# Find the difference between all columns of a given row of a matrix

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MAWE on 8 May 2023
Commented: MAWE on 8 May 2023
I have MXL matrix. For each row, I want to find the absolute difference between the columns, without repeating. For example, if I have a row
a = [a11 a12 a13 a14]
I want to find
[abs(a11-a12) abs(a11-a13) abs(a11-a14) abs(a12-a13) abs(a12-a14) abs(a13-a14)]
How can I do that withoug for loops?
EDIT: I found this method
pdist([2 3 1 4]',@(x,y) x-y)
which looks like what I'm looking for, but I need to extend this for a matrix, and perform the above for all rows.

Antoni Garcia-Herreros on 8 May 2023
Hello MAWE,
You could use the function nchoosek:
Something like this might work for your case:
A=rand(4,5); % Generate data for the example
perms = nchoosek(1:size(A,2),2); % Find all the possible permutations
D=abs(A(:,perms(:,2))-A(:,perms(:,1))) % Compute the difference
D = 4×10
0.1875 0.5928 0.3519 0.1090 0.4053 0.1644 0.0785 0.2409 0.4838 0.2429 0.3220 0.2441 0.1334 0.3684 0.0779 0.4555 0.6904 0.3775 0.6125 0.2350 0.4037 0.4237 0.0883 0.1470 0.8274 0.3155 0.2568 0.5120 0.5707 0.0587 0.5416 0.0068 0.6400 0.3387 0.5348 0.0984 0.2029 0.6332 0.3319 0.3013
Hope this helps
MAWE on 8 May 2023
Yes, that helped. It's exactly what I needed. Thanks!

Luca Ferro on 8 May 2023
Edited: Luca Ferro on 8 May 2023
a=[1 3 5 -3];
aPerms=nchoosek(a,2); %generates all unique couples
absDiff=abs(aPerms(:,1)-aPerms(:,2))' %absolute difference of said couples, ' to transpose
absDiff = 1×6
2 4 4 2 6 8
MAWE on 8 May 2023
Thanks, this seems to work on a vector. How can I extend to a matrix?

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