Add values in MATLAB matrix based on pairs

Question

Apologies if something similar has been asked before. It seems like it should be an easy problem on the face of it, but I'm having trouble describing this -- let alone solving it! Let's suppose I have a single 5 x 3 matrix that looks something like this:

A = [50  1  2
     75  2  3 
     20  2  3
     10  1  1
     90  1  2]

I want to sum the values in the first column wherever there is a pair in the 2nd and 3rd column that is duplicated somewhere else. So, I'm trying to transform A (above) into something like this 3 x 3 matrix B, where:

    B = [140  1  2
         95   2  3 
         10   1  1] 

Just the values from column 1 get added, and I need them to stay matched to the pair that "caused" them to combine. I guess I should also add that the order of values in columns 2 & 3 does matter in that 3,4 counts as a different pair than 4,3. (Of course my actual data include values in columns 2 & 3 that range well into the 100s, so writing an if statement for each possible combination isn't really a possibility...)

Any suggestions for this would be much appreciated! I was studying the documentation on 'find' and stumbled across something called 'ismember' -- do I need to be using some application of that?

Answer 1

The usual unique - accumarray couple is suited for the job:

[u, ~, v] = unique(A(:,2:end), 'rows', 'stable');
B = [accumarray(v, A(:,1)) u];