"""simple docstring"""




import numpy as np







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__ = 1e-12			,  lowerCamelCase__ = 100			,  ):





		"""simple docstring"""




		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__     )
		lowerCAmelCase__        =   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.

		lowerCAmelCase__        =   False
		lowerCAmelCase__        =   0
		lowerCAmelCase__        =   0
		lowerCAmelCase__        =   1e12

		while not convergence:
				# Multiple matrix by the vector.
				lowerCAmelCase__        =   np.dot(lowerCamelCase__			,  lowerCamelCase__     )
				# Normalize the resulting output vector.
				lowerCAmelCase__        =   w / np.linalg.norm(lowerCamelCase__     )
				# 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(lowerCamelCase__			,  np.dot(lowerCamelCase__			,  lowerCamelCase__     )     )

				# 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 							_UpperCAmelCase		(       ):





		"""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(lowerCamelCase__			,  lowerCamelCase__     )

				# Numpy implementation.

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			test_power_iteration()





"""simple docstring"""




import json
import os
import subprocess
import unittest
from ast import literal_eval

import pytest
from parameterized import parameterized, parameterized_class

from . import is_sagemaker_available


if is_sagemaker_available():
			from sagemaker import Session, TrainingJobAnalytics
			from sagemaker.huggingface import HuggingFace

@pytest.mark.skipif(
    literal_eval(os.getenv("TEST_SAGEMAKER" ,		"False"			)			) is not True ,		reason="Skipping test because should only be run when releasing minor transformers version" ,		)
@pytest.mark.usefixtures("sm_env"			)
@parameterized_class(
    [
        {
            "framework": "pytorch",
            "script": "run_glue_model_parallelism.py",
            "model_name_or_path": "roberta-large",
            "instance_type": "ml.p3dn.24xlarge",
            "results": {"train_runtime": 1600, "eval_accuracy": 0.3, "eval_loss": 1.2},
        },
        {
            "framework": "pytorch",
            "script": "run_glue.py",
            "model_name_or_path": "roberta-large",
            "instance_type": "ml.p3dn.24xlarge",
            "results": {"train_runtime": 1600, "eval_accuracy": 0.3, "eval_loss": 1.2},
        },
    ]			)
class       a_      (     unittest.TestCase			):




					def 						_SCREAMING_SNAKE_CASE						(	self						:     int     ):
							if self.framework == "pytorch":
									subprocess.run(
									    F"""cp ./examples/pytorch/text-classification/run_glue.py {self.env.test_path}/run_glue.py""".split()  ,						encoding="""utf-8"""  ,						check=snake_case__  ,						)
							assert hasattr(self  ,						"""env"""     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     str  ,						snake_case__						:     Optional[Any]     ):
							# configuration for running training on smdistributed Model Parallel
							lowerCAmelCase__        =   {
							    """enabled""": True,
							    """processes_per_host""": 8,
							}
							lowerCAmelCase__        =   {
							    """enabled""": True,
							    """parameters""": {
							        """microbatches""": 4,
							        """placement_strategy""": """spread""",
							        """pipeline""": """interleaved""",
							        """optimize""": """speed""",
							        """partitions""": 4,
							        """ddp""": True,
							    },
							}

							lowerCAmelCase__        =   {"""smdistributed""": {"""modelparallel""": smp_options}, """mpi""": mpi_options}

							lowerCAmelCase__        =   """trainer""" if self.script == """run_glue.py""" else """smtrainer"""
							# creates estimator
							return HuggingFace(
							    entry_point=self.script  ,						source_dir=self.env.test_path  ,						role=self.env.role  ,						image_uri=self.env.image_uri  ,						base_job_name=F"""{self.env.base_job_name}-{instance_count}-smp-{name_extension}"""  ,						instance_count=snake_case__  ,						instance_type=self.instance_type  ,						debugger_hook_config=snake_case__  ,						hyperparameters={
							        **self.env.hyperparameters,
							        """model_name_or_path""": self.model_name_or_path,
							        """max_steps""": 500,
							    }  ,						metric_definitions=self.env.metric_definitions  ,						distribution=snake_case__  ,						py_version="""py36"""  ,						)




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Union[str, Any]  ,						snake_case__						:     str     ):
							TrainingJobAnalytics(snake_case__     ).export_csv(F"""{self.env.test_path}/{job_name}_metrics.csv"""     )




					@parameterized.expand([(1,)]     )
					def 						_SCREAMING_SNAKE_CASE						(	self						:     List[Any]  ,						snake_case__						:     List[str]     ):
							# create estimator
							lowerCAmelCase__        =   self.create_estimator(snake_case__     )

							# run training
							estimator.fit()

							# result dataframe
							lowerCAmelCase__        =   TrainingJobAnalytics(estimator.latest_training_job.name     ).dataframe()

							# extract kpis
							lowerCAmelCase__        =   list(result_metrics_df[result_metrics_df.metric_name == """eval_accuracy"""]["""value"""]     )
							lowerCAmelCase__        =   list(result_metrics_df[result_metrics_df.metric_name == """eval_loss"""]["""value"""]     )
							# get train time from SageMaker job, this includes starting, preprocessing, stopping
							lowerCAmelCase__        =   (
							    Session().describe_training_job(estimator.latest_training_job.name     ).get("""TrainingTimeInSeconds"""  ,						999999     )
							)

							# assert kpis
							assert train_runtime <= self.results["train_runtime"]
							assert all(t >= self.results["""eval_accuracy"""] for t in eval_accuracy     )
							assert all(t <= self.results["""eval_loss"""] for t in eval_loss     )

							# dump tests result into json file to share in PR
							with open(F"""{estimator.latest_training_job.name}.json"""  ,						"""w"""     ) as outfile:
									json.dump({"""train_time""": train_runtime, """eval_accuracy""": eval_accuracy, """eval_loss""": eval_loss}  ,						snake_case__     )




