




import numpy as np







def 		lowercase__   (		__A:	np.ndarray							,__A:	np.ndarray							,__A:	float = 1e-12							,__A:	int = 1_0_0							,):





					'''simple docstring'''






					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				)
					__magic_name__							:	List[str]    							=							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.

					__magic_name__							:	Any    							=							False
					__magic_name__							:	Optional[int]    							=							0
					__magic_name__							:	Tuple    							=							0
					__magic_name__							:	Union[str, Any]    							=							1e12

					while not convergence:
										# Multiple matrix by the vector.
										__magic_name__							:	List[str]    							=							np.dot(__A							,__A				)
										# Normalize the resulting output vector.
										__magic_name__							:	Optional[int]    							=							w / np.linalg.norm(__A				)
										# Find rayleigh quotient
										# (faster than usual b/c we know vector is normalized already)
										__magic_name__							:	Any    							=							vector.conj().T if is_complex else vector.T
										__magic_name__							:	Any    							=							np.dot(__A							,np.dot(__A							,__A				)				)

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

										if error <= error_tol or iterations >= max_iterations:
															__magic_name__							:	Optional[Any]    							=							True

										__magic_name__							:	Any    							=							lambda_

					if is_complex:
										__magic_name__							:	int    							=							np.real(lambda_				)

					return lambda_, vector







def 		lowercase__   (		):





					'''simple docstring'''






					__magic_name__							:	Optional[Any]    							=							np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]				)
					__magic_name__							:	int    							=							np.array([4_1, 4, 2_0]				)
					__magic_name__							:	str    							=							real_input_matrix.astype(np.complexaaa				)
					__magic_name__							:	Optional[Any]    							=							np.triu(1J * complex_input_matrix							,1				)
					complex_input_matrix += imag_matrix
					complex_input_matrix += -1 * imag_matrix.T
					__magic_name__							:	Union[str, Any]    							=							np.array([4_1, 4, 2_0]				).astype(np.complexaaa				)

					for problem_type in ["real", "complex"]:
										if problem_type == "real":
															__magic_name__							:	Dict    							=							real_input_matrix
															__magic_name__							:	Optional[int]    							=							real_vector
										elif problem_type == "complex":
															__magic_name__							:	Dict    							=							complex_input_matrix
															__magic_name__							:	List[str]    							=							complex_vector

										# Our implementation.
										__magic_name__							,    __magic_name__							:	Optional[int]    							=							power_iteration(__A							,__A				)

										# Numpy implementation.

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









# flake8: noqa
# Lint as: python3

from typing import Dict, List, Optional, Type

from .. import config
from ..utils import logging
from .formatting import (
    ArrowFormatter,
    CustomFormatter,
    Formatter,
    PandasFormatter,
    PythonFormatter,
    TensorFormatter,
    format_table,
    query_table,
)
from .np_formatter import NumpyFormatter


__lowerCamelCase   :						int				=			logging.get_logger(__name__)

__lowerCamelCase   :						Dict[Optional[str], Type[Formatter]]				=			{}
__lowerCamelCase   :						Dict[Optional[str], str]				=			{}
__lowerCamelCase   :						Dict[Optional[str], Exception]				=			{}







def 		lowercase__   (		__A:	type							,__A:	Optional[str]							,__A:	Optional[List[str]] = None							,):





					'''simple docstring'''






					__magic_name__							:	Union[str, Any]    							=							aliases if aliases is not None else []
					if format_type in _FORMAT_TYPES:
										logger.warning(
										    F'''Overwriting format type \'{format_type}\' ({_FORMAT_TYPES[format_type].__name__} -> {formatter_cls.__name__})'''				)
					__magic_name__							:	Tuple    							=							formatter_cls
					for alias in set(aliases + [format_type]				):
										if alias in _FORMAT_TYPES_ALIASES:
															logger.warning(
															    F'''Overwriting format type alias \'{alias}\' ({_FORMAT_TYPES_ALIASES[alias]} -> {format_type})'''				)
										__magic_name__							:	Optional[int]    							=							format_type







def 		lowercase__   (		__A:	Exception							,__A:	Optional[str]							,__A:	Optional[List[str]] = None				):





					'''simple docstring'''






					__magic_name__							:	Union[str, Any]    							=							aliases if aliases is not None else []
					for alias in set(aliases + [format_type]				):
										__magic_name__							:	List[str]    							=							unavailable_error


# Here we define all the available formatting functions that can be used by `Dataset.set_format`
_register_formatter(PythonFormatter, None, aliases=['''python'''])
_register_formatter(ArrowFormatter, '''arrow''', aliases=['''pa''', '''pyarrow'''])
_register_formatter(NumpyFormatter, '''numpy''', aliases=['''np'''])
_register_formatter(PandasFormatter, '''pandas''', aliases=['''pd'''])
_register_formatter(CustomFormatter, '''custom''')

if config.TORCH_AVAILABLE:
	from .torch_formatter import TorchFormatter

	_register_formatter(TorchFormatter, '''torch''', aliases=['''pt''', '''pytorch'''])
else:
	__lowerCamelCase   :						str				=			ValueError('''PyTorch needs to be installed to be able to return PyTorch tensors.''')
	_register_unavailable_formatter(_torch_error, '''torch''', aliases=['''pt''', '''pytorch'''])

if config.TF_AVAILABLE:
	from .tf_formatter import TFFormatter

	_register_formatter(TFFormatter, '''tensorflow''', aliases=['''tf'''])
else:
	__lowerCamelCase   :						int				=			ValueError('''Tensorflow needs to be installed to be able to return Tensorflow tensors.''')
	_register_unavailable_formatter(_tf_error, '''tensorflow''', aliases=['''tf'''])

if config.JAX_AVAILABLE:
	from .jax_formatter import JaxFormatter

	_register_formatter(JaxFormatter, '''jax''', aliases=[])
else:
	__lowerCamelCase   :						str				=			ValueError('''JAX needs to be installed to be able to return JAX arrays.''')
	_register_unavailable_formatter(_jax_error, '''jax''', aliases=[])







def 		lowercase__   (		__A:	Optional[str]				):





					'''simple docstring'''






					if format_type in _FORMAT_TYPES_ALIASES:
										return _FORMAT_TYPES_ALIASES[format_type]
					else:
										return format_type







def 		lowercase__   (		__A:	Optional[str]							,**__A:	Any				):





					'''simple docstring'''






					__magic_name__							:	Tuple    							=							get_format_type_from_alias(__A				)
					if format_type in _FORMAT_TYPES:
										return _FORMAT_TYPES[format_type](**__A				)
					if format_type in _FORMAT_TYPES_ALIASES_UNAVAILABLE:
										raise _FORMAT_TYPES_ALIASES_UNAVAILABLE[format_type]
					else:
										raise ValueError(
										    F'''Return type should be None or selected in {list(type for type in _FORMAT_TYPES.keys() if type != None				)}, but got \'{format_type}\''''				)



