# Is there faster ranking for matrices than double sort()?

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Marin Genov on 16 Sep 2022
Edited: Marin Genov on 16 Sep 2022
I have a uint16 matrix, where I want to determine the rank of each element with respect to its column in sorted form. The sort function doesn't quite do this, but using the second output twice does it. I need to repeat this routine many times in my code, and profiling reveals that it's by far the slowest part. So, I was wondering if there is a faster way to accomplish this (double sort() seems a bit of an overkill for this perhaps).
Here is a MWE:
M = 50;
m = 50;
n = 2000;
A = randi(M,m,n,'uint16'); % generate an example matrix
% Ranking via double sort():
tic;
[~,I] = sort(A,1);
[~,R] = sort(I,1);
toc;

Bruno Luong on 16 Sep 2022
Edited: Bruno Luong on 16 Sep 2022
Not sure it is faster, but on the theorical complexity it is better (single sort).
A = randi(10,5,3)
A = 5×3
10 5 9 9 1 5 9 3 9 8 3 3 1 9 2
[~,I] = sort(A,1);
[m,n] = size(A);
R = zeros(m,n);
R(I+(0:n-1)*m) = repmat((1:m)',1,n)
R = 5×3
5 4 4 3 1 3 4 2 5 2 3 2 1 5 1
Marin Genov on 16 Sep 2022
Edited: Marin Genov on 16 Sep 2022
@Bruno Luong: Apologies, I forgot to rename the R from the new method after copying the code, so MATLAB compared the original output again with the old output that was still in the workspace. Everything seems fine now. Many thanks!

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