Merge output as one matrix in for loop

I have created a program

function A = large_elements(X)
[rows,column]=size(X);
cnt=0;
for i=1:rows%rows indices
    for j=1:column%column indices
        cnt=i+j;
        if cnt<X(i,j)
            A=[i j]
        else
            A=[]
        end 
    end
end
end

When I run the function I get my output

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

I can't store my output. It overwrites my previous result How can I represent all values of A in matrix form?

[James Tursa]

Are you looking for a way to fix up this function as you have it coded? (e.g., you could replace A = [i j] with A = [A;i j] and get rid of the else clause), or would you like us to suggest ways to vectorize this (eliminate the for loops)?

[ammar ansari]

I want to represent my output in a matrix form. Command A = [A;i j] provided me the desired output. Thanks for the help

[Stephen23]

Also the same question here:

http://www.mathworks.com/matlabcentral/answers/218259-get-elements-of-a-matrix-that-are-greater-than-sum-of-their-two-indices-in-row-major-order

Answer 1

[Stephen23]

The function given in the question locates every element of the input matrix X whose value is greater than the sum of its indices, and returns these indices, e.g.:

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

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 these three lines:

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

and outputs this:

>> Z = large_elements(5*ones(3))
Z =
   1     1     1
   1     1     0
   1     0     0

which are the logical indices of those values. Using logical indices is usually the fastest way of accessing and identifying elements of an array, so this would be an excellent choice of output. If it is strictly required to use subscript indices, then simply use find on the logical indices:

>> [r,c] = find(Z)
r =
   1
   2
   3
   1
   2
   1
c =
   1
   1
   1
   2
   2
   3