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plotting - Make a density list plot/histogram from large, pre-binned data set?


I have a large data set consisting of O(109) two-dimensional points. In order to save memory and time I have pre-binned these into a uniform grid of 500×500 bins using Fortran. When imported into Mathematica 8.0 as a table the resulting data look like:



data = {{0.388348, 0.388349, 9},{0.388348, 0.776699, 23},...},



where the first two items of each entry correspond to the x-y-coordinates of the upper-right-hand corner of the bin and the third is the count.


Edit:





  • For a sample of the raw data, raw=RandomReal[1,{1000000000,2}] is a good approximation. This is obviously unworkable.




  • For the binned data: binned=Table[{.01*Ceiling[raw[[i,1]]/.01],.01*Ceiling[raw[[i,2]]/.01],RandomInteger[1000]},{i,1,250000}].




I would like to plot this pre-binned data set in the form of a DensityHistogram, but my data format doesn't fit into what this function is expecting. I have reviewed a similar question for one-dimensional histograms at Histograms with pre-counted data, however I'm at a loss as to how to apply this to 2-D. I have also looked at doing




Image[Rescale[data]]



on the raw data. However, this crashes immediately with a SIGSEGV error that has the Wolfram Support team puzzled. Consequently, I haven't gone very far down this road.


Edit:



  • I have also tried ListDensityPlot[data,InterpolationOrder->0]. For the full data set, Mathematica hangs for over 10 minutes, at which point it runs out of memory and the kernel shuts down. For a subset of the data, I get something more reasonable, but I would need some way to scale this up to 5002 data points.


Making these plots seem to be something that is fairly easily done in Matplotlib, but I have already made some other plots in Mathematica and don't want to mess with different styles. I'm fairly new to Mathematica and don't have a good knowledge of all the functionality, unfortunately.


So, how can I make a DensityHistogram when the bins and counts have already been calculated?




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