Compute differences bewteen vectors in a matrix

Hi all, I have a question for you:

I have a matrix of the following type, where the i-th vector is a row vector:

A = [v1;v2;v3;v4;...;vN]

I want to compute all the possible differences between vectors, except the self-one. I mean: I need a first iteration that returns me [v1-v2;v1-v3;v1-v4;....;v1-vN] but I DON'T want to consider v1-v1; then at the next iteration I want [v2-v1; v2-v3; v2-v4;...;v2-vN] and i DON'T want v2-v2.

I need to do this for all the rows of my matrix A, I prefer to obtain only one difference-matrix at time because then I have to do some processing over it. So can you suggest me an algorithm that exactly does this?

Thanks

Answer 1

[Stephen23]

This is easy to achieve with basic indexing and an anonymous function:

>> A = randi(9,5,7)
A =
   4   4   5   9   4   7   1
   9   4   6   8   2   8   2
   9   7   2   1   7   9   8
   2   5   7   7   5   3   5
   2   7   1   4   6   6   5
>> fun = @(k) A(k,:) - A([1:k-1,k+1:end],:);
>> fun(1)
ans =
  -5   0  -1   1   2  -1  -1
  -5  -3   3   8  -3  -2  -7
   2  -1  -2   2  -1   4  -4
   2  -3   4   5  -2   1  -4
>> fun(2)
ans =
   5   0   1  -1  -2   1   1
   0  -3   4   7  -5  -1  -6
   7  -1  -1   1  -3   5  -3
   7  -3   5   4  -4   2  -3
>> fun(3)
ans =
   5   3  -3  -8   3   2   7
   0   3  -4  -7   5   1   6
   7   2  -5  -6   2   6   3
   7   0   1  -3   1   3   3
>> fun(4)
ans =
  -2   1   2  -2   1  -4   4
  -7   1   1  -1   3  -5   3
  -7  -2   5   6  -2  -6  -3
   0  -2   6   3  -1  -3   0
>> fun(5)
ans =
  -2   3  -4  -5   2  -1   4
  -7   3  -5  -4   4  -2   3
  -7   0  -1   3  -1  -3  -3
   0   2  -6  -3   1   3   0

Answer 2

[KSSV]

N = 10 ;
v = rand(N,1) ;
iwant = zeros(N-1,N) ;
for i = 1:N
    idx = setdiff(1:N,i) ;
    iwant(:,i) = v(i)-v(idx) ;
end

[Gianluca Ligresti]

This code work over your v, that is a row vector. Instead I have a MATRIX A and I have to perform the differences between row vectors, so this solution doesn't work for my case