import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

kb = 1.380649e-23  # Constante de Boltzmann

def helfrich_model(x, bend, stretch, kbT):
    bend = abs(bend)
    stretch = abs(stretch)
    term = stretch / bend + x**2
    result = kbT * (0.5 / stretch) * ((1 / x) - term ** -0.5)
    return result


def aproxHelfrich(x, y, T):
    x = np.array(x)
    y = np.array(y)
    kbT = kb * T

    def model_fixedT(x, bend, stretch):
        return helfrich_model(x, bend, stretch, kbT)

    try:
        popt, _ = curve_fit(model_fixedT, x, y, p0=[1.4e-19, 1e-7])
        bend, stretch = popt
        return abs(bend), abs(stretch)
    except RuntimeError:
        print("Error: La optimización no convergió")
        return None, None