Generate all possible combinations

Hi Guys,

I want to combine 4 matrix & get all the possible combinations

the example is

I have matrix A,B,C,D

A = [1;2]

B = [3;4]

C = [5;6]

D = [7;8]

I want to generate all matrix E Combinations

E = [1 3 5 7;1 3 5 8; 1 3 6 7; 1 3 6 8; 1 4 5 7;1 4 5 8; 1 4 6 7; 1 4 6 8;2 3 5 7;2 3 5 8; 2 3 6 7; 2 3 6 8; 2 4 5 7;2 4 5 8; 2 4 6 7; 2 4 6 8 ]

And is there any matlab function to generate it ?

thanks

Answer 1

[Bruno Luong]

A = [1;2]
B = [3;4]
C = [5;6]
D = [7;8]

L = {A,B,C,D};
n = length(L);
[L{:}] = ndgrid(L{end:-1:1});
L = cat(n+1,L{:});
L = fliplr(reshape(L,[],n))

Which gives

L =

     1     3     5     7
     1     3     5     8
     1     3     6     7
     1     3     6     8
     1     4     5     7
     1     4     5     8
     1     4     6     7
     1     4     6     8
     2     3     5     7
     2     3     5     8
     2     3     6     7
     2     3     6     8
     2     4     5     7
     2     4     5     8
     2     4     6     7
     2     4     6     8

[Rama Rao Naraparaju]

Thank You. Much appreciated.

Answer 2

[madhan ravi]

A = [1;2]
B = [3;4]
C = [5;6]
D = [7;8]
E=nchoosek([A(:); B(:) ;C(:); D(:)],4)

Answer 3

[Michael Hartmann]

Option: for one single vector

a=1:4

fliplr(combvec(a, a, a)')'

could also be

a=1:4

b=1:3

c=1:2

fliplr(combvec(a, b, c)')'

ans =

1 1 1

1 1 2

1 1 3

1 1 4

1 2 1

1 2 2

1 2 3

1 2 4

1 3 1

1 3 2

1 3 3

1 3 4

2 1 1

2 1 2

2 1 3

2 1 4

2 2 1

2 2 2

2 2 3

2 2 4

2 3 1

2 3 2

2 3 3

2 3 4

Answer 4

[Walter Roberson]

The meshgrid() solution that Bruno suggested to your earlier question can be extended to 3 arrays. For more arrays than that you need to switch to ndgrid() . ndgrid() and meshgrid() are very similar, but the first two dimensions are exchanged.

>> meshgrid(1:3,1:4)
ans =
     1     2     3
     1     2     3
     1     2     3
     1     2     3
>> ndgrid(1:3,1:4)
ans =
     1     1     1     1
     2     2     2     2
     3     3     3     3

With ndgrid, the length of the first parameter becomes the size of the first dimension, the length of the second paramter becomes the size of the second dimension, and so on.