From b701403c21a795ff7033cab5a753807c181517b1 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 13 Oct 2016 14:17:54 -0400
Subject: [PATCH] Add tests for Lyapunov games over the ice-cream cone.

---
 TODO                  |  1 -
 src/dunshire/games.py | 68 ++++++++++++++++++++++++++++++++++++++-----
 2 files changed, 61 insertions(+), 8 deletions(-)

diff --git a/TODO b/TODO
index 9699cd1..9b54805 100644
--- a/TODO
+++ b/TODO
@@ -21,4 +21,3 @@
 9. We only need to include the API docs for dunshire.games in the
    "user manual;" everything else can go in an appendix.
 
-10. Test Lyapunov games over the ice cream cone.
diff --git a/src/dunshire/games.py b/src/dunshire/games.py
index 1364fdd..3d4b09a 100644
--- a/src/dunshire/games.py
+++ b/src/dunshire/games.py
@@ -531,6 +531,39 @@ def _random_diagonal_matrix(dims):
     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
+    --------
+
+       >>> 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
@@ -825,15 +858,10 @@ class SymmetricLinearGameTest(TestCase):
         self.assertTrue(game.solution().game_value() >= -options.ABS_TOL)
 
 
-    def test_lyapunov_orthant(self):
+    def assert_lyapunov_works(self, L, K, e1, e2):
         """
-        Test that a Lyapunov game on the nonnegative orthant works.
+        Check that Lyapunov games act the way we expect.
         """
-        (L, K, e1, e2) = _random_orthant_params()
-
-        # Ignore that L, we need a diagonal (Lyapunov-like) one.
-        # (And we don't need to transpose those.)
-        L = _random_diagonal_matrix(K.dimension())
         game = SymmetricLinearGame(L, K, e1, e2)
         soln = game.solution()
 
@@ -852,3 +880,29 @@ class SymmetricLinearGameTest(TestCase):
         # 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())
+
+
+    def test_lyapunov_orthant(self):
+        """
+        Test that a Lyapunov game on the nonnegative orthant works.
+        """
+        (L, K, e1, e2) = _random_orthant_params()
+
+        # Ignore that L, we need a diagonal (Lyapunov-like) one.
+        # (And we don't need to transpose those.)
+        L = _random_diagonal_matrix(K.dimension())
+
+        self.assert_lyapunov_works(L, K, e1, e2)
+
+
+    def test_lyapunov_icecream(self):
+        """
+        Test that a Lyapunov game on the ice-cream cone works.
+        """
+        (L, K, e1, e2) = _random_icecream_params()
+
+        # Ignore that L, we need a diagonal (Lyapunov-like) one.
+        # (And we don't need to transpose those.)
+        L = _random_lyapunov_like_icecream(K.dimension())
+
+        self.assert_lyapunov_works(L, K, e1, e2)
-- 
2.44.2