content: import torch
  import torch.nn.functional as F
  from torch.autograd import Variable
  import numpy as np
  from math import exp
  
  
  def gaussian(window_size, sigma):
      gauss = torch.Tensor([exp(-(x - window_size // 2) ** 2 / float(2 * sigma ** 2)) for x in range(window_size)])
      return gauss / gauss.sum()
  
  
  def create_window(window_size, channel):
      _1D_window = gaussian(window_size, 1.5).unsqueeze(1)
      _2D_window = _1D_window.mm(_1D_window.t()).float().unsqueeze(0).unsqueeze(0)
      window = Variable(_2D_window.expand(channel, 1, window_size, window_size).contiguous())
      return window
  
  
  def _ssim(img1, img2, window, window_size, channel, use_padding, size_average=True):
  
      if use_padding:
          padding_size = window_size // 2
      else:
          padding_size = 0
  
      mu1 = F.conv2d(img1, window, padding=padding_size, groups=channel)
      mu2 = F.conv2d(img2, window, padding=padding_size, groups=channel)
  
      mu1_sq = mu1.pow(2)
      mu2_sq = mu2.pow(2)
      mu1_mu2 = mu1 * mu2
  
      sigma1_sq = F.conv2d(img1 * img1, window, padding=padding_size, groups=channel) - mu1_sq
      sigma2_sq = F.conv2d(img2 * img2, window, padding=padding_size, groups=channel) - mu2_sq
      sigma12 = F.conv2d(img1 * img2, window, padding=padding_size, groups=channel) - mu1_mu2
  
      C1 = 0.01 ** 2
      C2 = 0.03 ** 2
  
      ssim_map = ((2 * mu1_mu2 + C1) * (2 * sigma12 + C2)) / ((mu1_sq + mu2_sq + C1) * (sigma1_sq + sigma2_sq + C2))
  
      if size_average:
          return ssim_map.mean()
      else:
          return ssim_map.mean(1).mean(1).mean(1)
  
  
  class SSIM(torch.nn.Module):
      def __init__(self, window_size=11, use_padding=True, size_average=True):
          super(SSIM, self).__init__()
          self.window_size = window_size
          self.size_average = size_average
          self.use_padding = use_padding
          self.channel = 1
          self.window = create_window(window_size, self.channel)
  
      def forward(self, img1, img2):
          (_, channel, _, _) = img1.size()
  
          if channel == self.channel and self.window.data.type() == img1.data.type():
              window = self.window
          else:
              window = create_window(self.window_size, channel)
  
              if img1.is_cuda:
                  window = window.cuda(img1.get_device())
              window = window.type_as(img1)
  
              self.window = window
              self.channel = channel
  
          return _ssim(img1, img2, window, self.window_size, channel, self.use_padding, self.size_average)
  
  
  def ssim(img1, img2, use_padding=True, window_size=11, size_average=True):
      """SSIM only defined at intensity channel. For RGB or YUV or other image format, this function computes SSIm at each
      channel and averge them.
      :param img1:  (B, C, H, W)  float32 in [0, 1]
      :param img2:  (B, C, H, W)  float32 in [0, 1]
      :param use_padding: we use conv2d when we compute mean and var for each patch, this use_padding is for that conv2d.
      :param window_size: patch size
      :param size_average:
      :return:  a tensor that contains only one scalar.
      """
      (_, channel, _, _) = img1.size()
      window = create_window(window_size, channel)
  
      if img1.is_cuda:
          window = window.cuda(img1.get_device())
      window = window.type_as(img1)
  
      return _ssim(img1, img2, window, window_size, channel, use_padding, size_average)