3D Histogram from raw data

I am trying to create the a rainflow matrix out of time history of a load data. I can do it easily with the rainflow command but I am trying to learn how I can produce it myself. It is basically a 3D Histogram of three variables ( Mean, Range and Cycle count , random X,Y and Z let's say )

This is what a rainflow matrix looks like for reference.

For any dataset with X,Y and Z data, I undertand that the first step is to discretize X and Y . What I do not understand is how I can allot the Z value to each bins and ultimately plot something like this.

Answer 1

[Mathieu NOE]

hello

see example below - this is equivalent to hist3

% dummy data (col vectors)
x = rand(100,1);
y = rand(100,1);
z = rand(100,1);

%% bin the data (Hist3 clone)
nBins = 10; %number of bins (there will be nBins + 1 edges)
XEdge = linspace(min(x),max(x),nBins+1); 
YEdge = linspace(min(y),max(y),nBins+1); 
[~, xBin] = histc(x, XEdge);
[~, yBin] = histc(y, YEdge);
% count number of elements per (x,y) pair
[xIdx, yIdx] = meshgrid(1:nBins, 1:nBins); 
xyPairs = [xIdx(:), yIdx(:)]; 
Z = zeros(size(xyPairs,1),1); 
for i = 1:size(xyPairs,1)
    Z(i) = sum(ismember([xBin, yBin], xyPairs(i,:), 'rows')); 
end
% Reshape nPerBin to grid size
Z = reshape(Z, [nBins, nBins]);

% plot data 
figure(1)
b = bar3(Z);  
% change bar color to match Z value
for k = 1:length(b)
    zdata = b(k).ZData;
    b(k).CData = zdata;
    b(k).FaceColor = 'interp';
end
colorbar('vert');
% Change colormap
colormap jet
% Label the axes
xlabel('x')
ylabel('y')
title('hist3 simulation');   

[Biraj Khanal]

Hi Mathieu , this was really helpful to get started. I replaced the histc with histcounts ( which I believe is the same thing) . However, what you have done is basically counted the xy pairs in each bins and presented Z axis as the count. Note that you have not used the initial z data at all. What I am doing is trying to put those respective z data (because the data is a x,y,z pair) in each bin and make a sum of them to present as Z of the final histogram. I have done that changing a line of your code. Check the for loop.

%dummy data (col vectors)
x = rand(100,1);
y = rand(100,1);
z = rand(100,1);
%% bin the data (Hist3 clone)
nBins = 10; %number of bins (there will be nBins + 1 edges)

% XEdge = linspace(min(x),max(x),nBins+1); 
% YEdge = linspace(min(y),max(y),nBins+1); 
% [~, xBin] = histc(x, XEdge);
% [~, yBin] = histc(y, YEdge);

[~,XEdge,XBin] = histcounts(x,nBins);
[~,YEdge,YBin] = histcounts(y,nBins);


[xIdx, yIdx] = meshgrid(1:nBins, 1:nBins); 
xyPairs = [xIdx(:), yIdx(:)]; 

Z = zeros(size(xyPairs,1),1);

for i = 1:size(xyPairs,1)
    %Z(i) = sum(ismember([xBin, yBin], xyPairs(i,:), 'rows'));
    
    z_idx = find(ismember([XBin, YBin], xyPairs(i,:), 'rows'));
    Z(i) = sum(z(z_idx));
end

Z = reshape(Z, [nBins, nBins]);
%Z = flip(Z,1);
% plot data 
figure(1)
b = bar3(Z);  
% change bar color to match Z value
for k = 1:length(b)
    zdata = b(k).ZData;
    b(k).CData = zdata;
    b(k).FaceColor = 'interp';
end
colorbar('vert');
% Change colormap
colormap jet
% Label the axes
xlabel('x')
ylabel('y')
title('hist3 simulation');   

Now, there are couple of more things that I am trying to do:

1. As you can see, the mesh in XY is not as we generally liike to see, The Y bins should be flipped. If only for the sake of Z, I could just flip Z. But I believe there is a better way to arrange this.
2. Instead of the bin index, I want to see the edges so that the histogram is relatable to the original data.

Do you have some suggestion?

[Biraj Khanal]

For anyone having similar problem, here is what I did to address the issues in my comment above :

Z = flip(Z,1); %flips the bar graph
ylim([0 nBins+1 ]); % to make the grid well viyible
xlim([0 nBins+1]);
tick_num = 5; %set the number of ticks on x and y axis
x = 0: nBins/tick_num : nBins ; x = x+0.4 ; x(1) =0.6;  %first bin is plotted from x = 0.6 , each bin ends at edge+0.4 
y = x;
xticks(x)
yticks(y)
xticklabels([XEdge(1: nBins/tick_num :end)]);
yticklabels(flip([YEdge(1: nBins/tick_num :end)]));

If anyone can suggest simpler way to go about this, it would be great!!