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# Source code for astropy.wcs.wcsapi.low_level_api

    import abc
    import os

    import numpy as np

    __all__ = ["BaseLowLevelWCS", "validate_physical_types"]

    class BaseLowLevelWCS(metaclass=abc.ABCMeta):
        """
        Abstract base class for the low-level WCS interface.

        This is described in `APE 14: A shared Python interface for World Coordinate
        Systems <https://doi.org/10.5281/zenodo.1188875>`_.
        """

        @property
        @abc.abstractmethod
        def pixel_n_dim(self):
            """
            The number of axes in the pixel coordinate system.
            """

        @property
        @abc.abstractmethod
        def world_n_dim(self):
            """
            The number of axes in the world coordinate system.
            """

        @property
        @abc.abstractmethod
        def world_axis_physical_types(self):
            """
            An iterable of strings describing the physical type for each world axis.

            These should be names from the VO UCD1+ controlled Vocabulary
            (http://www.ivoa.net/documents/latest/UCDlist.html). If no matching UCD
            type exists, this can instead be ``"custom:xxx"``, where ``xxx`` is an
            arbitrary string.  Alternatively, if the physical type is
            unknown/undefined, an element can be `None`.
            """

        @property
        @abc.abstractmethod
        def world_axis_units(self):
            """
            An iterable of strings given the units of the world coordinates for each
            axis.

            The strings should follow the `IVOA VOUnit standard
            <http://ivoa.net/documents/VOUnits/>`_ (though as noted in the VOUnit
            specification document, units that do not follow this standard are still
            allowed, but just not recommended).
            """

        @abc.abstractmethod
        def pixel_to_world_values(self, *pixel_arrays):
            """
            Convert pixel coordinates to world coordinates.

            This method takes `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim` scalars or arrays as
            input, and pixel coordinates should be zero-based. Returns
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_n_dim` scalars or arrays in units given by
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_units`. Note that pixel coordinates are
            assumed to be 0 at the center of the first pixel in each dimension. If a
            pixel is in a region where the WCS is not defined, NaN should be returned.
            The coordinates should be specified in the ``(x, y)`` order, where for
            an image, ``x`` is the horizontal coordinate and ``y`` is the vertical
            coordinate.

            If `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_n_dim` is ``1``, this
            method returns a single scalar or array, otherwise a tuple of scalars or
            arrays is returned.
            """

        def array_index_to_world_values(self, *index_arrays):
            """
            Convert array indices to world coordinates.

            This is the same as `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_to_world_values` except that
            the indices should be given in ``(i, j)`` order, where for an image
            ``i`` is the row and ``j`` is the column (i.e. the opposite order to
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_to_world_values`).

            If `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_n_dim` is ``1``, this
            method returns a single scalar or array, otherwise a tuple of scalars or
            arrays is returned.
            """
            return self.pixel_to_world_values(*index_arrays[::-1])

        @abc.abstractmethod
        def world_to_pixel_values(self, *world_arrays):
            """
            Convert world coordinates to pixel coordinates.

            This method takes `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_n_dim` scalars or arrays as
            input in units given by `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_units`. Returns
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim` scalars or arrays. Note that pixel
            coordinates are assumed to be 0 at the center of the first pixel in each
            dimension. If a world coordinate does not have a matching pixel
            coordinate, NaN should be returned.  The coordinates should be returned in
            the ``(x, y)`` order, where for an image, ``x`` is the horizontal
            coordinate and ``y`` is the vertical coordinate.

            If `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim` is ``1``, this
            method returns a single scalar or array, otherwise a tuple of scalars or
            arrays is returned.
            """

        def world_to_array_index_values(self, *world_arrays):
            """
            Convert world coordinates to array indices.

            This is the same as `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_to_pixel_values` except that
            the indices should be returned in ``(i, j)`` order, where for an image
            ``i`` is the row and ``j`` is the column (i.e. the opposite order to
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_to_world_values`). The indices should be
            returned as rounded integers.

            If `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim` is ``1``, this
            method returns a single scalar or array, otherwise a tuple of scalars or
            arrays is returned.
            """
            pixel_arrays = self.world_to_pixel_values(*world_arrays)
            if self.pixel_n_dim == 1:
                pixel_arrays = (pixel_arrays,)
            else:
                pixel_arrays = pixel_arrays[::-1]
            array_indices = tuple(
                np.asarray(np.floor(pixel + 0.5), dtype=int) for pixel in pixel_arrays
            )
            return array_indices[0] if self.pixel_n_dim == 1 else array_indices

        @property
        @abc.abstractmethod
        def world_axis_object_components(self):
            """
            A list with `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_n_dim` elements giving information
            on constructing high-level objects for the world coordinates.

            Each element of the list is a tuple with three items:

            * The first is a name for the world object this world array
              corresponds to, which *must* match the string names used in
              `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_object_classes`. Note that names might
              appear twice because two world arrays might correspond to a single
              world object (e.g. a celestial coordinate might have both “ra” and
              “dec” arrays, which correspond to a single sky coordinate object).

            * The second element is either a string keyword argument name or a
              positional index for the corresponding class from
              `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_object_classes`.

            * The third argument is a string giving the name of the property
              to access on the corresponding class from
              `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_object_classes` in
              order to get numerical values. Alternatively, this argument can be a
              callable Python object that takes a high-level coordinate object and
              returns the numerical values suitable for passing to the low-level
              WCS transformation methods.

            See the document
            `APE 14: A shared Python interface for World Coordinate Systems
            <https://doi.org/10.5281/zenodo.1188875>`_ for examples.
            """

        @property
        @abc.abstractmethod
        def world_axis_object_classes(self):
            """
            A dictionary giving information on constructing high-level objects for
            the world coordinates.

            Each key of the dictionary is a string key from
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_object_components`, and each value is a
            tuple with three elements or four elements:

            * The first element of the tuple must be a class or a string specifying
              the fully-qualified name of a class, which will specify the actual
              Python object to be created.

            * The second element, should be a tuple specifying the positional
              arguments required to initialize the class. If
              `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_object_components` specifies that the
              world coordinates should be passed as a positional argument, this this
              tuple should include `None` placeholders for the world coordinates.

            * The third tuple element must be a dictionary with the keyword
              arguments required to initialize the class.

            * Optionally, for advanced use cases, the fourth element (if present)
              should be a callable Python object that gets called instead of the
              class and gets passed the positional and keyword arguments. It should
              return an object of the type of the first element in the tuple.

            Note that we don't require the classes to be Astropy classes since there
            is no guarantee that Astropy will have all the classes to represent all
            kinds of world coordinates. Furthermore, we recommend that the output be
            kept as human-readable as possible.

            The classes used here should have the ability to do conversions by
            passing an instance as the first argument to the same class with
            different arguments (e.g. ``Time(Time(...), scale='tai')``). This is
            a requirement for the implementation of the high-level interface.

            The second and third tuple elements for each value of this dictionary
            can in turn contain either instances of classes, or if necessary can
            contain serialized versions that should take the same form as the main
            classes described above (a tuple with three elements with the fully
            qualified name of the class, then the positional arguments and the
            keyword arguments). For low-level API objects implemented in Python, we
            recommend simply returning the actual objects (not the serialized form)
            for optimal performance. Implementations should either always or never
            use serialized classes to represent Python objects, and should indicate
            which of these they follow using the
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.serialized_classes` attribute.

            See the document
            `APE 14: A shared Python interface for World Coordinate Systems
            <https://doi.org/10.5281/zenodo.1188875>`_ for examples .
            """

        # The following three properties have default fallback implementations, so
        # they are not abstract.

        @property
        def array_shape(self):
            """
            The shape of the data that the WCS applies to as a tuple of length
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim` in ``(row, column)``
            order (the convention for arrays in Python).

            If the WCS is valid in the context of a dataset with a particular
            shape, then this property can be used to store the shape of the
            data. This can be used for example if implementing slicing of WCS
            objects. This is an optional property, and it should return `None`
            if a shape is not known or relevant.
            """
            if self.pixel_shape is None:
                return None
            else:
                return self.pixel_shape[::-1]

        @property
        def pixel_shape(self):
            """
            The shape of the data that the WCS applies to as a tuple of length
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim` in ``(x, y)``
            order (where for an image, ``x`` is the horizontal coordinate and ``y``
            is the vertical coordinate).

            If the WCS is valid in the context of a dataset with a particular
            shape, then this property can be used to store the shape of the
            data. This can be used for example if implementing slicing of WCS
            objects. This is an optional property, and it should return `None`
            if a shape is not known or relevant.

            If you are interested in getting a shape that is comparable to that of
            a Numpy array, you should use
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.array_shape` instead.
            """
            return None

        @property
        def pixel_bounds(self):
            """
            The bounds (in pixel coordinates) inside which the WCS is defined,
            as a list with `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim`
            ``(min, max)`` tuples.

            The bounds should be given in ``[(xmin, xmax), (ymin, ymax)]``
            order. WCS solutions are sometimes only guaranteed to be accurate
            within a certain range of pixel values, for example when defining a
            WCS that includes fitted distortions. This is an optional property,
            and it should return `None` if a shape is not known or relevant.

            The bounds can be a mix of values along dimensions where bounds exist,
            and None for other dimensions, e.g. ``[(xmin, xmax), None]``.
            """
            return None

        @property
        def pixel_axis_names(self):
            """
            An iterable of strings describing the name for each pixel axis.

            If an axis does not have a name, an empty string should be returned
            (this is the default behavior for all axes if a subclass does not
            override this property). Note that these names are just for display
            purposes and are not standardized.
            """
            return [""] * self.pixel_n_dim

        @property
        def world_axis_names(self):
            """
            An iterable of strings describing the name for each world axis.

            If an axis does not have a name, an empty string should be returned
            (this is the default behavior for all axes if a subclass does not
            override this property). Note that these names are just for display
            purposes and are not standardized. For standardized axis types, see
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.world_axis_physical_types`.
            """
            return [""] * self.world_n_dim

        @property
        def axis_correlation_matrix(self):
            """
            Returns an (`~astropy.wcs.wcsapi.BaseLowLevelWCS.world_n_dim`,
            `~astropy.wcs.wcsapi.BaseLowLevelWCS.pixel_n_dim`) matrix that
            indicates using booleans whether a given world coordinate depends on a
            given pixel coordinate.

            This defaults to a matrix where all elements are `True` in the absence
            of any further information. For completely independent axes, the
            diagonal would be `True` and all other entries `False`.
            """
            return np.ones((self.world_n_dim, self.pixel_n_dim), dtype=bool)

        @property
        def serialized_classes(self):
            """
            Indicates whether Python objects are given in serialized form or as
            actual Python objects.
            """
            return False

        def _as_mpl_axes(self):
            """Compatibility hook for Matplotlib and WCSAxes.

            With this method, one can do::

                from astropy.wcs import WCS
                import matplotlib.pyplot as plt
                wcs = WCS('filename.fits')
                fig = plt.figure()
                ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs)
                ...

            and this will generate a plot with the correct WCS coordinates on the
            axes.
            """
            from astropy.visualization.wcsaxes import WCSAxes

            return WCSAxes, {"wcs": self}

    UCDS_FILE = os.path.join(os.path.dirname(__file__), "data", "ucds.txt")
    with open(UCDS_FILE) as f:
        VALID_UCDS = {x.strip() for x in f.read().splitlines()[1:]}

    def validate_physical_types(physical_types):
        """
        Validate a list of physical types against the UCD1+ standard.
        """
        for physical_type in physical_types:
            if (
                physical_type is not None
                and physical_type not in VALID_UCDS
                and not physical_type.startswith("custom:")
            ):
                raise ValueError(
                    f"'{physical_type}' is not a valid IOVA UCD1+ physical type. It must be"
                    " a string specified in the list"
                    " (http://www.ivoa.net/documents/latest/UCDlist.html) or if no"
                    " matching type exists it can be any string prepended with 'custom:'."
                )