gaussian_log_prob_pytorch.py

import math
import torch
from torch.distributions import Normal

# standard univariate Gaussian (Normal)
mean = torch.zeros(1)
std = torch.ones(1)

# evaluate at the origin
value = torch.zeros(1)

# using built-in functions
normal = Normal(mean, std)
log_density = normal.log_prob(value)

# implemented from scratch
var = std.pow(2)
log_density = -0.5 * (math.log(2 * math.pi) + var.log() + (value - mean).pow(2) / var)