"""
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

"""