3D Histgram plot for [N,M] Matrix, visualize result monte carlo simulation

Dear all,

I have a question about the visualization of a matrix created by the use of a monte carlo analysis.

With the use of a monte carlo analysis for different cases ( different angle of the cone of a structure) a Matrix of 31*1000 has been created. For this example 1000 times the calculation result of the monte carlo simulation. And 31 times a different angle of the cone, 30 degrees till 60 degrees.

Now i would like to create a 3D histogram to visualize the results compared to eachother. For now i have: A=[31,1000] hist(A(1,:),30)

Which result in the histogram i like, the results of the monte carlo nicely stored in 30 bars. but only for angle 1 (30 deg).

I would like a z-axis (3D) to visualize the other angles of the histogram. Kind of a surf(A) commmand but then histograms. The hist3(A) command doesnt give the pleased result (only 2 columns possible) but gives an indication of how i would like my histgram 3D visualization.

I hope i'm clear enough. Can anyone help me with this one?

Answer 1

[arich82]

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');

Please accept this answer if it helps, or let me know in the comments if I've missed something.

[Niels van Dijk]

 Dear Arich82,

The visualization of this example is exactly what i'm looking for!

Unfortunately i can't manage to implement your guidelines correctly.

What am i doing wrong in my code? The input value is Fh_u, this is a matrix of 31*100000 Where 31 are the cone angles. And 100000 the number of simulations.

The code for the plot i have now is as follows:

figure (4)

bx1 = subplot(2,2,1);

edges = [1500000:2000000:2500000]; I dont know if correctly stated now, values of the simulation vary from 1.5 - 2.5 *10^6 Newton._

counts = histc(Fh_u,edges);

bar3(edges,counts);

grid on;

grid minor;

h = findobj(gca,'Type','patch');

h.FaceColor = [0 0.5 0.5];

h.EdgeColor = 'w';

title('Upward bending - F_h')

zlabel('Count')

ylabel('Newton')

xlabel('Angle of Cone')

Answer 2

[Mike Garrity]

Is histogram2 what you're looking for?

[Niels van Dijk]

Hi Mike, thank you for your quick reply. Tonight i will continue work on this project and sort it out. So let me get back at you then.

[A Lotgering]

Hi Mike Garrity, thanks again for your quick reply! I'm Alex his team mate for this assignment. I think we have to give some additional information because I think the histogram2 plot is not the one we are looking for.

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

If you take axis x,y,z. Horizontal x-axis is for the data stored in the N columns. vertical y-axis is for the frequency of those values to create a histogram (we call this 2D). Horizontal z-axis is for the 30 different cases for which we like to create a similar histogram in de x and y-axis.

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

[Mike Garrity]

I'm not quite sure I'm following. Do you mean something like this?

% Generate some fake data
npts = 1000;
data = zeros(30,npts);
for i=1:30
  data(i,:) = rand(1)*(randn(1,npts)-1) + rand(1)*(randn(1,npts)+1);
end

If so, the bad news is that I ran into a number of bugs trying to create this. The histogram object wasn't really happy with what I was trying to do to it. Here's what I came up with, but it's kind of lame.

% Create 30 histograms and rotate them into place
max_val = 0;
for i=1:30
  g = hgtransform('Matrix',makehgtform('translate',[0 i 0], ...
                                       'xrotate',pi/2));
  if i==1
      hold on
  end
  h = histogram(data(i,:),'BinWidth',.2,'FaceAlpha',1);
  h.Parent = g;
  max_val = max(max_val,max(h.Values));
end

% Setup axes correctly
set(gca,'SortMethod','depth')
xlim([-pi pi])
ylim([1 30])
zlim([0 max_val])
view(3)
xlabel('Value')
ylabel('Series')
zlabel('Probability')
box on

It might make more sense to use histcounts with bar3 or waterfall if this is the sort of thing you're after.