"""
Copyright, the CVXPY authors

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

import warnings

import numpy as np

# Only need Variable from expressions, but that would create a circular import.
from cvxpy.constraints.constraint import Constraint
from cvxpy.utilities import scopes


class NonPos(Constraint):
    """An inequality constraint of the form :math:`x \\leq 0`.

    The preferred way of creating an inequality constraint is through
    operator overloading. To constrain an expression ``x`` to be nonpositive,
    write ``x <= 0``; to constrain ``x`` to be nonnegative, write ``x >= 0``.

    Dual variables associated with this constraint are nonnegative, rather
    than nonpositive. As such, dual variables to this constraint belong to the
    polar cone rather than the dual cone.

    Note: strict inequalities are not supported, as they do not make sense in
    a numerical setting.

    Parameters
    ----------
    expr : Expression
        The expression to constrain.
    constr_id : int
        A unique id for the constraint.
    """

    DEPRECATION_MESSAGE = """
    Explicitly invoking "NonPos(expr)" to a create a constraint is deprecated.
    Please use operator overloading or "NonNeg(-expr)" instead.
    
    Sign conventions on dual variables associated with NonPos constraints may
    change in the future.
    """

    def __init__(self, expr, constr_id=None) -> None:
        warnings.warn(NonPos.DEPRECATION_MESSAGE, DeprecationWarning)
        super(NonPos, self).__init__([expr], constr_id)
        if not self.args[0].is_real():
            raise ValueError("Input to NonPos must be real.")

    def name(self) -> str:
        return "%s <= 0" % self.args[0]

    def is_dcp(self, dpp: bool = False) -> bool:
        """A NonPos constraint is DCP if its argument is convex."""
        if dpp:
            with scopes.dpp_scope():
                return self.args[0].is_convex()
        return self.args[0].is_convex()

    def is_dgp(self, dpp: bool = False) -> bool:
        return False

    def is_dqcp(self) -> bool:
        return self.args[0].is_quasiconvex()

    @property
    def residual(self):
        """The residual of the constraint.

        Returns
        ---------
        NumPy.ndarray
        """
        if self.expr.value is None:
            return None
        return np.maximum(self.expr.value, 0)

    def violation(self):
        res = self.residual
        if res is None:
            raise ValueError("Cannot compute the violation of an constraint "
                             "whose expression is None-valued.")
        viol = np.linalg.norm(res, ord=2)
        return viol


class NonNeg(Constraint):
    """A constraint of the form :math:`x \\geq 0`.

    The preferred way of creating an inequality constraint is through
    operator overloading. To constrain an expression ``x`` to be nonnegative,
    write ``x >= 0``; to constrain ``x`` to be nonpositive, write ``x <= 0``.

    Dual variables for these constraints are nonnegative. As such, they
    actually belong to this constraint class' corresponding dual cone.

    Parameters
    ----------
    expr : Expression
        The expression to constrain.
    constr_id : int
        A unique id for the constraint.
    """
    def __init__(self, expr, constr_id=None) -> None:
        super(NonNeg, self).__init__([expr], constr_id)
        if not self.args[0].is_real():
            raise ValueError("Input to NonNeg must be real.")

    def name(self) -> str:
        return "%s >= 0" % self.args[0]

    def is_dcp(self, dpp: bool = False) -> bool:
        """A non-negative constraint is DCP if its argument is concave."""
        if dpp:
            with scopes.dpp_scope():
                return self.args[0].is_concave()
        return self.args[0].is_concave()

    def is_dgp(self, dpp: bool = False) -> bool:
        return False

    def is_dqcp(self) -> bool:
        return self.args[0].is_quasiconcave()

    @property
    def residual(self):
        """The residual of the constraint.

        Returns
        ---------
        NumPy.ndarray
        """
        if self.expr.value is None:
            return None
        return np.abs(np.minimum(self.expr.value, 0))

    def violation(self):
        res = self.residual
        if res is None:
            raise ValueError("Cannot compute the violation of an constraint "
                             "whose expression is None-valued.")
        viol = np.linalg.norm(res, ord=2)
        return viol


class Inequality(Constraint):
    """A constraint of the form :math:`x \\leq y`.

    Dual variables to these constraints are always nonnegative.
    A constraint of this type affects the Lagrangian :math:`L` of a
    minimization problem by

        :math:`L += (x - y)^{T}(\\texttt{con.dual\\_value})`.

    The preferred way of creating one of these constraints is via
    operator overloading. The expression ``x <= y`` evaluates to
    ``Inequality(x, y)``, and the expression ``x >= y`` evaluates
    to ``Inequality(y, x)``.

    Parameters
    ----------
    lhs : Expression
        The expression to be upper-bounded by rhs
    rhs : Expression
        The expression to be lower-bounded by lhs
    constr_id : int
        A unique id for the constraint.
    """
    def __init__(self, lhs, rhs, constr_id=None) -> None:
        self._expr = lhs - rhs
        if self._expr.is_complex():
            raise ValueError("Inequality constraints cannot be complex.")
        super(Inequality, self).__init__([lhs, rhs], constr_id)

    def _construct_dual_variables(self, args) -> None:
        super(Inequality, self)._construct_dual_variables([self._expr])

    @property
    def expr(self):
        return self._expr

    def name(self) -> str:
        return "%s <= %s" % (self.args[0], self.args[1])

    @property
    def shape(self):
        """int : The shape of the constrained expression."""
        return self.expr.shape

    @property
    def size(self):
        """int : The size of the constrained expression."""
        return self.expr.size

    def is_dcp(self, dpp: bool = False) -> bool:
        """A non-positive constraint is DCP if its argument is convex."""
        if dpp:
            with scopes.dpp_scope():
                return self.expr.is_convex()
        return self.expr.is_convex()

    def is_dgp(self, dpp: bool = False) -> bool:
        if dpp:
            with scopes.dpp_scope():
                return (self.args[0].is_log_log_convex() and
                        self.args[1].is_log_log_concave())
        return (self.args[0].is_log_log_convex() and
                self.args[1].is_log_log_concave())

    def is_dpp(self, context='dcp') -> bool:
        if context.lower() == 'dcp':
            return self.is_dcp(dpp=True)
        elif context.lower() == 'dgp':
            return self.is_dgp(dpp=True)
        else:
            raise ValueError('Unsupported context ', context)

    def is_dqcp(self) -> bool:
        return (
            self.is_dcp() or
            (self.args[0].is_quasiconvex() and self.args[1].is_constant()) or
            (self.args[0].is_constant() and self.args[1].is_quasiconcave()))

    @property
    def residual(self):
        """The residual of the constraint.

        Returns
        ---------
        NumPy.ndarray
        """
        if self.expr.value is None:
            return None
        return np.maximum(self.expr.value, 0)