Find equal rows between two Matlab matrices

Question

I have a matrix index in Matlab with size GxN and a matrix A with size MxN.

Let me provide an example before presenting my question.

clear
N=3;
G=2;
M=5;

index=[1  2  3;
       13 14 15]; %GxN

A=[1  2  3; 
   5  6  7; 
   21 22 23; 
   1  2  3;
   13 14 15]; %MxN

I would like your help to construct a matrix Response with size GxM with Response(g,m)=1 if the row A(m,:) is equal to index(g,:) and zero otherwise.

Continuing the example above

Response= [1 0 0 1 0; 
           0 0 0 0 1]; %GxM

This code does what I want (taken from a previous question of mine - just to clarify: the current question is different)

Response=permute(any(all(bsxfun(@eq, reshape(index.', N, [], G), permute(A, [2 3 4 1])), 1), 2), [3 4 1 2]);

However, the command is extremely slow for my real matrix sizes (N=19, M=500, G=524288). I understand that I will not be able to get huge speed but anything that can improve on this is welcome.

Answer 1

Aproach 1: computing distances

If you have the Statistics Toolbox:

Response = ~(pdist2(index, A));

or:

Response = ~(pdist2(index, A, 'hamming'));

This works because pdist2 computes the distance between each pair of rows. Equal rows have distance 0. The logical negation ~ gives 1 for those pairs of rows, and 0 otherwise.

Approach 2: reducing rows to unique integer labels

This approach is faster on my machine:

[~,~,u] = unique([index; A], 'rows');
Response = bsxfun(@eq, u(1:G), u(G+1:end).');

It works by reducing rows to unique integer labels (using the third output of unique), and comparing the latter instead of the former.

For your size values this takes approximately 1 second on my computer:

clear
N = 19; M = 500; G = 524288;
index = randi(5,G,N); A = randi(5,M,N);
tic
[~,~,u] = unique([index; A], 'rows');
Response = bsxfun(@eq, u(1:G), u(G+1:end).');
toc

gives

Elapsed time is 1.081043 seconds.

Answer 2

MATLAB has a multitude of functions for working with sets, including setdiff, intersect, union etc. In this case, you can use the ismember function:

[~, Loc] = ismember(A,index,'rows');

Which gives:

Loc =
     1
     0
     0
     1
     2

And Response would be constructed as follows:

Response = (1:size(index,1) == Loc).';

Response =
  2×5 logical array
   1   0   0   1   0
   0   0   0   0   1