import torch
import matplotlib.pyplot as plt

a = 0
d = 1
x = torch.linspace(a-d,a+d,steps=501)
exact = torch.heaviside(x-a,torch.Tensor([0.5]))
epsilons = torch.logspace(-3,-1,steps=4)

fig,ax = plt.subplots(1,1,figsize=(12,5))

ax.plot(x,exact,label="$\Theta(x-a)$",color='gray',linewidth=2)
for epsilon in epsilons:
    y = torch.sigmoid((x-a)/epsilon)
    ax.plot(x,y,label=f"$\sigma(x-a;\ \epsilon={epsilon:1.3f})$")

ax.legend()
plt.show()

<>:12: SyntaxWarning: invalid escape sequence '\T'
<>:15: SyntaxWarning: invalid escape sequence '\s'
<>:12: SyntaxWarning: invalid escape sequence '\T'
<>:15: SyntaxWarning: invalid escape sequence '\s'
/var/folders/n6/31w3bfts7_58b4b84hkndpd80000gn/T/ipykernel_56644/354324248.py:12: SyntaxWarning: invalid escape sequence '\T'
  ax.plot(x,exact,label="$\Theta(x-a)$",color='gray',linewidth=2)
/var/folders/n6/31w3bfts7_58b4b84hkndpd80000gn/T/ipykernel_56644/354324248.py:15: SyntaxWarning: invalid escape sequence '\s'
  ax.plot(x,y,label=f"$\sigma(x-a;\ \epsilon={epsilon:1.3f})$")