Add a test for Lyapunov games over the orthant.

diff --git a/src/dunshire/games.py b/src/dunshire/games.py
index 65fc791b20bd0624ee714a724581eb1537fa2edf..279afdb16036fa7c36a072ab4564f075002a0721 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
@@ -838,3 +839,27 @@ class SymmetricLinearGameTest(TestCase):
 
         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)