From fbaecc56ec029d6f813d76e26bd8891a41416bf0 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 17 Sep 2015 01:12:40 -0400
Subject: [PATCH] Add the is_lyapunov_like() function to the cone.cone module.

---
 mjo/cone/cone.py | 49 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 7374fcf..f3543a1 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -685,3 +685,52 @@ def lyapunov_rank(K):
 
     beta += len(LL(K))
     return beta
+
+
+
+def is_lyapunov_like(L,K):
+    r"""
+    Determine whether or not ``L`` is Lyapunov-like on ``K``.
+
+    We say that ``L`` is Lyapunov-like on ``K`` if `\left\langle
+    L\left\lparenx\right\rparen,s\right\rangle = 0` for all pairs
+    `\left\langle x,s \right\rangle` in the complementarity set of
+    ``K``. It is known [Orlitzky]_ that this property need only be
+    checked for generators of ``K`` and its dual.
+
+    INPUT:
+
+    - ``L`` -- A linear transformation or matrix.
+
+    - ``K`` -- A polyhedral closed convex cone.
+
+    OUTPUT:
+
+    ``True`` if it can be proven that ``L`` is Lyapunov-like on ``K``,
+    and ``False`` otherwise.
+
+    .. WARNING::
+
+        If this function returns ``True``, then ``L`` is Lyapunov-like
+        on ``K``. However, if ``False`` is returned, that could mean one
+        of two things. The first is that ``L`` is definitely not
+        Lyapunov-like on ``K``. The second is more of an "I don't know"
+        answer, returned (for example) if we cannot prove that an inner
+        product is zero.
+
+    REFERENCES:
+
+    .. [Orlitzky] M. Orlitzky. The Lyapunov rank of an
+       improper cone (preprint).
+
+    EXAMPLES:
+
+    todo.
+
+    TESTS:
+
+    todo.
+
+    """
+    return all([(L*x).inner_product(s) == 0
+                for (x,s) in discrete_complementarity_set(K)])
-- 
2.43.2