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I have data of the form:

x1 y1
x2 y2
...

where each cuople x, y represents a point in the 2D plane.

I need a histogram of the point spread in the y-direction (eg. bin all points with similar y-value). This would be a projection on the y-axis, that is then turned into a histogram.

How would I go about this using gnuplot?

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So what you want is: how many points have the y-value equals to y for each y in the data set? –  cYrus Mar 24 '12 at 15:02
    
now just a histogram of the y values. –  romeovs Mar 24 '12 at 15:18
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1 Answer

There is no straightforward way to make an actual histogram, as this is not simply a plotting task but requires that the data be first sorted and binned. You can do that outside of gnuplot and plot the result from gnuplot simply with plot 'file' with histo.

Nevertheless, there are two main ways to do what you want entirely within gnuplot.

This first is an old trick that forces gnuplot to bin and sort the data for you using a little math and the smooth freq style. If your datafile is called "data" you can do:

w = 5
bin(x,wth) = width*floor(x/wth)
plot 'data' using (bin($2,bw)):(1.0) smooth freq with boxes

This works but has all the disadvantages of histograms, mainly that the appearance of your distribution will depend on your chosen bin width, which you can assign to "w" in the first line.

Recent (> = 4.4) releases of gnuplot can calculate a kernel density estimate, which is like a bin-independent histogram: it gives you a continuous distribution. Also, it does the binning and sorting for you! You just need to say

plot 'data' using 2:(.001) smooth kden

The .001 above will give you a normalized distribution if you have 1000 data points. You will want to substitute the reciprocal of the number of data points you have (or don't bother if you don't care whether your result is normalized).

I recommend the latter method if you have a recent version of gnuplot installed. There is a little more about this in my book about gnuplot, which just came out.

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