"""
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 _restrict_to_space

#
# Tests for _restrict_to_space.
#
def _look_isomorphic(K1, K2):
    r"""
    Test whether or not ``K1`` and ``K2`` look linearly isomorphic.

    This is a hack to get around the fact that it's difficult to tell
    when two cones are linearly isomorphic. Instead, we check a list of
    properties that should be preserved under linear isomorphism.

    OUTPUT:

    ``True`` if ``K1`` and ``K2`` look isomorphic, or ``False``
    if we can prove that they are not isomorphic.

    EXAMPLES:

    Any proper cone with three generators in `\mathbb{R}^{3}` is
    isomorphic to the nonnegative orthant::

        sage: K1 = Cone([(1,0,0), (0,1,0), (0,0,1)])
        sage: K2 = Cone([(1,2,3), (3, 18, 4), (66, 51, 0)])
        sage: _look_isomorphic(K1, K2)
        True

    Negating a cone gives you an isomorphic cone::

        sage: K = Cone([(0,2,-5), (-6, 2, 4), (0, 51, 0)])
        sage: _look_isomorphic(K, -K)
        True

    TESTS:

    Any cone is isomorphic to itself::

        sage: K = random_cone(max_ambient_dim = 8)
        sage: _look_isomorphic(K, K)
        True

    After applying an invertible matrix to the rows of a cone, the
    result should is isomorphic to the cone we started with::

        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: _look_isomorphic(K1, K2)
        True

    """
    if K1.lattice_dim() != K2.lattice_dim():
        return False

    if K1.nrays() != K2.nrays():
        return False

    if K1.dim() != K2.dim():
        return False

    if K1.lineality() != K2.lineality():
        return False

    if K1.is_solid() != K2.is_solid():
        return False

    if K1.is_strictly_convex() != K2.is_strictly_convex():
        return False

    if len(K1.lyapunov_like_basis()) != len(K2.lyapunov_like_basis()):
        return False

    C_of_K1 = K1.discrete_complementarity_set()
    C_of_K2 = K2.discrete_complementarity_set()
    if len(C_of_K1) != len(C_of_K2):
        return False

    if len(K1.facets()) != len(K2.facets()):
        return False

    return True


"""
Apply _restrict_to_space 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 = _restrict_to_space(K, K.span())
    sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
    sage: K_SP.is_proper()
    True
    sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
    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 = _restrict_to_space(K, K.span())
    sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
    sage: K_SP.is_proper()
    True
    sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
    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 = _restrict_to_space(K, K.span())
    sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
    sage: K_SP.is_proper()
    True
    sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
    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 = _restrict_to_space(K, K.span())
    sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
    sage: K_SP.is_proper()
    True
    sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
    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 = _restrict_to_space(K, J.span()).dual()
    sage: K_star_W = _restrict_to_space(K.dual(), J.span())
    sage: _look_isomorphic(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 = _restrict_to_space(K, J.span()).dual()
    sage: K_star_W = _restrict_to_space(K.dual(), J.span())
    sage: _look_isomorphic(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 = _restrict_to_space(K, J.span()).dual()
    sage: K_star_W = _restrict_to_space(K.dual(), J.span())
    sage: _look_isomorphic(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 = _restrict_to_space(K, J.span()).dual()
    sage: K_star_W = _restrict_to_space(K.dual(), J.span())
    sage: _look_isomorphic(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
``K.lyapunov_like_basis()``. 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(K.lyapunov_like_basis())
    True

::

    sage: set_random_seed()
    sage: K = random_cone(max_ambient_dim=8,
    ....:                 strictly_convex=True,
    ....:                 solid=False)
    sage: lyapunov_rank(K) == len(K.lyapunov_like_basis())
    True

::

    sage: set_random_seed()
    sage: K = random_cone(max_ambient_dim=8,
    ....:                 strictly_convex=False,
    ....:                 solid=True)
    sage: lyapunov_rank(K) == len(K.lyapunov_like_basis())
    True

::

    sage: set_random_seed()
    sage: K = random_cone(max_ambient_dim=8,
    ....:                 strictly_convex=False,
    ....:                 solid=False)
    sage: lyapunov_rank(K) == len(K.lyapunov_like_basis())
    True

"""