Add game accessor methods for its L, K, e1, e2, and dimension.

[dunshire.git] / test / symmetric_linear_game_test.py

diff --git a/test/symmetric_linear_game_test.py b/test/symmetric_linear_game_test.py
index 69c352ace384e0fda2f60023d6577bc37baaf315..bba2f7ccfcb48c38312e5d5849aae892d40eac31 100644 (file)
--- a/test/symmetric_linear_game_test.py
+++ b/test/symmetric_linear_game_test.py
@@ -2,272 +2,88 @@
 Unit tests for the :class:`SymmetricLinearGame` class.
 """
 
 Unit tests for the :class:`SymmetricLinearGame` class.
 """
 

-from math import sqrt
-from random import randint, uniform

 from unittest import TestCase
 
 from unittest import TestCase
 

-from cvxopt import matrix
-from dunshire.cones import NonnegativeOrthant, IceCream
+from dunshire.cones import NonnegativeOrthant

 from dunshire.games import SymmetricLinearGame
 from dunshire.games import SymmetricLinearGame

-from dunshire.matrices import (append_col, append_row, eigenvalues_re,
-                               identity, inner_product)
+from dunshire.matrices import eigenvalues_re, inner_product

 from dunshire import options
 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)

 
 

+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).
+"""

 
 

-def random_matrix(dims):
-    """
-    Generate a random square matrix.
-
-    Parameters
-    ----------
-
-    dims : int
-        The number of rows/columns you want in the returned matrix.
-
-    Returns
-    -------
-
-    matrix
-        A new matrix whose entries are random floats chosen uniformly from
-        the interval [-10, 10].
-
-    Examples
-    --------
-
-        >>> A = random_matrix(3)
-        >>> A.size
-        (3, 3)
-
-    """
-    return matrix([[uniform(-10, 10) for _ in range(dims)]
-                   for _ in range(dims)])
-
-
-def random_nonnegative_matrix(dims):
-    """
-    Generate a random square matrix with nonnegative entries.
-
-    Parameters
-    ----------
-
-    dims : int
-        The number of rows/columns you want in the returned matrix.
-
-    Returns
-    -------
-
-    matrix
-        A new matrix whose entries are random floats chosen uniformly from
-        the interval [0, 10].
-
-    Examples
-    --------
-
-        >>> A = random_nonnegative_matrix(3)
-        >>> A.size
-        (3, 3)
-        >>> all([entry >= 0 for entry in A])
-        True
-
-    """
-    L = random_matrix(dims)
-    return matrix([abs(entry) for entry in L], (dims, dims))
-
-
-def random_diagonal_matrix(dims):
-    """
-    Generate a random square matrix with zero off-diagonal entries.
-
-    These matrices are Lyapunov-like on the nonnegative orthant, as is
-    fairly easy to see.
-
-    Parameters
-    ----------
-
-    dims : int
-        The number of rows/columns you want in the returned matrix.
-
-    Returns
-    -------
-
-    matrix
-        A new matrix whose diagonal entries are random floats chosen
-        uniformly from the interval [-10, 10] and whose off-diagonal
-        entries are zero.
-
-    Examples
-    --------
-
-        >>> A = random_diagonal_matrix(3)
-        >>> A.size
-        (3, 3)
-        >>> A[0,1] == A[0,2] == A[1,0] == A[2,0] == A[1,2] == A[2,1] == 0
-        True
-
-    """
-    return matrix([[uniform(-10, 10)*int(i == j) for i in range(dims)]
-                   for j in range(dims)])
-
-
-def random_skew_symmetric_matrix(dims):
+# Tell pylint to shut up about the large number of methods.
+class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904

     """
     """

-    Generate a random skew-symmetrix matrix.
-
-    Parameters
-    ----------
-
-    dims : int
-        The number of rows/columns you want in the returned matrix.
-
-    Returns
-    -------
-
-    matrix
-        A new skew-matrix whose strictly above-diagonal entries are
-        random floats chosen uniformly from the interval [-10, 10].
-
-    Examples
-    --------
-
-        >>> A = random_skew_symmetric_matrix(3)
-        >>> A.size
-        (3, 3)
-
-        >>> from dunshire.matrices import norm
-        >>> A = random_skew_symmetric_matrix(randint(1, 10))
-        >>> norm(A + A.trans()) < options.ABS_TOL
-        True
-
+    Tests for the SymmetricLinearGame and Solution classes.

     """
     """

-    strict_ut = [[uniform(-10, 10)*int(i < j) for i in range(dims)]
-                 for j in range(dims)]
-
-    strict_ut = matrix(strict_ut, (dims, dims))
-    return strict_ut - strict_ut.trans()
-
-
-def random_lyapunov_like_icecream(dims):
-    r"""
-    Generate a random matrix Lyapunov-like on the ice-cream cone.
-
-    The form of these matrices is cited in Gowda and Tao
-    [GowdaTao]_. The scalar ``a`` and the vector ``b`` (using their
-    notation) are easy to generate. The submatrix ``D`` is a little
-    trickier, but it can be found noticing that :math:`C + C^{T} = 0`
-    for a skew-symmetric matrix :math:`C` implying that :math:`C + C^{T}
-    + \left(2a\right)I = \left(2a\right)I`. Thus we can stick an
-    :math:`aI` with each of :math:`C,C^{T}` and let those be our
-    :math:`D,D^{T}`.
-
-    Parameters
-    ----------
-
-    dims : int
-        The dimension of the ice-cream cone (not of the matrix you want!)
-        on which the returned matrix should be Lyapunov-like.
-
-    Returns
-    -------
-
-    matrix
-        A new matrix, Lyapunov-like on the ice-cream cone in ``dims``
-        dimensions, whose free entries are random floats chosen uniformly
-        from the interval [-10, 10].
+    def assert_within_tol(self, first, second, modifier=1):
+        """
+        Test that ``first`` and ``second`` are equal within a multiple of
+        our default tolerances.

 
 

-    References
-    ----------
+        Parameters
+        ----------

 
 

-    .. [GowdaTao] M. S. Gowda and J. Tao. On the bilinearity rank of a
-       proper cone and Lyapunov-like transformations. Mathematical
-       Programming, 147:155-170, 2014.
+        first : float
+            The first number to compare.

 
 

-    Examples
-    --------
+        second : float
+            The second number to compare.

 
 

-        >>> L = random_lyapunov_like_icecream(3)
-        >>> L.size
-        (3, 3)
-        >>> x = matrix([1,1,0])
-        >>> s = matrix([1,-1,0])
-        >>> abs(inner_product(L*x, s)) < options.ABS_TOL
-        True
+        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.

 
 

-    """
-    a = matrix([uniform(-10, 10)], (1, 1))
-    b = matrix([uniform(-10, 10) for _ in range(dims-1)], (dims-1, 1))
-    D = random_skew_symmetric_matrix(dims-1) + a*identity(dims-1)
-    row1 = append_col(a, b.trans())
-    row2 = append_col(b, D)
-    return append_row(row1, row2)
+        """
+        self.assertTrue(abs(first - second) < EPSILON*modifier)

 
 
 
 

-def random_orthant_params():
-    """
-    Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
-    random game over the nonnegative orthant.
-    """
-    ambient_dim = randint(1, 10)
-    K = NonnegativeOrthant(ambient_dim)
-    e1 = [uniform(0.5, 10) for _ in range(K.dimension())]
-    e2 = [uniform(0.5, 10) for _ in range(K.dimension())]
-    L = random_matrix(K.dimension())
-    return (L, K, matrix(e1), matrix(e2))
+    def assert_solution_exists(self, G):
+        """
+        Given  a SymmetricLinearGame, ensure that it has a solution.
+        """
+        soln = G.solution()

 
 

+        expected = G.payoff(soln.player1_optimal(), soln.player2_optimal())
+        self.assert_within_tol(soln.game_value(), expected, G.condition())

 
 

-def random_icecream_params():
-    """
-    Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
-    random game over the ice-cream cone.
-    """
-    # Use a minimum dimension of two to avoid divide-by-zero in
-    # the fudge factor we make up later.
-    ambient_dim = randint(2, 10)
-    K = IceCream(ambient_dim)
-    e1 = [1] # Set the "height" of e1 to one
-    e2 = [1] # And the same for e2
-
-    # If we choose the rest of the components of e1,e2 randomly
-    # between 0 and 1, then the largest the squared norm of the
-    # non-height part of e1,e2 could be is the 1*(dim(K) - 1). We
-    # need to make it less than one (the height of the cone) so
-    # that the whole thing is in the cone. The norm of the
-    # non-height part is sqrt(dim(K) - 1), and we can divide by
-    # twice that.
-    fudge_factor = 1.0 / (2.0*sqrt(K.dimension() - 1.0))
-    e1 += [fudge_factor*uniform(0, 1) for _ in range(K.dimension() - 1)]
-    e2 += [fudge_factor*uniform(0, 1) for _ in range(K.dimension() - 1)]
-    L = random_matrix(K.dimension())
-
-    return (L, K, matrix(e1), matrix(e2))

 
 
 
 

-# Tell pylint to shut up about the large number of methods.
-class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
-    """
-    Tests for the SymmetricLinearGame and Solution classes.
-    """
-    def assert_within_tol(self, first, second):
-        """
-        Test that ``first`` and ``second`` are equal within our default
-        tolerance.
+    def test_condition_lower_bound(self):

         """
         """

-        self.assertTrue(abs(first - second) < options.ABS_TOL)
+        Ensure that the condition number of a game is greater than or
+        equal to one.

 
 

-
-    def assert_solution_exists(self, L, K, e1, e2):
-        """
-        Given the parameters needed to construct a SymmetricLinearGame,
-        ensure that that game has a solution.
+        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.

         """
         """

-        # The matrix() constructor assumes that ``L`` is a list of
-        # columns, so we transpose it to agree with what
-        # SymmetricLinearGame() thinks.
-        G = SymmetricLinearGame(L.trans(), K, e1, e2)
-        soln = G.solution()
-
-        expected = inner_product(L*soln.player1_optimal(),
-                                 soln.player2_optimal())
-        self.assert_within_tol(soln.game_value(), expected)
+        G = random_orthant_game()
+        self.assertTrue(G.condition() >= 1.0)
+        G = random_icecream_game()
+        self.assertTrue(G.condition() >= 1.0)

 
 
     def test_solution_exists_orthant(self):
 
 
     def test_solution_exists_orthant(self):


@@ -278,8 +94,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         optimal solutions should give us the optimal game value when we
         apply the payoff operator to them.
         """
         optimal solutions should give us the optimal game value when we
         apply the payoff operator to them.
         """

-        (L, K, e1, e2) = random_orthant_params()
-        self.assert_solution_exists(L, K, e1, e2)
+        G = random_orthant_game()
+        self.assert_solution_exists(G)

 
 
     def test_solution_exists_icecream(self):
 
 
     def test_solution_exists_icecream(self):


@@ -287,8 +103,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         Like :meth:`test_solution_exists_nonnegative_orthant`, except
         over the ice cream cone.
         """
         Like :meth:`test_solution_exists_nonnegative_orthant`, except
         over the ice cream cone.
         """

-        (L, K, e1, e2) = random_icecream_params()
-        self.assert_solution_exists(L, K, e1, e2)
+        G = random_icecream_game()
+        self.assert_solution_exists(G)

 
 
     def test_negative_value_z_operator(self):
 
 
     def test_negative_value_z_operator(self):


@@ -304,18 +120,15 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         self.assertTrue(G.solution().game_value() < -options.ABS_TOL)
 
 
         self.assertTrue(G.solution().game_value() < -options.ABS_TOL)
 
 

-    def assert_scaling_works(self, L, K, e1, e2):
+    def assert_scaling_works(self, G):

         """
         Test that scaling ``L`` by a nonnegative number scales the value
         of the game by the same number.
         """
         """
         Test that scaling ``L`` by a nonnegative number scales the value
         of the game by the same number.
         """

-        game1 = SymmetricLinearGame(L, K, e1, e2)
-        value1 = game1.solution().game_value()
-
-        alpha = uniform(0.1, 10)
-        game2 = SymmetricLinearGame(alpha*L, K, e1, e2)
-        value2 = game2.solution().game_value()
-        self.assert_within_tol(alpha*value1, value2)
+        (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())

 
 
     def test_scaling_orthant(self):
 
 
     def test_scaling_orthant(self):


@@ -323,8 +136,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         Test that scaling ``L`` by a nonnegative number scales the value
         of the game by the same number over the nonnegative orthant.
         """
         Test that scaling ``L`` by a nonnegative number scales the value
         of the game by the same number over the nonnegative orthant.
         """

-        (L, K, e1, e2) = random_orthant_params()
-        self.assert_scaling_works(L, K, e1, e2)
+        G = random_orthant_game()
+        self.assert_scaling_works(G)

 
 
     def test_scaling_icecream(self):
 
 
     def test_scaling_icecream(self):


@@ -332,46 +145,41 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         The same test as :meth:`test_nonnegative_scaling_orthant`,
         except over the ice cream cone.
         """
         The same test as :meth:`test_nonnegative_scaling_orthant`,
         except over the ice cream cone.
         """

-        (L, K, e1, e2) = random_icecream_params()
-        self.assert_scaling_works(L, K, e1, e2)
+        G = random_icecream_game()
+        self.assert_scaling_works(G)

 
 
 
 

-    def assert_translation_works(self, L, K, e1, e2):
+    def assert_translation_works(self, G):

         """
         Check that translating ``L`` by alpha*(e1*e2.trans()) increases
         the value of the associated game by alpha.
         """
         # We need to use ``L`` later, so make sure we transpose it
         # before passing it in as a column-indexed matrix.
         """
         Check that translating ``L`` by alpha*(e1*e2.trans()) increases
         the value of the associated game by alpha.
         """
         # We need to use ``L`` later, so make sure we transpose it
         # before passing it in as a column-indexed matrix.

-        game1 = SymmetricLinearGame(L.trans(), K, e1, e2)
-        soln1 = game1.solution()
+        soln1 = G.solution()

         value1 = soln1.game_value()
         x_bar = soln1.player1_optimal()
         y_bar = soln1.player2_optimal()
 
         value1 = soln1.game_value()
         x_bar = soln1.player1_optimal()
         y_bar = soln1.player2_optimal()
 

-        alpha = uniform(-10, 10)
-        tensor_prod = e1*e2.trans()
-

         # This is the "correct" representation of ``M``, but COLUMN
         # indexed...
         # This is the "correct" representation of ``M``, but COLUMN
         # indexed...

-        M = L + alpha*tensor_prod
-
-        # so we have to transpose it when we feed it to the constructor.
-        game2 = SymmetricLinearGame(M.trans(), K, e1, e2)
-        value2 = game2.solution().game_value()
+        (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.
 
         # Make sure the same optimal pair works.

-        self.assert_within_tol(value2, inner_product(M*x_bar, y_bar))
+        self.assert_within_tol(value2,
+                               H.payoff(x_bar, y_bar),
+                               H.condition())

 
 
     def test_translation_orthant(self):
         """
         Test that translation works over the nonnegative orthant.
         """
 
 
     def test_translation_orthant(self):
         """
         Test that translation works over the nonnegative orthant.
         """

-        (L, K, e1, e2) = random_orthant_params()
-        self.assert_translation_works(L, K, e1, e2)
+        G = random_orthant_game()
+        self.assert_translation_works(G)

 
 
     def test_translation_icecream(self):
 
 
     def test_translation_icecream(self):


@@ -379,37 +187,37 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         The same as :meth:`test_translation_orthant`, except over the
         ice cream cone.
         """
         The same as :meth:`test_translation_orthant`, except over the
         ice cream cone.
         """

-        (L, K, e1, e2) = random_icecream_params()
-        self.assert_translation_works(L, K, e1, e2)
+        G = random_icecream_game()
+        self.assert_translation_works(G)

 
 
 
 

-    def assert_opposite_game_works(self, L, K, e1, e2):
+    def assert_opposite_game_works(self, G):

         """
         Check the value of the "opposite" game that gives rise to a
         value that is the negation of the original game. Comes from
         some corollary.
         """
         """
         Check the value of the "opposite" game that gives rise to a
         value that is the negation of the original game. Comes from
         some corollary.
         """

-        # We need to use ``L`` later, so make sure we transpose it
-        # before passing it in as a column-indexed matrix.
-        game1 = SymmetricLinearGame(L.trans(), K, e1, e2)
-

         # This is the "correct" representation of ``M``, but
         # COLUMN indexed...
         # This is the "correct" representation of ``M``, but
         # COLUMN indexed...

-        M = -L.trans()
+        M = -G.L().trans()

 
         # so we have to transpose it when we feed it to the constructor.
 
         # so we have to transpose it when we feed it to the constructor.

-        game2 = SymmetricLinearGame(M.trans(), K, e2, e1)
+        # Note: the condition number of ``H`` should be comparable to ``G``.
+        H = SymmetricLinearGame(M.trans(), G.K(), G.e2(), G.e1())

 
 

-        soln1 = game1.solution()
+        soln1 = G.solution()

         x_bar = soln1.player1_optimal()
         y_bar = soln1.player2_optimal()
         x_bar = soln1.player1_optimal()
         y_bar = soln1.player2_optimal()

-        soln2 = game2.solution()
+        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(),
 
         # 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):
 
 
     def test_opposite_game_orthant(self):


@@ -417,8 +225,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         Test the value of the "opposite" game over the nonnegative
         orthant.
         """
         Test the value of the "opposite" game over the nonnegative
         orthant.
         """

-        (L, K, e1, e2) = random_orthant_params()
-        self.assert_opposite_game_works(L, K, e1, e2)
+        G = random_orthant_game()
+        self.assert_opposite_game_works(G)

 
 
     def test_opposite_game_icecream(self):
 
 
     def test_opposite_game_icecream(self):


@@ -426,28 +234,25 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         Like :meth:`test_opposite_game_orthant`, except over the
         ice-cream cone.
         """
         Like :meth:`test_opposite_game_orthant`, except over the
         ice-cream cone.
         """

-        (L, K, e1, e2) = random_icecream_params()
-        self.assert_opposite_game_works(L, K, e1, e2)
+        G = random_icecream_game()
+        self.assert_opposite_game_works(G)

 
 
 
 

-    def assert_orthogonality(self, L, K, e1, e2):
+    def assert_orthogonality(self, G):

         """
         Two orthogonality relations hold at an optimal solution, and we
         check them here.
         """
         """
         Two orthogonality relations hold at an optimal solution, and we
         check them here.
         """

-        # We need to use ``L`` later, so make sure we transpose it
-        # before passing it in as a column-indexed matrix.
-        game = SymmetricLinearGame(L.trans(), K, e1, e2)
-        soln = game.solution()
+        soln = G.solution()

         x_bar = soln.player1_optimal()
         y_bar = soln.player2_optimal()
         value = soln.game_value()
 
         x_bar = soln.player1_optimal()
         y_bar = soln.player2_optimal()
         value = soln.game_value()
 

-        ip1 = inner_product(y_bar, L*x_bar - value*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*e2 - 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):
 
 
     def test_orthogonality_orthant(self):


@@ -455,8 +260,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         Check the orthgonality relationships that hold for a solution
         over the nonnegative orthant.
         """
         Check the orthgonality relationships that hold for a solution
         over the nonnegative orthant.
         """

-        (L, K, e1, e2) = random_orthant_params()
-        self.assert_orthogonality(L, K, e1, e2)
+        G = random_orthant_game()
+        self.assert_orthogonality(G)

 
 
     def test_orthogonality_icecream(self):
 
 
     def test_orthogonality_icecream(self):


@@ -464,8 +269,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         Check the orthgonality relationships that hold for a solution
         over the ice-cream cone.
         """
         Check the orthgonality relationships that hold for a solution
         over the ice-cream cone.
         """

-        (L, K, e1, e2) = random_icecream_params()
-        self.assert_orthogonality(L, K, e1, e2)
+        G = random_icecream_game()
+        self.assert_orthogonality(G)

 
 
     def test_positive_operator_value(self):
 
 
     def test_positive_operator_value(self):


@@ -476,53 +281,51 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         This test theoretically applies to the ice-cream cone as well,
         but we don't know how to make positive operators on that cone.
         """
         This test theoretically applies to the ice-cream cone as well,
         but we don't know how to make positive operators on that cone.
         """

-        (K, e1, e2) = random_orthant_params()[1:]
-        L = random_nonnegative_matrix(K.dimension())
+        G = random_positive_orthant_game()
+        self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)

 
 

-        game = SymmetricLinearGame(L, K, e1, e2)
-        self.assertTrue(game.solution().game_value() >= -options.ABS_TOL)

 
 

-
-    def assert_lyapunov_works(self, L, K, e1, e2):
+    def assert_lyapunov_works(self, G):

         """
         Check that Lyapunov games act the way we expect.
         """
         """
         Check that Lyapunov games act the way we expect.
         """

-        game = SymmetricLinearGame(L, K, e1, e2)
-        soln = game.solution()
+        soln = G.solution()

 
         # We only check for positive/negative stability if the game
         # value is not basically zero. If the value is that close to
         # zero, we just won't check any assertions.
 
         # We only check for positive/negative stability if the game
         # value is not basically zero. If the value is that close to
         # zero, we just won't check any assertions.

-        eigs = eigenvalues_re(L)
-        if soln.game_value() > options.ABS_TOL:
+        #
+        # See :meth:`assert_within_tol` for an explanation of the
+        # fudge factors.
+        eigs = eigenvalues_re(G.L())
+
+        if soln.game_value() > EPSILON:

             # L should be positive stable
             positive_stable = all([eig > -options.ABS_TOL for eig in eigs])
             self.assertTrue(positive_stable)
             # L should be positive stable
             positive_stable = all([eig > -options.ABS_TOL for eig in eigs])
             self.assertTrue(positive_stable)

-        elif soln.game_value() < -options.ABS_TOL:
+        elif soln.game_value() < -EPSILON:

             # 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.
             # 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 = game.dual().solution()
-        self.assert_within_tol(dualsoln.game_value(), soln.game_value())
+        dualsoln = G.dual().solution()
+        self.assert_within_tol(dualsoln.game_value(),
+                               soln.game_value(),
+                               G.condition())

 
 
     def test_lyapunov_orthant(self):
         """
         Test that a Lyapunov game on the nonnegative orthant works.
         """
 
 
     def test_lyapunov_orthant(self):
         """
         Test that a Lyapunov game on the nonnegative orthant works.
         """

-        (K, e1, e2) = random_orthant_params()[1:]
-        L = random_diagonal_matrix(K.dimension())
-
-        self.assert_lyapunov_works(L, K, e1, e2)
+        G = random_ll_orthant_game()
+        self.assert_lyapunov_works(G)

 
 
     def test_lyapunov_icecream(self):
         """
         Test that a Lyapunov game on the ice-cream cone works.
         """
 
 
     def test_lyapunov_icecream(self):
         """
         Test that a Lyapunov game on the ice-cream cone works.
         """

-        (K, e1, e2) = random_icecream_params()[1:]
-        L = random_lyapunov_like_icecream(K.dimension())
-
-        self.assert_lyapunov_works(L, K, e1, e2)
+        G = random_ll_icecream_game()
+        self.assert_lyapunov_works(G)