X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=dunshire%2Fgames.py;h=77c83300a586e7e9f8a98a766d242f98738635f1;hb=fa3639d3a5cc52e104a81dc75d8688c64c274a71;hp=672810de8094df7c37005cd5106fe5b8175888c4;hpb=5d752b41ea1f09292f9e64278ba81cf0b395c001;p=dunshire.git diff --git a/dunshire/games.py b/dunshire/games.py index 672810d..77c8330 100644 --- a/dunshire/games.py +++ b/dunshire/games.py @@ -4,12 +4,13 @@ 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 +from .cones import CartesianProduct, IceCream, NonnegativeOrthant from .errors import GameUnsolvableException, PoorScalingException from .matrices import (append_col, append_row, condition_number, identity, - inner_product) + inner_product, norm, specnorm) from . import options printing.options['dformat'] = options.FLOAT_FORMAT @@ -23,7 +24,7 @@ class Solution: -------- >>> print(Solution(10, matrix([1,2]), matrix([3,4]))) - Game value: 10.0000000 + Game value: 10.000... Player 1 optimal: [ 1] [ 2] @@ -809,6 +810,41 @@ class SymmetricLinearGame: return matrix([1], tc='d') + def player1_start(self): + """ + Return a feasible starting point for player one. + + This starting point is for the CVXOPT formulation and not for + the original game. The basic premise is that if you normalize + :meth:`e2`, then you get a point in :meth:`K` that makes a unit + inner product with :meth:`e2`. We then get to choose the primal + objective function value such that the constraint involving + :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? + height = self.e1()[0] + radius = norm(self.e1()[1:]) + dist = (height - radius) / sqrt(2) + else: + raise NotImplementedError + + nu = - specnorm(self.L())/(dist*norm(self.e2())) + x = matrix([nu,p], (self.dimension() + 1, 1)) + s = - self._G()*x + + return {'x': x, 's': s} + def solution(self): """ @@ -844,11 +880,11 @@ class SymmetricLinearGame: >>> e2 = [1,1,1] >>> SLG = SymmetricLinearGame(L, K, e1, e2) >>> print(SLG.solution()) - Game value: -6.1724138 + Game value: -6.172... Player 1 optimal: - [ 0.551...] - [-0.000...] - [ 0.448...] + [0.551...] + [0.000...] + [0.448...] Player 2 optimal: [0.448...] [0.000...] @@ -864,7 +900,7 @@ class SymmetricLinearGame: >>> e2 = [4,5,6] >>> SLG = SymmetricLinearGame(L, K, e1, e2) >>> print(SLG.solution()) - Game value: 0.0312500 + Game value: 0.031... Player 1 optimal: [0.031...] [0.062...] @@ -900,8 +936,8 @@ class SymmetricLinearGame: >>> print(SLG.solution()) Game value: 18.767... Player 1 optimal: - [-0.000...] - [ 9.766...] + [0.000...] + [9.766...] Player 2 optimal: [1.047...] [0.000...] @@ -918,8 +954,8 @@ class SymmetricLinearGame: >>> print(SLG.solution()) Game value: 24.614... Player 1 optimal: - [ 6.371...] - [-0.000...] + [6.371...] + [0.000...] Player 2 optimal: [2.506...] [0.000...] @@ -933,6 +969,7 @@ class SymmetricLinearGame: self.C().cvxopt_dims(), self.A(), self.b(), + primalstart=self.player1_start(), options=opts) except ValueError as error: if str(error) == 'math domain error':