X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=dunshire%2Fgames.py;h=f9877b334cfa3bcf2d60c6269ecbf4340de24eb1;hb=f5b5ef66e41ae0538eb32e4b8420c36a23b95361;hp=77c83300a586e7e9f8a98a766d242f98738635f1;hpb=fa3639d3a5cc52e104a81dc75d8688c64c274a71;p=dunshire.git

diff --git a/dunshire/games.py b/dunshire/games.py
index 77c8330..f9877b3 100644
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -4,8 +4,6 @@ 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 .errors import GameUnsolvableException, PoorScalingException
@@ -833,9 +831,10 @@ class SymmetricLinearGame:
             # 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?
+            # We use "2" because it's better numerically than sqrt(2).
             height = self.e1()[0]
             radius = norm(self.e1()[1:])
-            dist = (height - radius) / sqrt(2)
+            dist = (height - radius) / 2
         else:
             raise NotImplementedError
 
@@ -846,6 +845,38 @@ class SymmetricLinearGame:
         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?
+            # We use "2" because it's better numerically than sqrt(2).
+            height = self.e2()[0]
+            radius = norm(self.e2()[1:])
+            dist = (height - radius) / 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`.