Finding faster way to compute a matrix using MATLAB

Question

I am looking for a faster way to compute a matrix using MATLAB:

Given an m-by-n matrix A, I would like to return a matrix B with the additions of all ith and the jth rows such that j >= i. E.g., Let A=[1 2 3 4; 2 3 4 5; 3 4 5 6], then B can be computed as

idx=1;
nbrows=size(A,1);
B=zeros(nbrows*(nbrows+1)/2,size(A,2)); % the size of B can be determined
for i = 1:nbrows
  for j = i:nbrows
    B(idx,:) = A(i,:) + A(j,:);
    idx = idx + 1;
  end
end

Now, I have a very large A, and I would like to know how to compute the matrix B in a more efficient way.

How can this computation be sped-up?

@Wolfie As a not too big example, A=rand(5e3, 20), then the computation of B may takes a while. In fact, this kind of computations have to be repeated in my code, so that I need this step to be as fast as possible. — kaienfr

rahnema1 rahnema1 · Accepted Answer · 2020-10-19T11:00:39

Instead of iterating over rows you can precompute indexes of rows and iterate over columns:

nbcols = size(A, 2);

[r, c] = find(tril(true(nbrows)));

rc = [r c];

for i = 1:nbcols
    B(:, i) = sum(reshape(A(rc, i), [], 2), 2);
end

Equivalent possibly less efficient solution:

for i = 1:nbcols
    B(:, i) = A(r, i) + A(c, i);
end

As A is very large the completely vectorized solution:

B = A(r,:) + A(c,:);

shouldn't be more efficient than the loop version.

Finding faster way to compute a matrix using MATLAB

2 Answers