# Vectors seen as a combination of other vector's elements

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Luca Freilino on 12 Apr 2019
Edited: Luca Freilino on 12 Apr 2019
Hi everyone.
I have a problem that I think to be quite easy, but I can't succeed in solving it.
I have four vectors of different length (a, b, c, d). I'd like to have a final vector (V) which contains all the combinations of their elements.
eg, if I had a = [1 2 3], b = [4 5], c = , V should be [1 4 6; 1 5 6; 2 4 6; 2 5 6; 3 4 6; 3 5 6].
Now I'm using four nested for cycle, but I'd like to find a faster solution, without using the cycle but maybe some logical solutions.
P.S. I leave the portion of my code:
for n = 1:length(comb_n)
for i = 1:length(comb_i)
for c = 1:length(comb_c)
for a = 1:length(comb_a)
combinations(index,1:number_surrogates) = [comb_n(n,:), comb_i(i,:), comb_c(c,:), comb_a(a,:)];
index = index+1;
end
end
end
end

madhan ravi on 12 Apr 2019
[X,Y,Z]=meshgrid(a,b,c);
[X(:),Y(:),Z(:)]

Guillaume on 12 Apr 2019
Personally, I'd use ndgrid instead of meshgrid. ndgrid works for higher dimensions, and operates consistently on all dimensions whereas meshgrid swaps the order of the first two dimensions.
Both will produce the same result, just wih a different ordering.
madhan ravi on 12 Apr 2019
Yes, I agree.
Luca Freilino on 12 Apr 2019
I tried with meshgrid, but it doesn't work since I've always four vectors. I forgot to say that these vectors could be even matrices (eg the second one could be a (N,2) size). Could you explain me how to use the ndgrid? I know the function, but I have no idea which conditions should I use. Thanks, Luca

Guillaume on 12 Apr 2019
This is the generic version of Madhan's answer. Works for any (reasonable!) number of inputs.
in = {[1, 2, 3], [4, 5], 6}; %cell array of vectors.
combs = cell(size(in));
[combs{:}] = ndgrid(in{:});
combs = reshape(cat(numel(combs) + 1, combs{:}), [], numel(combs));
You could also download AllComb from the filexchange, which does the same.

Torsten on 12 Apr 2019
Why not simply reshaping matrices to vectors:
A = A(:)
before applying Guillaume's code ?
madhan ravi on 12 Apr 2019
Same thought as Torsten's but your question is most likely solved by Guillaume's method.
Luca Freilino on 12 Apr 2019
It's not a good solution or, at least, this is not good for my problem. I forward the code, it shoud be easier to explain:
v = [1 2 2 1];
a = 1:12;
b = 13:29;
c = 30:39;
d = 40:47;
A = nchoosek(a,v(1));
B = nchoosek(b,v(2));
C = nchoosek(c,v(3));
D = nchoosek(d,v(4));
What I need is the family of combination, like:
1 13 14 30 31 40;
1 13 14 30 31 41;
.........................
1 13 14 30 32 40;
.........................
.........................
.........................
12 28 29 38 39 47