MATLAB: How generate combination list of 4 independent vectors

combinationlist

Hello,
I have a question. I am trying to generate list of 4 vectors. For example v1=[ 1; 2; 3, 4]; v2=[ 5; 6; 7]; v3=[ 8; 9]; v4=[ 10] will generate matrix with 24 rows (number of possible combinations) and with 4 columns.
I tried to use 4 for-loops, but when input vectors have more elements (200 elements for each vector), the algorithm is starting to be slow. I would like to ask you for a help. Is there any other possible way or a matlab function to create this thing?
Thank You, Dominik.
M1_idx=[1; 2; 3; 4]; M2_idx=[5; 6; 7]; M3_idx=[8; 9]; M4_idx=[10];
[r1,c1] = size(M1_idx);
[r2,c2] = size(M2_idx);
[r3,c3] = size(M3_idx);
[r4,c4] = size(M4_idx);
K_mat = zeros(r1*r2*r3*r4,c1+c2+c3+c4);
for i=1:r1
   for j=1:r2 
       for k=1:r3
           for l=1:r4
                K_mat((i-1)*r2*r3*r4 + (j-1)*r3*r4 + (k-1)*r4 + l,:) = [M1_idx(i) M2_idx(j) M3_idx(k) M4_idx(l)];   
           end
       end
   end
end

Best Answer

A simple solution for a fixed number of vectors:
>> [x1,x2,x3,x4] = ndgrid(v1,v2,v3,v4);
>> M = [x1(:),x2(:),x3(:),x4(:)]
M =
    1    5    8   10
    2    5    8   10
    3    5    8   10
    4    5    8   10
    1    6    8   10
    2    6    8   10
    3    6    8   10
    4    6    8   10
    1    7    8   10
    2    7    8   10
    3    7    8   10
    4    7    8   10
    1    5    9   10
    2    5    9   10
    3    5    9   10
    4    5    9   10
    1    6    9   10
    2    6    9   10
    3    6    9   10
    4    6    9   10
    1    7    9   10
    2    7    9   10
    3    7    9   10
    4    7    9   10
A general solution which expands to any number of vectors (which should be stored in one cell array, as using numbered variables invariably leads to inefficient code):
>> C = {v1,v2,v3,v4}; % vectors should be stored in one cell array.
>> [C{:}] = ndgrid(C{:});
>> M = cell2mat(cellfun(@(m)m(:),C,'uni',0))
M =
    1    5    8   10
    2    5    8   10
    3    5    8   10
    4    5    8   10
    1    6    8   10
    2    6    8   10
    3    6    8   10
    4    6    8   10
    1    7    8   10
    2    7    8   10
    3    7    8   10
    4    7    8   10
    1    5    9   10
    2    5    9   10
    3    5    9   10
    4    5    9   10
    1    6    9   10
    2    6    9   10
    3    6    9   10
    4    6    9   10
    1    7    9   10
    2    7    9   10
    3    7    9   10
    4    7    9   10
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