import numpy as np
from scipy.optimize import curve_fit


def decay_model(x, amplitude, decay, baseline):
    return amplitude * np.exp(-decay * x) + baseline


x = np.linspace(0.0, 4.0, 9)
y = np.array([2.91, 1.77, 1.15, 0.82, 0.62, 0.51, 0.44, 0.41, 0.39])

initial_guess = (2.5, 1.0, 0.3)
bounds = (0.0, [5.0, 5.0, 2.0])

params, covariance = curve_fit(
    decay_model,
    x,
    y,
    p0=initial_guess,
    bounds=bounds,
)

stderr = np.sqrt(np.diag(covariance))
fit = decay_model(x, *params)
residuals = y - fit
rmse = np.sqrt(np.mean(residuals**2))
condition_number = np.linalg.cond(covariance)

print(f"parameters: amplitude={params[0]:.3f}, decay={params[1]:.3f}, baseline={params[2]:.3f}")
print(f"std_error: amplitude={stderr[0]:.3f}, decay={stderr[1]:.3f}, baseline={stderr[2]:.3f}")
print(f"rmse: {rmse:.3f}")
print(f"covariance_condition: {condition_number:.1f}")