"""Poisson-kernel random-attractor regularizer for complex latent ensembles."""
import numpy as np


def poisson_density(phases, x, eps=1e-8):
    phases = np.asarray(phases)
    x = complex(x)
    r2 = min(abs(x) ** 2, 1.0 - eps)
    u = np.exp(1j * phases)
    den = 1.0 + r2 - 2.0 * np.real(np.conj(x) * u)
    return (1.0 - r2) / np.maximum(den, eps)


def poisson_nll(phases, x, eps=1e-8):
    return float(-np.mean(np.log(poisson_density(phases, x, eps))))


def compose_affine(maps, z):
    """Apply maps in chronological order; each map is (q, a), T(z)=q*z+a."""
    for q, a in maps:
        z = q * z + a
    return z


def estimate_attractor(maps, probes):
    """Finite backward-composition estimate, with stopped-gradient semantics in numpy."""
    vals = [compose_affine(maps, complex(p)) for p in probes]
    return complex(np.mean(vals))


def pk_loss(phases, xhat, eps=1e-8):
    return poisson_nll(phases, xhat, eps)


def sample_poisson_phases(x, n, rng):
    """Exact boundary sampling via the disk automorphism of uniform circle points."""
    u = np.exp(2j * np.pi * rng.random(n))
    x = complex(x)
    w = (u + x) / (1.0 + np.conj(x) * u)
    return np.angle(w)