how do I combine only the vectors - Matlab

Question

How do I combine all the vectors in small subsets of vectors in Matlab?

a= [5 6 7] b = [8 9 10] c=[11 12 13] d=[14 15 16] e=[17 18 19]

a combine with b and c:

Outcome:

M1= [ 5 6 7 8 9 10 11 12 13]

a with b and d:

M2 = [5 6 7 8 9 10 14 15 16]

and so on .....

So, combine in groups of 3 without repetitions? Are all those vectors of lengths 3? — Divakar, Apr 16 '15 at 20:51

Luis Mendo · Accepted Answer · 2015-04-16T21:36:23.037

This answer covers the case for an arbitrary number of vectors. The vectors are assumed to be row vectors of equal length.

Let your example data be defined as

a = [5 6 7]; b = [8 9 10]; c = [11 12 13]; d = [14 15 16]; e = [17 18 19];
vectors = {a, b, c, d, e}; %// cell array with any number of row vectors of equal size
n = 3; %// desired subset size

Then: generate all combinations of indices, use that to index into vectors, concatenate into one big row vector, and reshape that to obtain the desired result:

combs = nchoosek(1:numel(vectors), n);
result = reshape([vectors{combs.'}], numel(vectors{1})*n, []).';

This gives a matrix whose first row is your M1, second row is M2 etc:

result =
     5     6     7     8     9    10    11    12    13
     5     6     7     8     9    10    14    15    16
     5     6     7     8     9    10    17    18    19
     5     6     7    11    12    13    14    15    16
     5     6     7    11    12    13    17    18    19
     5     6     7    14    15    16    17    18    19
     8     9    10    11    12    13    14    15    16
     8     9    10    11    12    13    17    18    19
     8     9    10    14    15    16    17    18    19
    11    12    13    14    15    16    17    18    19

Yes, as stated in my code. The OP example seems to suggest that. But the question is not clear — Luis Mendo, Apr 16 '15 at 21:29
You don't need to deal with cell arrays then I guess: `A = cat(1,a,b,c,d,e).'; out = reshape(A(:,nchoosek(1:5,3).'),9,[]).';`? Very similar to your existing one. — Divakar, Apr 16 '15 at 21:31
@Divakar Yes, for the 5-vector case I agree. I tried to make it more general so that it works for any number of vectors. I'll make that clearer in my answer — Luis Mendo, Apr 16 '15 at 21:34
Luis Mendo's answer is what I was looking for. A general approach for same size vectors. Thank you very much. — Emanuel, Apr 18 '15 at 06:09

score 1 · Answer 2 · answered Apr 16 '15 at 21:00

1

You can use the cat function:

res = cat(2,a,b,c);

or simply the [] syntax:

res = [a b c];

In both cases, res will contain [5 6 7 8 9 10 11 12 13].

Best,

answered Apr 16 '15 at 21:00

Ratbert

5,463
2
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score 0 · Answer 3 · edited May 23 '17 at 11:43

Use nchoosek.

a = [5 6 7]; b = [8 9]; c = [11 12 13]; d = [14 15 16]; e = [17 18 19];
N = 3;
x = {a,b,c,d,e};
y = nchoosek(x,N);

And you have all the combination of your arrays taken N at a time in a cell array. Each row i of the cell x is a combination, so to have it back as a row vector just do

horzcat(y{i,:})

Or, if you want to get them all and put them in a cell array of size n_combs

n_combs = size(y,1);
out = cell(0,n_combs);
for i = 1 : n_combs
    out{i} = horzcat(1, y{i,:});
end

There is no constraint on the size of the arrays that you want to combine, e.g., you can combine

a = [5 7]; b = [8 9]; c = [11]; d = [20 14 15 16]; e = [17 18 19];

However, if you must put together all the combination in a matrix, then the arrays have to be of the same size. In this case Luis Mendo's answer does the job.

Finally, if repetitions are allowed use nmultichoosek instead of nchoosek.

how do I combine only the vectors - Matlab

3 Answers3