MATLAB: How to find the element which is greater than or equal to its row and smaller or equal to its column in a matrix

homeworkMATLABmatrixorder

Hi everyone; I am going to find the saddle points of a matrix M. The question is given below…
Write a function called saddle that finds saddle points in the input matrix M. For the purposes of this problem, a saddle point is defined as an element whose value is greater than or equal to every element in its row, and less than or equal to every element in its column. Note that there may be more than one saddle point in M. Return a matrix indices that has exactly two columns. Each row of indices corresponds to one saddle point with the first element of the row containing the row index of the saddle point and the second column containing the column index. The saddle points are provided in indices in the same order they are located in M according to column-major ordering. If there is no saddle point in M, then indices is the empty array.
I am trying that code:
function indices = saddle(M)
[ rows,cols ] = size(M);
[valR,posR] = max(M,[],2);
[valC,posC] = min(M,[],1);
indices= [];
for i = 1:length(posR)
    if i == posC(posR(i))
        indices= [indices; i, posR(i)];
    end
end
end
It is running fine. But when i test my code for
>> mat=zeros(5,3)
mat =
       0     0     0
       0     0     0
       0     0     0
       0     0     0
       0     0     0
I am getting wrong output :
saddle(mat)
ans =
       1     1
the correct output must be
saddle(mat)
ans =
     1     1
     2     1
     3     1
     4     1
     5     1
     1     2
     2     2
     3     2
     4     2
     5     2
     1     3
     2     3
     3     3
     4     3
     5     3
What i am doing wrong?? Thanks in advance

Best Answer

Copying code from the internet is not always a good way to learn best-practice coding: Solving this problem using loops misses using MATLAB's excellent code vectorization abilities. It would be much neater and faster to use bsxfun instead, like this:
function idx = saddle(mat)
row_mx = bsxfun(@ge,mat,max(mat,[],2));
col_mn = bsxfun(@le,mat,min(mat,[],1));
[R,C] = find(row_mx & col_mn);
idx = [R,C];
end
Which gives this:
>> saddle(zeros(5,3))
ans =
   1     1
   2     1
   3     1
   4     1
   5     1
   1     2
   2     2
   3     2
   4     2
   5     2
   1     3
   2     3
   3     3
   4     3
   5     3
Related Question