23 February 2023 7:24:39.106 AM CVT_TEST FORTRAN90 version Test the CVT library. TEST01 CVT computes a Centroidal Voronoi Tessellation. Step SEED L2-Change Energy 0 123456789 0.309653E-01 1 123456789 0.626899 0.304522E-01 2 123456789 0.333360 0.210264E-01 3 123456789 0.179249 0.193221E-01 4 123456789 0.173155 0.184500E-01 5 123456789 0.118821 0.176636E-01 6 123456789 0.986684E-01 0.173446E-01 7 123456789 0.886221E-01 0.173859E-01 8 123456789 0.771003E-01 0.173894E-01 9 123456789 0.597540E-01 0.171858E-01 10 123456789 0.611275E-01 0.173404E-01 11 123456789 0.502326E-01 0.171415E-01 12 123456789 0.512062E-01 0.171416E-01 13 123456789 0.493207E-01 0.170369E-01 14 123456789 0.496932E-01 0.170388E-01 15 123456789 0.405789E-01 0.172511E-01 16 123456789 0.438412E-01 0.170764E-01 17 123456789 0.487524E-01 0.171249E-01 18 123456789 0.382920E-01 0.168852E-01 19 123456789 0.411614E-01 0.169773E-01 20 123456789 0.476885E-01 0.169003E-01 21 123456789 0.410833E-01 0.171755E-01 22 123456789 0.485684E-01 0.172373E-01 23 123456789 0.433994E-01 0.171271E-01 24 123456789 0.435961E-01 0.170640E-01 25 123456789 0.481561E-01 0.172296E-01 26 123456789 0.494649E-01 0.167943E-01 27 123456789 0.427868E-01 0.168985E-01 28 123456789 0.425736E-01 0.172508E-01 29 123456789 0.433809E-01 0.171787E-01 30 123456789 0.436435E-01 0.169902E-01 31 123456789 0.467814E-01 0.168989E-01 32 123456789 0.422945E-01 0.173279E-01 33 123456789 0.449288E-01 0.170678E-01 34 123456789 0.355023E-01 0.168250E-01 35 123456789 0.368119E-01 0.171303E-01 36 123456789 0.443622E-01 0.171304E-01 37 123456789 0.311912E-01 0.169865E-01 38 123456789 0.332591E-01 0.170208E-01 39 123456789 0.397834E-01 0.169917E-01 40 123456789 0.488425E-01 0.169274E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.488425E-01 CVT ENERGY = 0.169274E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.502931 0.476650 2 0.500514 0.151733 3 0.375878 0.815399 4 0.161266 0.161748 5 0.123515 0.830567 6 0.834608 0.498590 7 0.884272 0.832495 8 0.833689 0.165792 9 0.626485 0.826790 10 0.172241 0.490271 TEST02 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with twice the number of iterations. Step SEED L2-Change Energy 0 123456789 0.388989E-01 1 123456789 0.779924 0.376103E-01 2 123456789 0.276119 0.217688E-01 3 123456789 0.162960 0.196628E-01 4 123456789 0.132413 0.191811E-01 5 123456789 0.103897 0.186035E-01 6 123456789 0.972128E-01 0.183801E-01 7 123456789 0.899056E-01 0.181899E-01 8 123456789 0.110556 0.181437E-01 9 123456789 0.102798 0.179725E-01 10 123456789 0.837448E-01 0.177119E-01 11 123456789 0.959781E-01 0.172005E-01 12 123456789 0.680700E-01 0.171508E-01 13 123456789 0.620478E-01 0.172624E-01 14 123456789 0.619165E-01 0.173379E-01 15 123456789 0.639665E-01 0.172986E-01 16 123456789 0.496109E-01 0.173202E-01 17 123456789 0.529625E-01 0.170165E-01 18 123456789 0.515437E-01 0.169199E-01 19 123456789 0.360852E-01 0.170600E-01 20 123456789 0.455533E-01 0.169503E-01 21 123456789 0.513111E-01 0.170373E-01 22 123456789 0.517261E-01 0.171118E-01 23 123456789 0.511697E-01 0.173812E-01 24 123456789 0.519479E-01 0.170198E-01 25 123456789 0.427725E-01 0.169485E-01 26 123456789 0.361008E-01 0.168409E-01 27 123456789 0.369824E-01 0.169883E-01 28 123456789 0.424036E-01 0.170724E-01 29 123456789 0.507005E-01 0.170558E-01 30 123456789 0.470693E-01 0.169698E-01 31 123456789 0.439710E-01 0.170448E-01 32 123456789 0.468692E-01 0.170495E-01 33 123456789 0.496241E-01 0.170083E-01 34 123456789 0.467765E-01 0.168309E-01 35 123456789 0.488152E-01 0.171428E-01 36 123456789 0.371543E-01 0.168591E-01 37 123456789 0.370230E-01 0.168699E-01 38 123456789 0.464053E-01 0.169830E-01 39 123456789 0.288034E-01 0.169411E-01 40 123456789 0.318303E-01 0.171029E-01 41 123456789 0.377633E-01 0.170761E-01 42 123456789 0.582493E-01 0.171447E-01 43 123456789 0.451583E-01 0.168712E-01 44 123456789 0.453072E-01 0.169539E-01 45 123456789 0.413335E-01 0.169990E-01 46 123456789 0.533674E-01 0.170300E-01 47 123456789 0.478576E-01 0.171099E-01 48 123456789 0.473945E-01 0.169737E-01 49 123456789 0.365911E-01 0.170365E-01 50 123456789 0.422513E-01 0.169044E-01 51 123456789 0.391714E-01 0.167548E-01 52 123456789 0.460007E-01 0.170605E-01 53 123456789 0.519555E-01 0.169816E-01 54 123456789 0.471642E-01 0.168856E-01 55 123456789 0.514596E-01 0.168568E-01 56 123456789 0.532231E-01 0.170166E-01 57 123456789 0.587706E-01 0.170494E-01 58 123456789 0.426770E-01 0.171571E-01 59 123456789 0.411375E-01 0.171859E-01 60 123456789 0.536256E-01 0.169709E-01 61 123456789 0.417699E-01 0.170554E-01 62 123456789 0.454906E-01 0.170667E-01 63 123456789 0.275929E-01 0.170795E-01 64 123456789 0.417500E-01 0.168215E-01 65 123456789 0.394484E-01 0.169807E-01 66 123456789 0.576185E-01 0.169456E-01 67 123456789 0.575046E-01 0.171261E-01 68 123456789 0.543838E-01 0.170097E-01 69 123456789 0.402995E-01 0.170338E-01 70 123456789 0.327700E-01 0.172000E-01 71 123456789 0.420735E-01 0.171228E-01 72 123456789 0.357255E-01 0.169655E-01 73 123456789 0.383456E-01 0.170631E-01 74 123456789 0.412302E-01 0.170700E-01 75 123456789 0.540705E-01 0.170708E-01 76 123456789 0.477442E-01 0.169785E-01 77 123456789 0.548851E-01 0.170743E-01 78 123456789 0.412059E-01 0.170746E-01 79 123456789 0.416868E-01 0.169647E-01 80 123456789 0.419516E-01 0.168760E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 80 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 80 Difference IT_DIFF = 0.419516E-01 CVT ENERGY = 0.168760E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.880799 0.495410 2 0.499267 0.166256 3 0.117319 0.512585 4 0.368107 0.498318 5 0.835206 0.164915 6 0.834855 0.837116 7 0.631777 0.491899 8 0.162665 0.837850 9 0.502662 0.834908 10 0.168664 0.161318 TEST03 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with 100 times the sample points. Step SEED L2-Change Energy 0 123456789 0.269723E-01 1 123456789 0.557218 0.269801E-01 2 123456789 0.212266 0.205959E-01 3 123456789 0.149199 0.195835E-01 4 123456789 0.119363 0.191274E-01 5 123456789 0.973404E-01 0.188120E-01 6 123456789 0.835490E-01 0.185717E-01 7 123456789 0.755622E-01 0.183390E-01 8 123456789 0.735176E-01 0.181571E-01 9 123456789 0.726375E-01 0.179776E-01 10 123456789 0.725528E-01 0.178008E-01 11 123456789 0.664360E-01 0.176091E-01 12 123456789 0.598064E-01 0.174428E-01 13 123456789 0.504177E-01 0.173476E-01 14 123456789 0.445584E-01 0.172443E-01 15 123456789 0.352932E-01 0.172008E-01 16 123456789 0.288555E-01 0.171504E-01 17 123456789 0.265722E-01 0.171264E-01 18 123456789 0.224613E-01 0.171307E-01 19 123456789 0.201902E-01 0.171122E-01 20 123456789 0.169308E-01 0.171045E-01 21 123456789 0.133671E-01 0.170910E-01 22 123456789 0.123598E-01 0.170737E-01 23 123456789 0.126802E-01 0.170754E-01 24 123456789 0.108653E-01 0.170645E-01 25 123456789 0.111761E-01 0.170815E-01 26 123456789 0.967168E-02 0.170595E-01 27 123456789 0.844013E-02 0.170825E-01 28 123456789 0.502410E-02 0.170559E-01 29 123456789 0.688919E-02 0.170697E-01 30 123456789 0.586087E-02 0.170590E-01 31 123456789 0.645252E-02 0.170673E-01 32 123456789 0.574556E-02 0.170737E-01 33 123456789 0.483364E-02 0.170689E-01 34 123456789 0.534995E-02 0.170760E-01 35 123456789 0.543969E-02 0.170770E-01 36 123456789 0.416501E-02 0.170647E-01 37 123456789 0.640085E-02 0.170686E-01 38 123456789 0.511635E-02 0.170748E-01 39 123456789 0.406420E-02 0.170720E-01 40 123456789 0.708420E-02 0.170503E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.708420E-02 CVT ENERGY = 0.170503E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 1000000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.820073 0.627427 2 0.830839 0.878310 3 0.829603 0.121463 4 0.163848 0.166335 5 0.491301 0.166740 6 0.482192 0.501311 7 0.491848 0.834864 8 0.160382 0.499467 9 0.164743 0.832738 10 0.819745 0.371966 TEST04 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with Halton sampling. Step SEED L2-Change Energy 0 123456789 0.355763E-01 1 123466789 0.989280 0.355806E-01 2 123476789 0.327804 0.213721E-01 3 123486789 0.147472 0.197398E-01 4 123496789 0.105265 0.193291E-01 5 123506789 0.104984 0.190319E-01 6 123516789 0.103312 0.186477E-01 7 123526789 0.857844E-01 0.182689E-01 8 123536789 0.798406E-01 0.179652E-01 9 123546789 0.714230E-01 0.176886E-01 10 123556789 0.586510E-01 0.174965E-01 11 123566789 0.561437E-01 0.173723E-01 12 123576789 0.451151E-01 0.172648E-01 13 123586789 0.399465E-01 0.171984E-01 14 123596789 0.341265E-01 0.171737E-01 15 123606789 0.267409E-01 0.171270E-01 16 123616789 0.202665E-01 0.171176E-01 17 123626789 0.218955E-01 0.170977E-01 18 123636789 0.182991E-01 0.170910E-01 19 123646789 0.148562E-01 0.170860E-01 20 123656789 0.135339E-01 0.170821E-01 21 123666789 0.101624E-01 0.170698E-01 22 123676789 0.903745E-02 0.170779E-01 23 123686789 0.106074E-01 0.170707E-01 24 123696789 0.783264E-02 0.170636E-01 25 123706789 0.821664E-02 0.170705E-01 26 123716789 0.813565E-02 0.170701E-01 27 123726789 0.606320E-02 0.170659E-01 28 123736789 0.599618E-02 0.170659E-01 29 123746789 0.814500E-02 0.170626E-01 30 123756789 0.718348E-02 0.170728E-01 31 123766789 0.621050E-02 0.170529E-01 32 123776789 0.629991E-02 0.170660E-01 33 123786789 0.617592E-02 0.170679E-01 34 123796789 0.600866E-02 0.170614E-01 35 123806789 0.637180E-02 0.170658E-01 36 123816789 0.869658E-02 0.170625E-01 37 123826789 0.643572E-02 0.170637E-01 38 123836789 0.569350E-02 0.170629E-01 39 123846789 0.683016E-02 0.170610E-01 40 123856789 0.701682E-02 0.170624E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123866789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.701682E-02 CVT ENERGY = 0.170624E-01 SAMPLE = "halton". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.877304 0.831942 2 0.626400 0.820056 3 0.498106 0.159669 4 0.121959 0.829685 5 0.832515 0.165344 6 0.165523 0.164003 7 0.835486 0.493753 8 0.167434 0.491354 9 0.502648 0.481885 10 0.372419 0.819790 TEST05 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with grid sampling. Step SEED L2-Change Energy 0 123456789 0.320416E-01 1 123466789 0.801231 0.320416E-01 2 123476789 0.319949 0.225430E-01 3 123486789 0.178649 0.209683E-01 4 123496789 0.153657 0.201960E-01 5 123506789 0.130076 0.196154E-01 6 123516789 0.107179 0.192177E-01 7 123526789 0.922659E-01 0.189519E-01 8 123536789 0.778452E-01 0.187687E-01 9 123546789 0.695532E-01 0.186354E-01 10 123556789 0.646459E-01 0.185283E-01 11 123566789 0.627720E-01 0.184252E-01 12 123576789 0.685447E-01 0.182992E-01 13 123586789 0.730444E-01 0.181100E-01 14 123596789 0.726695E-01 0.178759E-01 15 123606789 0.675346E-01 0.176571E-01 16 123616789 0.596666E-01 0.174833E-01 17 123626789 0.521624E-01 0.173568E-01 18 123636789 0.436571E-01 0.172690E-01 19 123646789 0.387980E-01 0.172074E-01 20 123656789 0.345097E-01 0.171630E-01 21 123666789 0.278235E-01 0.171311E-01 22 123676789 0.250888E-01 0.171101E-01 23 123686789 0.199620E-01 0.170944E-01 24 123696789 0.173858E-01 0.170844E-01 25 123706789 0.144436E-01 0.170763E-01 26 123716789 0.116735E-01 0.170711E-01 27 123726789 0.963962E-02 0.170679E-01 28 123736789 0.874556E-02 0.170656E-01 29 123746789 0.687047E-02 0.170637E-01 30 123756789 0.522524E-02 0.170623E-01 31 123766789 0.387249E-02 0.170617E-01 32 123776789 0.347416E-02 0.170613E-01 33 123786789 0.229822E-02 0.170610E-01 34 123796789 0.387128E-02 0.170607E-01 35 123806789 0.274987E-02 0.170600E-01 36 123816789 0.128376E-02 0.170599E-01 37 123826789 0.392348E-03 0.170598E-01 38 123836789 0.374642E-03 0.170598E-01 39 123846789 0.382880E-03 0.170598E-01 40 123856789 0.439432E-06 0.170598E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123866789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.439432E-06 CVT ENERGY = 0.170598E-01 SAMPLE = "grid". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.626748 0.182378 2 0.835333 0.504972 3 0.163416 0.829068 4 0.122798 0.164278 5 0.877414 0.166938 6 0.165682 0.497579 7 0.830295 0.835000 8 0.373921 0.182063 9 0.492315 0.843102 10 0.501979 0.524642 TEST06 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, with FORTRAN90 RANDOM_NUMBER sampling. Step SEED L2-Change Energy 0 123456789 0.299730E-01 1 123476789 0.743591 0.299479E-01 2 123496789 0.304349 0.213489E-01 3 123516789 0.200073 0.193618E-01 4 123536789 0.167340 0.189370E-01 5 123556789 0.144201 0.182186E-01 6 123576789 0.100361 0.177140E-01 7 123596789 0.945832E-01 0.174637E-01 8 123616789 0.705362E-01 0.176416E-01 9 123636789 0.651153E-01 0.176142E-01 10 123656789 0.538522E-01 0.174616E-01 11 123676789 0.503282E-01 0.172410E-01 12 123696789 0.451019E-01 0.173175E-01 13 123716789 0.457586E-01 0.171584E-01 14 123736789 0.453307E-01 0.171920E-01 15 123756789 0.579677E-01 0.169978E-01 16 123776789 0.454601E-01 0.170668E-01 17 123796789 0.652983E-01 0.171392E-01 18 123816789 0.570474E-01 0.171013E-01 19 123836789 0.460068E-01 0.170850E-01 20 123856789 0.399093E-01 0.169071E-01 21 123876789 0.540915E-01 0.171639E-01 22 123896789 0.320336E-01 0.169509E-01 23 123916789 0.385751E-01 0.171671E-01 24 123936789 0.529251E-01 0.171323E-01 25 123956789 0.445995E-01 0.171730E-01 26 123976789 0.315478E-01 0.170467E-01 27 123996789 0.334742E-01 0.170078E-01 28 124016789 0.393387E-01 0.172723E-01 29 124036789 0.461537E-01 0.169625E-01 30 124056789 0.525241E-01 0.170206E-01 31 124076789 0.358139E-01 0.170527E-01 32 124096789 0.550281E-01 0.170654E-01 33 124116789 0.397081E-01 0.170333E-01 34 124136789 0.341034E-01 0.168864E-01 35 124156789 0.345508E-01 0.168057E-01 36 124176789 0.371303E-01 0.170254E-01 37 124196789 0.426709E-01 0.172106E-01 38 124216789 0.522805E-01 0.170384E-01 39 124236789 0.408595E-01 0.171365E-01 40 124256789 0.474518E-01 0.170835E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 124276789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.474518E-01 CVT ENERGY = 0.170835E-01 SAMPLE = "RANDOM". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.168698 0.509780 2 0.124349 0.174344 3 0.159475 0.837861 4 0.832792 0.500941 5 0.509557 0.523488 6 0.873790 0.169313 7 0.826324 0.832787 8 0.623062 0.178687 9 0.492598 0.840338 10 0.371270 0.177303 TEST07 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1, but with a different seed. Step SEED L2-Change Energy 0 987654321 0.314361E-01 1 987654321 0.890939 0.315186E-01 2 987654321 0.267732 0.207514E-01 3 987654321 0.207604 0.190462E-01 4 987654321 0.152801 0.183660E-01 5 987654321 0.117438 0.178097E-01 6 987654321 0.747526E-01 0.173048E-01 7 987654321 0.882475E-01 0.176734E-01 8 987654321 0.633264E-01 0.173796E-01 9 987654321 0.703072E-01 0.173834E-01 10 987654321 0.490918E-01 0.171459E-01 11 987654321 0.438028E-01 0.173200E-01 12 987654321 0.541599E-01 0.173010E-01 13 987654321 0.562244E-01 0.169875E-01 14 987654321 0.485277E-01 0.172295E-01 15 987654321 0.398894E-01 0.168992E-01 16 987654321 0.522472E-01 0.172667E-01 17 987654321 0.381642E-01 0.173176E-01 18 987654321 0.566715E-01 0.170587E-01 19 987654321 0.443775E-01 0.170111E-01 20 987654321 0.423596E-01 0.171101E-01 21 987654321 0.435313E-01 0.171986E-01 22 987654321 0.482575E-01 0.171659E-01 23 987654321 0.443399E-01 0.172604E-01 24 987654321 0.519207E-01 0.171185E-01 25 987654321 0.582495E-01 0.172172E-01 26 987654321 0.408642E-01 0.173608E-01 27 987654321 0.402890E-01 0.169678E-01 28 987654321 0.324952E-01 0.171226E-01 29 987654321 0.424608E-01 0.169649E-01 30 987654321 0.469679E-01 0.171011E-01 31 987654321 0.494555E-01 0.169245E-01 32 987654321 0.364986E-01 0.170210E-01 33 987654321 0.410905E-01 0.170554E-01 34 987654321 0.309487E-01 0.171198E-01 35 987654321 0.430866E-01 0.172107E-01 36 987654321 0.357008E-01 0.170324E-01 37 987654321 0.445298E-01 0.170062E-01 38 987654321 0.403370E-01 0.170388E-01 39 987654321 0.551248E-01 0.171645E-01 40 987654321 0.521584E-01 0.170787E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 987654321 Current SEED = 987654321 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.521584E-01 CVT ENERGY = 0.170787E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.504557 0.523567 2 0.165985 0.507049 3 0.499915 0.846417 4 0.841136 0.503603 5 0.377621 0.186535 6 0.169389 0.838216 7 0.876287 0.164834 8 0.125348 0.160314 9 0.632668 0.179557 10 0.831147 0.829668 TEST08 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1 with a different batch size. Step SEED L2-Change Energy 0 123456789 0.504028E-01 1 123456789 1.18902 0.501524E-01 2 123456789 0.439099 0.235011E-01 3 123456789 0.234601 0.196552E-01 4 123456789 0.169189 0.185123E-01 5 123456789 0.101754 0.177894E-01 6 123456789 0.874745E-01 0.178054E-01 7 123456789 0.823466E-01 0.176380E-01 8 123456789 0.720376E-01 0.176680E-01 9 123456789 0.778495E-01 0.173715E-01 10 123456789 0.689574E-01 0.171744E-01 11 123456789 0.609331E-01 0.174273E-01 12 123456789 0.598857E-01 0.173004E-01 13 123456789 0.499592E-01 0.172859E-01 14 123456789 0.559534E-01 0.175031E-01 15 123456789 0.589863E-01 0.172122E-01 16 123456789 0.487777E-01 0.173168E-01 17 123456789 0.486323E-01 0.173984E-01 18 123456789 0.759187E-01 0.173011E-01 19 123456789 0.519319E-01 0.173001E-01 20 123456789 0.724578E-01 0.171663E-01 21 123456789 0.449968E-01 0.172479E-01 22 123456789 0.545972E-01 0.172769E-01 23 123456789 0.482941E-01 0.171645E-01 24 123456789 0.513264E-01 0.170652E-01 25 123456789 0.373017E-01 0.172029E-01 26 123456789 0.466438E-01 0.171118E-01 27 123456789 0.394256E-01 0.171927E-01 28 123456789 0.396037E-01 0.169876E-01 29 123456789 0.429809E-01 0.170704E-01 30 123456789 0.446512E-01 0.170351E-01 31 123456789 0.479208E-01 0.171182E-01 32 123456789 0.295683E-01 0.168824E-01 33 123456789 0.353942E-01 0.170422E-01 34 123456789 0.297183E-01 0.170224E-01 35 123456789 0.261977E-01 0.171394E-01 36 123456789 0.492206E-01 0.169950E-01 37 123456789 0.331691E-01 0.170341E-01 38 123456789 0.343094E-01 0.170195E-01 39 123456789 0.415086E-01 0.170562E-01 40 123456789 0.331345E-01 0.169568E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.331345E-01 CVT ENERGY = 0.169568E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 5 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.834523 0.506064 2 0.632740 0.186993 3 0.165111 0.506128 4 0.376120 0.170794 5 0.500504 0.843181 6 0.171984 0.833735 7 0.495551 0.517184 8 0.121238 0.171509 9 0.877376 0.166408 10 0.833345 0.837859 TEST09 CVT computes a Centroidal Voronoi Tessellation. Repeat test 1 with a fixed sample set. (IT_FIXED = IT_MAX) Step SEED L2-Change Energy 0 123456789 0.279353E-01 1 123456789 0.689189 0.284959E-01 2 123456789 0.365141 0.211311E-01 3 123456789 0.157289 0.189142E-01 4 123456789 0.120268 0.187069E-01 5 123456789 0.122469 0.181857E-01 6 123456789 0.121413 0.179826E-01 7 123456789 0.101458 0.177775E-01 8 123456789 0.933646E-01 0.176100E-01 9 123456789 0.914125E-01 0.175732E-01 10 123456789 0.612889E-01 0.172871E-01 11 123456789 0.542542E-01 0.170511E-01 12 123456789 0.479794E-01 0.171860E-01 13 123456789 0.484514E-01 0.172495E-01 14 123456789 0.564077E-01 0.172399E-01 15 123456789 0.517314E-01 0.169728E-01 16 123456789 0.630367E-01 0.171257E-01 17 123456789 0.467054E-01 0.171127E-01 18 123456789 0.563344E-01 0.170851E-01 19 123456789 0.464270E-01 0.170478E-01 20 123456789 0.557953E-01 0.170437E-01 21 123456789 0.415276E-01 0.169475E-01 22 123456789 0.492741E-01 0.171916E-01 23 123456789 0.502052E-01 0.171163E-01 24 123456789 0.464374E-01 0.170074E-01 25 123456789 0.487008E-01 0.170411E-01 26 123456789 0.431032E-01 0.171541E-01 27 123456789 0.362987E-01 0.168340E-01 28 123456789 0.363105E-01 0.171246E-01 29 123456789 0.339911E-01 0.170278E-01 30 123456789 0.347254E-01 0.169577E-01 31 123456789 0.504406E-01 0.169896E-01 32 123456789 0.410187E-01 0.170704E-01 33 123456789 0.541705E-01 0.170724E-01 34 123456789 0.419117E-01 0.171617E-01 35 123456789 0.386910E-01 0.171242E-01 36 123456789 0.485863E-01 0.171196E-01 37 123456789 0.405567E-01 0.169897E-01 38 123456789 0.337415E-01 0.169916E-01 39 123456789 0.457094E-01 0.169777E-01 40 123456789 0.479067E-01 0.171901E-01 Dimension DIM_NUM = 2 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 40 Iterations IT_NUM = 40 Difference IT_DIFF = 0.479067E-01 CVT ENERGY = 0.171901E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 2 Col 1 0.826477 0.165401 2 0.837508 0.838684 3 0.636122 0.514747 4 0.165597 0.842371 5 0.366999 0.503794 6 0.884461 0.492920 7 0.501480 0.170297 8 0.167061 0.165005 9 0.497736 0.844446 10 0.117858 0.498658 TEST10 CVT computes a Centroidal Voronoi Tessellation. Compute 100 points in 3D. Step SEED L2-Change Energy 0 123456789 0.179281E-01 1 123456789 5.20125 0.180420E-01 2 123456789 2.41681 0.137024E-01 3 123456789 1.72576 0.127096E-01 4 123456789 1.36720 0.125813E-01 5 123456789 1.39327 0.125439E-01 6 123456789 1.31984 0.122243E-01 7 123456789 1.33693 0.121054E-01 8 123456789 1.20248 0.120558E-01 9 123456789 1.25401 0.120953E-01 10 123456789 1.15025 0.119923E-01 11 123456789 1.27693 0.120258E-01 12 123456789 1.12159 0.120019E-01 13 123456789 1.17203 0.119942E-01 14 123456789 1.13643 0.119237E-01 15 123456789 1.11621 0.119364E-01 16 123456789 1.18993 0.117298E-01 17 123456789 1.20263 0.118509E-01 18 123456789 1.19009 0.117629E-01 19 123456789 1.13520 0.117471E-01 20 123456789 1.14139 0.118798E-01 21 123456789 1.10632 0.117817E-01 22 123456789 1.11240 0.117525E-01 23 123456789 1.18218 0.118084E-01 24 123456789 1.18627 0.117343E-01 25 123456789 1.27526 0.117504E-01 26 123456789 1.07190 0.117207E-01 27 123456789 1.19097 0.117961E-01 28 123456789 1.14487 0.116820E-01 29 123456789 1.18546 0.117438E-01 30 123456789 1.23016 0.116652E-01 31 123456789 1.18173 0.116839E-01 32 123456789 1.09200 0.116960E-01 33 123456789 1.16242 0.115905E-01 34 123456789 1.10359 0.116428E-01 35 123456789 1.13251 0.115614E-01 36 123456789 1.05424 0.116483E-01 37 123456789 1.04327 0.117023E-01 38 123456789 1.09263 0.116688E-01 39 123456789 1.19258 0.115670E-01 40 123456789 1.12047 0.116541E-01 Dimension DIM_NUM = 3 Number of points N = 100 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 1.12047 CVT ENERGY = 0.116541E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 First 10 generators (rows): Row 1 2 3 Col 1 0.310292 0.262859 0.908770 2 0.383753 0.902663E-01 0.902876 3 0.277239 0.330217 0.923308E-01 4 0.992077E-01 0.691575 0.498114 5 0.581671 0.273855 0.902990 6 0.112833 0.720655 0.262540 7 0.904695 0.984514E-01 0.702951 8 0.670459 0.355804 0.351942 9 0.894996 0.384418 0.908782 10 0.250455 0.729198 0.899403 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 0.107239E-01 1 123456789 0.193841 0.102667E-01 2 123456789 0.176473 0.110316E-01 3 123456789 0.181849 0.107059E-01 4 123456789 0.210508 0.104309E-01 5 123456789 0.268044 0.106943E-01 6 123456789 0.268401 0.106489E-01 7 123456789 0.227885 0.104571E-01 8 123456789 0.143400 0.106020E-01 9 123456789 0.229708 0.106397E-01 10 123456789 0.202934 0.108563E-01 11 123456789 0.229310 0.104794E-01 12 123456789 0.200854 0.104062E-01 13 123456789 0.207097 0.104136E-01 14 123456789 0.197173 0.106641E-01 15 123456789 0.222943 0.107843E-01 16 123456789 0.202348 0.108131E-01 17 123456789 0.189209 0.105490E-01 18 123456789 0.214377 0.105999E-01 19 123456789 0.205336 0.105050E-01 20 123456789 0.246058 0.104379E-01 21 123456789 0.230879 0.107006E-01 22 123456789 0.181404 0.104217E-01 23 123456789 0.198231 0.997274E-02 24 123456789 0.217976 0.104736E-01 25 123456789 0.219134 0.105213E-01 26 123456789 0.179569 0.108127E-01 27 123456789 0.186392 0.103875E-01 28 123456789 0.219970 0.104553E-01 29 123456789 0.204658 0.107711E-01 30 123456789 0.201979 0.106392E-01 31 123456789 0.201496 0.107810E-01 32 123456789 0.208053 0.102581E-01 33 123456789 0.213850 0.105519E-01 34 123456789 0.211321 0.104928E-01 35 123456789 0.153917 0.102799E-01 36 123456789 0.243760 0.998903E-02 37 123456789 0.203771 0.105015E-01 38 123456789 0.217544 0.102113E-01 39 123456789 0.228163 0.107092E-01 40 123456789 0.240069 0.106517E-01 Dimension DIM_NUM = 2 Number of points N = 16 Initial SEED = 123456789 Current SEED = 123456789 INIT = "user initialization". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.240069 CVT ENERGY = 0.106517E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 1000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 Final generators (rows): Row 1 2 Col 1 0.132035 0.135589 2 0.124071 0.382855 3 0.131457 0.621367 4 0.131116 0.869593 5 0.387561 0.105600 6 0.364861 0.330320 7 0.356145 0.577322 8 0.374200 0.872383 9 0.630539 0.131226 10 0.631729 0.408182 11 0.620166 0.633348 12 0.628275 0.904972 13 0.869548 0.119567 14 0.854760 0.366171 15 0.863646 0.625513 16 0.872711 0.886868 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_INIT = 100000 Print output values of SEED and R #3. We expect that: * the values of R #1 and R #2 differ; AND * the values of R #1 and R #3 agree. Step SEED L2-Change Energy 0 100000 0.319453E-01 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 = 0.00000 CVT ENERGY = 0.319453E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 R #1: Row 1 2 Col 1 0.178011 0.267496 2 0.899398 0.178154 3 0.376843 0.169492 4 0.432013 0.686540 5 0.648466 0.377665 6 0.420190 0.807298 7 0.667322 0.363600 8 0.396627 0.564998 9 0.888168 0.766650 10 0.592999 0.234742 Step SEED L2-Change Energy 0 200000 0.344387E-01 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 = 0.00000 CVT ENERGY = 0.344387E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 R #2: Row 1 2 Col 1 0.948561E-01 0.504447 2 0.898758 0.849051 3 0.661362 0.268806 4 0.967167 0.761997E-01 5 0.409146 0.432786 6 0.255507 0.113727 7 0.167391 0.979560 8 0.744060 0.178568 9 0.728129 0.147244 10 0.223265E-01 0.736878 Step SEED L2-Change Energy 0 100000 0.410327E-01 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 = 0.00000 CVT ENERGY = 0.410327E-01 SAMPLE = "uniform". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 R #3: Row 1 2 Col 1 0.554354 0.148290E-01 2 0.479255E-01 0.734321 3 0.357638 0.437615E-02 4 0.689398 0.830134 5 0.802367 0.694300 6 0.913008 0.409996 7 0.984027 0.177370 8 0.691596E-01 0.484429 9 0.748005 0.920220 10 0.876088 0.606742 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 0.120696E-01 1 123456789 4.16632 0.122075E-01 2 123456789 1.84420 0.719082E-02 3 123456789 1.35847 0.638428E-02 4 123456789 1.10058 0.605507E-02 5 123456789 1.01612 0.601544E-02 6 123456789 0.952513 0.578869E-02 7 123456789 0.933908 0.572262E-02 8 123456789 0.810550 0.568430E-02 9 123456789 0.788747 0.562584E-02 10 123456789 0.808379 0.564353E-02 11 123456789 0.790244 0.554961E-02 12 123456789 0.777324 0.556115E-02 13 123456789 0.767064 0.551105E-02 14 123456789 0.765591 0.553735E-02 15 123456789 0.837265 0.552551E-02 16 123456789 0.788357 0.552606E-02 17 123456789 0.822884 0.548284E-02 18 123456789 0.803051 0.542590E-02 19 123456789 0.744782 0.542518E-02 20 123456789 0.744412 0.538152E-02 21 123456789 0.798655 0.538707E-02 22 123456789 0.848725 0.532967E-02 23 123456789 0.820204 0.538200E-02 24 123456789 0.729948 0.530233E-02 25 123456789 0.757121 0.542066E-02 26 123456789 0.722383 0.533660E-02 27 123456789 0.719867 0.534191E-02 28 123456789 0.780688 0.538110E-02 29 123456789 0.702055 0.527690E-02 30 123456789 0.690733 0.531988E-02 31 123456789 0.758666 0.534935E-02 32 123456789 0.713943 0.531964E-02 33 123456789 0.760731 0.530406E-02 34 123456789 0.768463 0.532686E-02 35 123456789 0.814998 0.531395E-02 36 123456789 0.733817 0.528586E-02 37 123456789 0.698367 0.526637E-02 38 123456789 0.709448 0.529320E-02 39 123456789 0.743764 0.528756E-02 40 123456789 0.739103 0.526694E-02 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 = 0.739103 CVT ENERGY = 0.526694E-02 SAMPLE = "user". Samples SAMPLE_NUM = 10000 Sampling BATCH size = 1000 EPSILON (unit roundoff) = 0.222045E-15 TEST14 Generate a CVT in the interval [0,1] using 10 points. Step SEED L2-Change Energy 0 123456789 0.369834E-02 1 123456789 0.294600 0.371336E-02 2 123456789 0.112191 0.126089E-02 3 123456789 0.614857E-01 0.101379E-02 4 123456789 0.395585E-01 0.935609E-03 5 123456789 0.273259E-01 0.907696E-03 6 123456789 0.240368E-01 0.891746E-03 7 123456789 0.188019E-01 0.876279E-03 8 123456789 0.161800E-01 0.872246E-03 9 123456789 0.152048E-01 0.862968E-03 10 123456789 0.135003E-01 0.857039E-03 11 123456789 0.114068E-01 0.854058E-03 12 123456789 0.974312E-02 0.852868E-03 13 123456789 0.824073E-02 0.849850E-03 14 123456789 0.889674E-02 0.847703E-03 15 123456789 0.750491E-02 0.845280E-03 16 123456789 0.670571E-02 0.843591E-03 17 123456789 0.738866E-02 0.843781E-03 18 123456789 0.578677E-02 0.844018E-03 19 123456789 0.464059E-02 0.838509E-03 20 123456789 0.599915E-02 0.837435E-03 21 123456789 0.563044E-02 0.838350E-03 22 123456789 0.425478E-02 0.834801E-03 23 123456789 0.375355E-02 0.834402E-03 24 123456789 0.376236E-02 0.840915E-03 25 123456789 0.488278E-02 0.836907E-03 26 123456789 0.386346E-02 0.835219E-03 27 123456789 0.344887E-02 0.836220E-03 28 123456789 0.442241E-02 0.830742E-03 29 123456789 0.305833E-02 0.830203E-03 30 123456789 0.488219E-02 0.833496E-03 31 123456789 0.267105E-02 0.840660E-03 32 123456789 0.341262E-02 0.835322E-03 33 123456789 0.379842E-02 0.835705E-03 34 123456789 0.321761E-02 0.835360E-03 35 123456789 0.312761E-02 0.837221E-03 36 123456789 0.266631E-02 0.832149E-03 37 123456789 0.345492E-02 0.831623E-03 38 123456789 0.215419E-02 0.836560E-03 39 123456789 0.229869E-02 0.833935E-03 40 123456789 0.360041E-02 0.833767E-03 Dimension DIM_NUM = 1 Number of points N = 10 Initial SEED = 123456789 Current SEED = 123456789 INIT = "uniform". Max iterations IT_MAX = 40 IT_FIXED (fixed samples) 1 Iterations IT_NUM = 40 Difference IT_DIFF = 0.360041E-02 CVT ENERGY = 0.833767E-03 SAMPLE = "uniform". Samples SAMPLE_NUM = 100000 Sampling BATCH size = 10000 EPSILON (unit roundoff) = 0.222045E-15 Generators (rows): Row 1 Col 1 0.742992 2 0.484093E-01 3 0.339613 4 0.143931 5 0.241127 6 0.948686 7 0.438349 8 0.640890 9 0.845812 10 0.539358 CVT_TEST Normal end of execution. 23 February 2023 7:24:45.709 AM