


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray






def 	__lowerCamelCase						(							lowerCamelCase__		:						float  ,							lowerCamelCase__		:						float  ,							lowerCamelCase__		:						bool = False      ):





			'''simple docstring'''




			if radian_mode:
						return [magnitude * cos(lowerCamelCase__      ), magnitude * sin(lowerCamelCase__      )]
			return [magnitude * cos(radians(lowerCamelCase__      )      ), magnitude * sin(radians(lowerCamelCase__      )      )]






def 	__lowerCamelCase						(							lowerCamelCase__		:						NDArray[floataa]  ,							lowerCamelCase__		:						NDArray[floataa]  ,							lowerCamelCase__		:						float = 10**-1      ):





			'''simple docstring'''




			lowerCamelCase    		=  cross(lowerCamelCase__  ,							lowerCamelCase__      )
			lowerCamelCase    		=  sum(lowerCamelCase__      )
			return abs(lowerCamelCase__      ) < eps


if __name__ == "__main__":
		# Test to check if it works
		UpperCAmelCase   :    Dict     =		array(
		    [
		        polar_force(7_1_8.4, 1_80 - 30),
		        polar_force(8_7_9.5_4, 45),
		        polar_force(1_00, -90),
		    ]
		)

		UpperCAmelCase   :    NDArray[floataa]     =		array([[0, 0], [0, 0], [0, 0]])

		assert in_static_equilibrium(forces, location)

		# Problem 1 in image_data/2D_problems.jpg
		UpperCAmelCase   :    Optional[int]     =		array(
		    [
		        polar_force(30 * 9.8_1, 15),
		        polar_force(2_15, 1_80 - 45),
		        polar_force(2_64, 90 - 30),
		    ]
		)

		UpperCAmelCase   :    Optional[Any]     =		array([[0, 0], [0, 0], [0, 0]])

		assert in_static_equilibrium(forces, location)

		# Problem in image_data/2D_problems_1.jpg
		UpperCAmelCase   :    List[str]     =		array([[0, -20_00], [0, -12_00], [0, 1_56_00], [0, -1_24_00]])

		UpperCAmelCase   :    Optional[int]     =		array([[0, 0], [6, 0], [10, 0], [12, 0]])

		assert in_static_equilibrium(forces, location)

		import doctest

		doctest.testmod()





import logging
from dataclasses import dataclass, field
from typing import Optional

from seqaseq_trainer import arg_to_scheduler

from transformers import TrainingArguments


UpperCAmelCase   :    Optional[Any]     =		logging.getLogger(__name__)







@dataclass
class        __lowercase       (							a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Optional[float]			       =		field(
		    default=0.0			,							metadata={"help": "The label smoothing epsilon to apply (if not zero)."}  )
		UpperCamelCase     :					bool			       =		field(default=a_			,							metadata={"help": "Whether to SortishSamler or not."}  )
		UpperCamelCase     :					bool			       =		field(
		    default=a_			,							metadata={"help": "Whether to use generate to calculate generative metrics (ROUGE, BLEU)."}  )
		UpperCamelCase     :					bool			       =		field(default=a_			,							metadata={"help": "whether to use adafactor"}  )
		UpperCamelCase     :					Optional[float]			       =		field(
		    default=a_			,							metadata={"help": "Encoder layer dropout probability. Goes into model.config."}  )
		UpperCamelCase     :					Optional[float]			       =		field(
		    default=a_			,							metadata={"help": "Decoder layer dropout probability. Goes into model.config."}  )
		UpperCamelCase     :					Optional[float]			       =		field(default=a_			,							metadata={"help": "Dropout probability. Goes into model.config."}  )
		UpperCamelCase     :					Optional[float]			       =		field(
		    default=a_			,							metadata={"help": "Attention dropout probability. Goes into model.config."}  )
		UpperCamelCase     :					Optional[str]			       =		field(
		    default="linear"			,							metadata={"help": f'''Which lr scheduler to use. Selected in {sorted(arg_to_scheduler.keys()  )}'''}			,							)

