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Vectors seen as a combination of other vector's elements

Asked by Luca Freilino on 12 Apr 2019
Latest activity Edited by 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 = [6], 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.
Thank you in advance. Luca
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

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2 Answers

Answer by madhan ravi
on 12 Apr 2019

[X,Y,Z]=meshgrid(a,b,c);
[X(:),Y(:),Z(:)]

  3 Comments

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.
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

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Answer by 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.

  6 Comments

Why not simply reshaping matrices to vectors:
A = A(:)
before applying Guillaume's code ?
Same thought as Torsten's but your question is most likely solved by Guillaume's method.
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

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