--------
>>> print(Solution(10, matrix([1,2]), matrix([3,4])))
- Game value: 10.0000000
+ Game value: 10.000...
Player 1 optimal:
[ 1]
[ 2]
return {'x': x, 's': s}
+ 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}
+
+
def solution(self):
"""
Solve this linear game and return a :class:`Solution`.
>>> e2 = [1,1,1]
>>> SLG = SymmetricLinearGame(L, K, e1, e2)
>>> print(SLG.solution())
- Game value: -6.1724138
+ Game value: -6.172...
Player 1 optimal:
- [ 0.551...]
- [-0.000...]
- [ 0.448...]
+ [0.551...]
+ [0.000...]
+ [0.448...]
Player 2 optimal:
[0.448...]
[0.000...]
>>> e2 = [4,5,6]
>>> SLG = SymmetricLinearGame(L, K, e1, e2)
>>> print(SLG.solution())
- Game value: 0.0312500
+ Game value: 0.031...
Player 1 optimal:
[0.031...]
[0.062...]
>>> print(SLG.solution())
Game value: 18.767...
Player 1 optimal:
- [-0.000...]
- [ 9.766...]
+ [0.000...]
+ [9.766...]
Player 2 optimal:
[1.047...]
[0.000...]
>>> print(SLG.solution())
Game value: 24.614...
Player 1 optimal:
- [ 6.371...]
- [-0.000...]
+ [6.371...]
+ [0.000...]
Player 2 optimal:
[2.506...]
[0.000...]
self.C().cvxopt_dims(),
self.A(),
self.b(),
+ primalstart=self.player1_start(),
options=opts)
except ValueError as error:
if str(error) == 'math domain error':