from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
					import torch

if is_torch_tpu_available(check_device=False):
					import torch_xla.core.xla_model as xm


_lowerCamelCase					:   Union[str, Any]							=		logging.get_logger(__name__)


@dataclass
class 						lowercase    (     a     ):
							lowercase__						:       Optional[int]								=							[
							    """no_inference""",
							    """no_cuda""",
							    """no_tpu""",
							    """no_speed""",
							    """no_memory""",
							    """no_env_print""",
							    """no_multi_process""",
							]




							def __init__(						self   :					Optional[Any]	,							**_UpperCamelCase   :					Optional[Any]      )					->				Union[str, Any]:



												'''simple docstring'''

												for deprecated_arg in self.deprecated_args:
																	if deprecated_arg in kwargs:
																						SCREAMING_SNAKE_CASE    			=       deprecated_arg[3:]
																						setattr(self	,							_UpperCamelCase	,							not kwargs.pop(_UpperCamelCase      )      )
																						logger.warning(
																						    F"{deprecated_arg} is depreciated. Please use --no_{positive_arg} or"
																						    F" {positive_arg}={kwargs[positive_arg]}"      )

												SCREAMING_SNAKE_CASE    			=       kwargs.pop("torchscript"	,							self.torchscript      )
												SCREAMING_SNAKE_CASE    			=       kwargs.pop("torch_xla_tpu_print_metrics"	,							self.torch_xla_tpu_print_metrics      )
												SCREAMING_SNAKE_CASE    			=       kwargs.pop("fp16_opt_level"	,							self.fpaa_opt_level      )
												super().__init__(**_UpperCamelCase      )

							lowercase__						:       bool								=							field(default=a				,       metadata={"""help""": """Trace the models using torchscript"""}     )
							lowercase__						:       bool								=							field(default=a				,       metadata={"""help""": """Print Xla/PyTorch tpu metrics"""}     )
							lowercase__						:       str								=							field(
							    default="""O1"""				,       metadata={
							        """help""": (
							            """For fp16: Apex AMP optimization level selected in ['O0', 'O1', 'O2', and 'O3']. """
							            """See details at https://nvidia.github.io/apex/amp.html"""
							        )
							    }				,       )




							@cached_property
							def 	__snake_case(						self   :					Any      )					->				Tuple["torch.device", int]:



												'''simple docstring'''

												requires_backends(self	,							["torch"]      )
												logger.info("PyTorch: setting up devices"      )
												if not self.cuda:
																	SCREAMING_SNAKE_CASE    			=       torch.device("cpu"      )
																	SCREAMING_SNAKE_CASE    			=       0
												elif is_torch_tpu_available():
																	SCREAMING_SNAKE_CASE    			=       xm.xla_device()
																	SCREAMING_SNAKE_CASE    			=       0
												else:
																	SCREAMING_SNAKE_CASE    			=       torch.device("cuda" if torch.cuda.is_available() else "cpu"      )
																	SCREAMING_SNAKE_CASE    			=       torch.cuda.device_count()
												return device, n_gpu




							@property
							def 	__snake_case(						self   :					Any      )					->				List[str]:



												'''simple docstring'''

												return is_torch_tpu_available() and self.tpu




							@property
							def 	__snake_case(						self   :					Dict      )					->				int:



												'''simple docstring'''

												requires_backends(self	,							["torch"]      )
												# TODO(PVP): currently only single GPU is supported
												return torch.cuda.current_device()




							@property
							def 	__snake_case(						self   :					Optional[Any]      )					->				"torch.device":



												'''simple docstring'''

												requires_backends(self	,							["torch"]      )
												return self._setup_devices[0]




							@property
							def 	__snake_case(						self   :					Dict      )					->				List[Any]:



												'''simple docstring'''

												requires_backends(self	,							["torch"]      )
												return self._setup_devices[1]





							@property
							def 	__snake_case(						self   :					int      )					->				List[str]:



												'''simple docstring'''

												return self.n_gpu > 0





import numpy as np





def 	__lowerCamelCase							(UpperCAmelCase__     :							np.ndarray      , UpperCAmelCase__     :							np.ndarray      , UpperCAmelCase__     :							float = 1e-12      , UpperCAmelCase__     :							int = 1_0_0      , ):
					assert np.shape(UpperCAmelCase__  )[0] == np.shape(UpperCAmelCase__  )[1]
					# Ensure proper dimensionality.
					assert np.shape(UpperCAmelCase__  )[0] == np.shape(UpperCAmelCase__  )[0]
					# Ensure inputs are either both complex or both real
					assert np.iscomplexobj(UpperCAmelCase__  ) == np.iscomplexobj(UpperCAmelCase__  )
					SCREAMING_SNAKE_CASE    			=       np.iscomplexobj(UpperCAmelCase__  )
					if is_complex:
										# Ensure complex input_matrix is Hermitian
										assert np.array_equal(UpperCAmelCase__      , 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.

					SCREAMING_SNAKE_CASE    			=       False
					SCREAMING_SNAKE_CASE    			=       0
					SCREAMING_SNAKE_CASE    			=       0
					SCREAMING_SNAKE_CASE    			=       1e12

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

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

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

										SCREAMING_SNAKE_CASE    			=       lambda_

					if is_complex:
										SCREAMING_SNAKE_CASE    			=       np.real(lambda_  )

					return lambda_, vector





def 	__lowerCamelCase							():
					SCREAMING_SNAKE_CASE    			=       np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]  )
					SCREAMING_SNAKE_CASE    			=       np.array([4_1, 4, 2_0]  )
					SCREAMING_SNAKE_CASE    			=       real_input_matrix.astype(np.complexaaa  )
					SCREAMING_SNAKE_CASE    			=       np.triu(1j * complex_input_matrix      , 1  )
					complex_input_matrix += imag_matrix
					complex_input_matrix += -1 * imag_matrix.T
					SCREAMING_SNAKE_CASE    			=       np.array([4_1, 4, 2_0]  ).astype(np.complexaaa  )

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

										# Our implementation.
										SCREAMING_SNAKE_CASE			,   SCREAMING_SNAKE_CASE    			=       power_iteration(UpperCAmelCase__      , UpperCAmelCase__  )

										# Numpy implementation.

										# Get eigenvalues and eigenvectors using built-in numpy
										# eigh (eigh used for symmetric or hermetian matrices).
										SCREAMING_SNAKE_CASE			,   SCREAMING_SNAKE_CASE    			=       np.linalg.eigh(UpperCAmelCase__  )
										# Last eigenvalue is the maximum one.
										SCREAMING_SNAKE_CASE    			=       eigen_values[-1]
										# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
										SCREAMING_SNAKE_CASE    			=       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(UpperCAmelCase__  ) - np.abs(UpperCAmelCase__  )  ) <= 1e-6


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_power_iteration()




