Compute all combinations of given vectors into a matrix

Hi all,

I have 4 vectors:

a=[1:4]'
b=[5:10]'
c=[11:15]'
d=[16:20]'

I want to calculate all 2-combinations like this:

1) append the second vector to the first one (e.g.: A=[a;b], B=[a;c], etc...);

2) calculate all the comcinations of the second vector appended to the first one;

3) put everything into a matrix: C=[A,B,etc...]

I don't want to make combinations of all the elements of the vectors, I just want to append the vectors as they are and combine them.

Anyone having an idea?

Thanks,

Matt

[Jan]

The question is not clear. For 4 vectors the job seems to be trivial and you can do this manually. I do not understand the point 2) and 3).

Answer 1

[KSSV]

A = [ {1:4} ; {5:10} ; {11:15} ;{16:20}] ;

idx = 1:length(A) ;
%%append the second vector to the first one (e.g.: A=[a;b], B=[a;c], etc...);
id = randperm(3)+1 ;
A1 = cell(3,1) ;
for i = 1:length(id)
    A1{i} = [A{1} A{id(i)}] ;
end
%%put everything into a matrix: C=[A,B,etc...]
id = perms(idx) ;
A2 = cell(size(id,1),1) ;
for i = 1:size(id,1)
    A2{i} = [A{id(i,:)}] ;
end

Answer 2

[Guillaume]

Your question is not clear at all. Assuming you want to generate all combinations {[a;b], [a;c], [a;d], [b;c], [b;d], [c;d]}, you could just generate them manually since there's only 6. A generic method would be:

a=[1:4]'
b=[5:10]'
c=[11:15]'
d=[16:20]'

allvectors = {a, b, c, d};
combs = nchoosek(1:numel(allvectors), 2);
result = cell(1, size(combs, 1));
for row = 1:size(combs, 1)
   result{row} = vertcat(allvectors{combs(row, :)});
end

Note that because of the different length of your input vectors, it's not possible to make a matrix out of result.