Create a matrix with unique coloms and rows

I want to generate a matrix which looks like this:

     2     2     3     3     1     1
     1     3     2     1     3     2
     3     1     1     2     2     3

The specifications of the matrix is:

1. A column contains numbers from one to the length of the column.
2. Each number occur two times in each row
3. Each number occur one time in each column
4. No columns are pairwise equal more than one time.

The 3x6 matrix is generated using following code:

post = 3; 
team = 6;

A = [];

stop = 0;
number_of_matrix = 0;
unique_matrix = 0;
B = zeros(post,post);

while stop == 0
for i = 1:team
    A(:,i) = randsample(post,post); % Genrates a random matrix
end

number_of_matrix = number_of_matrix + 1;

for i = 1:post
    B(:,i) = sum(A==i,2); 
end

k = 0;
vector = zeros(1,50);
if unique(B) == 2
    for m = 1:size(A,2)
        for n = 1:size(A,2)
            k = k + 1; 
            if n ~= m
                vector(k) = sum(A(:,n) == A(:,m)); 
             end
         end
     end
end

 if unique(B) == 2
      if max(vector) <= 1
          stop=1;
      end
  end
  end
  disp(A)

I want to generate a 6x12 matrix, but this code is very ineffective. I have tried three different approaches, but none of them are faster that this one.

My question is: Does anyone know how to make this code more effective?

Answer 1

[Matt Fig]

Your matrix can be made with this:

perms(1:3).'  
% For larger problems even ordered sets take time!!

This is significantly faster, as far as the mechanics of the code. Yet as N grows the search space grows exponentially, so if you really want a random array it will take time....

N = 4;  % This is the number of rows.
P = 1:N;
P = P(ones(1,N*2),:);
S = size(P,1);

while true
    K = Shuffle(P,2);  % Shuffle is on the FEX

      bf = 0;
      for ii = 1:N
          if any(sum(K==ii)~=2)
              bf = 1;
              break
          end
      end

      if ~bf
          break
      end
  end

K = K.'

[Azzi Abdelmalek]

Matt he said 6x12

[Matt Fig]

Yeah, I was showing how to generate the array he did show.

[antlhem]

Hi, should I just change N if I want a bigger matrix? How can I use to create only binary numbers? I need a 1500x1500.

[antlhem]

So far this works for me guys, if anyone needs bigger arrays:

row=1500;
col=1500;
Aunique=randi([0 1],1,col);%start

while size(Aunique,1)<row
    arow=randi([0 1],1,col);
    not_equal=1;
    rowi=1;
    while rowi<=size(Aunique,1)
        if isequal(arow(1,:),Aunique(rowi,:))~=1
            rowi=rowi+1;            
        else
            not_equal=0;
            break;
        end
    end
	
    if not_equal==1
        Aunique=cat(1,Aunique,arow);    
    end
end

B = unique(Aunique,'rows');%verification