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# Source code for astropy.nddata.utils

    # Licensed under a 3-clause BSD style license - see LICENSE.rst
    """
    This module includes helper functions for array operations.
    """

    import functools
    from collections.abc import Callable
    from copy import deepcopy
    from typing import Literal, TypeAlias, TypeVar, overload

    import numpy as np
    from numpy.typing import NDArray

    from astropy import units as u
    from astropy.coordinates import SkyCoord
    from astropy.io.fits.hdu.compressed import CompImageSection
    from astropy.io.fits.hdu.image import Section
    from astropy.wcs import Sip
    from astropy.wcs.utils import proj_plane_pixel_scales, skycoord_to_pixel

    __all__ = [
        "Cutout2D",
        "NoOverlapError",
        "PartialOverlapError",
        "add_array",
        "extract_array",
        "overlap_slices",
        "subpixel_indices",
    ]

    DT = TypeVar("DT", bound=np.generic)
    LimitRoundingMethod: TypeAlias = Callable[[float], float]

    class NoOverlapError(ValueError):
        """Raised when determining the overlap of non-overlapping arrays."""

    class PartialOverlapError(ValueError):
        """Raised when arrays only partially overlap."""

    def overlap_slices(
        large_array_shape: int | tuple[int, ...],
        small_array_shape: int | tuple[int, ...],
        position: float | tuple[float, ...],
        mode: Literal["partial", "trim", "strict"] = "partial",
        *,
        limit_rounding_method: LimitRoundingMethod = np.ceil,
    ) -> tuple[tuple[slice, ...], tuple[slice, ...]]:
        """
        Get slices for the overlapping part of a small and a large array.

        Given a certain position of the center of the small array, with
        respect to the large array, tuples of slices are returned which can be
        used to extract, add or subtract the small array at the given
        position. This function takes care of the correct behavior at the
        boundaries, where the small array is cut of appropriately.
        Integer positions are at the pixel centers.

        Parameters
        ----------
        large_array_shape : tuple of int or int
            The shape of the large array (for 1D arrays, this can be an
            `int`).
        small_array_shape : int or tuple thereof
            The shape of the small array (for 1D arrays, this can be an
            `int`).  See the ``mode`` keyword for additional details.
        position : number or tuple thereof
            The position of the small array's center with respect to the
            large array.  The pixel coordinates should be in the same order
            as the array shape.  Integer positions are at the pixel centers.
            For any axis where ``small_array_shape`` is even, the position
            is rounded up, e.g. extracting two elements with a center of
            ``1`` will define the extracted region as ``[0, 1]``.
        mode : {'partial', 'trim', 'strict'}, optional
            In ``'partial'`` mode, a partial overlap of the small and the
            large array is sufficient.  The ``'trim'`` mode is similar to
            the ``'partial'`` mode, but ``slices_small`` will be adjusted to
            return only the overlapping elements.  In the ``'strict'`` mode,
            the small array has to be fully contained in the large array,
            otherwise an `~astropy.nddata.utils.PartialOverlapError` is
            raised.  In all modes, non-overlapping arrays will raise a
            `~astropy.nddata.utils.NoOverlapError`.
        limit_rounding_method : callable
            The rounding method when calculating the minimum and maximum pixel indices.
            This must be a callable function. Examples: `~numpy.ceil`, `~numpy.floor`,
            `~numpy.round`. Default is `~numpy.ceil`.

        Returns
        -------
        slices_large : tuple of slice
            A tuple of slice objects for each axis of the large array, such
            that ``large_array[slices_large]`` extracts the region of the
            large array that overlaps with the small array.
        slices_small : tuple of slice
            A tuple of slice objects for each axis of the small array, such
            that ``small_array[slices_small]`` extracts the region that is
            inside the large array.
        """
        if mode not in ["partial", "trim", "strict"]:
            raise ValueError('Mode can be only "partial", "trim", or "strict".')
        if np.isscalar(small_array_shape):
            small_array_shape = (small_array_shape,)
        if np.isscalar(large_array_shape):
            large_array_shape = (large_array_shape,)
        if np.isscalar(position):
            position = (position,)

        if any(~np.isfinite(position)):
            raise ValueError("Input position contains invalid values (NaNs or infs).")

        if len(small_array_shape) != len(large_array_shape):
            raise ValueError(
                '"large_array_shape" and "small_array_shape" must '
                "have the same number of dimensions."
            )

        if len(small_array_shape) != len(position):
            raise ValueError(
                '"position" must have the same number of dimensions as "small_array_shape".'
            )

        if not callable(limit_rounding_method):
            raise ValueError("Limit rounding method must be a callable function.")

        # define the min/max pixel indices
        # round according to the limit_rounding_method
        try:
            indices_min = [
                int(limit_rounding_method(pos - (small_shape / 2.0)))
                for (pos, small_shape) in zip(position, small_array_shape)
            ]
        except (TypeError, ValueError) as exc:
            raise ValueError(
                "Limit rounding method must accept a single number as input and return a single number."
            ) from exc
        indices_max = [
            int(idx_min + small_shape)
            for (idx_min, small_shape) in zip(indices_min, small_array_shape)
        ]

        for e_max in indices_max:
            if e_max < 0 or (e_max == 0 and small_array_shape != (0, 0)):
                raise NoOverlapError("Arrays do not overlap.")
        for e_min, large_shape in zip(indices_min, large_array_shape):
            if e_min >= large_shape:
                raise NoOverlapError("Arrays do not overlap.")

        if mode == "strict":
            for e_min in indices_min:
                if e_min < 0:
                    raise PartialOverlapError("Arrays overlap only partially.")
            for e_max, large_shape in zip(indices_max, large_array_shape):
                if e_max > large_shape:
                    raise PartialOverlapError("Arrays overlap only partially.")

        # Set up slices
        slices_large = tuple(
            slice(max(0, indices_min), min(large_shape, indices_max))
            for (indices_min, indices_max, large_shape) in zip(
                indices_min, indices_max, large_array_shape
            )
        )
        if mode == "trim":
            slices_small = tuple(slice(0, slc.stop - slc.start) for slc in slices_large)
        else:
            slices_small = tuple(
                slice(
                    max(0, -indices_min),
                    min(large_shape - indices_min, indices_max - indices_min),
                )
                for (indices_min, indices_max, large_shape) in zip(
                    indices_min, indices_max, large_array_shape
                )
            )

        return slices_large, slices_small

    @overload
    def extract_array(
        array_large: NDArray[DT],
        shape: int | tuple[int, ...],
        position: float | tuple[float, ...],
        mode: Literal["partial", "trim", "strict"],
        fill_value: float,
        return_position: Literal[True],
        *,
        limit_rounding_method: LimitRoundingMethod = np.ceil,
    ) -> tuple[NDArray[DT], tuple[float, ...]]: ...

    @overload
    def extract_array(
        array_large: NDArray[DT],
        shape: int | tuple[int, ...],
        position: float | tuple[float, ...],
        mode: Literal["partial", "trim", "strict"] = "partial",
        fill_value: float = np.nan,
        return_position: Literal[False] = False,
        *,
        limit_rounding_method: LimitRoundingMethod = np.ceil,
    ) -> NDArray[DT]: ...

    def extract_array(
        array_large,
        shape,
        position,
        mode="partial",
        fill_value=np.nan,
        return_position=False,
        *,
        limit_rounding_method=np.ceil,
    ):
        """
        Extract a smaller array of the given shape and position from a
        larger array.

        Parameters
        ----------
        array_large : ndarray
            The array from which to extract the small array.
        shape : int or tuple thereof
            The shape of the extracted array (for 1D arrays, this can be an
            `int`).  See the ``mode`` keyword for additional details.
        position : number or tuple thereof
            The position of the small array's center with respect to the
            large array.  The pixel coordinates should be in the same order
            as the array shape.  Integer positions are at the pixel centers
            (for 1D arrays, this can be a number).
        mode : {'partial', 'trim', 'strict'}, optional
            The mode used for extracting the small array.  For the
            ``'partial'`` and ``'trim'`` modes, a partial overlap of the
            small array and the large array is sufficient.  For the
            ``'strict'`` mode, the small array has to be fully contained
            within the large array, otherwise an
            `~astropy.nddata.utils.PartialOverlapError` is raised.   In all
            modes, non-overlapping arrays will raise a
            `~astropy.nddata.utils.NoOverlapError`.  In ``'partial'`` mode,
            positions in the small array that do not overlap with the large
            array will be filled with ``fill_value``.  In ``'trim'`` mode
            only the overlapping elements are returned, thus the resulting
            small array may be smaller than the requested ``shape``.
        fill_value : number, optional
            If ``mode='partial'``, the value to fill pixels in the extracted
            small array that do not overlap with the input ``array_large``.
            ``fill_value`` will be changed to have the same ``dtype`` as the
            ``array_large`` array, with one exception. If ``array_large``
            has integer type and ``fill_value`` is ``np.nan``, then a
            `ValueError` will be raised.
        return_position : bool, optional
            If `True`, return the coordinates of ``position`` in the
            coordinate system of the returned array.
        limit_rounding_method : callable
            The rounding method when calculating the minimum and maximum pixel indices.
            This must be a callable function. Examples: `~numpy.ceil`, `~numpy.floor`,
            `~numpy.round`. Default is `~numpy.ceil`.

        Returns
        -------
        array_small : ndarray
            The extracted array.
        new_position : tuple
            If ``return_position`` is true, this tuple will contain the
            coordinates of the input ``position`` in the coordinate system
            of ``array_small``. Note that for partially overlapping arrays,
            ``new_position`` might actually be outside of the
            ``array_small``; ``array_small[new_position]`` might give wrong
            results if any element in ``new_position`` is negative.

        Examples
        --------
        We consider a large array with the shape 11x10, from which we extract
        a small array of shape 3x5:

        >>> import numpy as np
        >>> from astropy.nddata.utils import extract_array
        >>> large_array = np.arange(110).reshape((11, 10))
        >>> extract_array(large_array, (3, 5), (7, 7))
        array([[65, 66, 67, 68, 69],
               [75, 76, 77, 78, 79],
               [85, 86, 87, 88, 89]])
        """
        if np.isscalar(shape):
            shape = (shape,)
        if np.isscalar(position):
            position = (position,)

        if mode not in ["partial", "trim", "strict"]:
            raise ValueError("Valid modes are 'partial', 'trim', and 'strict'.")

        large_slices, small_slices = overlap_slices(
            array_large.shape,
            shape,
            position,
            mode=mode,
            limit_rounding_method=limit_rounding_method,
        )
        extracted_array = array_large[large_slices]
        if return_position:
            new_position = [i - s.start for i, s in zip(position, large_slices)]

        # Extracting on the edges is presumably a rare case, so treat special here
        if (extracted_array.shape != shape) and (mode == "partial"):
            extracted_array_large = np.zeros(shape, dtype=extracted_array.dtype)
            try:
                extracted_array_large[:] = fill_value
            except ValueError as exc:
                exc.args += (
                    "fill_value is inconsistent with the data type of "
                    "the input array (e.g., fill_value cannot be set to "
                    "np.nan if the input array has integer type). Please "
                    "change either the input array dtype or the "
                    "fill_value.",
                )
                raise exc

            extracted_array_large[small_slices] = extracted_array
            extracted_array = extracted_array_large
            if return_position:
                new_position = [i + s.start for i, s in zip(new_position, small_slices)]
        if return_position:
            return extracted_array, tuple(new_position)
        else:
            return extracted_array

    def add_array(
        array_large: NDArray[DT],
        array_small: NDArray[DT],
        position: tuple[float, ...],
        *,
        limit_rounding_method: LimitRoundingMethod = np.ceil,
    ) -> NDArray[DT]:
        """
        Add a smaller array at a given position in a larger array.

        Parameters
        ----------
        array_large : ndarray
            Large array.
        array_small : ndarray
            Small array to add. Can be equal to ``array_large`` in size in a given
            dimension, but not larger.
        position : tuple
            Position of the small array's center, with respect to the large array.
            Coordinates should be in the same order as the array shape.
        limit_rounding_method : callable
            The rounding method when calculating the minimum and maximum pixel indices.
            This must be a callable function. Examples: `~numpy.ceil`, `~numpy.floor`,
            `~numpy.round`. Default is `~numpy.ceil`.

        Returns
        -------
        new_array : ndarray
            The new array formed from the sum of ``array_large`` and
            ``array_small``.

        Notes
        -----
        The addition is done in-place.

        Examples
        --------
        We consider a large array of zeros with the shape 5x5 and a small
        array of ones with a shape of 3x3:

        >>> import numpy as np
        >>> from astropy.nddata.utils import add_array
        >>> large_array = np.zeros((5, 5))
        >>> small_array = np.ones((3, 3))
        >>> add_array(large_array, small_array, (1, 2))  # doctest: +FLOAT_CMP
        array([[0., 1., 1., 1., 0.],
               [0., 1., 1., 1., 0.],
               [0., 1., 1., 1., 0.],
               [0., 0., 0., 0., 0.],
               [0., 0., 0., 0., 0.]])
        """
        # Check if large array is not smaller
        if all(
            large_shape >= small_shape
            for (large_shape, small_shape) in zip(array_large.shape, array_small.shape)
        ):
            large_slices, small_slices = overlap_slices(
                array_large.shape,
                array_small.shape,
                position,
                limit_rounding_method=limit_rounding_method,
            )
            array_large[large_slices] += array_small[small_slices]
            return array_large
        else:
            raise ValueError("Can't add array. Small array too large.")

    def subpixel_indices(position, subsampling):
        """
        Convert decimal points to indices, given a subsampling factor.

        This discards the integer part of the position and uses only the decimal
        place, and converts this to a subpixel position depending on the
        subsampling specified. The center of a pixel corresponds to an integer
        position.

        Parameters
        ----------
        position : ndarray or array-like
            Positions in pixels.
        subsampling : int
            Subsampling factor per pixel.

        Returns
        -------
        indices : ndarray
            The integer subpixel indices corresponding to the input positions.

        Examples
        --------
        If no subsampling is used, then the subpixel indices returned are always 0:

        >>> from astropy.nddata.utils import subpixel_indices
        >>> subpixel_indices([1.2, 3.4, 5.6], 1)  # doctest: +FLOAT_CMP
        array([0., 0., 0.])

        If instead we use a subsampling of 2, we see that for the two first values
        (1.1 and 3.4) the subpixel position is 1, while for 5.6 it is 0. This is
        because the values of 1, 3, and 6 lie in the center of pixels, and 1.1 and
        3.4 lie in the left part of the pixels and 5.6 lies in the right part.

        >>> subpixel_indices([1.2, 3.4, 5.5], 2)  # doctest: +FLOAT_CMP
        array([1., 1., 0.])
        """
        # Get decimal points
        fractions = np.modf(np.asanyarray(position) + 0.5)[0]
        return np.floor(fractions * subsampling)

    class Cutout2D:
        """
        Create a cutout object from a 2D array.

        The returned object will contain a 2D cutout array.  If
        ``copy=False`` (default), the cutout array is a view into the
        original ``data`` array, otherwise the cutout array will contain a
        copy of the original data.

        If a `~astropy.wcs.WCS` object is input, then the returned object
        will also contain a copy of the original WCS, but updated for the
        cutout array.

        For example usage, see :ref:`astropy:cutout_images`.

        .. warning::

            The cutout WCS object does not currently handle cases where the
            input WCS object contains distortion lookup tables described in
            the `FITS WCS distortion paper
            <https://www.atnf.csiro.au/people/mcalabre/WCS/dcs_20040422.pdf>`__.

        Parameters
        ----------
        data : ndarray
            The 2D data array from which to extract the cutout array.

        position : tuple or `~astropy.coordinates.SkyCoord`
            The position of the cutout array's center with respect to
            the ``data`` array.  The position can be specified either as
            a ``(x, y)`` tuple of pixel coordinates or a
            `~astropy.coordinates.SkyCoord`, in which case ``wcs`` is a
            required input.

        size : int, array-like, or `~astropy.units.Quantity`
            The size of the cutout array along each axis.  If ``size``
            is a scalar number or a scalar `~astropy.units.Quantity`,
            then a square cutout of ``size`` will be created.  If
            ``size`` has two elements, they should be in ``(ny, nx)``
            order.  Scalar numbers in ``size`` are assumed to be in
            units of pixels.  ``size`` can also be a
            `~astropy.units.Quantity` object or contain
            `~astropy.units.Quantity` objects.  Such
            `~astropy.units.Quantity` objects must be in pixel or
            angular units.  For all cases, ``size`` will be converted to
            an integer number of pixels, rounding the nearest
            integer.  See the ``mode`` keyword for additional details on
            the final cutout size.

            .. note::
                If ``size`` is in angular units, the cutout size is
                converted to pixels using the pixel scales along each
                axis of the image at the ``CRPIX`` location.  Projection
                and other non-linear distortions are not taken into
                account.

        wcs : `~astropy.wcs.WCS`, optional
            A WCS object associated with the input ``data`` array.  If
            ``wcs`` is not `None`, then the returned cutout object will
            contain a copy of the updated WCS for the cutout data array.

        mode : {'trim', 'partial', 'strict'}, optional
            The mode used for creating the cutout data array.  For the
            ``'partial'`` and ``'trim'`` modes, a partial overlap of the
            cutout array and the input ``data`` array is sufficient.
            For the ``'strict'`` mode, the cutout array has to be fully
            contained within the ``data`` array, otherwise an
            `~astropy.nddata.utils.PartialOverlapError` is raised.   In
            all modes, non-overlapping arrays will raise a
            `~astropy.nddata.utils.NoOverlapError`.  In ``'partial'``
            mode, positions in the cutout array that do not overlap with
            the ``data`` array will be filled with ``fill_value``.  In
            ``'trim'`` mode only the overlapping elements are returned,
            thus the resulting cutout array may be smaller than the
            requested ``shape``.

        fill_value : float or int, optional
            If ``mode='partial'``, the value to fill pixels in the
            cutout array that do not overlap with the input ``data``.
            ``fill_value`` must have the same ``dtype`` as the input
            ``data`` array.

        copy : bool, optional
            If `False` (default), then the cutout data will be a view
            into the original ``data`` array.  If `True`, then the
            cutout data will hold a copy of the original ``data`` array.

        limit_rounding_method : callable
            The rounding method when calculating the minimum and maximum pixel indices.
            This must be a callable function. Examples: `~numpy.ceil`, `~numpy.floor`,
            `~numpy.round`. Default is `~numpy.ceil`.

        Attributes
        ----------
        data : 2D `~numpy.ndarray`
            The 2D cutout array.

        shape : (2,) tuple
            The ``(ny, nx)`` shape of the cutout array.

        shape_input : (2,) tuple
            The ``(ny, nx)`` shape of the input (original) array.

        input_position_cutout : (2,) tuple
            The (unrounded) ``(x, y)`` position with respect to the cutout
            array.

        input_position_original : (2,) tuple
            The original (unrounded) ``(x, y)`` input position (with respect
            to the original array).

        slices_original : (2,) tuple of slice object
            A tuple of slice objects for the minimal bounding box of the
            cutout with respect to the original array.  For
            ``mode='partial'``, the slices are for the valid (non-filled)
            cutout values.

        slices_cutout : (2,) tuple of slice object
            A tuple of slice objects for the minimal bounding box of the
            cutout with respect to the cutout array.  For
            ``mode='partial'``, the slices are for the valid (non-filled)
            cutout values.

        xmin_original, ymin_original, xmax_original, ymax_original : float
            The minimum and maximum ``x`` and ``y`` indices of the minimal
            rectangular region of the cutout array with respect to the
            original array.  For ``mode='partial'``, the bounding box
            indices are for the valid (non-filled) cutout values.  These
            values are the same as those in `bbox_original`.

        xmin_cutout, ymin_cutout, xmax_cutout, ymax_cutout : float
            The minimum and maximum ``x`` and ``y`` indices of the minimal
            rectangular region of the cutout array with respect to the
            cutout array.  For ``mode='partial'``, the bounding box indices
            are for the valid (non-filled) cutout values.  These values are
            the same as those in `bbox_cutout`.

        wcs : `~astropy.wcs.WCS` or None
            A WCS object associated with the cutout array if a ``wcs``
            was input.

        Examples
        --------
        >>> import numpy as np
        >>> from astropy.nddata.utils import Cutout2D
        >>> from astropy import units as u
        >>> data = np.arange(20.).reshape(5, 4)
        >>> cutout1 = Cutout2D(data, (2, 2), (3, 3))
        >>> print(cutout1.data)  # doctest: +FLOAT_CMP
        [[ 5.  6.  7.]
         [ 9. 10. 11.]
         [13. 14. 15.]]

        >>> print(cutout1.center_original)
        (2.0, 2.0)
        >>> print(cutout1.center_cutout)
        (1.0, 1.0)
        >>> print(cutout1.origin_original)
        (1, 1)

        >>> cutout2 = Cutout2D(data, (2, 2), 3)
        >>> print(cutout2.data)  # doctest: +FLOAT_CMP
        [[ 5.  6.  7.]
         [ 9. 10. 11.]
         [13. 14. 15.]]

        >>> size = u.Quantity([3, 3], u.pixel)
        >>> cutout3 = Cutout2D(data, (0, 0), size)
        >>> print(cutout3.data)  # doctest: +FLOAT_CMP
        [[0. 1.]
         [4. 5.]]

        >>> cutout4 = Cutout2D(data, (0, 0), (3 * u.pixel, 3))
        >>> print(cutout4.data)  # doctest: +FLOAT_CMP
        [[0. 1.]
         [4. 5.]]

        >>> cutout5 = Cutout2D(data, (0, 0), (3, 3), mode='partial')
        >>> print(cutout5.data)  # doctest: +FLOAT_CMP
        [[nan nan nan]
         [nan  0.  1.]
         [nan  4.  5.]]
        """

        def __init__(
            self,
            data,
            position,
            size,
            wcs=None,
            mode="trim",
            fill_value=np.nan,
            copy=False,
            *,
            limit_rounding_method: LimitRoundingMethod = np.ceil,
        ):
            if wcs is None:
                wcs = getattr(data, "wcs", None)

            if isinstance(position, SkyCoord):
                if wcs is None:
                    raise ValueError("wcs must be input if position is a SkyCoord")
                position = skycoord_to_pixel(position, wcs, mode="all")  # (x, y)

            if np.isscalar(size):
                size = np.repeat(size, 2)

            # special handling for a scalar Quantity
            if isinstance(size, u.Quantity):
                size = np.atleast_1d(size)
                if len(size) == 1:
                    size = np.repeat(size, 2)

            if len(size) > 2:
                raise ValueError("size must have at most two elements")

            shape = np.zeros(2).astype(int)
            pixel_scales = None
            # ``size`` can have a mixture of int and Quantity (and even units),
            # so evaluate each axis separately
            for axis, side in enumerate(size):
                if not isinstance(side, u.Quantity):
                    shape[axis] = int(np.round(side))  # pixels
                else:
                    if side.unit == u.pixel:
                        shape[axis] = int(np.round(side.value))
                    elif side.unit.physical_type == "angle":
                        if wcs is None:
                            raise ValueError(
                                "wcs must be input if any element of size has angular units"
                            )
                        if pixel_scales is None:
                            pixel_scales = u.Quantity(
                                proj_plane_pixel_scales(wcs), wcs.wcs.cunit[axis]
                            )
                        shape[axis] = int(np.round((side / pixel_scales[axis]).decompose()))
                    else:
                        raise ValueError(
                            "shape can contain Quantities with only pixel or angular units"
                        )

            if not isinstance(
                data, (Section, CompImageSection)
            ):  # Accept lazy-loaded image sections
                data = np.asanyarray(data)
            # reverse position because extract_array and overlap_slices
            # use (y, x), but keep the input position
            pos_yx = position[::-1]

            cutout_data, input_position_cutout = extract_array(
                data,
                tuple(shape),
                pos_yx,
                mode=mode,
                fill_value=fill_value,
                return_position=True,
                limit_rounding_method=limit_rounding_method,
            )
            if copy:
                cutout_data = np.copy(cutout_data)
            self.data = cutout_data

            self.input_position_cutout = input_position_cutout[::-1]  # (x, y)
            slices_original, slices_cutout = overlap_slices(
                data.shape,
                shape,
                pos_yx,
                mode=mode,
                limit_rounding_method=limit_rounding_method,
            )

            self.slices_original = slices_original
            self.slices_cutout = slices_cutout

            self.shape = self.data.shape
            self.input_position_original = position
            self.shape_input = shape

            (
                (self.ymin_original, self.ymax_original),
                (self.xmin_original, self.xmax_original),
            ) = self.bbox_original

            (
                (self.ymin_cutout, self.ymax_cutout),
                (self.xmin_cutout, self.xmax_cutout),
            ) = self.bbox_cutout

            # the true origin pixel of the cutout array, including any
            # filled cutout values
            self._origin_original_true = (
                self.origin_original[0] - self.slices_cutout[1].start,
                self.origin_original[1] - self.slices_cutout[0].start,
            )

            if wcs is not None:
                self.wcs = deepcopy(wcs)
                self.wcs.wcs.crpix -= self._origin_original_true
                self.wcs.array_shape = self.data.shape
                if wcs.sip is not None:
                    self.wcs.sip = Sip(
                        wcs.sip.a,
                        wcs.sip.b,
                        wcs.sip.ap,
                        wcs.sip.bp,
                        wcs.sip.crpix - self._origin_original_true,
                    )
            else:
                self.wcs = None

        def to_original_position(self, cutout_position):
            """
            Convert an ``(x, y)`` position in the cutout array to the original
            ``(x, y)`` position in the original large array.

            Parameters
            ----------
            cutout_position : tuple
                The ``(x, y)`` pixel position in the cutout array.

            Returns
            -------
            original_position : tuple
                The corresponding ``(x, y)`` pixel position in the original
                large array.

            See Also
            --------
            to_cutout_position
            """
            return tuple(cutout_position[i] + self.origin_original[i] for i in [0, 1])

        def to_cutout_position(self, original_position):
            """
            Convert an ``(x, y)`` position in the original large array to
            the ``(x, y)`` position in the cutout array.

            Parameters
            ----------
            original_position : tuple
                The ``(x, y)`` pixel position in the original large array.

            Returns
            -------
            cutout_position : tuple
                The corresponding ``(x, y)`` pixel position in the cutout
                array.

            See Also
            --------
            to_original_position
            """
            return tuple(original_position[i] - self.origin_original[i] for i in [0, 1])

        def plot_on_original(self, ax=None, fill=False, **kwargs):
            """
            Plot the cutout region on a matplotlib Axes instance.

            Parameters
            ----------
            ax : `matplotlib.axes.Axes` instance, optional
                If `None`, then the current `matplotlib.axes.Axes` instance
                is used.

            fill : bool, optional
                Set whether to fill the cutout patch.  The default is
                `False`.

            kwargs : optional
                Any keyword arguments accepted by `matplotlib.patches.Patch`.

            Returns
            -------
            ax : `matplotlib.axes.Axes` instance
                The matplotlib Axes instance constructed in the method if
                ``ax=None``.  Otherwise the output ``ax`` is the same as the
                input ``ax``.
            """
            import matplotlib.patches as mpatches
            import matplotlib.pyplot as plt

            kwargs["fill"] = fill

            if ax is None:
                ax = plt.gca()

            xmin = self.xmin_original - 0.5
            xmax = self.xmax_original + 0.5

            ymin = self.ymin_original - 0.5
            ymax = self.ymax_original + 0.5

            pos_xy = (xmin, ymin)
            width = xmax - xmin
            height = ymax - ymin

            patch = mpatches.Rectangle(pos_xy, width, height, angle=0.0, **kwargs)
            ax.add_patch(patch)

            return ax

        @staticmethod
        def _calc_center(slices):
            """
            Calculate the center position.  The center position will be
            fractional for even-sized arrays.  For ``mode='partial'``, the
            central position is calculated for the valid (non-filled) cutout
            values.
            """
            return tuple(0.5 * (slices[i].start + slices[i].stop - 1) for i in [1, 0])

        @staticmethod
        def _calc_bbox(slices):
            """
            Calculate a minimal bounding box in the form ``((ymin, ymax),
            (xmin, xmax))``.  Note these are pixel locations, not slice
            indices.  For ``mode='partial'``, the bounding box indices are
            for the valid (non-filled) cutout values.
            """
            # (stop - 1) to return the max pixel location, not the slice index
            return (
                (slices[0].start, slices[0].stop - 1),
                (slices[1].start, slices[1].stop - 1),
            )

        @functools.cached_property
        def origin_original(self):
            """
            The ``(x, y)`` index of the origin pixel of the cutout with
            respect to the original array.  For ``mode='partial'``, the
            origin pixel is calculated for the valid (non-filled) cutout
            values.
            """
            return (self.slices_original[1].start, self.slices_original[0].start)

        @functools.cached_property
        def origin_cutout(self):
            """
            The ``(x, y)`` index of the origin pixel of the cutout with
            respect to the cutout array.  For ``mode='partial'``, the origin
            pixel is calculated for the valid (non-filled) cutout values.
            """
            return (self.slices_cutout[1].start, self.slices_cutout[0].start)

        @staticmethod
        def _round(a):
            """
            Round the input to the nearest integer.

            If two integers are equally close, the value is rounded up.
            Note that this is different from `np.round`, which rounds to the
            nearest even number.
            """
            return int(np.floor(a + 0.5))

        @functools.cached_property
        def position_original(self):
            """
            The ``(x, y)`` position index (rounded to the nearest pixel) in
            the original array.
            """
            return (
                self._round(self.input_position_original[0]),
                self._round(self.input_position_original[1]),
            )

        @functools.cached_property
        def position_cutout(self):
            """
            The ``(x, y)`` position index (rounded to the nearest pixel) in
            the cutout array.
            """
            return (
                self._round(self.input_position_cutout[0]),
                self._round(self.input_position_cutout[1]),
            )

        @functools.cached_property
        def center_original(self):
            """
            The central ``(x, y)`` position of the cutout array with respect
            to the original array.  For ``mode='partial'``, the central
            position is calculated for the valid (non-filled) cutout values.
            """
            return self._calc_center(self.slices_original)

        @functools.cached_property
        def center_cutout(self):
            """
            The central ``(x, y)`` position of the cutout array with respect
            to the cutout array.  For ``mode='partial'``, the central
            position is calculated for the valid (non-filled) cutout values.
            """
            return self._calc_center(self.slices_cutout)

        @functools.cached_property
        def bbox_original(self):
            """
            The bounding box ``((ymin, ymax), (xmin, xmax))`` of the minimal
            rectangular region of the cutout array with respect to the
            original array.  For ``mode='partial'``, the bounding box
            indices are for the valid (non-filled) cutout values.
            """
            return self._calc_bbox(self.slices_original)

        @functools.cached_property
        def bbox_cutout(self):
            """
            The bounding box ``((ymin, ymax), (xmin, xmax))`` of the minimal
            rectangular region of the cutout array with respect to the
            cutout array.  For ``mode='partial'``, the bounding box indices
            are for the valid (non-filled) cutout values.
            """
            return self._calc_bbox(self.slices_cutout)