Move some excessive tests into a new module, cone.tests.

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index e40579fa634dc51afc8eaf83ff5b3e68025180b5..48b4061748281e0ebcb3ef19e9872be824666ba5 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -167,51 +167,7 @@ def _rho(K, K2=None):
     If we do this according to our paper, then the result is proper::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim = 8,
-        ....:                 strictly_convex=False,
-        ....:                 solid=False)
-        sage: K_S = _rho(K)
-        sage: K_SP = _rho(K_S.dual()).dual()
-        sage: K_SP.is_proper()
-        True
-        sage: K_SP = _rho(K_S, K_S.dual())
-        sage: K_SP.is_proper()
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim = 8,
-        ....:                 strictly_convex=True,
-        ....:                 solid=False)
-        sage: K_S = _rho(K)
-        sage: K_SP = _rho(K_S.dual()).dual()
-        sage: K_SP.is_proper()
-        True
-        sage: K_SP = _rho(K_S, K_S.dual())
-        sage: K_SP.is_proper()
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim = 8,
-        ....:                 strictly_convex=False,
-        ....:                 solid=True)
-        sage: K_S = _rho(K)
-        sage: K_SP = _rho(K_S.dual()).dual()
-        sage: K_SP.is_proper()
-        True
-        sage: K_SP = _rho(K_S, K_S.dual())
-        sage: K_SP.is_proper()
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim = 8,
-        ....:                 strictly_convex=True,
-        ....:                 solid=True)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: K_S = _rho(K)
         sage: K_SP = _rho(K_S.dual()).dual()
         sage: K_SP.is_proper()
@@ -220,50 +176,12 @@ def _rho(K, K2=None):
         sage: K_SP.is_proper()
         True
 
-    Test Proposition 7 in our paper concerning the duals and
+    Test the proposition in our paper concerning the duals and
     restrictions. Generate a random cone, then create a subcone of
     it. The operation of dual-taking should then commute with rho::
 
         sage: set_random_seed()
-        sage: J = random_cone(max_ambient_dim = 8,
-        ....:                 solid=False,
-        ....:                 strictly_convex=False)
-        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
-        sage: K_W_star = _rho(K, J).dual()
-        sage: K_star_W = _rho(K.dual(), J)
-        sage: _basically_the_same(K_W_star, K_star_W)
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: J = random_cone(max_ambient_dim = 8,
-        ....:                 solid=True,
-        ....:                 strictly_convex=False)
-        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
-        sage: K_W_star = _rho(K, J).dual()
-        sage: K_star_W = _rho(K.dual(), J)
-        sage: _basically_the_same(K_W_star, K_star_W)
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: J = random_cone(max_ambient_dim = 8,
-        ....:                 solid=False,
-        ....:                 strictly_convex=True)
-        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
-        sage: K_W_star = _rho(K, J).dual()
-        sage: K_star_W = _rho(K.dual(), J)
-        sage: _basically_the_same(K_W_star, K_star_W)
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: J = random_cone(max_ambient_dim = 8,
-        ....:                 solid=True,
-        ....:                 strictly_convex=True)
+        sage: J = random_cone(max_ambient_dim = 8)
         sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
         sage: K_W_star = _rho(K, J).dual()
         sage: K_star_W = _rho(K.dual(), J)
@@ -685,46 +603,6 @@ def lyapunov_rank(K):
         sage: lyapunov_rank(K1) == lyapunov_rank(K2)
         True
 
-    Just to be sure, test a few more::
-
-        sage: K1 = random_cone(max_ambient_dim=8,
-        ....:                  strictly_convex=True,
-        ....:                  solid=True)
-        sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
-        sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
-        sage: lyapunov_rank(K1) == lyapunov_rank(K2)
-        True
-
-    ::
-
-        sage: K1 = random_cone(max_ambient_dim=8,
-        ....:                  strictly_convex=True,
-        ....:                  solid=False)
-        sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
-        sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
-        sage: lyapunov_rank(K1) == lyapunov_rank(K2)
-        True
-
-    ::
-
-        sage: K1 = random_cone(max_ambient_dim=8,
-        ....:                  strictly_convex=False,
-        ....:                  solid=True)
-        sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
-        sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
-        sage: lyapunov_rank(K1) == lyapunov_rank(K2)
-        True
-
-    ::
-
-        sage: K1 = random_cone(max_ambient_dim=8,
-        ....:                  strictly_convex=False,
-        ....:                  solid=False)
-        sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
-        sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
-        sage: lyapunov_rank(K1) == lyapunov_rank(K2)
-        True
-
     The dual cone `K^{*}` of ``K`` should have the same Lyapunov rank as ``K``
     itself [Rudolf et al.]_::
 
@@ -733,42 +611,6 @@ def lyapunov_rank(K):
         sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
         True
 
-    Make sure we exercise the non-strictly-convex/non-solid case::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=False,
-        ....:                 solid=False)
-        sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
-        True
-
-    Let's check the other permutations as well, just to be sure::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=False,
-        ....:                 solid=True)
-        sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=True,
-        ....:                 solid=False)
-        sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=True,
-        ....:                 solid=True)
-        sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
-        True
-
     The Lyapunov rank of a proper polyhedral cone in `n` dimensions can
     be any number between `1` and `n` inclusive, excluding `n-1`
     [Gowda/Tao]_. By accident, the `n-1` restriction will hold for the
@@ -810,40 +652,10 @@ def lyapunov_rank(K):
         sage: actual == expected
         True
 
-    The Lyapunov rank of a proper cone is just the dimension of ``LL(K)``::
+    The Lyapunov rank of any cone is just the dimension of ``LL(K)``::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=True,
-        ....:                 solid=True)
-        sage: lyapunov_rank(K) == len(LL(K))
-        True
-
-    In fact the same can be said of any cone. These additional tests
-    just increase our confidence that the reduction scheme works::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=True,
-        ....:                 solid=False)
-        sage: lyapunov_rank(K) == len(LL(K))
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=False,
-        ....:                 solid=True)
-        sage: lyapunov_rank(K) == len(LL(K))
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_ambient_dim=8,
-        ....:                 strictly_convex=False,
-        ....:                 solid=False)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: lyapunov_rank(K) == len(LL(K))
         True
 

diff --git a/mjo/cone/tests.py b/mjo/cone/tests.py
new file mode 100644 (file)
index 0000000..b9dc2e0
--- /dev/null
+++ b/mjo/cone/tests.py
@@ -0,0 +1,256 @@
+"""
+Additional tests for the mjo.cone.cone module. These are extra
+properties that we'd like to check, but which are overkill for inclusion
+into Sage.
+"""
+
+# Sage doesn't load ~/.sage/init.sage during testing (sage -t), so we
+# have to explicitly mangle our sitedir here so that "mjo.cone"
+# resolves.
+from os.path import abspath
+from site import addsitedir
+addsitedir(abspath('../../'))
+
+from sage.all import *
+
+# The double-import is needed to get the underscore methods.
+from mjo.cone.cone import *
+from mjo.cone.cone import _basically_the_same, _rho
+
+#
+# Tests for _rho.
+#
+"""
+Apply _rho according to our paper (to obtain our main result). Test all
+four parameter combinations::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim = 8,
+    ....:                 strictly_convex=False,
+    ....:                 solid=False)
+    sage: K_S = _rho(K)
+    sage: K_SP = _rho(K_S.dual()).dual()
+    sage: K_SP.is_proper()
+    True
+    sage: K_SP = _rho(K_S, K_S.dual())
+    sage: K_SP.is_proper()
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim = 8,
+    ....:                 strictly_convex=True,
+    ....:                 solid=False)
+    sage: K_S = _rho(K)
+    sage: K_SP = _rho(K_S.dual()).dual()
+    sage: K_SP.is_proper()
+    True
+    sage: K_SP = _rho(K_S, K_S.dual())
+    sage: K_SP.is_proper()
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim = 8,
+    ....:                 strictly_convex=False,
+    ....:                 solid=True)
+    sage: K_S = _rho(K)
+    sage: K_SP = _rho(K_S.dual()).dual()
+    sage: K_SP.is_proper()
+    True
+    sage: K_SP = _rho(K_S, K_S.dual())
+    sage: K_SP.is_proper()
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim = 8,
+    ....:                 strictly_convex=True,
+    ....:                 solid=True)
+    sage: K_S = _rho(K)
+    sage: K_SP = _rho(K_S.dual()).dual()
+    sage: K_SP.is_proper()
+    True
+    sage: K_SP = _rho(K_S, K_S.dual())
+    sage: K_SP.is_proper()
+    True
+
+Test the proposition in our paper concerning the duals and
+restrictions. Generate a random cone, then create a subcone of
+it. The operation of dual-taking should then commute with rho. Test
+all parameter combinations::
+
+
+    sage: set_random_seed()
+    sage: J = random_cone(max_ambient_dim = 8,
+    ....:                 solid=False,
+    ....:                 strictly_convex=False)
+    sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+    sage: K_W_star = _rho(K, J).dual()
+    sage: K_star_W = _rho(K.dual(), J)
+    sage: _basically_the_same(K_W_star, K_star_W)
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: J = random_cone(max_ambient_dim = 8,
+    ....:                 solid=True,
+    ....:                 strictly_convex=False)
+    sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+    sage: K_W_star = _rho(K, J).dual()
+    sage: K_star_W = _rho(K.dual(), J)
+    sage: _basically_the_same(K_W_star, K_star_W)
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: J = random_cone(max_ambient_dim = 8,
+    ....:                 solid=False,
+    ....:                 strictly_convex=True)
+    sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+    sage: K_W_star = _rho(K, J).dual()
+    sage: K_star_W = _rho(K.dual(), J)
+    sage: _basically_the_same(K_W_star, K_star_W)
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: J = random_cone(max_ambient_dim = 8,
+    ....:                 solid=True,
+    ....:                 strictly_convex=True)
+    sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+    sage: K_W_star = _rho(K, J).dual()
+    sage: K_star_W = _rho(K.dual(), J)
+    sage: _basically_the_same(K_W_star, K_star_W)
+    True
+
+"""
+
+
+#
+# Lyapunov rank tests
+#
+"""
+
+The Lyapunov rank is invariant under a linear isomorphism. Check all
+combinations of parameters::
+
+    sage: K1 = random_cone(max_ambient_dim=8,
+    ....:                  strictly_convex=True,
+    ....:                  solid=True)
+    sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
+    sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
+    sage: lyapunov_rank(K1) == lyapunov_rank(K2)
+    True
+
+::
+
+    sage: K1 = random_cone(max_ambient_dim=8,
+    ....:                  strictly_convex=True,
+    ....:                  solid=False)
+    sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
+    sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
+    sage: lyapunov_rank(K1) == lyapunov_rank(K2)
+    True
+
+::
+
+    sage: K1 = random_cone(max_ambient_dim=8,
+    ....:                  strictly_convex=False,
+    ....:                  solid=True)
+    sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
+    sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
+    sage: lyapunov_rank(K1) == lyapunov_rank(K2)
+    True
+
+::
+
+    sage: K1 = random_cone(max_ambient_dim=8,
+    ....:                  strictly_convex=False,
+    ....:                  solid=False)
+    sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
+    sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
+    sage: lyapunov_rank(K1) == lyapunov_rank(K2)
+    True
+
+The Lyapunov rank of a dual cone should be the same as the original
+cone. Check all combinations of parameters::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=False,
+    ....:                 solid=False)
+    sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=False,
+    ....:                 solid=True)
+    sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=True,
+    ....:                 solid=False)
+    sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=True,
+    ....:                 solid=True)
+    sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
+    True
+
+The Lyapunov rank of a cone ``K`` is the dimension of ``LL(K)``. Check
+all combinations of parameters::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=True,
+    ....:                 solid=True)
+    sage: lyapunov_rank(K) == len(LL(K))
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=True,
+    ....:                 solid=False)
+    sage: lyapunov_rank(K) == len(LL(K))
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=False,
+    ....:                 solid=True)
+    sage: lyapunov_rank(K) == len(LL(K))
+    True
+
+::
+
+    sage: set_random_seed()
+    sage: K = random_cone(max_ambient_dim=8,
+    ....:                 strictly_convex=False,
+    ....:                 solid=False)
+    sage: lyapunov_rank(K) == len(LL(K))
+    True
+
+"""