X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Fsymmetric_linear_game_test.py;h=cf305f0ae133699a1be00a3dce8c27c72c9f2a7c;hb=dd58b25641f37f52b7327b1b779a606c33e230eb;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..cf305f0 100644 --- a/test/symmetric_linear_game_test.py +++ b/test/symmetric_linear_game_test.py @@ -4,101 +4,154 @@ 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_orthant(self): """ - Given a SymmetricLinearGame, ensure that it has a solution. + If we solve the same game twice over the nonnegative orthant, + then we should get the same solution both times. The solution to + a game is not unique, but the process we use is (as far as we + know) deterministic. """ - soln = G.solution() + G = random_orthant_game() + self.assert_solutions_dont_change(G) + + def test_solutions_dont_change_icecream(self): + """ + If we solve the same game twice over the ice-cream cone, then we + should get the same solution both times. The solution to a game + is not unique, but the process we use is (as far as we know) + deterministic. + """ + G = random_icecream_game() + self.assert_solutions_dont_change(G) + + def assert_solutions_dont_change(self, G): + """ + Solve ``G`` twice and check that the solutions agree. + """ + 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): + def assert_player1_start_valid(self, G): """ - Ensure that the condition number of a game is greater than or - equal to one. + Ensure that player one's starting point satisfies both the + equality and cone inequality in the CVXOPT primal problem. + """ + x = G.player1_start()['x'] + s = G.player1_start()['s'] + s1 = s[0:G.dimension()] + s2 = s[G.dimension():] + self.assert_within_tol(norm(G.A()*x - G.b()), 0) + self.assertTrue((s1, s2) in G.C()) - It should be safe to compare these floats directly: we compute - the condition number as the ratio of one nonnegative real number - to a smaller nonnegative real number. + + def test_player1_start_valid_orthant(self): + """ + Ensure that player one's starting point is feasible over the + nonnegative orthant. """ G = random_orthant_game() - self.assertTrue(G.condition() >= 1.0) + self.assert_player1_start_valid(G) + + + def test_player1_start_valid_icecream(self): + """ + Ensure that player one's starting point is feasible over the + ice-cream cone. + """ G = random_icecream_game() - self.assertTrue(G.condition() >= 1.0) + self.assert_player1_start_valid(G) + + + def assert_player2_start_valid(self, G): + """ + Check that player two's starting point satisfies both the + cone inequality in the CVXOPT dual problem. + """ + z = G.player2_start()['z'] + z1 = z[0:G.dimension()] + z2 = z[G.dimension():] + self.assertTrue((z1, z2) in G.C()) - def test_solution_exists_orthant(self): + def test_player2_start_valid_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. + Ensure that player two's starting point is feasible over the + nonnegative orthant. """ G = random_orthant_game() - self.assert_solution_exists(G) + self.assert_player2_start_valid(G) - def test_solution_exists_icecream(self): + def test_player2_start_valid_icecream(self): """ - Like :meth:`test_solution_exists_nonnegative_orthant`, except - over the ice cream cone. + Ensure that player two's starting point is feasible over the + ice-cream cone. """ G = random_icecream_game() - self.assert_solution_exists(G) + self.assert_player2_start_valid(G) - def test_negative_value_z_operator(self): + def test_condition_lower_bound(self): """ - Test the example given in Gowda/Ravindran of a Z-matrix with - negative game value on the nonnegative orthant. + Ensure that the condition number of a game is greater than or + equal to one. + + It should be safe to compare these floats directly: we compute + the condition number as the ratio of one nonnegative real number + to a smaller nonnegative real number. """ - 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) + G = random_orthant_game() + self.assertTrue(G.condition() >= 1.0) + G = random_icecream_game() + self.assertTrue(G.condition() >= 1.0) def assert_scaling_works(self, G): @@ -107,9 +160,14 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 of the game by the same number. """ (alpha, H) = random_nn_scaling(G) - value1 = G.solution().game_value() - value2 = H.solution().game_value() - self.assert_within_tol(alpha*value1, value2) + soln1 = G.solution() + soln2 = H.solution() + value1 = soln1.game_value() + value2 = soln2.game_value() + modifier1 = G.tolerance_scale(soln1) + modifier2 = H.tolerance_scale(soln2) + modifier = max(modifier1, modifier2) + self.assert_within_tol(alpha*value1, value2, modifier) def test_scaling_orthant(self): @@ -147,10 +205,11 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_translation(G) value2 = H.solution().game_value() - self.assert_within_tol(value1 + alpha, value2) + modifier = G.tolerance_scale(soln1) + 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): @@ -176,24 +235,26 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 value that is the negation of the original game. Comes from some corollary. """ - # This is the "correct" representation of ``M``, but - # COLUMN indexed... - M = -G._L.trans() - - # so we have to transpose it when we feed it to the constructor. + # Since L is a CVXOPT matrix, it will be transposed automatically. # Note: the condition number of ``H`` should be comparable to ``G``. - H = SymmetricLinearGame(M.trans(), G._K, G._e2, G._e1) + H = SymmetricLinearGame(-G.L(), 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()) + modifier = G.tolerance_scale(soln1) + self.assert_within_tol(-soln1.game_value(), + soln2.game_value(), + modifier) - # Make sure the switched optimal pair works. + # 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(), - inner_product(M*y_bar, x_bar)) + H.payoff(y_bar, x_bar), + modifier) + def test_opposite_game_orthant(self): @@ -224,11 +285,12 @@ 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) + modifier = G.tolerance_scale(soln) + self.assert_within_tol(ip1, 0, modifier) + self.assert_within_tol(ip2, 0, modifier) def test_orthogonality_orthant(self): @@ -273,20 +335,20 @@ 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. dualsoln = G.dual().solution() - self.assert_within_tol(dualsoln.game_value(), soln.game_value()) + mod = G.tolerance_scale(soln) + self.assert_within_tol(dualsoln.game_value(), soln.game_value(), mod) def test_lyapunov_orthant(self):