


import numpy as np

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : List[Any]      ,					SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : Optional[int] = 1E-12      ,					SCREAMING_SNAKE_CASE__      : Optional[Any] = 1_00      ,					):
     assert np.shape(_lowerCAmelCase    )[0] == np.shape(_lowerCAmelCase    )[1]
     # Ensure proper dimensionality.
     assert np.shape(_lowerCAmelCase    )[0] == np.shape(_lowerCAmelCase    )[0]
     # Ensure inputs are either both complex or both real
     assert np.iscomplexobj(_lowerCAmelCase    ) == np.iscomplexobj(_lowerCAmelCase    )
     __UpperCamelCase   							=np.iscomplexobj(_lowerCAmelCase    )
     if is_complex:
          # Ensure complex input_matrix is Hermitian
          assert np.array_equal(_lowerCAmelCase      ,					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.

     __UpperCamelCase   							=False
     __UpperCamelCase   							=0
     __UpperCamelCase   							=0
     __UpperCamelCase   							=1E12

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

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

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

          __UpperCamelCase   							=lambda_

     if is_complex:
          __UpperCamelCase   							=np.real(lambda_    )

     return lambda_, vector

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

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

          # Our implementation.
          __UpperCamelCase   							=power_iteration(_lowerCAmelCase      ,					_lowerCAmelCase    )

          # Numpy implementation.

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   test_power_iteration()









import inspect
import os
import unittest
from dataclasses import dataclass

import torch

from accelerate import Accelerator, DistributedDataParallelKwargs, GradScalerKwargs
from accelerate.state import AcceleratorState
from accelerate.test_utils import execute_subprocess_async, require_cuda, require_multi_gpu
from accelerate.utils import KwargsHandler






@dataclass
class    UpperCAmelCase__	( A_		):



    """simple docstring"""






    UpperCAmelCase__						:		int              =  0
    UpperCAmelCase__						:		bool              =  False
    UpperCAmelCase__						:		float              =  3.0






class    UpperCAmelCase__	( unittest.TestCase		):



    """simple docstring"""






    def _a (      self   )  ->	Any:
         # If no defaults are changed, `to_kwargs` returns an empty dict.
         self.assertDictEqual(MockClass().to_kwargs() ,       {}   )
         self.assertDictEqual(MockClass(a=2   ).to_kwargs() ,       {'a': 2}   )
         self.assertDictEqual(MockClass(a=2 ,       b=A_   ).to_kwargs() ,       {'a': 2, 'b': True}   )
         self.assertDictEqual(MockClass(a=2 ,       c=2.25   ).to_kwargs() ,       {'a': 2, 'c': 2.25}   )






    @require_cuda
    def _a (      self   )  ->	Union[str, Any]:
         # If no defaults are changed, `to_kwargs` returns an empty dict.
         __UpperCamelCase   							=GradScalerKwargs(init_scale=1024 ,       growth_factor=2   )
         AcceleratorState._reset_state()
         __UpperCamelCase   							=Accelerator(mixed_precision='fp16' ,       kwargs_handlers=[scaler_handler]   )
         print(accelerator.use_fpaa   )
         __UpperCamelCase   							=accelerator.scaler

         # Check the kwargs have been applied
         self.assertEqual(scaler._init_scale ,       1024.0   )
         self.assertEqual(scaler._growth_factor ,       2.0   )

         # Check the other values are at the default
         self.assertEqual(scaler._backoff_factor ,       0.5   )
         self.assertEqual(scaler._growth_interval ,       2000   )
         self.assertEqual(scaler._enabled ,       A_   )






    @require_multi_gpu
    def _a (      self   )  ->	Optional[int]:
         __UpperCamelCase   							=['torchrun', f'--nproc_per_node={torch.cuda.device_count()}', inspect.getfile(self.__class__   )]
         execute_subprocess_async(A_ ,       env=os.environ.copy()   )


if __name__ == "__main__":
   _A			=						DistributedDataParallelKwargs(bucket_cap_mb=15, find_unused_parameters=True)
   _A			=						Accelerator(kwargs_handlers=[ddp_scaler])
   _A			=						torch.nn.Linear(100, 200)
   _A			=						accelerator.prepare(model)

   # Check the values changed in kwargs
   _A			=						''
   _A			=						model.bucket_bytes_cap // (1024 * 1024)
   if observed_bucket_cap_map != 15:
      error_msg += f"Kwargs badly passed, should have `15` but found {observed_bucket_cap_map}.\n"
   if model.find_unused_parameters is not True:
      error_msg += f"Kwargs badly passed, should have `True` but found {model.find_unused_parameters}.\n"

   # Check the values of the defaults
   if model.dim != 0:
      error_msg += f"Default value not respected, should have `0` but found {model.dim}.\n"
   if model.broadcast_buffers is not True:
      error_msg += f"Default value not respected, should have `True` but found {model.broadcast_buffers}.\n"
   if model.gradient_as_bucket_view is not False:
      error_msg += f"Default value not respected, should have `False` but found {model.gradient_as_bucket_view}.\n"

   # Raise error at the end to make sure we don't stop at the first failure.
   if len(error_msg) > 0:
      raise ValueError(error_msg)





