X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2Fdunshire%2Fsymmetric_linear_game.py;h=968d9ca630c0af2fa15e780747785e9705f82ddc;hb=002b5370da24f083d2088c3482cf076615a13563;hp=e92e8200ad93e97d76b61f3453d40649fcdadcc0;hpb=56ea961887d507114174af5f92b8c3c77b0b7a50;p=dunshire.git diff --git a/src/dunshire/symmetric_linear_game.py b/src/dunshire/symmetric_linear_game.py index e92e820..968d9ca 100644 --- a/src/dunshire/symmetric_linear_game.py +++ b/src/dunshire/symmetric_linear_game.py @@ -21,6 +21,10 @@ class Solution: the value of the game, and both players' strategies. """ def __init__(self, game_value, p1_optimal, p2_optimal): + """ + Create a new Solution object from a game value and two optimal + strategies for the players. + """ self._game_value = game_value self._player1_optimal = p1_optimal self._player2_optimal = p2_optimal @@ -35,11 +39,21 @@ class Solution: * The optimal strategy of player one. * The optimal strategy of player two. - """ + EXAMPLES: + + >>> print(Solution(10, matrix([1,2]), matrix([3,4]))) + Game value: 10.0000000 + Player 1 optimal: + [ 1] + [ 2] + Player 2 optimal: + [ 3] + [ 4] + """ tpl = 'Game value: {:.7f}\n' \ 'Player 1 optimal:{:s}\n' \ - 'Player 2 optimal:{:s}\n' + 'Player 2 optimal:{:s}' p1_str = '\n{!s}'.format(self.player1_optimal()) p1_str = '\n '.join(p1_str.splitlines()) @@ -50,14 +64,23 @@ class Solution: def game_value(self): + """ + Return the game value for this solution. + """ return self._game_value def player1_optimal(self): + """ + Return player one's optimal strategy in this solution. + """ return self._player1_optimal def player2_optimal(self): + """ + Return player two's optimal strategy in this solution. + """ return self._player2_optimal @@ -79,7 +102,6 @@ class SymmetricLinearGame: The ambient space is assumed to be the span of ``K``. """ - def __init__(self, L, K, e1, e2): """ INPUT: @@ -107,19 +129,137 @@ class SymmetricLinearGame: if not K.contains_strict(self._e2): raise ValueError('the point e2 must lie in the interior of K') + def __str__(self): + """ + Return a string representatoin of this game. + + EXAMPLES: + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(3) + >>> L = [[1,-1,-12],[-5,2,-15],[-15,-3,1]] + >>> e1 = [1,1,1] + >>> e2 = [1,2,3] + >>> SLG = SymmetricLinearGame(L, K, e1, e2) + >>> print(SLG) + The linear game (L, K, e1, e2) where + L = [ 1 -5 -15] + [ -1 2 -3] + [-12 -15 1], + K = Nonnegative orthant in the real 3-space, + e1 = [ 1] + [ 1] + [ 1], + e2 = [ 1] + [ 2] + [ 3]. + + """ + tpl = 'The linear game (L, K, e1, e2) where\n' \ + ' L = {:s},\n' \ + ' K = {!s},\n' \ + ' e1 = {:s},\n' \ + ' e2 = {:s}.' + L_str = '\n '.join(str(self._L).splitlines()) + e1_str = '\n '.join(str(self._e1).splitlines()) + e2_str = '\n '.join(str(self._e2).splitlines()) + return tpl.format(L_str, str(self._K), e1_str, e2_str) + + def solution(self): + """ + Solve this linear game and return a Solution object. + + OUTPUT: + + If the cone program associated with this game could be + successfully solved, then a Solution object containing the + game's value and optimal strategies is returned. If the game + could *not* be solved -- which should never happen -- then a + GameUnsolvableException is raised. It can be printed to get the + raw output from CVXOPT. + + EXAMPLES: + + This example is computed in Gowda and Ravindran in the section + "The value of a Z-transformation": + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(3) + >>> L = [[1,-1,-12],[-5,2,-15],[-15,-3,1]] + >>> e1 = [1,1,1] + >>> e2 = [1,1,1] + >>> SLG = SymmetricLinearGame(L, K, e1, e2) + >>> print(SLG.solution()) + Game value: -6.1724138 + Player 1 optimal: + [ 0.5517241] + [-0.0000000] + [ 0.4482759] + Player 2 optimal: + [0.4482759] + [0.0000000] + [0.5517241] + + The value of the following game can be computed using the fact + that the identity is invertible: + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(3) + >>> L = [[1,0,0],[0,1,0],[0,0,1]] + >>> e1 = [1,2,3] + >>> e2 = [4,5,6] + >>> SLG = SymmetricLinearGame(L, K, e1, e2) + >>> print(SLG.solution()) + Game value: 0.0312500 + Player 1 optimal: + [0.0312500] + [0.0625000] + [0.0937500] + Player 2 optimal: + [0.1250000] + [0.1562500] + [0.1875000] + + """ + # The cone "C" that appears in the statement of the CVXOPT + # conelp program. C = CartesianProduct(self._K, self._K) + + # The column vector "b" that appears on the right-hand side of + # Ax = b in the statement of the CVXOPT conelp program. b = matrix([1], tc='d') + # A column of zeros that fits K. zero = matrix(0, (self._K.dimension(), 1), tc='d') + + # The column vector "h" that appears on the right-hand side of + # Gx + s = h in the statement of the CVXOPT conelp program. h = matrix([zero, zero]) + + # The column vector "c" that appears in the objective function + # value in the statement of the CVXOPT conelp program. c = matrix([-1, zero]) + + # The matrix "G" that appears on the left-hand side of Gx + s = h + # in the statement of the CVXOPT conelp program. G = append_row(append_col(zero, -identity(self._K.dimension())), append_col(self._e1, -self._L)) - A = matrix([0, self._e1], (1, self._K.dimension() + 1), 'd') + # The matrix "A" that appears on the right-hand side of Ax = b + # in the statement of the CVXOPT conelp program. + A = matrix([0, self._e2], (1, self._K.dimension() + 1), 'd') + + # Actually solve the thing and obtain a dictionary describing + # what happened. soln_dict = solvers.conelp(c, G, h, C.cvxopt_dims(), A, b) + # The "status" field contains "optimal" if everything went + # according to plan. Other possible values are "primal + # infeasible", "dual infeasible", "unknown", all of which + # mean we didn't get a solution. That should never happen, + # because by construction our game has a solution, and thus + # the cone program should too. if soln_dict['status'] != 'optimal': raise GameUnsolvableException(soln_dict) @@ -128,3 +268,34 @@ class SymmetricLinearGame: p2_optimal = soln_dict['z'][self._K.dimension():] return Solution(p1_value, p1_optimal, p2_optimal) + + def dual(self): + """ + Return the dual game to this game. + + EXAMPLES: + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(3) + >>> L = [[1,-1,-12],[-5,2,-15],[-15,-3,1]] + >>> e1 = [1,1,1] + >>> e2 = [1,2,3] + >>> SLG = SymmetricLinearGame(L, K, e1, e2) + >>> print(SLG.dual()) + The linear game (L, K, e1, e2) where + L = [ 1 -1 -12] + [ -5 2 -15] + [-15 -3 1], + K = Nonnegative orthant in the real 3-space, + e1 = [ 1] + [ 2] + [ 3], + e2 = [ 1] + [ 1] + [ 1]. + + """ + return SymmetricLinearGame(self._L.trans(), + self._K, # Since "K" is symmetric. + self._e2, + self._e1)