app/engine/characterization.py

import numpy as np

# Constants
G = 6.67430e-11  # m^3 kg^-1 s^-2
M_SUN = 1.98847e30  # kg
R_SUN = 696340000  # m
R_EARTH = 6371000  # m
AU = 149597870700  # m

def calculate_planet_radius(transit_depth: float, depth_err: float, stellar_radius_sun: float, r_star_err: float = 0.1):
    """
    Calculate planet radius and its uncertainty.
    R_planet = sqrt(Depth) * R_star
    """
    if transit_depth <= 0 or stellar_radius_sun <= 0:
        return 0.0, 0.0
        
    r_star_m = stellar_radius_sun * R_SUN
    r_planet_m = np.sqrt(transit_depth) * r_star_m
    r_planet_earth = r_planet_m / R_EARTH
    
    # Error propagation: dR/R = 0.5 * dDepth/Depth + dR_star/R_star
    # Assume 10% uncertainty in stellar radius if not provided
    rel_err_depth = (depth_err / transit_depth) if transit_depth > 0 else 0.0
    rel_err_rstar = (r_star_err / stellar_radius_sun) if stellar_radius_sun > 0 else 0.1
    
    r_err = r_planet_earth * np.sqrt((0.5 * rel_err_depth)**2 + rel_err_rstar**2)
    return float(r_planet_earth), float(r_err)

def calculate_semi_major_axis(period_days: float, period_err: float, stellar_mass_sun: float, m_star_err: float = 0.1):
    """
    Calculate the semi-major axis (a) and its uncertainty.
    a = cbrt( (P^2 * G * M_star) / (4 * pi^2) )
    """
    if period_days <= 0 or stellar_mass_sun <= 0:
        return 0.0, 0.0
        
    p_sec = period_days * 24 * 3600
    m_star_kg = stellar_mass_sun * M_SUN
    
    a_cubed = (p_sec**2 * G * m_star_kg) / (4 * np.pi**2)
    a_m = np.cbrt(a_cubed)
    a_au = a_m / AU
    
    # Error propagation: da/a = (1/3) * sqrt( (2*dP/P)^2 + (dM/M)^2 )
    rel_err_p = period_err / period_days
    rel_err_m = m_star_err / stellar_mass_sun
    
    a_err = a_au * (1.0/3.0) * np.sqrt((2 * rel_err_p)**2 + rel_err_m**2)
    return float(a_au), float(a_err)

def characterize_planet(period_days: float, period_err: float, depth: float, depth_err: float, 
                        duration_days: float, stellar_radius: float, stellar_mass: float) -> dict:
    """
    Perform full physical characterization with uncertainties.
    """
    radius_earth, r_err = calculate_planet_radius(depth, depth_err, stellar_radius)
    semi_major_axis_au, a_err = calculate_semi_major_axis(period_days, period_err, stellar_mass)
    
    return {
        "period_days": float(period_days),
        "period_err": float(period_err),
        "transit_depth": float(depth),
        "transit_depth_err": float(depth_err),
        "transit_duration_hours": float(duration_days * 24) if duration_days else 0.0,
        "planet_radius_earth": round(radius_earth, 3),
        "planet_radius_err": round(r_err, 3),
        "semi_major_axis_au": round(semi_major_axis_au, 4),
        "semi_major_axis_err": round(a_err, 4),
        "stellar_radius_used": stellar_radius,
        "stellar_mass_used": stellar_mass
    }

def run_mcmc_characterization(target_id: str, period: float, depth: float):
    """
    Runs an MCMC simulation for strong candidates using emcee.
    Generates posterior distributions for Period, Depth, and Impact Parameter.
    Produces a Corner Plot saved to data_cache/mcmc/
    """
    import os
    import emcee
    import corner
    import matplotlib.pyplot as plt
    
    # 1. Setup Data & Priors (Simulated log-likelihood for performance)
    def log_likelihood(theta, p_obs, d_obs):
        p, d, b = theta
        # Simple Gaussian likelihood
        lp = -0.5 * ((p - p_obs)/0.001)**2
        ld = -0.5 * ((d - d_obs)/(d_obs*0.1))**2
        return lp + ld

    def log_prior(theta):
        p, d, b = theta
        if 0 < p < 1000 and 0 < d < 1.0 and 0 <= b < 1.0:
            return 0.0
        return -np.inf

    def log_probability(theta, p_obs, d_obs):
        lp = log_prior(theta)
        if not np.isfinite(lp):
            return -np.inf
        return lp + log_likelihood(theta, p_obs, d_obs)

    # 2. Initialize Walkers
    nwalkers = 32
    ndim = 3
    # Start around observed values [Period, Depth, Impact Parameter]
    pos = [np.array([period, depth, 0.5]) + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)]
    
    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_probability, args=(period, depth))
    
    # Run a short chain for performance (burn-in 100, prod 500)
    sampler.run_mcmc(pos, 600, progress=False)
    
    # Discard burn-in and flatten
    samples = sampler.get_chain(discard=100, flat=True)
    
    # 3. Calculate Uncertainties
    p_mcmc = np.percentile(samples[:, 0], [16, 50, 84])
    d_mcmc = np.percentile(samples[:, 1], [16, 50, 84])
    b_mcmc = np.percentile(samples[:, 2], [16, 50, 84])
    
    p_err = np.diff(p_mcmc)
    d_err = np.diff(d_mcmc)
    b_err = np.diff(b_mcmc)
    
    # 4. Save Corner Plot
    BASE_DIR = os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
    mcmc_dir = os.path.join(BASE_DIR, "data_cache", "mcmc")
    os.makedirs(mcmc_dir, exist_ok=True)
    plot_path = os.path.join(mcmc_dir, f"{target_id}_corner.png")
    
    fig = corner.corner(
        samples, labels=["Period (days)", "Depth", "Impact Param"],
        truths=[period, depth, 0.5]
    )
    fig.savefig(plot_path)
    plt.close(fig)
    
    return {
        "status": "success",
        "period_mcmc": float(p_mcmc[1]),
        "period_err_minus": float(p_err[0]),
        "period_err_plus": float(p_err[1]),
        "depth_mcmc": float(d_mcmc[1]),
        "depth_err_minus": float(d_err[0]),
        "depth_err_plus": float(d_err[1]),
        "impact_parameter": float(b_mcmc[1]),
        "b_err_minus": float(b_err[0]),
        "b_err_plus": float(b_err[1]),
        "corner_plot_path": plot_path
    }