From 8371d92c42c7faded26d8ef327129ad6d8c72d73 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 11 Nov 2016 09:39:59 -0500
Subject: [PATCH] Add the player2_start() method and some tests for it.

---
 dunshire/games.py                  | 31 ++++++++++++++++++++++++++++++
 test/symmetric_linear_game_test.py | 23 ++++++++++++++++++++++
 2 files changed, 54 insertions(+)

diff --git a/dunshire/games.py b/dunshire/games.py
index 77c8330..0a47391 100644
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -846,6 +846,37 @@ class SymmetricLinearGame:
         return {'x': x, 's': s}
 
 
+    def player2_start(self):
+        """
+        Return a feasible starting point for player two.
+        """
+        q = self.e1() / (norm(self.e1()) ** 2)
+
+        # Compute the distance from p to the outside of K.
+        if isinstance(self.K(), NonnegativeOrthant):
+            # How far is it to a wall?
+            dist = min(list(self.e2()))
+        elif isinstance(self.K(), IceCream):
+            # How far is it to the boundary of the ball that defines
+            # the ice-cream cone at a given height? Now draw a
+            # 45-45-90 triangle and the shortest distance to the
+            # outside of the cone should be 1/sqrt(2) of that.
+            # It works in R^2, so it works everywhere, right?
+            height = self.e2()[0]
+            radius = norm(self.e2()[1:])
+            dist = (height - radius) / sqrt(2)
+        else:
+            raise NotImplementedError
+
+        omega = specnorm(self.L())/(dist*norm(self.e1()))
+        y = matrix([omega])
+        z2 = q
+        z1 = y*self.e2() - self.L().trans()*z2
+        z = matrix([z1,z2], (self.dimension()*2, 1))
+
+        return {'y': y, 'z': z}
+
+
     def solution(self):
         """
         Solve this linear game and return a :class:`Solution`.
diff --git a/test/symmetric_linear_game_test.py b/test/symmetric_linear_game_test.py
index b6bd9b8..6327592 100644
--- a/test/symmetric_linear_game_test.py
+++ b/test/symmetric_linear_game_test.py
@@ -93,6 +93,29 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
         self.assert_player1_start_valid(G)
 
 
+    def assert_player2_start_valid(self, G):
+        z = G.player2_start()['z']
+        z1 = z[0:G.dimension()]
+        z2 = z[G.dimension():]
+        self.assertTrue((z1,z2) in G.C())
+
+
+    def test_player2_start_valid_orthant(self):
+        """
+        Ensure that player two's starting point is in the orthant.
+        """
+        G = random_orthant_game()
+        self.assert_player2_start_valid(G)
+
+
+    def test_player2_start_valid_icecream(self):
+        """
+        Ensure that player two's starting point is in the ice-cream cone.
+        """
+        G = random_icecream_game()
+        self.assert_player2_start_valid(G)
+
+
     def test_condition_lower_bound(self):
         """
         Ensure that the condition number of a game is greater than or
-- 
2.44.2