import matplotlib.pyplot as plt
import numpy as np

def      lowercase_							(     _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			float):
    lowercase__					:  List[str]          =							len(_lowerCamelCase)  # Number of training samples
    lowercase__					:  Optional[Any]          =							np.eye(_lowerCamelCase)  # Initialize weights as identity matrix
    for j in range(_lowerCamelCase):
        lowercase__					:  Optional[Any]          =							point - x_train[j]
        lowercase__					:  str          =							np.exp(diff @ diff.T / (-2.0 * tau**2))

    return weights

def      lowercase_							(     _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			float):
    lowercase__					:  Tuple          =							weight_matrix(_lowerCamelCase						,      _lowerCamelCase						,      _lowerCamelCase)
    lowercase__					:  List[Any]          =							np.linalg.inv(x_train.T @ weight_mat @ x_train) @ (
        x_train.T @ weight_mat @ y_train.T
    )

    return weight

def      lowercase_							(     _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			float):
    lowercase__					:  Any          =							np.zeros(len(_lowerCamelCase))  # Initialize array of predictions
    for i, item in enumerate(_lowerCamelCase):
        lowercase__					:  Optional[Any]          =							item @ local_weight(_lowerCamelCase						,      _lowerCamelCase						,      _lowerCamelCase						,      _lowerCamelCase)

    return y_pred

def      lowercase_							(     _lowerCamelCase				:			str						,      _lowerCamelCase				:			str						,      _lowerCamelCase				:			str):
    import seaborn as sns

    lowercase__					:  int          =							sns.load_dataset(_lowerCamelCase)
    lowercase__					:  int          =							np.array(data[x_name])
    lowercase__					:  Dict          =							np.array(data[y_name])

    lowercase__					:  Union[str, Any]          =							np.ones(len(_lowerCamelCase))

    # pairing elements of one and x_data
    lowercase__					:  List[Any]          =							np.column_stack((one, x_data))

    return x_train, x_data, y_data

def      lowercase_							(     _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			np.ndarray						,      _lowerCamelCase				:			str						,      _lowerCamelCase				:			str						,      ):
    lowercase__					:  List[str]          =							np.sort(_lowerCamelCase						,      axis=0)
    plt.scatter(_lowerCamelCase						,      _lowerCamelCase						,      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(_lowerCamelCase)
    plt.ylabel(_lowerCamelCase)
    plt.show()


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      # Demo with a dataset from the seaborn module
      UpperCamelCase				,						UpperCamelCase				,						UpperCamelCase    				=		load_data('''tips''', '''total_bill''', '''tip''')
      UpperCamelCase    				=		local_weight_regression(training_data_x, tip, 5)
      plot_preds(training_data_x, predictions, total_bill, tip, '''total_bill''', '''tip''')




def      lowercase_							(     _lowerCamelCase				:			str):
    lowercase__					:  Union[str, Any]          =							0
    for plain_chr in plain_text:
        lowercase__					:  Union[str, Any]          =							(
            ord(_lowerCamelCase) + (hash_value << 6) + (hash_value << 16) - hash_value
        )
    return hash_value



