MATLAB: How to pick up all combination of numbers from multiple vectors

cell arraysloopsMATLAB

I have a number of vectors, probably with different lengths, e.g., a=[1 2 3], b=[4 5 6 7] and c=[8 9 10 11 12]. From a, b and c I have 3*4*5=60 possible points, e.g., one possibility is (1,4,8). If I know the number of vectors and the length of each vector in advance, this is easy to program. However, I want to write a general code that can find all these combinations regardless of the number of vectors and their individual lengths

Best Answer

Don't store your vectors separately. Instead, learn to use tools like cell arrays, which make things hugely more efficient.
V = {[1 2 3],[4 5 6 7],[8 9 10 11 12]};
Next, how do you use a cell array for this purpose? You pass the elements into ndgrid, using what is called acomma separated list. (Or meshgrid.) That is what you get when you type V{:}, a comma separated list. It allows you to pass in each element of the cell array into a function as if each element of the cell array was an argument of the function.
For example, if we did this:
[G1,G2,G3] = ndgrid(V{:});
Hmm. That creates three different arrays, that do contain all combinations of the elements of those vectors if you look carefully. But here we don't want to split the results into n different named arrays. We want a cell array as output. So now, try this:
C = cell(1,numel(V));
[C{:}] = ndgrid(V{:})
C =
  1×3 cell array
    {3×4×5 double}    {3×4×5 double}    {3×4×5 double}
Better. We have captured the output from ndgrid back into a cell array. But what we probably wanted was one flat array, with three columns, and here, 60 rows. We could convert each of those arrays into a column vector easily enough.
C = cellfun(@(X) reshape(X,[],1),C,'UniformOutput',false)
C =
  1×3 cell array
    {60×1 double}    {60×1 double}    {60×1 double}
And, now finally, just convert C into a flat array, using a tool like horzcat. (square brackets will suffice. That is...
C = horzcat(C{:})
C =
     1     4     8
     2     4     8
     3     4     8
     1     5     8
     2     5     8
     3     5     8
     1     6     8
     2     6     8
     3     6     8
     1     7     8
     2     7     8
     3     7     8
     1     4     9
     2     4     9
     3     4     9
     1     5     9
     
     ...
         
     2     7    12
     3     7    12
As you should see, nothing I did was dependent on the size of the arrays, the length of the vectors, the number of different vectors. That was all driven by the one initial cell array as I created it. Learn to use MATLAB, as it was designed to be used.
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