Finding a critical point in matrix

Question

I'm attempting to find a critical point in a matrix. The value at index (i,j) should be greater than or equal to all elements in its row, and less than or equal to all elements in its column.

Here is what I have (it's off but I'm close):

function C = critical(A)
[nrow ncol] = size(A);
C = [];
for i = 1:nrow
    for j = 1:ncol
        if (A(i,j) >= A(i,1:end)) && (A(i,j) <= A(1:end,j))
            C = [C ; A(i,j)]
        end
    end
end

Answer 1

You can use logical indexing.

minI = min(A,[],1);
maxI = max(A,[],2);
[row,col] = find(((A.'==maxI.').' & A==minI) ==1)

---

Details

Remember that Matlab is column major. We therefore transpose A and maxI.

A = [

   3   4   1   1   2
   2   4   2   1   4
   4   3   2   1   2
   3   3   1   1   1
   2   3   0   2   1];

A.'==maxI.'
ans =

   0   0   1   1   0
   1   1   0   1   1
   0   0   0   0   0
   0   0   0   0   0
   0   1   0   0   0

Then do the minimum

A==minI
ans =

   0   0   0   1   0
   1   0   0   1   0
   0   1   0   1   0
   0   1   0   1   1
   1   1   1   0   1    

And then multiply the two

((A.'==maxI.').' & A==minI)
ans =

   0   0   0   0   0
   0   0   0   0   0
   0   0   0   0   0
   0   1   0   0   0
   0   1   0   0   0

Then find the rows and cols

[row,col] = find(((A.'==maxI.').' & A==minI) ==1)

row =

   4
   5

col =

   2
   2