Test the dual game value of a Lyapunov game over the orthant.

[dunshire.git] / src / dunshire / games.py

diff --git a/src/dunshire/games.py b/src/dunshire/games.py
index 692a0ae550305c3ae56833d500c263498f070889..a039e1f232ff12395e5f0634de1dde7b3cdcfb10 100644 (file)
--- a/src/dunshire/games.py
+++ b/src/dunshire/games.py
@@ -14,7 +14,8 @@ from unittest import TestCase
 from cvxopt import matrix, printing, solvers
 from cones import CartesianProduct, IceCream, NonnegativeOrthant
 from errors import GameUnsolvableException
-from matrices import append_col, append_row, identity, inner_product, norm
+from matrices import (append_col, append_row, eigenvalues_re, identity,
+                      inner_product, norm)
 import options
 
 printing.options['dformat'] = options.FLOAT_FORMAT
@@ -504,7 +505,7 @@ class SymmetricLinearGame:
 
 
 
-def _random_square_matrix(dims):
+def _random_matrix(dims):
     """
     Generate a random square (``dims``-by-``dims``) matrix,
     represented as a list of rows. This is used only by the
@@ -512,6 +513,23 @@ def _random_square_matrix(dims):
     """
     return [[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, represented as a list of rows. This is used
+    only by the :class:`SymmetricLinearGameTest` class.
+    """
+    L = _random_matrix(dims)
+    return [[abs(entry) for entry in row] for row in L]
+
+def _random_diagonal_matrix(dims):
+    """
+    Generate a random square (``dims``-by-``dims``) matrix with nonzero
+    entries only on the diagonal, represented as a list of rows. This is
+    used only by the :class:`SymmetricLinearGameTest` class.
+    """
+    return [[uniform(-10, 10)*int(i == j) for i in range(dims)]
+            for j in range(dims)]
 
 def _random_orthant_params():
     """
@@ -523,7 +541,7 @@ def _random_orthant_params():
     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_square_matrix(K.dimension())
+    L = _random_matrix(K.dimension())
     return (L, K, e1, e2)
 
 
@@ -550,7 +568,7 @@ def _random_icecream_params():
     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_square_matrix(K.dimension())
+    L = _random_matrix(K.dimension())
 
     return (L, K, e1, e2)
 
@@ -814,11 +832,38 @@ class SymmetricLinearGameTest(TestCase):
         This test theoretically applies to the ice-cream cone as well,
         but we don't know how to make positive operators on that cone.
         """
-        (L, K, e1, e2) = _random_orthant_params()
+        (_, K, e1, e2) = _random_orthant_params()
 
-        # Make the entries of ``L`` nonnegative... this makes it a
-        # positive operator on ``K``.
-        L = [[abs(entry) for entry in row] for row in L]
+        # Ignore that L, we need a nonnegative one.
+        L = _random_nonnegative_matrix(K.dimension())
 
         game = SymmetricLinearGame(L, K, e1, e2)
         self.assertTrue(game.solution().game_value() >= -options.ABS_TOL)
+
+    def test_lyapunov_orthant(self):
+        """
+        Test that a Lyapunov game on the nonnegative orthant works.
+        """
+        (_, K, e1, e2) = _random_orthant_params()
+
+        # Ignore that L, we need a diagonal (Lyapunov-like) one.
+        L = _random_diagonal_matrix(K.dimension())
+        game = SymmetricLinearGame(L, K, e1, e2)
+        soln = game.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.
+        L = matrix(L).trans()
+        if soln.game_value() > options.ABS_TOL:
+            # L should be positive stable
+            ps = all([eig > -options.ABS_TOL for eig in  eigenvalues_re(L)])
+            self.assertTrue(ps)
+        elif soln.game_value() < -options.ABS_TOL:
+            # L should be negative stable
+            ns = all([eig < options.ABS_TOL for eig in  eigenvalues_re(L)])
+            self.assertTrue(ns)
+
+        # 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())