Optimize matlab triple for loop

Question

I have a large matrix samples, I want to make another matrix sampleProb which is the same size, but modified as below:

%samples is a 1000*1000 matrix, M = 1000 sampleProb = zeros(1000); for i = 1:size(samples, 2) for j = 1:M for k = 1:M if (k ~= j) sampleProb(j, i) = sampleProb(j, i) + normcdf(samples(j, i) - samples(k, i)); end end end end sampleProb = sampleProb./M; 

I know it's best to avoid for loops when possible in Matlab and operations should be vectorised, but I can't figure out what to do. How can I optimise this for performance?

Answer 1

Introduction and solution code

Since you mentioned making the output matrix sampleProb, I am assuming it to be initialized as all zeros. So, here's the vectorized implementation with the mighty bsxfun -

%// Get the subtractions sub1 = bsxfun(@minus,samples,permute(samples,[3 2 1])) %// Calculate the sum of normcdf's in a vectorized fashion sampleProb = bsxfun(@minus,sum(normcdf(sub1),3),normcdf(sub1(1,:,1)))./M 

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Benchmarking

Benchmarking Code with M = 100 -

M = 100; samples = rand(M,M); sampleProb1 = zeros(M,M); disp('---------------------------------------- With Original Approach') tic for i = 1:size(samples, 2) for j = 1:M for k = 1:M if (k ~= j) sampleProb1(j, i) = sampleProb1(j, i) + normcdf(samples(j, i) - samples(k, i)); end end end end sampleProb1 = sampleProb1./M; toc, clear sampleProb1 i j k disp('---------------------------------------- With Proposed Approach') tic %// Get the subtractions sub1 = bsxfun(@minus,samples,permute(samples,[3 2 1])); %// Calculate the sum of normcdf's in a vectorized fashion sampleProb = bsxfun(@minus,sum(normcdf(sub1),3),normcdf(sub1(1,:,1)))./M; toc 

Runtime results -

---------------------------------------- With Original Approach Elapsed time is 21.425729 seconds. ---------------------------------------- With Proposed Approach Elapsed time is 0.046284 seconds.