'''simple docstring'''




from __future__ import annotations

from typing import Any




def 				lowerCamelCase      ( *UpperCAmelCase__			:   Optional[int]					)     -> Optional[int]:
							if all(_check_not_integer(UpperCAmelCase__					) for m in matrix_s					):
														for i in matrix_s[1:]:
																					_verify_matrix_sizes(matrix_s[0] , UpperCAmelCase__					)
														return [[sum(UpperCAmelCase__					) for t in zip(*UpperCAmelCase__					)] for m in zip(*UpperCAmelCase__					)]
							raise TypeError("""Expected a matrix, got int/list instead"""					)




def 				lowerCamelCase      ( UpperCAmelCase__			:   str , UpperCAmelCase__			:   Any					)     -> Optional[Any]:
							if (
							    _check_not_integer(UpperCAmelCase__					)
							    and _check_not_integer(UpperCAmelCase__					)
							    and _verify_matrix_sizes(UpperCAmelCase__ , UpperCAmelCase__					)
							):
														return [[i - j for i, j in zip(*UpperCAmelCase__					)] for m in zip(UpperCAmelCase__ , UpperCAmelCase__					)]
							raise TypeError("""Expected a matrix, got int/list instead"""					)




def 				lowerCamelCase      ( UpperCAmelCase__			:   Tuple , UpperCAmelCase__			:   int					)     -> Union[str, Any]:
							return [[x * n for x in row] for row in matrix]




def 				lowerCamelCase      ( UpperCAmelCase__			:   Any , UpperCAmelCase__			:   Tuple					)     -> List[str]:
							if _check_not_integer(UpperCAmelCase__					) and _check_not_integer(UpperCAmelCase__					):
														lowercase_		,		lowercase_   :     Any									=			_verify_matrix_sizes(UpperCAmelCase__ , UpperCAmelCase__					)

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




def 				lowerCamelCase      ( UpperCAmelCase__			:   List[Any]					)     -> List[str]:
							lowercase_   :     List[Any]									=			int(UpperCAmelCase__					)
							return [[int(row == column					) for column in range(UpperCAmelCase__					)] for row in range(UpperCAmelCase__					)]




def 				lowerCamelCase      ( UpperCAmelCase__			:   Union[str, Any] , UpperCAmelCase__			:   Tuple = True					)     -> Union[str, Any]:
							if _check_not_integer(UpperCAmelCase__					):
														if return_map:
																					return map(UpperCAmelCase__ , zip(*UpperCAmelCase__					)					)
														else:
																					return list(map(UpperCAmelCase__ , zip(*UpperCAmelCase__					)					)					)
							raise TypeError("""Expected a matrix, got int/list instead"""					)




def 				lowerCamelCase      ( UpperCAmelCase__			:   Optional[int] , UpperCAmelCase__			:   List[Any] , UpperCAmelCase__			:   List[str]					)     -> Dict:
							lowercase_   :     Optional[int]									=			matrix[:row] + matrix[row + 1 :]
							return [row[:column] + row[column + 1 :] for row in minor]




def 				lowerCamelCase      ( UpperCAmelCase__			:   Optional[Any]					)     -> Tuple:
							if len(UpperCAmelCase__					) == 1:
														return matrix[0][0]

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




def 				lowerCamelCase      ( UpperCAmelCase__			:   Tuple					)     -> Optional[Any]:
							lowercase_   :     Optional[Any]									=			determinant(UpperCAmelCase__					)
							if det == 0:
														return None

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

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




def 				lowerCamelCase      ( UpperCAmelCase__			:   List[str]					)     -> Union[str, Any]:
							return not isinstance(UpperCAmelCase__ , UpperCAmelCase__					) and not isinstance(matrix[0] , UpperCAmelCase__					)




def 				lowerCamelCase      ( UpperCAmelCase__			:   List[str]					)     -> Union[str, Any]:
							return len(UpperCAmelCase__					), len(matrix[0]					)




def 				lowerCamelCase      ( UpperCAmelCase__			:   Union[str, Any] , UpperCAmelCase__			:   Tuple					)     -> Dict:
							lowercase_   :     Tuple									=			_shape(UpperCAmelCase__					) + _shape(UpperCAmelCase__					)
							if shape[0] != shape[3] or shape[1] != shape[2]:
														lowercase_   :     List[str]									=			(
														    """operands could not be broadcast together with shape """
														    F'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
														)
														raise ValueError(UpperCAmelCase__					)
							return (shape[0], shape[2]), (shape[1], shape[3])




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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()












import matplotlib.pyplot as plt
import numpy as np




def  A_(      A					,   A					,   A ):
	UpperCAmelCase_		    =  len(A )  # Number of training samples
	UpperCAmelCase_		    =  np.eye(A )  # Initialize weights as identity matrix
	for j in range(A ):
		UpperCAmelCase_		    =  point - x_train[j]
		UpperCAmelCase_		    =  np.exp(diff @ diff.T / (-2.0 * tau**2) )

	return weights




def  A_(      A					,   A					,   A					,   A ):
	UpperCAmelCase_		    =  weight_matrix(A					,   A					,   A )
	UpperCAmelCase_		    =  np.linalg.inv(x_train.T @ weight_mat @ x_train ) @ (
	    x_train.T @ weight_mat @ y_train.T
	)

	return weight




def  A_(      A					,   A					,   A ):
	UpperCAmelCase_		    =  np.zeros(len(A ) )  # Initialize array of predictions
	for i, item in enumerate(A ):
		UpperCAmelCase_		    =  item @ local_weight(A					,   A					,   A					,   A )

	return y_pred




def  A_(      A					,   A					,   A ):
	import seaborn as sns

	UpperCAmelCase_		    =  sns.load_dataset(A )
	UpperCAmelCase_		    =  np.array(data[x_name] )
	UpperCAmelCase_		    =  np.array(data[y_name] )

	UpperCAmelCase_		    =  np.ones(len(A ) )

	# pairing elements of one and x_data
	UpperCAmelCase_		    =  np.column_stack((one, x_data) )

	return x_train, x_data, y_data




def  A_(      A					,   A					,   A					,   A					,   A					,   A					,   ):
	UpperCAmelCase_		    =  np.sort(A					,   axis=0 )
	plt.scatter(A					,   A					,   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(A )
	plt.ylabel(A )
	plt.show()


if __name__ == "__main__":
				import doctest

				doctest.testmod()

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


