How to use Matlab's bsxfun to solve cumulative sum

Question

I have the following (slow) piece of code:

% A is n-by-m matrix
% B is n-by-m-by-d matrix
% C is n-by-m-by-d matrix
% R is 1-by-d vector

A=zeros(n,m);
for i=1:d
    A = A + sum(B(:,:,1:i),3).*(R(i)-C(:,:,i));
end

I would like to make it more efficient by using the magical bsxfun to lose the loop. Can you show me how to do that?

Answer 1

This way -

A = sum(cumsum(B,3).*bsxfun(@minus,permute(R,[1 3 2]),C),3)

With size parameters n,m,d as 200 each, the runtimes were

----------------------------------- With Proposed Approach
Elapsed time is 0.054771 seconds.
----------------------------------- With Original Approach
Elapsed time is 2.514884 seconds.

More reasons to use bsxfun and vectorization!!

---

Benchmarking

Benchmarking Code -

n = 10;
m = 1000;
d = 3;
num_iter = 10000;

B = rand(n,m,d);
C = rand(n,m,d);
R = rand(1,d);

%// Warm up tic/toc.
for k = 1:100000
    tic(); elapsed = toc();
end

disp(['********************* d = ' num2str(d) ' ************************'])

disp('----------------------------------- With Proposed Approach')
tic
for iter = 1:num_iter
    A1 = sum(cumsum(B,3).*bsxfun(@minus,permute(R,[1 3 2]),C),3);
end
toc

disp('----------------------------------- With Original Approach')
tic
for iter = 1:num_iter
    
    A = zeros(n,m);
    for i=1:d
        A = A + sum(B(:,:,1:i),3).*(R(i)-C(:,:,i));
    end
end
toc

Runtimes at my end were -

********************* d = 3 ************************
----------------------------------- With Proposed Approach
Elapsed time is 0.856972 seconds.
----------------------------------- With Original Approach
Elapsed time is 1.703564 seconds.



********************* d = 9 ************************
----------------------------------- With Proposed Approach
Elapsed time is 2.098253 seconds.
----------------------------------- With Original Approach
Elapsed time is 9.518418 seconds.