How to plot a histogram in a waterfall plot?

Hello,

I'd like to plot multiple histograms in a waterfall-like diagram. Does somebody know a way to that?

Example:

http://cloud.originlab.com/www/resources/graph_gallery/images_galleries_new/3DHistogramsWithDistributionFit.png

I don't want to use a three-dimensional plot as bar3 would give me, as I want the bars to be plane as in the pictured linked above.

Any hints or links would be highly appreciated!

Thank you!

[dpb]

I was able to make a very crude similar-looking thing with waterfall by using the pdf line from a fitdist object and then a stairs-like plot by using the bar plot x,y values. But, the rendering of the face color was lousy and then when added the second pdf, the rendering went completely bonkers.

All in all, that isn't a fruitful way forward I think.

Unfortunately, altho one can put a histogram on the same axes; it's in the x-y plane instead of the x-z plane. AFAICT there's no way to rotate the axes so one would have to write the code to draw the plane at the right angle from basic projections.

This is the result after the addition I spoke of; the front one looked not too awful bad until added the other and the patching went away...

Don't have to have the colorbar, I just put that on there as I was messing w/ CData values to try to match a color...you can see the two forms in outline form aren't bad before trying the color rendition to simulate a histogram...I don't know if there's any way to solve that rendering problem or not...

[Nicolai]

Thank you very much for your answer!

Answer 1

[Adam Danz]

The bars will have to have a width value but you can make that value very small to appear as flat.

For bar3(Z), when Z is a matrix, there will be one colored group of bar for each column of Z and each group will be centered along the same x-value. This demo shows how to 1) change the space between the groups and 2) decrease the widths of each bar so they appear flat.

See inline comments for details.

% Load built-in data and plot a typical bar3() plot.  
load count.dat
clf()
h = bar3(count(1:11,:)); 
xlabel('X-AXIS')
ylabel('Y-AXIS')
zlabel('Z-AXIS')

% Define the desired x-coordintes for each group of bars
% (must have the same number of elements as 'h')
newX = [1, 5, 9]; 
% Or, use
% newX = linspace(1,100,numel(h)); 

% Define bar width in depth 
barWidths = 0.2; 

% Extend x-axis limit
xlim([min(newX)-barWidths, max(newX)+barWidths])

% Reposition each group of bars
for i = 1:numel(h)
    currentVals = [min(h(i).XData,[],'all'), max(h(i).XData,[],'all')]; 
    h(i).XData(h(i).XData == currentVals(1)) = newX(i)-(barWidths/2); 
    h(i).XData(h(i).XData == currentVals(2)) = newX(i)+(barWidths/2); 
end

% Change x-ticks
ax = h(1).Parent; 
originalLabels = ax.XTickLabel; 
ax.XTick = newX; 
ax.XTickLabel = originalLabels;

You can also turn off the black edge lines which will help hide the depth of each bar (not shown in the image below).

set(h, 'EdgeColor', 'none')

[Nicolai]

Thank you very much for your answer!

This looks pretty good 👏

[Adam Danz]

Glad I could help!

[dpb]

But can you figure out how to add the pdf on top on that axis, Adam?

Or any way to change its orientation to run in the x-axis direction a la waterfall to create the overlaid look OP wants?

[Adam Danz]

The choice of axes is arbitrary. I just changed the axis labels below and the viewing angle.

The pdfs (or whatever those curves are) can be added using plot3() while remembering that the x and y axes are swapped. The curves below are gaussians with mean and std computed from bar heights.

% Load built-in data and plot a typical bar3() plot.  
clf()
rawdata = randn(100,4); 
data = arrayfun(@(i){histcounts(rawdata(:,i),10)'}, 1:size(rawdata,2)); 
data = round([data{:}] .* [.5 .75 1 1.25]);
h = bar3(data,.90); 
xlabel('Y-AXIS')
ylabel('X-AXIS')
zlabel('Z-AXIS')
view([-145, 15])
hold on

% Define the desired x-coordintes for each group of bars
% (must have the same number of elements as 'h') 
newX = linspace(1,100,numel(h)); 

% Define bar width in depth 
barWidths = 0.1; 

% Extend x-axis limit
xlim([min(newX)-barWidths, max(newX)+barWidths])

% Define gaus func
gaus = @(x,mu,sig,amp)amp*exp(-(((x-mu).^2)/(2*sig.^2)));
xCurve = linspace(.5,size(data,1)+.5, 100);

% Reposition each group of bars
for i = 1:numel(h)
    currentVals = [min(h(i).XData,[],'all'), max(h(i).XData,[],'all')]; 
    h(i).XData(h(i).XData == currentVals(1)) = newX(i)-(barWidths/2); 
    h(i).XData(h(i).XData == currentVals(2)) = newX(i)+(barWidths/2); 
    
    % Add bar-fits (assuming normal dist)
    [mu,sig] = normfit(repelem(1:size(data,1), data(:,i))); 
    yCurve = gaus(xCurve, mu, sig, max(data(:,i))); 
    plot3(repmat(newX(i), size(xCurve)),xCurve, yCurve, 'k-', 'LineWidth', 3)
    
end

% Change x-ticks
ax = h(1).Parent; 
originalLabels = ax.XTickLabel; 
ax.XTick = newX; 
ax.XTickLabel = originalLabels;

set(h, 'EdgeColor', [.5 .5 .5])

Answer 2

[Abdolkarim Mohammadi]

I think there is no function to draw this in one command. However, it can be drawn using patch() and plot3(). Use the following code. You must have all of your data in one matrix. If there are different number of observations in each variable, you can pad shorter variables with NaNs.

%% create dataset

rng (0);
Data = 50 + randn(80,5) - 2*(1:5);
Data = vertcat (Data,[50,50,50,NaN,NaN]);

%% draw plot 
figure ('Position', [748,86,560,545]);

% get number of variables (columns of Data) 
NumVariables = size(Data,2);

% colors we cycle through
Colors = [
	0 0.4470 0.7410	
	0.8500 0.3250 0.0980	
	0.9290 0.6940 0.1250	
	0.4940 0.1840 0.5560	
	0.4660 0.6740 0.1880	
	0.3010 0.7450 0.9330	
	0.6350 0.0780 0.1840	
	];

% define relative bar width
RelativeBarWidth = 0.9;  

% a template for vertices 
VerticesTemplate = [
	0	1	0
	1	1	0
	1	1	1
	0	1	1
	];

hold ('on')

% for each variable 
for i1 = 1:NumVariables
	
	% ---- Bar plot -------------
	
	% remove nans 
	CurrentData = Data(isfinite(Data(:,i1)),i1);
	
	% calculate bin counts and bin edges 
	[BinCounts,BinEdges] = histcounts(CurrentData);
	
	% calculate number of bins 
	NumBins = numel(BinCounts);
	
	% create vertices 
	Vertices = zeros(4*NumBins,3);
	
	for i2 = 1:NumBins 
		Temp = VerticesTemplate;
		Temp([1,4],1) = BinEdges(i2)   + (1-RelativeBarWidth)*(BinEdges(i2+1)-BinEdges(i2));
		Temp([2,3],1) = BinEdges(i2+1) - (1-RelativeBarWidth)*(BinEdges(i2+1)-BinEdges(i2));
		Temp(:,2) = i1;
		Temp(:,3) = Temp(:,3) * BinCounts(i2);
		Vertices((i2-1)*4+1:i2*4,:) = Temp;
	end
	
	% create faces 
	Faces = reshape(1:4*NumBins,[4,NumBins])';
	
	% draw bar plot 
	patch ('Faces', Faces, 'Vertices', Vertices, ...
		'FaceVertexCData', repmat(Colors(i1,:),[NumBins,1]), ...
		'FaceColor', 'Flat', ...
		'EdgeColor', [0.6,0.6,0.6]);
	
	% ---- Normal distribution -------------
	
	% define accuracy 
	NumPoints = 101;
	
	% calculate statistics 
	VarMin  = min  (CurrentData);
	VarMax  = max  (CurrentData);
	VarMean = mean (CurrentData);
	VarStd  = std  (CurrentData,1);
	
	% create x and calculate z for the line 
 
	% LineX = linspace (VarMin,VarMax,NumPoints)'; % shorter, non-adjustable tails
	LineX = linspace (VarMean-3.5*VarStd,VarMean+3.5*VarStd,NumPoints)'; % longer, adjustable tails	
	LineY = repmat(i1,[NumPoints,1]);
	LineZ = pdf('Normal',LineX,VarMean,VarStd) * sum(BinCounts,2);
	
	% draw the line 
	plot3 (LineX, LineY, LineZ, ...
		'Color', 'k', ...
		'LineWidth', 2);
	
end

hold ('off')

%% adjust axes 

view ([-35,33]);

xlabel ('Bin center');
yticklabels (["Americans","Europs","Asia","Africa","Oceania"]);
zlabel ('Counts');

box ('on');
grid ('on');

ax = gca;
ax.Projection = 'Perspective';

[dpb]

Very nice!!! I hadn't wanted to try to dig into actual patches...

[Adam Danz]

Looks good, Abdolkarim Mohammadi-Balani!

[Abdolkarim Mohammadi]

Many thanks dpb and Adam Danz :)

[dpb]

No problem...kudos when due! :)

Only thing I see that could possibly be just a little enhancement to the visualization would be to extend the pdf ranges a little further so the pdf curves come closer to the baseline than do for a couple of the cases...but that's nit-picking and easy enough for the OP to add.

[Abdolkarim Mohammadi]

You are right. The short tails were based on min and max and looked a little weird. I replaced it with tails based on deviations from the mean. It is now closer to what OP posted.

[dpb]

+1