


"""simple docstring"""




import unittest
from dataclasses import dataclass

import pytest

from accelerate.commands.config.config_args import SageMakerConfig
from accelerate.utils import ComputeEnvironment
from accelerate.utils.launch import _convert_nargs_to_dict
@dataclass
class 					lowerCAmelCase	(					lowerCamelCase_    ):




		'''simple docstring'''







		SCREAMING_SNAKE_CASE_						:     int								=     ComputeEnvironment.AMAZON_SAGEMAKER
		SCREAMING_SNAKE_CASE_						:     Optional[int]								=     True
		SCREAMING_SNAKE_CASE_						:     Any								=     """ml.p3.2xlarge"""
		SCREAMING_SNAKE_CASE_						:     Union[str, Any]								=     """accelerate_sagemaker_execution_role"""
		SCREAMING_SNAKE_CASE_						:     Dict								=     """hf-sm"""
		SCREAMING_SNAKE_CASE_						:     List[str]								=     """us-east-1"""
		SCREAMING_SNAKE_CASE_						:     str								=     1
		SCREAMING_SNAKE_CASE_						:     int								=     """accelerate-sagemaker-1"""
		SCREAMING_SNAKE_CASE_						:     List[Any]								=     """1.6"""
		SCREAMING_SNAKE_CASE_						:     Dict								=     """4.4"""
		SCREAMING_SNAKE_CASE_						:     Optional[int]								=     """train.py"""
		SCREAMING_SNAKE_CASE_						:     Tuple								=     [
		    """--model_name_or_path""",
		    """bert""",
		    """--do_train""",
		    """False""",
		    """--epochs""",
		    """3""",
		    """--learning_rate""",
		    """5e-5""",
		    """--max_steps""",
		    """50.5""",
		]
		SCREAMING_SNAKE_CASE_						:     Tuple								=     [
		    """--model_name_or_path""",
		    """bert""",
		    """--do_train""",
		    """--do_test""",
		    """False""",
		    """--do_predict""",
		    """--epochs""",
		    """3""",
		    """--learning_rate""",
		    """5e-5""",
		    """--max_steps""",
		    """50.5""",
		]





class 					lowerCAmelCase	(					unittest.TestCase    ):




		'''simple docstring'''







		def 							__A						(	self				)     ->							str:
								# If no defaults are changed, `to_kwargs` returns an empty dict.
								SCREAMING_SNAKE_CASE													=					_convert_nargs_to_dict(MockLaunchConfig.success_training_script_args				)
								assert isinstance(converted_args['model_name_or_path']						,       lowerCAmelCase__				)
								assert isinstance(converted_args['do_train']						,       lowerCAmelCase__				)
								assert isinstance(converted_args['epochs']						,       lowerCAmelCase__				)
								assert isinstance(converted_args['learning_rate']						,       lowerCAmelCase__				)
								assert isinstance(converted_args['max_steps']						,       lowerCAmelCase__				)

								with pytest.raises(lowerCAmelCase__				):
														_convert_nargs_to_dict(MockLaunchConfig.fail_training_script_args				)






"""simple docstring"""




from math import isclose, sqrt


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float  )   ->						tuple[float, float, float]:
						SCREAMING_SNAKE_CASE													=					point_y / 4 / point_x
						SCREAMING_SNAKE_CASE													=					2 * normal_gradient / (1 + normal_gradient * normal_gradient)
						SCREAMING_SNAKE_CASE													=					(1 - normal_gradient * normal_gradient) / (
						    1 + normal_gradient * normal_gradient
						)
						SCREAMING_SNAKE_CASE													=					(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
						SCREAMING_SNAKE_CASE													=					outgoing_gradient**2 + 4
						SCREAMING_SNAKE_CASE													=					2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
						SCREAMING_SNAKE_CASE													=					(point_y - outgoing_gradient * point_x) ** 2 - 1_00

						SCREAMING_SNAKE_CASE													=					(
						    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
						) / (2 * quadratic_term)
						SCREAMING_SNAKE_CASE													=					(
						    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
						) / (2 * quadratic_term)

						# two solutions, one of which is our input point
						SCREAMING_SNAKE_CASE													=					x_minus if isclose(SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_  ) else x_plus
						SCREAMING_SNAKE_CASE													=					point_y + outgoing_gradient * (next_x - point_x)

						return next_x, next_y, outgoing_gradient


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float = 1.4 ,			SCREAMING_SNAKE_CASE_		:				float = -9.6  )   ->						int:
						SCREAMING_SNAKE_CASE													=					0
						SCREAMING_SNAKE_CASE													=					first_x_coord
						SCREAMING_SNAKE_CASE													=					first_y_coord
						SCREAMING_SNAKE_CASE													=					(10.1 - point_y) / (0.0 - point_x)

						while not (-0.01 <= point_x <= 0.01 and point_y > 0):
												SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE													=					next_point(SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_  )
												num_reflections += 1

						return num_reflections


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


