"""
Copyright 2013 Steven Diamond

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.
"""

from typing import List, Tuple

import numpy as np

import cvxpy.interface as intf
import cvxpy.lin_ops.lin_op as lo
import cvxpy.lin_ops.lin_utils as lu
import cvxpy.utilities as u
from cvxpy.atoms.affine.affine_atom import AffAtom
from cvxpy.constraints.constraint import Constraint
from cvxpy.expressions.constants.parameter import is_param_free
from cvxpy.utilities.warn import CvxpyDeprecationWarning, warn


class conv(AffAtom):
    """ 1D discrete convolution of two vectors.

    The discrete convolution :math:`c` of vectors :math:`a` and :math:`b` of
    lengths :math:`n` and :math:`m`, respectively, is a length-:math:`(n+m-1)`
    vector where

    .. math::

        c_k = \\sum_{i+j=k} a_ib_j, \\quad k=0, \\ldots, n+m-2.

    Parameters
    ----------
    lh_expr : Constant
        A constant 1D vector or a 2D column vector.
    rh_expr : Expression
        A 1D vector or a 2D column vector.
    """

    def __init__(self, lh_expr, rh_expr) -> None:
        warn("conv is deprecated. Use convolve instead.", CvxpyDeprecationWarning)
        super(conv, self).__init__(lh_expr, rh_expr)

    @AffAtom.numpy_numeric
    def numeric(self, values):
        """Convolve the two values.
        """
        flat_values = list(map(intf.from_2D_to_1D, values))
        output = np.convolve(flat_values[0], flat_values[1])
        if values[0].ndim == 2 or values[1].ndim == 2:
            return output[:, None]
        else:
            return output

    def validate_arguments(self) -> None:
        """Checks that both arguments are vectors, and the first is constant.
        """
        if not self.args[0].is_vector() or not self.args[1].is_vector():
            raise ValueError("The arguments to conv must resolve to a 1-d array")
        if not self.args[0].is_constant():
            raise ValueError("The first argument to conv must be constant.")

    def is_atom_convex(self) -> bool:
        """Is the atom convex?
        """
        # TODO support a non-constant first argument.
        if u.scopes.dpp_scope_active():
            # conv is not DPP if any parameters are present.
            c = self.args[0]
            return c.is_constant() and is_param_free(c)
        else:
            return self.args[0].is_constant()

    def is_atom_concave(self) -> bool:
        """Is the atom concave?
        """
        return self.is_atom_convex()

    def shape_from_args(self) -> Tuple[int, int]:
        """The sum of the argument dimensions - 1.
        """
        lh_length = self.args[0].size
        rh_length = self.args[1].size
        output_length = lh_length + rh_length - 1
        if self.args[0].ndim == 2 or self.args[1].ndim == 2:
            return (output_length, 1)
        else:
            return (output_length,)

    def sign_from_args(self) -> Tuple[bool, bool]:
        """Same as times.
        """
        return u.sign.mul_sign(self.args[0], self.args[1])

    def is_incr(self, idx) -> bool:
        """Is the composition non-decreasing in argument idx?
        """
        return self.args[0].is_nonneg()

    def is_decr(self, idx) -> bool:
        """Is the composition non-increasing in argument idx?
        """
        return self.args[0].is_nonpos()

    def graph_implementation(
        self, arg_objs, shape: Tuple[int, ...], data=None
    ) -> Tuple[lo.LinOp, List[Constraint]]:
        """Convolve two vectors.

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

        Returns
        -------
        tuple
            (LinOp for objective, list of constraints)
        """
        return (lu.conv(arg_objs[0], arg_objs[1], shape), [])


class convolve(AffAtom):
    """ 1D discrete convolution of two vectors.

    The discrete convolution :math:`c` of vectors :math:`a` and :math:`b` of
    lengths :math:`n` and :math:`m`, respectively, is a length-:math:`(n+m-1)`
    vector where

    .. math::

        c_k = \\sum_{i+j=k} a_ib_j, \\quad k=0, \\ldots, n+m-2.

    Matches numpy.convolve

    Parameters
    ----------
    lh_expr : Constant
        A constant scalar or 1D vector.
    rh_expr : Expression
        A scalar or 1D vector.
    """
    # TODO work with right hand constant.
    # TODO(akshayka): make DGP-compatible

    @AffAtom.numpy_numeric
    def numeric(self, values):
        """Convolve the two values.
        """
        return np.convolve(values[0], values[1])

    def validate_arguments(self) -> None:
        """Checks that both arguments are vectors, and the first is constant.
        """
        if not self.args[0].ndim <= 1 or not self.args[1].ndim <= 1:
            raise ValueError("The arguments to conv must be scalar or 1D.")
        if not self.args[0].is_constant():
            raise ValueError("The first argument to conv must be constant.")

    def is_atom_convex(self) -> bool:
        """Is the atom convex?
        """
        # TODO support a non-constant first argument.
        if u.scopes.dpp_scope_active():
            # conv is not DPP if any parameters are present.
            c = self.args[0]
            return c.is_constant() and is_param_free(c)
        else:
            return self.args[0].is_constant()

    def is_atom_concave(self) -> bool:
        """Is the atom concave?
        """
        return self.is_atom_convex()

    def shape_from_args(self) -> Tuple[int, int]:
        """The sum of the argument dimensions - 1.
        """
        lh_length = self.args[0].size
        rh_length = self.args[1].size
        return (lh_length + rh_length - 1,)

    def sign_from_args(self) -> Tuple[bool, bool]:
        """Same as times.
        """
        return u.sign.mul_sign(self.args[0], self.args[1])

    def is_incr(self, idx) -> bool:
        """Is the composition non-decreasing in argument idx?
        """
        return self.args[0].is_nonneg()

    def is_decr(self, idx) -> bool:
        """Is the composition non-increasing in argument idx?
        """
        return self.args[0].is_nonpos()

    def graph_implementation(
        self, arg_objs, shape: Tuple[int, ...], data=None
    ) -> Tuple[lo.LinOp, List[Constraint]]:
        """Convolve two vectors.

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

        Returns
        -------
        tuple
            (LinOp for objective, list of constraints)
        """
        return (lu.conv(arg_objs[0], arg_objs[1], shape), [])
