





from math import radians as angle_to_radians
from math import sin

# Acceleration Constant on Earth (unit m/s^2)
UpperCamelCase__ :			List[str]       	=			9.8_0665




def  A_(      A					,   A ):

	# Ensure valid instance
	if not isinstance(A					,   (int, float) ):
		raise TypeError("""Invalid velocity. Should be a positive number.""" )

	if not isinstance(A					,   (int, float) ):
		raise TypeError("""Invalid angle. Range is 1-90 degrees.""" )

	# Ensure valid angle
	if angle > 90 or angle < 1:
		raise ValueError("""Invalid angle. Range is 1-90 degrees.""" )

	# Ensure valid velocity
	if init_velocity < 0:
		raise ValueError("""Invalid velocity. Should be a positive number.""" )




def  A_(      A					,   A ):
	check_args(A					,   A )
	UpperCAmelCase_		    =  angle_to_radians(2 * angle )
	return round(init_velocity**2 * sin(A ) / g					,   2 )




def  A_(      A					,   A ):
	check_args(A					,   A )
	UpperCAmelCase_		    =  angle_to_radians(A )
	return round(init_velocity**2 * sin(A ) ** 2 / (2 * g)					,   2 )




def  A_(      A					,   A ):
	check_args(A					,   A )
	UpperCAmelCase_		    =  angle_to_radians(A )
	return round(2 * init_velocity * sin(A ) / g					,   2 )




def  A_(      ):
	UpperCAmelCase_    ,						UpperCAmelCase_		    =  25, 20
	assert horizontal_distance(A					,   A ) == 40.97
	assert max_height(A					,   A ) == 3.73
	assert total_time(A					,   A ) == 1.74


if __name__ == "__main__":
				from doctest import testmod

				testmod()

				# Get input from user
				UpperCamelCase__ :			Optional[int]       	=			float(input("""Initial Velocity: """).strip())

				# Get input from user
				UpperCamelCase__ :			Dict       	=			float(input("""angle: """).strip())

				# Print results
				print()
				print("""Results: """)
				print(f"Horizontal Distance: {horizontal_distance(init_vel, angle)!s} [m]")
				print(f"Maximum Height: {max_height(init_vel, angle)!s} [m]")
				print(f"Total Time: {total_time(init_vel, angle)!s} [s]")









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""")


