






import numpy as np
from numpy import floataa
from numpy.typing import NDArray





def 						A_					(						lowercase_	,  lowercase_			)				->NDArray[floataa]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE    ,   SCREAMING_SNAKE_CASE				    =		np.shape(lowercase_			)

 SCREAMING_SNAKE_CASE				    =		np.zeros((rows, 1)	,  dtype=lowercase_			)
 for row in reversed(range(lowercase_			)			):
  SCREAMING_SNAKE_CASE				    =		0
  for col in range(row + 1	,  lowercase_			):
   total += coefficients[row, col] * x[col]

  SCREAMING_SNAKE_CASE				    =		(vector[row] - total) / coefficients[row, row]

 return x





def 						A_					(						lowercase_	,  lowercase_			)				->NDArray[floataa]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE    ,   SCREAMING_SNAKE_CASE				    =		np.shape(lowercase_			)
 if rows != columns:
  return np.array(()	,  dtype=lowercase_			)

 # augmented matrix
 SCREAMING_SNAKE_CASE				    =		np.concatenate((coefficients, vector)	,  axis=1			)
 SCREAMING_SNAKE_CASE				    =		augmented_mat.astype('float64'			)

 # scale the matrix leaving it triangular
 for row in range(rows - 1			):
  SCREAMING_SNAKE_CASE				    =		augmented_mat[row, row]
  for col in range(row + 1	,  lowercase_			):
   SCREAMING_SNAKE_CASE				    =		augmented_mat[col, row] / pivot
   augmented_mat[col, :] -= factor * augmented_mat[row, :]

 SCREAMING_SNAKE_CASE				    =		retroactive_resolution(
     augmented_mat[:, 0:columns]	,  augmented_mat[:, columns : columns + 1]			)

 return x


if __name__ == "__main__":
      import doctest

      doctest.testmod()











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""")


