Proj/PyProj Convert between ocentric and ographic latitudes

Question

I am trying to use Pyproj to perform the conversion between ocentric and ographic latitudes. I can do this using the cct command line tool:

echo 0 45 | cct -z0 +proj=geoc +a=3396190 +b=3376200
  0.0000000000   44.6617680466        0.0000           inf

based on the docs here.

When attempting to do this with Pyproj, I would expect to be able to define the projects and then apply the transformation. Something akin to:

from pyproj import Proj, transform
ocentric = Proj(proj='geoc', a=3396190, b=3376200)
ographic = Proj(proj='latlon', a=3396190, b=3376200)

ographic(0,45)

I can get the ographic projection to instantiate without an issue, but the ocentric projection fails with an invalid CRS error: CRSError: Input is not a CRS: +proj=geoc +a=3396190 +b=3376200 +type=crs

If you have been able to define a geocentric projection on a custom ellipsoid, then how did you do it?

Note: I also tried:

from pyproj import Proj, transform
ocentric = Proj(proj='latlon', geoc=1, a=3396190, b=3376200)
ographic = Proj(proj='latlon', a=3396190, b=3376200)

transform(ocentric, ographic, 0, 45)

and I get an error that the input is not a transformation. I believe that geoc is being silently ignored in this example.

---

With help from @snowman2, I was able to define a pipeline to make the conversion work as follows.

trans = pyproj.transformer.Transformer.from_pipeline('+proj=pipeline +a=3396190 +b=3376200 +step +proj=geoc')
lon, lat = trans.transform(0, np.radians(45), errcheck=True)
np.degrees(lat) = #44.6617680466192

Note the weird np.radians call. When I run this transformation using 45 (as in degrees, which should be the default because radians=False is the transform default) I see: ProjError: transform error: latitude or longitude exceeded limits.

Answer 1

Based on the input from @snowman2 I was able to find a solution:

trans = pyproj.transformer.Transformer.from_pipeline('+proj=pipeline +a=3396190 +b=3376200 +step +proj=geoc')
lon, lat = trans.transform(0, np.radians(45), errcheck=True)
np.degrees(lat) = #44.6617680466192

The inverse is then:

itrans = pyproj.transformer.Transformer.from_pipeline('+proj=pipeline +a=3396190 +b=3376200 +step +proj=geoc +inv')
nlon, nlat = itrans.transform(lon, lat, errcheck=True, radians=True)
print(nlon, np.degrees(nlat))

The unit conversion is expected because of how the pipeline works. The proj pipeline documenation was really good for helping with the syntax of the Proj string.