text: """Differential privacy computing of count, sum, mean, variance."""
  
  import numpy as np
  import pipeline_dp
  # TODO: import only modules https://google.github.io/styleguide/pyguide.html#22-imports
  from pipeline_dp.aggregate_params import NoiseKind
  from dataclasses import dataclass
  from pydp.algorithms import numerical_mechanisms as dp_mechanisms
  
  
  @dataclass
  class MeanVarParams:
      """The parameters used for computing the dp sum, count, mean, variance."""
  
      eps: float
      delta: float
      low: float
      high: float
      max_partitions_contributed: int
      max_contributions_per_partition: int
      noise_kind: NoiseKind  # Laplace or Gaussian
  
      def l0_sensitivity(self):
          """"Returns the L0 sensitivity of the parameters."""
          return self.max_partitions_contributed
  
      def squares_interval(self):
          """Returns the bounds of the interval [low^2, high^2]."""
          if self.low < 0 and self.high > 0:
              return 0, max(self.low**2, self.high**2)
          return self.low**2, self.high**2
  
  
  def compute_middle(low: float, high: float):
      """"Returns the middle point of the interval [low, high]."""
      return low + (high - low) / 2
  
  
  def compute_l1_sensitivity(l0_sensitivity: float, linf_sensitivity: float):
      """Calculates the L1 sensitivity based on the L0 and Linf sensitivities.
  
      Args:
          l0_sensitivity: The L0 sensitivity.
          linf_sensitivity: The Linf sensitivity.
  
      Returns:
          The L1 sensitivity.
      """
      return l0_sensitivity * linf_sensitivity
  
  
  def compute_l2_sensitivity(l0_sensitivity: float, linf_sensitivity: float):
      """Calculates the L2 sensitivity based on the L0 and Linf sensitivities.
  
      Args:
          l0_sensitivity: The L0 sensitivity.
          linf_sensitivity: The Linf sensitivity.
  
      Returns:
          The L2 sensitivity.
      """
      return np.sqrt(l0_sensitivity) * linf_sensitivity
  
  
  def compute_sigma(eps: float, delta: float, l2_sensitivity: float):
      """Returns the optimal value of sigma for the Gaussian mechanism.
  
      Args:
          eps: The epsilon value.
          delta: The delta value.
          l2_sensitivity: The L2 sensitivity.
      """
      # TODO: use named arguments, when argument names are added in PyDP on PR
      # https://github.com/OpenMined/PyDP/pull/398.
      return dp_mechanisms.GaussianMechanism(eps, delta, l2_sensitivity).std
  
  
  def apply_laplace_mechanism(value: float, eps: float, l1_sensitivity: float):
      """Applies the Laplace mechanism to the value.
  
      Args:
          value: The initial value.
          eps: The epsilon value.
          l1_sensitivity: The L1 sensitivity.
  
      Returns:
          The value resulted after adding the noise.
      """
      mechanism = dp_mechanisms.LaplaceMechanism(epsilon=eps,
                                                 sensitivity=l1_sensitivity)
      return mechanism.add_noise(1.0 * value)
  
  
  def apply_gaussian_mechanism(value: float, eps: float, delta: float,
                               l2_sensitivity: float):
      """Applies the Gaussian mechanism to the value.
  
      Args:
          value: The initial value.
          eps: The epsilon value.
          delta: The delta value.
          l2_sensitivity: The L2 sensitivity.
  
      Returns:
          The value resulted after adding the noise.
      """
      # TODO: use named arguments, when argument names are added in PyDP on PR
      # https://github.com/OpenMined/PyDP/pull/398.
      mechanism = dp_mechanisms.GaussianMechanism(eps, delta, l2_sensitivity)
      return mechanism.add_noise(1.0 * value)
  
  
  def _add_random_noise(
      value: float,
      eps: float,
      delta: float,
      l0_sensitivity: float,
      linf_sensitivity: float,
      noise_kind: NoiseKind,
  ):
      """Adds random noise according to the parameters.
  
      Args:
          value: The initial value.
          eps: The epsilon value.
          delta: The delta value.
          l0_sensitivity: The L0 sensitivity.
          linf_sensitivity: The Linf sensitivity.
          noise_kind: The kind of noise used.
  
      Returns:
          The value resulted after adding the random noise.
      """
      if noise_kind == NoiseKind.LAPLACE:
          l1_sensitivity = compute_l1_sensitivity(l0_sensitivity,
                                                  linf_sensitivity)
          return apply_laplace_mechanism(value, eps, l1_sensitivity)
      if noise_kind == NoiseKind.GAUSSIAN:
          l2_sensitivity = compute_l2_sensitivity(l0_sensitivity,
                                                  linf_sensitivity)
          return apply_gaussian_mechanism(value, eps, delta, l2_sensitivity)
      raise ValueError("Noise kind must be either Laplace or Gaussian.")
  
  
  @dataclass
  class AdditiveVectorNoiseParams:
      eps_per_coordinate: float
      delta_per_coordinate: float
      max_norm: float
      l0_sensitivity: float
      linf_sensitivity: float
      norm_kind: pipeline_dp.NormKind
      noise_kind: NoiseKind
  
  
  def _clip_vector(vec: np.ndarray, max_norm: float,
                   norm_kind: pipeline_dp.NormKind):
      norm_kind = norm_kind.value  # type: str
      if norm_kind == "linf":
          return np.clip(vec, -max_norm, max_norm)
      if norm_kind in {"l1", "l2"}:
          norm_kind = int(norm_kind[-1])
          vec_norm = np.linalg.norm(vec, ord=norm_kind)
          mul_coef = min(1, max_norm / vec_norm)
          return vec * mul_coef
      raise NotImplementedError(
          f"Vector Norm of kind '{norm_kind}' is not supported.")
  
  
  def add_noise_vector(vec: np.ndarray, noise_params: AdditiveVectorNoiseParams):
      """Adds noise to vector to make the vector sum computation (eps, delta)-DP.
  
      Args:
          vec: the queried raw vector
          noise_params: parameters of the noise to add to the computation
      """
      vec = _clip_vector(vec, noise_params.max_norm, noise_params.norm_kind)
      vec = np.array([
          _add_random_noise(
              s,
              noise_params.eps_per_coordinate,
              noise_params.delta_per_coordinate,
              noise_params.l0_sensitivity,
              noise_params.linf_sensitivity,
              noise_params.noise_kind,
          ) for s in vec
      ])
      return vec
  
  
  def equally_split_budget(eps: float, delta: float, no_mechanisms: int):
      """Equally splits the budget (eps, delta) between a given number of mechanisms.
  
      Args:
          eps, delta: The available budget.
          no_mechanisms: The number of mechanisms between which we split the budget.
  
      Raises:
          ValueError: The number of mechanisms must be a positive integer.
  
      Returns:
          An array with the split budgets.
      """
      if no_mechanisms <= 0:
          raise ValueError("The number of mechanisms must be a positive integer.")
  
      # These variables are used to keep track of the budget used.
      # In this way, we can improve accuracy of floating-point operations.
      eps_used = delta_used = 0
      budgets = []
  
      for _ in range(no_mechanisms - 1):
          budget = (eps / no_mechanisms, delta / no_mechanisms)
          eps_used += budget[0]
          delta_used += budget[1]
          budgets.append(budget)
  
      budgets.append((eps - eps_used, delta - delta_used))
      return budgets
  
  
  def compute_dp_count(count: int, dp_params: MeanVarParams):
      """Computes DP count.
  
      Args:
          count: Non-DP count.
          dp_params: The parameters used at computing the noise.
  
      Raises:
          ValueError: The noise kind is invalid.
      """
      l0_sensitivity = dp_params.l0_sensitivity()
      linf_sensitivity = dp_params.max_contributions_per_partition
  
      return _add_random_noise(
          count,
          dp_params.eps,
          dp_params.delta,
          l0_sensitivity,
          linf_sensitivity,
          dp_params.noise_kind,
      )
  
  
  def compute_dp_sum(sum: float, dp_params: MeanVarParams):
      """Computes DP sum.
  
      Args:
          sum: Non-DP sum.
          dp_params: The parameters used at computing the noise.
  
      Raises:
          ValueError: The noise kind is invalid.
      """
      l0_sensitivity = dp_params.l0_sensitivity()
      linf_sensitivity = dp_params.max_contributions_per_partition * max(
          abs(dp_params.low), abs(dp_params.high))
  
      return _add_random_noise(
          sum,
          dp_params.eps,
          dp_params.delta,
          l0_sensitivity,
          linf_sensitivity,
          dp_params.noise_kind,
      )
  
  
  def _compute_mean(
      count: float,
      dp_count: float,
      sum: float,
      low: float,
      high: float,
      eps: float,
      delta: float,
      l0_sensitivity: float,
      max_contributions_per_partition: float,
      noise_kind: NoiseKind,
  ):
      """Helper function to compute the DP mean of a raw sum using the DP count.
  
      Args:
          count: Non-DP count.
          dp_count: DP count.
          sum: Non-DP sum.
          low, high: The lowest/highest contribution.
          eps, delta: The budget allocated.
          l0_sensitivity: The L0 sensitivity.
          max_contributions_per_partition: The maximum number of contributions
              per partition.
          noise_kind: The kind of noise used.
  
      Raises:
          ValueError: The noise kind is invalid.
  
      Returns:
          The anonymized mean.
      """
      middle = compute_middle(low, high)
      linf_sensitivity = max_contributions_per_partition * abs(middle - low)
  
      normalized_sum = sum - count * middle
      dp_normalized_sum = _add_random_noise(normalized_sum, eps, delta,
                                            l0_sensitivity, linf_sensitivity,
                                            noise_kind)
      return dp_normalized_sum / dp_count + middle
  
  
  def compute_dp_mean(count: int, sum: float, dp_params: MeanVarParams):
      """Computes DP mean.
  
      Args:
          count: Non-DP count.
          sum: Non-DP sum.
          dp_params: The parameters used at computing the noise.
  
      Raises:
          ValueError: The noise kind is invalid.
  
      Returns:
          The tuple of anonymized count, sum and mean.
      """
      # Splits the budget equally between the two mechanisms.
      (count_eps, count_delta), (sum_eps, sum_delta) = equally_split_budget(
          dp_params.eps, dp_params.delta, 2)
      l0_sensitivity = dp_params.l0_sensitivity()
  
      dp_count = _add_random_noise(
          count,
          count_eps,
          count_delta,
          l0_sensitivity,
          dp_params.max_contributions_per_partition,
          dp_params.noise_kind,
      )
  
      dp_mean = _compute_mean(
          count,
          dp_count,
          sum,
          dp_params.low,
          dp_params.high,
          sum_eps,
          sum_delta,
          l0_sensitivity,
          dp_params.max_contributions_per_partition,
          dp_params.noise_kind,
      )
      return dp_count, dp_mean * dp_count, dp_mean
  
  
  def compute_dp_var(count: int, sum: float, sum_squares: float,
                     dp_params: MeanVarParams):
      """Computes DP variance.
  
      Args:
          count: Non-DP count.
          sum: Non-DP sum.
          sum_squares: Non-DP sum of squares.
          dp_params: The parameters used at computing the noise.
  
      Raises:
          ValueError: The noise kind is invalid.
  
      Returns:
          The tuple of anonymized count, sum, sum_squares and variance.
      """
      # Splits the budget equally between the three mechanisms.
      (
          (count_eps, count_delta),
          (sum_eps, sum_delta),
          (sum_squares_eps, sum_squares_delta),
      ) = equally_split_budget(dp_params.eps, dp_params.delta, 3)
      l0_sensitivity = dp_params.l0_sensitivity()
  
      dp_count = _add_random_noise(
          count,
          count_eps,
          count_delta,
          l0_sensitivity,
          dp_params.max_contributions_per_partition,
          dp_params.noise_kind,
      )
  
      # Computes and adds noise to the mean.
      dp_mean = _compute_mean(
          count,
          dp_count,
          sum,
          dp_params.low,
          dp_params.high,
          sum_eps,
          sum_delta,
          l0_sensitivity,
          dp_params.max_contributions_per_partition,
          dp_params.noise_kind,
      )
  
      squares_low, squares_high = dp_params.squares_interval()
  
      # Computes and adds noise to the mean of squares.
      dp_mean_squares = _compute_mean(count, dp_count, sum_squares, squares_low,
                                      squares_high, sum_squares_eps,
                                      sum_squares_delta, l0_sensitivity,
                                      dp_params.max_contributions_per_partition,
                                      dp_params.noise_kind)
  
      dp_var = dp_mean_squares - dp_mean**2
      return dp_count, dp_mean * dp_count, dp_mean_squares * dp_count, dp_var
  