


"""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   _snake_case    (    _snake_case					:      Tuple			, _snake_case					:      Union[str, Any]			, _snake_case					:      int      ):
      seed(1      )
      return [gauss(lowercase__			, lowercase__      ) for _ in range(lowercase__      )]


def   _snake_case    (    _snake_case					:      Any			, _snake_case					:      str      ):
      return [k for k in range(lowercase__      ) for _ in range(instance_count[k]      )]


def   _snake_case    (    _snake_case					:      Optional[int]			, _snake_case					:      int      ):
      return sum(lowercase__      ) / instance_count


def   _snake_case    (    _snake_case					:      List[str]			, _snake_case					:      Union[str, Any]      ):
      return instance_count / total_count


def   _snake_case    (    _snake_case					:      List[Any]			, _snake_case					:      Optional[int]			, _snake_case					:      List[Any]      ):
      lowerCAmelCase       :						Dict							= []  # An empty list to store all squared differences
      # iterate over number of elements in items
      for i in range(len(lowercase__      )      ):
            # 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
      lowerCAmelCase       :						Any							= len(lowercase__      )  # Number of classes in dataset
      return 1 / (total_count - n_classes) * sum(lowercase__      )


def   _snake_case    (    _snake_case					:      Tuple			, _snake_case					:      List[str]			, _snake_case					:      Tuple			, _snake_case					:      Tuple      ):
      lowerCAmelCase       :						List[Any]							= []
      # for loop iterates over number of elements in list
      for i in range(len(lowercase__      )      ):
            # for loop iterates over number of inner items of each element
            for j in range(len(x_items[i]      )      ):
                  lowerCAmelCase       :						List[str]							= []  # 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(lowercase__      )      ):
                        # 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(lowercase__      )

      return [result.index(max(lowercase__      )      ) for result in results]


def   _snake_case    (    _snake_case					:      Union[str, Any]			, _snake_case					:      Dict      ):
      lowerCAmelCase       :						List[Any]							= sum(1 for i, j in zip(lowercase__			, lowercase__      ) 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(lowercase__      )) * 100


snake_case__		:  Any     					=					TypeVar('''num''')


def   _snake_case    (    _snake_case					:      List[str]			, _snake_case					:      Union[str, Any]			, _snake_case					:      Any			, _snake_case					:      int = lambda _snake_case      : True			, _snake_case					:      Dict = None			, ):
      while True:
            try:
                  lowerCAmelCase       :						int							= input_type(input(lowercase__      ).strip() or default      )
                  if condition(lowercase__      ):
                        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   _snake_case    (    ):
      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
            lowerCAmelCase       :						List[str]							= valid_input(
                input_type=lowercase__			, condition=lambda _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
            lowerCAmelCase       :						Tuple							= valid_input(
                input_type=lowercase__			, 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('''-''' * 100      )

            # Trying to get number of instances in classes and theirs means to generate
            # dataset
            lowerCAmelCase       :						List[str]							= []  # An empty list to store instance counts of classes in dataset
            for i in range(lowercase__      ):
                  lowerCAmelCase       :						Dict							= valid_input(
                      input_type=lowercase__			, 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(lowercase__      )
            print('''-''' * 100      )

            # An empty list to store values of user-entered means of classes
            lowerCAmelCase       :						Tuple							= []
            for a in range(lowercase__      ):
                  lowerCAmelCase       :						str							= valid_input(
                      input_type=lowercase__			, input_msg=(f'''Enter the value of mean for class_{a+1}: ''')			, err_msg='''This is an invalid value.'''			, )
                  user_means.append(lowercase__      )
            print('''-''' * 100      )

            print('''Standard deviation: '''			, lowercase__      )
            # print out the number of instances in classes in separated line
            for i, count in enumerate(lowercase__			, 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(lowercase__			, 1      ):
                  print(f'''Mean of class_{i} is: {user_mean}'''      )
            print('''-''' * 100      )

            # Generating training dataset drawn from gaussian distribution
            lowerCAmelCase       :						List[Any]							= [
                gaussian_distribution(user_means[j]			, lowercase__			, counts[j]      )
                for j in range(lowercase__      )
            ]
            print('''Generated Normal Distribution: \n'''			, lowercase__      )
            print('''-''' * 100      )

            # Generating Ys to detecting corresponding classes
            lowerCAmelCase       :						List[str]							= y_generator(lowercase__			, lowercase__      )
            print('''Generated Corresponding Ys: \n'''			, lowercase__      )
            print('''-''' * 100      )

            # Calculating the value of actual mean for each class
            lowerCAmelCase       :						List[str]							= [calculate_mean(counts[k]			, x[k]      ) for k in range(lowercase__      )]
            # for loop iterates over number of elements in 'actual_means' list and print
            # out them in separated line
            for i, actual_mean in enumerate(lowercase__			, 1      ):
                  print(f'''Actual(Real) mean of class_{i} is: {actual_mean}'''      )
            print('''-''' * 100      )

            # Calculating the value of probabilities for each class
            lowerCAmelCase       :						List[str]							= [
                calculate_probabilities(counts[i]			, sum(lowercase__      )      ) for i in range(lowercase__      )
            ]

            # for loop iterates over number of elements in 'probabilities' list and print
            # out them in separated line
            for i, probability in enumerate(lowercase__			, 1      ):
                  print(f'''Probability of class_{i} is: {probability}'''      )
            print('''-''' * 100      )

            # Calculating the values of variance for each class
            lowerCAmelCase       :						Union[str, Any]							= calculate_variance(lowercase__			, lowercase__			, sum(lowercase__      )      )
            print('''Variance: '''			, lowercase__      )
            print('''-''' * 100      )

            # Predicting Y values
            # storing predicted Y values in 'pre_indexes' variable
            lowerCAmelCase       :						Optional[int]							= predict_y_values(lowercase__			, lowercase__			, lowercase__			, lowercase__      )
            print('''-''' * 100      )

            # Calculating Accuracy of the model
            print(f'''Accuracy: {accuracy(lowercase__			, lowercase__      )}'''      )
            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()









'''simple docstring'''






def    lowercase_   (		lowercase__ = 400_0000    ) ->int:

						if n <= 1:
												return 0
						_snake_case: Union[str, Any]	       =		0
						_snake_case: List[Any]	       =		2
						_snake_case: Any	       =		0
						while 4 * b + a <= n:
												_snake_case       ,    _snake_case: int	       =		b, 4 * b + a
												count += a
						return count + b


if __name__ == "__main__":
		print(F'{solution() = }')





