Need help - How to generate predefined subsets?

All:

I have a 5 X 4 matrix defined as

v = [

1 2 3 4;

5 6 7 8 ;

9 10 11 12;

13 14 15 16;

17 18 19 20];

I need to write a code to generate all possible unique combinations of a group of 4 elements. The group needs to contain 1 element from each column. For example:

C1 = 1 2 3 4

C2 = 1 6 7 8

C3 = 1 14 19 20

...

Any help will be greatly appreciated.

Answer 1

[the cyclist]

Here's one way. There might be better ones.

Download this code from the File Exchange:

http://www.mathworks.com/matlabcentral/fileexchange/24325-combinator-combinations-and-permutations

Then run this code:

v = [1  2  3  4;
     5  6  7  8 ;
     9 10 11 12;
    13 14 15 16;
    17 18 19 20];

arrayOfIndices = combinator(5,4);

C = [v(arrayOfIndices(:,1),1), ...
     v(arrayOfIndices(:,2),2), ...
     v(arrayOfIndices(:,3),3), ...
     v(arrayOfIndices(:,4),4)];

This will put all the combinations into one 625 X 4 array, C.

Answer 2

[Teja Muppirala]

Another idea:

[C1,C2,C3,C4] = ndgrid(1:5);
allCombinations = [v(C1,1) v(C2,2) v(C3,3) v(C4,4)]

Or a more flexible way, which will work for any sized v:

[nRows, nCols] = size(v);
C = cell(1,nCols);
[C{:}] = ndgrid(1:nRows);

C = cell2mat(cellfun(@(x)x(:),C,'uniform',0));
C = bsxfun(@plus, C,nRows*(0:nCols-1) );
allCombinations = v(C)