"""
Copyright 2013 Steven Diamond

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

CVXPY is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with CVXPY.  If not, see <http://www.gnu.org/licenses/>.
"""

import cvxpy.utilities as u
import cvxpy.lin_ops.lin_utils as lu
from cvxpy.atoms.elementwise.elementwise import Elementwise
import numpy as np

class max_elemwise(Elementwise):
    """ Elementwise maximum. """

    def __init__(self, arg1, arg2, *args):
        """Requires at least 2 arguments.
        """
        super(max_elemwise, self).__init__(arg1, arg2, *args)

    @Elementwise.numpy_numeric
    def numeric(self, values):
        """Returns the elementwise maximum.
        """
        return reduce(np.maximum, values)

    def sign_from_args(self):
        """Determins the sign of max_elemwise from the arguments' signs.

        Reduces the list of argument signs according to the following rules:
            POSITIVE, ANYTHING = POSITIVE
            ZERO, UNKNOWN = POSITIVE
            ZERO, ZERO = ZERO
            ZERO, NEGATIVE = ZERO
            UNKNOWN, NEGATIVE = UNKNOWN
            NEGATIVE, NEGATIVE = NEGATIVE

        Returns
        -------
        Sign
            The Sign of the expression.
        """
        arg_signs = [arg._dcp_attr.sign for arg in self.args]
        if u.Sign.POSITIVE in arg_signs:
            max_sign = u.Sign.POSITIVE
        elif u.Sign.ZERO in arg_signs:
            if u.Sign.UNKNOWN in arg_signs:
                max_sign = u.Sign.POSITIVE
            else:
                max_sign = u.Sign.ZERO
        elif u.Sign.UNKNOWN in arg_signs:
            max_sign = u.Sign.UNKNOWN
        else:
            max_sign = u.Sign.NEGATIVE

        return max_sign

    def func_curvature(self):
        """The function's default curvature is convex.
        """
        return u.Curvature.CONVEX

    def monotonicity(self):
        """The function is increasing in each argument.
        """
        return len(self.args)*[u.monotonicity.INCREASING]

    @staticmethod
    def graph_implementation(arg_objs, size, data=None):
        """Reduces the atom to an affine expression and list of constraints.

        Parameters
        ----------
        arg_objs : list
            LinExpr for each argument.
        size : tuple
            The size of the resulting expression.
        data :
            Additional data required by the atom.

        Returns
        -------
        tuple
            (LinOp for objective, list of constraints)
        """
        t = lu.create_var(size)
        constraints = []
        for obj in arg_objs:
            # Promote obj.
            if obj.size != size:
                obj = lu.promote(obj, size)
            constraints.append(lu.create_leq(obj, t))
        return (t, constraints)
