adding counts of ordered pairs

I have a sequence of by 3 arrays, say , , …, that are generated within a loop. That is, the number of rows of each array varies, but each array has three columns. The first two columns represent ordered pairs. The third column is the count of those ordered pairs. I want to "add" these together so that I get an array that accumulates the counts of these ordered pairs into a new array that is with the same structure. For example, if is

A1=[1 4 3;
    3 5 1;
    12 4 7;
    13 5 2;
    14 1 1];

and is

A1=[1 5 1;
    13 5 1;
    13 7 3;
    14 1 5];

then the cumulative matrix should be

A=[1 4 3;
    1 5 1;
    3 5 1;
    12 4 7;
    13 5 3;
    13 7 3;
    14 1 6];

The arrays being "summed" in this way have hundreds of entries and are themselves summaries of arrays with thousands of entries, so efficiency matters.

Answer 1

[Bjorn Gustavsson]

One way to go about this is to use sparse:

A1 = [1 4 3;
      3 5 1;
      12 4 7;
      13 5 2;
      14 1 1];
A2 = [1 5 1;
      13 5 1;
      13 7 3;
      14 1 5];
A_all = sparse([A1(:,1);A2(:,1)],[A1(:,2);A2(:,2)],[A1(:,3);A2(:,3)]);
[I1,I2,Val] = find(A_all);   
[~,idx1] = sort(I1);         
disp([I1(idx1),I2(idx1),Val(idx1)])

HTH

[Barbara Margolius]

I am going to time both your answer and Bruno's to see which works best. I accepted yours because I suspect with my data it will be faster.

[Bruno Luong]

This will save you a sort

A1 = [1 4 3;
    3 5 1;
    12 4 7;
    13 5 2;
    14 1 1];
A2 = [1 5 1;
    13 5 1;
    13 7 3;
    14 1 5];

A_all = sparse([A1(:,2);A2(:,2)],[A1(:,1);A2(:,1)],[A1(:,3);A2(:,3)]);
[I2,I1,Val] = find(A_all);        
A = [I1,I2,Val]

A = 7×3

1 4 3 1 5 1 3 5 1 12 4 7 13 5 3 13 7 3 14 1 6

Answer 2

[Bruno Luong]

A1=[1 4 3;
    3 5 1;
    12 4 7;
    13 5 2;
    14 1 1];
A2=[1 5 1;
    13 5 1;
    13 7 3;
    14 1 5];

A12=[A1; A2];
[A12u,~,J]=unique(A12(:,1:2),'rows','stable');
A=[A12u,accumarray(J,A12(:,3))]

A = 7×3

1 4 3 3 5 1 12 4 7 13 5 3 14 1 6 1 5 1 13 7 3

[Barbara Margolius]

Thanks! Bjorn's answer also works. I am guessing his will be faster with my data, so I accepted it.

[Bruno Luong]

I hope you don't have such case where Bjorn's method fails

A1=[1 1 1];
A2=[1 1 -1];

or pairs are not integer >= 1.

[Barbara Margolius]

pairs are all integers (the result of floor function plus 1); third column is countdata, so should be ok.

[Bruno Luong]

floor can returns 0 no?

[Barbara Margolius]

yup, see edit.

[Bjorn Gustavsson]

@Bruno Luong: The amount of subconsious/implicit assumptions I make when writing QD-solutions is a bit frightening.

[Bruno Luong]

That's called "intuition".