"""simple docstring"""




import numpy as np
def 							lowerCAmelCase(     __lowerCamelCase				,    __lowerCamelCase				,    __lowerCamelCase = 1e-1_2				,    __lowerCamelCase = 100				,    ):
					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						)
					__a		 =       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.

					__a		 =       False
					__a		 =       0
					__a		 =       0
					__a		 =       1e1_2

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

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

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

										__a		 =       lambda_

					if is_complex:
										__a		 =       np.real(lambda_						)

					return lambda_, vector
def 							lowerCAmelCase(     ):
					__a		 =       np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]						)
					__a		 =       np.array([41, 4, 20]						)
					__a		 =       real_input_matrix.astype(np.complexaaa						)
					__a		 =       np.triu(1j * complex_input_matrix				,    1						)
					complex_input_matrix += imag_matrix
					complex_input_matrix += -1 * imag_matrix.T
					__a		 =       np.array([41, 4, 20]						).astype(np.complexaaa						)

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

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

										# Numpy implementation.

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





import numpy as np
from sklearn.datasets import fetch_california_housing
from sklearn.metrics import mean_absolute_error, mean_squared_error
from sklearn.model_selection import train_test_split
from xgboost import XGBRegressor
def 							lowerCAmelCase(     __lowerCamelCase						):
					return (data["data"], data["target"])
def 							lowerCAmelCase(     __lowerCamelCase				,    __lowerCamelCase				,    __lowerCamelCase						):
					__a		 =       XGBRegressor(verbosity=0				,    random_state=42						)
					xgb.fit(__lowerCamelCase				,    __lowerCamelCase						)
					# Predict target for test data
					__a		 =       xgb.predict(__lowerCamelCase						)
					__a		 =       predictions.reshape(len(__lowerCamelCase						)				,    1						)
					return predictions
def 							lowerCAmelCase(     ):
					__a		 =       fetch_california_housing()
					__a ,				__a		 =       data_handling(__lowerCamelCase						)
					__a ,				__a ,				__a ,				__a		 =       train_test_split(
					    __lowerCamelCase				,    __lowerCamelCase				,    test_size=0.25				,    random_state=1						)
					__a		 =       xgboost(__lowerCamelCase				,    __lowerCamelCase				,    __lowerCamelCase						)
					# Error printing
					print(f'''Mean Absolute Error : {mean_absolute_error(__lowerCamelCase				,    __lowerCamelCase						)}'''						)
					print(f'''Mean Square Error  : {mean_squared_error(__lowerCamelCase				,    __lowerCamelCase						)}'''						)


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)
	main()




