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

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.

Answer 1

[Antoni Garcia-Herreros]

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]

Yes, that helped. It's exactly what I needed. Thanks!

Answer 2

[Luca Ferro]

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]

Thanks, this seems to work on a vector. How can I extend to a matrix?