text: # MIT License
  #
  # Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2018
  #
  # Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
  # documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
  # rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit
  # persons to whom the Software is furnished to do so, subject to the following conditions:
  #
  # The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
  # Software.
  #
  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
  # WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  # SOFTWARE.
  """
  This module implements the total variance minimization defence `TotalVarMin`.
  
  | Paper link: https://openreview.net/forum?id=SyJ7ClWCb
  
  | Please keep in mind the limitations of defences. For more information on the limitations of this defence,
      see https://arxiv.org/abs/1802.00420 . For details on how to evaluate classifier security in general, see
      https://arxiv.org/abs/1902.06705
  """
  from __future__ import absolute_import, division, print_function, unicode_literals
  
  import logging
  from typing import Optional, Tuple, TYPE_CHECKING
  
  import numpy as np
  from scipy.optimize import minimize
  from tqdm import tqdm
  
  from art.config import ART_NUMPY_DTYPE
  from art.defences.preprocessor.preprocessor import Preprocessor
  
  if TYPE_CHECKING:
      from art.utils import CLIP_VALUES_TYPE
  
  logger = logging.getLogger(__name__)
  
  
  class TotalVarMin(Preprocessor):
      """
      Implement the total variance minimization defence approach.
  
      | Paper link: https://openreview.net/forum?id=SyJ7ClWCb
  
      | Please keep in mind the limitations of defences. For more information on the limitations of this
          defence, see https://arxiv.org/abs/1802.00420 . For details on how to evaluate classifier security in general,
          see https://arxiv.org/abs/1902.06705
      """
  
      params = ["prob", "norm", "lamb", "solver", "max_iter", "clip_values"]
  
      def __init__(
          self,
          prob: float = 0.3,
          norm: int = 2,
          lamb: float = 0.5,
          solver: str = "L-BFGS-B",
          max_iter: int = 10,
          clip_values: Optional["CLIP_VALUES_TYPE"] = None,
          apply_fit: bool = False,
          apply_predict: bool = True,
      ):
          """
          Create an instance of total variance minimization.
  
          :param prob: Probability of the Bernoulli distribution.
          :param norm: The norm (positive integer).
          :param lamb: The lambda parameter in the objective function.
          :param solver: Current support: `L-BFGS-B`, `CG`, `Newton-CG`.
          :param max_iter: Maximum number of iterations when performing optimization.
          :param clip_values: Tuple of the form `(min, max)` representing the minimum and maximum values allowed
                 for features.
          :param apply_fit: True if applied during fitting/training.
          :param apply_predict: True if applied during predicting.
          """
          super().__init__()
          self._is_fitted = True
          self._apply_fit = apply_fit
          self._apply_predict = apply_predict
          self.prob = prob
          self.norm = norm
          self.lamb = lamb
          self.solver = solver
          self.max_iter = max_iter
          self.clip_values = clip_values
          self._check_params()
  
      @property
      def apply_fit(self) -> bool:
          return self._apply_fit
  
      @property
      def apply_predict(self) -> bool:
          return self._apply_predict
  
      def __call__(self, x: np.ndarray, y: Optional[np.ndarray] = None) -> Tuple[np.ndarray, Optional[np.ndarray]]:
          """
          Apply total variance minimization to sample `x`.
  
          :param x: Sample to compress with shape `(batch_size, width, height, depth)`.
          :param y: Labels of the sample `x`. This function does not affect them in any way.
          :return: Similar samples.
          """
          if len(x.shape) == 2:
              raise ValueError(
                  "Feature vectors detected. Variance minimization can only be applied to data with spatial dimensions."
              )
          x_preproc = x.copy()
  
          # Minimize one input at a time
          for i, x_i in enumerate(tqdm(x_preproc, desc="Variance minimization")):
              mask = (np.random.rand(*x_i.shape) < self.prob).astype("int")
              x_preproc[i] = self._minimize(x_i, mask)
  
          if self.clip_values is not None:
              np.clip(x_preproc, self.clip_values[0], self.clip_values[1], out=x_preproc)
  
          return x_preproc.astype(ART_NUMPY_DTYPE), y
  
      def estimate_gradient(self, x: np.ndarray, grad: np.ndarray) -> np.ndarray:
          return grad
  
      def _minimize(self, x: np.ndarray, mask: np.ndarray) -> np.ndarray:
          """
          Minimize the total variance objective function.
  
          :param x: Original image.
          :param mask: A matrix that decides which points are kept.
          :return: A new image.
          """
          z_min = x.copy()
  
          for i in range(x.shape[2]):
              res = minimize(
                  self._loss_func,
                  z_min[:, :, i].flatten(),
                  (x[:, :, i], mask[:, :, i], self.norm, self.lamb),
                  method=self.solver,
                  jac=self._deri_loss_func,
                  options={"maxiter": self.max_iter},
              )
              z_min[:, :, i] = np.reshape(res.x, z_min[:, :, i].shape)
  
          return z_min
  
      @staticmethod
      def _loss_func(z_init: np.ndarray, x: np.ndarray, mask: np.ndarray, norm: int, lamb: float) -> float:
          """
          Loss function to be minimized.
  
          :param z_init: Initial guess.
          :param x: Original image.
          :param mask: A matrix that decides which points are kept.
          :param norm: The norm (positive integer).
          :param lamb: The lambda parameter in the objective function.
          :return: Loss value.
          """
          res = np.sqrt(np.power(z_init - x.flatten(), 2).dot(mask.flatten()))
          z_init = np.reshape(z_init, x.shape)
          res += lamb * np.linalg.norm(z_init[1:, :] - z_init[:-1, :], norm, axis=1).sum()
          res += lamb * np.linalg.norm(z_init[:, 1:] - z_init[:, :-1], norm, axis=0).sum()
  
          return res
  
      @staticmethod
      def _deri_loss_func(z_init: np.ndarray, x: np.ndarray, mask: np.ndarray, norm: int, lamb: float) -> float:
          """
          Derivative of loss function to be minimized.
  
          :param z_init: Initial guess.
          :param x: Original image.
          :param mask: A matrix that decides which points are kept.
          :param norm: The norm (positive integer).
          :param lamb: The lambda parameter in the objective function.
          :return: Derivative value.
          """
          # First compute the derivative of the first component of the loss function
          nor1 = np.sqrt(np.power(z_init - x.flatten(), 2).dot(mask.flatten()))
          if nor1 < 1e-6:
              nor1 = 1e-6
          der1 = ((z_init - x.flatten()) * mask.flatten()) / (nor1 * 1.0)
  
          # Then compute the derivative of the second component of the loss function
          z_init = np.reshape(z_init, x.shape)
  
          if norm == 1:
              z_d1 = np.sign(z_init[1:, :] - z_init[:-1, :])
              z_d2 = np.sign(z_init[:, 1:] - z_init[:, :-1])
          else:
              z_d1_norm = np.power(np.linalg.norm(z_init[1:, :] - z_init[:-1, :], norm, axis=1), norm - 1)
              z_d2_norm = np.power(np.linalg.norm(z_init[:, 1:] - z_init[:, :-1], norm, axis=0), norm - 1)
              z_d1_norm[z_d1_norm < 1e-6] = 1e-6
              z_d2_norm[z_d2_norm < 1e-6] = 1e-6
              z_d1_norm = np.repeat(z_d1_norm[:, np.newaxis], z_init.shape[1], axis=1)
              z_d2_norm = np.repeat(z_d2_norm[np.newaxis, :], z_init.shape[0], axis=0)
              z_d1 = norm * np.power(z_init[1:, :] - z_init[:-1, :], norm - 1) / z_d1_norm
              z_d2 = norm * np.power(z_init[:, 1:] - z_init[:, :-1], norm - 1) / z_d2_norm
  
          der2 = np.zeros(z_init.shape)
          der2[:-1, :] -= z_d1
          der2[1:, :] += z_d1
          der2[:, :-1] -= z_d2
          der2[:, 1:] += z_d2
          der2 = lamb * der2.flatten()
  
          # Total derivative
          return der1 + der2
  
      def fit(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> None:
          """
          No parameters to learn for this method; do nothing.
          """
          pass
  
      def _check_params(self) -> None:
          if not isinstance(self.prob, (float, int)) or self.prob < 0.0 or self.prob > 1.0:
              logger.error("Probability must be between 0 and 1.")
              raise ValueError("Probability must be between 0 and 1.")
  
          if not isinstance(self.norm, (int, np.int)) or self.norm <= 0:
              logger.error("Norm must be a positive integer.")
              raise ValueError("Norm must be a positive integer.")
  
          if not (self.solver == "L-BFGS-B" or self.solver == "CG" or self.solver == "Newton-CG"):
              logger.error("Current support only L-BFGS-B, CG, Newton-CG.")
              raise ValueError("Current support only L-BFGS-B, CG, Newton-CG.")
  
          if not isinstance(self.max_iter, (int, np.int)) or self.max_iter <= 0:
              logger.error("Number of iterations must be a positive integer.")
              raise ValueError("Number of iterations must be a positive integer.")
  
          if self.clip_values is not None:
  
              if len(self.clip_values) != 2:
                  raise ValueError("`clip_values` should be a tuple of 2 floats containing the allowed data range.")
  
              if np.array(self.clip_values[0] >= self.clip_values[1]).any():
                  raise ValueError("Invalid `clip_values`: min >= max.")
  