X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2Fdunshire%2Fsymmetric_linear_game.py;h=b6489ba6de43877dd5707a39b3d7811dd9d2e4a7;hb=daf22c1bf9368faf42d9b045e8ad437183542362;hp=07385d7c3fd25c847a25bc7bee8f38b2b1341263;hpb=6332794f1ecd2af0afdf5eab527bebcaaa9f58a2;p=dunshire.git diff --git a/src/dunshire/symmetric_linear_game.py b/src/dunshire/symmetric_linear_game.py index 07385d7..b6489ba 100644 --- a/src/dunshire/symmetric_linear_game.py +++ b/src/dunshire/symmetric_linear_game.py @@ -6,13 +6,15 @@ to solve a linear game. """ from cvxopt import matrix, printing, solvers +from unittest import TestCase from cones import CartesianProduct from errors import GameUnsolvableException -from matrices import append_col, append_row, identity +from matrices import append_col, append_row, identity, inner_product +import options -printing.options['dformat'] = '%.7f' -solvers.options['show_progress'] = False +printing.options['dformat'] = options.FLOAT_FORMAT +solvers.options['show_progress'] = options.VERBOSE class Solution: @@ -39,11 +41,21 @@ 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()) @@ -96,22 +108,106 @@ class SymmetricLinearGame: """ INPUT: - - ``L`` -- an n-by-b matrix represented as a list of lists - of real numbers. + - ``L`` -- an square matrix represented as a list of lists + of real numbers. ``L`` itself is interpreted as a list of + ROWS, which agrees with (for example) SageMath and NumPy, + but not with CVXOPT (whose matrix constructor accepts a + list of columns). - ``K`` -- a SymmetricCone instance. - - ``e1`` -- the interior point of ``K`` belonging to player one, - as a column vector. - - - ``e2`` -- the interior point of ``K`` belonging to player two, - as a column vector. - + - ``e1`` -- the interior point of ``K`` belonging to player one; + it can be of any enumerable type having the correct length. + + - ``e2`` -- the interior point of ``K`` belonging to player two; + it can be of any enumerable type having the correct length. + + EXAMPLES: + + Lists can (and probably should) be used for every argument: + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(2) + >>> L = [[1,0],[0,1]] + >>> e1 = [1,1] + >>> e2 = [1,1] + >>> G = SymmetricLinearGame(L, K, e1, e2) + >>> print(G) + The linear game (L, K, e1, e2) where + L = [ 1 0] + [ 0 1], + K = Nonnegative orthant in the real 2-space, + e1 = [ 1] + [ 1], + e2 = [ 1] + [ 1]. + + The points ``e1`` and ``e2`` can also be passed as some other + enumerable type (of the correct length) without much harm, since + there is no row/column ambiguity: + + >>> import cvxopt + >>> import numpy + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(2) + >>> L = [[1,0],[0,1]] + >>> e1 = cvxopt.matrix([1,1]) + >>> e2 = numpy.matrix([1,1]) + >>> G = SymmetricLinearGame(L, K, e1, e2) + >>> print(G) + The linear game (L, K, e1, e2) where + L = [ 1 0] + [ 0 1], + K = Nonnegative orthant in the real 2-space, + e1 = [ 1] + [ 1], + e2 = [ 1] + [ 1]. + + However, ``L`` will always be intepreted as a list of rows, even + if it is passed as a ``cvxopt.base.matrix`` which is otherwise + indexed by columns: + + >>> import cvxopt + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(2) + >>> L = [[1,2],[3,4]] + >>> e1 = [1,1] + >>> e2 = e1 + >>> G = SymmetricLinearGame(L, K, e1, e2) + >>> print(G) + The linear game (L, K, e1, e2) where + L = [ 1 2] + [ 3 4], + K = Nonnegative orthant in the real 2-space, + e1 = [ 1] + [ 1], + e2 = [ 1] + [ 1]. + >>> L = cvxopt.matrix(L) + >>> print(L) + [ 1 3] + [ 2 4] + + >>> G = SymmetricLinearGame(L, K, e1, e2) + >>> print(G) + The linear game (L, K, e1, e2) where + L = [ 1 2] + [ 3 4], + K = Nonnegative orthant in the real 2-space, + e1 = [ 1] + [ 1], + e2 = [ 1] + [ 1]. """ self._K = K self._e1 = matrix(e1, (K.dimension(), 1)) self._e2 = matrix(e2, (K.dimension(), 1)) - self._L = matrix(L, (K.dimension(), K.dimension())) + + # Our input ``L`` is indexed by rows but CVXOPT matrices are + # indexed by columns, so we need to transpose the input before + # feeding it to CVXOPT. + self._L = matrix(L, (K.dimension(), K.dimension())).trans() if not K.contains_strict(self._e1): raise ValueError('the point e1 must lie in the interior of K') @@ -122,8 +218,39 @@ class SymmetricLinearGame: def __str__(self): """ Return a string representatoin of this game. + + EXAMPLES: + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(3) + >>> L = [[1,-5,-15],[-1,2,-3],[-12,-15,1]] + >>> 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]. + """ - return "a game" + tpl = 'The linear game (L, K, e1, e2) where\n' \ + ' L = {:s},\n' \ + ' K = {!s},\n' \ + ' e1 = {:s},\n' \ + ' e2 = {:s}.' + 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), indented_e1, indented_e2) + def solution(self): """ @@ -137,6 +264,49 @@ class SymmetricLinearGame: 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,-5,-15],[-1,2,-3],[-12,-15,1]] + >>> 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. @@ -164,7 +334,7 @@ class SymmetricLinearGame: # 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._e1], (1, self._K.dimension() + 1), 'd') + A = matrix([0, self._e2], (1, self._K.dimension() + 1), 'd') # Actually solve the thing and obtain a dictionary describing # what happened. @@ -188,8 +358,62 @@ class SymmetricLinearGame: def dual(self): """ Return the dual game to this game. + + EXAMPLES: + + >>> from cones import NonnegativeOrthant + >>> K = NonnegativeOrthant(3) + >>> L = [[1,-5,-15],[-1,2,-3],[-12,-15,1]] + >>> 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(), + return SymmetricLinearGame(self._L, # It will be transposed in __init__(). self._K, # Since "K" is symmetric. self._e2, self._e1) + + +class SymmetricLinearGameTest(TestCase): + + def assertEqualWithinTol(self, first, second): + """ + Test that ``first`` and ``second`` are equal within our default + tolerance. + """ + self.assertTrue(abs(first - second) < options.ABS_TOL) + + + def test_solution_exists(self): + """ + Every linear game has a solution, so we should be able to solve + every symmetric linear game. Pick some parameters randomly and + give it a shot. + """ + from cones import NonnegativeOrthant + from random import randint, uniform + ambient_dim = randint(1,10) + K = NonnegativeOrthant(ambient_dim) + e1 = [uniform(0.1, 10) for idx in range(ambient_dim)] + e2 = [uniform(0.1, 10) for idx in range(ambient_dim)] + L = [[uniform(-10, 10) for i in range(ambient_dim)] + for j in range(ambient_dim)] + G = SymmetricLinearGame(L, K, e1, e2) + soln = G.solution() + L_matrix = matrix(L).trans() + expected = inner_product(L_matrix*soln.player1_optimal(), + soln.player2_optimal()) + self.assertEqualWithinTol(soln.game_value(), expected)