MATLAB: Sorting permutations of binary variables

Question

hi,

I have matrix representing all unique combinations of 6 binary variables:

N=6;
sZ=2^N;    
vec = 0:sZ-1;
Z=dec2bin(vec);
Zl=double(reshape(logical(Z(:)-'0'),sZ,[]));
[~,sInx]=sort(sum(Zl,2),'ascend');
Zls=Zl(sInx,:);
Zls(1,:)=[]

–

Zls =
     0     0     0     0     0     1
     0     0     0     0     1     0
     0     0     0     1     0     0
     0     0     1     0     0     0
     0     1     0     0     0     0
     1     0     0     0     0     0
     0     0     0     0     1     1
     0     0     0     1     0     1
   (...)
     1     1     1     1     0     1
     1     1     1     1     1     0
     1     1     1     1     1     1

My goal is to have this matrix sorted in the following way:

• Start with unit row vectors:

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

..

• Then have all row vectors with two ones, starting with row vectors that start with 1 in column 1 (and continuing with rows where 1 starts in column 2 etc)

1     1    0     0     0     0  
1     0    1     0     0     0
1     0    0     1     0     0
(...) 
0     1    1     0     0     0  
0     1    0     1     0     0 
(...) 
0     0    1     1     0     0  
0     0    1     0     1     0 

etc

• Then have all row vectors with three ones, starting with row vectors that start with 1 in colum 1 …

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

etc. etc.

Until the last row is

1     1    1     1     1     1 

Any advice either on how to sort the matrix Zls above or on how to generate this sorted matrix directly would be appreciated! Thank you for your help!

Answer 1

Try this

N=6;
A = repmat({[0,1]}, 1, N);
M = combvec(A{:}).';
M(1, :) = [];
grps = splitapply(@(x) {x}, M, sum(M,2));
Z = cellfun(@(x) {flipud(sortrows(x))}, grps);
Z = vertcat(Z{:});

Result

>> Z
Z =
     1     0     0     0     0     0
     0     1     0     0     0     0
     0     0     1     0     0     0
     0     0     0     1     0     0
     0     0     0     0     1     0
     0     0     0     0     0     1
     1     1     0     0     0     0
     1     0     1     0     0     0
     1     0     0     1     0     0
     1     0     0     0     1     0
     1     0     0     0     0     1
     0     1     1     0     0     0
     0     1     0     1     0     0
     0     1     0     0     1     0
     0     1     0     0     0     1
     0     0     1     1     0     0
     0     0     1     0     1     0
     0     0     1     0     0     1
     0     0     0     1     1     0
     0     0     0     1     0     1
     0     0     0     0     1     1
     1     1     1     0     0     0
     1     1     0     1     0     0
     1     1     0     0     1     0
     1     1     0     0     0     1
     1     0     1     1     0     0
     1     0     1     0     1     0
     1     0     1     0     0     1
     1     0     0     1     1     0
     1     0     0     1     0     1
     1     0     0     0     1     1
     0     1     1     1     0     0
     0     1     1     0     1     0
     0     1     1     0     0     1
     0     1     0     1     1     0
     0     1     0     1     0     1
     0     1     0     0     1     1
     0     0     1     1     1     0
     0     0     1     1     0     1
     0     0     1     0     1     1
     0     0     0     1     1     1
     1     1     1     1     0     0
     1     1     1     0     1     0
     1     1     1     0     0     1
     1     1     0     1     1     0
     1     1     0     1     0     1
     1     1     0     0     1     1
     1     0     1     1     1     0
     1     0     1     1     0     1
     1     0     1     0     1     1
     1     0     0     1     1     1
     0     1     1     1     1     0
     0     1     1     1     0     1
     0     1     1     0     1     1
     0     1     0     1     1     1
     0     0     1     1     1     1
     1     1     1     1     1     0
     1     1     1     1     0     1
     1     1     1     0     1     1
     1     1     0     1     1     1
     1     0     1     1     1     1
     0     1     1     1     1     1
     1     1     1     1     1     1