ellipticity definition

[sibirrer]

https://github.com/skypyproject/skypy/blob/55436b0bcec4e3ce79a92ba9ce6e91f1d96e7ea7/skypy/galaxy/ellipticity.py#L25

There are several different ellipticity definitions, such as eccentricity, minor/major axis ratio, ellipticity modulus, etc. I think it's important to define the definition clearly upfront.

[itrharrison]

I would be happy to abide by the GalSim naming convention

reduced shear
    :math:`|g| = \frac{a - b}{a + b}`
distortion
    :math:`|e| = \frac{a^2 - b^2}{a^2 + b^2}`
conformal shear
    :math:`\eta = \log(b/a)`
minor-to-major axis ratio
    :math:`q = \frac{b}{a}`

These can be thought of as a magnitude and a real-space position angle :math:`\beta`, or as
two components, e.g., :math:`g_1` and :math:`g_2`, with:

.. math::

    g_1 &= |g| \cos(2 \beta) \\
    g_2 &= |g| \sin(2 \beta)

[ntessore]

We are using the ellipticity (a-b)/(a+b). For the sake of clarity I would think it best we use no other definition. Agree that this should be stated clearly, a good place would be the galaxies package documentation page.

[sibirrer]

thanks @itrharrison @ntessore . I agree that we should consistently only use one definition, and g_1, g_2 is a good choice. Feel free to close this issue.