Matrix with all possibilities

Dear all,

I would like to create a matrix with all possibilities, such as the following: [1 1 1; 1 1 0; 1 0 1; 0 1 1; 1 0 0; 0 1 0; 0 0 1; 0 0 0]

I have tried to use nchoosek([0 0 0 1 1 1],3) but this function fails in ordering. Furthermore I tried C = npermutek([ones(1,3) zeros(1,3)],3); D = unique(C,'rows'), but this one gives a out of memory error for larger vectors (8 instead of 3). For this function see: http://www.mathworks.com/matlabcentral/fileexchange/11462-npermutek/

How to create such a matrix?

Answer 1

[Jan]

Searching the FileExchange for the terms "combinations" and "permutations" helps to find:

• http://www.mathworks.com/matlabcentral/fileexchange/26242-vchoosekro as fast C-Mex function,
• http://www.mathworks.com/matlabcentral/fileexchange/24325-combinator-combinations-and-permutations as general M-functions for combinations/permutations with or without repetitions and ordering.

Answer 2

[Azzi Abdelmalek]

out=[]
n=3
for k=1:n
  s=[ones(2^(n-k ),1) ;zeros(2^(n-k ),1)]
  s=repmat(s,2^(k-1),1)
  out=[out s]
end

Answer 3

[Roger Stafford]

Here is a variation on Azzi's solution:

 A = ones(2^n,n);
 p = 1;
 for k = 0:n-1
   A(p+1:2*p,n-k:n) = [zeros(p,1),A(1:p,n-k+1:n)];
   p = 2*p;
 end

To count up instead of down, swap the 'ones' and 'zeros' calls.

Answer 4

[Antonio Adaldo]

The matrix that you want is the same as the matrix containing the binary digits of the numbers from zero to seven. For example: "0 0 0" is zero, "0 0 1" is one, "0 1 0" is two, etc.

If you have Communications Toolbox installed, MATLAB offers the function "de2bi" to produce that matrix. For example:

de2bi(0:7)

ans =

     0     0     0
     1     0     0
     0     1     0
     1     1     0
     0     0     1
     1     0     1
     0     1     1
     1     1     1

Documentation for "de2bi" is found here: https://www.mathworks.com/help/comm/ref/de2bi.html