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All combinations of input (v4.1, feb 2016)



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ALLCOMB - All combinations
B = ALLCOMB(A1,A2,A3,...,AN) returns all combinations of the elements
in the arrays 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. This functionality is also
known as the Cartesian Product. The arguments can be numerical and/or
characters, or they can be cell arrays.

allcomb([1 3 5],[-3 8],[0 1]) % numerical input:
% -> [ 1 -3 0
% 1 -3 1
% 1 8 0
% ...
% 5 -3 1
% 5 8 1 ] ; % a 12-by-3 array

allcomb('abc','XY') % character arrays
% -> [ aX ; aY ; bX ; bY ; cX ; cY] % a 6-by-2 character array

allcomb('xy',[65 66]) % a combination
% -> ['xA' ; 'xB' ; 'yA' ; 'yB'] % a 4-by-2 character array

allcomb({'hello','Bye'},{'Joe', 10:12},{99999 []}) % all cell arrays
% -> { 'hello' 'Joe' [99999]
% 'hello' 'Joe' []
% 'hello' [1x3 double] [99999]
% 'hello' [1x3 double] []
% 'Bye' 'Joe' [99999]
% 'Bye' 'Joe' []
% 'Bye' [1x3 double] [99999]
% 'Bye' [1x3 double] [] } ; % a 8-by-3 cell array

ALLCOMB(..., 'matlab') causes the first column to change fastest which
is consistent with matlab indexing. Example:
% -> [ 1 3 5 ; 1 4 5 ; 1 3 6 ; ... ; 2 4 6 ]

If one of the arguments is empty, ALLCOMB returns a 0-by-N empty array.

See also nchoosek, perms, ndgrid
and nchoose, combn, kthcombn (matlab Central FEX)

Comments and Ratings (55)

Jos (10584)

Jos (10584) (view profile)

@Mendi Barel: You can use simple comma-separated list expansion for this:
C = {[1 2],[1 2 3],[5 6]})

Mendi Barel

Great. Better to add support for dynamic size pf vectors. For example this kind of input:

allcomb({[1 2],[1 2 3],[5 6]})

Hello everybody, I have submitted a question regarding this function at Matlab's question section. Please feel free to have a look at:
I am having trouble with the input.


@shiva, can you explain better your position about the memory?


This is like combntns, very useful. I don't know why matlab developer removed it from the library.




YS (view profile)

Mihir Shah


midhun (view profile)

Is it possible to set a constraint. I mean each combination in A should satisfy a condition. If

A= 0 0
1 0
2 0
0 1
1 1
2 1
0 2
1 2
2 2
0 3
1 3
2 3

Then I need only a combination that satisfies
B*A'=constant (for some matrix B).

If I generate all combination for 20 vectors using combvec, I am getting around 400,000 combinations, But I need only 200 of them which satisfies my condition.

Is it possible to pass a matrix as input argument to allcomb so that the input arguments are columns of matrix?...


midhun (view profile)

Is it possible to set a constraint. I mean each combination in A should satisfy a condition. If

A= 0 0
1 0
2 0
0 1
1 1
2 1
0 2
1 2
2 2
0 3
1 3
2 3

Then I need only a combination that satisfies
B*A'=constant (for some matrix B).

If I generate all combination for 20 vectors using combvec, I am getting around 400,000 combinations, But I need only 200 of them which satisfies my condition.

To make allcomb work with cell inputs and 'matlab' parameter, you need to add the line:


after the if statement (line 69)


Kenan Turbic

Sergei P.

Jos (10584)

Jos (10584) (view profile)

@Alexander Implementing this would require the Statistics Toolbox. However, you can easily generate the table yourself, using ALLCOMB on the indices. I assume you should be able to do something like this:

idxAB = allcomb(1:numel(A),1:numel(B))
out = [A(idxAB(:,1)) B(idxAB(:,2))]


Excellent function! Given that this function can be used to create combinations of selections from a number of categories (A1...AN), could you allow it to operate on categorical arrays? The output could be either a table (preferably) or cell array, as in the example below.

A = categorical({'A1','A2'})
B = categorical({'B1','B2','B3'})

% -> Var1 Var2
% ____ ____
% A1 B1
% A1 B2
% A1 B3
% A2 B1
% A2 B2
% A2 B3



shiva (view profile)

This is an awesome piece of code!
Although i have an request, like say when I have a 5 or more large vectors (eg.,-200:200) i encounter memory problems.
I was thinking like,
1) check the maximum variable size for the particular computer.
2) if the size of the generated variable is more than the maximum size permitted store the intermediate result in a "mat" file. clear the contents of the variable and append the successive results to the end of the "mat" file

Julian Gomez



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) ;

raj singh

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

Jos (10584)

Jos (10584) (view profile)

@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

Moshe Lindner (view profile)

Jos (10584)

Jos (10584) (view profile)

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


Amri (view profile)

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


K E (view profile)

Why not built in to Matlab?

Jos (10584)

Jos (10584) (view profile)

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

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

Great and easy to use!


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

Mike Sheppard

Mike Sheppard (view profile)

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

Very efficient in my case.

Bruno Luong

Bruno Luong (view profile)

Bruno Luong

Bruno Luong (view profile)

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

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)

Jos (10584) (view profile)

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)

Jos (10584) (view profile)

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

Bruno Luong

Bruno Luong (view profile)

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

Lin Li (view profile)


Jose (view profile)

Very nice!

Jan Simon

Jan Simon (view profile)

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 (view profile)

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.



fixed error noted by Richard


v4.0 accepts cell arrays as input


now accepts character arrays


remove superfluous line of code (thanks to Edward)


(2.1, feb 2011) - fixed the check of the last argument when the last argument was neither a char or a double.


Convinced by Bruno, I decided to change the behavior when an input is empty (now returns empty instead of ignoring the input).


little speed improvement as suggested by Jan Simon

Too hasty in my first revision ...

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