



'''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  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		seed(1     )
		return [gauss(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ) for _ in range(SCREAMING_SNAKE_CASE     )]







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		return [k for k in range(SCREAMING_SNAKE_CASE     ) for _ in range(instance_count[k]     )]







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		return sum(SCREAMING_SNAKE_CASE     ) / instance_count







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		return instance_count / total_count







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:Tuple										=      []  # 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
		SCREAMING_SNAKE_CASE_						:Optional[Any]										=      len(SCREAMING_SNAKE_CASE     )  # Number of classes in dataset
		return 1 / (total_count - n_classes) * sum(SCREAMING_SNAKE_CASE     )







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:Optional[Any]										=      []
		# 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]     )     ):
						SCREAMING_SNAKE_CASE_						: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(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  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:Any										=      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     )) * 100


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







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE = lambda SCREAMING_SNAKE_CASE     : True ,		SCREAMING_SNAKE_CASE = None ,		):
		while True:
				try:
						SCREAMING_SNAKE_CASE_						:List[Any]										=      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  SCREAMING_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
				SCREAMING_SNAKE_CASE_						:Optional[Any]										=      valid_input(
				    input_type=SCREAMING_SNAKE_CASE ,		condition=lambda SCREAMING_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
				SCREAMING_SNAKE_CASE_						:Optional[int]										=      valid_input(
				    input_type=SCREAMING_SNAKE_CASE ,		condition=lambda SCREAMING_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
				SCREAMING_SNAKE_CASE_						:Tuple										=      []  # An empty list to store instance counts of classes in dataset
				for i in range(SCREAMING_SNAKE_CASE     ):
						SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      valid_input(
						    input_type=SCREAMING_SNAKE_CASE ,		condition=lambda SCREAMING_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('-' * 100     )

				# An empty list to store values of user-entered means of classes
				SCREAMING_SNAKE_CASE_						:str										=      []
				for a in range(SCREAMING_SNAKE_CASE     ):
						SCREAMING_SNAKE_CASE_						:Dict										=      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('-' * 100     )

				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('-' * 100     )

				# 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('-' * 100     )

				# Generating training dataset drawn from gaussian distribution
				SCREAMING_SNAKE_CASE_						:Any										=      [
				    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('-' * 100     )

				# Generating Ys to detecting corresponding classes
				SCREAMING_SNAKE_CASE_						:str										=      y_generator(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )
				print('Generated Corresponding Ys: \n' ,		SCREAMING_SNAKE_CASE     )
				print('-' * 100     )

				# Calculating the value of actual mean for each class
				SCREAMING_SNAKE_CASE_						:Dict										=      [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('-' * 100     )

				# Calculating the value of probabilities for each class
				SCREAMING_SNAKE_CASE_						:Optional[Any]										=      [
				    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('-' * 100     )

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

				# Predicting Y values
				# storing predicted Y values in 'pre_indexes' variable
				SCREAMING_SNAKE_CASE_						:Any										=      predict_y_values(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )
				print('-' * 100     )

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







import matplotlib.pyplot as plt
import numpy as np







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:str										=      len(SCREAMING_SNAKE_CASE     )  # Number of training samples
		SCREAMING_SNAKE_CASE_						:List[Any]										=      np.eye(SCREAMING_SNAKE_CASE     )  # Initialize weights as identity matrix
		for j in range(SCREAMING_SNAKE_CASE     ):
				SCREAMING_SNAKE_CASE_						:Tuple										=      point - x_train[j]
				SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.exp(diff @ diff.T / (-2.0 * tau**2)     )

		return weights







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      weight_matrix(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )
		SCREAMING_SNAKE_CASE_						:str										=      np.linalg.inv(x_train.T @ weight_mat @ x_train     ) @ (
		    x_train.T @ weight_mat @ y_train.T
		)

		return weight







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      np.zeros(len(SCREAMING_SNAKE_CASE     )     )  # Initialize array of predictions
		for i, item in enumerate(SCREAMING_SNAKE_CASE     ):
				SCREAMING_SNAKE_CASE_						:Dict										=      item @ local_weight(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )

		return y_pred







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		import seaborn as sns

		SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      sns.load_dataset(SCREAMING_SNAKE_CASE     )
		SCREAMING_SNAKE_CASE_						:Tuple										=      np.array(data[x_name]     )
		SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.array(data[y_name]     )

		SCREAMING_SNAKE_CASE_						:str										=      np.ones(len(SCREAMING_SNAKE_CASE     )     )

		# pairing elements of one and x_data
		SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.column_stack((one, x_data)     )

		return x_train, x_data, y_data







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		):
		SCREAMING_SNAKE_CASE_						:Tuple										=      np.sort(SCREAMING_SNAKE_CASE ,		axis=0     )
		plt.scatter(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		color='blue'     )
		plt.plot(
		    x_train_sorted[:, 1] ,		preds[x_train[:, 1].argsort(0     )] ,		color='yellow' ,		linewidth=5 ,		)
		plt.title('Local Weighted Regression'     )
		plt.xlabel(SCREAMING_SNAKE_CASE     )
		plt.ylabel(SCREAMING_SNAKE_CASE     )
		plt.show()


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# Demo with a dataset from the seaborn module
							SCREAMING_SNAKE_CASE__	,							SCREAMING_SNAKE_CASE__	,							SCREAMING_SNAKE_CASE__     : str				=   load_data("""tips""", """total_bill""", """tip""")
							SCREAMING_SNAKE_CASE__     : str				=   local_weight_regression(training_data_x, tip, 5)
							plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")
