Parametric fits: BazinFit and VillarFit¶

Parametric fits extract physically motivated parameters from transient flux light curves.

Synthetic SN-like light curve¶

In [ ]:

import light_curve as lc
import numpy as np

rng = np.random.default_rng(1)
t = np.linspace(-20, 100, 80)
# Bazin: f(t) = A * exp(-(t-t0)/fall) / (1 + exp(-(t-t0)/rise)) + B
A, t0, rise, fall, B = 100.0, 10.0, 5.0, 25.0, 5.0
flux = A * np.exp(-(t - t0) / fall) / (1 + np.exp(-(t - t0) / rise)) + B
flux_err = np.sqrt(flux) * 0.1
flux += rng.normal(0, flux_err)
print(f'n_obs: {len(t)}, peak flux: {flux.max():.1f}')

import light_curve as lc import numpy as np rng = np.random.default_rng(1) t = np.linspace(-20, 100, 80) # Bazin: f(t) = A * exp(-(t-t0)/fall) / (1 + exp(-(t-t0)/rise)) + B A, t0, rise, fall, B = 100.0, 10.0, 5.0, 25.0, 5.0 flux = A * np.exp(-(t - t0) / fall) / (1 + np.exp(-(t - t0) / rise)) + B flux_err = np.sqrt(flux) * 0.1 flux += rng.normal(0, flux_err) print(f'n_obs: {len(t)}, peak flux: {flux.max():.1f}')

n_obs: 80, peak flux: 65.6

BazinFit¶

Fits a rising/falling exponential (Bazin function) with 5 free parameters: ( f(t) = A \cdot e^{-(t-t_0)/t_\text{fall}} / (1 + e^{-(t-t_0)/t_\text{rise}}) + B )

Output: amplitude, rise time, fall time, reference time, baseline, and reduced (\chi^2).

In [ ]:

fit = lc.BazinFit(algorithm='mcmc-ceres')
result = fit(t, flux, flux_err)
for name, val in zip(fit.names, result):
    print(f'  {name:30s} = {val:.4f}')

fit = lc.BazinFit(algorithm='mcmc-ceres') result = fit(t, flux, flux_err) for name, val in zip(fit.names, result): print(f' {name:30s} = {val:.4f}')

VillarFit¶

Fits the Villar function — a more flexible Gaussian+plateau model for SN classification with 7 parameters:

In [ ]:

vfit = lc.VillarFit(algorithm='ceres')
result_v = vfit(t, flux, flux_err)
for name, val in zip(vfit.names, result_v):
    print(f'  {name:30s} = {val:.4f}')

vfit = lc.VillarFit(algorithm='ceres') result_v = vfit(t, flux, flux_err) for name, val in zip(vfit.names, result_v): print(f' {name:30s} = {val:.4f}')

Notes¶

• Both features operate on flux light curves (not magnitude). Use positive flux values.
• Available solvers: 'ceres' (fast, gradient), 'mcmc-ceres' (MCMC + refinement), 'lmsder' (requires GSL).
• See also LinexpFit for the linear-exponential model.
• API reference