+ def player2_start(self):
+ """
+ Return a feasible starting point for player two.
+ """
+ q = self.e1() / (norm(self.e1()) ** 2)
+
+ # Compute the distance from p to the outside of K.
+ if isinstance(self.K(), NonnegativeOrthant):
+ # How far is it to a wall?
+ dist = min(list(self.e2()))
+ elif isinstance(self.K(), IceCream):
+ # How far is it to the boundary of the ball that defines
+ # the ice-cream cone at a given height? Now draw a
+ # 45-45-90 triangle and the shortest distance to the
+ # outside of the cone should be 1/sqrt(2) of that.
+ # It works in R^2, so it works everywhere, right?
+ height = self.e2()[0]
+ radius = norm(self.e2()[1:])
+ dist = (height - radius) / sqrt(2)
+ else:
+ raise NotImplementedError
+
+ omega = specnorm(self.L())/(dist*norm(self.e1()))
+ y = matrix([omega])
+ z2 = q
+ z1 = y*self.e2() - self.L().trans()*z2
+ z = matrix([z1,z2], (self.dimension()*2, 1))
+
+ return {'y': y, 'z': z}
+
+