printing.options['dformat'] = options.FLOAT_FORMAT
+
class Solution:
"""
A representation of the solution of a linear game. It should contain
self.A(),
self.b(),
primalstart=self.player1_start(),
+ dualstart=self.player2_start(),
options=opts)
except ValueError as error:
if str(error) == 'math domain error':
printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise GameUnsolvableException(self, soln_dict)
+ # For the game value, we could use any of:
+ #
+ # * p1_value
+ # * p2_value
+ # * (p1_value + p2_value)/2
+ # * the game payoff
+ #
+ # We want the game value to be the payoff, however, so it
+ # makes the most sense to just use that, even if it means we
+ # can't test the fact that p1_value/p2_value are close to the
+ # payoff.
+ payoff = self.payoff(p1_optimal, p2_optimal)
+ soln = Solution(payoff, p1_optimal, p2_optimal)
+
# The "optimal" and "unknown" results, we actually treat the
# same. Even if CVXOPT bails out due to numerical difficulty,
# it will have some candidate points in mind. If those
# close enough (one could be low by ABS_TOL, the other high by
# it) because otherwise CVXOPT might return "unknown" and give
# us two points in the cone that are nowhere near optimal.
- if abs(p1_value - p2_value) > 2*options.ABS_TOL:
+ #
+ if abs(p1_value - p2_value) > self.epsilon_scale(soln)*options.ABS_TOL:
printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise GameUnsolvableException(self, soln_dict)
printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise GameUnsolvableException(self, soln_dict)
- # For the game value, we could use any of:
- #
- # * p1_value
- # * p2_value
- # * (p1_value + p2_value)/2
- # * the game payoff
- #
- # We want the game value to be the payoff, however, so it
- # makes the most sense to just use that, even if it means we
- # can't test the fact that p1_value/p2_value are close to the
- # payoff.
- payoff = self.payoff(p1_optimal, p2_optimal)
- return Solution(payoff, p1_optimal, p2_optimal)
+ return soln
def condition(self):
of the game by the same number.
"""
(alpha, H) = random_nn_scaling(G)
- value1 = G.solution().game_value()
- value2 = H.solution().game_value()
- modifier = 4*max(abs(alpha), 1)
+ soln1 = G.solution()
+ soln2 = H.solution()
+ value1 = soln1.game_value()
+ value2 = soln2.game_value()
+ modifier1 = G.epsilon_scale(soln1)
+ modifier2 = H.epsilon_scale(soln2)
+ modifier = max(modifier1, modifier2)
self.assert_within_tol(alpha*value1, value2, modifier)
(alpha, H) = random_translation(G)
value2 = H.solution().game_value()
- modifier = 4*max(abs(alpha), 1)
+ modifier = G.epsilon_scale(soln1)
self.assert_within_tol(value1 + alpha, value2, modifier)
# Make sure the same optimal pair works.
y_bar = soln1.player2_optimal()
soln2 = H.solution()
- # The modifier of 4 is because each could be off by 2*ABS_TOL,
- # which is how far apart the primal/dual objectives have been
- # observed being.
- self.assert_within_tol(-soln1.game_value(), soln2.game_value(), 4)
+ mod = G.epsilon_scale(soln1)
+ self.assert_within_tol(-soln1.game_value(), soln2.game_value(), mod)
# 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(), H.payoff(y_bar, x_bar), 4)
+ self.assert_within_tol(soln2.game_value(), H.payoff(y_bar, x_bar), mod)
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)
- # Huh.. well, y_bar and x_bar can each be epsilon away, but
- # x_bar is scaled by L, so that's (norm(L) + 1), and then
- # value could be off by epsilon, so that's another norm(e1) or
- # norm(e2). On the other hand, this test seems to pass most of
- # the time even with a modifier of one. How about.. four?
- self.assert_within_tol(ip1, 0, 4)
- self.assert_within_tol(ip2, 0, 4)
+ modifier = G.epsilon_scale(soln)
+ self.assert_within_tol(ip1, 0, modifier)
+ self.assert_within_tol(ip2, 0, modifier)
def test_orthogonality_orthant(self):
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.
- # The modifier of 4 is because even though the games are dual,
- # CVXOPT doesn't know that, and each could be off by 2*ABS_TOL.
dualsoln = G.dual().solution()
- self.assert_within_tol(dualsoln.game_value(), soln.game_value(), 4)
+ mod = G.epsilon_scale(soln)
+ self.assert_within_tol(dualsoln.game_value(), soln.game_value(), mod)
def test_lyapunov_orthant(self):