How to construct a binary matrix reporting 1 in case of equal rows of two arrays of different dimensions?

Hi, I have a matrix nxk

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

and a matrix B mxk (m can be > = or < n)

B=[ 2 3; 4 5; 1 2; 5 6; 10 23; 7 8]

Each row of B is different.

I want to construct a matrix C nxm in which the hi-th element is 1 if A(h,:)=B(i,:), i.e.

C=[0 0 1 0 0 0; 0 0 0 0 0 0; 0 0 0 1 0 0; 0 0 0 0 0 1];

without looping.

[Image Analyst]

Why the fear of looping for such a nano-sized matrix? Too much caffeine?

[MRC]

The matrices in my code are much much bigger. This is just an example.

Answer 1

[Ashish Gudla]

You could create the 'C' matrix with all zeros and then, find the positions where its supposed to be '1' and replace it.

To find the positions where there would be '1', you can use "ismember" function with rows( see doc ) to get the lowest index of each row in A that appears in B.

[a1,~] = size(A);
[b1,~] = size(B);
[~,t2]=ismember(A,B,'rows'); 
t1 = 1:a1;
t1= t1(t2~=0); %ignore zero indices
t2 = t2(t2~=0);
C = zeros(a1,b1); 
i = sub2ind(size(C),t1,t2');
C(i) =1;

Answer 2

[Chris Turnes]

One way to do this without looping would be to exploit the property that two vectors w and v are equal if and only if

Using this, you could construct each term and compare:

>> IP = A*B.';
>> An = sum(abs(A).^2, 2); % abs only necessary if data is complex
>> Bn = sum(abs(B).^2, 2);
>> C = (IP == An*ones(1, length(Bn))) & (IP == ones(length(An), 1)*Bn.');

This is a way of vectorizing the operation, but it will use much more memory than looping would.