






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__   (  __snake_case					:							float  , __snake_case					:							float  , __snake_case					:							int						):


			'''simple docstring'''


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




def   lowercase__   (  __snake_case					:							int  , __snake_case					:							list						):


			'''simple docstring'''


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




def   lowercase__   (  __snake_case					:							int  , __snake_case					:							list						):


			'''simple docstring'''


			return sum(__snake_case						) / instance_count




def   lowercase__   (  __snake_case					:							int  , __snake_case					:							int						):


			'''simple docstring'''


			return instance_count / total_count




def   lowercase__   (  __snake_case					:							list  , __snake_case					:							list  , __snake_case					:							int						):


			'''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list  , __snake_case					:							list  , __snake_case					:							float  , __snake_case					:							list						):


			'''simple docstring'''


			UpperCAmelCase_					:   Optional[int]   =		[]
			# for loop iterates over number of elements in list
			for i in range(len(__snake_case						)						):
						# for loop iterates over number of inner items of each element
						for j in range(len(x_items[i]						)						):
									UpperCAmelCase_					:   Optional[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(__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(__snake_case						)

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




def   lowercase__   (  __snake_case					:							list  , __snake_case					:							list						):


			'''simple docstring'''


			UpperCAmelCase_					:   Tuple   =		sum(1 for i, j in zip(__snake_case  , __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(__snake_case						)) * 100


__UpperCAmelCase										=		TypeVar('num')




def   lowercase__   (  __snake_case					:							Callable[[object], num]  , __snake_case					:							str  , __snake_case					:							str  , __snake_case					:							Callable[[num], bool] = lambda __snake_case						: True  , __snake_case					:							str | None = None  , ):


			'''simple docstring'''


			while True:
						try:
									UpperCAmelCase_					:   Dict   =		input_type(input(__snake_case						).strip() or default						)
									if condition(__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   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_					:   Union[str, Any]   =		valid_input(
						    input_type=__snake_case  , condition=lambda __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
						UpperCAmelCase_					:   List[str]   =		valid_input(
						    input_type=__snake_case  , condition=lambda __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
						UpperCAmelCase_					:   str   =		[]  # An empty list to store instance counts of classes in dataset
						for i in range(__snake_case						):
									UpperCAmelCase_					:   Dict   =		valid_input(
									    input_type=__snake_case  , condition=lambda __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(__snake_case						)
						print('-' * 100						)

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

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

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

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

						# Calculating the value of actual mean for each class
						UpperCAmelCase_					:   str   =		[calculate_mean(counts[k]  , x[k]						) for k in range(__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(__snake_case  , 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(__snake_case						)						) for i in range(__snake_case						)
						]

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

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

						# Predicting Y values
						# storing predicted Y values in 'pre_indexes' variable
						UpperCAmelCase_					:   str   =		predict_y_values(__snake_case  , __snake_case  , __snake_case  , __snake_case						)
						print('-' * 100						)

						# Calculating Accuracy of the model
						print(F"Accuracy: {accuracy(__snake_case  , __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()














from __future__ import annotations

from typing import Any




def   lowercase__   (  *__snake_case					:							list[list[int]]						):


					'''simple docstring'''


					if all(_check_not_integer(__snake_case						) for m in matrix_s						):
										for i in matrix_s[1:]:
															_verify_matrix_sizes(matrix_s[0]  , __snake_case						)
										return [[sum(__snake_case						) for t in zip(*__snake_case						)] for m in zip(*__snake_case						)]
					raise TypeError('Expected a matrix, got int/list instead'						)




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					if (
					    _check_not_integer(__snake_case						)
					    and _check_not_integer(__snake_case						)
					    and _verify_matrix_sizes(__snake_case  , __snake_case						)
					):
										return [[i - j for i, j in zip(*__snake_case						)] for m in zip(__snake_case  , __snake_case						)]
					raise TypeError('Expected a matrix, got int/list instead'						)




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							int | float						):


					'''simple docstring'''


					return [[x * n for x in row] for row in matrix]




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					if _check_not_integer(__snake_case						) and _check_not_integer(__snake_case						):
										UpperCAmelCase_ ,						UpperCAmelCase_					:   str   =		_verify_matrix_sizes(__snake_case  , __snake_case						)

					if cols[0] != rows[1]:
										UpperCAmelCase_					:   Dict   =		(
										    'Cannot multiply matrix of dimensions '
										    F"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
										)
										raise ValueError(__snake_case						)
					return [
					    [sum(m * n for m, n in zip(__snake_case  , __snake_case						)						) for j in zip(*__snake_case						)] for i in matrix_a
					]




def   lowercase__   (  __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[Any]   =		int(__snake_case						)
					return [[int(row == column						) for column in range(__snake_case						)] for row in range(__snake_case						)]




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							bool = True						):


					'''simple docstring'''


					if _check_not_integer(__snake_case						):
										if return_map:
															return map(__snake_case  , zip(*__snake_case						)						)
										else:
															return list(map(__snake_case  , zip(*__snake_case						)						)						)
					raise TypeError('Expected a matrix, got int/list instead'						)




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							int  , __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   Any   =		matrix[:row] + matrix[row + 1 :]
					return [row[:column] + row[column + 1 :] for row in minor]




def   lowercase__   (  __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					if len(__snake_case						) == 1:
										return matrix[0][0]

					return sum(
					    x * determinant(minor(__snake_case  , 0  , __snake_case						)						) * (-1) ** i
					    for i, x in enumerate(matrix[0]						)						)




def   lowercase__   (  __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[int]   =		determinant(__snake_case						)
					if det == 0:
										return None

					UpperCAmelCase_					:   List[str]   =		[
					    [determinant(minor(__snake_case  , __snake_case  , __snake_case						)						) for j in range(len(__snake_case						)						)]
					    for i in range(len(__snake_case						)						)
					]

					UpperCAmelCase_					:   List[str]   =		[
					    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]						)]
					    for row in range(len(__snake_case						)						)
					]
					UpperCAmelCase_					:   Tuple   =		list(transpose(__snake_case						)						)
					return scalar_multiply(__snake_case  , 1 / det						)




def   lowercase__   (  __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					return not isinstance(__snake_case  , __snake_case						) and not isinstance(matrix[0]  , __snake_case						)




def   lowercase__   (  __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					return len(__snake_case						), len(matrix[0]						)




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							list[list[int]]						):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[Any]   =		_shape(__snake_case						) + _shape(__snake_case						)
					if shape[0] != shape[3] or shape[1] != shape[2]:
										UpperCAmelCase_					:   Optional[int]   =		(
										    'operands could not be broadcast together with shape '
										    F"({shape[0], shape[1]}), ({shape[2], shape[3]})"
										)
										raise ValueError(__snake_case						)
					return (shape[0], shape[2]), (shape[1], shape[3])




def   lowercase__   (  ):


					'''simple docstring'''


					UpperCAmelCase_					:   Tuple   =		[[12, 10], [3, 9]]
					UpperCAmelCase_					:   Optional[int]   =		[[3, 4], [7, 4]]
					UpperCAmelCase_					:   List[str]   =		[[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
					UpperCAmelCase_					:   str   =		[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
					print(F"Add Operation, {add(__snake_case  , __snake_case						) = } \n"						)
					print(
					    F"Multiply Operation, {multiply(__snake_case  , __snake_case						) = } \n"  , )
					print(F"Identity: {identity(5						)}\n"						)
					print(F"Minor of {matrix_c} = {minor(__snake_case  , 1  , 2						)} \n"						)
					print(F"Determinant of {matrix_b} = {determinant(__snake_case						)} \n"						)
					print(F"Inverse of {matrix_d} = {inverse(__snake_case						)}\n"						)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()






