Plot histogram for multiple cases in 3 dimensions

Hi, I'm Alex and I would like to ask a question regarding the possibilities of a histogram plot.

I like to plot a "2D" histogram from a 30 by N matrix. In this 30 by N matrix data from a Monte Carlo simulation is stored for 30 different cases. The data stored in de N colums can be used for the "2D" histogram plot. However, there comes the problem. I like to plot a "2D" histogram of every case into one single '3D' plot.

If you take axis x,y,z. The plot would be something like: Horizontal x-axis is for the data stored in the N columns (Data from Monte Carlo simulation). The Vertical y-axis is for the frequency of those values to create a histogram (I call this 2D). The Horizontal z-axis is for the 30 different cases for which I like to create a similar histogram in the x- and y-axis.

The confusion is the way "2D" or "3D" histograms work. I'm not interested in a comparison histogram between the values of every case. I simply want to show every histogram into one single figure so I can show the trent between the different cases.

Thanks in advance!

Is this even possible with histograms or should we use a different plot style?

Answer 1

[Satyajeet Sasmal]

Hi Andy,

Have you tried using the "hist3" and bar3 functions? Please see the sample code below:

vec_x = [1 2 4 5 7 8 9 3 8 7 2]';

vec_y = [1 3 9 5 7 8 1 3 2 9 2]';

vec_bin_edges = 0:9;

hist3([vec_x vec_y], 'Edges', {vec_bin_edges, vec_bin_edges});

mat_joint = hist3([vec_x vec_y], 'Edges', {vec_bin_edges, vec_bin_edges});

figure

bar3(mat_joint, 1);

axis tight

Here are the documentation links for bar3 and hist3 respectively:

http://www.mathworks.com/help/matlab/ref/bar3.html

http://www.mathworks.com/help/stats/hist3.html

-Satya

Answer 2

[A Lotgering]

I found the answer:

The following worked for me. It seems like you just want a histogram for each of the 30 cases. If so, this is done very simply using histc and bar3 (essentially just two lines of code; three if you don't use the default edges):

rng(0);
% make dummy data
ncases = 30;
N = 1000;
data = NaN(ncases, N);
for k = 1:ncases
    % generate a dummy random-normal distribution
    % with random mean and random standard deviation
    data(k, :) = rand(1) + rand(1)*randn(N, 1);
end
% generate data for histograms: 1 histogram per column
edges = [-5:0.5:5]; % bin edges
counts = histc(data, edges, 2); % specify dim 2 to act column-wise
% plot results
hf = figure;
ha = axes;
hb = bar3(edges, counts.'); % note the transpose to get the colors right
xlabel('case number')
ylabel('bins');
zlabel('count');

[Image Analyst]

That's actually a 2-D histogram. There are two dimensions, two independent axes. One called bins and one called "case number" - that's two. It's being displayed as a perspective plot where the third dimension a height representing the value of the histogram, but it's still a 2-D plot because there are two independent dimensions -- two indexes to the histogram array.

If you want a third dimension, you could perhaps use scatter3 where you plot markers in 3-D (again, a perspective graph) where the marker size or marker color represents the value of the histogram at that 3-D location.

[Belal Essam]

Thank you @A Lotgering.