

from __future__ import annotations
def   _lowerCAmelCase(						__A      ):
  UpperCAmelCase          =	[0] * max_one

  for i in range(0 ,							__A      ):
    UpperCAmelCase          =	i

  for i in range(2 ,							__A      ):
    if totients[i] == i:
      for j in range(__A ,							__A ,							__A      ):
        totients[j] -= totients[j] // i

  return totients
def   _lowerCAmelCase(						__A ,							__A      ):
  return sorted(str(__A      )      ) == sorted(str(__A      )      )
def   _lowerCAmelCase(						__A = 10000000      ):
  UpperCAmelCase          =	1  # i
  UpperCAmelCase          =	0  # φ(i)
  UpperCAmelCase          =	get_totients(max_n + 1      )

  for i in range(2 ,							max_n + 1      ):
    UpperCAmelCase          =	totients[i]

    if i * min_denominator < min_numerator * t and has_same_digits(__A ,							__A      ):
      UpperCAmelCase          =	i
      UpperCAmelCase          =	t

  return min_numerator


if __name__ == "__main__":
      print(f"{solution() = }")






import matplotlib.pyplot as plt
import numpy as np
def   _lowerCAmelCase(						__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   _lowerCAmelCase(						__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   _lowerCAmelCase(						__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   _lowerCAmelCase(						__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   _lowerCAmelCase(						__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
      lowerCAmelCase__,			lowerCAmelCase__,			lowerCAmelCase__							=			load_data("tips", "total_bill", "tip")
      lowerCAmelCase__							=			local_weight_regression(training_data_x, tip, 5)
      plot_preds(training_data_x, predictions, total_bill, tip, "total_bill", "tip")



