X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=dunshire%2Fgames.py;h=3ed89bb3f2f70b30d0313cbe5a578e4f53e47421;hb=e41ad668f4f16d8948181ae307cb98430b37ed1d;hp=ff3ec0001b4c3508ceef2c43afb6d13ffb7d403f;hpb=428ef4a28dc25409df02f6af024043c21307a646;p=dunshire.git diff --git a/dunshire/games.py b/dunshire/games.py index ff3ec00..3ed89bb 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 @@ -335,12 +336,12 @@ class SymmetricLinearGame: ' e1 = {:s},\n' \ ' e2 = {:s},\n' \ ' Condition((L, K, e1, e2)) = {:f}.' - indented_L = '\n '.join(str(self._L).splitlines()) - indented_e1 = '\n '.join(str(self._e1).splitlines()) - indented_e2 = '\n '.join(str(self._e2).splitlines()) + indented_L = '\n '.join(str(self.L()).splitlines()) + indented_e1 = '\n '.join(str(self.e1()).splitlines()) + indented_e2 = '\n '.join(str(self.e2()).splitlines()) return tpl.format(indented_L, - str(self._K), + str(self.K()), indented_e1, indented_e2, self.condition()) @@ -581,7 +582,7 @@ class SymmetricLinearGame: return matrix(0, (self.dimension(), 1), tc='d') - def _A(self): + def A(self): """ Return the matrix ``A`` used in our CVXOPT construction. @@ -609,12 +610,12 @@ class SymmetricLinearGame: >>> e1 = [1,1,1] >>> e2 = [1,2,3] >>> SLG = SymmetricLinearGame(L, K, e1, e2) - >>> print(SLG._A()) + >>> print(SLG.A()) [0.0000000 1.0000000 2.0000000 3.0000000] """ - return matrix([0, self._e2], (1, self.dimension() + 1), 'd') + return matrix([0, self.e2()], (1, self.dimension() + 1), 'd') @@ -657,7 +658,7 @@ class SymmetricLinearGame: """ identity_matrix = identity(self.dimension()) return append_row(append_col(self._zero(), -identity_matrix), - append_col(self._e1, -self._L)) + append_col(self.e1(), -self.L())) def _c(self): @@ -698,7 +699,7 @@ class SymmetricLinearGame: return matrix([-1, self._zero()]) - def _C(self): + def C(self): """ Return the cone ``C`` used in our CVXOPT construction. @@ -720,7 +721,7 @@ class SymmetricLinearGame: >>> e1 = [1,2,3] >>> e2 = [1,1,1] >>> SLG = SymmetricLinearGame(L, K, e1, e2) - >>> print(SLG._C()) + >>> print(SLG.C()) Cartesian product of dimension 6 with 2 factors: * Nonnegative orthant in the real 3-space * Nonnegative orthant in the real 3-space @@ -770,7 +771,7 @@ class SymmetricLinearGame: @staticmethod - def _b(): + def b(): """ Return the ``b`` vector used in our CVXOPT construction. @@ -801,7 +802,7 @@ class SymmetricLinearGame: >>> e1 = [1,2,3] >>> e2 = [1,1,1] >>> SLG = SymmetricLinearGame(L, K, e1, e2) - >>> print(SLG._b()) + >>> print(SLG.b()) [1.0000000] @@ -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): """ @@ -926,13 +962,13 @@ class SymmetricLinearGame: """ try: - opts = {'show_progress': options.VERBOSE} + opts = {'show_progress': False} soln_dict = solvers.conelp(self._c(), self._G(), self._h(), - self._C().cvxopt_dims(), - self._A(), - self._b(), + self.C().cvxopt_dims(), + self.A(), + self.b(), options=opts) except ValueError as error: if str(error) == 'math domain error': @@ -1036,7 +1072,7 @@ class SymmetricLinearGame: True """ - return (condition_number(self._G()) + condition_number(self._A()))/2 + return (condition_number(self._G()) + condition_number(self.A()))/2 def dual(self): @@ -1072,10 +1108,10 @@ class SymmetricLinearGame: Condition((L, K, e1, e2)) = 44.476... """ - # We pass ``self._L`` right back into the constructor, because + # We pass ``self.L()`` right back into the constructor, because # it will be transposed there. And keep in mind that ``self._K`` # is its own dual. - return SymmetricLinearGame(self._L, - self._K, - self._e2, - self._e1) + return SymmetricLinearGame(self.L(), + self.K(), + self.e2(), + self.e1())