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ListPlot3D equal distance between ticks

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123203] ListPlot3D equal distance between ticks
  • From: Reuben Trapdoor <reubentrapdoor at gmail.com>
  • Date: Sat, 26 Nov 2011 05:08:25 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Greetings,

I'm trying to create a ListPlot3D similiar to this plot:
http://ec2-46-51-156-184.eu-west-1.compute.amazonaws.com/plot.pdf

The data I'm using for this looks like this:

data={{64,4,886442},{64,8,1185834},{64,16,1413761},{64,32,1898121},
{64,64,2399946},
{128,4,972785},{128,8,1371712},{128,16,1686386},{128,32,2101359},
{128,64,2299103},{128,128,2774413},
{256,4,1049274},{256,8,1530701},{256,16,1939484},{256,32,2337994},
{256,64,2702634},{256,128,2983199},{256,256,2929728},
{512,4,1073619},{512,8,1616539},{512,16,2024052},{512,32,2502566},
{512,64,2829915},{512,128,3146670},{512,256,3262064},
{512,512,2887220},
{1024,4,1086305},{1024,8,1650442},{1024,16,2121919},{1024,32,2583900},
{1024,64,2942022},{1024,128,3207567},{1024,256,3282425},
{1024,512,3156755},{1024,1024,2555417},
{2048,4,1073467},{2048,8,1660245},{2048,16,2100079},{2048,32,2537572},
{2048,64,2875243},{2048,128,3073723},{2048,256,3104566},
{2048,512,2964345},{2048,1024,2506901},{2048,2048,1714511},
{4096,4,1033969},{4096,8,1528609},{4096,16,1890461},{4096,32,2252783},
{4096,64,2491328},{4096,128,2640815},{4096,256,2635402},
{4096,512,2562866},{4096,1024,2145756},{4096,2048,1733719},
{4096,4096,1428083},
{8192,4,998199},{8192,8,1386424},{8192,16,1685432},{8192,32,1971052},
{8192,64,2156951},{8192,128,2262451},{8192,256,2304342},
{8192,512,2258912},{8192,1024,1940664},{8192,2048,1631496},
{8192,4096,1596806},{8192,8192,1445765},
{16384,4,978483},{16384,8,1333778},{16384,16,1606614},
{16384,32,1865958},{16384,64,2033732},{16384,128,2131524},
{16384,256,2175623},{16384,512,2153382},{16384,1024,1877695},
{16384,2048,1595343},{16384,4096,1568972},{16384,8192,1572797},
{16384,16384,1490747},
{32768,64,1610544},{32768,128,1696389},{32768,256,1722995},
{32768,512,1668664},{32768,1024,1602488},{32768,2048,1366884},
{32768,4096,1367506},{32768,8192,1321937},{32768,16384,1364166},
{65536,64,204449},{65536,128,191577},{65536,256,189472},
{65536,512,185264},{65536,1024,185199},{65536,2048,179748},
{65536,4096,181658},{65536,8192,181922},{65536,16384,181214},
{131072,64,115968},{131072,128,113258},{131072,256,113912},
{131072,512,114549},{131072,1024,113049},{131072,2048,112721},
{131072,4096,112474},{131072,8192,113360},{131072,16384,113072},
{262144,64,96775},{262144,128,96559},{262144,256,95376},
{262144,512,96565},{262144,1024,95877},{262144,2048,95397},
{262144,4096,95393},{262144,8192,96221},{262144,16384,96566},
{524288,64,88793},{524288,128,88772},{524288,256,88736},
{524288,512,88827},{524288,1024,88946},{524288,2048,88239},
{524288,4096,88660},{524288,8192,88474},{524288,16384,88666},
{1048576,64,85800},{1048576,128,85825},{1048576,256,85842},
{1048576,512,85808},{1048576,1024,85763},{1048576,2048,85723},
{1048576,4096,85651},{1048576,8192,85784},{1048576,16384,85697}};

And by using:
ListPointPlot3D[data,AxesLabel->{"File size (KB)","Record
size(KB)","Speed (KB/s)"},ColorFunction->Function[{x,y,z},Hue[z]],
Ticks-
>{{64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576},
{4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384},
{500000,1000000,1500000,2000000,2500000,3000000,3500000}}]

Result: http://ec2-46-51-156-184.eu-west-1.compute.amazonaws.com/plot2.pdf
I get a plot that doesn't show all the data, due to the exponential
distance between each datapoint. All the data below x=131072 doesn't
show at all, there is just a grey flat area there. Furthermore the z
axis doesn't show any ticks at all. So I'm wondering if there is a way
I can make the distance between each of these ticks the same length,
as they would in excel. I havent been able to find a log axis version
of ListPlot3D for example.

I also tried to change the data to look like this:

data={{1,1,886442},{1,2,1185834},{1,3,1413761},{1,4,1898121},
{1,5,2399946},
{2,1,972785},{2,2,1371712},{2,3,1686386},{2,4,2101359},{2,5,2299103},
{2,6,2774413},
{3,1,1049274},{3,2,1530701},{3,3,1939484},{3,4,2337994},{3,5,2702634},
{3,6,2983199},{3,7,2929728},
{4,1,1073619},{4,2,1616539},{4,3,2024052},{4,4,2502566},{4,5,2829915},
{4,6,3146670},{4,7,3262064},{4,8,2887220},
{5,1,1086305},{5,2,1650442},{5,3,2121919},{5,4,2583900},{5,5,2942022},
{5,6,3207567},{5,7,3282425},{5,8,3156755},{5,9,2555417},
{6,1,1073467},{6,2,1660245},{6,3,2100079},{6,4,2537572},{6,5,2875243},
{6,6,3073723},{6,7,3104566},{6,8,2964345},{6,9,2506901},
{6,10,1714511},
{7,1,1033969},{7,2,1528609},{7,3,1890461},{7,4,2252783},{7,5,2491328},
{7,6,2640815},{7,7,2635402},{7,8,2562866},{7,9,2145756},{7,10,1733719},
{7,11,1428083},
{8,1,998199},{8,2,1386424},{8,3,1685432},{8,4,1971052},{8,5,2156951},
{8,6,2262451},{8,7,2304342},{8,8,2258912},{8,9,1940664},{8,10,1631496},
{8,11,1596806},{8,12,1445765},
{9,1,978483},{9,2,1333778},{9,3,1606614},{9,4,1865958},{9,5,2033732},
{9,6,2131524},{9,7,2175623},{9,8,2153382},{9,9,1877695},{9,10,1595343},
{9,11,1568972},{9,12,1572797},{9,13,1490747},
{10,1,0},{10,2,0},{10,3,0},{10,4,0},{10,5,1610544},{10,6,1696389},
{10,7,1722995},{10,8,1668664},{10,9,1602488},{10,10,1366884},
{10,11,1367506},{10,12,1321937},{10,13,1364166},
{11,1,0},{11,2,0},{11,3,0},{11,4,0},{11,5,204449},{11,6,191577},
{11,7,189472},{11,8,185264},{11,9,185199},{11,10,179748},
{11,11,181658},{11,12,181922},{11,13,181214},
{12,1,0},{12,2,0},{12,3,0},{12,4,0},{12,5,115968},{12,6,113258},
{12,7,113912},{12,8,114549},{12,9,113049},{12,10,112721},
{12,11,112474},{12,12,113360},{12,13,113072},
{13,1,0},{13,2,0},{13,3,0},{13,4,0},{13,5,96775},{13,6,96559},
{13,7,95376},{13,8,96565},{13,9,95877},{13,10,95397},{13,11,95393},
{13,12,96221},{13,13,96566},
{14,1,0},{14,2,0},{14,3,0},{14,4,0},{14,5,88793},{14,6,88772},
{14,7,88736},{14,8,88827},{14,9,88946},{14,10,88239},{14,11,88660},
{14,12,88474},{14,13,88666},
{15,1,0},{15,2,0},{15,3,0},{15,4,0},{15,5,85800},{15,6,85825},
{15,7,85842},{15,8,85808},{15,9,85763},{15,10,85723},{15,11,85651},
{15,12,85784},{15,13,85697}};

And by using
ListPlot3D[data,  AxesLabel -> {"File size (KB)", "Record size(KB)",
"Speed (KB/s)"}, ColorFunction -> Function[{x, y, z}, Hue[z]],
Ticks -> {{64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768,
65536, 131072, 262144, 524288, 1048576}, {4, 8, 16, 32, 64, 128, 256,
512, 1024, 2048, 4096, 8192, 16384}, {500000, 1000000, 1500000,
2000000, 2500000, 3000000, 3500000}}]

Results: http://ec2-46-51-156-184.eu-west-1.compute.amazonaws.com/plot1.pdf
Which gives me a useable plot, however all the x and y axis ticks are
incorrect of course. Does anyone have a suggestion for solving this
problem? Note that I have to create more than 20 plots like this so
changing the data as little as possible would be best.

Thanks in advance for any suggestions.



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