perturb.m

   1 function x_hat = perturb(x, epsilon)
   2   %
   3   % Generate a perturbed copy of ``x``, that is, a vector (or matrix)
   4   % of the form ``x + dx`` where ``dx`` has same dimensions as x and
   5   % negligible norm.
   6   %
   7   % INPUT:
   8   %
   9   %   ``x`` -- The vector or matrix to perturb.
  10   %
  11   %   ``epsilon`` -- An upper bound for the entries of ``dx``.
  12   %
  13   % OUTPUT:
  14   %
  15   %   ``x_hat`` -- A perturbed copy of ``x``; ``x_hat == x + dx``.
  16   %
  17
  18   % If no epsilon was given, make something up.
  19   if (nargin < 2)
  20     epsilon = 1e-10;
  21   end
  22
  23   % This creates a vector or matrix whose entries lie in [-1,1].
  24   dx = 2*rand(size(x)) - 1;
  25
  26   % First normalize delta, using the infinity norm for speed (since
  27   % it doesn't matter).
  28   dx = dx / norm(dx, 'inf');
  29
  30   % Now scale it so that its largest entry is
  31   dx = dx * norm(x,'inf') * epsilon;
  32
  33   x_hat = x + dx;
  34 end