How to get the combinations of elements of two arrays?

Hi! I need to generate the combinations of elements of two arrays with different lengths. For example, if

A = [1,2,3]; B = [4,5];

I wish to get all combinations of elements from two arrays as

C = [1 4;1 5;2 4;2 5;3 4;3 5];

What comes to my mind is

[m,n] = meshgrid(A,B');
[C(:,1),C(:,2)] = deal(reshape(m,[],1),reshape(n,[],1));

Is there any more straight way to accomplish this?

And further, if I have three or more arrays to combine, what should I do?

Answer 1

[Stephen23]

A = [1,2,3];
B = [4,5];
[n,m] = ndgrid(B,A);
out = [m(:),n(:)]

out = 6×2

1 4 1 5 2 4 2 5 3 4 3 5

"And further, if I have three or more arrays to combine, what should I do?"

Put them all in a cell array and use two comma-separated lists:

C = {A,B};
[C{end:-1:1}] = ndgrid(C{end:-1:1});

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/1656435-tutorial-comma-separated-lists-and-how-to-use-them

EDIT: using CAT & RESHAPE is probably the most efficient approach:

n = numel(C);
E = reshape(cat(n,C{:}),[],n)

E = 6×2

1 4 1 5 2 4 2 5 3 4 3 5

This approach is from Dyuman Joshi's comment here:

https://www.mathworks.com/matlabcentral/answers/433424-how-to-get-the-combinations-of-elements-of-two-arrays#comment_2937731

[Hemming]

Woooo! It works. Thanks a lot!

[Dyuman Joshi]

@Stephen23, you can avoid using cellfun()

A = [1 2 3];
B = [4 5];
C = [2 3 5 7];

D = {A,B,C};

n = numel(D);
E = D;
[E{end:-1:1}] = ndgrid(E{end:-1:1});
E = reshape(cat(n,E{:}),[],n)

E = 24×3

1 4 2 1 4 3 1 4 5 1 4 7 1 5 2 1 5 3 1 5 5 1 5 7 2 4 2 2 4 3

[Stephen23]

@Dyuman Joshi: thank you, that is a very good approach! I copied it into my answer so that it does not get lost in the comments.

[Dyuman Joshi]

You are welcome!

Note that the usage of the indices in reverse order is to obtain the output in lexicographical manner (in the order of the values provided in the inputs).

Answer 2

[Jeff Miller]

You might like allcomb on File Exchange:

For example:

>> A = [1,2,3]; B = [4,5];

>> C=allcomb(A,B)

C =

1 4

1 5

2 4

2 5

3 4

3 5

[Hemming]

Nice choice! And this code performs faster than the above one (MATLAB R2016a) although both adopt the similar method. Thanks a lot!

Answer 3

[Mike Croucher]

As of MATLAB R2023a, the new combinations function can do this for you. Details at The new combinations function in MATLAB – for cartesian products and parameter sweeps » The MATLAB Blog - MATLAB & Simulink (mathworks.com)

>> A = [1,2,3];B=[4,5];
>> C = combinations(A,B)

C =

6×2 table

A    B
_    _

1    4
1    5
2    4
2    5
3    4
3    5

The result is a table. When all data types are compatible (as is the case here) you can get the matrix like this

>> C.Variables

ans =

1     4
1     5
2     4
2     5
3     4
3     5

Answer 4

[ROHIT KHATRI]

In MATLAB R2017b allcomb and combinations codes not working. So please tell me what can i do?

[Stephen23]

https://www.mathworks.com/matlabcentral/answers/433424-how-to-get-the-combinations-of-elements-of-two-arrays#answer_350184