

import math
def   _lowerCAmelCase(						__A      ):

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5 ,							int(math.sqrt(__A      ) + 1      ) ,							6      ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True
def   _lowerCAmelCase(						__A = 600851475143      ):

  try:
    UpperCAmelCase          =	int(__A      )
  except (TypeError, ValueError):
    raise TypeError("Parameter n must be int or castable to int."      )
  if n <= 0:
    raise ValueError("Parameter n must be greater than or equal to one."      )
  UpperCAmelCase          =	0
  if is_prime(__A      ):
    return n
  while n % 2 == 0:
    n //= 2
  if is_prime(__A      ):
    return n
  for i in range(3 ,							int(math.sqrt(__A      )      ) + 1 ,							2      ):
    if n % i == 0:
      if is_prime(n // i      ):
        UpperCAmelCase          =	n // i
        break
      elif is_prime(__A      ):
        UpperCAmelCase          =	i
  return max_number


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")



