How do I select a single, random, non-zero array from a matrix?

I have a matrix consisting of an equal amount of ones and zeros, randomly distributed. I want a random one to change into a zero, and a random zero to change into a one, so in the end I always end up with the same amount of ones and zeros.

How do I accomplish this? Thanks in advance,

Chris

Answer 1

[the cyclist]

There are almost certainly ways to make this more efficient, but here is a conceptually straightforward way to do this:

% Starting matrix
M = [ 0  1  0;
      1  0  1;
      0  1  0;
      1  0  1];

numberElements = numel(M);

% You can run the following as many times as you want,
% to change a pair of 0/1.

indexToOnes = find(M);
indexToZeros = setxor(indexToOnes,1:numberElements);

indexChangeToZero = indexToOnes(randi(numel(indexToOnes)));
indexChangeToOne  = indexToZeros(randi(numel(indexToZeros)));

M(indexChangeToZero) = 0;
M(indexChangeToOne)  = 1;

[Chris Smit]

Thank you so much, really helpful!

Answer 2

[John D'Errico]

A = rand(5,5) > 0.5
A =
   1     0     0     0     0
   1     0     0     1     1
   0     1     1     1     0
   1     1     1     0     1
   0     0     1     0     0

takejustone = @(x) x(ceil(numel(x)*rand(1)));
i1 = takejustone(find(A));
i0 = takejustone(find(~A));

A([i1,i0]) = ~A([i1,i0])
A =
   1     0     0     0     0
   1     1     0     1     1
   0     1     1     0     0
   1     1     1     0     1
   0     0     1     0     0

So i swapped the (2,2) element from a 1 into a 0, and the (3,4) element went from a 0 into a 1.

[Chris Smit]

Works perfectly, thanks a lot.