



import numpy as np

def      __lowercase(						UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ = 1E-12 , UpperCAmelCase__ = 100 , ):


      """simple docstring"""



      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__			)
      lowerCamelCase             =		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.

      lowerCamelCase             =		False
      lowerCamelCase             =		0
      lowerCamelCase             =		0
      lowerCamelCase             =		1E12

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

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

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

            lowerCamelCase             =		lambda_

      if is_complex:
            lowerCamelCase             =		np.real(lambda_			)

      return lambda_, vector

def      __lowercase(						):


      """simple docstring"""



      lowerCamelCase             =		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]			)
      lowerCamelCase             =		np.array([41, 4, 20]			)
      lowerCamelCase             =		real_input_matrix.astype(np.complexaaa			)
      lowerCamelCase             =		np.triu(1j * complex_input_matrix , 1			)
      complex_input_matrix += imag_matrix
      complex_input_matrix += -1 * imag_matrix.T
      lowerCamelCase             =		np.array([41, 4, 20]			).astype(np.complexaaa			)

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

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

            # Numpy implementation.

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




from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_tf_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_tf_available():
     import tensorflow as tf


a_    :  Any						  =		logging.get_logger(__name__)





@dataclass
class  lowerCamelCase__	(    UpperCAmelCase_):
     """simple docstring"""



     _A      =      [
         'no_inference',
         'no_cuda',
         'no_tpu',
         'no_speed',
         'no_memory',
         'no_env_print',
         'no_multi_process',
     ]







     def __init__(self					,      **__a     ):






           '''simple docstring'''



           for deprecated_arg in self.deprecated_args:
                 if deprecated_arg in kwargs:
                       lowerCamelCase             =		deprecated_arg[3:]
                       lowerCamelCase             =		not kwargs.pop(__a     )
                       logger.warning(
                           F"""{deprecated_arg} is depreciated. Please use --no-{positive_arg} or"""
                           F""" {positive_arg}={kwargs[positive_arg]}"""     )
           lowerCamelCase             =		kwargs.pop("tpu_name"					,      self.tpu_name     )
           lowerCamelCase             =		kwargs.pop("device_idx"					,      self.device_idx     )
           lowerCamelCase             =		kwargs.pop("eager_mode"					,      self.eager_mode     )
           lowerCamelCase             =		kwargs.pop("use_xla"					,      self.use_xla     )
           super().__init__(**__a     )

     _A      =      field(
         default=UpperCAmelCase_							,     metadata={'help': 'Name of TPU'}							,     )
     _A      =      field(
         default=0							,     metadata={'help': 'CPU / GPU device index. Defaults to 0.'}							,     )
     _A      =      field(default=UpperCAmelCase_							,     metadata={'help': 'Benchmark models in eager model.'})
     _A      =      field(
         default=UpperCAmelCase_							,     metadata={
             'help': 'Benchmark models using XLA JIT compilation. Note that `eager_model` has to be set to `False`.'
         }							,     )







     @cached_property
     def     _a   (self     ):






           '''simple docstring'''



           requires_backends(self					,      ["tf"]     )
           lowerCamelCase             =		None
           if self.tpu:
                 try:
                       if self.tpu_name:
                             lowerCamelCase             =		tf.distribute.cluster_resolver.TPUClusterResolver(self.tpu_name     )
                       else:
                             lowerCamelCase             =		tf.distribute.cluster_resolver.TPUClusterResolver()
                 except ValueError:
                       lowerCamelCase             =		None
           return tpu







     @cached_property
     def     _a   (self     ):






           '''simple docstring'''



           requires_backends(self					,      ["tf"]     )
           if self.is_tpu:
                 tf.config.experimental_connect_to_cluster(self._setup_tpu     )
                 tf.tpu.experimental.initialize_tpu_system(self._setup_tpu     )

                 lowerCamelCase             =		tf.distribute.TPUStrategy(self._setup_tpu     )
           else:
                 # currently no multi gpu is allowed
                 if self.is_gpu:
                       # TODO: Currently only single GPU is supported
                       tf.config.set_visible_devices(self.gpu_list[self.device_idx]					,      "GPU"     )
                       lowerCamelCase             =		tf.distribute.OneDeviceStrategy(device=F"""/gpu:{self.device_idx}"""     )
                 else:
                       tf.config.set_visible_devices([]					,      "GPU"     )  # disable GPU
                       lowerCamelCase             =		tf.distribute.OneDeviceStrategy(device=F"""/cpu:{self.device_idx}"""     )

           return strategy







     @property
     def     _a   (self     ):






           '''simple docstring'''



           requires_backends(self					,      ["tf"]     )
           return self._setup_tpu is not None







     @property
     def     _a   (self     ):






           '''simple docstring'''



           requires_backends(self					,      ["tf"]     )
           return self._setup_strategy







     @property
     def     _a   (self     ):






           '''simple docstring'''



           requires_backends(self					,      ["tf"]     )
           return tf.config.list_physical_devices("GPU"     )







     @property
     def     _a   (self     ):






           '''simple docstring'''



           requires_backends(self					,      ["tf"]     )
           if self.cuda:
                 return len(self.gpu_list     )
           return 0







     @property
     def     _a   (self     ):






           '''simple docstring'''



           return self.n_gpu > 0