Vectors seen as a combination of other vector's elements

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

Answer 1

[madhan ravi]

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

[X(:),Y(:),Z(:)]

[Guillaume]

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]

Yes, I agree.

[Luca Freilino]

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

Answer 2

[Guillaume]

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.

[Luca Freilino]

Hi, thank you. I tried your solution and it works, but just if I had vectors. I forgot to say that i could have even matrices. Do you have ohter ideas?

Thank you again for your help.

Luca

[Guillaume]

What would the output be if you had matrices as inputs, e.g.

in = {[1 2;3 4], [5 6 7;8 9 10; 11 12 13]}
combs = ???

[Luca Freilino]

It would be: [1 2 5 6 7; 1 2 8 9 10; 1 2 11 12 13; 3 4 5 6 7; 3 4 8 9 10; 3 4 11 12 13]

[Torsten]

Why not simply reshaping matrices to vectors:

A = A(:)

before applying Guillaume's code ?

[madhan ravi]

Same thought as Torsten's but your question is most likely solved by Guillaume's method.

[Luca Freilino]

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