code: def log_normal_pdf(x, mean, logvar):
      const = (
          torch.from_numpy(np.array([2.0 * np.pi])).float().to(x.device)
      )
      const = torch.log(const)
      return -0.5 * (
          const + logvar + (x - mean) ** 2.0 / torch.exp(logvar)
      )
  
imports: import os
  import argparse
  import logging
  import time
  import numpy
  import numpy.random
  import matplotlib
  import matplotlib.pyplot
  import torch
  import torch.nn
  import torch.optim
  import torch.nn.functional
label_desc: Use image node_id 2 for calling a global function with example usage: log_normal_pdf(x, mean, logvar) and returns: unknown