random_positive_definite_matrix.m

   1 function A = random_positive_definite_matrix(integerN, max_entry = realmax)
   2   %
   3   % Generate a random, symmetric positive-definite (SPD) matrix.
   4   %
   5   % Since all (SPD) matrices are diagonalizable and have positive
   6   % eigenvalues, it seems likely that we can generate an SPD matrix by
   7   % combining random orthogonal matrices with a diagonal matrix of
   8   % random eigenvalues.
   9   %
  10   % I have no proof/evidence that this approach is sound.
  11   %
  12   % INPUT:
  13   %
  14   %   - ``integerN`` -- The dimension of the resulting matrix.
  15   %
  16   %   - ``max_entry`` -- (optional) Upper bound on the entries.
  17   %
  18   % OUTPUT:
  19   %
  20   %   - ``A`` -- A symmetric, positive definite matrix.
  21   %
  22   U = random_orthogonal_matrix(integerN);
  23   d = unifrnd(eps, max_entry, 1, integerN);
  24   D = diag(d);
  25   A = U*D*U';
  26 end