Obtain 2D Histogram from 3D matrix and 2D pdf

Hello,

I've got a 2D matrix of values

nK=10; nM=100; nZ=50;
Cz = rand(nK,nM,nZ); % list of values depends on 3 quantities

that I want to histogram with edges

CzEdges = [0:0.1:1]; % where values in the 3D Matrix should be hist'd

Each element of the Cz has a corresponding probabilty defined in a matrix

p_K_M = rand(nC,nK); % 2D pdf, (please never mind the normalization) NB: sum(p_C_M,'all') = 1
p_K_M = p_K_M/sum(p_K_M,'all'); % normalized 

that is indepent of the variable (z).

I would like a 2D histogram/pdf of the Cz's but would like to avoid looping and masking as in;

P_Cz = zeros(icz,iz); % the 2D pdf = fxn of only 1 original variable, (and another the Cz values themselves i.e. the histogram Edges)
for iz=1:nZ
    thisCz = squeeze(Cz(:,:,iz)); % get the values at the z

    for icz=1:length(CzEdges)-1
        % get indices where Cz is in correct bin
        hasCorrectCz = ( CzEdges(icz) < thisCz ) & ( thisCz < CzEdges(icz+1) );
        
        if ~any(hasCorrectCz)
           continue
        end
        % "weigh" each index with corresponding value from 2D pdf
        P_Cz(icz, iz) = sum( p_K_M(hasCorrectCz) ); 
    end
end

Is it possible to use hist3 (I dislike the inputs and I don't think they map well to my variabels as they're constructed), or accumarray to dot times the Cz's with the 2D pdf (p_K_M) or perhaps a generalized histcounts and dot times of a repmatted p_K_M?

I feel like I'm missing a neat function that makes this go from 2 loops to a ~3 liner or something. I really appreciate any tips you have. Please let me know if I've made an error (I "translated" my variables to something easier to parse, but may have done something stupid.)

Cheers,

Michael B.

[Michael Bowles]

I had a bit of an epiphany and believe I'm much closer to the answer but still ened a little push.

Since I aim to 2D histogram the Czs as a fucniton of Cz and z I can use repmat to expand the probability matrix

threeDimJointPDF = repmat(p_K_M,[1 1 nZ]);

and then do the saem for the z's

[~,~,threeDimZ] = ndgrid([1:nK],[1:nM],z); % the values only matter for the z, just need correct dimensions

Now I want to use accumarray or use do a weighted histogram for the splayed out lists!

[Michael Bowles]

With the list of Zs Czs and Ps, I'd like to use predefiend Cz and Z edges e.g.

zEdges = [0:80]; % and the CzEdges from before
CzEdges=[0:0.1:1]; % to sum the threeDimJointPDF (third column of the)
allZs_Czs_Ps = [threeDimZ(:) Cz(:) threeDimJointPDF(:)];

Answer 1

[Bruno Luong]

Check this out

[Michael Bowles]

This is neat. I'm sort of hoping for something a little more transparent (or really native). I suppose I'll accept if no one else chimes in. Thank you.