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
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
)
46 def test_condition_lower_bound(self
):
48 Ensure that the condition number of a game is greater than or
51 It should be safe to compare these floats directly: we compute
52 the condition number as the ratio of one nonnegative real number
53 to a smaller nonnegative real number.
55 G
= random_orthant_game()
56 self
.assertTrue(G
.condition() >= 1.0)
57 G
= random_icecream_game()
58 self
.assertTrue(G
.condition() >= 1.0)
61 def assert_scaling_works(self
, G
):
63 Test that scaling ``L`` by a nonnegative number scales the value
64 of the game by the same number.
66 (alpha
, H
) = random_nn_scaling(G
)
67 value1
= G
.solution().game_value()
68 value2
= H
.solution().game_value()
69 modifier
= 4*max(abs(alpha
), 1)
70 self
.assert_within_tol(alpha
*value1
, value2
, modifier
)
73 def test_scaling_orthant(self
):
75 Test that scaling ``L`` by a nonnegative number scales the value
76 of the game by the same number over the nonnegative orthant.
78 G
= random_orthant_game()
79 self
.assert_scaling_works(G
)
82 def test_scaling_icecream(self
):
84 The same test as :meth:`test_nonnegative_scaling_orthant`,
85 except over the ice cream cone.
87 G
= random_icecream_game()
88 self
.assert_scaling_works(G
)
91 def assert_translation_works(self
, G
):
93 Check that translating ``L`` by alpha*(e1*e2.trans()) increases
94 the value of the associated game by alpha.
96 # We need to use ``L`` later, so make sure we transpose it
97 # before passing it in as a column-indexed matrix.
99 value1
= soln1
.game_value()
100 x_bar
= soln1
.player1_optimal()
101 y_bar
= soln1
.player2_optimal()
103 # This is the "correct" representation of ``M``, but COLUMN
105 (alpha
, H
) = random_translation(G
)
106 value2
= H
.solution().game_value()
108 modifier
= 4*max(abs(alpha
), 1)
109 self
.assert_within_tol(value1
+ alpha
, value2
, modifier
)
111 # Make sure the same optimal pair works.
112 self
.assert_within_tol(value2
, H
.payoff(x_bar
, y_bar
), modifier
)
115 def test_translation_orthant(self
):
117 Test that translation works over the nonnegative orthant.
119 G
= random_orthant_game()
120 self
.assert_translation_works(G
)
123 def test_translation_icecream(self
):
125 The same as :meth:`test_translation_orthant`, except over the
128 G
= random_icecream_game()
129 self
.assert_translation_works(G
)
132 def assert_opposite_game_works(self
, G
):
134 Check the value of the "opposite" game that gives rise to a
135 value that is the negation of the original game. Comes from
138 # This is the "correct" representation of ``M``, but
142 # so we have to transpose it when we feed it to the constructor.
143 # Note: the condition number of ``H`` should be comparable to ``G``.
144 H
= SymmetricLinearGame(M
.trans(), G
.K(), G
.e2(), G
.e1())
147 x_bar
= soln1
.player1_optimal()
148 y_bar
= soln1
.player2_optimal()
151 # The modifier of 4 is because each could be off by 2*ABS_TOL,
152 # which is how far apart the primal/dual objectives have been
154 self
.assert_within_tol(-soln1
.game_value(), soln2
.game_value(), 4)
156 # Make sure the switched optimal pair works. Since x_bar and
157 # y_bar come from G, we use the same modifier.
158 self
.assert_within_tol(soln2
.game_value(), H
.payoff(y_bar
, x_bar
), 4)
162 def test_opposite_game_orthant(self
):
164 Test the value of the "opposite" game over the nonnegative
167 G
= random_orthant_game()
168 self
.assert_opposite_game_works(G
)
171 def test_opposite_game_icecream(self
):
173 Like :meth:`test_opposite_game_orthant`, except over the
176 G
= random_icecream_game()
177 self
.assert_opposite_game_works(G
)
180 def assert_orthogonality(self
, G
):
182 Two orthogonality relations hold at an optimal solution, and we
186 x_bar
= soln
.player1_optimal()
187 y_bar
= soln
.player2_optimal()
188 value
= soln
.game_value()
190 ip1
= inner_product(y_bar
, G
.L()*x_bar
- value
*G
.e1())
191 ip2
= inner_product(value
*G
.e2() - G
.L().trans()*y_bar
, x_bar
)
193 # Huh.. well, y_bar and x_bar can each be epsilon away, but
194 # x_bar is scaled by L, so that's (norm(L) + 1), and then
195 # value could be off by epsilon, so that's another norm(e1) or
196 # norm(e2). On the other hand, this test seems to pass most of
197 # the time even with a modifier of one. How about.. four?
198 self
.assert_within_tol(ip1
, 0, 4)
199 self
.assert_within_tol(ip2
, 0, 4)
202 def test_orthogonality_orthant(self
):
204 Check the orthgonality relationships that hold for a solution
205 over the nonnegative orthant.
207 G
= random_orthant_game()
208 self
.assert_orthogonality(G
)
211 def test_orthogonality_icecream(self
):
213 Check the orthgonality relationships that hold for a solution
214 over the ice-cream cone.
216 G
= random_icecream_game()
217 self
.assert_orthogonality(G
)
220 def test_positive_operator_value(self
):
222 Test that a positive operator on the nonnegative orthant gives
223 rise to a a game with a nonnegative value.
225 This test theoretically applies to the ice-cream cone as well,
226 but we don't know how to make positive operators on that cone.
228 G
= random_positive_orthant_game()
229 self
.assertTrue(G
.solution().game_value() >= -options
.ABS_TOL
)
232 def assert_lyapunov_works(self
, G
):
234 Check that Lyapunov games act the way we expect.
238 # We only check for positive/negative stability if the game
239 # value is not basically zero. If the value is that close to
240 # zero, we just won't check any assertions.
242 # See :meth:`assert_within_tol` for an explanation of the
244 eigs
= eigenvalues_re(G
.L())
246 if soln
.game_value() > options
.ABS_TOL
:
247 # L should be positive stable
248 positive_stable
= all([eig
> -options
.ABS_TOL
for eig
in eigs
])
249 self
.assertTrue(positive_stable
)
250 elif soln
.game_value() < -options
.ABS_TOL
:
251 # L should be negative stable
252 negative_stable
= all([eig
< options
.ABS_TOL
for eig
in eigs
])
253 self
.assertTrue(negative_stable
)
255 # The dual game's value should always equal the primal's.
256 # The modifier of 4 is because even though the games are dual,
257 # CVXOPT doesn't know that, and each could be off by 2*ABS_TOL.
258 dualsoln
= G
.dual().solution()
259 self
.assert_within_tol(dualsoln
.game_value(), soln
.game_value(), 4)
262 def test_lyapunov_orthant(self
):
264 Test that a Lyapunov game on the nonnegative orthant works.
266 G
= random_ll_orthant_game()
267 self
.assert_lyapunov_works(G
)
270 def test_lyapunov_icecream(self
):
272 Test that a Lyapunov game on the ice-cream cone works.
274 G
= random_ll_icecream_game()
275 self
.assert_lyapunov_works(G
)