X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Ftests.py;fp=mjo%2Fcone%2Ftests.py;h=b9dc2e064d771de1eb9bb02184a5d4d1df8ea319;hb=af3e2ce56ad6561c5c9b1b6cf3df22d690550618;hp=0000000000000000000000000000000000000000;hpb=98637c981445d35a061878923baf3ae4651ecb0b;p=sage.d.git

diff --git a/mjo/cone/tests.py b/mjo/cone/tests.py
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+++ b/mjo/cone/tests.py
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+"""
+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
+
+"""