"""
Spherically-symmetric grids in 2 and 3 dimensions. These are grids that only
discretize the radial direction, assuming symmetry with respect to all angles.

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

from abc import ABCMeta
from typing import TYPE_CHECKING, Any, Dict, Generator, Tuple, Union

import numpy as np

from ..tools.cache import cached_property
from ..tools.docstrings import fill_in_docstring
from ..tools.plotting import plot_on_axes
from ..tools.spherical import volume_from_radius
from .base import DimensionError, GridBase, _check_shape, discretize_interval
from .cartesian import CartesianGrid

if TYPE_CHECKING:
    from .boundaries.axes import Boundaries  # @UnusedImport


PI_4 = 4 * np.pi
PI_43 = 4 / 3 * np.pi


class SphericalGridBase(GridBase, metaclass=ABCMeta):  # lgtm [py/missing-equals]
    r"""Base class for d-dimensional spherical grids with angular symmetry

    The angular symmetry implies that states only depend on the radial
    coordinate :math:`r`, which is discretized uniformly as


    .. math::
        r_i = R_\mathrm{inner} + \left(i + \frac12\right) \Delta r
        \quad \text{for} \quad i = 0, \ldots, N - 1
        \quad \text{with} \quad
            \Delta r = \frac{R_\mathrm{outer} - R_\mathrm{inner}}{N}

    where :math:`R_\mathrm{outer}` is the outer radius of the grid and
    :math:`R_\mathrm{inner}` corresponds to a possible inner radius, which is
    zero by default. The radial direction is discretized by :math:`N` support
    points.
    """

    periodic = [False]  # the radial axis is not periodic
    num_axes = 1  # the number of independent axes

    def __init__(
        self, radius: Union[float, Tuple[float, float]], shape: Union[Tuple[int], int]
    ):
        r"""
        Args:
            radius (float or tuple of floats):
                radius :math:`R_\mathrm{outer}` in case a simple float is given.
                If a tuple is supplied it is interpreted as the inner and outer
                radius, :math:`(R_\mathrm{inner}, R_\mathrm{outer})`.
            shape (tuple or int): A single number setting the number :math:`N`
                of support points along the radial coordinate
        """
        super().__init__()
        shape_list = _check_shape(shape)
        if not len(shape_list) == 1:
            raise ValueError(f"`shape` must be a single number, not {shape_list}")
        self._shape: Tuple[int] = (int(shape_list[0]),)

        try:
            r_inner, r_outer = radius  # type: ignore
        except TypeError:
            r_inner, r_outer = 0, float(radius)  # type: ignore

        if r_inner < 0:
            raise ValueError("Inner radius must be positive")
        if r_inner >= r_outer:
            raise ValueError("Outer radius must be larger than inner radius")

        # radial discretization
        rs, dr = discretize_interval(r_inner, r_outer, self.shape[0])

        self._axes_coords = (rs,)
        self._axes_bounds = ((r_inner, r_outer),)
        self._discretization = np.array((dr,))

    @property
    def state(self) -> Dict[str, Any]:
        """ state: the state of the grid """
        return {"radius": self.radius, "shape": self.shape}

    @property
    def has_hole(self) -> bool:
        """ returns whether the inner radius is larger than zero """
        return self.axes_bounds[0][0] > 0

    @classmethod
    def from_state(cls, state: Dict[str, Any]) -> "SphericalGridBase":  # type: ignore
        """create a field from a stored `state`.

        Args:
            state (dict):
                The state from which the grid is reconstructed.
        """
        state_copy = state.copy()
        obj = cls(radius=state_copy.pop("radius"), shape=state_copy.pop("shape"))
        if state_copy:
            raise ValueError(f"State items {state_copy.keys()} were not used")
        return obj

    @property
    def radius(self) -> Union[float, Tuple[float, float]]:
        """ float: radius of the sphere """
        r_inner, r_outer = self.axes_bounds[0]
        if r_inner == 0:
            return r_outer
        else:
            return r_inner, r_outer

    @property
    def volume(self) -> float:
        """ float: total volume of the grid """
        r_inner, r_outer = self.axes_bounds[0]
        volume = volume_from_radius(r_outer, dim=self.dim)
        if r_inner > 0:
            volume -= volume_from_radius(r_inner, dim=self.dim)
        return volume

    @cached_property()
    def cell_volume_data(self) -> Tuple[np.ndarray]:
        """ tuple of :class:`~numpy.ndarray`: the volumes of all cells """
        dr = self.discretization[0]
        rs = self.axes_coords[0]
        volumes_h = volume_from_radius(rs + 0.5 * dr, dim=self.dim)
        volumes_l = volume_from_radius(rs - 0.5 * dr, dim=self.dim)
        return ((volumes_h - volumes_l).reshape(self.shape[0]),)

    def contains_point(self, point: np.ndarray) -> np.ndarray:
        """check whether the point is contained in the grid

        Args:
            point (:class:`~numpy.ndarray`): Coordinates of the point
        """
        point = np.atleast_1d(point)
        if point.shape[-1] != self.dim:
            raise DimensionError("Dimension mismatch")
        r = np.linalg.norm(point, axis=-1)

        r_inner, r_outer = self.axes_bounds[0]
        return r_inner <= r <= r_outer  # type: ignore

    def get_random_point(
        self,
        boundary_distance: float = 0,
        cartesian: bool = True,
        avoid_center: bool = False,
    ) -> np.ndarray:
        """return a random point within the grid

        Note that these points will be uniformly distributed on the radial axis,
        which implies that they are not uniformly distributed in the volume.

        Args:
            boundary_distance (float): The minimal distance this point needs to
                have from all boundaries.
            cartesian (bool): Determines whether the point is returned in
                Cartesian coordinates or grid coordinates.
            avoid_center (bool): Determines whether the boundary distance
                should also be kept from the center, i.e., whether points close
                to the center are returned.

        Returns:
            :class:`~numpy.ndarray`: The coordinates of the point
        """
        # handle the boundary distance
        r_inner, r_outer = self.axes_bounds[0]
        r_min = r_inner
        if avoid_center:
            r_min += boundary_distance
        r_mag = r_outer - boundary_distance - r_min

        if r_mag <= 0:
            raise RuntimeError("Random points would be too close to boundary")

        # create random point
        r = np.array([r_mag * np.random.random() + r_min])
        if cartesian:
            return self.point_to_cartesian(r)
        else:
            return r

    def get_line_data(self, data: np.ndarray, extract: str = "auto") -> Dict[str, Any]:
        """return a line cut along the radial axis

        Args:
            data (:class:`~numpy.ndarray`):
                The values at the grid points
            extract (str):
                Determines which cut is done through the grid. This parameter is
                mainly supplied for a consistent interface and has no effect for
                polar grids.

        Returns:
            A dictionary with information about the line cut, which is
            convenient for plotting.
        """
        if extract not in {"auto", "r", "radial"}:
            raise ValueError(f"Unknown extraction method `{extract}`")

        return {
            "data_x": self.axes_coords[0],
            "data_y": data,
            "extent_x": self.axes_bounds[0],
            "label_x": self.axes[0],
        }

    def get_image_data(
        self,
        data: np.ndarray,
        performance_goal: str = "speed",
        fill_value: float = 0,
        masked: bool = True,
    ) -> Dict[str, Any]:
        """return a 2d-image of the data

        Args:
            data (:class:`~numpy.ndarray`):
                The values at the grid points
            performance_goal (str):
                Determines the method chosen for interpolation. Possible options
                are `speed` and `quality`.
            fill_value (float):
                The value assigned to invalid positions (those inside the hole
                or outside the region).
            masked (bool):
                Whether a :class:`numpy.ma.MaskedArray` is returned for the data
                instead of the normal :class:`~numpy.ndarray`.

        Returns:
            A dictionary with information about the image, which is  convenient
            for plotting.
        """
        from scipy import interpolate

        _, r_outer = self.axes_bounds[0]
        r_data = self.axes_coords[0]

        if self.has_hole:
            num = int(np.ceil(r_outer / self.discretization[0]))
            x_positive, _ = discretize_interval(0, r_outer, num)
        else:
            x_positive = r_data

        x = np.r_[-x_positive[::-1], x_positive]
        xs, ys = np.meshgrid(x, x, indexing="ij")
        r_img = np.hypot(xs, ys)

        if performance_goal == "speed":
            # interpolate over the new coordinates using linear interpolation
            f = interpolate.interp1d(
                r_data,
                data,
                copy=False,
                bounds_error=False,
                fill_value=fill_value,
                assume_sorted=True,
            )
            data_int = f(r_img.flat).reshape(r_img.shape)

        elif performance_goal == "quality":
            # interpolate over the new coordinates using radial base function
            f = interpolate.Rbf(r_data, data, function="cubic")
            data_int = f(r_img)

        else:
            raise ValueError(f"Performance goal `{performance_goal}` undefined")

        if masked:
            mask = (r_img < r_data[0]) | (r_data[-1] < r_img)
            data_int = np.ma.masked_array(data_int, mask=mask)

        return {
            "data": data_int,
            "x": x,
            "y": x,
            "extent": (-r_outer, r_outer, -r_outer, r_outer),
            "label_x": "x",
            "label_y": "y",
        }

    def iter_mirror_points(
        self, point: np.ndarray, with_self: bool = False, only_periodic: bool = True
    ) -> Generator:
        """generates all mirror points corresponding to `point`

        Args:
            point (:class:`~numpy.ndarray`): the point within the grid
            with_self (bool): whether to include the point itself
            only_periodic (bool): whether to only mirror along periodic axes

        Returns:
            A generator yielding the coordinates that correspond to mirrors
        """
        if with_self:
            yield np.asanyarray(point, dtype=np.double)

    def point_from_cartesian(self, points: np.ndarray) -> np.ndarray:
        """convert points given in Cartesian coordinates to this grid

        Args:
            points (:class:`~numpy.ndarray`):
                Points given in Cartesian coordinates.

        Returns:
            :class:`~numpy.ndarray`: Points given in the coordinates of the grid
        """
        points = np.atleast_1d(points)
        assert points.shape[-1] == self.dim, f"Point must have {self.dim} coordinates"
        return np.linalg.norm(points, axis=-1, keepdims=True)  # type: ignore

    def cell_to_point(self, cells: np.ndarray, cartesian: bool = True) -> np.ndarray:
        """convert cell coordinates to real coordinates

        This function returns points restricted to the x-axis, i.e., the
        y-coordinate will be zero.

        Args:
            cells (:class:`~numpy.ndarray`):
                Indices of the cells whose center coordinates are requested.
                This can be float values to indicate positions relative to the
                cell center.
            cartesian (bool):
                Determines whether the point is returned in Cartesian
                coordinates or grid coordinates.

        Returns:
            :class:`~numpy.ndarray`: The center points of the respective cells
        """
        cells = np.atleast_1d(cells)
        assert cells.shape[-1] == self.num_axes, f"Require {self.num_axes} coordinates"

        # convert from cells indices to grid coordinates
        r_inner, _ = self.axes_bounds[0]
        points = r_inner + (cells + 0.5) * self.discretization[0]
        if cartesian:
            return self.point_to_cartesian(points)
        else:
            return points  # type: ignore

    def point_to_cell(self, points: np.ndarray) -> np.ndarray:
        """Determine cell(s) corresponding to given point(s)

        Args:
            points (:class:`~numpy.ndarray`): Real coordinates

        Returns:
            :class:`~numpy.ndarray`: The indices of the respective cells
        """
        # convert from grid coordinates to cells indices
        r = self.point_from_cartesian(points)
        r_inner, _ = self.axes_bounds[0]
        cells = (r - r_inner) / self.discretization[0]
        return cells.astype(np.intc)  # type: ignore

    def difference_vector_real(self, p1: np.ndarray, p2: np.ndarray) -> np.ndarray:
        """return the vector pointing from p1 to p2.

        In case of periodic boundary conditions, the shortest vector is returned

        Args:
            p1 (:class:`~numpy.ndarray`): First point(s)
            p2 (:class:`~numpy.ndarray`): Second point(s)

        Returns:
            :class:`~numpy.ndarray`: The difference vectors between the points
                with periodic boundary conditions applied.
        """
        return np.atleast_1d(p2) - np.atleast_1d(p1)  # type: ignore

    def polar_coordinates_real(
        self, origin=None, *, ret_angle: bool = False, **kwargs
    ) -> Union[np.ndarray, Tuple[np.ndarray, ...]]:
        """return spherical coordinates associated with the grid

        Args:
            origin:
                Place holder variable to comply with the interface
            ret_angle (bool):
                Determines whether angles are returned alongside the distance. If
                `False` only the distance to the origin is returned for each support
                point of the grid. If `True`, the distance and angles are returned. Note
                that in the case of spherical grids, this angle is zero by convention.
        """
        # check the consistency of the origin argument, which can be set for other grids
        if origin is not None:
            origin = np.array(origin, dtype=np.double, ndmin=1)
            if not np.array_equal(origin, np.zeros(self.dim)):
                raise RuntimeError(f"Origin must be {str([0]*self.dim)}")

        # the distance to the origin is exactly the radial coordinate
        rs = self.axes_coords[0]
        if ret_angle:
            return (rs,) + (np.zeros_like(rs),) * (self.dim - 1)
        else:
            return rs

    @fill_in_docstring
    def get_boundary_conditions(self, bc="natural", rank: int = 0) -> "Boundaries":
        """constructs boundary conditions from a flexible data format.

        If the inner boundary condition for a grid without a hole is not specified, this
        condition is automatically set to a vanishing derivative at :math:`r=0`.

        Args:
            bc (str or list or tuple or dict):
                The boundary conditions applied to the field.
                {ARG_BOUNDARIES}
            rank (int):
                The tensorial rank of the value associated with the boundary
                conditions.

        Raises:
            ValueError: If the data given in `bc` cannot be read
            PeriodicityError: If the boundaries are not compatible with the
                periodic axes of the grid.
        """
        from .boundaries import Boundaries  # @Reimport
        from .boundaries.axis import BoundaryPair
        from .boundaries.local import BCBase, NeumannBC

        if self.has_hole:
            # grid has holes => specify two boundary conditions
            return Boundaries.from_data(self, bc, rank=rank)

        if isinstance(bc, Boundaries):
            # a full boundary instance is given
            return bc

        if bc == "natural" or bc == "auto_periodic_neumann":
            # a simple value is given => use it for the outer boundary
            return Boundaries.from_data(self, "derivative", rank=rank)
        elif bc == "auto_periodic_dirichlet":
            # a simple value is given => use it for the outer boundary
            return Boundaries.from_data(self, "value", rank=rank)
        else:
            # a more complex value is given for the boundary
            try:
                # try interpreting it as a value for the outer boundary
                b_outer = BCBase.from_data(self, 0, upper=True, data=bc, rank=rank)
            except ValueError:
                # if this fails, try interpreting the value as the full BC
                bcs = Boundaries.from_data(self, bc, rank=rank)
            else:
                self._logger.warning(
                    "The inner boundary condition was not specified. Assuming a "
                    "vanishing derivative at r=0."
                )
                b_inner = NeumannBC(self, 0, upper=False, rank=rank)
                bcs = Boundaries([BoundaryPair(b_inner, b_outer)])
            return bcs

    def get_cartesian_grid(self, mode: str = "valid", num: int = None) -> CartesianGrid:
        """return a Cartesian grid for this spherical one

        Args:
            mode (str):
                Determines how the grid is determined. Setting it to 'valid' (or
                'inscribed') only returns points that are fully resolved in the
                spherical grid, e.g., the Cartesian grid is inscribed in the sphere.
                Conversely, 'full' (or 'circumscribed') returns all data, so the
                Cartesian grid is circumscribed.
            num (int):
                Number of support points along each axis of the returned grid.

        Returns:
            :class:`pde.grids.cartesian.CartesianGrid`: The requested grid
        """
        # pick how the grid is determined
        if mode == "valid":
            if self.has_hole:
                self._logger.warn("The sphere has holes, so not all points are valid")
            bounds = self.radius / np.sqrt(self.dim)
        elif mode == "inscribed":
            bounds = self.radius / np.sqrt(self.dim)
        elif mode == "full" or mode == "circumscribed":
            bounds = self.radius
        else:
            raise ValueError(f"Unsupported mode `{mode}`")

        # determine the grid points
        if num is None:
            num = 2 * round(bounds / self.discretization[0])
        grid_bounds = [(-bounds, bounds)] * self.dim
        return CartesianGrid(grid_bounds, num)

    @plot_on_axes()
    def plot(self, ax, **kwargs):
        r"""visualize the spherically symmetric grid in two dimensions

        Args:
            {PLOT_ARGS}
            \**kwargs: Extra arguments are passed on the to the matplotlib
                plotting routines, e.g., to set the color of the lines
        """
        from matplotlib import collections, patches

        kwargs.setdefault("edgecolor", kwargs.get("color", "k"))
        kwargs.setdefault("facecolor", "none")
        (rb,) = self.axes_bounds
        rmax = rb[1]

        # draw circular parts
        circles = []
        for r in np.linspace(*rb, self.shape[0] + 1):
            if r == 0:
                c = patches.Circle((0, 0), 0.01 * rmax)
            else:
                c = patches.Circle((0, 0), r)
            circles.append(c)
        ax.add_collection(collections.PatchCollection(circles, **kwargs))

        ax.set_xlim(-rmax, rmax)
        ax.set_xlabel("x")
        ax.set_ylim(-rmax, rmax)
        ax.set_ylabel("y")
        ax.set_aspect(1)


class PolarGrid(SphericalGridBase):
    r"""2-dimensional polar grid assuming angular symmetry

    The angular symmetry implies that states only depend on the radial
    coordinate :math:`r`, which is discretized uniformly as

    .. math::
        r_i = R_\mathrm{inner} + \left(i + \frac12\right) \Delta r
        \quad \text{for} \quad i = 0, \ldots, N - 1
        \quad \text{with} \quad
            \Delta r = \frac{R_\mathrm{outer} - R_\mathrm{inner}}{N}

    where :math:`R_\mathrm{outer}` is the outer radius of the grid and
    :math:`R_\mathrm{inner}` corresponds to a possible inner radius, which is
    zero by default. The radial direction is discretized by :math:`N` support
    points.
    """

    dim = 2  # dimension of the described space
    axes = ["r"]
    axes_symmetric = ["phi"]
    coordinate_constraints = [0, 1]  # axes not described explicitly

    def point_to_cartesian(self, points: np.ndarray) -> np.ndarray:
        """convert coordinates of a point to Cartesian coordinates

        This function returns points along the y-coordinate, i.e, the x
        coordinates will be zero.

        Returns:
            :class:`~numpy.ndarray`: The Cartesian coordinates of the point
        """
        points = np.atleast_1d(points)
        if points.shape[-1] != self.num_axes:
            raise DimensionError(f"Shape {points.shape} cannot denote points")

        y = points[..., 0]
        x = np.zeros_like(y)
        return np.stack((x, y), axis=-1)


class SphericalGrid(SphericalGridBase):
    r"""3-dimensional spherical grid assuming spherical symmetry

    The symmetry implies that states only depend on the radial coordinate
    :math:`r`, which is discretized as follows:

    .. math::
        r_i = R_\mathrm{inner} + \left(i + \frac12\right) \Delta r
        \quad \text{for} \quad i = 0, \ldots, N - 1
        \quad \text{with} \quad
            \Delta r = \frac{R_\mathrm{outer} - R_\mathrm{inner}}{N}

    where :math:`R_\mathrm{outer}` is the outer radius of the grid and
    :math:`R_\mathrm{inner}` corresponds to a possible inner radius, which is
    zero by default. The radial direction is discretized by :math:`N` support
    points.
    """

    dim = 3  # dimension of the described space
    axes = ["r"]
    axes_symmetric = ["theta", "phi"]
    coordinate_constraints = [0, 1, 2]  # axes not described explicitly

    def point_to_cartesian(self, points: np.ndarray) -> np.ndarray:
        """convert coordinates of a point to Cartesian coordinates

        This function returns points along the z-coordinate, i.e, the x and y
        coordinates will be zero.

        Args:
            points (:class:`~numpy.ndarray`):
                Points given in the coordinates of the grid

        Returns:
            :class:`~numpy.ndarray`: The Cartesian coordinates of the point
        """
        points = np.atleast_1d(points)
        if points.shape[-1] != self.num_axes:
            raise DimensionError(f"Shape {points.shape} cannot denote points")
        z = points[..., 0]
        x = np.zeros_like(z)
        return np.stack((x, x, z), axis=-1)
