Get elements of a matrix that are greater than sum of their two indices in row major order

I'm Writing a function called `large_elements` that takes input an array named `X` that is a matrix or a vector. The function identifies those elements of `X` that are greater than the sum of their two indexes.

For example, if the element `X(2,3)` is `6`, then that element would be identified because `6 > (2 + 3)`. The output of the function gives the indexes(row and column sub) of such elements found in *row-major order*. It is a matrix with exactly two columns. The first column contains the row indexes, while the second column contains the corresponding column indexes.

Here is an example, the statement

    indexes = large_elements([1 4; 5 2; 6 0]) 
should give the output like this: 

    [1 2; 2 1; 3 1]
If no such element exists,
the function returns an
`empty array`.

I have came up with the following code

    function indexes = large_elements(A)
        [r c] = size(A);
        ind = 1;
        for ii = 1:r
            for jj = 1:c
                if A(ii,jj) > ii + jj
                    indexes(ind,:) = [ii jj];
                    ind = ind + 1;
                else
                    indexes = [];
                end
           end  
        end
    end

But the results are not as expected. Any help would be appreciated.

[Stephen23]

An interesting coincidence:

http://www.mathworks.com/matlabcentral/answers/217809-merge-output-as-one-matrix-in-for-loop

Answer 1

[Andrei Bobrov]

a = [1 4; 5 2; 6 0]; % your data

n = size(a);
[x,y]=ndgrid(1:n(1),1:n(2));
[ii,jj] = find(a > (x + y));
out = sortrows([ii(:),jj(:)],1);

or

n = size(a);
[ii,jj] = find(a > hankel(2:n(1)+1,(1:n(2))+n(1)));
out = sortrows([ii(:),jj(:)],1);

or

n = size(a)
[ii,jj] = find(a > bsxfun(@plus,(1:n(1))',1:n(2)));
out = sortrows([ii(:),jj(:)],1);

or

n = size(a');
[ii,jj] = find(a' > bsxfun(@plus,(1:n(1))',1:n(2)));
out = [jj(:),ii(:)];

[Alisha Ali]

doesn't work correctly for [1 4; 5 2; 6 0]

[Jan]

@Alisha: Please explain, which version is not working properly and which problem you observe.

Answer 2

[Stephen23]

Solving this kind of problem using two nested loops is very poor use of MATLAB, especially as the output array is growing inside the loops: without any array preallocation this is a slow and very inefficient use of MATLAB. It would be much faster and much simpler using vectorized code, such as this:

function Z = large_elements(X)
[r,c] = size(X);
[r,c] = find(X > bsxfun(@plus, (1:r)', 1:c));
Z = sortrows([r,c]);

which outputs this when run:

>> large_elements(5*ones(3))
ans =
   1     1
   1     2
   1     3
   2     1
   2     2
   3     1

[Stephen23]

Using the sample data:

>> A = [1 4; 5 2; 6 0]
A =
     1     4
     5     2
     6     0
>> large_elements(A)
ans =
     1     2
     2     1
     3     1