"""A Allen-Cahn equation.

.. codeauthor:: David Zwicker <david.zwicker@ds.mpg.de>
"""

from __future__ import annotations

from typing import TYPE_CHECKING

import numpy as np

from ..fields import ScalarField
from ..grids.boundaries import set_default_bc
from ..tools.docstrings import fill_in_docstring
from .base import PDEBase, expr_prod

if TYPE_CHECKING:
    from collections.abc import Callable

    import torch

    from ..grids.boundaries.axes import BoundariesData
    from ..tools.typing import NumericArray


class AllenCahnPDE(PDEBase):
    r"""A simple Allen-Cahn equation.

    The mathematical definition is

    .. math::
        \partial_t c = \gamma \nabla^2 c - c^3 + c

    where :math:`c` is a scalar field and :math:`\gamma` sets the (squared) interfacial
    width.
    """

    explicit_time_dependence = False
    default_bc = "auto_periodic_neumann"
    """Default boundary condition used when no specific conditions are chosen."""

    interface_width: float

    @fill_in_docstring
    def __init__(
        self,
        interface_width: float = 1,
        mobility: float = 1,
        *,
        bc: BoundariesData | None = None,
    ):
        """
        Args:
            interface_width (float):
                The diffusivity of the described species
            mobility (float):
                The rate at which the structures evolve
            bc:
                The boundary conditions applied to the field.
                {ARG_BOUNDARIES}
        """
        super().__init__()

        self.interface_width = interface_width
        self.mobility = mobility
        self.bc = set_default_bc(bc, self.default_bc)

    @property
    def expression(self) -> str:
        """str: the expression of the right hand side of this PDE"""
        expr = f"{expr_prod(self.interface_width, '∇²c')} - c³ + c"
        if np.isclose(self.mobility, 1):
            return expr
        return expr_prod(self.mobility, f"({expr})")

    def evolution_rate(  # type: ignore
        self,
        state: ScalarField,
        t: float = 0,
    ) -> ScalarField:
        """Evaluate the right hand side of the PDE.

        Args:
            state (:class:`~pde.fields.ScalarField`):
                The scalar field describing the concentration distribution
            t (float):
                The current time point

        Returns:
            :class:`~pde.fields.ScalarField`:
            Scalar field describing the evolution rate of the PDE
        """
        if not isinstance(state, ScalarField):
            msg = "`state` must be ScalarField"
            raise TypeError(msg)
        laplace = state.laplace(bc=self.bc, label="evolution rate", args={"t": t})
        rhs = self.interface_width * laplace - state**3 + state
        return self.mobility * rhs  # type: ignore

    def make_pde_rhs_numba(
        self, state: ScalarField
    ) -> Callable[[NumericArray, float], NumericArray]:
        """Create a compiled function evaluating the right hand side of the PDE.

        Args:
            state (:class:`~pde.fields.ScalarField`):
                An example for the state defining the grid and data types

        Returns:
            A function with signature `(state_data, t)`, which can be called
            with an instance of :class:`~numpy.ndarray` of the state data and
            the time to obtained an instance of :class:`~numpy.ndarray` giving
            the evolution rate.
        """
        interface_width = self.interface_width
        mobility = self.mobility
        laplace = state.grid.make_operator("laplace", bc=self.bc, backend="numba")

        def pde_rhs(state_data: NumericArray, t: float = 0) -> NumericArray:
            """Compiled helper function evaluating right hand side."""
            return mobility * (
                interface_width * laplace(state_data, args={"t": t})
                - state_data**3
                + state_data
            )

        return pde_rhs

    def make_pde_rhs_torch(
        self, state: ScalarField
    ) -> Callable[[torch.Tensor, float], torch.Tensor]:
        """Create a compiled function evaluating the right hand side of the PDE.

        Args:
            state (:class:`~pde.fields.ScalarField`):
                An example for the state defining the grid and data types

        Returns:
            A function with signature `(state_data, t)`, which can be called
            with an instance of :class:`torch.Tensor` of the state data and
            the time to obtained an instance of :class:`torch.Tensor` giving
            the evolution rate.
        """
        interface_width = self.interface_width
        mobility = self.mobility
        laplace = state.grid.make_operator(
            operator="laplace",
            bc=self.bc,
            backend="torch",
            native=True,
            dtype=state.dtype,
        )

        def pde_rhs(state_data: torch.Tensor, t: float = 0) -> torch.Tensor:
            """Compiled helper function evaluating right hand side."""
            return mobility * (
                interface_width * laplace(state_data, args={"t": t})
                - state_data**3
                + state_data
            )

        return pde_rhs
