How do I make a (2^m x m) dimensional matrix containing all possible combinations of 1s and 0s?

I need to make an n x m matrix with arbitrary m such that n is the number of possible ways to write a m length vector of 1s and 0s (2^m). Example: if m=2, n=4 meaning I have: [1 0], [0 1], [0,0], and [1,1] and can construct the matrix [1 0;0 1;0 0;1 1].

I can not figure out the code to scale this up to higher m in the case where I may have m=3,4,5... and n becomes too large to enter manually. I want to be able to automatically generate the same kind of matrix for any value of m.

This is the Rstudio code someone gave me but I can't translate it:

for(j in 1:m) S <- cbind(S,rep(c(1,0),each=2^(m-j),times=2^(j-1)))

Any help would be much appreciated!

Thank you!

Answer 1

[Matt J]

The lazy way

result = dec2bin(0:2^m-1,m)-'0'

[Thomas Casey]

This worked! Thank you!

Answer 2

[Matt J]

A non-lazy way

   [c{m:-1:1}]=ndgrid([0,1]); 
   result=reshape( cat(m+1,c{:}),[],m)

[Thomas Casey]

This one didn't work, it doesn't matter for me because your "lazy way" worked for what I need but if anyone else is interested...

Thanks again!

[Matt J]

Works fine for me...

    >> m=3;  [c{m:-1:1}]=ndgrid([0,1]); 
       result=reshape( cat(m+1,c{:}),[],m)   

    result =

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

[Matt J]

but if anyone else is interested...

If anyone else is interested, this method is preferable when speed matters. Compare,

    m=20;

    tic;
     [c{m:-1:1}]=ndgrid([0,1]); 
      result=reshape( cat(m+1,c{:}),[],m) ;
    toc
    %Elapsed time is 0.090184 seconds.

    tic;

     result = dec2bin(0:2^m-1,m)-'0';

    toc
    %Elapsed time is 1.032300 seconds.

[Thomas Casey]

Yea it worked when I copied and pasted, I must have typed something wrong the first time. That is the fastest way, another person suggested this:

m=3;
mat = nan(2^m,m);
for idx = 1:m
 mat(:,idx) = repmat([zeros(2^(m-idx),1);ones(2^(m-idx),1)],2^(idx-1),1);
end;

which is slower but still much much faster than dec2bin.

On my computer, m=3, I got 0.003s (reshape), 0.3s (dec2bin), and 0.0056s (repmat).

Thanks again!