



'''simple docstring'''



import numpy as np



def 	_A							( _lowerCAmelCase	, _lowerCAmelCase	, _lowerCAmelCase = 1e-1_2	, _lowerCAmelCase = 100	, ):



							"""simple docstring"""



							assert np.shape(_lowerCAmelCase       )[0] == np.shape(_lowerCAmelCase       )[1]
							# Ensure proper dimensionality.
							assert np.shape(_lowerCAmelCase       )[0] == np.shape(_lowerCAmelCase       )[0]
							# Ensure inputs are either both complex or both real
							assert np.iscomplexobj(_lowerCAmelCase       ) == np.iscomplexobj(_lowerCAmelCase       )
							__lowercase													=np.iscomplexobj(_lowerCAmelCase       )
							if is_complex:
														# Ensure complex input_matrix is Hermitian
														assert np.array_equal(_lowerCAmelCase	, input_matrix.conj().T       )

							# Set convergence to False. Will define convergence when we exceed max_iterations
							# or when we have small changes from one iteration to next.

							__lowercase													=False
							__lowercase													=0
							__lowercase													=0
							__lowercase													=1e1_2

							while not convergence:
														# Multiple matrix by the vector.
														__lowercase													=np.dot(_lowerCAmelCase	, _lowerCAmelCase       )
														# Normalize the resulting output vector.
														__lowercase													=w / np.linalg.norm(_lowerCAmelCase       )
														# Find rayleigh quotient
														# (faster than usual b/c we know vector is normalized already)
														__lowercase													=vector.conj().T if is_complex else vector.T
														__lowercase													=np.dot(_lowerCAmelCase	, np.dot(_lowerCAmelCase	, _lowerCAmelCase       )       )

														# Check convergence.
														__lowercase													=np.abs(lambda_ - lambda_previous       ) / lambda_
														iterations += 1

														if error <= error_tol or iterations >= max_iterations:
																					__lowercase													=True

														__lowercase													=lambda_

							if is_complex:
														__lowercase													=np.real(lambda_       )

							return lambda_, vector



def 	_A							( ):



							"""simple docstring"""



							__lowercase													=np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]       )
							__lowercase													=np.array([41, 4, 20]       )
							__lowercase													=real_input_matrix.astype(np.complexaaa       )
							__lowercase													=np.triu(1J * complex_input_matrix	, 1       )
							complex_input_matrix += imag_matrix
							complex_input_matrix += -1 * imag_matrix.T
							__lowercase													=np.array([41, 4, 20]       ).astype(np.complexaaa       )

							for problem_type in ["real", "complex"]:
														if problem_type == "real":
																					__lowercase													=real_input_matrix
																					__lowercase													=real_vector
														elif problem_type == "complex":
																					__lowercase													=complex_input_matrix
																					__lowercase													=complex_vector

														# Our implementation.
														__lowercase						,					__lowercase													=power_iteration(_lowerCAmelCase	, _lowerCAmelCase       )

														# Numpy implementation.

														# Get eigenvalues and eigenvectors using built-in numpy
														# eigh (eigh used for symmetric or hermetian matrices).
														__lowercase						,					__lowercase													=np.linalg.eigh(_lowerCAmelCase       )
														# Last eigenvalue is the maximum one.
														__lowercase													=eigen_values[-1]
														# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
														__lowercase													=eigen_vectors[:, -1]

														# Check our implementation and numpy gives close answers.
														assert np.abs(eigen_value - eigen_value_max       ) <= 1e-6
														# Take absolute values element wise of each eigenvector.
														# as they are only unique to a minus sign.
														assert np.linalg.norm(np.abs(_lowerCAmelCase       ) - np.abs(_lowerCAmelCase       )       ) <= 1e-6


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		test_power_iteration()





"""simple docstring"""

from collections import Counter

import numpy as np
from sklearn import datasets
from sklearn.model_selection import train_test_split

SCREAMING_SNAKE_CASE_            =    datasets.load_iris()

SCREAMING_SNAKE_CASE_            =    np.array(data['''data'''])
SCREAMING_SNAKE_CASE_            =    np.array(data['''target'''])
SCREAMING_SNAKE_CASE_            =    data['''target_names''']

SCREAMING_SNAKE_CASE_       ,    SCREAMING_SNAKE_CASE_       ,    SCREAMING_SNAKE_CASE_       ,    SCREAMING_SNAKE_CASE_            =    train_test_split(X, y)




def      lowercase__    (       lowerCAmelCase					:       Optional[int]			,					lowerCAmelCase					:       Any			)			->   Optional[Any]:






    """simple docstring"""




    return np.linalg.norm(np.array(lowerCAmelCase			) - np.array(lowerCAmelCase			)			)




def      lowercase__    (       lowerCAmelCase					:       str			,					lowerCAmelCase					:       Any			,					lowerCAmelCase					:       List[Any]			,					lowerCAmelCase					:       Tuple			,					lowerCAmelCase					:       Dict=5			)			->   str:






    """simple docstring"""




    UpperCAmelCase          =       zip(lowerCAmelCase			,					lowerCAmelCase			)
    # List of distances of all points from the point to be classified
    UpperCAmelCase          =       []
    for data_point in data:
        UpperCAmelCase          =       euclidean_distance(data_point[0]			,					lowerCAmelCase			)
        distances.append((distance, data_point[1])			)
    # Choosing 'k' points with the least distances.
    UpperCAmelCase          =       [i[1] for i in sorted(lowerCAmelCase			)[:k]]
    # Most commonly occurring class among them
    # is the class into which the point is classified
    UpperCAmelCase          =       Counter(lowerCAmelCase			).most_common(1			)[0][0]
    return classes[result]


if __name__ == "__main__":
   print(classifier(X_train, y_train, classes, [4.4, 3.1, 1.3, 1.4]))



