ALLCOMB

All combinations of input (v3.0, may 2012)

Description

B = ALLCOMB(A1,A2,A3,...,AN) returns all combinations of the elements in A1, A2, ..., and AN. B is P-by-N matrix is which P is the product of the number of elements of the N inputs.

Empty inputs yields an empty matrix B of size 0-by-N. Note that previous versions (1.x) simply ignored empty inputs.

Example:
allcomb([1 3 5],[-3 8],[0 1]) ;
        1 -3 0
        1 -3 1
        1 8 0
        ...
        5 -3 1
        5 8 0
        5 8 1
     
ALLCOMB(A1,..AN,'matlab') causes the first column to change fastest. This is more consistent with matlab indexing. Example:
allcomb(1:2,3:4,5:6,'matlab') %->
       1 3 5
       2 3 5
       1 4 5
       ...
       2 4 6
 
This functionality is also known as the cartesian product.

ALLCOMB also accepts character arrays:
allcomb('abc','XY')
       aX
       aY
       bX
       bY
       cX
       cY

See also <COMBN> here on the FEX

Acknowledgements

This file inspired Create Unique Interaction Variables.

• MATLAB release: MATLAB 6.5 (R13)

[Matthieu]

Hello,

I wanted to have the index of the computed combinaison.

I propose this solution if other people id interested:

[A index] = allcomb(varargin)
...
...

if nargout>1
create_index = @(x) cellfun(@(y) 1:numel(y), x, 'UniformOutput', false);
idx = create_index(args);
[index{ii}] = ndgrid(idx{ii});
index = reshape(cat(ni+1,index{:}),[],ni) ;
end

[raj singh]

superb, i was trying for this problem, but this Ans solved my problem within second

[Jos (10584)]

@Ofer To combine strings with doubles you can use a cell array. You can use allcomb to retrieve the indices, as in

D = [10 11] % doubles
S = {'s1','s2','s3'}
ix = allcomb(1:numel(D), 1:numel(S))

[Ofer Rozen]

great function. how can i combine strings with doubles?

[Moshe Lindner]

 

[Jos (10584)]

@Amri, good suggestion! I will update the file shortly.

[Amri]

it works only with double variables !?
i need the same function but with caracters ?

[K E]

Why not built in to Matlab?

[Jos (10584)]

Thanks Edward, a small glitch on my side ... fixed in version 2.2

[Edward Sciberras]

Jos, I think you're missing a semicolon in line 60 for ischar(argn). Results in 0 being printed in the terminal without this.

[Harry MacDowel]

Great and easy to use!

[Forrest]

Can you explain how to install this and get it to work?

[Mike Sheppard]

In the Neural Network Toolbox there is combvec, which produces the same results as the examples.
combvec([1 3 5],[-3 8],[0 1])
combvec(1:2,3:4,5:6)
If you have the toolbox the combvec might be helpful, if not then allcomb might help for general.

[Marco Uzielli]

Very efficient in my case.

[Bruno Luong]

 

[Bruno Luong]

Here is a debate that will convince you Jos.

A cartesian's product of n sets has a cardinal equals to the product of cardinals of each set.

NCOMB must return [prod(numel(xi)) x n] size array.

An empty set has zeros cardinal, thus all comb MUST return 0 x n.

This is a correct answer.

Why this is important. Here is an example

In post #4 of this thread
http://www.mathworks.com/matlabcentral/newsreader/view_thread/299532

I used NDGRID to generate a combination of 2 sets. NDGRID handles correctly empty configuration, this my code can directly work. I can't replace with ALLCOMB because the empty set is not consistently handle.

[Jos (10584)]

Somehow my first reply to Bruno does not show up. I wanted to say to Bruno "maybe I can issue a warning when an input is empty".
If ALLCOMB returns empty or ignores an empty input is, in my opinion, a matter of debate.

[Jos (10584)]

Hmm, there already is a warning ... I should read my own code more carefully ...

[Bruno Luong]

Jos, IMO allcomb returns incorrect result when one of the argument is is empty

It should return an empty (0xn) array where n is the number of arguments.

[Lin Li]

 

[Jose]

 

[Peter]

Very nice!

[Jan Simon]

Comapct and fast algorithm - thanks!
The flipping can be omitted to save time:
[A{1:ni}] = ndgrid(args{ii}) ;
A = reshape(cat(ni+1,A{:}),[],ni) ;
A = A(:,ii) ;
==>
[A{ii}] = ndgrid(args{ii}) ;
A = reshape(cat(ni+1,A{:}),[],ni) ;
E.g. for ALLCOMB(1:100, 1:100, 1:100) this is 24% faster on my machine (Matlab 2009a, WinXP, 32 bit).

[Andrea Asoni]

very useful. it is possible to have the exact same thing for symbolic objects (i am working with tomSym)?

[Tsinghua Jun]

so powerful, it is what I've been looking for~~

[fabio]

easy things are always the best! Great!

[Merrill Birdno]

Thanks! I've been looking for something like this.

[Marco Vilela]

Good job

[Tom Pinkiewicz]

Great, just what I wanted!

[Jiying Yin]

where can I find allcomb.m file? Thanks!

[kinor Mueller]

nice function, poor not to find it in matlab itself ;-)

[Jarek Zwolski]

I'd lost some time before I found it. This short piece of code sloves my problem and does it excellent. Thanks

[Antoni J. Canós]

Excellent! That's what I needed!

[Jos van der Geest]

I just updated this file: a minor "bug" was removed when none of the inputs were empty. I also added the option to let the first argument move most rapidly, as suggested by John D'Errico.

[John D'Errico]

Good help, error checks, not much to say here. Only one comment: I'd argue that the first argument should move most rapidly, to be consistent with Matlab indexing.