



'''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   lowercase_	(   lowerCAmelCase__	:  Any			,							lowerCAmelCase__	:  Tuple			,							lowerCAmelCase__	:  Dict ):

			"""simple docstring"""





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


def   lowercase_	(   lowerCAmelCase__	:  Union[str, Any]			,							lowerCAmelCase__	:  str ):

			"""simple docstring"""





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


def   lowercase_	(   lowerCAmelCase__	:  List[Any]			,							lowerCAmelCase__	:  List[str] ):

			"""simple docstring"""





			return sum(lowerCAmelCase__ ) / instance_count


def   lowercase_	(   lowerCAmelCase__	:  Dict			,							lowerCAmelCase__	:  List[Any] ):

			"""simple docstring"""





			return instance_count / total_count


def   lowercase_	(   lowerCAmelCase__	:  Optional[int]			,							lowerCAmelCase__	:  Optional[int]			,							lowerCAmelCase__	:  Tuple ):

			"""simple docstring"""





			__UpperCAmelCase   :      Any										=     []  # 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
			__UpperCAmelCase   :      Optional[int]										=     len(lowerCAmelCase__ )  # Number of classes in dataset
			return 1 / (total_count - n_classes) * sum(lowerCAmelCase__ )


def   lowercase_	(   lowerCAmelCase__	:  Union[str, Any]			,							lowerCAmelCase__	:  Dict			,							lowerCAmelCase__	:  List[str]			,							lowerCAmelCase__	:  Optional[int] ):

			"""simple docstring"""





			__UpperCAmelCase   :      Optional[Any]										=     []
			# 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] ) ):
									__UpperCAmelCase   :      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   lowercase_	(   lowerCAmelCase__	:  Union[str, Any]			,							lowerCAmelCase__	:  int ):

			"""simple docstring"""





			__UpperCAmelCase   :      Tuple										=     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


_UpperCamelCase											=			TypeVar('''num''')


def   lowercase_	(   lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  List[Any]			,							lowerCAmelCase__	:  List[str]			,							lowerCAmelCase__	:  List[str] = lambda lowerCAmelCase__ : True			,							lowerCAmelCase__	:  List[str] = None			,							):

			"""simple docstring"""





			while True:
						try:
									__UpperCAmelCase   :      Optional[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   lowercase_	(   ):

			"""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
						__UpperCAmelCase   :      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
						__UpperCAmelCase   :      Union[str, 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
						__UpperCAmelCase   :      Optional[int]										=     []  # An empty list to store instance counts of classes in dataset
						for i in range(lowerCAmelCase__ ):
									__UpperCAmelCase   :      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
						__UpperCAmelCase   :      List[str]										=     []
						for a in range(lowerCAmelCase__ ):
									__UpperCAmelCase   :      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
						__UpperCAmelCase   :      Tuple										=     [
						    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
						__UpperCAmelCase   :      Any										=     y_generator(lowerCAmelCase__			,							lowerCAmelCase__ )
						print("""Generated Corresponding Ys: \n"""			,							lowerCAmelCase__ )
						print("""-""" * 100 )

						# Calculating the value of actual mean for each class
						__UpperCAmelCase   :      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
						__UpperCAmelCase   :      List[str]										=     [
						    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
						__UpperCAmelCase   :      List[str]										=     calculate_variance(lowerCAmelCase__			,							lowerCAmelCase__			,							sum(lowerCAmelCase__ ) )
						print("""Variance: """			,							lowerCAmelCase__ )
						print("""-""" * 100 )

						# Predicting Y values
						# storing predicted Y values in 'pre_indexes' variable
						__UpperCAmelCase   :      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'''
from __future__ import annotations

from typing import Any



class _A  :





		def __init__(     self ,       __UpperCAmelCase ,       __UpperCAmelCase				)       ->     None:  # noqa: A002

					'''simple docstring'''
					__UpperCAmelCase   :      Tuple										=     item
					__UpperCAmelCase   :      str										=     next



class _A  :





		def __init__(     self				)       ->     None:

					'''simple docstring'''
					__UpperCAmelCase   :      Node | None										=     None
					__UpperCAmelCase   :      Optional[int]										=     0





		def 							__A       (     self ,       __UpperCAmelCase				)       ->     None:

					'''simple docstring'''
					__UpperCAmelCase   :      Optional[Any]										=     Node(__UpperCAmelCase ,       self.head				)
					self.size += 1





		def 							__A       (     self				)       ->     Any:

					'''simple docstring'''
					# Switched 'self.is_empty()' to 'self.head is None'
					# because mypy was considering the possibility that 'self.head'
					# can be None in below else part and giving error
					if self.head is None:
								return None
					else:
								__UpperCAmelCase   :      str										=     self.head.item
								__UpperCAmelCase   :      Tuple										=     self.head.next
								self.size -= 1
								return item





		def 							__A       (     self				)       ->     bool:

					'''simple docstring'''
					return self.head is None





		def __str__(     self				)       ->     str:

					'''simple docstring'''
					if self.is_empty():
								return ""
					else:
								__UpperCAmelCase   :      Union[str, Any]										=     self.head
								__UpperCAmelCase   :      List[Any]										=     """"""
								__UpperCAmelCase   :      list[str]										=     []
								while iterate:
											item_list.append(str(iterate.item				)				)
											__UpperCAmelCase   :      Any										=     iterate.next

								__UpperCAmelCase   :      Dict										=     """ --> """.join(__UpperCAmelCase				)

								return item_str





		def __len__(     self				)       ->     int:

					'''simple docstring'''
					return self.size




