2 Unit tests for the :class:`SymmetricLinearGame` class.
5 from unittest
import TestCase
7 from dunshire
.games
import SymmetricLinearGame
8 from dunshire
.matrices
import eigenvalues_re
, inner_product
, norm
9 from dunshire
import options
10 from .randomgen
import (random_icecream_game
, random_ll_icecream_game
,
11 random_ll_orthant_game
, random_nn_scaling
,
12 random_orthant_game
, random_positive_orthant_game
,
16 # Tell pylint to shut up about the large number of methods.
17 class SymmetricLinearGameTest(TestCase
): # pylint: disable=R0904
19 Tests for the SymmetricLinearGame and Solution classes.
21 def assert_within_tol(self
, first
, second
, modifier
=1):
23 Test that ``first`` and ``second`` are equal within a multiple of
24 our default tolerances.
30 The first number to compare.
33 The second number to compare.
36 A scaling factor (default: 1) applied to the default
37 tolerance for this comparison. If you have a poorly-
38 conditioned matrix, for example, you may want to set this
42 self
.assertTrue(abs(first
- second
) < options
.ABS_TOL
*modifier
)
45 def test_solutions_dont_change_orthant(self
):
46 G
= random_orthant_game()
47 self
.assert_solutions_dont_change(G
)
49 def test_solutions_dont_change_icecream(self
):
50 G
= random_icecream_game()
51 self
.assert_solutions_dont_change(G
)
53 def assert_solutions_dont_change(self
, G
):
55 If we solve the same problem twice, we should get
56 the same answer both times.
60 p1_diff
= norm(soln1
.player1_optimal() - soln2
.player1_optimal())
61 p2_diff
= norm(soln1
.player2_optimal() - soln2
.player2_optimal())
62 gv_diff
= abs(soln1
.game_value() - soln2
.game_value())
64 p1_close
= p1_diff
< options
.ABS_TOL
65 p2_close
= p2_diff
< options
.ABS_TOL
66 gv_close
= gv_diff
< options
.ABS_TOL
68 self
.assertTrue(p1_close
and p2_close
and gv_close
)
71 def test_condition_lower_bound(self
):
73 Ensure that the condition number of a game is greater than or
76 It should be safe to compare these floats directly: we compute
77 the condition number as the ratio of one nonnegative real number
78 to a smaller nonnegative real number.
80 G
= random_orthant_game()
81 self
.assertTrue(G
.condition() >= 1.0)
82 G
= random_icecream_game()
83 self
.assertTrue(G
.condition() >= 1.0)
86 def assert_scaling_works(self
, G
):
88 Test that scaling ``L`` by a nonnegative number scales the value
89 of the game by the same number.
91 (alpha
, H
) = random_nn_scaling(G
)
92 value1
= G
.solution().game_value()
93 value2
= H
.solution().game_value()
94 modifier
= 4*max(abs(alpha
), 1)
95 self
.assert_within_tol(alpha
*value1
, value2
, modifier
)
98 def test_scaling_orthant(self
):
100 Test that scaling ``L`` by a nonnegative number scales the value
101 of the game by the same number over the nonnegative orthant.
103 G
= random_orthant_game()
104 self
.assert_scaling_works(G
)
107 def test_scaling_icecream(self
):
109 The same test as :meth:`test_nonnegative_scaling_orthant`,
110 except over the ice cream cone.
112 G
= random_icecream_game()
113 self
.assert_scaling_works(G
)
116 def assert_translation_works(self
, G
):
118 Check that translating ``L`` by alpha*(e1*e2.trans()) increases
119 the value of the associated game by alpha.
121 # We need to use ``L`` later, so make sure we transpose it
122 # before passing it in as a column-indexed matrix.
124 value1
= soln1
.game_value()
125 x_bar
= soln1
.player1_optimal()
126 y_bar
= soln1
.player2_optimal()
128 # This is the "correct" representation of ``M``, but COLUMN
130 (alpha
, H
) = random_translation(G
)
131 value2
= H
.solution().game_value()
133 modifier
= 4*max(abs(alpha
), 1)
134 self
.assert_within_tol(value1
+ alpha
, value2
, modifier
)
136 # Make sure the same optimal pair works.
137 self
.assert_within_tol(value2
, H
.payoff(x_bar
, y_bar
), modifier
)
140 def test_translation_orthant(self
):
142 Test that translation works over the nonnegative orthant.
144 G
= random_orthant_game()
145 self
.assert_translation_works(G
)
148 def test_translation_icecream(self
):
150 The same as :meth:`test_translation_orthant`, except over the
153 G
= random_icecream_game()
154 self
.assert_translation_works(G
)
157 def assert_opposite_game_works(self
, G
):
159 Check the value of the "opposite" game that gives rise to a
160 value that is the negation of the original game. Comes from
163 # This is the "correct" representation of ``M``, but
167 # so we have to transpose it when we feed it to the constructor.
168 # Note: the condition number of ``H`` should be comparable to ``G``.
169 H
= SymmetricLinearGame(M
.trans(), G
.K(), G
.e2(), G
.e1())
172 x_bar
= soln1
.player1_optimal()
173 y_bar
= soln1
.player2_optimal()
176 # The modifier of 4 is because each could be off by 2*ABS_TOL,
177 # which is how far apart the primal/dual objectives have been
179 self
.assert_within_tol(-soln1
.game_value(), soln2
.game_value(), 4)
181 # Make sure the switched optimal pair works. Since x_bar and
182 # y_bar come from G, we use the same modifier.
183 self
.assert_within_tol(soln2
.game_value(), H
.payoff(y_bar
, x_bar
), 4)
187 def test_opposite_game_orthant(self
):
189 Test the value of the "opposite" game over the nonnegative
192 G
= random_orthant_game()
193 self
.assert_opposite_game_works(G
)
196 def test_opposite_game_icecream(self
):
198 Like :meth:`test_opposite_game_orthant`, except over the
201 G
= random_icecream_game()
202 self
.assert_opposite_game_works(G
)
205 def assert_orthogonality(self
, G
):
207 Two orthogonality relations hold at an optimal solution, and we
211 x_bar
= soln
.player1_optimal()
212 y_bar
= soln
.player2_optimal()
213 value
= soln
.game_value()
215 ip1
= inner_product(y_bar
, G
.L()*x_bar
- value
*G
.e1())
216 ip2
= inner_product(value
*G
.e2() - G
.L().trans()*y_bar
, x_bar
)
218 # Huh.. well, y_bar and x_bar can each be epsilon away, but
219 # x_bar is scaled by L, so that's (norm(L) + 1), and then
220 # value could be off by epsilon, so that's another norm(e1) or
221 # norm(e2). On the other hand, this test seems to pass most of
222 # the time even with a modifier of one. How about.. four?
223 self
.assert_within_tol(ip1
, 0, 4)
224 self
.assert_within_tol(ip2
, 0, 4)
227 def test_orthogonality_orthant(self
):
229 Check the orthgonality relationships that hold for a solution
230 over the nonnegative orthant.
232 G
= random_orthant_game()
233 self
.assert_orthogonality(G
)
236 def test_orthogonality_icecream(self
):
238 Check the orthgonality relationships that hold for a solution
239 over the ice-cream cone.
241 G
= random_icecream_game()
242 self
.assert_orthogonality(G
)
245 def test_positive_operator_value(self
):
247 Test that a positive operator on the nonnegative orthant gives
248 rise to a a game with a nonnegative value.
250 This test theoretically applies to the ice-cream cone as well,
251 but we don't know how to make positive operators on that cone.
253 G
= random_positive_orthant_game()
254 self
.assertTrue(G
.solution().game_value() >= -options
.ABS_TOL
)
257 def assert_lyapunov_works(self
, G
):
259 Check that Lyapunov games act the way we expect.
263 # We only check for positive/negative stability if the game
264 # value is not basically zero. If the value is that close to
265 # zero, we just won't check any assertions.
267 # See :meth:`assert_within_tol` for an explanation of the
269 eigs
= eigenvalues_re(G
.L())
271 if soln
.game_value() > options
.ABS_TOL
:
272 # L should be positive stable
273 positive_stable
= all([eig
> -options
.ABS_TOL
for eig
in eigs
])
274 self
.assertTrue(positive_stable
)
275 elif soln
.game_value() < -options
.ABS_TOL
:
276 # L should be negative stable
277 negative_stable
= all([eig
< options
.ABS_TOL
for eig
in eigs
])
278 self
.assertTrue(negative_stable
)
280 # The dual game's value should always equal the primal's.
281 # The modifier of 4 is because even though the games are dual,
282 # CVXOPT doesn't know that, and each could be off by 2*ABS_TOL.
283 dualsoln
= G
.dual().solution()
284 self
.assert_within_tol(dualsoln
.game_value(), soln
.game_value(), 4)
287 def test_lyapunov_orthant(self
):
289 Test that a Lyapunov game on the nonnegative orthant works.
291 G
= random_ll_orthant_game()
292 self
.assert_lyapunov_works(G
)
295 def test_lyapunov_icecream(self
):
297 Test that a Lyapunov game on the ice-cream cone works.
299 G
= random_ll_icecream_game()
300 self
.assert_lyapunov_works(G
)