Plots of several tolerant Loss functions used by ceres

tolerant_loss.py

import numpy as np
import matplotlib.pyplot as plt


x = np.arange(0.001, 5, 0.001)

def Huber(a, d):
  x = np.zeros_like(a) 
  x[a<d] = 0.5 * a[a<d]**2
  x[a>=d] = d * (np.abs(a[a>=d]) - 0.5 * d)
 
  return x

def Cauchy(s):
  return np.log(1+s)

def ArcTan(s, a):
  return a* np.arctan(s / a)
 

plt.plot(x, Huber(x, 1), label="huber 1") 
plt.plot(x, Huber(x, 2), label="huber 2") 
plt.plot(x, Cauchy(x), label="cauchy")
plt.plot(x, ArcTan(x, 1), label="arctan")
plt.plot(x, ArcTan(x, 2), label="arctan2")
plt.plot(x, 0.5*x**2, label="squared")
plt.legend()
plt.ylim(0, 5)
plt.show()