How to create all possible combinations in MATLAB

Hi everyone,

I have a vector of 8 columns, x=[a b c d e f g h];

where all letters are integer vectors as follows

a=1:1:20;b=1:1:6; c=1:1:15; d=1:1:26; e=1:1:56; f=1:1:56; g=1:1:11; and h=1:1:31 ;

I would like to make a matrix which includes all possible combinations of these letters and have this size

columns = 6

rows= 20*6*15*26*56*56*11*31;

all possible combinations are needed in my situation.

for example; the first combination should look like this : [1 1 1 1 1 1 1 1]

and the last combination should look like this : [20 6 15 26 56 56 11 31]

and the final matrix should look like this ComMat= [1 1 1 1 1 1 1 1; ...... ; 20 6 15 26 56 56 11 31];

I appreciate your support!

Answer 1

[Stephen23]

Download Jos's excellent allcomb, and simply use it like this:

allcomb(a,b,c,...)

I leave it up to you to decide if this is possible with your computer memory, or even worth computing at all. Here is a smaller example of its output using the first three of your input vectors:

>> allcomb(a,b,c)
ans =
    1    1    1
    1    1    2
    1    1    3
    1    1    4
    1    1    5
    1    1    6
    1    1    7
    1    1    8
    1    1    9
    1    1   10
    1    1   11
    1    1   12
    1    1   13
    1    1   14
    1    1   15
    1    2    1
    1    2    2
    1    2    3
    1    2    4
    1    2    5
    1    2    6
    1    2    7
    1    2    8
  ... lots of lines
   20    5    9
   20    5   10
   20    5   11
   20    5   12
   20    5   13
   20    5   14
   20    5   15
   20    6    1
   20    6    2
   20    6    3
   20    6    4
   20    6    5
   20    6    6
   20    6    7
   20    6    8
   20    6    9
   20    6   10
   20    6   11
   20    6   12
   20    6   13
   20    6   14
   20    6   15
>>

[Mohammed Albahlal]

Thank you for the support