



"""simple docstring"""
from math import isclose, sqrt
def    A_  (			_lowercase,					_lowercase,					_lowercase	):







						'''simple docstring'''


						snake_case_ :List[Any]						=			point_y / 4 / point_x
						snake_case_ :Any						=			2 * normal_gradient / (1 + normal_gradient * normal_gradient)
						snake_case_ :Tuple						=			(1 - normal_gradient * normal_gradient) / (
						    1 + normal_gradient * normal_gradient
						)
						snake_case_ :str						=			(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

						# to find the next point, solve the simultaeneous equations:
						# y^2 + 4x^2 = 100
						# y - b = m * (x - a)
						# ==> A x^2 + B x + C = 0
						snake_case_ :Tuple						=			outgoing_gradient**2 + 4
						snake_case_ :List[str]						=			2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
						snake_case_ :Dict						=			(point_y - outgoing_gradient * point_x) ** 2 - 100

						snake_case_ :Optional[Any]						=			(
						    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term	)
						) / (2 * quadratic_term)
						snake_case_ :List[Any]						=			(
						    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term	)
						) / (2 * quadratic_term)

						# two solutions, one of which is our input point
						snake_case_ :Dict						=			x_minus if isclose(_lowercase,					_lowercase	) else x_plus
						snake_case_ :Optional[Any]						=			point_y + outgoing_gradient * (next_x - point_x)

						return next_x, next_y, outgoing_gradient
def    A_  (			_lowercase = 1.4,					_lowercase = -9.6	):







						'''simple docstring'''


						snake_case_ :int						=			0
						snake_case_ :float						=			first_x_coord
						snake_case_ :float						=			first_y_coord
						snake_case_ :float						=			(10.1 - point_y) / (0.0 - point_x)

						while not (-0.01 <= point_x <= 0.01 and point_y > 0):
												snake_case_,       snake_case_,       snake_case_ :List[Any]						=			next_point(_lowercase,					_lowercase,					_lowercase	)
												num_reflections += 1

						return num_reflections


if __name__ == "__main__":
						print(F"""{solution() = }""")





'''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.py''',
            '''model_name_or_path''': '''distilbert-base-cased''',
            '''instance_type''': '''ml.p3.16xlarge''',
            '''results''': {'''train_runtime''': 6_5_0, '''eval_accuracy''': 0.7, '''eval_loss''': 0.6},
        },
        {
            '''framework''': '''pytorch''',
            '''script''': '''run_ddp.py''',
            '''model_name_or_path''': '''distilbert-base-cased''',
            '''instance_type''': '''ml.p3.16xlarge''',
            '''results''': {'''train_runtime''': 6_0_0, '''eval_accuracy''': 0.7, '''eval_loss''': 0.6},
        },
        {
            '''framework''': '''tensorflow''',
            '''script''': '''run_tf_dist.py''',
            '''model_name_or_path''': '''distilbert-base-cased''',
            '''instance_type''': '''ml.p3.16xlarge''',
            '''results''': {'''train_runtime''': 6_0_0, '''eval_accuracy''': 0.6, '''eval_loss''': 0.7},
        },
    ]     )
class        lowerCAmelCase_(				unittest.TestCase     ):
  '''simple docstring'''




  def 							UpperCAmelCase_	(    self      )    ->		Optional[Any]:
      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=__UpperCAmelCase  ,)
      assert hasattr(self  ,"""env"""      )




  def 							UpperCAmelCase_	(    self  ,__UpperCAmelCase      )    ->		Optional[Any]:
      lowerCAmelCase__ :  Optional[int]							      =					F"""{self.env.base_job_name}-{instance_count}-{'ddp' if 'ddp' in self.script else 'smd'}"""
      # distributed data settings
      lowerCAmelCase__ :  Any							      =					{"""smdistributed""": {"""dataparallel""": {"""enabled""": True}}} if self.script != """run_ddp.py""" else None

      # 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=__UpperCAmelCase  ,instance_count=__UpperCAmelCase  ,instance_type=self.instance_type  ,debugger_hook_config=__UpperCAmelCase  ,hyperparameters={**self.env.distributed_hyperparameters, """model_name_or_path""": self.model_name_or_path}  ,metric_definitions=self.env.metric_definitions  ,distribution=__UpperCAmelCase  ,py_version="""py36"""  ,)




  def 							UpperCAmelCase_	(    self  ,__UpperCAmelCase      )    ->		Optional[Any]:
      TrainingJobAnalytics(__UpperCAmelCase      ).export_csv(F"""{self.env.test_path}/{job_name}_metrics.csv"""      )






  @parameterized.expand([(2,)]      )
  def 							UpperCAmelCase_	(    self  ,__UpperCAmelCase      )    ->		Any:
      # create estimator
      lowerCAmelCase__ :  List[Any]							      =					self.create_estimator(__UpperCAmelCase      )

      # run training
      estimator.fit()

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

      # extract kpis
      lowerCAmelCase__ :  int							      =					list(result_metrics_df[result_metrics_df.metric_name == """eval_accuracy"""]["""value"""]      )
      lowerCAmelCase__ :  List[Any]							      =					list(result_metrics_df[result_metrics_df.metric_name == """eval_loss"""]["""value"""]      )
      # get train time from SageMaker job, this includes starting, preprocessing, stopping
      lowerCAmelCase__ :  List[str]							      =					(
          Session().describe_training_job(estimator.latest_training_job.name      ).get("""TrainingTimeInSeconds"""  ,99_9999      )
      )

      # 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}  ,__UpperCAmelCase      )


