virgil.angles

Angles sampled as 2-D vectors, so that no prior has a wrap boundary. Put an AngleVector in a priors dict under an angle's path (in degrees, such as a binary's "pa" or an orbit's node), and fit, gauss_newton_mass and numpyro_model sample a vector v = r(cos θ, sin θ) at the site "<path>_vec" instead of the angle. The model receives θ in degrees, in [0°, 360°): numpyro_model records it as the deterministic site "<path>", and fit reports both.

from virgil.angles import AngleVector

priors = {"pa": AngleVector()}            # uniform, no wall at 0°/360°
priors = {"pa": AngleVector(350.0, 20.0)} # von Mises, mean 350°, κ = 20
priors = {"node": AngleVector(100.0, 4.0, axial=True)}  # known modulo 180°

The radius has a ring prior, ∝ exp(−(r − 1)²/2s²), whose mode is the unit circle, so that maximum a posteriori fits stay away from the origin, where θ is undefined. A von Mises prior enters as the chord √κ (v̂ − m̂), the same form as virgil's unprojected phase residuals (2 sin(Δ/2)/σ, with κ = 1/σ²), so every term has a least-squares form and Levenberg–Marquardt takes it. The density is normalized in the plane (with the von Mises normalizer on the circle, through i0e), so evidences stay normalized. The default, a uniform angle, is the invariant prior; a von Mises prior is strong information from an external measurement.

For orbits, orientation_priors samples 2Ω and ϖ = Ω + ω for position-only fits (so the node ambiguity is one point, not two modes), or Ω and ϖ when RVs fix the node.

Credit. The construction follows Octofitter's UniformCircular (Thompson et al. 2023, AJ 166, 164) and exoplanet's Angle (Foreman-Mackey et al. 2021, JOSS 6, 3285), which sample v ~ N(0, I). The ring and the von Mises chords are virgil's. No code is taken from either.