How to apply function on every pair of rows of a matrix?

Hi, I'm new to matlab and I need help. I'm supposed to make a m x n matrix called M and it's elements are -1, 1 and 0.

I need to write a function called d(x,y) which returns 1 if (x = -1) and (y = 1). And returns 0 otherwise.

and another function called h(m(i),m(k)) which calculates the sum of d(m(i,j),m(k,j)) in every column and it is defined to find the distance between row i and row k:

For example Suppose M = [-1 0 -1; 1 -1 -1; 0 1 1].

If I calculate h for the 1st row and 2nd row(i = 1 and k = 2) it's Sum of d(m(1,j),m(2,j) for j from 1 to 3 which is d(m11,m21) + d(m12,m22) + d(m13,m23) = d(-1,1) + d(0,-1) + d(-1,-1) = 0+ 0 + 0 =0 .

Then I need h for every pair of rows. I'm confused. I tried writing d function as follows:

 function d = d( x, y )
 if (x==1) & (y==-1)
     d = 1;
 else
     d = 0;
 end    
 end

Then I tried to find h for row 1 and row 2 of the example matrix:

 M = [-1 0 -1; 1 -1 -1; 0 1 1];
 m=size(M,1);
 n=size(M,2);
 for i=1:2
     h = sum(d(M(i,1:n)));
 end

h returns 0 and works fine. I need to repeat this for every pair of matrix rows. For example for M which has 3 rows there will be 3 pairs of rows (3 choose 2) and h must be 1 x 3 (one sum for every pair).

Answer 1

[Stephen23]

Perhaps something like this:

d = @(x,y)+(x==1&y==-1);
sum(bsxfun(d,permute(M,[1,3,2]),permute(M,[3,2,1])),3)

And tested:

>> M = [-1 0 -1; 1 -1 -1; 0 1 1]
M =
  -1   0  -1
   1  -1  -1
   0   1   1
>> d = @(x,y)+(x==1&y==-1);
>> sum(bsxfun(d,permute(M,[1,3,2]),permute(M,[3,2,1])),3)
ans =
   0   0   0
   1   0   1
   0   1   1

[Soul Free]

I know how permute works but I don't understand why you used it. Also matrix M is an example, I need the answer for a much bigger matrix. I think I should use for to apply it on different columns but I don't know how.

[Stephen23]

"I know how permute works but I don't understand why you used it."

I rearranged the matrix in two ways, such that each permute of it had either the rows or columns arranged along the third dimension. I then used bsxfun to apply function d to those arrays, and the results are summed along the third dimension. Thus d is applied to all row/column combinations.

"Also matrix M is an example, I need the answer for a much bigger matrix"

My code is not written for any specific matrix. As long as your memory can hold it, my code will also process larger matrices.

"I think I should use for to apply it on different columns but I don't know how."

for loops are explained in the introductory tutorials, practice using them and you will understand them better:

https://www.mathworks.com/help/matlab/getting-started-with-matlab.html

[Soul Free]

Thanks for your explanation. I think sum must be a vector, I need one sum for every pair of rows (every sum is calculated for all columns according to the function in the image of my question). I'm sorry but I can't understand why your answer is a matrix. I think it should be [0 0 0]. I edited my question a bit.

[Stephen23]

@Soul Free: the screenshot in your question

shows that the row indices i and k are not specified or summed over. As far as I can tell, this means you will have all combinations of rows i=1:m and k=1:m, thus giving an mxm matrix. If this is not the correct interpretation, please explain in more detail. It would also help if you provided the expected output for your example matrix M.

[Soul Free]

Thanks for your answer. I think i and k are constants every time we calculate h and I want h for j=1:n (j shows the column index of matrix, i and k are rows and are from 1 to m not n) for every pair of rows.(for all combinations of i=1:m and k=1:m) This explains more:

HD is supposed to return the distance of row i and row k. so for example if my matrix has 3 rows I'll have 3 pair of rows (3 choose 2) and HD must be 1 x 3. One HD for every pair of i=1:n and k=1:n where i ~=k.