

import numpy as np



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							float = 1e-12	,       SCREAMING_SNAKE_CASE_:							int = 1_0_0	,       )			->      tuple[float, np.ndarray]:




				'''simple docstring'''





				assert np.shape(SCREAMING_SNAKE_CASE_      )[0] == np.shape(SCREAMING_SNAKE_CASE_      )[1]
				# Ensure proper dimensionality.
				assert np.shape(SCREAMING_SNAKE_CASE_      )[0] == np.shape(SCREAMING_SNAKE_CASE_      )[0]
				# Ensure inputs are either both complex or both real
				assert np.iscomplexobj(SCREAMING_SNAKE_CASE_      ) == np.iscomplexobj(SCREAMING_SNAKE_CASE_      )
				A__        =			np.iscomplexobj(SCREAMING_SNAKE_CASE_      )
				if is_complex:
								# Ensure complex input_matrix is Hermitian
								assert np.array_equal(SCREAMING_SNAKE_CASE_	,       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__        =			1e12

				while not convergence:
								# Multiple matrix by the vector.
								A__        =			np.dot(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      )
								# Normalize the resulting output vector.
								A__        =			w / np.linalg.norm(SCREAMING_SNAKE_CASE_      )
								# 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(SCREAMING_SNAKE_CASE_	,       np.dot(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      )      )

								# 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__							(	)			->      None:




				'''simple docstring'''





				A__        =			np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]      )
				A__        =			np.array([4_1, 4, 2_0]      )
				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([4_1, 4, 2_0]      ).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__    ,				A__        =			power_iteration(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      )

								# Numpy implementation.

								# Get eigenvalues and eigenvectors using built-in numpy
								# eigh (eigh used for symmetric or hermetian matrices).
								A__    ,				A__        =			np.linalg.eigh(SCREAMING_SNAKE_CASE_      )
								# 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(SCREAMING_SNAKE_CASE_      ) - np.abs(SCREAMING_SNAKE_CASE_      )      ) <= 1e-6


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	test_power_iteration()




from typing import Union

import fire
import torch
from tqdm import tqdm



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							str	,       SCREAMING_SNAKE_CASE_:							str = "cpu"	,       SCREAMING_SNAKE_CASE_:							Union[str, None] = None      )			->      None:




				'''simple docstring'''





				A__        =			torch.load(SCREAMING_SNAKE_CASE_	,       map_location=SCREAMING_SNAKE_CASE_      )
				for k, v in tqdm(state_dict.items()      ):
								if not isinstance(SCREAMING_SNAKE_CASE_	,       torch.Tensor      ):
												raise TypeError("FP16 conversion only works on paths that are saved state dicts, like pytorch_model.bin"      )
								A__        =			v.half()
				if save_path is None:  # overwrite src_path
								A__        =			src_path
				torch.save(SCREAMING_SNAKE_CASE_	,       SCREAMING_SNAKE_CASE_      )


if __name__ == "__main__":
	fire.Fire(convert)

