From 3ee9db27adb69d68871ef26ec22ef144f351e99d Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 30 Oct 2016 18:51:57 -0400 Subject: [PATCH] Halve the definition of the condition number of a game. --- dunshire/errors.py | 4 ++-- dunshire/games.py | 25 ++++++++++++++++--------- 2 files changed, 18 insertions(+), 11 deletions(-) diff --git a/dunshire/errors.py b/dunshire/errors.py index 61fe43d..7cd8342 100644 --- a/dunshire/errors.py +++ b/dunshire/errors.py @@ -91,7 +91,7 @@ class GameUnsolvableException(Exception): [0.1000000], e2 = [3.0000000] [0.1000000], - Condition((L, K, e1, e2)) = 8.311277. + Condition((L, K, e1, e2)) = 4.155638. CVXOPT returned: dual infeasibility: None dual objective: 1.0 @@ -192,7 +192,7 @@ class PoorScalingException(Exception): [0.1000000], e2 = [3.0000000] [0.1000000], - Condition((L, K, e1, e2)) = 8.311277. + Condition((L, K, e1, e2)) = 4.155638. """ def __init__(self, game): diff --git a/dunshire/games.py b/dunshire/games.py index 46092c3..c841caa 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)) = 31.834895. 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)) = 1.707107. 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)) = 1.707107. 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)) = 6.073771. >>> 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)) = 6.073771. """ def __init__(self, L, K, e1, e2): @@ -520,11 +520,18 @@ class SymmetricLinearGame: 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 -------- @@ -535,12 +542,12 @@ class SymmetricLinearGame: >>> e2 = e1 >>> SLG = SymmetricLinearGame(L, K, e1, e2) >>> actual = SLG._condition() - >>> expected = 3.6180339887498953 + >>> 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 +580,7 @@ class SymmetricLinearGame: e2 = [ 1] [ 1] [ 1], - Condition((L, K, e1, e2)) = 88.953530. + Condition((L, K, e1, e2)) = 44.476765. """ # We pass ``self._L`` right back into the constructor, because -- 2.44.2