code: def integrate_samples(volume_range, ts, density, channels):
      r"""
      Function integrating the model output.
  
      Args:
          volume_range: Specifies the integral range [t0, t1]
          ts: timesteps
          density: torch.Tensor [batch_size, *shape, n_samples, 1]
          channels: torch.Tensor [batch_size, *shape, n_samples, n_channels]
      returns:
          channels: integrated rgb output weights: torch.Tensor [batch_size, *shape, n_samples, 1] (density
          *transmittance)[i] weight for each rgb output at [..., i, :]. transmittance: transmittance of this volume
      )
      """
  
      # 1. Calculate the weights
      _, _, dt = volume_range.partition(ts)
      ddensity = density * dt
  
      mass = torch.cumsum(ddensity, dim=-2)
      transmittance = torch.exp(-mass[..., -1, :])
  
      alphas = 1.0 - torch.exp(-ddensity)
      Ts = torch.exp(
          torch.cat(
              [torch.zeros_like(mass[..., :1, :]), -mass[..., :-1, :]],
              dim=-2,
          )
      )
      # This is the probability of light hitting and reflecting off of
      # something at depth [..., i, :].
      weights = alphas * Ts
  
      # 2. Integrate channels
      channels = torch.sum(channels * weights, dim=-2)
  
      return channels, weights, transmittance
  
imports: import math
  from dataclasses import dataclass
  from typing import Dict, Optional, Tuple
  import numpy
  import torch
  import torch.nn.functional
  from torch import nn
  from ...configuration_utils import ConfigMixin, register_to_config
  from ...models import ModelMixin
  from ...utils import BaseOutput
  from .camera import create_pan_cameras
label_desc: Use image node_id 6 for calling a global function with example usage: integrate_samples(volume_range, ts, density, channels) and returns: channels,  weights,  transmittance