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 = (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.
-
-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.
class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
modifier : float
A scaling factor (default: 1) applied to the default
- ``EPSILON`` for this comparison. If you have a poorly-
+ 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*modifier)
+ 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)
- expected = inner_product(G._L*soln.player1_optimal(),
- soln.player2_optimal())
- self.assert_within_tol(soln.game_value(), expected, G.condition())
+ 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())
+ p1_close = p1_diff < options.ABS_TOL
+ p2_close = p2_diff < options.ABS_TOL
+ gv_close = gv_diff < options.ABS_TOL
- def test_condition_lower_bound(self):
+ self.assertTrue(p1_close and p2_close and gv_close)
+
+
+ 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):
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, H.condition())
+ 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):
(alpha, H) = random_translation(G)
value2 = H.solution().game_value()
- self.assert_within_tol(value1 + alpha, value2, H.condition())
+ 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),
- H.condition())
+ self.assert_within_tol(value2, H.payoff(x_bar, y_bar), modifier)
def test_translation_orthant(self):
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()
+ modifier = G.tolerance_scale(soln1)
self.assert_within_tol(-soln1.game_value(),
soln2.game_value(),
- H.condition())
+ 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.condition())
+ H.payoff(y_bar, x_bar),
+ modifier)
+
def test_opposite_game_orthant(self):
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, G.condition())
+ 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, G.condition())
+ modifier = G.tolerance_scale(soln)
+ self.assert_within_tol(ip1, 0, modifier)
+ self.assert_within_tol(ip2, 0, modifier)
def test_orthogonality_orthant(self):
#
# 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(),
- G.condition())
+ mod = G.tolerance_scale(soln)
+ self.assert_within_tol(dualsoln.game_value(), soln.game_value(), mod)
def test_lyapunov_orthant(self):
projects / dunshire.git / blobdiff