Producing a histogram in Matlab with out using Hist

Question

I am using histograms in Matlab to look at the distribution of some data from my experiments. I want to find the mean distribution (mean height of the bars) from a group of tests then produce an average histogram.

By using this code:

data = zeros(26,31);

for i = 1:length(files6)
    x = csvread(files6(i).name);
    
    x = x(1:end,:);
    time = x(:,1);
    variable = x(:,3);
    
    thing(:,1) = x(:,1);
    thing(:,2) = x(:,3);
    figure()
    binCenter = {0:tbinstep:tbinend 0:varbinstep:varbinend};
    hist3(thing, 'Ctrs', binCenter, 'CDataMode','auto','FaceColor','interp');
    colorbar
    
    [N,C] = hist3(thing, 'Ctrs', binCenter);
    data = data + N;
    
    clearvars x time variable
end
    
avedata = data / i;

I can find the mean of N, which will be the Z value for the plot (histogram) I want, and I have X,Y (which are the same for all tests) from:

x = 0:tbinstep:tbinend;
y = 0:varbinstep:varbinend;

But how do I bring these together to make the graphical out that shows the average height of the bars? I can't use hist3 again as that will just calculate the distribution of avedata.

AT THE RISK OF STARTING AN XY PROBLEM using bar3 has been suggested, but that asks the question "how do I go from 2 vectors and a matrix to 1 matrix bar3 can handle? I.e. how do I plot x(1), y(1), avedata(1,1) and so on for all the data points in avedata?"

TIA

Answer 1

By looking at hist3 source code in matlab r2014b, it has his own plotting implemented inside that prepares data and plot it using surf method. Here is a function that reproduce the same output highly inspired from the hist3 function with your options ('CDataMode','auto','FaceColor','interp'). You can put this in a new file called hist3plot.m:

function [ h ] = hist3plot( N, C )
%HIST3PLOT Summary of this function goes here
%   Detailed explanation goes here

xBins = C{1};
yBins = C{2};

% Computing edges and width
nbins = [length(xBins), length(yBins)];
xEdges = [0.5*(3*xBins(1)-xBins(2)), 0.5*(xBins(2:end)+xBins(1:end-1)), 0.5*(3*xBins(end)-xBins(end-1))];
yEdges = [0.5*(3*yBins(1)-yBins(2)), 0.5*(yBins(2:end)+yBins(1:end-1)), 0.5*(3*yBins(end)-yBins(end-1))];
xWidth = xEdges(2:end)-xEdges(1:end-1);
yWidth = yEdges(2:end)-yEdges(1:end-1);
del = .001; % space between bars, relative to bar size
% Build x-coords for the eight corners of each bar.
xx = xEdges;
xx = [xx(1:nbins(1))+del*xWidth; xx(2:nbins(1)+1)-del*xWidth];
xx = [reshape(repmat(xx(:)',2,1),4,nbins(1)); NaN(1,nbins(1))];
xx = [repmat(xx(:),1,4) NaN(5*nbins(1),1)];
xx = repmat(xx,1,nbins(2));
% Build y-coords for the eight corners of each bar.
yy = yEdges;
yy = [yy(1:nbins(2))+del*yWidth; yy(2:nbins(2)+1)-del*yWidth];
yy = [reshape(repmat(yy(:)',2,1),4,nbins(2)); NaN(1,nbins(2))];
yy = [repmat(yy(:),1,4) NaN(5*nbins(2),1)];
yy = repmat(yy',nbins(1),1);
% Build z-coords for the eight corners of each bar.
zz = zeros(5*nbins(1), 5*nbins(2));
zz(5*(1:nbins(1))-3, 5*(1:nbins(2))-3) = N;
zz(5*(1:nbins(1))-3, 5*(1:nbins(2))-2) = N;
zz(5*(1:nbins(1))-2, 5*(1:nbins(2))-3) = N;
zz(5*(1:nbins(1))-2, 5*(1:nbins(2))-2) = N;
% Plot the bars in a light steel blue.
cc = repmat(cat(3,.75,.85,.95), [size(zz) 1]);
% Plot the surface
h = surf(xx, yy, zz, cc, 'CDataMode','auto','FaceColor','interp');
% Setting x-axis and y-axis limits
xlim([yBins(1)-yWidth(1) yBins(end)+yWidth(end)]) % x-axis limit
ylim([xBins(1)-xWidth(1) xBins(end)+xWidth(end)]) % y-axis limit

end

You can then call this function when you want to plot outputs from Matlab's hist3 function. Note that this can handle non uniform positionning of bins:

close all; clear all;

data = rand(10000,2);
xBins = [0,0.1,0.3,0.5,0.6,0.8,1];
yBins = [0,0.1,0.3,0.5,0.6,0.8,1];

figure()
hist3(data, {xBins yBins}, 'CDataMode','auto','FaceColor','interp')
title('Using hist3')

figure()
[N,C] = hist3(data, {xBins yBins});
hist3plot(N, C); % The function is called here
title('Using hist3plot')

Here is a comparison of the two outputs:

Answer 2

So if I understand your question and code correctly, you are plotting the distribution of multiple experiments' data as histograms, then you want to calculate the average shape of all the previous histograms.

I usually avoid giving approaches the asker isn't explicitly asking for, but for this one I must comment that it is a very strange thing to do. I've never heard of calculating the average shape of multiple histograms before. So just in case, you could simply append all your experiment's data into a single variable, and plot a normalized histogram of that using histogram2. This code outputs a relative frequency histogram. (Other normalization methods)

% Append all data in a single matrix
x = []
for i = 1:length(files6)
    x = [x; csvread(files6(i).name)];
end

% Plot normalized bivariate histogram, normalized
xEdges = 0:tbinstep:tbinend;
yEdges = 0:varbinstep:varbinend;
histogram2(x(:,1), x(:,3), xEdges, yEdges, 'Normalize', 'Probability')

---

Now, if you really are looking to draw the average shape of multiple histograms, then yes, use bar3. Since bar3 doesn't accept an (x,y) value argument, you can follow the other answer, or modify the XTickLabel and YTickLabel property to match whatever your bin range is, afterwards.

... % data = yourAverageData;

% Save axis handle to `h`
h = bar3(data);

% Set property of axis
h.XTickLabels = 0:tbinstep:tbinend;
h.YTickLabels = 0:varbinstep:varbinend;