text: import numpy as np
  import torch
  import torch.nn as nn
  
  # note: all dct related functions are either exactly as or based on those
  # at https://github.com/zh217/torch-dct
  def dct(x, norm=None):
      """
      Discrete Cosine Transform, Type II (a.k.a. the DCT)
      For the meaning of the parameter `norm`, see:
      https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
      :param x: the input signal
      :param norm: the normalization, None or 'ortho'
      :return: the DCT-II of the signal over the last dimension
      """
      x_shape = x.shape
      N = x_shape[-1]
      x = x.contiguous().view(-1, N)
  
      v = torch.cat([x[:, ::2], x[:, 1::2].flip([1])], dim=1)
  
      Vc = torch.rfft(v, 1, onesided=False)
  
      k = - torch.arange(N, dtype=x.dtype, device=x.device)[None, :] * np.pi / (2 * N)
      W_r = torch.cos(k)
      W_i = torch.sin(k)
  
      V = Vc[:, :, 0] * W_r - Vc[:, :, 1] * W_i
  
      if norm == 'ortho':
          V[:, 0] /= np.sqrt(N) * 2
          V[:, 1:] /= np.sqrt(N / 2) * 2
  
      V = 2 * V.view(*x_shape)
  
      return V
  
  def idct(X, norm=None):
      """
      The inverse to DCT-II, which is a scaled Discrete Cosine Transform, Type III
      Our definition of idct is that idct(dct(x)) == x
      For the meaning of the parameter `norm`, see:
      https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
      :param X: the input signal
      :param norm: the normalization, None or 'ortho'
      :return: the inverse DCT-II of the signal over the last dimension
      """
  
      x_shape = X.shape
      N = x_shape[-1]
  
      X_v = X.contiguous().view(-1, x_shape[-1]) / 2
  
      if norm == 'ortho':
          X_v[:, 0] *= np.sqrt(N) * 2
          X_v[:, 1:] *= np.sqrt(N / 2) * 2
  
      k = torch.arange(x_shape[-1], dtype=X.dtype, device=X.device)[None, :] * np.pi / (2 * N)
      W_r = torch.cos(k)
      W_i = torch.sin(k)
  
      V_t_r = X_v
      V_t_r = V_t_r.to(device)
      V_t_i = torch.cat([X_v[:, :1] * 0, -X_v.flip([1])[:, :-1]], dim=1)
      V_t_i = V_t_i.to(device)
  
      V_r = V_t_r * W_r - V_t_i * W_i
      V_i = V_t_r * W_i + V_t_i * W_r
  
      V = torch.cat([V_r.unsqueeze(2), V_i.unsqueeze(2)], dim=2)
  
      v = torch.irfft(V, 1, onesided=False)
      x = v.new_zeros(v.shape)
      x[:, ::2] += v[:, :N - (N // 2)]
      x[:, 1::2] += v.flip([1])[:, :N // 2]
  
      return x.view(*x_shape)
  
  def dct_2d(x, norm=None):
      """
      2-dimensional Discrete Cosine Transform, Type II (a.k.a. the DCT)
      For the meaning of the parameter `norm`, see:
      https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
      :param x: the input signal
      :param norm: the normalization, None or 'ortho'
      :return: the DCT-II of the signal over the last 2 dimensions
      """
      X1 = dct(x, norm=norm)
      X2 = dct(X1.transpose(-1, -2), norm=norm)
      return X2.transpose(-1, -2)
  
  def idct_2d(X, norm=None):
      """
      The inverse to 2D DCT-II, which is a scaled Discrete Cosine Transform, Type III
      Our definition of idct is that idct_2d(dct_2d(x)) == x
      For the meaning of the parameter `norm`, see:
      https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
      :param X: the input signal
      :param norm: the normalization, None or 'ortho'
      :return: the DCT-II of the signal over the last 2 dimensions
      """
      x1 = idct(X, norm=norm)
      x2 = idct(x1.transpose(-1, -2), norm=norm)
      return x2.transpose(-1, -2)
  
  def extract_patches_2d(img,patch_shape,step=[1.0,1.0],batch_first=False):
      """
          source: https://gist.github.com/dem123456789/23f18fd78ac8da9615c347905e64fc78
      """
      patch_H, patch_W = patch_shape[0], patch_shape[1]
      if(img.size(2) < patch_H):
          num_padded_H_Top = (patch_H - img.size(2))//2
          num_padded_H_Bottom = patch_H - img.size(2) - num_padded_H_Top
          padding_H = nn.ConstantPad2d((0, 0, num_padded_H_Top, num_padded_H_Bottom), 0)
          img = padding_H(img)
      if(img.size(3) < patch_W):
          num_padded_W_Left = (patch_W - img.size(3))//2
          num_padded_W_Right = patch_W - img.size(3) - num_padded_W_Left
          padding_W = nn.ConstantPad2d((num_padded_W_Left,num_padded_W_Right, 0, 0), 0)
          img = padding_W(img)
      step_int = [0, 0]
      step_int[0] = int(patch_H*step[0]) if(isinstance(step[0], float)) else step[0]
      step_int[1] = int(patch_W*step[1]) if(isinstance(step[1], float)) else step[1]
      patches_fold_H = img.unfold(2, patch_H, step_int[0])
      if((img.size(2) - patch_H) % step_int[0] != 0):
          patches_fold_H = torch.cat((patches_fold_H,
                                      img[:, :, -patch_H:, :].permute(0,1,3,2).unsqueeze(2)),dim=2)
      patches_fold_HW = patches_fold_H.unfold(3, patch_W, step_int[1])
      if((img.size(3) - patch_W) % step_int[1] != 0):
          patches_fold_HW = torch.cat((patches_fold_HW,
                                       patches_fold_H[:, :, :, -patch_W:, :].permute(0, 1, 2, 4, 3).unsqueeze(3)), dim=3)
      patches = patches_fold_HW.permute(2, 3, 0, 1, 4, 5)
      patches = patches.reshape(-1, img.size(0), img.size(1), patch_H, patch_W)
      if(batch_first):
          patches = patches.permute(1, 0, 2, 3, 4)
      return patches
  