



import numpy as np



def __lowerCAmelCase (     SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_ = 1e-12						,  SCREAMING_SNAKE_CASE_ = 100						,  ):
			assert np.shape(A_  )[0] == np.shape(A_  )[1]
			# Ensure proper dimensionality.
			assert np.shape(A_  )[0] == np.shape(A_  )[0]
			# Ensure inputs are either both complex or both real
			assert np.iscomplexobj(A_  ) == np.iscomplexobj(A_  )
			lowercase__					  =				np.iscomplexobj(A_  )
			if is_complex:
						# Ensure complex input_matrix is Hermitian
						assert np.array_equal(A_						,  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__					  =				1e12

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

						# 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 __lowerCAmelCase (     ):
			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(A_						,  A_  )

						# Numpy implementation.

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


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_power_iteration()









import json
from typing import Iterator, List, Union

from tokenizers import AddedToken, Regex, Tokenizer, decoders, normalizers, pre_tokenizers, trainers
from tokenizers.implementations.base_tokenizer import BaseTokenizer
from tokenizers.models import Unigram
from tokenizers.processors import TemplateProcessing
class 				_snake_case			(					lowercase__):




				def __init__(						self					:						Optional[Any],					__lowercase					:						str = "▁",					__lowercase					:						bool = True,					__lowercase					:						Union[str, AddedToken] = "<unk>",					__lowercase					:						Union[str, AddedToken] = "</s>",					__lowercase					:						Union[str, AddedToken] = "<pad>",					):
							lowercase__					  =				{
							    "pad": {"id": 0, "token": pad_token},
							    "eos": {"id": 1, "token": eos_token},
							    "unk": {"id": 2, "token": unk_token},
							}

							lowercase__					  =				[None] * len(self.special_tokens						)
							for token_dict in self.special_tokens.values():
										lowercase__					  =				token_dict["token"]

							lowercase__					  =				Tokenizer(Unigram()						)

							lowercase__					  =				normalizers.Sequence(
							    [
							        normalizers.Nmt(),
							        normalizers.NFKC(),
							        normalizers.Replace(Regex(" {2,}"						),					" "						),
							        normalizers.Lowercase(),
							    ]						)
							lowercase__					  =				pre_tokenizers.Sequence(
							    [
							        pre_tokenizers.Metaspace(replacement=__lowercase,					add_prefix_space=__lowercase						),
							        pre_tokenizers.Digits(individual_digits=__lowercase						),
							        pre_tokenizers.Punctuation(),
							    ]						)
							lowercase__					  =				decoders.Metaspace(replacement=__lowercase,					add_prefix_space=__lowercase						)

							lowercase__					  =				TemplateProcessing(
							    single=F'''$A {self.special_tokens["eos"]["token"]}''',					special_tokens=[(self.special_tokens["eos"]["token"], self.special_tokens["eos"]["id"])],					)

							lowercase__					  =				{
							    "model": "SentencePieceUnigram",
							    "replacement": replacement,
							    "add_prefix_space": add_prefix_space,
							}

							super().__init__(__lowercase,					__lowercase						)




				def 							A__      (						self					:						Union[str, Any],					__lowercase					:						Union[str, List[str]],					__lowercase					:						int = 8000,					__lowercase					:						bool = True,					):
							lowercase__					  =				trainers.UnigramTrainer(
							    vocab_size=__lowercase,					special_tokens=self.special_tokens_list,					show_progress=__lowercase,					)

							if isinstance(__lowercase,					__lowercase						):
										lowercase__					  =				[files]
							self._tokenizer.train(__lowercase,					trainer=__lowercase						)

							self.add_unk_id()




				def 							A__      (						self					:						List[Any],					__lowercase					:						Union[Iterator[str], Iterator[Iterator[str]]],					__lowercase					:						int = 8000,					__lowercase					:						bool = True,					):
							lowercase__					  =				trainers.UnigramTrainer(
							    vocab_size=__lowercase,					special_tokens=self.special_tokens_list,					show_progress=__lowercase,					)

							self._tokenizer.train_from_iterator(__lowercase,					trainer=__lowercase						)

							self.add_unk_id()




				def 							A__      (						self					:						str						):
							lowercase__					  =				json.loads(self._tokenizer.to_str()						)

							lowercase__					  =				self.special_tokens["unk"]["id"]

							lowercase__					  =				Tokenizer.from_str(json.dumps(__lowercase						)						)




