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

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

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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. Matlab link|improve this question edited Nov 17 '09 at 16:07gnovice48k44895 asked Nov 17 '09 at 16:04gurwinder6719 100% accept rate.

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}.

– gurwinder Nov 17 '09 at 16:36 @gurwinder: The code above is general enough to handle whatever size a may be. If a is 100-by-20, you will end up performing 4950 comparisons, so comparisons will be a 4950-by-2 matrix and keys will be a cell array with 4950 elements (where each cell contains a set of common keys for the respective comparison). – gnovice Nov 17 '09 at 16:43 +1 good use of the nchoosek function!

– Amro Nov 17 '09 at 17:24 @Amro: Thanks. I was tempted to use my HANKEL solution again (stackoverflow.com/questions/1702140/…), but NCHOOSEK is a bit clearer, and I figured the OP would be working with relatively small matrices. – gnovice Nov 17 '09 at 17:30.

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.

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