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

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MathWorks Support Team
编辑： MathWorks Support Team 2023-4-19
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]

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采纳的回答

MathWorks Support Team
编辑：MathWorks Support Team 2023-4-19
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.
  2 个评论
Adam Danz
Adam Danz 2018-7-25
+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
Adam Danz 2021-12-7
编辑：Adam Danz 2021-12-7
Ran in:
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

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更多回答（2 个）

stewpend0us
stewpend0us 2017-1-30
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.
  1 个评论
Rik
Rik 2017-7-19
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...

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Steven Lord
Steven Lord 2023-3-16
Ran in:
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"

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