text: import typing as T
  
  import numpy as np
  import numpy.typing as npt
  import xarray as xr
  
  from sarsen import geocoding, orbit
  
  
  def test_secant_method() -> None:
      def ufunc(
          t: npt.ArrayLike,
      ) -> T.Tuple[npt.NDArray[np.float64], npt.NDArray[np.float64]]:
          ft: npt.NDArray[np.float64] = np.asarray(t).astype("float64")
          retval = 1.0 + 0.015 * ft - 0.0001 * ft**2 + 0.00003 * ft**3
          return retval, retval
  
      t_start: npt.NDArray[np.timedelta64] = np.array([np.timedelta64(-100, "ns")])
  
      # stop with df threshold
      res, _, _, _ = geocoding.secant_method(ufunc, -t_start, t_start, diff_ufunc=0.1)
  
      assert isinstance(res, np.ndarray)
      assert res.size == 1
      assert res[0] == np.timedelta64(-27, "ns")
  
      # stop with dt threshold
      res, _, _, _ = geocoding.secant_method(ufunc, -t_start, t_start, diff_ufunc=0.01)
  
      assert res[0] == np.timedelta64(-27, "ns")
  
      t_start = np.ones((2, 2), dtype="timedelta64[ns]") * 100  # type: ignore
  
      res, _, _, _ = geocoding.secant_method(ufunc, -t_start, t_start, diff_ufunc=0.1)
  
      assert res.shape == t_start.shape
      assert np.all(res == np.timedelta64(-27, "ns"))
  
  
  def test_zero_doppler_plane_distance(
      dem_ecef: xr.DataArray, orbit_ds: xr.Dataset
  ) -> None:
      orbit_interpolator = orbit.OrbitPolyfitIterpolator.from_position(orbit_ds.position)
  
      res0, res1 = geocoding.zero_doppler_plane_distance(
          dem_ecef,
          orbit_interpolator.position(),
          orbit_interpolator.velocity(),
          orbit_ds.azimuth_time,
      )
  
      assert isinstance(res0, xr.DataArray)
      assert isinstance(res1, xr.DataArray)
  
  
  def test_backward_geocode(dem_ecef: xr.DataArray, orbit_ds: xr.Dataset) -> None:
      orbit_interpolator = orbit.OrbitPolyfitIterpolator.from_position(orbit_ds.position)
  
      res = geocoding.backward_geocode(
          dem_ecef,
          orbit_interpolator.position(),
          orbit_interpolator.velocity(),
      )
  
      assert isinstance(res, xr.Dataset)
  