





import numpy as np





def 					lowerCAmelCase_			(	__a     ,   __a     ,   __a = 1e-12     ,   __a = 100     ,   )					->		tuple[float, np.ndarray]:







  """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		)
  lowerCamelCase__:				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.

  lowerCamelCase__:				int        =False
  lowerCamelCase__:				List[str]        =0
  lowerCamelCase__:				int        =0
  lowerCamelCase__:				int        =1e12

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

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

    if error <= error_tol or iterations >= max_iterations:
      lowerCamelCase__:				Any        =True

    lowerCamelCase__:				List[Any]        =lambda_

  if is_complex:
    lowerCamelCase__:				Dict        =np.real(lambda_		)

  return lambda_, vector





def 					lowerCAmelCase_			(	)					->		None:







  """simple docstring"""





  lowerCamelCase__:				Union[str, Any]        =np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]		)
  lowerCamelCase__:				Dict        =np.array([41, 4, 20]		)
  lowerCamelCase__:				Any        =real_input_matrix.astype(np.complexaaa		)
  lowerCamelCase__:				int        =np.triu(1J * complex_input_matrix     ,   1		)
  complex_input_matrix += imag_matrix
  complex_input_matrix += -1 * imag_matrix.T
  lowerCamelCase__:				List[Any]        =np.array([41, 4, 20]		).astype(np.complexaaa		)

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

    # Our implementation.
    lowerCamelCase__  , lowerCamelCase__:				str        =power_iteration(__a     ,   __a		)

    # Numpy implementation.

    # Get eigenvalues and eigenvectors using built-in numpy
    # eigh (eigh used for symmetric or hermetian matrices).
    lowerCamelCase__  , lowerCamelCase__:				int        =np.linalg.eigh(__a		)
    # Last eigenvalue is the maximum one.
    lowerCamelCase__:				Any        =eigen_values[-1]
    # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
    lowerCamelCase__:				Tuple        =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 inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_huggingface_suite,
    require_multi_gpu,
    require_single_gpu,
)
from accelerate.utils import patch_environment



@require_huggingface_suite
class        _SCREAMING_SNAKE_CASE						(     unittest.TestCase   ):







 '''simple docstring'''

 def 							SCREAMING_SNAKE_CASE_ (self    :       Optional[int])	->Tuple:



   '''simple docstring'''



   lowerCamelCase__:				List[str]        =inspect.getfile(accelerate.test_utils)
   lowerCamelCase__:				str        =os.path.sep.join(
       mod_file.split(os.path.sep)[:-1] + ["scripts", "external_deps", "test_metrics.py"])

   from accelerate.test_utils.scripts.external_deps import test_metrics  # noqa: F401

   lowerCamelCase__:				str        =test_metrics

 @require_cpu
 def 							SCREAMING_SNAKE_CASE_ (self    :       int)	->Any:



   '''simple docstring'''



   debug_launcher(self.test_metrics.main	,			num_processes=1)

 @require_cpu
 def 							SCREAMING_SNAKE_CASE_ (self    :       int)	->int:



   '''simple docstring'''



   debug_launcher(self.test_metrics.main)

 @require_single_gpu
 def 							SCREAMING_SNAKE_CASE_ (self    :       Any)	->int:



   '''simple docstring'''



   self.test_metrics.main()







 @require_multi_gpu
 def 							SCREAMING_SNAKE_CASE_ (self    :       Tuple)	->Dict:



   '''simple docstring'''



   print(F"""Found {torch.cuda.device_count()} devices.""")
   lowerCamelCase__:				Optional[Any]        =["torchrun", F"""--nproc_per_node={torch.cuda.device_count()}""", self.test_file_path]
   with patch_environment(omp_num_threads=1):
     execute_subprocess_async(UpperCAmelCase_	,			env=os.environ.copy())

