Add an epsilon_scale() method for games.

[dunshire.git] / dunshire / games.py

diff --git a/dunshire/games.py b/dunshire/games.py
index bb808cb592d8e013d390e69ee1b6527fc64db583..ae1426a2c611f7e315f94fc5fea0e98f1da0905b 100644 (file)
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -322,6 +322,8 @@ class SymmetricLinearGame:
         if not self._e2 in K:
             raise ValueError('the point e2 must lie in the interior of K')
 
+        # Initial value of cached method.
+        self._L_specnorm_value = None
 
 
     def __str__(self):
@@ -821,7 +823,7 @@ class SymmetricLinearGame:
         """
         p = self.e2() / (norm(self.e2()) ** 2)
         dist = self.K().ball_radius(self.e1())
-        nu = - specnorm(self.L())/(dist*norm(self.e2()))
+        nu = - self._L_specnorm()/(dist*norm(self.e2()))
         x = matrix([nu, p], (self.dimension() + 1, 1))
         s = - self._G()*x
 
@@ -834,7 +836,7 @@ class SymmetricLinearGame:
         """
         q = self.e1() / (norm(self.e1()) ** 2)
         dist = self.K().ball_radius(self.e2())
-        omega = specnorm(self.L())/(dist*norm(self.e1()))
+        omega = self._L_specnorm()/(dist*norm(self.e1()))
         y = matrix([omega])
         z2 = q
         z1 = y*self.e2() - self.L().trans()*z2
@@ -843,6 +845,23 @@ class SymmetricLinearGame:
         return {'y': y, 'z': z}
 
 
+    def _L_specnorm(self):
+        """
+        Compute the spectral norm of ``L`` and cache it.
+        """
+        if self._L_specnorm_value is None:
+            self._L_specnorm_value = specnorm(self.L())
+        return self._L_specnorm_value
+
+    def epsilon_scale(self, solution):
+        # Don't return anything smaller than 1... we can't go below
+        # out "minimum tolerance."
+        norm_p1_opt = norm(solution.player1_optimal())
+        norm_p2_opt = norm(solution.player2_optimal())
+        scale = self._L_specnorm()*(norm_p1_opt + norm_p2_opt)
+        return max(1, scale)
+
+
     def solution(self):
         """
         Solve this linear game and return a :class:`Solution`.