code: 
  
  
  
  
  
  
  import inspect
  import warnings
  
  import torch
  
  from .state import AcceleratorState, GradientState
  from .utils import DistributedType, honor_type, is_tpu_available
  
  
  if is_tpu_available(check_device=False):
   import torch_xla.core.xla_model as xm
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			Optional[int]  ,						SCREAMING_SNAKE_CASE__						:			Dict ):
      if isinstance(SCREAMING_SNAKE_CASE__  ,						(list, tuple) ):
          return honor_type(SCREAMING_SNAKE_CASE__  ,						(move_to_device(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) for t in state) )
      elif isinstance(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ):
          return type(SCREAMING_SNAKE_CASE__ )({k: move_to_device(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) for k, v in state.items()} )
      elif isinstance(SCREAMING_SNAKE_CASE__  ,						torch.Tensor ):
          return state.to(SCREAMING_SNAKE_CASE__ )
      return state
  
  
  
  
  
  
  
  class     UpperCAmelCase_		(      torch.optim.Optimizer				):
  
  
  
        """simple docstring"""
        def __init__(       self					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_=True					,       SCREAMING_SNAKE_CASE_=None				)       ->   Optional[Any]:
            UpperCamelCase :List[str]										=     optimizer
            UpperCamelCase :str										=     scaler
            UpperCamelCase :Dict										=     AcceleratorState()
            UpperCamelCase :Optional[int]										=     GradientState()
            UpperCamelCase :Optional[Any]										=     device_placement
            UpperCamelCase :Optional[int]										=     False
            UpperCamelCase :Any										=     None
  
            # Handle device placement
            if device_placement:
                UpperCamelCase :int										=     self.optimizer.state_dict()
                if self.accelerator_state.distributed_type == DistributedType.TPU:
                    xm.send_cpu_data_to_device(lowerCamelCase__					,       self.accelerator_state.device				)
                else:
                    UpperCamelCase :List[str]										=     move_to_device(lowerCamelCase__					,       self.accelerator_state.device				)
                self.optimizer.load_state_dict(lowerCamelCase__				)
        @property
        def 					UpperCAmelCase		(       self				)       ->   List[Any]:
            return self.optimizer.state
        @state.setter
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_				)       ->   List[Any]:
            UpperCamelCase :Tuple										=     state
        @property
        def 					UpperCAmelCase		(       self				)       ->   List[Any]:
            return self.optimizer.param_groups
        @param_groups.setter
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_				)       ->   Optional[int]:
            UpperCamelCase :Tuple										=     param_groups
        @property
        def 					UpperCAmelCase		(       self				)       ->   Any:
            return self.optimizer.defaults
        @defaults.setter
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_				)       ->   str:
            UpperCamelCase :int										=     defaults
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_				)       ->   Tuple:
            self.optimizer.add_param_group(lowerCamelCase__				)
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_				)       ->   Tuple:
            if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
                xm.send_cpu_data_to_device(lowerCamelCase__					,       self.accelerator_state.device				)
            self.optimizer.load_state_dict(lowerCamelCase__				)
        def 					UpperCAmelCase		(       self				)       ->   str:
            return self.optimizer.state_dict()
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_=None				)       ->   List[Any]:
            if self.gradient_state.sync_gradients:
                UpperCamelCase :int										=     "set_to_none" in inspect.signature(self.optimizer.zero_grad				).parameters
                if accept_arg:
                    if set_to_none is None:
                        UpperCamelCase :Dict										=     False
                    self.optimizer.zero_grad(set_to_none=lowerCamelCase__				)
                else:
                    if set_to_none is not None:
                        raise ValueError('''`set_to_none` for Optimizer.zero_grad` is not supported by this optimizer.'''				)
                    self.optimizer.zero_grad()
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_=None				)       ->   int:
            if self.gradient_state.sync_gradients:
                if self.accelerator_state.distributed_type == DistributedType.TPU:
                    UpperCamelCase :Union[str, Any]										=     {"closure": closure} if closure is not None else {}
                    xm.optimizer_step(self.optimizer					,       optimizer_args=lowerCamelCase__				)
                elif self.scaler is not None:
                    UpperCamelCase :Any										=     False
                    if self._last_scale is None:
                        # `get_scale` is an async operation requiring full synchronization
                        # on CPU and GPUs before finishing. As a result, we store away
                        # the prior one to reduce the call overhead
                        UpperCamelCase :Optional[int]										=     self.scaler.get_scale()
                        UpperCamelCase :Optional[Any]										=     True
                    self.scaler.step(self.optimizer					,       lowerCamelCase__				)
                    self.scaler.update()
                    UpperCamelCase :Tuple										=     self.scaler.get_scale()
                    if not new_scale:
                        # If we reduced the loss scale, it means the optimizer step was skipped because of gradient overflow.
                        UpperCamelCase :Optional[Any]										=     scale_after < self._last_scale
                    UpperCamelCase :Dict										=     scale_after
  
                else:
                    self.optimizer.step(lowerCamelCase__				)
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_				)       ->   int:
            for param_group in self.optimizer.param_groups:
                UpperCamelCase :List[str]										=     [parameters_map.get(lowerCamelCase__					,       lowerCamelCase__				) for p in param_group["params"]]
        @property
        def 					UpperCAmelCase		(       self				)       ->   int:
            warnings.warn(
                '''The `is_overflow` property is deprecated and will be removed in version 1.0 of Accelerate use '''
                '''`optimizer.step_was_skipped` instead.'''					,       lowerCamelCase__					,       )
            return self._is_overflow
        @property
        def 					UpperCAmelCase		(       self				)       ->   List[Any]:
            return self._is_overflow
        def __getstate__(       self				)       ->   Optional[Any]:
            return self.__dict__.copy()
  
  
  
  
        def __setstate__(       self					,       SCREAMING_SNAKE_CASE_				)       ->   List[str]:
            self.__dict__.update(lowerCamelCase__				)
  
  
  
  
style_context: 
  
  
  
  
  
  
  from collections.abc import Callable
  from math import log
  from os import name, system
  from random import gauss, seed
  from typing import TypeVar
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			int ):
      seed(1 )
      return [gauss(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) for _ in range(SCREAMING_SNAKE_CASE__ )]
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			list ):
      return [k for k in range(SCREAMING_SNAKE_CASE__ ) for _ in range(instance_count[k] )]
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			list ):
      return sum(SCREAMING_SNAKE_CASE__ ) / instance_count
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int  ,						SCREAMING_SNAKE_CASE__						:			int ):
      return instance_count / total_count
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :Optional[Any]										=     []  # An empty list to store all squared differences
      # iterate over number of elements in items
      for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
          # for loop iterates over number of elements in inner layer of items
          for j in range(len(items[i] ) ):
              # appending squared differences to 'squared_diff' list
              squared_diff.append((items[i][j] - means[i]) ** 2 )
  
      # one divided by (the number of all instances - number of classes) multiplied by
      # sum of all squared differences
      UpperCamelCase :Tuple										=     len(SCREAMING_SNAKE_CASE__ )  # Number of classes in dataset
      return 1 / (total_count - n_classes) * sum(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			float  ,						SCREAMING_SNAKE_CASE__						:			list ):
      UpperCamelCase :Dict										=     []
      # for loop iterates over number of elements in list
      for i in range(len(SCREAMING_SNAKE_CASE__ ) ):
          # for loop iterates over number of inner items of each element
          for j in range(len(x_items[i] ) ):
              UpperCamelCase :List[Any]										=     []  # to store all discriminant values of each item as a list
              # for loop iterates over number of classes we have in our dataset
              for k in range(len(SCREAMING_SNAKE_CASE__ ) ):
                  # appending values of discriminants for each class to 'temp' list
                  temp.append(
                      x_items[i][j] * (means[k] / variance)
                      - (means[k] ** 2 / (2 * variance))
                      + log(probabilities[k] ) )
              # appending discriminant values of each item to 'results' list
              results.append(SCREAMING_SNAKE_CASE__ )
  
      return [result.index(max(SCREAMING_SNAKE_CASE__ ) ) for result in results]
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			list  ,						SCREAMING_SNAKE_CASE__						:			list ):
      UpperCamelCase :List[Any]										=     sum(1 for i, j in zip(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ) if i == j )
      # percentage of accuracy equals to number of correct predictions divided by number
      # of all data and multiplied by 100
      return (correct / len(SCREAMING_SNAKE_CASE__ )) * 100
  
  
  __snake_case							      =						TypeVar("""num""")
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			Callable[[object], num]  ,						SCREAMING_SNAKE_CASE__						:			str  ,						SCREAMING_SNAKE_CASE__						:			str  ,						SCREAMING_SNAKE_CASE__						:			Callable[[num], bool] = lambda SCREAMING_SNAKE_CASE__ : True  ,						SCREAMING_SNAKE_CASE__						:			str | None = None  ,						):
      while True:
          try:
              UpperCamelCase :List[Any]										=     input_type(input(SCREAMING_SNAKE_CASE__ ).strip() or default )
              if condition(SCREAMING_SNAKE_CASE__ ):
                  return user_input
              else:
                  print(F'''{user_input}: {err_msg}''' )
                  continue
          except ValueError:
              print(
                  F'''{user_input}: Incorrect input type, expected {input_type.__name__!r}''' )
  
  
  def 						_A     (       ):
      while True:
          print(''' Linear Discriminant Analysis '''.center(50  ,						'''*''' ) )
          print('''*''' * 50  ,						'''\n''' )
          print('''First of all we should specify the number of classes that''' )
          print('''we want to generate as training dataset''' )
          # Trying to get number of classes
          UpperCamelCase :List[Any]										=     valid_input(
              input_type=SCREAMING_SNAKE_CASE__  ,						condition=lambda SCREAMING_SNAKE_CASE__ : x > 0  ,						input_msg='''Enter the number of classes (Data Groupings): '''  ,						err_msg='''Number of classes should be positive!'''  ,						)
  
          print('''-''' * 100 )
  
          # Trying to get the value of standard deviation
          UpperCamelCase :Any										=     valid_input(
              input_type=SCREAMING_SNAKE_CASE__  ,						condition=lambda SCREAMING_SNAKE_CASE__ : x >= 0  ,						input_msg=(
                  '''Enter the value of standard deviation'''
                  '''(Default value is 1.0 for all classes): '''
              )  ,						err_msg='''Standard deviation should not be negative!'''  ,						default='''1.0'''  ,						)
  
          print('''-''' * 100 )
  
          # Trying to get number of instances in classes and theirs means to generate
          # dataset
          UpperCamelCase :Tuple										=     []  # An empty list to store instance counts of classes in dataset
          for i in range(SCREAMING_SNAKE_CASE__ ):
              UpperCamelCase :List[Any]										=     valid_input(
                  input_type=SCREAMING_SNAKE_CASE__  ,						condition=lambda SCREAMING_SNAKE_CASE__ : x > 0  ,						input_msg=(F'''Enter The number of instances for class_{i+1}: ''')  ,						err_msg='''Number of instances should be positive!'''  ,						)
              counts.append(SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # An empty list to store values of user-entered means of classes
          UpperCamelCase :Union[str, Any]										=     []
          for a in range(SCREAMING_SNAKE_CASE__ ):
              UpperCamelCase :str										=     valid_input(
                  input_type=SCREAMING_SNAKE_CASE__  ,						input_msg=(F'''Enter the value of mean for class_{a+1}: ''')  ,						err_msg='''This is an invalid value.'''  ,						)
              user_means.append(SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          print('''Standard deviation: '''  ,						SCREAMING_SNAKE_CASE__ )
          # print out the number of instances in classes in separated line
          for i, count in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Number of instances in class_{i} is: {count}''' )
          print('''-''' * 100 )
  
          # print out mean values of classes separated line
          for i, user_mean in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Mean of class_{i} is: {user_mean}''' )
          print('''-''' * 100 )
  
          # Generating training dataset drawn from gaussian distribution
          UpperCamelCase :Tuple										=     [
              gaussian_distribution(user_means[j]  ,						SCREAMING_SNAKE_CASE__  ,						counts[j] )
              for j in range(SCREAMING_SNAKE_CASE__ )
          ]
          print('''Generated Normal Distribution: \n'''  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Generating Ys to detecting corresponding classes
          UpperCamelCase :int										=     y_generator(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
          print('''Generated Corresponding Ys: \n'''  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Calculating the value of actual mean for each class
          UpperCamelCase :Tuple										=     [calculate_mean(counts[k]  ,						x[k] ) for k in range(SCREAMING_SNAKE_CASE__ )]
          # for loop iterates over number of elements in 'actual_means' list and print
          # out them in separated line
          for i, actual_mean in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Actual(Real) mean of class_{i} is: {actual_mean}''' )
          print('''-''' * 100 )
  
          # Calculating the value of probabilities for each class
          UpperCamelCase :Dict										=     [
              calculate_probabilities(counts[i]  ,						sum(SCREAMING_SNAKE_CASE__ ) ) for i in range(SCREAMING_SNAKE_CASE__ )
          ]
  
          # for loop iterates over number of elements in 'probabilities' list and print
          # out them in separated line
          for i, probability in enumerate(SCREAMING_SNAKE_CASE__  ,						1 ):
              print(F'''Probability of class_{i} is: {probability}''' )
          print('''-''' * 100 )
  
          # Calculating the values of variance for each class
          UpperCamelCase :int										=     calculate_variance(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						sum(SCREAMING_SNAKE_CASE__ ) )
          print('''Variance: '''  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Predicting Y values
          # storing predicted Y values in 'pre_indexes' variable
          UpperCamelCase :Any										=     predict_y_values(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )
          print('''-''' * 100 )
  
          # Calculating Accuracy of the model
          print(F'''Accuracy: {accuracy(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ )}''' )
          print('''-''' * 100 )
          print(''' DONE '''.center(100  ,						'''+''' ) )
  
          if input('''Press any key to restart or \'q\' for quit: ''' ).strip().lower() == "q":
              print('''\n''' + '''GoodBye!'''.center(100  ,						'''-''' ) + '''\n''' )
              break
          system('''cls''' if name == '''nt''' else '''clear''' )  # noqa: S605
  
  
  if __name__ == "__main__":
   main()
  
  
  
  
  
  