Nonlinear least square fit

import os
import matplotlib.pyplot as plt
import numpy as np
import scipy
os.chdir('/home/vg/Downloads/projects/ex19')
os.getcwd()
beta=(0.25,0.75,0.5)
def f(x,b0,b1,b2):
    return b0+b1*np.exp(-b2*x**2)

xdata=np.linspace(0,5,50)
y=f(xdata,*beta)
ydata=y+0.05*np.random.randn(len(xdata))
def g(beta):
    return ydata-f(xdata,*beta)

beta_start=(1,1,1)
beta_opt,beta_cov=scipy.optimize.leastsq(g,beta_start)
print(beta_opt)
fig,ax=plt.subplots()
ax.scatter(xdata,ydata,label='samples')
ax.plot(xdata,y,'r',lw=2,label='true model')
ax.plot(xdata,f(xdata,*beta_opt),'b',lw=2,label='fitted model')
ax.set_xlim(0,5)
ax.set_xlabel(r"$x$",fontsize=18)
ax.set_ylabel(r"$f(x,\beta)$",fontsize=18)
ax.legend()
ax.set_title("Nonlinear least square fitting")
plt.savefig("example19.png", dpi=100)
plt.show()
plt.close()
beta_opt,beta_cov=scipy.optimize.curve_fit(f,xdata,ydata)
print(beta_opt)