






'''simple docstring'''

def 						_UpperCAmelCase     (	a		:						float    ,      a		:						float    ,      a		:						float				)      ->      list[int]:





						"""simple docstring"""
						if hue < 0 or hue > 3_6_0:
												raise Exception('hue should be between 0 and 360'				)

						if saturation < 0 or saturation > 1:
												raise Exception('saturation should be between 0 and 1'				)

						if value < 0 or value > 1:
												raise Exception('value should be between 0 and 1'				)

						lowercase_   : Optional[int]   	=      value * saturation
						lowercase_   : Tuple   	=      hue / 6_0
						lowercase_   : Dict   	=      chroma * (1 - abs(hue_section % 2 - 1				))
						lowercase_   : str   	=      value - chroma

						if hue_section >= 0 and hue_section <= 1:
												lowercase_   : str   	=      round(2_5_5 * (chroma + match_value)				)
												lowercase_   : List[Any]   	=      round(2_5_5 * (second_largest_component + match_value)				)
												lowercase_   : int   	=      round(2_5_5 * (match_value)				)
						elif hue_section > 1 and hue_section <= 2:
												lowercase_   : Any   	=      round(2_5_5 * (second_largest_component + match_value)				)
												lowercase_   : Optional[Any]   	=      round(2_5_5 * (chroma + match_value)				)
												lowercase_   : str   	=      round(2_5_5 * (match_value)				)
						elif hue_section > 2 and hue_section <= 3:
												lowercase_   : List[str]   	=      round(2_5_5 * (match_value)				)
												lowercase_   : Any   	=      round(2_5_5 * (chroma + match_value)				)
												lowercase_   : Union[str, Any]   	=      round(2_5_5 * (second_largest_component + match_value)				)
						elif hue_section > 3 and hue_section <= 4:
												lowercase_   : List[str]   	=      round(2_5_5 * (match_value)				)
												lowercase_   : Any   	=      round(2_5_5 * (second_largest_component + match_value)				)
												lowercase_   : Optional[Any]   	=      round(2_5_5 * (chroma + match_value)				)
						elif hue_section > 4 and hue_section <= 5:
												lowercase_   : Any   	=      round(2_5_5 * (second_largest_component + match_value)				)
												lowercase_   : str   	=      round(2_5_5 * (match_value)				)
												lowercase_   : int   	=      round(2_5_5 * (chroma + match_value)				)
						else:
												lowercase_   : List[Any]   	=      round(2_5_5 * (chroma + match_value)				)
												lowercase_   : List[str]   	=      round(2_5_5 * (match_value)				)
												lowercase_   : List[Any]   	=      round(2_5_5 * (second_largest_component + match_value)				)

						return [red, green, blue]






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						int    ,      a		:						int				)      ->      list[float]:





						"""simple docstring"""
						if red < 0 or red > 2_5_5:
												raise Exception('red should be between 0 and 255'				)

						if green < 0 or green > 2_5_5:
												raise Exception('green should be between 0 and 255'				)

						if blue < 0 or blue > 2_5_5:
												raise Exception('blue should be between 0 and 255'				)

						lowercase_   : Any   	=      red / 2_5_5
						lowercase_   : Dict   	=      green / 2_5_5
						lowercase_   : Dict   	=      blue / 2_5_5
						lowercase_   : Optional[int]   	=      max(a    ,      a    ,      a				)
						lowercase_   : List[Any]   	=      value - min(a    ,      a    ,      a				)
						lowercase_   : Union[str, Any]   	=      0 if value == 0 else chroma / value

						if chroma == 0:
												lowercase_   : List[Any]   	=      0.0
						elif value == float_red:
												lowercase_   : int   	=      6_0 * (0 + (float_green - float_blue) / chroma)
						elif value == float_green:
												lowercase_   : Optional[Any]   	=      6_0 * (2 + (float_blue - float_red) / chroma)
						else:
												lowercase_   : Dict   	=      6_0 * (4 + (float_red - float_green) / chroma)

						lowercase_   : str   	=      (hue + 3_6_0) % 3_6_0

						return [hue, saturation, value]






def 						_UpperCAmelCase     (	a		:						list[float]    ,      a		:						list[float]				)      ->      bool:





						"""simple docstring"""
						lowercase_   : Optional[Any]   	=      abs(hsv_a[0] - hsv_a[0]				) < 0.2
						lowercase_   : Optional[int]   	=      abs(hsv_a[1] - hsv_a[1]				) < 0.0_02
						lowercase_   : Tuple   	=      abs(hsv_a[2] - hsv_a[2]				) < 0.0_02

						return check_hue and check_saturation and check_value








'''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 						_UpperCAmelCase     (	a		:						float    ,      a		:						float    ,      a		:						int				)      ->      list:





						"""simple docstring"""
						seed(1				)
						return [gauss(a    ,      a				) for _ in range(a				)]






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						list				)      ->      list:





						"""simple docstring"""
						return [k for k in range(a				) for _ in range(instance_count[k]				)]






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						list				)      ->      float:





						"""simple docstring"""
						return sum(a				) / instance_count






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						int				)      ->      float:





						"""simple docstring"""
						return instance_count / total_count






def 						_UpperCAmelCase     (	a		:						list    ,      a		:						list    ,      a		:						int				)      ->      float:





						"""simple docstring"""
						lowercase_   : str   	=      []  # An empty list to store all squared differences
						# iterate over number of elements in items
						for i in range(len(a				)				):
												# 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
						lowercase_   : Tuple   	=      len(a				)  # Number of classes in dataset
						return 1 / (total_count - n_classes) * sum(a				)






def 						_UpperCAmelCase     (	a		:						list    ,      a		:						list    ,      a		:						float    ,      a		:						list				)      ->      list:





						"""simple docstring"""
						lowercase_   : str   	=      []
						# for loop iterates over number of elements in list
						for i in range(len(a				)				):
												# for loop iterates over number of inner items of each element
												for j in range(len(x_items[i]				)				):
																		lowercase_   : Any   	=      []  # 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(a				)				):
																								# 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(a				)

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






def 						_UpperCAmelCase     (	a		:						list    ,      a		:						list				)      ->      float:





						"""simple docstring"""
						lowercase_   : Optional[Any]   	=      sum(1 for i, j in zip(a    ,      a				) 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(a				)) * 1_0_0


A:   Union[str, Any]						=					TypeVar("num")






def 						_UpperCAmelCase     (	a		:						Callable[[object], num]    ,      a		:						str    ,      a		:						str    ,      a		:						Callable[[num], bool] = lambda a				: True    ,      a		:						str | None = None    ,      )      ->      num:





						"""simple docstring"""
						while True:
												try:
																		lowercase_   : int   	=      input_type(input(a				).strip() or default				)
																		if condition(a				):
																								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 						_UpperCAmelCase     (	)      ->      List[str]:





						"""simple docstring"""
						while True:
												print(' Linear Discriminant Analysis '.center(5_0    ,      '*'				)				)
												print('*' * 5_0    ,      '\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
												lowercase_   : Dict   	=      valid_input(
												    input_type=a    ,      condition=lambda a				: x > 0    ,      input_msg='Enter the number of classes (Data Groupings): '    ,      err_msg='Number of classes should be positive!'    ,      )

												print('-' * 1_0_0				)

												# Trying to get the value of standard deviation
												lowercase_   : List[Any]   	=      valid_input(
												    input_type=a    ,      condition=lambda a				: 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('-' * 1_0_0				)

												# Trying to get number of instances in classes and theirs means to generate
												# dataset
												lowercase_   : Any   	=      []  # An empty list to store instance counts of classes in dataset
												for i in range(a				):
																		lowercase_   : Union[str, Any]   	=      valid_input(
																		    input_type=a    ,      condition=lambda a				: x > 0    ,      input_msg=(f"Enter The number of instances for class_{i+1}: ")    ,      err_msg='Number of instances should be positive!'    ,      )
																		counts.append(a				)
												print('-' * 1_0_0				)

												# An empty list to store values of user-entered means of classes
												lowercase_   : int   	=      []
												for a in range(a				):
																		lowercase_   : Union[str, Any]   	=      valid_input(
																		    input_type=a    ,      input_msg=(f"Enter the value of mean for class_{a+1}: ")    ,      err_msg='This is an invalid value.'    ,      )
																		user_means.append(a				)
												print('-' * 1_0_0				)

												print('Standard deviation: '    ,      a				)
												# print out the number of instances in classes in separated line
												for i, count in enumerate(a    ,      1				):
																		print(f"Number of instances in class_{i} is: {count}"				)
												print('-' * 1_0_0				)

												# print out mean values of classes separated line
												for i, user_mean in enumerate(a    ,      1				):
																		print(f"Mean of class_{i} is: {user_mean}"				)
												print('-' * 1_0_0				)

												# Generating training dataset drawn from gaussian distribution
												lowercase_   : Optional[int]   	=      [
												    gaussian_distribution(user_means[j]    ,      a    ,      counts[j]				)
												    for j in range(a				)
												]
												print('Generated Normal Distribution: \n'    ,      a				)
												print('-' * 1_0_0				)

												# Generating Ys to detecting corresponding classes
												lowercase_   : Optional[int]   	=      y_generator(a    ,      a				)
												print('Generated Corresponding Ys: \n'    ,      a				)
												print('-' * 1_0_0				)

												# Calculating the value of actual mean for each class
												lowercase_   : str   	=      [calculate_mean(counts[k]    ,      x[k]				) for k in range(a				)]
												# for loop iterates over number of elements in 'actual_means' list and print
												# out them in separated line
												for i, actual_mean in enumerate(a    ,      1				):
																		print(f"Actual(Real) mean of class_{i} is: {actual_mean}"				)
												print('-' * 1_0_0				)

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

												# for loop iterates over number of elements in 'probabilities' list and print
												# out them in separated line
												for i, probability in enumerate(a    ,      1				):
																		print(f"Probability of class_{i} is: {probability}"				)
												print('-' * 1_0_0				)

												# Calculating the values of variance for each class
												lowercase_   : List[str]   	=      calculate_variance(a    ,      a    ,      sum(a				)				)
												print('Variance: '    ,      a				)
												print('-' * 1_0_0				)

												# Predicting Y values
												# storing predicted Y values in 'pre_indexes' variable
												lowercase_   : Tuple   	=      predict_y_values(a    ,      a    ,      a    ,      a				)
												print('-' * 1_0_0				)

												# Calculating Accuracy of the model
												print(f"Accuracy: {accuracy(a    ,      a				)}"				)
												print('-' * 1_0_0				)
												print(' DONE '.center(1_0_0    ,      '+'				)				)

												if input('Press any key to restart or \'q\' for quit: '				).strip().lower() == "q":
																		print('\n' + 'GoodBye!'.center(1_0_0    ,      '-'				) + '\n'				)
																		break
												system('cls' if name == 'nt' else 'clear'				)  # noqa: S605


if __name__ == "__main__":
						main()
