
"""simple docstring"""

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		(							snake_case :str							,   snake_case :Union[str, Any]							,   snake_case :int						) ->      list:
 seed(1						)
 return [gauss(_SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE						) for _ in range(_SCREAMING_SNAKE_CASE						)]






def 				A		(							snake_case :Optional[int]							,   snake_case :str						) ->      list:
 return [k for k in range(_SCREAMING_SNAKE_CASE						) for _ in range(instance_count[k]						)]






def 				A		(							snake_case :int							,   snake_case :Optional[Any]						) ->      float:
 return sum(_SCREAMING_SNAKE_CASE						) / instance_count






def 				A		(							snake_case :Union[str, Any]							,   snake_case :str						) ->      float:
 return instance_count / total_count






def 				A		(							snake_case :Any							,   snake_case :List[Any]							,   snake_case :Optional[int]						) ->      float:
 __UpperCamelCase							    =			[]  # 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							    =			len(_SCREAMING_SNAKE_CASE						)  # Number of classes in dataset
 return 1 / (total_count - n_classes) * sum(_SCREAMING_SNAKE_CASE						)






def 				A		(							snake_case :Optional[Any]							,   snake_case :Any							,   snake_case :Optional[int]							,   snake_case :Dict						) ->      list:
 __UpperCamelCase							    =			[]
 # 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							    =			[]  # 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		(							snake_case :int							,   snake_case :str						) ->      float:
 __UpperCamelCase							    =			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						)) * 1_0_0


UpperCamelCase      :							List[Any]          =					TypeVar("num")






def 				A		(							snake_case :str							,   snake_case :Any							,   snake_case :str							,   snake_case :List[Any] = lambda snake_case						: True							,   snake_case :Dict = None							,   ) ->      num:






 while True:
  try:
   __UpperCamelCase							    =			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		(							) ->      Any:






 while True:
  print(' Linear Discriminant Analysis '.center(5_0							,   '*'						)						)
  print('*' * 5_0							,   '\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							    =			valid_input(
      input_type=_SCREAMING_SNAKE_CASE							,   condition=lambda snake_case						: x > 0							,   input_msg='Enter the number of classes (Data Groupings): '							,   err_msg='Number of classes should be positive!'							,   )

  print('-' * 1_0_0						)

  # Trying to get the value of standard deviation
  __UpperCamelCase							    =			valid_input(
      input_type=_SCREAMING_SNAKE_CASE							,   condition=lambda 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('-' * 1_0_0						)

  # Trying to get number of instances in classes and theirs means to generate
  # dataset
  __UpperCamelCase							    =			[]  # An empty list to store instance counts of classes in dataset
  for i in range(_SCREAMING_SNAKE_CASE						):
   __UpperCamelCase							    =			valid_input(
       input_type=_SCREAMING_SNAKE_CASE							,   condition=lambda 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('-' * 1_0_0						)

  # An empty list to store values of user-entered means of classes
  __UpperCamelCase							    =			[]
  for a in range(_SCREAMING_SNAKE_CASE						):
   __UpperCamelCase							    =			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('-' * 1_0_0						)

  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('-' * 1_0_0						)

  # 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('-' * 1_0_0						)

  # Generating training dataset drawn from gaussian distribution
  __UpperCamelCase							    =			[
      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('-' * 1_0_0						)

  # Generating Ys to detecting corresponding classes
  __UpperCamelCase							    =			y_generator(_SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE						)
  print('Generated Corresponding Ys: \n'							,   _SCREAMING_SNAKE_CASE						)
  print('-' * 1_0_0						)

  # Calculating the value of actual mean for each class
  __UpperCamelCase							    =			[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('-' * 1_0_0						)

  # Calculating the value of probabilities for each class
  __UpperCamelCase							    =			[
      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('-' * 1_0_0						)

  # Calculating the values of variance for each class
  __UpperCamelCase							    =			calculate_variance(_SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE							,   sum(_SCREAMING_SNAKE_CASE						)						)
  print('Variance: '							,   _SCREAMING_SNAKE_CASE						)
  print('-' * 1_0_0						)

  # Predicting Y values
  # storing predicted Y values in 'pre_indexes' variable
  __UpperCamelCase							    =			predict_y_values(_SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE						)
  print('-' * 1_0_0						)

  # Calculating Accuracy of the model
  print(f'Accuracy: {accuracy(_SCREAMING_SNAKE_CASE							,   _SCREAMING_SNAKE_CASE						)}'						)
  print('-' * 1_0_0						)
  print(' DONE '.center(1_0_0							,   '+'						)						)

  if input('Press any key to restart or \'q\' for quit: '						).strip().lower() == "q":
   print('\n' + 'GoodBye!'.center(1_0_0							,   '-'						) + '\n'						)
   break
  system('cls' if name == 'nt' else 'clear'						)  # noqa: S605


if __name__ == "__main__":
      main()





import torch

from accelerate import Accelerator, DistributedType
class    _UpperCamelCase:

						def __enter__(					self		:			str			):
													if self.enabled:
																				_UpperCAmelCase  :			int	       =		self.model.no_sync()
																				self.model_sync_obj.__enter__()

													return self

						def __exit__(					self		:			str	,						_lowerCamelCase		:			Union[str, Any]	,						_lowerCamelCase		:			Tuple	,						_lowerCamelCase		:			Optional[Any]			):
													if self.enabled:
																				# Average all models on exit
																				self._sync_and_avg_model_params()
																				self.model_sync_obj.__exit__(_lowerCamelCase	,						_lowerCamelCase	,						_lowerCamelCase			)

						def __init__(					self		:			str	,						_lowerCamelCase		:			Accelerator	,						_lowerCamelCase		:			torch.nn.Module	,						_lowerCamelCase		:			int	,						_lowerCamelCase		:			bool = True			):
													if accelerator.distributed_type not in [
													    DistributedType.NO,
													    DistributedType.MULTI_CPU,
													    DistributedType.MULTI_GPU,
													]:
																				raise NotImplementedError("LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)"			)
													_UpperCAmelCase  :			Any	       =		enabled and accelerator.distributed_type != DistributedType.NO
													_UpperCAmelCase  :			str	       =		0
													if self.enabled:
																				_UpperCAmelCase  :			Tuple	       =		accelerator
																				_UpperCAmelCase  :			List[str]	       =		model
																				_UpperCAmelCase  :			Dict	       =		local_sgd_steps

						def 						a__ (					self		:			Optional[int]			):
													self.num_steps += 1
													if not self.enabled:
																				return

													if self.num_steps % self.local_sgd_steps == 0:
																				self._sync_and_avg_model_params()






						def 						a__ (					self		:			Tuple			):
													self.accelerator.wait_for_everyone()
													with self.accelerator.autocast():
																				for param in self.model.parameters():
																											_UpperCAmelCase  :			Optional[Any]	       =		self.accelerator.reduce(param.data	,						reduction="mean"			)




