X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Fsymmetric_linear_game_test.py;h=bba2f7ccfcb48c38312e5d5849aae892d40eac31;hb=2b44481f8a79cbab75ddc0f73eea813b66e17d62;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..bba2f7c 100644 --- a/test/symmetric_linear_game_test.py +++ b/test/symmetric_linear_game_test.py @@ -13,18 +13,22 @@ from .randomgen import (RANDOM_MAX, random_icecream_game, random_nn_scaling, random_orthant_game, random_positive_orthant_game, random_translation) -EPSILON = 2*2*RANDOM_MAX*options.ABS_TOL +EPSILON = (1 + 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. +Often we will want to compare two solutions, say for games that are +equivalent. If the first game value is low by ``ABS_TOL`` and the second +is high by ``ABS_TOL``, then the total could be off by ``2*ABS_TOL``. We +also subject solutions to translations and scalings, which adds to or +scales their error. If the first game is low by ``ABS_TOL`` and the +second is high by ``ABS_TOL`` before scaling, then after scaling, the +second could be high by ``RANDOM_MAX*ABS_TOL``. That is the rationale +for the factor of ``1 + RANDOM_MAX`` in ``EPSILON``. Since ``1 + +RANDOM_MAX`` is greater than ``2*ABS_TOL``, we don't need to handle the +first issue mentioned (both solutions off by the same amount in opposite +directions). """ # Tell pylint to shut up about the large number of methods. @@ -32,12 +36,28 @@ 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 + ``EPSILON`` 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) < EPSILON*modifier) def assert_solution_exists(self, G): @@ -46,9 +66,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 """ soln = G.solution() - expected = inner_product(G._L*soln.player1_optimal(), - soln.player2_optimal()) - self.assert_within_tol(soln.game_value(), expected) + expected = G.payoff(soln.player1_optimal(), soln.player2_optimal()) + self.assert_within_tol(soln.game_value(), expected, G.condition()) @@ -109,7 +128,7 @@ 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) + self.assert_within_tol(alpha*value1, value2, H.condition()) def test_scaling_orthant(self): @@ -147,10 +166,12 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_translation(G) value2 = H.solution().game_value() - self.assert_within_tol(value1 + alpha, value2) + self.assert_within_tol(value1 + alpha, value2, H.condition()) # 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), + H.condition()) def test_translation_orthant(self): @@ -178,22 +199,25 @@ 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()) + self.assert_within_tol(-soln1.game_value(), + soln2.game_value(), + H.condition()) # Make sure the switched optimal pair works. self.assert_within_tol(soln2.game_value(), - inner_product(M*y_bar, x_bar)) + H.payoff(y_bar, x_bar), + H.condition()) def test_opposite_game_orthant(self): @@ -224,11 +248,11 @@ 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()) + self.assert_within_tol(ip1, 0, G.condition()) - ip2 = inner_product(value*G._e2 - G._L.trans()*y_bar, x_bar) - self.assert_within_tol(ip2, 0) + ip2 = inner_product(value*G.e2() - G.L().trans()*y_bar, x_bar) + self.assert_within_tol(ip2, 0, G.condition()) def test_orthogonality_orthant(self): @@ -273,7 +297,7 @@ 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: # L should be positive stable @@ -286,7 +310,9 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 # The dual game's value should always equal the primal's. dualsoln = G.dual().solution() - self.assert_within_tol(dualsoln.game_value(), soln.game_value()) + self.assert_within_tol(dualsoln.game_value(), + soln.game_value(), + G.condition()) def test_lyapunov_orthant(self):