I'm attempting to generate a 3D histogram for a large set of two-dimensional coordinates ($\approx 10^7$). the x- and y-components of each coordinate are rounded to the nearest integer, and these rounded values are used as indices in a histogram matrix counting the number of coordinates rounded to the same integer values.

For example, if we have some list of elements:


We would add $+2$ to position {102, 101} in the histogram matrix, and $+1$ to the position {500, 2761}.

Here's the piece of code I'm running:

ElementList = Table[{RandomReal[{1, 2000}], RandomReal[{1, 2000}]}, {x, 1, 10^7}];

HistogramDimX = 2000;
HistogramDimY = HistogramDimX;

ImageMatrix = Array[0 &, Length[ElementList]];
ImageMatrixHistogram = Array[0 &, {HistogramDimX, HistogramDimY}];

For[i = 1, i <= Length[ElementList], i++,

RoundedCoordinate = Round[ElementList[[i]]];
Round[RoundedCoordinate[[2]]]]] += 1;


MatrixPlot[ImageMatrixHistogram, ColorFunctionScaling -> True, MaxPlotPoints -> 10^12]

This takes 94.7 seconds to run on a single X5690 3.47 GHz Intel Xeon(R) CPU. Is there a way to significantly speed this process up, and use a more efficient data structure that scales proportionally with the number of elements in ElementList rather than the dimensions of the histogram matrix (i.e. HistogramDimX & HistogramDimY)? I suppose I'd very much like the output to look something like the output of MatrixPlot in the above example.

Directly applying MatrixPlot to the data works terribly, which I suppose is due to some auto-interpolation occurring.

  • $\begingroup$ How about MatrixPlot[HistogramList[ElementList, {1, 2000, 1}][[2]]]? But do you really want a 2000x2000 image? $\endgroup$ – Sjoerd C. de Vries Jul 8 '13 at 21:27
  • $\begingroup$ @SjoerdC.deVries I need an image of that size - however, I'm wondering, do I also need a matrix of that size as a data structure? $\endgroup$ – WTP Jul 8 '13 at 22:02
  • $\begingroup$ Using my answer to this question: Plotting large datasets, you get a very fast result: Colorize[Image[ImageMatrixHistogram, ImageSize -> 800], ColorFunction -> "TemperatureMap"]. So I think this question is a duplicate of the linked one. $\endgroup$ – Jens Jul 8 '13 at 22:28
  • $\begingroup$ @Jens Reviewing your answer in the question, I agree with your assessment. Nice work. $\endgroup$ – WTP Jul 8 '13 at 22:45