X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Fsymmetric_linear_game_test.py;h=936a7e869283b4fd9ee2e82ddccefa5ef7253658;hb=96a9491fcc4c7df4c73f9617f2185586b0226b78;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..936a7e8 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): @@ -48,7 +68,7 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 expected = inner_product(G._L*soln.player1_optimal(), soln.player2_optimal()) - self.assert_within_tol(soln.game_value(), expected) + self.assert_within_tol(soln.game_value(), expected, G.condition()) @@ -109,7 +129,7 @@ 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 +167,12 @@ 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, + inner_product(H._L*x_bar, y_bar), + H.condition()) def test_translation_orthant(self): @@ -189,11 +211,14 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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)) + inner_product(M*y_bar, x_bar), + H.condition()) def test_opposite_game_orthant(self): @@ -225,10 +250,10 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 value = soln.game_value() ip1 = inner_product(y_bar, G._L*x_bar - value*G._e1) - self.assert_within_tol(ip1, 0) + 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) + self.assert_within_tol(ip2, 0, G.condition()) def test_orthogonality_orthant(self): @@ -286,7 +311,9 @@ 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):