






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
A_	:	Optional[Any]				=				20

# Time between time steps in seconds
A_	:	Optional[int]				=				INTERVAL / 1000




class        _lowerCAmelCase:





							"""simple docstring"""







							def __init__(      self						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase = 1.0						,    _lowerCamelCase = 1.0						,    _lowerCamelCase = "blue"						,    ):
									UpperCamelCase_:      Optional[int]					   =       position_x
									UpperCamelCase_:      List[str]					   =       position_y
									UpperCamelCase_:      Any					   =       velocity_x
									UpperCamelCase_:      Optional[Any]					   =       velocity_y
									UpperCamelCase_:      List[Any]					   =       mass
									UpperCamelCase_:      Tuple					   =       size
									UpperCamelCase_:      Optional[Any]					   =       color





							@property
							def     _a					(      self							):
									return self.position_x, self.position_y





							@property
							def     _a					(      self							):
									return self.velocity_x, self.velocity_y





							def     _a					(      self						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase							):
									self.velocity_x += force_x * delta_time
									self.velocity_y += force_y * delta_time





							def     _a					(      self						,    _lowerCamelCase							):
									self.position_x += self.velocity_x * delta_time
									self.position_y += self.velocity_y * delta_time







class        _lowerCAmelCase:





							"""simple docstring"""







							def __init__(      self						,    _lowerCamelCase						,    _lowerCamelCase = 1.0						,    _lowerCamelCase = 1.0						,    _lowerCamelCase = 0.0						,    ):
									UpperCamelCase_:      Any					   =       bodies
									UpperCamelCase_:      Dict					   =       gravitation_constant
									UpperCamelCase_:      Union[str, Any]					   =       time_factor
									UpperCamelCase_:      Optional[int]					   =       softening_factor





							def __len__(      self							):
									return len(self.bodies							)





							def     _a					(      self						,    _lowerCamelCase							):
									for bodya in self.bodies:
											UpperCamelCase_:      Any					   =       0.0
											UpperCamelCase_:      List[str]					   =       0.0
											for bodya in self.bodies:
													if bodya != bodya:
															UpperCamelCase_:      Tuple					   =       bodya.position_x - bodya.position_x
															UpperCamelCase_:      Union[str, Any]					   =       bodya.position_y - bodya.position_y

															# Calculation of the distance using Pythagoras's theorem
															# Extra factor due to the softening technique
															UpperCamelCase_:      List[str]					   =       (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(_lowerCamelCase						,    _lowerCamelCase						,    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 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__						) ->       None:
		body_system.update_system(UpperCAmelCase__						)

		# Update the positions of the patches
		for patch, body in zip(UpperCAmelCase__			,					body_system.bodies						):
				UpperCamelCase_:      Union[str, Any]					   =       (body.position_x, body.position_y)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__ = -1			,					UpperCAmelCase__ = 1			,					UpperCAmelCase__ = -1			,					UpperCAmelCase__ = 1			,					) ->       None:
		UpperCamelCase_:      Union[str, Any]					   =       plt.figure()
		fig.canvas.set_window_title(UpperCAmelCase__						)
		UpperCamelCase_:      Optional[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
		UpperCamelCase_:      Optional[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(UpperCAmelCase__						)

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

		UpperCamelCase_:      Optional[Any]					   =       animation.FuncAnimation(  # noqa: F841
		    UpperCAmelCase__			,					UpperCAmelCase__			,					interval=UpperCAmelCase__			,					blit=UpperCAmelCase__						)

		plt.show()

def 						snake_case      () ->       BodySystem:
		UpperCamelCase_:      Optional[Any]					   =       0.970_0436
		UpperCamelCase_:      Optional[Any]					   =       -0.2430_8753
		UpperCamelCase_:      Optional[Any]					   =       0.4_6620_3685
		UpperCamelCase_:      List[Any]					   =       0.4323_6573

		UpperCamelCase_:      Optional[Any]					   =       [
		    Body(UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__			,					size=0.2			,					color='red'						),
		    Body(-position_x			,					-position_y			,					UpperCAmelCase__			,					UpperCAmelCase__			,					size=0.2			,					color='green'						),
		    Body(0			,					0			,					-2 * velocity_x			,					-2 * velocity_y			,					size=0.2			,					color='blue'						),
		]
		return BodySystem(UpperCAmelCase__			,					time_factor=3						)

def 						snake_case      () ->       BodySystem:
		UpperCamelCase_:      Any					   =       7.3476E22
		UpperCamelCase_:      int					   =       5.972E24
		UpperCamelCase_:      Optional[Any]					   =       1_0_2_2
		UpperCamelCase_:      str					   =       3_8_4_3_9_9_0_0_0
		UpperCamelCase_:      Dict					   =       6.674E-11

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

		UpperCamelCase_:      Optional[Any]					   =       Body(-earth_moon_distance			,					0			,					0			,					UpperCAmelCase__			,					UpperCAmelCase__			,					1_0_0_0_0_0_0_0			,					'grey'						)
		UpperCamelCase_:      Optional[Any]					   =       Body(0			,					0			,					0			,					UpperCAmelCase__			,					UpperCAmelCase__			,					5_0_0_0_0_0_0_0			,					'blue'						)
		return BodySystem([earth, moon]			,					UpperCAmelCase__			,					time_factor=1_0_0_0_0_0_0						)

def 						snake_case      () ->       BodySystem:
		UpperCamelCase_:      str					   =       []
		for _ in range(1_0						):
				UpperCamelCase_:      Union[str, Any]					   =       random.uniform(-0.5			,					0.5						)
				UpperCamelCase_:      Dict					   =       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						)			,					UpperCAmelCase__			,					UpperCAmelCase__			,					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(UpperCAmelCase__			,					0.01			,					1_0			,					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(),
			    -430000000,
			    430000000,
			    -430000000,
			    430000000,
			)
			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_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


A_	:	List[Any]				=				{
    'configuration_openai': ['OPENAI_GPT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'OpenAIGPTConfig'],
    'tokenization_openai': ['OpenAIGPTTokenizer'],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_	:	List[str]				=				['OpenAIGPTTokenizerFast']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_	:	Any				=				[
       'OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'OpenAIGPTDoubleHeadsModel',
       'OpenAIGPTForSequenceClassification',
       'OpenAIGPTLMHeadModel',
       'OpenAIGPTModel',
       'OpenAIGPTPreTrainedModel',
       'load_tf_weights_in_openai_gpt',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_	:	str				=				[
       'TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFOpenAIGPTDoubleHeadsModel',
       'TFOpenAIGPTForSequenceClassification',
       'TFOpenAIGPTLMHeadModel',
       'TFOpenAIGPTMainLayer',
       'TFOpenAIGPTModel',
       'TFOpenAIGPTPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_openai import OPENAI_GPT_PRETRAINED_CONFIG_ARCHIVE_MAP, OpenAIGPTConfig
   from .tokenization_openai import OpenAIGPTTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_openai_fast import OpenAIGPTTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_openai import (
          OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          OpenAIGPTDoubleHeadsModel,
          OpenAIGPTForSequenceClassification,
          OpenAIGPTLMHeadModel,
          OpenAIGPTModel,
          OpenAIGPTPreTrainedModel,
          load_tf_weights_in_openai_gpt,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_openai import (
          TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFOpenAIGPTDoubleHeadsModel,
          TFOpenAIGPTForSequenceClassification,
          TFOpenAIGPTLMHeadModel,
          TFOpenAIGPTMainLayer,
          TFOpenAIGPTModel,
          TFOpenAIGPTPreTrainedModel,
      )

else:
   import sys

   A_	:	str				=				_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)