Indexing a matrix using predetermined rule

Question

I have a 72x3 double that looks like this

1   1   24  
1   1   125  
2   3   17  
6   2   54  
5   1   110  
4   4   55  
6   2   200
1   4   16  
3   3   87  
...  
6   2   63  

I would like to be able to find a value from column 3 based on the combination of values from column 1 and 2. For instance, let's call any value from column 1 m, value from column 2 n, and the corresponding value from column 3 p. If m=2, n=3, this will correspond to row 3 and thus p would be 17. If m=5, n=1, this will give us row 5 and thus b would be 110. Note that there will be cases where a set of m and n will give us two or more rows. An example would be m=1 and n1=1, which should yield 24 from the first row and 125 from the second row. In this case, the output should be [24 125]. Similarly, a combination and m=6 and n= 2 would give [54 200 63]. m ranges from 1 to 6 and n ranges from 1 to 4. Any combination of m and n would yield no more than 4 outputs. Could anyone help me with this indexing problem?

Thank you so much.

Alex

Answer 1

One approach assuming A to be the input N x 3 array -

%// Find unique rows using the first two columns of A
[unqA12,~,idx] = unique(A(:,1:2),'rows')

%// Group elements from 3rd column of A based on the indexing pairs from
%// first coloumns of A and have these as a cell array
A3vals = accumarray(idx,A(:,3),[],@(x) {x})

%// Horizontally concatenate these results to present the final output
out = [num2cell(unqA12) A3vals]

Sample run on the given input yields the output as -

out = 
    [1]    [1]    [2x1 double]
    [1]    [4]    [        16]
    [2]    [3]    [        17]
    [3]    [3]    [        87]
    [4]    [4]    [        55]
    [5]    [1]    [       110]
    [6]    [2]    [3x1 double]

---

Or with arrayfun -

%// Find unique rows using the first two columns of A
[unqA12,~,idx] = unique(A(:,1:2),'rows')

%// Use arrayfun to do the groupings instead of accumarray this time 
out = [num2cell(unqA12) arrayfun(@(n) A(idx==n,3),1:max(idx),'Uni',0).']

Please note that the order of the third column elements won't be preserved in the first approach, but the second approach would do so.

Answer 2

This wont be the fastest way, but another approach for beginners like me :)

in = [1   1   24; 
      1   1   125;
      2   3   17;
      6   2   54;  
      5   1   110;
      4   4   55;
      6   2   200;
      1   4   16;
      3   3   87];
m = input('Enter m ');
n = input('Enter n ');
Idx = all((cat(2,in(:,1) == m, in(:,2) == n)),2); 
out = in(:,3);
out1 = out(Idx);

Results:

Enter m 6
Enter n 2

ans =

    54
   200
----------------

Enter m 2
Enter n 3

ans =

    17

Answer 3

If you only want the result for a given combination of m and n, you can use just indexing:

m = 6;
n = 2;
result = x(x(:,1)==m & x(:,2)==n, 3).';