X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=dunshire%2Fgames.py;h=bb808cb592d8e013d390e69ee1b6527fc64db583;hb=2132f293d3ab198630f9fa26151eed52b21512fb;hp=77c83300a586e7e9f8a98a766d242f98738635f1;hpb=fa3639d3a5cc52e104a81dc75d8688c64c274a71;p=dunshire.git

diff --git a/dunshire/games.py b/dunshire/games.py
index 77c8330..bb808cb 100644
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -4,10 +4,8 @@ Symmetric linear games and their solutions.
 This module contains the main :class:`SymmetricLinearGame` class that
 knows how to solve a linear game.
 """
-from math import sqrt
-
 from cvxopt import matrix, printing, solvers
-from .cones import CartesianProduct, IceCream, NonnegativeOrthant
+from .cones import CartesianProduct
 from .errors import GameUnsolvableException, PoorScalingException
 from .matrices import (append_col, append_row, condition_number, identity,
                        inner_product, norm, specnorm)
@@ -822,30 +820,29 @@ class SymmetricLinearGame:
         :meth:`L` is satisfied.
         """
         p = self.e2() / (norm(self.e2()) ** 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.e1()))
-        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.e1()[0]
-            radius = norm(self.e1()[1:])
-            dist = (height - radius) / sqrt(2)
-        else:
-            raise NotImplementedError
-
+        dist = self.K().ball_radius(self.e1())
         nu = - specnorm(self.L())/(dist*norm(self.e2()))
-        x = matrix([nu,p], (self.dimension() + 1, 1))
+        x = matrix([nu, p], (self.dimension() + 1, 1))
         s = - self._G()*x
 
         return {'x': x, 's': s}
 
 
+    def player2_start(self):
+        """
+        Return a feasible starting point for player two.
+        """
+        q = self.e1() / (norm(self.e1()) ** 2)
+        dist = self.K().ball_radius(self.e2())
+        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`.