text: import cv2
  import math
  import numpy as np
  import random
  
  # -------------------------------------------------------------------- #
  # --------------------------- blur kernels --------------------------- #
  # -------------------------------------------------------------------- #
  
  
  def sigma_matrix2(sig_x, sig_y, theta):
      """Calculate the rotated sigma matrix (two dimensional matrix).
  
      Args:
          sig_x (float):
          sig_y (float):
          theta (float): Radian measurement.
  
      Returns:
          ndarray: Rotated sigma matrix.
      """
      D = np.array([[sig_x**2, 0], [0, sig_y**2]])
      U = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])
      return np.dot(U, np.dot(D, U.T))
  
  
  def mesh_grid(kernel_size):
      """Generate the mesh grid, centering at zero.
  
      Args:
          kernel_size (int):
  
      Returns:
          xy (ndarray): with the shape (kernel_size, kernel_size, 2)
          xx (ndarray): with the shape (kernel_size, kernel_size)
          yy (ndarray): with the shape (kernel_size, kernel_size)
      """
      ax = np.arange(-kernel_size // 2 + 1., kernel_size // 2 + 1.)
      xx, yy = np.meshgrid(ax, ax)
      xy = np.hstack((xx.reshape((kernel_size * kernel_size, 1)), yy.reshape(kernel_size * kernel_size,
                                                                             1))).reshape(kernel_size, kernel_size, 2)
      return xy, xx, yy
  
  
  def pdf2(sigma_matrix, grid):
      """Calculate PDF of the bivariate Gaussian distribution.
  
      Args:
          sigma_matrix (ndarray): with the shape (2, 2)
          grid (ndarray): generated by :func:`mesh_grid`,
              with the shape (K, K, 2), K is the kernel size.
  
      Returns:
          kernel (ndarrray): un-normalized kernel.
      """
      inverse_sigma = np.linalg.inv(sigma_matrix)
      kernel = np.exp(-0.5 * np.sum(np.dot(grid, inverse_sigma) * grid, 2))
      return kernel
  
  
  def mass_center_shift(kernel_size, kernel):
      """Calculate the shift of the mass center of a kenrel.
  
      Args:
          kernel_size (int):
          kernel (ndarray): normalized kernel.
  
      Returns:
          delta_h (float):
          delta_w (float):
      """
      ax = np.arange(-kernel_size // 2 + 1., kernel_size // 2 + 1.)
      col_sum, row_sum = np.sum(kernel, axis=0), np.sum(kernel, axis=1)
      delta_h = np.dot(row_sum, ax)
      delta_w = np.dot(col_sum, ax)
      return delta_h, delta_w
  
  
  def bivariate_anisotropic_Gaussian(kernel_size, sig_x, sig_y, theta, grid=None):
      """Generate a bivariate anisotropic Gaussian kernel.
  
      Args:
          kernel_size (int):
          sig_x (float):
          sig_y (float):
          theta (float): Radian measurement.
          grid (ndarray, optional): generated by :func:`mesh_grid`,
              with the shape (K, K, 2), K is the kernel size. Default: None
  
      Returns:
          kernel (ndarray): normalized kernel.
      """
      if grid is None:
          grid, _, _ = mesh_grid(kernel_size)
      sigma_matrix = sigma_matrix2(sig_x, sig_y, theta)
      kernel = pdf2(sigma_matrix, grid)
      kernel = kernel / np.sum(kernel)
      return kernel
  
  
  def bivariate_isotropic_Gaussian(kernel_size, sig, grid=None):
      """Generate a bivariate isotropic Gaussian kernel.
  
      Args:
          kernel_size (int):
          sig (float):
          grid (ndarray, optional): generated by :func:`mesh_grid`,
              with the shape (K, K, 2), K is the kernel size. Default: None
  
      Returns:
          kernel (ndarray): normalized kernel.
      """
      if grid is None:
          grid, _, _ = mesh_grid(kernel_size)
      sigma_matrix = np.array([[sig**2, 0], [0, sig**2]])
      kernel = pdf2(sigma_matrix, grid)
      kernel = kernel / np.sum(kernel)
      return kernel
  
  
  def random_bivariate_anisotropic_Gaussian(kernel_size,
                                            sigma_x_range,
                                            sigma_y_range,
                                            rotation_range,
                                            noise_range=None,
                                            strict=False):
      """Randomly generate bivariate anisotropic Gaussian kernels.
  
      Args:
          kernel_size (int):
          sigma_x_range (tuple): [0.6, 5]
          sigma_y_range (tuple): [0.6, 5]
          rotation range (tuple): [-math.pi, math.pi]
          noise_range(tuple, optional): multiplicative kernel noise,
              [0.75, 1.25]. Default: None
  
      Returns:
          kernel (ndarray):
      """
      assert kernel_size % 2 == 1, 'Kernel size must be an odd number.'
      assert sigma_x_range[0] < sigma_x_range[1], 'Wrong sigma_x_range.'
      assert sigma_y_range[0] < sigma_y_range[1], 'Wrong sigma_y_range.'
      assert rotation_range[0] < rotation_range[1], 'Wrong rotation_range.'
      sigma_x = np.random.uniform(sigma_x_range[0], sigma_x_range[1])
      sigma_y = np.random.uniform(sigma_y_range[0], sigma_y_range[1])
      if strict:
          sigma_max = np.max([sigma_x, sigma_y])
          sigma_min = np.min([sigma_x, sigma_y])
          sigma_x, sigma_y = sigma_max, sigma_min
      rotation = np.random.uniform(rotation_range[0], rotation_range[1])
  
      kernel = bivariate_anisotropic_Gaussian(kernel_size, sigma_x, sigma_y, rotation)
  
      # add multiplicative noise
      if noise_range is not None:
          assert noise_range[0] < noise_range[1], 'Wrong noise range.'
          noise = np.random.uniform(noise_range[0], noise_range[1], size=kernel.shape)
          kernel = kernel * noise
      kernel = kernel / np.sum(kernel)
      if strict:
          return kernel, sigma_x, sigma_y, rotation
      else:
          return kernel
  
  
  def random_bivariate_isotropic_Gaussian(kernel_size, sigma_range, noise_range=None, strict=False):
      """Randomly generate bivariate isotropic Gaussian kernels.
  
      Args:
          kernel_size (int):
          sigma_range (tuple): [0.6, 5]
          noise_range(tuple, optional): multiplicative kernel noise,
              [0.75, 1.25]. Default: None
  
      Returns:
          kernel (ndarray):
      """
      assert kernel_size % 2 == 1, 'Kernel size must be an odd number.'
      assert sigma_range[0] < sigma_range[1], 'Wrong sigma_x_range.'
      sigma = np.random.uniform(sigma_range[0], sigma_range[1])
  
      kernel = bivariate_isotropic_Gaussian(kernel_size, sigma)
  
      # add multiplicative noise
      if noise_range is not None:
          assert noise_range[0] < noise_range[1], 'Wrong noise range.'
          noise = np.random.uniform(noise_range[0], noise_range[1], size=kernel.shape)
          kernel = kernel * noise
      kernel = kernel / np.sum(kernel)
      if strict:
          return kernel, sigma
      else:
          return kernel
  
  
  def random_mixed_kernels(kernel_list,
                           kernel_prob,
                           kernel_size=21,
                           sigma_x_range=(0.6, 5),
                           sigma_y_range=(0.6, 5),
                           rotation_range=(-math.pi, math.pi),
                           beta_range=(0.5, 8),
                           noise_range=None):
      """Randomly generate mixed kernels.
  
      Args:
          kernel_list (tuple): a list name of kenrel types,
              support ['iso', 'aniso']
          kernel_prob (tuple): corresponding kernel probability for each
              kernel type
          kernel_size (int):
          sigma_x_range (tuple): [0.6, 5]
          sigma_y_range (tuple): [0.6, 5]
          rotation range (tuple): [-math.pi, math.pi]
          beta_range (tuple): [0.5, 8]
          noise_range(tuple, optional): multiplicative kernel noise,
              [0.75, 1.25]. Default: None
  
      Returns:
          kernel (ndarray):
      """
      kernel_type = random.choices(kernel_list, kernel_prob)[0]
      if kernel_type == 'iso':
          kernel = random_bivariate_isotropic_Gaussian(kernel_size, sigma_x_range, noise_range=noise_range)
      elif kernel_type == 'aniso':
          kernel = random_bivariate_anisotropic_Gaussian(
              kernel_size, sigma_x_range, sigma_y_range, rotation_range, noise_range=noise_range)
  
      # add multiplicative noise
      if noise_range is not None:
          assert noise_range[0] < noise_range[1], 'Wrong noise range.'
          noise = np.random.uniform(noise_range[0], noise_range[1], size=kernel.shape)
          kernel = kernel * noise
      kernel = kernel / np.sum(kernel)
      return kernel
  
  
  # ------------------------------------------------------------- #
  # --------------------------- noise --------------------------- #
  # ------------------------------------------------------------- #
  
  # ----------------------- Gaussian Noise ----------------------- #
  
  
  def generate_gaussian_noise(img, sigma=10, gray_noise=False):
      """Generate Gaussian noise.
  
      Args:
          img (Numpy array): Input image, shape (h, w, c), range [0, 1], float32.
          sigma (float): Noise scale (measured in range 255). Default: 10.
  
      Returns:
          (Numpy array): Returned noisy image, shape (h, w, c), range[0, 1],
              float32.
      """
      noise = np.float32(np.random.randn(*(img.shape))) * sigma / 255.
      if gray_noise:
          noise = np.float32(np.random.randn(*(img.shape[0:2]))) * sigma / 255.
          noise = np.expand_dims(noise, axis=2).repeat(3, axis=2)
      else:
          noise = np.float32(np.random.randn(*(img.shape))) * sigma / 255.
      return noise
  
  
  def add_gaussian_noise(img, sigma=10, clip=True, rounds=False, gray_noise=False):
      """Add Gaussian noise.
  
      Args:
          img (Numpy array): Input image, shape (h, w, c), range [0, 1], float32.
          sigma (float): Noise scale (measured in range 255). Default: 10.
  
      Returns:
          (Numpy array): Returned noisy image, shape (h, w, c), range[0, 1],
              float32.
      """
      noise = generate_gaussian_noise(img, sigma, gray_noise)
      out = img + noise
      if clip and rounds:
          out = np.clip((out * 255.0).round(), 0, 255) / 255.
      elif clip:
          out = np.clip(out, 0, 1)
      elif rounds:
          out = (out * 255.0).round() / 255.
      return out
  
  
  # ----------------------- Random Gaussian Noise ----------------------- #
  def random_generate_gaussian_noise(img, sigma_range=(0, 10), gray_prob=0):
      sigma = np.random.uniform(sigma_range[0], sigma_range[1])
      if np.random.uniform() < gray_prob:
          gray_noise = True
      else:
          gray_noise = False
      return generate_gaussian_noise(img, sigma, gray_noise)
  
  
  def random_add_gaussian_noise(img, sigma_range=(0, 1.0), gray_prob=0, clip=True, rounds=False):
      noise = random_generate_gaussian_noise(img, sigma_range, gray_prob)
      out = img + noise
      if clip and rounds:
          out = np.clip((out * 255.0).round(), 0, 255) / 255.
      elif clip:
          out = np.clip(out, 0, 1)
      elif rounds:
          out = (out * 255.0).round() / 255.
      return out
  
  
  # ------------------------------------------------------------------------ #
  # --------------------------- JPEG compression --------------------------- #
  # ------------------------------------------------------------------------ #
  
  
  def add_jpg_compression(img, quality=90):
      """Add JPG compression artifacts.
  
      Args:
          img (Numpy array): Input image, shape (h, w, c), range [0, 1], float32.
          quality (float): JPG compression quality. 0 for lowest quality, 100 for
              best quality. Default: 90.
  
      Returns:
          (Numpy array): Returned image after JPG, shape (h, w, c), range[0, 1],
              float32.
      """
      img = np.clip(img, 0, 1)
      encode_param = [int(cv2.IMWRITE_JPEG_QUALITY), quality]
      _, encimg = cv2.imencode('.jpg', img * 255., encode_param)
      img = np.float32(cv2.imdecode(encimg, 1)) / 255.
      return img
  
  
  def random_add_jpg_compression(img, quality_range=(90, 100)):
      """Randomly add JPG compression artifacts.
  
      Args:
          img (Numpy array): Input image, shape (h, w, c), range [0, 1], float32.
          quality_range (tuple[float] | list[float]): JPG compression quality
              range. 0 for lowest quality, 100 for best quality.
              Default: (90, 100).
  
      Returns:
          (Numpy array): Returned image after JPG, shape (h, w, c), range[0, 1],
              float32.
      """
      quality = np.random.uniform(quality_range[0], quality_range[1])
      return add_jpg_compression(img, quality)
  