text: """
  The transformer module is for performing cartographic transformations.
  """
  __all__ = [
      "transform",
      "itransform",
      "Transformer",
      "TransformerGroup",
      "AreaOfInterest",
  ]
  import threading
  import warnings
  from abc import ABC, abstractmethod
  from array import array
  from dataclasses import dataclass
  from itertools import chain, islice
  from pathlib import Path
  from typing import Any, Iterable, Iterator, List, Optional, Tuple, Union, overload
  
  from pyproj import CRS
  from pyproj._compat import cstrencode
  from pyproj._crs import AreaOfUse, CoordinateOperation
  from pyproj._transformer import (  # noqa: F401 pylint: disable=unused-import
      AreaOfInterest,
      _Transformer,
      _TransformerGroup,
      proj_version_str,
  )
  from pyproj.datadir import get_user_data_dir
  from pyproj.enums import ProjVersion, TransformDirection, WktVersion
  from pyproj.exceptions import ProjError
  from pyproj.sync import _download_resource_file
  from pyproj.utils import _convertback, _copytobuffer
  
  
  class TransformerMaker(ABC):
      """
      .. versionadded:: 3.1.0
  
      Base class for generating new instances
      of the Cython _Transformer class for
      thread safety in the Transformer class.
      """
  
      @abstractmethod
      def __call__(self) -> _Transformer:
          """
          Returns
          -------
          _Transformer
          """
          raise NotImplementedError
  
  
  @dataclass(frozen=True)
  class TransformerUnsafe(TransformerMaker):
      """
      .. versionadded:: 3.1.0
  
      Returns the original Cython _Transformer
      and is not thread-safe.
      """
  
      transformer: _Transformer
  
      def __call__(self) -> _Transformer:
          """
          Returns
          -------
          _Transformer
          """
          return self.transformer
  
  
  @dataclass(frozen=True)
  class TransformerFromCRS(TransformerMaker):
      """
      .. versionadded:: 3.1.0
  
      Generates a Cython _Transformer class from input CRS data.
      """
  
      crs_from: bytes
      crs_to: bytes
      always_xy: bool
      area_of_interest: Optional[AreaOfInterest]
      authority: Optional[str]
      accuracy: Optional[str]
      allow_ballpark: Optional[bool]
  
      def __call__(self) -> _Transformer:
          """
          Returns
          -------
          _Transformer
          """
          return _Transformer.from_crs(
              self.crs_from,
              self.crs_to,
              always_xy=self.always_xy,
              area_of_interest=self.area_of_interest,
              authority=self.authority,
              accuracy=self.accuracy,
              allow_ballpark=self.allow_ballpark,
          )
  
  
  @dataclass(frozen=True)
  class TransformerFromPipeline(TransformerMaker):
      """
      .. versionadded:: 3.1.0
  
      Generates a Cython _Transformer class from input pipeline data.
      """
  
      proj_pipeline: bytes
  
      def __call__(self) -> _Transformer:
          """
          Returns
          -------
          _Transformer
          """
          return _Transformer.from_pipeline(self.proj_pipeline)
  
  
  class TransformerGroup(_TransformerGroup):
      """
      The TransformerGroup is a set of possible transformers from one CRS to another.
  
      .. versionadded:: 2.3.0
  
      .. warning:: CoordinateOperation and Transformer objects
                   returned are not thread-safe.
  
      From PROJ docs::
  
          The operations are sorted with the most relevant ones first: by
          descending area (intersection of the transformation area with the
          area of interest, or intersection of the transformation with the
          area of use of the CRS), and by increasing accuracy. Operations
          with unknown accuracy are sorted last, whatever their area.
  
      """
  
      def __init__(
          self,
          crs_from: Any,
          crs_to: Any,
          skip_equivalent: bool = False,
          always_xy: bool = False,
          area_of_interest: Optional[AreaOfInterest] = None,
      ) -> None:
          """Get all possible transformations from a :obj:`pyproj.crs.CRS`
          or input used to create one.
  
          .. deprecated:: 3.1 skip_equivalent
  
          Parameters
          ----------
          crs_from: pyproj.crs.CRS or input used to create one
              Projection of input data.
          crs_to: pyproj.crs.CRS or input used to create one
              Projection of output data.
          skip_equivalent: bool, default=False
              DEPRECATED: If true, will skip the transformation operation
              if input and output projections are equivalent.
          always_xy: bool, default=False
              If true, the transform method will accept as input and return as output
              coordinates using the traditional GIS order, that is longitude, latitude
              for geographic CRS and easting, northing for most projected CRS.
          area_of_interest: :class:`pyproj.transformer.AreaOfInterest`, optional
              The area of interest to help order the transformations based on the
              best operation for the area.
  
          """
          if skip_equivalent:
              warnings.warn(
                  "skip_equivalent is deprecated.",
                  DeprecationWarning,
                  stacklevel=2,
              )
  
          super().__init__(
              CRS.from_user_input(crs_from)._crs,
              CRS.from_user_input(crs_to)._crs,
              always_xy=always_xy,
              area_of_interest=area_of_interest,
          )
          for iii, transformer in enumerate(self._transformers):
              # pylint: disable=unsupported-assignment-operation
              self._transformers[iii] = Transformer(TransformerUnsafe(transformer))
  
      @property
      def transformers(self) -> List["Transformer"]:
          """
          list[:obj:`Transformer`]:
              List of available :obj:`Transformer`
              associated with the transformation.
          """
          return self._transformers
  
      @property
      def unavailable_operations(self) -> List[CoordinateOperation]:
          """
          list[:obj:`pyproj.crs.CoordinateOperation`]:
              List of :obj:`pyproj.crs.CoordinateOperation` that are not
              available due to missing grids.
          """
          return self._unavailable_operations
  
      @property
      def best_available(self) -> bool:
          """
          bool: If True, the best possible transformer is available.
          """
          return self._best_available
  
      def download_grids(
          self,
          directory: Optional[Union[str, Path]] = None,
          open_license: bool = True,
          verbose: bool = False,
      ) -> None:
          """
          .. versionadded:: 3.0.0
  
          Download missing grids that can be downloaded automatically.
  
          .. warning:: There are cases where the URL to download the grid is missing.
                       In those cases, you can enable enable
                       :ref:`debugging-internal-proj` and perform a
                       transformation. The logs will show the grids PROJ searches for.
  
          Parameters
          ----------
          directory: str or Path, optional
              The directory to download the grids to.
              Defaults to :func:`pyproj.datadir.get_user_data_dir`
          open_license: bool, default=True
              If True, will only download grids with an open license.
          verbose: bool, default=False
              If True, will print information about grids downloaded.
          """
          if directory is None:
              directory = get_user_data_dir(True)
          # pylint: disable=not-an-iterable
          for unavailable_operation in self.unavailable_operations:
              for grid in unavailable_operation.grids:
                  if (
                      not grid.available
                      and grid.url.endswith(grid.short_name)
                      and grid.direct_download
                      and (grid.open_license or not open_license)
                  ):
                      _download_resource_file(
                          file_url=grid.url,
                          short_name=grid.short_name,
                          directory=directory,
                          verbose=verbose,
                      )
                  elif not grid.available and verbose:
                      warnings.warn(f"Skipped: {grid}")
  
      def __repr__(self) -> str:
          return (
              f"<TransformerGroup: best_available={self.best_available}>\n"
              f"- transformers: {len(self.transformers)}\n"
              f"- unavailable_operations: {len(self.unavailable_operations)}"
          )
  
  
  class TransformerLocal(threading.local):
      """
      Threading local instance for cython _Transformer class.
  
      For more details, see:
      https://github.com/pyproj4/pyproj/issues/782
      """
  
      def __init__(self):
          self.transformer = None  # Initialises in each thread
          super().__init__()
  
  
  class Transformer:
      """
      The Transformer class is for facilitating re-using
      transforms without needing to re-create them. The goal
      is to make repeated transforms faster.
  
      Additionally, it provides multiple methods for initialization.
  
      .. versionadded:: 2.1.0
  
      """
  
      def __init__(
          self,
          transformer_maker: Union[TransformerMaker, None] = None,
      ) -> None:
          if not isinstance(transformer_maker, TransformerMaker):
              ProjError.clear()
              raise ProjError(
                  "Transformer must be initialized using: "
                  "'from_crs', 'from_pipeline', or 'from_proj'."
              )
  
          self._local = TransformerLocal()
          self._local.transformer = transformer_maker()
          self._transformer_maker = transformer_maker
  
      @property
      def _transformer(self):
          """
          The Cython _Transformer object for this thread.
  
          Returns
          -------
          _Transformer
          """
          if self._local.transformer is None:
              self._local.transformer = self._transformer_maker()
          return self._local.transformer
  
      @property
      def name(self) -> str:
          """
          str: Name of the projection.
          """
          return self._transformer.id
  
      @property
      def description(self) -> str:
          """
          str: Description of the projection.
          """
          return self._transformer.description
  
      @property
      def definition(self) -> str:
          """
          str: Definition of the projection.
          """
          return self._transformer.definition
  
      @property
      def has_inverse(self) -> bool:
          """
          bool: True if an inverse mapping exists.
          """
          return self._transformer.has_inverse
  
      @property
      def accuracy(self) -> float:
          """
          float: Expected accuracy of the transformation. -1 if unknown.
          """
          return self._transformer.accuracy
  
      @property
      def area_of_use(self) -> AreaOfUse:
          """
          .. versionadded:: 2.3.0
  
          Returns
          -------
          AreaOfUse:
              The area of use object with associated attributes.
          """
          return self._transformer.area_of_use
  
      @property
      def remarks(self) -> str:
          """
          .. versionadded:: 2.4.0
  
          Returns
          -------
          str:
              Remarks about object.
          """
          return self._transformer.remarks
  
      @property
      def scope(self) -> str:
          """
          .. versionadded:: 2.4.0
  
          Returns
          -------
          str:
              Scope of object.
          """
          return self._transformer.scope
  
      @property
      def operations(self) -> Optional[Tuple[CoordinateOperation]]:
          """
          .. versionadded:: 2.4.0
  
          Returns
          -------
          Tuple[CoordinateOperation]:
              The operations in a concatenated operation.
          """
          return self._transformer.operations
  
      @property
      def is_network_enabled(self) -> bool:
          """
          .. versionadded:: 3.0.0
  
          bool:
              If the network is enabled.
          """
          return self._transformer.is_network_enabled
  
      @staticmethod
      def from_proj(
          proj_from: Any,
          proj_to: Any,
          skip_equivalent: bool = False,
          always_xy: bool = False,
          area_of_interest: Optional[AreaOfInterest] = None,
      ) -> "Transformer":
          """Make a Transformer from a :obj:`pyproj.Proj` or input used to create one.
  
          .. versionadded:: 2.1.2 skip_equivalent
          .. versionadded:: 2.2.0 always_xy
          .. versionadded:: 2.3.0 area_of_interest
          .. deprecated:: 3.1 skip_equivalent
  
          Parameters
          ----------
          proj_from: :obj:`pyproj.Proj` or input used to create one
              Projection of input data.
          proj_to: :obj:`pyproj.Proj` or input used to create one
              Projection of output data.
          skip_equivalent: bool, default=False
              DEPRECATED: If true, will skip the transformation operation
              if input and output projections are equivalent.
          always_xy: bool, default=False
              If true, the transform method will accept as input and return as output
              coordinates using the traditional GIS order, that is longitude, latitude
              for geographic CRS and easting, northing for most projected CRS.
          area_of_interest: :class:`pyproj.transformer.AreaOfInterest`, optional
              The area of interest to help select the transformation.
  
          Returns
          -------
          Transformer
  
          """
          # pylint: disable=import-outside-toplevel
          from pyproj import Proj
  
          if not isinstance(proj_from, Proj):
              proj_from = Proj(proj_from)
          if not isinstance(proj_to, Proj):
              proj_to = Proj(proj_to)
  
          return Transformer.from_crs(
              proj_from.crs,
              proj_to.crs,
              skip_equivalent=skip_equivalent,
              always_xy=always_xy,
              area_of_interest=area_of_interest,
          )
  
      @staticmethod
      def from_crs(
          crs_from: Any,
          crs_to: Any,
          skip_equivalent: bool = False,
          always_xy: bool = False,
          area_of_interest: Optional[AreaOfInterest] = None,
          authority: Optional[str] = None,
          accuracy: Optional[float] = None,
          allow_ballpark: Optional[bool] = None,
      ) -> "Transformer":
          """Make a Transformer from a :obj:`pyproj.crs.CRS` or input used to create one.
  
          .. versionadded:: 2.1.2 skip_equivalent
          .. versionadded:: 2.2.0 always_xy
          .. versionadded:: 2.3.0 area_of_interest
          .. versionadded:: 3.1.0 authority, accuracy, allow_ballpark
          .. deprecated:: 3.1 skip_equivalent
  
          Parameters
          ----------
          crs_from: pyproj.crs.CRS or input used to create one
              Projection of input data.
          crs_to: pyproj.crs.CRS or input used to create one
              Projection of output data.
          skip_equivalent: bool, default=False
              DEPRECATED: If true, will skip the transformation operation
              if input and output projections are equivalent.
          always_xy: bool, default=False
              If true, the transform method will accept as input and return as output
              coordinates using the traditional GIS order, that is longitude, latitude
              for geographic CRS and easting, northing for most projected CRS.
          area_of_interest: :class:`pyproj.transformer.AreaOfInterest`, optional
              The area of interest to help select the transformation.
          authority: str, optional
              When not specified, coordinate operations from any authority will be
              searched, with the restrictions set in the
              authority_to_authority_preference database table related to the
              authority of the source/target CRS themselves. If authority is set
              to “any”, then coordinate operations from any authority will be
              searched. If authority is a non-empty string different from "any",
              then coordinate operations will be searched only in that authority
              namespace (e.g. EPSG). Requires PROJ 8+.
          accuracy: float, optional
              The minimum desired accuracy (in metres) of the candidate
              coordinate operations. Requires PROJ 8+.
          allow_ballpark: bool, optional
              Set to False to disallow the use of Ballpark transformation
              in the candidate coordinate operations. Default is to allow.
              Requires PROJ 8+.
  
          Returns
          -------
          Transformer
  
          """
          if skip_equivalent:
              warnings.warn(
                  "skip_equivalent is deprecated.",
                  DeprecationWarning,
                  stacklevel=2,
              )
  
          return Transformer(
              TransformerFromCRS(
                  cstrencode(CRS.from_user_input(crs_from).srs),
                  cstrencode(CRS.from_user_input(crs_to).srs),
                  always_xy=always_xy,
                  area_of_interest=area_of_interest,
                  authority=authority,
                  accuracy=accuracy if accuracy is None else str(accuracy),
                  allow_ballpark=allow_ballpark,
              )
          )
  
      @staticmethod
      def from_pipeline(proj_pipeline: str) -> "Transformer":
          """Make a Transformer from a PROJ pipeline string.
  
          :ref:`pipeline`
  
          .. versionadded:: 3.1.0 AUTH:CODE string suppor (e.g. EPSG:1671)
  
          Allowed input:
            - a PROJ string
            - a WKT string
            - a PROJJSON string
            - an object code (e.g. "EPSG:1671"
              "urn:ogc:def:coordinateOperation:EPSG::1671")
            - an object name. e.g "ITRF2014 to ETRF2014 (1)".
              In that case as uniqueness is not guaranteed,
              heuristics are applied to determine the appropriate best match.
            - a OGC URN combining references for concatenated operations
              (e.g. "urn:ogc:def:coordinateOperation,coordinateOperation:EPSG::3895,
              coordinateOperation:EPSG::1618")
  
          Parameters
          ----------
          proj_pipeline: str
              Projection pipeline string.
  
          Returns
          -------
          Transformer
  
          """
          return Transformer(TransformerFromPipeline(cstrencode(proj_pipeline)))
  
      @overload
      def transform(  # pylint: disable=invalid-name
          self,
          xx: Any,
          yy: Any,
          radians: bool = False,
          errcheck: bool = False,
          direction: Union[TransformDirection, str] = TransformDirection.FORWARD,
          inplace: bool = False,
      ) -> Tuple[Any, Any]:
          ...
  
      @overload
      def transform(  # pylint: disable=invalid-name
          self,
          xx: Any,
          yy: Any,
          zz: Any,
          radians: bool = False,
          errcheck: bool = False,
          direction: Union[TransformDirection, str] = TransformDirection.FORWARD,
          inplace: bool = False,
      ) -> Tuple[Any, Any, Any]:
          ...
  
      @overload
      def transform(  # pylint: disable=invalid-name
          self,
          xx: Any,
          yy: Any,
          zz: Any,
          tt: Any,
          radians: bool = False,
          errcheck: bool = False,
          direction: Union[TransformDirection, str] = TransformDirection.FORWARD,
          inplace: bool = False,
      ) -> Tuple[Any, Any, Any, Any]:
          ...
  
      def transform(  # pylint: disable=invalid-name
          self,
          xx,
          yy,
          zz=None,
          tt=None,
          radians=False,
          errcheck=False,
          direction=TransformDirection.FORWARD,
          inplace=False,
      ):
          """
          Transform points between two coordinate systems.
  
          .. versionadded:: 2.1.1 errcheck
          .. versionadded:: 2.2.0 direction
          .. versionadded:: 3.2.0 inplace
  
          Parameters
          ----------
          xx: scalar or array (numpy or python)
              Input x coordinate(s).
          yy: scalar or array (numpy or python)
              Input y coordinate(s).
          zz: scalar or array (numpy or python), optional
              Input z coordinate(s).
          tt: scalar or array (numpy or python), optional
              Input time coordinate(s).
          radians: bool, default=False
              If True, will expect input data to be in radians and will return radians
              if the projection is geographic. Otherwise, it uses degrees.
              Ignored for pipeline transformations with pyproj 2,
              but will work in pyproj 3.
          errcheck: bool, default=False
              If True, an exception is raised if the errors are found in the process.
              If False, ``inf`` is returned for errors.
          direction: pyproj.enums.TransformDirection, optional
              The direction of the transform.
              Default is :attr:`pyproj.enums.TransformDirection.FORWARD`.
          inplace: bool, default=False
              If True, will attempt to write the results to the input array
              instead of returning a new array. This will fail if the input
              is not an array in C order with the double data type.
  
          Example
          --------
  
          >>> from pyproj import Transformer
          >>> transformer = Transformer.from_crs("epsg:4326", "epsg:3857")
          >>> x3, y3 = transformer.transform(33, 98)
          >>> f"{x3:.3f}  {y3:.3f}"
          '10909310.098  3895303.963'
          >>> pipeline_str = (
          ...     "+proj=pipeline +step +proj=longlat +ellps=WGS84 "
          ...     "+step +proj=unitconvert +xy_in=rad +xy_out=deg"
          ... )
          >>> pipe_trans = Transformer.from_pipeline(pipeline_str)
          >>> xt, yt = pipe_trans.transform(2.1, 0.001)
          >>> f"{xt:.3f}  {yt:.3f}"
          '2.100  0.001'
          >>> transproj = Transformer.from_crs(
          ...     {"proj":'geocent', "ellps":'WGS84', "datum":'WGS84'},
          ...     "EPSG:4326",
          ...     always_xy=True,
          ... )
          >>> xpj, ypj, zpj = transproj.transform(
          ...     -2704026.010,
          ...     -4253051.810,
          ...     3895878.820,
          ...     radians=True,
          ... )
          >>> f"{xpj:.3f} {ypj:.3f} {zpj:.3f}"
          '-2.137 0.661 -20.531'
          >>> transprojr = Transformer.from_crs(
          ...     "EPSG:4326",
          ...     {"proj":'geocent', "ellps":'WGS84', "datum":'WGS84'},
          ...     always_xy=True,
          ... )
          >>> xpjr, ypjr, zpjr = transprojr.transform(xpj, ypj, zpj, radians=True)
          >>> f"{xpjr:.3f} {ypjr:.3f} {zpjr:.3f}"
          '-2704026.010 -4253051.810 3895878.820'
          >>> transformer = Transformer.from_proj("epsg:4326", 4326)
          >>> xeq, yeq = transformer.transform(33, 98)
          >>> f"{xeq:.0f}  {yeq:.0f}"
          '33  98'
  
          """
          # process inputs, making copies that support buffer API.
          inx, x_data_type = _copytobuffer(xx, inplace=inplace)
          iny, y_data_type = _copytobuffer(yy, inplace=inplace)
          if zz is not None:
              inz, z_data_type = _copytobuffer(zz, inplace=inplace)
          else:
              inz = None
          if tt is not None:
              intime, t_data_type = _copytobuffer(tt, inplace=inplace)
          else:
              intime = None
          # call pj_transform.  inx,iny,inz buffers modified in place.
          self._transformer._transform(
              inx,
              iny,
              inz=inz,
              intime=intime,
              direction=direction,
              radians=radians,
              errcheck=errcheck,
          )
          # if inputs were lists, tuples or floats, convert back.
          outx = _convertback(x_data_type, inx)
          outy = _convertback(y_data_type, iny)
          return_data: Tuple[Any, ...] = (outx, outy)
          if inz is not None:
              return_data += (_convertback(z_data_type, inz),)
          if intime is not None:
              return_data += (_convertback(t_data_type, intime),)
          return return_data
  
      def itransform(
          self,
          points: Any,
          switch: bool = False,
          time_3rd: bool = False,
          radians: bool = False,
          errcheck: bool = False,
          direction: Union[TransformDirection, str] = TransformDirection.FORWARD,
      ) -> Iterator[Iterable]:
          """
          Iterator/generator version of the function pyproj.Transformer.transform.
  
          .. versionadded:: 2.1.1 errcheck
          .. versionadded:: 2.2.0 direction
  
          Parameters
          ----------
          points: list
              List of point tuples.
          switch: bool, default=False
              If True x, y or lon,lat coordinates of points are switched to y, x
              or lat, lon. Default is False.
          time_3rd: bool, default=False
              If the input coordinates are 3 dimensional and the 3rd dimension is time.
          radians: bool, default=False
              If True, will expect input data to be in radians and will return radians
              if the projection is geographic. Otherwise, it uses degrees.
              Ignored for pipeline transformations with pyproj 2,
              but will work in pyproj 3.
          errcheck: bool, default=False
              If True, an exception is raised if the errors are found in the process.
              If False, ``inf`` is returned for errors.
          direction: pyproj.enums.TransformDirection, optional
              The direction of the transform.
              Default is :attr:`pyproj.enums.TransformDirection.FORWARD`.
  
  
          Example
          --------
  
          >>> from pyproj import Transformer
          >>> transformer = Transformer.from_crs(4326, 2100)
          >>> points = [(22.95, 40.63), (22.81, 40.53), (23.51, 40.86)]
          >>> for pt in transformer.itransform(points): '{:.3f} {:.3f}'.format(*pt)
          '2221638.801 2637034.372'
          '2212924.125 2619851.898'
          '2238294.779 2703763.736'
          >>> pipeline_str = (
          ...     "+proj=pipeline +step +proj=longlat +ellps=WGS84 "
          ...     "+step +proj=unitconvert +xy_in=rad +xy_out=deg"
          ... )
          >>> pipe_trans = Transformer.from_pipeline(pipeline_str)
          >>> for pt in pipe_trans.itransform([(2.1, 0.001)]):
          ...     '{:.3f} {:.3f}'.format(*pt)
          '2.100 0.001'
          >>> transproj = Transformer.from_crs(
          ...     {"proj":'geocent', "ellps":'WGS84', "datum":'WGS84'},
          ...     "EPSG:4326",
          ...     always_xy=True,
          ... )
          >>> for pt in transproj.itransform(
          ...     [(-2704026.010, -4253051.810, 3895878.820)],
          ...     radians=True,
          ... ):
          ...     '{:.3f} {:.3f} {:.3f}'.format(*pt)
          '-2.137 0.661 -20.531'
          >>> transprojr = Transformer.from_crs(
          ...     "EPSG:4326",
          ...     {"proj":'geocent', "ellps":'WGS84', "datum":'WGS84'},
          ...     always_xy=True,
          ... )
          >>> for pt in transprojr.itransform(
          ...     [(-2.137, 0.661, -20.531)],
          ...     radians=True
          ... ):
          ...     '{:.3f} {:.3f} {:.3f}'.format(*pt)
          '-2704214.394 -4254414.478 3894270.731'
          >>> transproj_eq = Transformer.from_proj(
          ...     'EPSG:4326',
          ...     '+proj=longlat +datum=WGS84 +no_defs +type=crs',
          ...     always_xy=True,
          ... )
          >>> for pt in transproj_eq.itransform([(-2.137, 0.661)]):
          ...     '{:.3f} {:.3f}'.format(*pt)
          '-2.137 0.661'
  
          """
          point_it = iter(points)  # point iterator
          # get first point to check stride
          try:
              fst_pt = next(point_it)
          except StopIteration:
              raise ValueError("iterable must contain at least one point") from None
  
          stride = len(fst_pt)
          if stride not in (2, 3, 4):
              raise ValueError("points can contain up to 4 coordinates")
  
          if time_3rd and stride != 3:
              raise ValueError("'time_3rd' is only valid for 3 coordinates.")
  
          # create a coordinate sequence generator etc. x1,y1,z1,x2,y2,z2,....
          # chain so the generator returns the first point that was already acquired
          coord_gen = chain(
              fst_pt, (coords[c] for coords in point_it for c in range(stride))
          )
  
          while True:
              # create a temporary buffer storage for
              # the next 64 points (64*stride*8 bytes)
              buff = array("d", islice(coord_gen, 0, 64 * stride))
              if len(buff) == 0:
                  break
  
              self._transformer._transform_sequence(
                  stride,
                  buff,
                  switch=switch,
                  direction=direction,
                  time_3rd=time_3rd,
                  radians=radians,
                  errcheck=errcheck,
              )
  
              for point in zip(*([iter(buff)] * stride)):
                  yield point
  
      def transform_bounds(
          self,
          left: float,
          bottom: float,
          right: float,
          top: float,
          densify_pts: int = 21,
          radians: bool = False,
          errcheck: bool = False,
          direction: Union[TransformDirection, str] = TransformDirection.FORWARD,
      ) -> Tuple[float, float, float, float]:
          """
          .. versionadded:: 3.1.0
  
          Transform boundary densifying the edges to account for nonlinear
          transformations along these edges and extracting the outermost bounds.
  
          If the destination CRS is geographic and right < left then the bounds
          crossed the antimeridian. In this scenario there are two polygons,
          one on each side of the antimeridian. The first polygon should be
          constructed with (left, bottom, 180, top) and the second with
          (-180, bottom, top, right).
  
          To construct the bounding polygons with shapely::
  
              def bounding_polygon(left, bottom, right, top):
                  if right < left:
                      return shapely.geometry.MultiPolygon(
                          [
                              shapely.geometry.box(left, bottom, 180, top),
                              shapely.geometry.box(-180, bottom, right, top),
                          ]
                      )
                  return shapely.geometry.box(left, bottom, right, top)
  
          When projecting from polar projections to geographic,
          lon, lat output order is required. The 'always_xy' flag
          in the 'from_crs' constructor can help ensure that is the case.
  
  
          Parameters
          ----------
          left: float
              Left bounding coordinate in source CRS.
          bottom: float
              Bottom bounding coordinate in source CRS.
          right: float
              Right bounding coordinate in source CRS.
          top: float
              Top bounding coordinate in source CRS.
          densify_points: uint, default=21
              Number of points to add to each edge to account for nonlinear edges
              produced by the transform process. Large numbers will produce worse
              performance.
          radians: bool, default=False
              If True, will expect input data to be in radians and will return radians
              if the projection is geographic. Otherwise, it uses degrees.
          errcheck: bool, default=False
              If True, an exception is raised if the errors are found in the process.
              If False, ``inf`` is returned for errors.
          direction: pyproj.enums.TransformDirection, optional
              The direction of the transform.
              Default is :attr:`pyproj.enums.TransformDirection.FORWARD`.
  
          Returns
          -------
          left, bottom, right, top: float
              Outermost coordinates in target coordinate reference system.
          """
          return self._transformer._transform_bounds(
              left=left,
              bottom=bottom,
              right=right,
              top=top,
              densify_pts=densify_pts,
              radians=radians,
              errcheck=errcheck,
              direction=direction,
          )
  
      def to_proj4(
          self,
          version: Union[ProjVersion, str] = ProjVersion.PROJ_5,
          pretty: bool = False,
      ) -> str:
          """
          Convert the projection to a PROJ string.
  
          .. versionadded:: 3.1.0
  
          Parameters
          ----------
          version: pyproj.enums.ProjVersion
              The version of the PROJ string output.
              Default is :attr:`pyproj.enums.ProjVersion.PROJ_5`.
          pretty: bool, default=False
              If True, it will set the output to be a multiline string.
  
          Returns
          -------
          str:
              The PROJ string.
  
          """
          return self._transformer.to_proj4(version=version, pretty=pretty)
  
      def to_wkt(
          self,
          version: Union[WktVersion, str] = WktVersion.WKT2_2019,
          pretty: bool = False,
      ) -> str:
          """
          Convert the projection to a WKT string.
  
          Version options:
            - WKT2_2015
            - WKT2_2015_SIMPLIFIED
            - WKT2_2019
            - WKT2_2019_SIMPLIFIED
            - WKT1_GDAL
            - WKT1_ESRI
  
  
          Parameters
          ----------
          version: pyproj.enums.WktVersion, optional
              The version of the WKT output.
              Default is :attr:`pyproj.enums.WktVersion.WKT2_2019`.
          pretty: bool, default=False
              If True, it will set the output to be a multiline string.
  
          Returns
          -------
          str:
              The WKT string.
          """
          return self._transformer.to_wkt(version=version, pretty=pretty)
  
      def to_json(self, pretty: bool = False, indentation: int = 2) -> str:
          """
          Convert the projection to a JSON string.
  
          .. versionadded:: 2.4.0
  
          Parameters
          ----------
          pretty: bool, default=False
              If True, it will set the output to be a multiline string.
          indentation: int, default=2
              If pretty is True, it will set the width of the indentation.
  
          Returns
          -------
          str:
              The JSON string.
          """
          return self._transformer.to_json(pretty=pretty, indentation=indentation)
  
      def to_json_dict(self) -> dict:
          """
          Convert the projection to a JSON dictionary.
  
          .. versionadded:: 2.4.0
  
          Returns
          -------
          dict:
              The JSON dictionary.
          """
          return self._transformer.to_json_dict()
  
      def __str__(self) -> str:
          return self.definition
  
      def __repr__(self) -> str:
          return (
              f"<{self._transformer.type_name}: {self.name}>\n"
              f"Description: {self.description}\n"
              f"Area of Use:\n{self.area_of_use or '- undefined'}"
          )
  
      def __eq__(self, other: Any) -> bool:
          if not isinstance(other, Transformer):
              return False
          return self._transformer.__eq__(other._transformer)
  
      def is_exact_same(self, other: Any) -> bool:
          """
          Check if the Transformer objects are the exact same.
          If it is not a Transformer, then it returns False.
  
          Parameters
          ----------
          other: Any
  
          Returns
          -------
          bool
          """
          if not isinstance(other, Transformer):
              return False
          return self._transformer.is_exact_same(other._transformer)
  
  
  def transform(  # pylint: disable=invalid-name
      p1: Any,
      p2: Any,
      x: Any,
      y: Any,
      z: Any = None,
      tt: Any = None,
      radians: bool = False,
      errcheck: bool = False,
      skip_equivalent: bool = False,
      always_xy: bool = False,
  ):
      """
      .. versionadded:: 2.1.2 skip_equivalent
      .. versionadded:: 2.2.0 always_xy
      .. deprecated::3.1 skip_equivalent
  
      .. deprecated:: 2.6.1
          This function is deprecated. See: :ref:`upgrade_transformer`
  
      x2, y2, z2 = transform(p1, p2, x1, y1, z1)
  
      Transform points between two coordinate systems defined by the
      Proj instances p1 and p2.
  
      The points x1,y1,z1 in the coordinate system defined by p1 are
      transformed to x2,y2,z2 in the coordinate system defined by p2.
  
      z1 is optional, if it is not set it is assumed to be zero (and
      only x2 and y2 are returned). If the optional keyword
      'radians' is True (default is False), then all input and
      output coordinates will be in radians instead of the default
      of degrees for geographic input/output projections.
      If the optional keyword 'errcheck' is set to True an
      exception is raised if the transformation is
      invalid. By default errcheck=False and ``inf`` is returned for an
      invalid transformation (and no exception is raised).
      If `always_xy` is toggled, the transform method will accept as
      input and return as output coordinates using the traditional GIS order,
      that is longitude, latitude for geographic CRS and easting,
      northing for most projected CRS.
  
      In addition to converting between cartographic and geographic
      projection coordinates, this function can take care of datum
      shifts (which cannot be done using the __call__ method of the
      Proj instances). It also allows for one of the coordinate
      systems to be geographic (proj = 'latlong').
  
      x,y and z can be numpy or regular python arrays, python
      lists/tuples or scalars. Arrays are fastest.  For projections in
      geocentric coordinates, values of x and y are given in meters.
      z is always meters.
  
      Example usage:
  
      >>> from pyproj import Proj, transform
      >>> # projection 1: UTM zone 15, grs80 ellipse, NAD83 datum
      >>> # (defined by epsg code 26915)
      >>> p1 = Proj('epsg:26915', preserve_units=False)
      >>> # projection 2: UTM zone 15, clrk66 ellipse, NAD27 datum
      >>> p2 = Proj('epsg:26715', preserve_units=False)
      >>> # find x,y of Jefferson City, MO.
      >>> x1, y1 = p1(-92.199881,38.56694)
      >>> # transform this point to projection 2 coordinates.
      >>> x2, y2 = transform(p1,p2,x1,y1)
      >>> '%9.3f %11.3f' % (x1,y1)
      '569704.566 4269024.671'
      >>> '%9.3f %11.3f' % (x2,y2)
      '569722.342 4268814.028'
      >>> '%8.3f %5.3f' % p2(x2,y2,inverse=True)
      ' -92.200 38.567'
      >>> # process 3 points at a time in a tuple
      >>> lats = (38.83,39.32,38.75) # Columbia, KC and StL Missouri
      >>> lons = (-92.22,-94.72,-90.37)
      >>> x1, y1 = p1(lons,lats)
      >>> x2, y2 = transform(p1,p2,x1,y1)
      >>> xy = x1+y1
      >>> '%9.3f %9.3f %9.3f %11.3f %11.3f %11.3f' % xy
      '567703.344 351730.944 728553.093 4298200.739 4353698.725 4292319.005'
      >>> xy = x2+y2
      >>> '%9.3f %9.3f %9.3f %11.3f %11.3f %11.3f' % xy
      '567721.149 351747.558 728569.133 4297989.112 4353489.645 4292106.305'
      >>> lons, lats = p2(x2,y2,inverse=True)
      >>> xy = lons+lats
      >>> '%8.3f %8.3f %8.3f %5.3f %5.3f %5.3f' % xy
      ' -92.220  -94.720  -90.370 38.830 39.320 38.750'
      """
      warnings.warn(
          (
              "This function is deprecated. "
              "See: https://pyproj4.github.io/pyproj/stable/"
              "gotchas.html#upgrading-to-pyproj-2-from-pyproj-1"
          ),
          DeprecationWarning,
          stacklevel=2,
      )
      return Transformer.from_proj(
          p1, p2, skip_equivalent=skip_equivalent, always_xy=always_xy
      ).transform(xx=x, yy=y, zz=z, tt=tt, radians=radians, errcheck=errcheck)
  
  
  def itransform(  # pylint: disable=invalid-name
      p1: Any,
      p2: Any,
      points: Iterable[Iterable],
      switch: bool = False,
      time_3rd: bool = False,
      radians: bool = False,
      errcheck: bool = False,
      skip_equivalent: bool = False,
      always_xy: bool = False,
  ):
      """
      .. versionadded:: 2.1.2 skip_equivalent
      .. versionadded:: 2.2.0 always_xy
      .. deprecated::3.1 skip_equivalent
  
      .. deprecated:: 2.6.1
          This function is deprecated. See: :ref:`upgrade_transformer`
  
      points2 = itransform(p1, p2, points1)
      Iterator/generator version of the function pyproj.transform.
      Transform points between two coordinate systems defined by the
      Proj instances p1 and p2. This function can be used as an alternative
      to pyproj.transform when there is a need to transform a big number of
      coordinates lazily, for example when reading and processing from a file.
      Points1 is an iterable/generator of coordinates x1,y1(,z1) or lon1,lat1(,z1)
      in the coordinate system defined by p1. Points2 is an iterator that returns tuples
      of x2,y2(,z2) or lon2,lat2(,z2) coordinates in the coordinate system defined by p2.
      z are provided optionally.
  
      Points1 can be:
          - a tuple/list of tuples/lists i.e. for 2d points: [(xi,yi),(xj,yj),....(xn,yn)]
          - a Nx3 or Nx2 2d numpy array where N is the point number
          - a generator of coordinates (xi,yi) for 2d points or (xi,yi,zi) for 3d
  
      If optional keyword 'switch' is True (default is False) then x, y or lon,lat
      coordinates of points are switched to y, x or lat, lon.
      If the optional keyword 'radians' is True (default is False),
      then all input and output coordinates will be in radians instead
      of the default of degrees for geographic input/output projections.
      If the optional keyword 'errcheck' is set to True an
      exception is raised if the transformation is
      invalid. By default errcheck=False and ``inf`` is returned for an
      invalid transformation (and no exception is raised).
      If `always_xy` is toggled, the transform method will accept as
      input and return as output coordinates using the traditional GIS order,
      that is longitude, latitude for geographic CRS and easting, northing
      for most projected CRS.
  
  
      Example usage:
  
      >>> from pyproj import Proj, itransform
      >>> # projection 1: WGS84
      >>> # (defined by epsg code 4326)
      >>> p1 = Proj('epsg:4326', preserve_units=False)
      >>> # projection 2: GGRS87 / Greek Grid
      >>> p2 = Proj('epsg:2100', preserve_units=False)
      >>> # Three points with coordinates lon, lat in p1
      >>> points = [(22.95, 40.63), (22.81, 40.53), (23.51, 40.86)]
      >>> # transform this point to projection 2 coordinates.
      >>> for pt in itransform(p1,p2,points, always_xy=True): '%6.3f %7.3f' % pt
      '411050.470 4497928.574'
      '399060.236 4486978.710'
      '458553.243 4523045.485'
      >>> for pt in itransform(4326, 4326, [(30, 60)]):
      ...     '{:.0f} {:.0f}'.format(*pt)
      '30 60'
  
      """
      warnings.warn(
          (
              "This function is deprecated. "
              "See: https://pyproj4.github.io/pyproj/stable/"
              "gotchas.html#upgrading-to-pyproj-2-from-pyproj-1"
          ),
          DeprecationWarning,
          stacklevel=2,
      )
      return Transformer.from_proj(
          p1, p2, skip_equivalent=skip_equivalent, always_xy=always_xy
      ).itransform(
          points, switch=switch, time_3rd=time_3rd, radians=radians, errcheck=errcheck
      )
  