Rows without repetitions - MATLAB

Question

I have a matrix (4096x4) containing all possible combinations of four values taken from a pool of 8 numbers.

...
3    63    39     3
3    63    39    19
3    63    39    23
3    63    39    39
...

I am only interested in the rows of the matrix that contain four unique values. In the above section, for example, the first and last row should be removed, giving us -

...
3    63    39    19
3    63    39    23
...

My current solution feels inelegant-- basically, I iterate across every row and add it to a result matrix if it contains four unique values:

result = [];
for row = 1:size(matrix,1)
    if length(unique(matrix(row,:)))==4
        result =  cat(1,result,matrix(row,:));
    end
end

Is there a better way ?

`nchoosek` would be my recommended approach too. @rwong: You can pass a vector instead of a number as first input, and then you get the combinations, not just the count. For example, `nchoosek(1:8,4)` — Luis Mendo, Feb 08 '15 at 03:39

score 3 · Accepted Answer · edited Jun 20 '20 at 09:12

Approach #1

diff and sort based approach that must be pretty efficient -

sortedmatrix = sort(matrix,2)
result = matrix(all(diff(sortedmatrix,[],2)~=0,2),:)

Breaking it down to few steps for explanation

Sort along the columns, so that the duplicate values in each row end up next to each other. We used sort for this task.
Find the difference between consecutive elements, which will catch those duplicate after sorting. diff was the tool for this purpose.
For any row with at least one zero indicates rows with duplicate rows. To put it other way, any row with no zero would indicate rows with no duplicate rows, which we are looking to have in the output. all got us the job done here to get a logical array of such matches.
Finally, we have used matrix indexing to select those rows from matrix to get the expected output.

Approach #2

This could be an experimental bsxfun based approach as it won't be memory-efficient -

matches = bsxfun(@eq,matrix,permute(matrix,[1 3 2]))
result = matrix(all(all(sum(matches,2)==1,2),3),:)

Breaking it down to few steps for explanation

Find a logical array of matches for every element against all others in the same row with bsxfun.
Look for "non-duplicity" by summing those matches along dim-2 of matches and then finding all ones elements along dim-2 and dim-3 getting us the same indexing array as had with our previous diff + sort based approach.
Use the binary indexing array to select the appropriate rows from matrix for the final output.

Approach #3

Taking help from MATLAB File-exchange's post combinator and assuming you have the pool of 8 values in an array named pool8, you can directly get result like so -

result = pool8(combinator(8,4,'p'))

combinator(8,4,'p') basically gets us the indices for 8 elements taken 4 at once and without repetitions. We use these indices to index into the pool and get the expected output.

Approach 1 was exactly the sort of thing i was hoping to find out about! — Nolan Conaway, Feb 07 '15 at 18:10

score 1 · Answer 2 · edited Feb 07 '15 at 09:05

For a pool of a finite number this will work. Create is unique array, go through each number in pool, count the number of times it comes up in the row, and only keep IsUnique to 1 if there are either one or zero numbers found. Next, find positions where the IsUnique is still 1, extract those rows and we finish.

matrix = [3,63,39,3;3,63,39,19;3,63,39,23;3,63,39,39;3,63,39,39;3,63,39,39];
    IsUnique = ones(size(matrix,1),1);
    pool = [3,63,39,19,23,6,7,8];
    for NumberInPool = 1:8    
        Temp = sum((matrix == pool(NumberInPool))')';
        IsUnique = IsUnique .* (Temp<2);
    end
    UniquePositions = find(IsUnique==1);
    result = matrix(UniquePositions,:)

Rows without repetitions - MATLAB

2 Answers2

Approach #1

Approach #2

Approach #3