How can I generate all possible combinations of a given number of vectors?

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GaetanWid
GaetanWid 2018-3-13
编辑： Birdman 2018-3-13
Hello, I'm currently trying to generate all possible combinations of given vectors in all possible matrices.
If n=2 the possible vectors are [1 0;0 1;2 0;0 2] If n=3 the possible vectors are [1 0 0;0 1 0;0 0 1;2 0 0;0 2 0;0 0 2]
I generate a matrix with the possible vectors: In this case n=3
B=3;
D_possibilities1=diag(ones(1,B),0);
D_possibilities2=diag(2*ones(1,B),0);
D_possibilities=zeros(B*2,B);
for i=1:B
D_possibilities(i,:)=D_possibilities1(i,:);
D_possibilities(B+i,:)=D_possibilities2(i,:);
end
Now I'm struggling to generate all possible matrices with all possible combinations
Any help is welcome, thanks

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回答（2 个）

Karsten Reuß
Karsten Reuß 2018-3-13
编辑：Karsten Reuß 2018-3-13
There are several commands you may try, depending on if you want replacement/no replacement/ ordering matters or not,
One command is "perms":
perms(0:2)
If the ordering does not matter, you have fewer combinations. In this case the command "combnk" will help
combnk(0:3,3)
Another interesting command that may help you is "nchoosek". In this code you combine the command with "perms", so the ordering matters:
n = 6; k = 2;
nk = nchoosek(1:n,k);
p=zeros(0,k);
for i=1:size(nk,1),
pi = perms(nk(i,:));
p = unique([p; pi],'rows');
end
Birdman
Birdman 2018-3-13
编辑：Birdman 2018-3-13
Hope this is what you want:
clear C;
n=3;
for i=1:n
C{i,1}=unique(perms([zeros(1,n-1) i]),'rows');
end
C=fliplr(cell2mat(C));
C(any(C>2,2),:)=[]
Change n and observe the result you want.

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