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

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Soul Free 2018-7-29

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编辑： Stephen23 2018-8-1

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).

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Answer 1

Stephen23 2018-7-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/412610-how-to-apply-function-on-every-pair-of-rows-of-a-matrix#answer_330841

编辑：Stephen23 2018-7-30

在 MATLAB Online 中打开

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

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Stephen23 2018-7-31

编辑：Stephen23 2018-8-1

@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 2018-7-31

编辑：Soul Free 2018-7-31

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.

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