X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Fsymmetric_linear_game_test.py;h=887831a44a68aeae7e8b25514154cfbe53f0309c;hb=d90b0b66e1983af5268fb1784907004e12b48dfa;hp=470cf6a116aeb578a89450671abfbb6f73f1e9de;hpb=ac39a0b32d176fa78ecd5cf4ef21676e3bd56d6c;p=dunshire.git diff --git a/test/symmetric_linear_game_test.py b/test/symmetric_linear_game_test.py index 470cf6a..887831a 100644 --- a/test/symmetric_linear_game_test.py +++ b/test/symmetric_linear_game_test.py @@ -4,52 +4,61 @@ Unit tests for the :class:`SymmetricLinearGame` class. from unittest import TestCase -from dunshire.cones import NonnegativeOrthant from dunshire.games import SymmetricLinearGame -from dunshire.matrices import eigenvalues_re, inner_product +from dunshire.matrices import eigenvalues_re, inner_product, norm from dunshire import options -from .randomgen import (RANDOM_MAX, random_icecream_game, - random_ll_icecream_game, random_ll_orthant_game, - random_nn_scaling, random_orthant_game, - random_positive_orthant_game, random_translation) +from .randomgen import (random_icecream_game, random_ll_icecream_game, + random_ll_orthant_game, random_nn_scaling, + random_orthant_game, random_positive_orthant_game, + random_translation) -EPSILON = 2*2*RANDOM_MAX*options.ABS_TOL -""" -This is the tolerance constant including fudge factors that we use to -determine whether or not two numbers are equal in tests. - -The factor of two is because if we compare two solutions, both -of which may be off by ``ABS_TOL``, then the result could be off -by ``2*ABS_TOL``. The factor of ``RANDOM_MAX`` allows for -scaling a result (by ``RANDOM_MAX``) that may be off by -``ABS_TOL``. The final factor of two is to allow for the edge -cases where we get an "unknown" result and need to lower the -CVXOPT tolerance by a factor of two. -""" # Tell pylint to shut up about the large number of methods. class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 """ Tests for the SymmetricLinearGame and Solution classes. """ - def assert_within_tol(self, first, second): + def assert_within_tol(self, first, second, modifier=1): """ Test that ``first`` and ``second`` are equal within a multiple of our default tolerances. + + Parameters + ---------- + + first : float + The first number to compare. + + second : float + The second number to compare. + + modifier : float + A scaling factor (default: 1) applied to the default + tolerance for this comparison. If you have a poorly- + conditioned matrix, for example, you may want to set this + greater than one. + """ - self.assertTrue(abs(first - second) < EPSILON) + self.assertTrue(abs(first - second) < options.ABS_TOL*modifier) - def assert_solution_exists(self, G): + def test_solutions_dont_change(self): """ - Given a SymmetricLinearGame, ensure that it has a solution. + If we solve the same problem twice, we should get + the same answer both times. """ - soln = G.solution() + G = random_orthant_game() + soln1 = G.solution() + soln2 = G.solution() + p1_diff = norm(soln1.player1_optimal() - soln2.player1_optimal()) + p2_diff = norm(soln1.player2_optimal() - soln2.player2_optimal()) + gv_diff = abs(soln1.game_value() - soln2.game_value()) - expected = inner_product(G._L*soln.player1_optimal(), - soln.player2_optimal()) - self.assert_within_tol(soln.game_value(), expected) + p1_close = p1_diff < options.ABS_TOL + p2_close = p2_diff < options.ABS_TOL + gv_close = gv_diff < options.ABS_TOL + self.assertTrue(p1_close and p2_close and gv_close) def test_condition_lower_bound(self): @@ -67,40 +76,6 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 self.assertTrue(G.condition() >= 1.0) - def test_solution_exists_orthant(self): - """ - Every linear game has a solution, so we should be able to solve - every symmetric linear game over the NonnegativeOrthant. Pick - some parameters randomly and give it a shot. The resulting - optimal solutions should give us the optimal game value when we - apply the payoff operator to them. - """ - G = random_orthant_game() - self.assert_solution_exists(G) - - - def test_solution_exists_icecream(self): - """ - Like :meth:`test_solution_exists_nonnegative_orthant`, except - over the ice cream cone. - """ - G = random_icecream_game() - self.assert_solution_exists(G) - - - def test_negative_value_z_operator(self): - """ - Test the example given in Gowda/Ravindran of a Z-matrix with - negative game value on the nonnegative orthant. - """ - K = NonnegativeOrthant(2) - e1 = [1, 1] - e2 = e1 - L = [[1, -2], [-2, 1]] - G = SymmetricLinearGame(L, K, e1, e2) - self.assertTrue(G.solution().game_value() < -options.ABS_TOL) - - def assert_scaling_works(self, G): """ Test that scaling ``L`` by a nonnegative number scales the value @@ -109,7 +84,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_nn_scaling(G) value1 = G.solution().game_value() value2 = H.solution().game_value() - self.assert_within_tol(alpha*value1, value2) + modifier = 4*max(abs(alpha), 1) + self.assert_within_tol(alpha*value1, value2, modifier) def test_scaling_orthant(self): @@ -147,10 +123,11 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_translation(G) value2 = H.solution().game_value() - self.assert_within_tol(value1 + alpha, value2) + modifier = 4*max(abs(alpha), 1) + self.assert_within_tol(value1 + alpha, value2, modifier) # Make sure the same optimal pair works. - self.assert_within_tol(value2, inner_product(H._L*x_bar, y_bar)) + self.assert_within_tol(value2, H.payoff(x_bar, y_bar), modifier) def test_translation_orthant(self): @@ -178,22 +155,26 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 """ # This is the "correct" representation of ``M``, but # COLUMN indexed... - M = -G._L.trans() + M = -G.L().trans() # so we have to transpose it when we feed it to the constructor. # Note: the condition number of ``H`` should be comparable to ``G``. - H = SymmetricLinearGame(M.trans(), G._K, G._e2, G._e1) + H = SymmetricLinearGame(M.trans(), G.K(), G.e2(), G.e1()) soln1 = G.solution() x_bar = soln1.player1_optimal() y_bar = soln1.player2_optimal() soln2 = H.solution() - self.assert_within_tol(-soln1.game_value(), soln2.game_value()) + # The modifier of 4 is because each could be off by 2*ABS_TOL, + # which is how far apart the primal/dual objectives have been + # observed being. + self.assert_within_tol(-soln1.game_value(), soln2.game_value(), 4) + + # Make sure the switched optimal pair works. Since x_bar and + # y_bar come from G, we use the same modifier. + self.assert_within_tol(soln2.game_value(), H.payoff(y_bar, x_bar), 4) - # Make sure the switched optimal pair works. - self.assert_within_tol(soln2.game_value(), - inner_product(M*y_bar, x_bar)) def test_opposite_game_orthant(self): @@ -224,11 +205,16 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 y_bar = soln.player2_optimal() value = soln.game_value() - ip1 = inner_product(y_bar, G._L*x_bar - value*G._e1) - self.assert_within_tol(ip1, 0) + ip1 = inner_product(y_bar, G.L()*x_bar - value*G.e1()) + ip2 = inner_product(value*G.e2() - G.L().trans()*y_bar, x_bar) - ip2 = inner_product(value*G._e2 - G._L.trans()*y_bar, x_bar) - self.assert_within_tol(ip2, 0) + # Huh.. well, y_bar and x_bar can each be epsilon away, but + # x_bar is scaled by L, so that's (norm(L) + 1), and then + # value could be off by epsilon, so that's another norm(e1) or + # norm(e2). On the other hand, this test seems to pass most of + # the time even with a modifier of one. How about.. four? + self.assert_within_tol(ip1, 0, 4) + self.assert_within_tol(ip2, 0, 4) def test_orthogonality_orthant(self): @@ -273,20 +259,22 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 # # See :meth:`assert_within_tol` for an explanation of the # fudge factors. - eigs = eigenvalues_re(G._L) + eigs = eigenvalues_re(G.L()) - if soln.game_value() > EPSILON: + if soln.game_value() > options.ABS_TOL: # L should be positive stable positive_stable = all([eig > -options.ABS_TOL for eig in eigs]) self.assertTrue(positive_stable) - elif soln.game_value() < -EPSILON: + elif soln.game_value() < -options.ABS_TOL: # L should be negative stable negative_stable = all([eig < options.ABS_TOL for eig in eigs]) self.assertTrue(negative_stable) # The dual game's value should always equal the primal's. + # The modifier of 4 is because even though the games are dual, + # CVXOPT doesn't know that, and each could be off by 2*ABS_TOL. dualsoln = G.dual().solution() - self.assert_within_tol(dualsoln.game_value(), soln.game_value()) + self.assert_within_tol(dualsoln.game_value(), soln.game_value(), 4) def test_lyapunov_orthant(self):