 0.211817 11 50.0244 51.8364 0.310950 Area discrepancy = 4.32583 Area iteration 19 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.109091 0.127469E-01 2 0.977040E-01 0.127273 0.126065E-01 3 0.195408 0.236364 0.160555E-01 4 0.390816 0.781818 0.290744E-01 5 0.781632 0.690909 0.324846E-01 6 1.56326 2.05455 0.491471E-01 7 3.12653 2.81818 0.901683E-01 8 6.25305 5.74545 0.892524E-01 9 12.5061 13.6545 0.150026 10 25.0122 25.1455 0.214693 11 50.0244 48.6364 0.303745 Area discrepancy = 4.58946 Area iteration 20 Desired, Actual, Linear Cell Volume Volume Weight 1 0.488520E-01 0.181818E-01 0.865125E-02 2 0.977040E-01 0.727273E-01 0.112024E-01 3 0.195408 0.163636 0.148059E-01 4 0.390816 0.400000 0.208484E-01 5 0.781632 0.654545 0.350426E-01 6 1.56326 1.29091 0.434795E-01 7 3.12653 2.87273 0.963228E-01 8 6.25305 6.14545 0.944348E-01 9 12.5061 12.2727 0.145619 10 25.0122 24.4364 0.217167 11 50.0244 51.6727 0.312427 Area discrepancy = 3.31497 Cell generators: 1 0.930961E+01 0.587414E+01 2 0.657194E+01 0.127021E+01 3 0.335935E+01 0.980036E+01 4 0.967309E+01 0.308059E+00 5 0.166957E+01 0.558304E+01 6 0.559921E+00 0.536808E+01 7 0.736179E+00 0.953238E+00 8 0.846299E+01 0.109992E+01 9 0.151743E+01 0.805269E+01 10 0.317022E+01 0.240721E+01 11 0.680426E+01 0.629256E+01 Cell volumes: 1 0.181818E-01 2 0.727273E-01 3 0.163636E+00 4 0.400000E+00 5 0.654545E+00 6 0.129091E+01 7 0.287273E+01 8 0.614545E+01 9 0.122727E+02 10 0.244364E+02 11 0.516727E+02 CVT_SIZE_PRB Normal end of execution. December 4 2002 10:37:06.481 AM