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

[sage.d.git] / mjo / cone / cone.py

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index baff1a7bbea4943206bc323040ef5d554d40ead4..48b4061748281e0ebcb3ef19e9872be824666ba5 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -44,14 +44,14 @@ def _basically_the_same(K1, K2):
 
     Any cone is basically the same as itself::
 
-        sage: K = random_cone(max_dim = 8)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: _basically_the_same(K, K)
         True
 
     After applying an invertible matrix to the rows of a cone, the
     result should be basically the same as the cone we started with::
 
-        sage: K1 = random_cone(max_dim = 8)
+        sage: K1 = random_cone(max_ambient_dim = 8)
         sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
         sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
         sage: _basically_the_same(K1, K2)
@@ -126,7 +126,7 @@ def _rho(K, K2=None):
     The projected cone should always be solid::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: K_S = _rho(K)
         sage: K_S.is_solid()
         True
@@ -135,7 +135,7 @@ def _rho(K, K2=None):
     dimension as the space we restricted it to::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: K_S = _rho(K, K.dual() )
         sage: K_S.lattice_dim() == K.dual().dim()
         True
@@ -143,14 +143,14 @@ def _rho(K, K2=None):
     This function should not affect the dimension of a cone::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: K.dim() == _rho(K).dim()
         True
 
     Nor should it affect the lineality of a cone::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: K.lineality() == _rho(K).lineality()
         True
 
@@ -158,7 +158,7 @@ def _rho(K, K2=None):
     increase::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8)
+        sage: K = random_cone(max_ambient_dim = 8)
         sage: K.lineality() >= _rho(K).lineality()
         True
         sage: K.lineality() >= _rho(K, K.dual()).lineality()
@@ -167,7 +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_dim = 8, strictly_convex=False, solid=False)
+        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()
@@ -176,78 +176,12 @@ def _rho(K, K2=None):
         sage: K_SP.is_proper()
         True
 
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_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_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_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 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_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_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_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_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)
@@ -348,7 +282,7 @@ def discrete_complementarity_set(K):
     components of the complementarity set of the original cone::
 
         sage: set_random_seed()
-        sage: K1 = random_cone(max_dim=6)
+        sage: K1 = random_cone(max_ambient_dim=6)
         sage: K2 = K1.dual()
         sage: expected = [(x,s) for (s,x) in discrete_complementarity_set(K2)]
         sage: actual = discrete_complementarity_set(K1)
@@ -359,7 +293,7 @@ def discrete_complementarity_set(K):
     complementary::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=6)
+        sage: K = random_cone(max_ambient_dim=6)
         sage: dcs = discrete_complementarity_set(K)
         sage: sum([x.inner_product(s).abs() for (x,s) in dcs])
         0
@@ -452,7 +386,7 @@ def LL(K):
     of the cone::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: C_of_K = discrete_complementarity_set(K)
         sage: l = [ (L*x).inner_product(s) for (x,s) in C_of_K for L in LL(K) ]
         sage: sum(map(abs, l))
@@ -464,7 +398,7 @@ def LL(K):
     \right)`
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: LL2 = [ L.transpose() for L in LL(K.dual()) ]
         sage: V = VectorSpace( K.lattice().base_field(), K.lattice_dim()^2)
         sage: LL1_vecs = [ V(m.list()) for m in LL(K) ]
@@ -650,8 +584,12 @@ def lyapunov_rank(K):
     [Rudolf et al.]_::
 
         sage: set_random_seed()
-        sage: K1 = random_cone(max_dim=8, strictly_convex=True, solid=True)
-        sage: K2 = random_cone(max_dim=8, strictly_convex=True, solid=True)
+        sage: K1 = random_cone(max_ambient_dim=8,
+        ....:                  strictly_convex=True,
+        ....:                  solid=True)
+        sage: K2 = random_cone(max_ambient_dim=8,
+        ....:                  strictly_convex=True,
+        ....:                  solid=True)
         sage: K = K1.cartesian_product(K2)
         sage: lyapunov_rank(K) == lyapunov_rank(K1) + lyapunov_rank(K2)
         True
@@ -659,39 +597,7 @@ def lyapunov_rank(K):
     The Lyapunov rank is invariant under a linear isomorphism
     [Orlitzky/Gowda]_::
 
-        sage: K1 = random_cone(max_dim = 8)
-        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
-
-    Just to be sure, test a few more::
-
-        sage: K1 = random_cone(max_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_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_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_dim=8, strictly_convex=False, solid=False)
+        sage: K1 = random_cone(max_ambient_dim = 8)
         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)
@@ -701,35 +607,7 @@ def lyapunov_rank(K):
     itself [Rudolf et al.]_::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8)
-        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_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_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_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_dim=8, strictly_convex=True, solid=True)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
         True
 
@@ -740,7 +618,9 @@ def lyapunov_rank(K):
     the Lyapunov rank of the trivial cone will be zero::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8, strictly_convex=True, solid=True)
+        sage: K = random_cone(max_ambient_dim=8,
+        ....:                 strictly_convex=True,
+        ....:                 solid=True)
         sage: b = lyapunov_rank(K)
         sage: n = K.lattice_dim()
         sage: (n == 0 or 1 <= b) and b <= n
@@ -752,7 +632,7 @@ def lyapunov_rank(K):
     Lyapunov rank `n-1` in `n` dimensions::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: b = lyapunov_rank(K)
         sage: n = K.lattice_dim()
         sage: b == n-1
@@ -762,7 +642,7 @@ def lyapunov_rank(K):
     reduced to that of a proper cone [Orlitzky/Gowda]_::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: actual = lyapunov_rank(K)
         sage: K_S = _rho(K)
         sage: K_SP = _rho(K_S.dual()).dual()
@@ -772,39 +652,19 @@ def lyapunov_rank(K):
         sage: actual == expected
         True
 
-    The Lyapunov rank of a proper cone is just the dimension of ``LL(K)``::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_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_dim=8, strictly_convex=True, solid=False)
-        sage: lyapunov_rank(K) == len(LL(K))
-        True
-
-    ::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_dim=8, strictly_convex=False, solid=True)
-        sage: lyapunov_rank(K) == len(LL(K))
-        True
-
-    ::
+    The Lyapunov rank of any cone is just the dimension of ``LL(K)``::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8, strictly_convex=False, solid=False)
+        sage: K = random_cone(max_ambient_dim=8)
         sage: lyapunov_rank(K) == len(LL(K))
         True
 
     Test Theorem 3 in [Orlitzky/Gowda]_::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim=8, strictly_convex=True, solid=True)
+        sage: K = random_cone(max_ambient_dim=8,
+        ....:                 strictly_convex=True,
+        ....:                 solid=True)
         sage: L = ToricLattice(K.lattice_dim() + 1)
         sage: K = Cone([ r.list() + [0] for r in K.rays() ], lattice=L)
         sage: lyapunov_rank(K) >= K.lattice_dim()