How do I compare elements of one row with every other row in the same matrix in MATLAB?

Question

I have the matrix:

a = [ 1 2 3 4;
      2 4 5 6;
      4 6 8 9]

and I want to compare every row with every other two rows one by one. If they share the same key then the result will tell they have a common key.

Answer 1

Here's one solution (which is generalizable to larger matrices than the sample in the question):

comparisons = nchoosek(1:size(a,1),2);
N = size(comparisons,1);
keys = cell(N,1);
for i = 1:N
  keys{i} = intersect(a(comparisons(i,1),:),a(comparisons(i,2),:));
end

The function NCHOOSEK is used to generate all of the unique combinations of row comparisons. For the matrix a in your question, you will get comparisons = [1 2; 1 3; 2 3], meaning that we will need to compare rows 1 and 2, then 1 and 3, and finally 2 and 3. keys is a cell array that stores the results of each comparison. For each comparison, the function INTERSECT is used to find the common values (i.e. keys). For the matrix a given in the question, you will get keys = {[2 4], 4, [4 6]}.

Answer 2

Using @gnovice's idea of getting all combinations with nchoosek, I propose yet another two solutions:

• one using ismember (as noted by @loren)
• the other using bsxfun with the eq function handle

The only difference is that intersect sorts and keeps only the unique common keys.

a = randi(30, [100 20]);
%# a = sort(a,2);

comparisons = nchoosek(1:size(a,1),2);
N = size(comparisons,1);
keys1 = cell(N,1);
keys2 = cell(N,1);
keys3 = cell(N,1);

tic
for i=1:N
    keys1{i} = intersect(a(comparisons(i,1),:),a(comparisons(i,2),:));
end
toc

tic
for i=1:N
    query = a(comparisons(i,1),:);
    set = a(comparisons(i,2),:);
    keys2{i} = query( ismember(query, set) );             %# unique(...)
end
toc


tic
for i=1:N
    query = a(comparisons(i,1),:);
    set = a(comparisons(i,2),:)';
    keys3{i} = query( any(bsxfun(@eq, query, set),1) );   %'# unique(...)
end
toc

... with the following time comparisons:

Elapsed time is 0.713333 seconds.
Elapsed time is 0.289812 seconds.
Elapsed time is 0.135602 seconds.

Note that even by sorting a beforehand and adding a call to unique inside the loops (commented parts), these two methods are still faster than intersect.