permutation_matrices.m

   1 function PMs = permutation_matrices(integerN)
   2   ## Generate all permutation matrices of size ``integerN``.
   3   ##
   4   ## INPUT:
   5   ##
   6   ##   - ``integerN`` -- The dimension of the resulting matrices.
   7   ##
   8   ## OUTPUT:
   9   ##
  10   ##   - ``PMs`` -- A cell array of permutation matrices.
  11   ##
  12
  13   if (integerN < 1)
  14     PMs = NA;
  15     return;
  16   end
  17
  18   ## Append to this as we generate them.
  19   PMs = {};
  20
  21   ## Generate all permutations of [1,2,...,integerN].
  22   permutations = perms([1:integerN]);
  23
  24   for idx = [ 1 : factorial(integerN) ]
  25     sigma = permutations(idx,:);
  26     ## Create a permutation matrix from the permutation, sigma.
  27     P = eye(integerN) (sigma,:);
  28     PMs{end+1} = P;
  29   end
  30
  31 end