Add a ball_radius() method for cones and use it to compute starting points.

[dunshire.git] / dunshire / games.py

diff --git a/dunshire/games.py b/dunshire/games.py
index f9877b334cfa3bcf2d60c6269ecbf4340de24eb1..bb808cb592d8e013d390e69ee1b6527fc64db583 100644 (file)
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -5,7 +5,7 @@ This module contains the main :class:`SymmetricLinearGame` class that
 knows how to solve a linear game.
 """
 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)
@@ -820,26 +820,9 @@ 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?
-            # We use "2" because it's better numerically than sqrt(2).
-            height = self.e1()[0]
-            radius = norm(self.e1()[1:])
-            dist = (height - radius) / 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}
@@ -850,29 +833,12 @@ class SymmetricLinearGame:
         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
-
+        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))
+        z = matrix([z1, z2], (self.dimension()*2, 1))
 
         return {'y': y, 'z': z}