Loop over combinations of elements of several vectors

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diego solerpolo
diego solerpolo 2023-10-18
评论： Dyuman Joshi 2023-10-18
In the simplest case, if I have vectors , I want to loop over all the possible combinations of their elements, that is, over I wat to do the same thing in a general case where I have and arbitrary number of vectors with respective dimensions , with denoting the k-th component of vector ; that is, I want to loop over all the combinations of elements . How to do this for a general number of vectors? For now, the only thing I came up with is to make nested loops for each vector, but I want some code whose structure does not depend on the number of vectors.
Thanks for your time!

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回答（2 个）

Dyuman Joshi
Dyuman Joshi 2023-10-18
Ran in:
Use ndgrid -
x1 = 1:5;
x2 = [2 3 5 7 11];
x3 = [2 4 6 8 10];
%Store vectors in a cell array
x = {x1,x2,x3};
n = numel(x);
%Preallocate
C = cell(1,n);
%Reverse order to get the proper order when concatenating
[C{end:-1:1}] = ndgrid(x{end:-1:1});
%Concatenate and reshape the data corresponding to number of vectors
out = reshape(cat(n,C{:}),[],n);
disp(out)
1 2 2 1 2 4 1 2 6 1 2 8 1 2 10 1 3 2 1 3 4 1 3 6 1 3 8 1 3 10 1 5 2 1 5 4 1 5 6 1 5 8 1 5 10 1 7 2 1 7 4 1 7 6 1 7 8 1 7 10 1 11 2 1 11 4 1 11 6 1 11 8 1 11 10 2 2 2 2 2 4 2 2 6 2 2 8 2 2 10 2 3 2 2 3 4 2 3 6 2 3 8 2 3 10 2 5 2 2 5 4 2 5 6 2 5 8 2 5 10 2 7 2 2 7 4 2 7 6 2 7 8 2 7 10 2 11 2 2 11 4 2 11 6 2 11 8 2 11 10 3 2 2 3 2 4 3 2 6 3 2 8 3 2 10 3 3 2 3 3 4 3 3 6 3 3 8 3 3 10 3 5 2 3 5 4 3 5 6 3 5 8 3 5 10 3 7 2 3 7 4 3 7 6 3 7 8 3 7 10 3 11 2 3 11 4 3 11 6 3 11 8 3 11 10 4 2 2 4 2 4 4 2 6 4 2 8 4 2 10 4 3 2 4 3 4 4 3 6 4 3 8 4 3 10 4 5 2 4 5 4 4 5 6 4 5 8 4 5 10 4 7 2 4 7 4 4 7 6 4 7 8 4 7 10 4 11 2 4 11 4 4 11 6 4 11 8 4 11 10 5 2 2 5 2 4 5 2 6 5 2 8 5 2 10 5 3 2 5 3 4 5 3 6 5 3 8 5 3 10 5 5 2 5 5 4 5 5 6 5 5 8 5 5 10 5 7 2 5 7 4 5 7 6 5 7 8 5 7 10 5 11 2 5 11 4 5 11 6 5 11 8 5 11 10
Chunru
Chunru 2023-10-18
Ran in:
You can use combinations.
% arbitrary number of vectors with arbitrary size
v{1}=rand(3,1);
v{2}=rand(2,1);
v{3}=rand(2,1);
p =table2array(combinations(v{:}))
p = 12×3
0.0085 0.6301 0.2202 0.0085 0.6301 0.6508 0.0085 0.7299 0.2202 0.0085 0.7299 0.6508 0.8834 0.6301 0.2202 0.8834 0.6301 0.6508 0.8834 0.7299 0.2202 0.8834 0.7299 0.6508 0.4095 0.6301 0.2202 0.4095 0.6301 0.6508
for i=1:size(p,1) % only one loop instead of nested loop
p(i, :) % this is the combination and do whatever you want in the loop
end
ans = 1×3
0.0085 0.6301 0.2202
ans = 1×3
0.0085 0.6301 0.6508
ans = 1×3
0.0085 0.7299 0.2202
ans = 1×3
0.0085 0.7299 0.6508
ans = 1×3
0.8834 0.6301 0.2202
ans = 1×3
0.8834 0.6301 0.6508
ans = 1×3
0.8834 0.7299 0.2202
ans = 1×3
0.8834 0.7299 0.6508
ans = 1×3
0.4095 0.6301 0.2202
ans = 1×3
0.4095 0.6301 0.6508
ans = 1×3
0.4095 0.7299 0.2202
ans = 1×3
0.4095 0.7299 0.6508

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