Summing values for duplicate rows and columns

I have a vector of rows, columns, and values that I will use to create a sparse matrix:

rows = [1 2 3 1]; columns = [1 1 2 1]; values = [10 50 25 90];

Notice the duplicates:

(1,1) 10 (1,1) 90

What I need is to eliminate (row,column) duplicates by summing the values corresponding to these duplicates for each.

The solution in the current example is:

rows = [1 2 3]; columns = [1 1 2]; values = [100 50 25];

What operation on the three initial vectors reduce them to the solution above?

Answer 1

[Andrei Bobrov]

A = accumarray([[1 2 3 1]',[1 1 2 1]'],[10 50 25 90]',[],[],[],1);

[Ulrik William Nash]

Hi Andrei, that didn't appear to work. Please note I have added a little more information under my comment to Walter.

[Andrei Bobrov]

corrected

[Ulrik William Nash]

Thank you Andrei, that was very instructive.

Answer 2

[Walter Roberson]

sparse(row, columns, values) is defined to do exactly this kind of totals.

If for some reason you need the simplified outputs afterwards, you can

[r, c, v] = find() on the sparse matrix.

[Ulrik William Nash]

Hi Walter,

I think my explanation needs a little more background. I have coded a procedure for constructing a large transition matrix. I do this by sequentially amending the r, c, v vectors shown below:

        r = [r i];
        c = [c indx];
        s = [s transition_probs(ii,1)];

Unfortunately, due to the underlying process, a given combination of indexes for r and c may carry numerous probabilities. So, once I have finished my procedure, I must sum the values corresponding to duplicate r,c combinations.

[Walter Roberson]

result = sparse(r, c, s);
[summary_r, summary_c, summary_s] = find(result);