X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=dunshire%2Fgames.py;h=1f672abeb3870f45b13a8d9d169e8df0f1059d98;hb=299bf2d606eb245ec78f2e20826836c0bb5bfc07;hp=46092c380eca141ff993313bd30ec55989a32ed8;hpb=1e02fd12b64e090e0b0ab0d3fecbd9c1b18d0fcf;p=dunshire.git

diff --git a/dunshire/games.py b/dunshire/games.py
index 46092c3..1f672ab 100644
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -222,7 +222,7 @@ class SymmetricLinearGame:
           e2 = [ 1]
                [ 2]
                [ 3],
-          Condition((L, K, e1, e2)) = 63.669790.
+          Condition((L, K, e1, e2)) = 31.834...
 
     Lists can (and probably should) be used for every argument::
 
@@ -241,7 +241,7 @@ class SymmetricLinearGame:
                [ 1],
           e2 = [ 1]
                [ 1],
-          Condition((L, K, e1, e2)) = 3.414214.
+          Condition((L, K, e1, e2)) = 1.707...
 
     The points ``e1`` and ``e2`` can also be passed as some other
     enumerable type (of the correct length) without much harm, since
@@ -264,7 +264,7 @@ class SymmetricLinearGame:
                [ 1],
           e2 = [ 1]
                [ 1],
-          Condition((L, K, e1, e2)) = 3.414214.
+          Condition((L, K, e1, e2)) = 1.707...
 
     However, ``L`` will always be intepreted as a list of rows, even
     if it is passed as a :class:`cvxopt.base.matrix` which is
@@ -286,7 +286,7 @@ class SymmetricLinearGame:
                [ 1],
           e2 = [ 1]
                [ 1],
-          Condition((L, K, e1, e2)) = 12.147542.
+          Condition((L, K, e1, e2)) = 6.073...
         >>> L = cvxopt.matrix(L)
         >>> print(L)
         [ 1  3]
@@ -302,7 +302,7 @@ class SymmetricLinearGame:
                [ 1],
           e2 = [ 1]
                [ 1],
-          Condition((L, K, e1, e2)) = 12.147542.
+          Condition((L, K, e1, e2)) = 6.073...
 
     """
     def __init__(self, L, K, e1, e2):
@@ -346,7 +346,7 @@ class SymmetricLinearGame:
                           str(self._K),
                           indented_e1,
                           indented_e2,
-                          self._condition())
+                          self.condition())
 
 
     def _zero(self):
@@ -419,13 +419,13 @@ class SymmetricLinearGame:
             >>> print(SLG.solution())
             Game value: -6.1724138
             Player 1 optimal:
-              [ 0.5517241]
-              [-0.0000000]
-              [ 0.4482759]
+              [ 0.551...]
+              [-0.000...]
+              [ 0.448...]
             Player 2 optimal:
-              [0.4482759]
-              [0.0000000]
-              [0.5517241]
+              [0.448...]
+              [0.000...]
+              [0.551...]
 
         The value of the following game can be computed using the fact
         that the identity is invertible::
@@ -439,13 +439,13 @@ class SymmetricLinearGame:
             >>> print(SLG.solution())
             Game value: 0.0312500
             Player 1 optimal:
-              [0.0312500]
-              [0.0625000]
-              [0.0937500]
+              [0.031...]
+              [0.062...]
+              [0.093...]
             Player 2 optimal:
-              [0.1250000]
-              [0.1562500]
-              [0.1875000]
+              [0.125...]
+              [0.156...]
+              [0.187...]
 
         """
         # The cone "C" that appears in the statement of the CVXOPT
@@ -505,7 +505,13 @@ class SymmetricLinearGame:
             # objectives match (within a tolerance) and that the
             # primal/dual optimal solutions are within the cone (to a
             # tolerance as well).
-            if abs(p1_value - p2_value) > options.ABS_TOL:
+            #
+            # The fudge factor of two is basically unjustified, but
+            # makes intuitive sense when you imagine that the primal
+            # value could be under the true optimal by ``ABS_TOL``
+            # and the dual value could be over by the same amount.
+            #
+            if abs(p1_value - p2_value) > 2*options.ABS_TOL:
                 raise GameUnsolvableException(self, soln_dict)
             if (p1_optimal not in self._K) or (p2_optimal not in self._K):
                 raise GameUnsolvableException(self, soln_dict)
@@ -513,18 +519,25 @@ class SymmetricLinearGame:
         return Solution(p1_value, p1_optimal, p2_optimal)
 
 
-    def _condition(self):
+    def condition(self):
         r"""
         Return the condition number of this game.
 
         In the CVXOPT construction of this game, two matrices ``G`` and
         ``A`` appear. When those matrices are nasty, numerical problems
         can show up. We define the condition number of this game to be
-        the sum of the condition numbers of ``G`` and ``A`` in the
+        the average of the condition numbers of ``G`` and ``A`` in the
         CVXOPT construction. If the condition number of this game is
         high, then you can expect numerical difficulty (such as
         :class:`PoorScalingException`).
 
+        Returns
+        -------
+
+        float
+            A real number greater than or equal to one that measures how
+            bad this game is numerically.
+
         Examples
         --------
 
@@ -534,13 +547,13 @@ class SymmetricLinearGame:
         >>> e1 = [1]
         >>> e2 = e1
         >>> SLG = SymmetricLinearGame(L, K, e1, e2)
-        >>> actual = SLG._condition()
-        >>> expected = 3.6180339887498953
+        >>> actual = SLG.condition()
+        >>> expected = 1.8090169943749477
         >>> abs(actual - expected) < options.ABS_TOL
         True
 
         """
-        return condition_number(self._G()) + condition_number(self._A())
+        return (condition_number(self._G()) + condition_number(self._A()))/2
 
 
     def dual(self):
@@ -573,7 +586,7 @@ class SymmetricLinearGame:
               e2 = [ 1]
                    [ 1]
                    [ 1],
-              Condition((L, K, e1, e2)) = 88.953530.
+              Condition((L, K, e1, e2)) = 44.476...
 
         """
         # We pass ``self._L`` right back into the constructor, because