



"""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__  (						__lowerCamelCase							:       float				,						__lowerCamelCase							:       float				,						__lowerCamelCase							:       int      ):
			"""simple docstring"""
			seed(1      )
			return [gauss(__lowerCamelCase				,						__lowerCamelCase      ) for _ in range(__lowerCamelCase      )]






def 	snake_case__  (						__lowerCamelCase							:       int				,						__lowerCamelCase							:       list      ):
			"""simple docstring"""
			return [k for k in range(__lowerCamelCase      ) for _ in range(instance_count[k]      )]






def 	snake_case__  (						__lowerCamelCase							:       int				,						__lowerCamelCase							:       list      ):
			"""simple docstring"""
			return sum(__lowerCamelCase      ) / instance_count






def 	snake_case__  (						__lowerCamelCase							:       int				,						__lowerCamelCase							:       int      ):
			"""simple docstring"""
			return instance_count / total_count






def 	snake_case__  (						__lowerCamelCase							:       list				,						__lowerCamelCase							:       list				,						__lowerCamelCase							:       int      ):
			"""simple docstring"""
			lowerCamelCase__						:						str						      =[]  # An empty list to store all squared differences
			# iterate over number of elements in items
			for i in range(len(__lowerCamelCase      )      ):
						# 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__						:						List[str]						      =len(__lowerCamelCase      )  # Number of classes in dataset
			return 1 / (total_count - n_classes) * sum(__lowerCamelCase      )






def 	snake_case__  (						__lowerCamelCase							:       list				,						__lowerCamelCase							:       list				,						__lowerCamelCase							:       float				,						__lowerCamelCase							:       list      ):
			"""simple docstring"""
			lowerCamelCase__						:						List[str]						      =[]
			# for loop iterates over number of elements in list
			for i in range(len(__lowerCamelCase      )      ):
						# for loop iterates over number of inner items of each element
						for j in range(len(x_items[i]      )      ):
									lowerCamelCase__						:						Optional[int]						      =[]  # 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(__lowerCamelCase      )      ):
												# 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(__lowerCamelCase      )

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






def 	snake_case__  (						__lowerCamelCase							:       list				,						__lowerCamelCase							:       list      ):
			"""simple docstring"""
			lowerCamelCase__						:						Union[str, Any]						      =sum(1 for i, j in zip(__lowerCamelCase				,						__lowerCamelCase      ) 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(__lowerCamelCase      )) * 100


_lowercase					:					Optional[int] 		=		TypeVar("num")






def 	snake_case__  (						__lowerCamelCase							:       Callable[[object], num]				,						__lowerCamelCase							:       str				,						__lowerCamelCase							:       str				,						__lowerCamelCase							:       Callable[[num], bool] = lambda __lowerCamelCase      : True				,						__lowerCamelCase							:       str | None = None				,						):
			"""simple docstring"""
			while True:
						try:
									lowerCamelCase__						:						int						      =input_type(input(__lowerCamelCase      ).strip() or default      )
									if condition(__lowerCamelCase      ):
												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__  (						):
			"""simple docstring"""
			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__						:						Optional[int]						      =valid_input(
						    input_type=__lowerCamelCase				,						condition=lambda __lowerCamelCase      : 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__						:						Any						      =valid_input(
						    input_type=__lowerCamelCase				,						condition=lambda __lowerCamelCase      : 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(__lowerCamelCase      ):
									lowerCamelCase__						:						Optional[int]						      =valid_input(
									    input_type=__lowerCamelCase				,						condition=lambda __lowerCamelCase      : x > 0				,						input_msg=(f'''Enter The number of instances for class_{i+1}: ''')				,						err_msg='''Number of instances should be positive!'''				,						)
									counts.append(__lowerCamelCase      )
						print('''-''' * 100      )

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

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

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

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

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

						# Calculating the value of probabilities for each class
						lowerCamelCase__						:						int						      =[
						    calculate_probabilities(counts[i]				,						sum(__lowerCamelCase      )      ) for i in range(__lowerCamelCase      )
						]

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

						# Calculating the values of variance for each class
						lowerCamelCase__						:						List[str]						      =calculate_variance(__lowerCamelCase				,						__lowerCamelCase				,						sum(__lowerCamelCase      )      )
						print('''Variance: '''				,						__lowerCamelCase      )
						print('''-''' * 100      )

						# Predicting Y values
						# storing predicted Y values in 'pre_indexes' variable
						lowerCamelCase__						:						Optional[Any]						      =predict_y_values(__lowerCamelCase				,						__lowerCamelCase				,						__lowerCamelCase				,						__lowerCamelCase      )
						print('''-''' * 100      )

						# Calculating Accuracy of the model
						print(f'''Accuracy: {accuracy(__lowerCamelCase				,						__lowerCamelCase      )}'''      )
						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 	snake_case__  (						__lowerCamelCase							:       int = 998001      ):
			"""simple docstring"""

			# fetches the next number
			for number in range(n - 1				,						9999				,						-1      ):
						lowerCamelCase__						:						Optional[int]						      =str(__lowerCamelCase      )

						# checks whether 'str_number' is a palindrome.
						if str_number == str_number[::-1]:
									lowerCamelCase__						:						Optional[int]						      =999

									# if 'number' is a product of two 3-digit numbers
									# then number is the answer otherwise fetch next number.
									while divisor != 99:
												if (number % divisor == 0) and (len(str(number // divisor      )      ) == 3.0):
															return number
												divisor -= 1
			raise ValueError('''That number is larger than our acceptable range.'''      )


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




