"""
The doubly-nonnegative cone in `S^{n}` is the set of all such matrices
that both,

  a) are positive semidefinite

  b) have only nonnegative entries

It is represented typically by either `\mathcal{D}^{n}` or
`\mathcal{DNN}`.

"""

from sage.all import *

# 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 mjo.cone.symmetric_psd import factor_psd



def is_doubly_nonnegative(A):
    """
    Determine whether or not the matrix ``A`` is doubly-nonnegative.

    INPUT:

      - ``A`` - The matrix in question

    OUTPUT:

    Either ``True`` if ``A`` is doubly-nonnegative, or ``False``
    otherwise.

    EXAMPLES:

    Every completely positive matrix is doubly-nonnegative::

        sage: v = vector(map(abs, random_vector(ZZ, 10)))
        sage: A = v.column() * v.row()
        sage: is_doubly_nonnegative(A)
        True

    The following matrix is nonnegative but non positive semidefinite::

        sage: A = matrix(ZZ, [[1, 2], [2, 1]])
        sage: is_doubly_nonnegative(A)
        False

    """

    if A.base_ring() == SR:
        msg = 'The base ring of ``A`` cannot be the Symbolic Ring'
        raise ValueError.new(msg)

    # First make sure that ``A`` is symmetric.
    if not A.is_symmetric():
        return False

    # Check that all of the entries of ``A`` are nonnegative.
    if not all([ a >= 0 for a in A.list() ]):
        return False

    # If ``A`` is symmetric and non-negative, we only need to check
    # that it is positive semidefinite. For that we can consult its
    # minimum eigenvalue, which should be zero or greater. Since ``A``
    # is symmetric, its eigenvalues are guaranteed to be real.
    return min(A.eigenvalues()) >= 0



def is_extreme_doubly_nonnegative(A):
    """
    Returns ``True`` if the given matrix is an extreme matrix of the
    doubly-nonnegative cone, and ``False`` otherwise.
    """
    raise NotImplementedError()