




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
SCREAMING_SNAKE_CASE : List[Any]          =    20

# Time between time steps in seconds
SCREAMING_SNAKE_CASE : List[Any]          =    INTERVAL / 10_00





class 					snake_case__  :





	def __init__(  self				,    UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_ = 1.0				,    UpperCamelCase_ = 1.0				,    UpperCamelCase_ = "blue"				,    )		->			None:
								"""simple docstring"""






								a_       :   List[str]			=	position_x
								a_       :   List[str]			=	position_y
								a_       :   List[Any]			=	velocity_x
								a_       :   Dict			=	velocity_y
								a_       :   List[Any]			=	mass
								a_       :   int			=	size
								a_       :   Any			=	color





	@property
	def     A				(  self							)		->			tuple[float, float]:
								"""simple docstring"""






								return self.position_x, self.position_y





	@property
	def     A				(  self							)		->			tuple[float, float]:
								"""simple docstring"""






								return self.velocity_x, self.velocity_y





	def     A				(  self				,    UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_							)		->			None:
								"""simple docstring"""






								self.velocity_x += force_x * delta_time
								self.velocity_y += force_y * delta_time





	def     A				(  self				,    UpperCamelCase_							)		->			None:
								"""simple docstring"""






								self.position_x += self.velocity_x * delta_time
								self.position_y += self.velocity_y * delta_time





class 					snake_case__  :





	def __init__(  self				,    UpperCamelCase_				,    UpperCamelCase_ = 1.0				,    UpperCamelCase_ = 1.0				,    UpperCamelCase_ = 0.0				,    )		->			None:
								"""simple docstring"""






								a_       :   List[Any]			=	bodies
								a_       :   int			=	gravitation_constant
								a_       :   List[str]			=	time_factor
								a_       :   Optional[int]			=	softening_factor





	def __len__(  self							)		->			int:
								"""simple docstring"""






								return len(self.bodies							)





	def     A				(  self				,    UpperCamelCase_							)		->			None:
								"""simple docstring"""






								for bodya in self.bodies:
															a_       :   List[str]			=	0.0
															a_       :   Dict			=	0.0
															for bodya in self.bodies:
																						if bodya != bodya:
																													a_       :   Dict			=	bodya.position_x - bodya.position_x
																													a_       :   List[str]			=	bodya.position_y - bodya.position_y

																													# Calculation of the distance using Pythagoras's theorem
																													# Extra factor due to the softening technique
																													a_       :   Optional[Any]			=	(dif_x**2 + dif_y**2 + self.softening_factor) ** (
																													    1 / 2
																													)

																													# Newton's law of universal gravitation.
																													force_x += (
																													    self.gravitation_constant * bodya.mass * dif_x / distance**3
																													)
																													force_y += (
																													    self.gravitation_constant * bodya.mass * dif_y / distance**3
																													)

            # Update the body's velocity once all the force components have been added
															bodya.update_velocity(UpperCamelCase_				,    UpperCamelCase_				,    delta_time * self.time_factor							)

								# Update the positions only after all the velocities have been updated
								for body in self.bodies:
															body.update_position(delta_time * self.time_factor							)





def 						_lowerCamelCase		(							SCREAMING_SNAKE_CASE_				: BodySystem	,	SCREAMING_SNAKE_CASE_				: float	,	SCREAMING_SNAKE_CASE_				: list[plt.Circle]      ):






							"""simple docstring"""



							body_system.update_system(SCREAMING_SNAKE_CASE_      )

							# Update the positions of the patches
							for patch, body in zip(SCREAMING_SNAKE_CASE_	,	body_system.bodies      ):
														a_       :   int			=	(body.position_x, body.position_y)





def 						_lowerCamelCase		(							SCREAMING_SNAKE_CASE_				: str	,	SCREAMING_SNAKE_CASE_				: BodySystem	,	SCREAMING_SNAKE_CASE_				: float = -1	,	SCREAMING_SNAKE_CASE_				: float = 1	,	SCREAMING_SNAKE_CASE_				: float = -1	,	SCREAMING_SNAKE_CASE_				: float = 1	,	):






							"""simple docstring"""



							a_       :   Dict			=	plt.figure()
							fig.canvas.set_window_title(SCREAMING_SNAKE_CASE_      )
							a_       :   int			=	plt.axes(
							    xlim=(x_start, x_end)	,	ylim=(y_start, y_end)      )  # Set section to be plotted
							plt.gca().set_aspect("""equal"""      )  # Fix aspect ratio

							# Each body is drawn as a patch by the plt-function
							a_       :   Union[str, Any]			=	[
							    plt.Circle((body.position_x, body.position_y)	,	body.size	,	fc=body.color      )
							    for body in body_system.bodies
							]

							for patch in patches:
														ax.add_patch(SCREAMING_SNAKE_CASE_      )

							# Function called at each step of the animation
							def update(SCREAMING_SNAKE_CASE_				: int      ) -> list[plt.Circle]:
														update_step(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      )
														return patches

							a_       :   int			=	animation.FuncAnimation(  # noqa: F841
							    SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	interval=SCREAMING_SNAKE_CASE_	,	blit=SCREAMING_SNAKE_CASE_      )

							plt.show()





def 						_lowerCamelCase		(							):






							"""simple docstring"""



							a_       :   Optional[int]			=	0.9_700_436
							a_       :   int			=	-0.24_308_753
							a_       :   Tuple			=	0.466_203_685
							a_       :   Tuple			=	0.43_236_573

							a_       :   Any			=	[
							    Body(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	size=0.2	,	color="""red"""      ),
							    Body(-position_x	,	-position_y	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	size=0.2	,	color="""green"""      ),
							    Body(0	,	0	,	-2 * velocity_x	,	-2 * velocity_y	,	size=0.2	,	color="""blue"""      ),
							]
							return BodySystem(SCREAMING_SNAKE_CASE_	,	time_factor=3      )





def 						_lowerCamelCase		(							):






							"""simple docstring"""



							a_       :   Tuple			=	7.3476e22
							a_       :   Union[str, Any]			=	5.972e24
							a_       :   int			=	10_22
							a_       :   Optional[Any]			=	3_84_39_90_00
							a_       :   int			=	6.674e-11

							# Calculation of the respective velocities so that total impulse is zero,
							# i.e. the two bodies together don't move
							a_       :   Optional[int]			=	earth_mass * velocity_dif / (earth_mass + moon_mass)
							a_       :   Optional[int]			=	moon_velocity - velocity_dif

							a_       :   Optional[Any]			=	Body(-earth_moon_distance	,	0	,	0	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	10_00_00_00	,	"""grey"""      )
							a_       :   Optional[Any]			=	Body(0	,	0	,	0	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	50_00_00_00	,	"""blue"""      )
							return BodySystem([earth, moon]	,	SCREAMING_SNAKE_CASE_	,	time_factor=1_00_00_00      )





def 						_lowerCamelCase		(							):






							"""simple docstring"""



							a_       :   Dict			=	[]
							for _ in range(10      ):
														a_       :   Union[str, Any]			=	random.uniform(-0.5	,	0.5      )
														a_       :   str			=	random.uniform(-0.5	,	0.5      )

														# Bodies are created pairwise with opposite velocities so that the
														# total impulse remains zero
														bodies.append(
														    Body(
														        random.uniform(-0.5	,	0.5      )	,	random.uniform(-0.5	,	0.5      )	,	SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_	,	size=0.05	,	)      )
														bodies.append(
														    Body(
														        random.uniform(-0.5	,	0.5      )	,	random.uniform(-0.5	,	0.5      )	,	-velocity_x	,	-velocity_y	,	size=0.05	,	)      )
							return BodySystem(SCREAMING_SNAKE_CASE_	,	0.01	,	10	,	0.1      )


if __name__ == "__main__":
	plot("Figure-8 solution to the 3-body-problem", example_a(), -2, 2, -2, 2)
	plot(
	    "Moon's orbit around the earth",
	    example_a(),
	    -4_30_00_00_00,
	    4_30_00_00_00,
	    -4_30_00_00_00,
	    4_30_00_00_00,
	)
	plot("Random system with many bodies", example_a(), -1.5, 1.5, -1.5, 1.5)






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


SCREAMING_SNAKE_CASE : Optional[Any]          =    {
    "configuration_camembert": ["CAMEMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP", "CamembertConfig", "CamembertOnnxConfig"],
}

try:
	if not is_sentencepiece_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	SCREAMING_SNAKE_CASE : Optional[int]          =    ["CamembertTokenizer"]

try:
	if not is_tokenizers_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	SCREAMING_SNAKE_CASE : Any          =    ["CamembertTokenizerFast"]

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	SCREAMING_SNAKE_CASE : Union[str, Any]          =    [
	    "CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST",
	    "CamembertForCausalLM",
	    "CamembertForMaskedLM",
	    "CamembertForMultipleChoice",
	    "CamembertForQuestionAnswering",
	    "CamembertForSequenceClassification",
	    "CamembertForTokenClassification",
	    "CamembertModel",
	    "CamembertPreTrainedModel",
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	SCREAMING_SNAKE_CASE : List[Any]          =    [
	    "TF_CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST",
	    "TFCamembertForCausalLM",
	    "TFCamembertForMaskedLM",
	    "TFCamembertForMultipleChoice",
	    "TFCamembertForQuestionAnswering",
	    "TFCamembertForSequenceClassification",
	    "TFCamembertForTokenClassification",
	    "TFCamembertModel",
	    "TFCamembertPreTrainedModel",
	]


if TYPE_CHECKING:
	from .configuration_camembert import CAMEMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, CamembertConfig, CamembertOnnxConfig

	try:
		if not is_sentencepiece_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_camembert import CamembertTokenizer

	try:
		if not is_tokenizers_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_camembert_fast import CamembertTokenizerFast

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_camembert import (
		    CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
		    CamembertForCausalLM,
		    CamembertForMaskedLM,
		    CamembertForMultipleChoice,
		    CamembertForQuestionAnswering,
		    CamembertForSequenceClassification,
		    CamembertForTokenClassification,
		    CamembertModel,
		    CamembertPreTrainedModel,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_camembert import (
		    TF_CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TFCamembertForCausalLM,
		    TFCamembertForMaskedLM,
		    TFCamembertForMultipleChoice,
		    TFCamembertForQuestionAnswering,
		    TFCamembertForSequenceClassification,
		    TFCamembertForTokenClassification,
		    TFCamembertModel,
		    TFCamembertPreTrainedModel,
		)

else:
	import sys

	SCREAMING_SNAKE_CASE : Any          =    _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


