




import numpy as np







def 	_a      (						SCREAMING_SNAKE_CASE_							:				np.ndarray      ,      SCREAMING_SNAKE_CASE_							:				np.ndarray      ,      SCREAMING_SNAKE_CASE_							:				float = 1E-12      ,      SCREAMING_SNAKE_CASE_							:				int = 1_00      ,      ):
					assert np.shape(SCREAMING_SNAKE_CASE_     )[0] == np.shape(SCREAMING_SNAKE_CASE_     )[1]
					# Ensure proper dimensionality.
					assert np.shape(SCREAMING_SNAKE_CASE_     )[0] == np.shape(SCREAMING_SNAKE_CASE_     )[0]
					# Ensure inputs are either both complex or both real
					assert np.iscomplexobj(SCREAMING_SNAKE_CASE_     ) == np.iscomplexobj(SCREAMING_SNAKE_CASE_     )
					__lowerCAmelCase				   =       np.iscomplexobj(SCREAMING_SNAKE_CASE_     )
					if is_complex:
										# Ensure complex input_matrix is Hermitian
										assert np.array_equal(SCREAMING_SNAKE_CASE_      ,      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(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
										# Normalize the resulting output vector.
										__lowerCAmelCase				   =       w / np.linalg.norm(SCREAMING_SNAKE_CASE_     )
										# 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(SCREAMING_SNAKE_CASE_      ,      np.dot(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )     )

										# 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 	_a      (						):
					__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(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )

										# Numpy implementation.

										# Get eigenvalues and eigenvectors using built-in numpy
										# eigh (eigh used for symmetric or hermetian matrices).
										__lowerCAmelCase   ,							__lowerCAmelCase				   =       np.linalg.eigh(SCREAMING_SNAKE_CASE_     )
										# 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(SCREAMING_SNAKE_CASE_     ) - np.abs(SCREAMING_SNAKE_CASE_     )     ) <= 1E-6


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					test_power_iteration()












"""simple docstring"""


import os
import tempfile
import unittest
from pathlib import Path

from transformers import AutoConfig, is_torch_available
from transformers.testing_utils import require_torch, torch_device


if is_torch_available():
       from transformers import PyTorchBenchmark, PyTorchBenchmarkArguments


@require_torch
class 					snake_case		(							unittest.TestCase						):


   '''simple docstring'''

   def 				_SCREAMING_SNAKE_CASE				(	self :     Any,       _lowerCamelCase :     Optional[int]  ):

     '''simple docstring'''
     for model_result in results.values():
       for batch_size, sequence_length in zip(model_result['''bs'''],       model_result['''ss''']  ):
         __A									= model_result['''result'''][batch_size][sequence_length]
         self.assertIsNotNone(_lowerCamelCase  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[Any]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[Any]  ):

     '''simple docstring'''
     __A									= '''sgugger/tiny-distilbert-classification'''
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       only_pretrain_model=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Any  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       torchscript=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   @unittest.skipIf(torch_device == '''cpu''',       '''Cant do half precision'''  )
   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[Any]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       fpaa=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Dict  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= AutoConfig.from_pretrained(_lowerCamelCase  )
     # set architectures equal to `None`
     __A									= None
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase,       configs=[config]  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     int  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_train_result  )
     self.check_results_dict_not_empty(results.memory_train_result  )


   @unittest.skipIf(torch_device == '''cpu''',       '''Can\'t do half precision'''  )
   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[int]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       fpaa=_lowerCamelCase,       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_train_result  )
     self.check_results_dict_not_empty(results.memory_train_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     str  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= AutoConfig.from_pretrained(_lowerCamelCase  )
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase,       configs=[config]  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     List[Any]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tinier_bart'''
     __A									= AutoConfig.from_pretrained(_lowerCamelCase  )
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase,       configs=[config]  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_inference_result  )
     self.check_results_dict_not_empty(results.memory_inference_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[Any]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     __A									= AutoConfig.from_pretrained(_lowerCamelCase  )
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase,       configs=[config]  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_train_result  )
     self.check_results_dict_not_empty(results.memory_train_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Dict  ):

     '''simple docstring'''
     __A									= '''sshleifer/tinier_bart'''
     __A									= AutoConfig.from_pretrained(_lowerCamelCase  )
     __A									= PyTorchBenchmarkArguments(
         models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       multi_process=_lowerCamelCase,       )
     __A									= PyTorchBenchmark(_lowerCamelCase,       configs=[config]  )
     __A									= benchmark.run()
     self.check_results_dict_not_empty(results.time_train_result  )
     self.check_results_dict_not_empty(results.memory_train_result  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[Any]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''
     with tempfile.TemporaryDirectory() as tmp_dir:
       __A									= PyTorchBenchmarkArguments(
           models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       save_to_csv=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       inference_time_csv_file=os.path.join(_lowerCamelCase,       '''inf_time.csv'''  ),       train_memory_csv_file=os.path.join(_lowerCamelCase,       '''train_mem.csv'''  ),       inference_memory_csv_file=os.path.join(_lowerCamelCase,       '''inf_mem.csv'''  ),       train_time_csv_file=os.path.join(_lowerCamelCase,       '''train_time.csv'''  ),       env_info_csv_file=os.path.join(_lowerCamelCase,       '''env.csv'''  ),       multi_process=_lowerCamelCase,       )
       __A									= PyTorchBenchmark(_lowerCamelCase  )
       benchmark.run()
       self.assertTrue(Path(os.path.join(_lowerCamelCase,       '''inf_time.csv'''  )  ).exists()  )
       self.assertTrue(Path(os.path.join(_lowerCamelCase,       '''train_time.csv'''  )  ).exists()  )
       self.assertTrue(Path(os.path.join(_lowerCamelCase,       '''inf_mem.csv'''  )  ).exists()  )
       self.assertTrue(Path(os.path.join(_lowerCamelCase,       '''train_mem.csv'''  )  ).exists()  )
       self.assertTrue(Path(os.path.join(_lowerCamelCase,       '''env.csv'''  )  ).exists()  )






   def 				_SCREAMING_SNAKE_CASE				(	self :     Union[str, Any]  ):

     '''simple docstring'''
     __A									= '''sshleifer/tiny-gpt2'''

     def _check_summary_is_not_empty(_lowerCamelCase :     List[Any]  ):
       self.assertTrue(hasattr(_lowerCamelCase,       '''sequential'''  )  )
       self.assertTrue(hasattr(_lowerCamelCase,       '''cumulative'''  )  )
       self.assertTrue(hasattr(_lowerCamelCase,       '''current'''  )  )
       self.assertTrue(hasattr(_lowerCamelCase,       '''total'''  )  )

     with tempfile.TemporaryDirectory() as tmp_dir:
       __A									= PyTorchBenchmarkArguments(
           models=[MODEL_ID],       training=_lowerCamelCase,       inference=_lowerCamelCase,       sequence_lengths=[8],       batch_sizes=[1],       log_filename=os.path.join(_lowerCamelCase,       '''log.txt'''  ),       log_print=_lowerCamelCase,       trace_memory_line_by_line=_lowerCamelCase,       multi_process=_lowerCamelCase,       )
       __A									= PyTorchBenchmark(_lowerCamelCase  )
       __A									= benchmark.run()
       _check_summary_is_not_empty(result.inference_summary  )
       _check_summary_is_not_empty(result.train_summary  )
       self.assertTrue(Path(os.path.join(_lowerCamelCase,       '''log.txt'''  )  ).exists()  )




