How can I obtain all possible combinations of given vectors in MATLAB?

I want to obtain all possible combinations of a set of vectors. For example, if

a=1:3; b=4:5

I want to generate the following vector:

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

Answer 1

[MathWorks Support Team]

There are several ways to obtain all possible combinations of a set of vectors.

a) If the set consists of 2 vectors, a and b, you can execute the following code:

[A,B] = meshgrid(a,b);
c=cat(2,A',B');
d=reshape(c,[],2);

b) If the set consists of 2 or more vectors, you can use the Neural Network Toolbox function COMBVEC to achieve the desired result. More information about COMBVEC function can be obtained form the following link:

https://www.mathworks.com/help/deeplearning/ref/combvec.html

c) If Neural Network Toolbox is not available, you can achieve the desired result from MATLAB Central file exchange* function through the following link:

https://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin

*Note that MathWorks does not guarantee or warrant the use or content of these submissions. Any questions, issues, or complaints should be directed to the contributing author.

[Adam Danz]

+1 To add to this...

to avoid repeat combinations in the form of [20 30; 30 20]

d = unique(sort(d,2), 'rows')

And to remove self-combinations such as [20 20]

d(d(:,1)==d(:,2),:) = []

[Adam Danz]

Note that ndgrid provides more compatible results with combvec, rather than using meshgrid.

a = 1:3;
b = 5:6;
c= 12:14;

M1 = combvec(a,b,c)

M1 = 3×18

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 5 5 5 6 6 6 5 5 5 6 6 6 5 5 5 6 6 6 12 12 12 12 12 12 13 13 13 13 13 13 14 14 14 14 14 14

[an, bn, cn] = ndgrid(a,b,c); 
M2 = [an(:), bn(:), cn(:)]'

M2 = 3×18

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 5 5 5 6 6 6 5 5 5 6 6 6 5 5 5 6 6 6 12 12 12 12 12 12 13 13 13 13 13 13 14 14 14 14 14 14

isequal(M1,M2) % same as combvec

ans = logical
   1

[am, bm, cm] = meshgrid(a,b,c); 
M3 = [am(:), bm(:), cm(:)]'

M3 = 3×18

1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 12 12 12 12 12 12 13 13 13 13 13 13 14 14 14 14 14 14

isequal(M1,M3) % requires reshaping

ans = logical
   0

Answer 2

[stewpend0us]

This worked for me (probably the same thing that's going on in the "ALLCOMB" function that was suggested):

 elements = {1:2, 3:5, 6:7, 8:10}; %cell array with N vectors to combine
 combinations = cell(1, numel(elements)); %set up the varargout result
 [combinations{:}] = ndgrid(elements{:});
 combinations = cellfun(@(x) x(:), combinations,'uniformoutput',false); %there may be a better way to do this
 result = [combinations{:}]; % NumberOfCombinations by N matrix. Each row is unique.

[Rik]

Thanks, it took quite some effort to find this answer. I'm glad I don't have to hack something with a decision tree or n nested loops...

Answer 3

[Steven Lord]

As of release R2023a you can use the combinations function in MATLAB for this task.

T = combinations(1:3, 4:6)

T = 9×2 table
    Var1    Var2
    ____    ____

     1       4  
     1       5  
     1       6  
     2       4  
     2       5  
     2       6  
     3       4  
     3       5  
     3       6  

While combinations does return a table, if the data in all of the inputs are compatibly typed you can extract the contents of the table as a matrix in one line.

M = combinations(1:3, 4:6).Variables

M = 9×2

1 4 1 5 1 6 2 4 2 5 2 6 3 4 3 5 3 6

The table output allows for mixing of types.

T = combinations(1:3, ["red", "blue", "green"])

T = 9×2 table
    Var1     Var2  
    ____    _______

     1      "red"  
     1      "blue" 
     1      "green"
     2      "red"  
     2      "blue" 
     2      "green"
     3      "red"  
     3      "blue" 
     3      "green"