"""
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
+ ``EPSILON`` 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) < EPSILON*modifier)
def assert_solution_exists(self, G):
"""
soln = G.solution()
- expected = inner_product(G._L*soln.player1_optimal(),
- soln.player2_optimal())
- self.assert_within_tol(soln.game_value(), expected)
+ expected = G.payoff(soln.player1_optimal(), soln.player2_optimal())
+ self.assert_within_tol(soln.game_value(), expected, G.condition())
(alpha, H) = random_nn_scaling(G)
value1 = G.solution().game_value()
value2 = H.solution().game_value()
- self.assert_within_tol(alpha*value1, value2)
+ self.assert_within_tol(alpha*value1, value2, H.condition())
def test_scaling_orthant(self):
(alpha, H) = random_translation(G)
value2 = H.solution().game_value()
- self.assert_within_tol(value1 + alpha, value2)
+ self.assert_within_tol(value1 + alpha, value2, H.condition())
# 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),
+ H.condition())
def test_translation_orthant(self):
"""
# This is the "correct" representation of ``M``, but
# COLUMN indexed...
- M = -G._L.trans()
+ M = -G.L().trans()
# so we have to transpose it when we feed it to the constructor.
# Note: the condition number of ``H`` should be comparable to ``G``.
- H = SymmetricLinearGame(M.trans(), G._K, G._e2, G._e1)
+ H = SymmetricLinearGame(M.trans(), 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())
+ self.assert_within_tol(-soln1.game_value(),
+ soln2.game_value(),
+ H.condition())
# Make sure the switched optimal pair works.
self.assert_within_tol(soln2.game_value(),
- inner_product(M*y_bar, x_bar))
+ H.payoff(y_bar, x_bar),
+ H.condition())
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)
+ ip1 = inner_product(y_bar, G.L()*x_bar - value*G.e1())
+ self.assert_within_tol(ip1, 0, G.condition())
- ip2 = inner_product(value*G._e2 - G._L.trans()*y_bar, x_bar)
- self.assert_within_tol(ip2, 0)
+ ip2 = inner_product(value*G.e2() - G.L().trans()*y_bar, x_bar)
+ self.assert_within_tol(ip2, 0, G.condition())
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:
# L should be positive 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())
+ self.assert_within_tol(dualsoln.game_value(),
+ soln.game_value(),
+ G.condition())
def test_lyapunov_orthant(self):