Relation between two vectors elements

Hi all,

suppose I have two vectors:

A = [1 2 3 4 5 6 7 8 9 10];
B = [4 7 8 2 1 10 3 5 9 6];

Ho can I say, the first element in B is the fourth element in A? In other workds, look at each element in B, what is its position/order/index in A? How can I establish a connection between both vectors' elements?

Thanks.

Answer 1

[Torsten]

Determine the permutation matrix P for which P*A = B:

A = [1 2 3 4 5 6 7 8 9 10].';
B = [4 7 8 2 1 10 3 5 9 6].';
P = bsxfun(@eq, A', B);
isequal(P * A, B)

[Lama Hamadeh]

Thank you for your answer.

Jsut to extend further here. What about I want to compare between two matrices row wise. Say that I have the following two matrices:

A = [1 2; 3 1; 4 1; 5 2];
B = [4 1; 5 2; 1 2; 3 1];

How can I produce such a permutation matix of them?

Thanks.

[Lama Hamadeh]

I think I have done it.

Perm =zeros(size(A,1),size(B,1));

for i = 1:size(A,1)
    for j = 1:size(B,1)
        if A(i,:) == B(j,:)
            Perm(i,j) = 1;
        else
            Perm(i,j) = 0;
        end
    end
end

[Torsten]

This code checks whether there are permutation matrices PL and PR such that

PL*A*PR = B,

i.e. whether there are permutations of the rows and columns of A such that you can arrive at B.

A = [1 2; 3 1; 4 1; 5 2];
B = [4 1; 5 2; 1 2; 3 1]; 
I1 = eye(size(A,1));
[~,a1] = sortrows(sort(A,2));
[~,b1] = sortrows(sort(B,2));
I2 = eye(size(A,2));
[~,a2] = sortrows(sort(A,1).');
[~,b2] = sortrows(sort(B,1).');
PL = I1(a1(b1),:)
PR = I2(:,a2(b2))
isequal(PL*A*PR,B)

Answer 2

[Geoff Hayes]

@Lama Hamadeh - consider using intersect and in particular this example.