Change EPSILON to something more conservative in the test suite.

[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 5adbb2ddd11942faf3c31354513b62ab6877e853..da72fd03cca7215602ff81174a906795ffc189a9 100644 (file)
--- a/test/symmetric_linear_game_test.py
+++ b/test/symmetric_linear_game_test.py
@@ -1,116 +1,35 @@
-# These few are used only for tests.
-from math import sqrt
-from random import randint, uniform
+"""
+Unit tests for the :class:`SymmetricLinearGame` class.
+"""
+

 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

-
-def _random_matrix(dims):
-    """
-    Generate a random square (``dims``-by-``dims``) matrix. This is used
-    only by the :class:`SymmetricLinearGameTest` class.
-    """
-    return matrix([[uniform(-10, 10) for i in range(dims)]
-                   for j in range(dims)])
-
-def _random_nonnegative_matrix(dims):
-    """
-    Generate a random square (``dims``-by-``dims``) matrix with
-    nonnegative entries. This is used only by the
-    :class:`SymmetricLinearGameTest` class.
-    """
-    L = _random_matrix(dims)
-    return matrix([abs(entry) for entry in L], (dims, dims))
-
-def _random_diagonal_matrix(dims):
-    """
-    Generate a random square (``dims``-by-``dims``) matrix with nonzero
-    entries only on the diagonal. This is used only by the
-    :class:`SymmetricLinearGameTest` class.
-    """
-    return matrix([[uniform(-10, 10)*int(i == j) for i in range(dims)]
-                   for j in range(dims)])
-
-
-def _random_skew_symmetric_matrix(dims):
-    """
-    Generate a random skew-symmetrix (``dims``-by-``dims``) matrix.
-
-    Examples
-    --------
-
-        >>> from dunshire.matrices import norm
-        >>> A = _random_skew_symmetric_matrix(randint(1, 10))
-        >>> norm(A + A.trans()) < options.ABS_TOL
-        True
-
-    """
-    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):
-    """
-    Generate a random Lyapunov-like matrix over the ice-cream cone in
-    ``dims`` dimensions.
-    """
-    a = matrix([uniform(-10, 10)], (1, 1))
-    b = matrix([uniform(-10, 10) for idx 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)
-
-
-def _random_orthant_params():
-    """
-    Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
-    random game over the nonnegative orthant. This is only used by
-    the :class:`SymmetricLinearGameTest` class.
-    """
-    ambient_dim = randint(1, 10)
-    K = NonnegativeOrthant(ambient_dim)
-    e1 = [uniform(0.5, 10) for idx in range(K.dimension())]
-    e2 = [uniform(0.5, 10) for idx in range(K.dimension())]
-    L = _random_matrix(K.dimension())
-    return (L, K, matrix(e1), matrix(e2))
-
-
-def _random_icecream_params():
-    """
-    Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
-    random game over the ice cream cone. This is only used by
-    the :class:`SymmetricLinearGameTest` class.
-    """
-    # 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 idx in range(K.dimension() - 1)]
-    e2 += [fudge_factor*uniform(0, 1) for idx in range(K.dimension() - 1)]
-    L = _random_matrix(K.dimension())
-
-    return (L, K, matrix(e1), matrix(e2))
-
+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).
+"""

 
 # Tell pylint to shut up about the large number of methods.
 class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
 
 # Tell pylint to shut up about the large number of methods.
 class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904


@@ -119,37 +38,39 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
     """
     def assert_within_tol(self, first, second):
         """
     """
     def assert_within_tol(self, first, second):
         """

-        Test that ``first`` and ``second`` are equal within our default
-        tolerance.
-        """
-        self.assertTrue(abs(first - second) < options.ABS_TOL)
-
-
-    def assert_norm_within_tol(self, first, second):
-        """
-        Test that ``first`` and ``second`` vectors are equal in the
-        sense that the norm of their difference is within our default
-        tolerance.
+        Test that ``first`` and ``second`` are equal within a multiple of
+        our default tolerances.

         """
         """

-        self.assert_within_tol(norm(first - second), 0)
+        self.assertTrue(abs(first - second) < EPSILON)

 
 
 
 

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

         """
         """

-        Given the parameters needed to construct a SymmetricLinearGame,
-        ensure that that game has a solution.
+        Given  a SymmetricLinearGame, ensure that it has a solution.

         """
         """

-        # 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()
 
         soln = G.solution()
 

-        expected = inner_product(L*soln.player1_optimal(),
+        expected = inner_product(G._L*soln.player1_optimal(),

                                  soln.player2_optimal())
         self.assert_within_tol(soln.game_value(), expected)
 
 
                                  soln.player2_optimal())
         self.assert_within_tol(soln.game_value(), expected)
 
 

+
+    def test_condition_lower_bound(self):
+        """
+        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.
+        """
+        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):
         """
         Every linear game has a solution, so we should be able to solve
     def test_solution_exists_orthant(self):
         """
         Every linear game has a solution, so we should be able to solve


@@ -158,8 +79,8 @@ 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):


@@ -167,8 +88,8 @@ 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):


@@ -184,17 +105,14 @@ 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()
+        (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)
 
 


@@ -203,8 +121,8 @@ 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):


@@ -212,46 +130,39 @@ 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)
 
         # Make sure the same optimal pair works.
 
         self.assert_within_tol(value1 + alpha, value2)
 
         # Make sure the same optimal pair works.

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

 
 
     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):


@@ -259,31 +170,28 @@ 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())
 


@@ -297,8 +205,8 @@ 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):


@@ -306,27 +214,24 @@ 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)
+        ip1 = inner_product(y_bar, G._L*x_bar - value*G._e1)

         self.assert_within_tol(ip1, 0)
 
         self.assert_within_tol(ip1, 0)
 

-        ip2 = inner_product(value*e2 - 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)
 
 
         self.assert_within_tol(ip2, 0)
 
 


@@ -335,8 +240,8 @@ 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):


@@ -344,8 +249,8 @@ 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):


@@ -356,35 +261,35 @@ 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()
+        dualsoln = G.dual().solution()

         self.assert_within_tol(dualsoln.game_value(), soln.game_value())
 
 
         self.assert_within_tol(dualsoln.game_value(), soln.game_value())
 
 


@@ -392,17 +297,13 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         """
         Test that a Lyapunov game on the nonnegative orthant works.
         """
         """
         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)