




def  lowerCAmelCase  (	UpperCAmelCase       )  ->list:






					"""simple docstring"""






					if len(UpperCAmelCase       ) <= 1:
										return data
					else:
										return [
										    *quick_sort([e for e in data[1:] if e <= data[0]]       ),
										    data[0],
										    *quick_sort([e for e in data[1:] if e > data[0]]       ),
										]


if __name__ == "__main__":
				import doctest

				doctest.testmod()









from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->list:






					"""simple docstring"""






					seed(1       )
					return [gauss(UpperCAmelCase,	UpperCAmelCase       ) for _ in range(UpperCAmelCase       )]







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->list:






					"""simple docstring"""






					return [k for k in range(UpperCAmelCase       ) for _ in range(instance_count[k]       )]







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->float:






					"""simple docstring"""






					return sum(UpperCAmelCase       ) / instance_count







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->float:






					"""simple docstring"""






					return instance_count / total_count







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->float:






					"""simple docstring"""






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







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->list:






					"""simple docstring"""






					__magic_name__					:							int		   =							[]
					# for loop iterates over number of elements in list
					for i in range(len(UpperCAmelCase       )       ):
										# for loop iterates over number of inner items of each element
										for j in range(len(x_items[i]       )       ):
															__magic_name__					:							Dict		   =							[]  # 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(UpperCAmelCase       )       ):
																				# 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(UpperCAmelCase       )

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







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->float:






					"""simple docstring"""






					__magic_name__					:							Optional[Any]		   =							sum(1 for i, j in zip(UpperCAmelCase,	UpperCAmelCase       ) 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(UpperCAmelCase       )) * 100


lowercase_		=							TypeVar('''num''')







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase = lambda UpperCAmelCase       : True,	UpperCAmelCase = None,	)  ->num:






					"""simple docstring"""






					while True:
										try:
															__magic_name__					:							List[Any]		   =							input_type(input(UpperCAmelCase       ).strip() or default       )
															if condition(UpperCAmelCase       ):
																				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  lowerCAmelCase  (	)  ->str:






					"""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
										__magic_name__					:							List[Any]		   =							valid_input(
										    input_type=UpperCAmelCase,	condition=lambda UpperCAmelCase       : 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
										__magic_name__					:							Any		   =							valid_input(
										    input_type=UpperCAmelCase,	condition=lambda UpperCAmelCase       : 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
										__magic_name__					:							Optional[Any]		   =							[]  # An empty list to store instance counts of classes in dataset
										for i in range(UpperCAmelCase       ):
															__magic_name__					:							Dict		   =							valid_input(
															    input_type=UpperCAmelCase,	condition=lambda UpperCAmelCase       : x > 0,	input_msg=(F'''Enter The number of instances for class_{i+1}: '''),	err_msg='''Number of instances should be positive!''',	)
															counts.append(UpperCAmelCase       )
										print('''-''' * 100       )

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

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

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

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

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

										# Calculating the value of probabilities for each class
										__magic_name__					:							Union[str, Any]		   =							[
										    calculate_probabilities(counts[i],	sum(UpperCAmelCase       )       ) for i in range(UpperCAmelCase       )
										]

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

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

										# Predicting Y values
										# storing predicted Y values in 'pre_indexes' variable
										__magic_name__					:							List[Any]		   =							predict_y_values(UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )
										print('''-''' * 100       )

										# Calculating Accuracy of the model
										print(F'''Accuracy: {accuracy(UpperCAmelCase,	UpperCAmelCase       )}'''       )
										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()



