X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=dunshire%2Fgames.py;h=cfb62a33d8a2666828323019729af0f1b5ab99d7;hb=709cd03fff79e76f9fd78ba70711ea2694607e05;hp=f9877b334cfa3bcf2d60c6269ecbf4340de24eb1;hpb=f5b5ef66e41ae0538eb32e4b8420c36a23b95361;p=dunshire.git diff --git a/dunshire/games.py b/dunshire/games.py index f9877b3..cfb62a3 100644 --- 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) @@ -13,6 +13,7 @@ from . import options printing.options['dformat'] = options.FLOAT_FORMAT + class Solution: """ A representation of the solution of a linear game. It should contain @@ -322,6 +323,8 @@ 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): @@ -820,26 +823,9 @@ 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 - - nu = - specnorm(self.L())/(dist*norm(self.e2())) - x = matrix([nu,p], (self.dimension() + 1, 1)) + dist = self.K().ball_radius(self.e1()) + nu = - self._L_specnorm()/(dist*norm(self.e2())) + x = matrix([nu, p], (self.dimension() + 1, 1)) s = - self._G()*x return {'x': x, 's': s} @@ -850,33 +836,33 @@ 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 - - omega = specnorm(self.L())/(dist*norm(self.e1())) + dist = self.K().ball_radius(self.e2()) + omega = self._L_specnorm()/(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} + 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`. @@ -1001,6 +987,7 @@ class SymmetricLinearGame: self.A(), self.b(), primalstart=self.player1_start(), + dualstart=self.player2_start(), options=opts) except ValueError as error: if str(error) == 'math domain error': @@ -1035,6 +1022,20 @@ class SymmetricLinearGame: printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT raise GameUnsolvableException(self, soln_dict) + # For the game value, we could use any of: + # + # * p1_value + # * p2_value + # * (p1_value + p2_value)/2 + # * the game payoff + # + # We want the game value to be the payoff, however, so it + # makes the most sense to just use that, even if it means we + # can't test the fact that p1_value/p2_value are close to the + # payoff. + payoff = self.payoff(p1_optimal, p2_optimal) + soln = Solution(payoff, p1_optimal, p2_optimal) + # The "optimal" and "unknown" results, we actually treat the # same. Even if CVXOPT bails out due to numerical difficulty, # it will have some candidate points in mind. If those @@ -1045,7 +1046,8 @@ class SymmetricLinearGame: # close enough (one could be low by ABS_TOL, the other high by # it) because otherwise CVXOPT might return "unknown" and give # us two points in the cone that are nowhere near optimal. - if abs(p1_value - p2_value) > 2*options.ABS_TOL: + # + if abs(p1_value - p2_value) > self.epsilon_scale(soln)*options.ABS_TOL: printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT raise GameUnsolvableException(self, soln_dict) @@ -1055,19 +1057,7 @@ class SymmetricLinearGame: printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT raise GameUnsolvableException(self, soln_dict) - # For the game value, we could use any of: - # - # * p1_value - # * p2_value - # * (p1_value + p2_value)/2 - # * the game payoff - # - # We want the game value to be the payoff, however, so it - # makes the most sense to just use that, even if it means we - # can't test the fact that p1_value/p2_value are close to the - # payoff. - payoff = self.payoff(p1_optimal, p2_optimal) - return Solution(payoff, p1_optimal, p2_optimal) + return soln def condition(self):