


'''simple docstring'''

from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowerCamelCase							:       List[str]  						=     20

# Time between time steps in seconds
lowerCamelCase							:       Tuple  						=     INTERVAL / 1_000
class   __lowerCAmelCase						:





						'''simple docstring'''






						def __init__(self   :   Optional[int]       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   str = "blue"       ,						):

													'''simple docstring'''







													lowercase__				      =			position_x
													lowercase__				      =			position_y
													lowercase__				      =			velocity_x
													lowercase__				      =			velocity_y
													lowercase__				      =			mass
													lowercase__				      =			size
													lowercase__				      =			color



						@property
						def 				UpperCamelCase__		(self   :   str			):

													'''simple docstring'''







													return self.position_x, self.position_y



						@property
						def 				UpperCamelCase__		(self   :   int			):

													'''simple docstring'''







													return self.velocity_x, self.velocity_y



						def 				UpperCamelCase__		(self   :   str       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float			):

													'''simple docstring'''







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






						def 				UpperCamelCase__		(self   :   Optional[int]       ,						UpperCamelCase   :   float			):

													'''simple docstring'''







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






class   __lowerCAmelCase						:





						'''simple docstring'''






						def __init__(self   :   int       ,						UpperCamelCase   :   list[Body]       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   float = 0.0       ,						):

													'''simple docstring'''







													lowercase__				      =			bodies
													lowercase__				      =			gravitation_constant
													lowercase__				      =			time_factor
													lowercase__				      =			softening_factor



						def __len__(self   :   Any			):

													'''simple docstring'''







													return len(self.bodies			)






						def 				UpperCamelCase__		(self   :   Any       ,						UpperCamelCase   :   float			):

													'''simple docstring'''







													for bodya in self.bodies:
																				lowercase__				      =			0.0
																				lowercase__				      =			0.0
																				for bodya in self.bodies:
																											if bodya != bodya:
																																		lowercase__				      =			bodya.position_x - bodya.position_x
																																		lowercase__				      =			bodya.position_y - bodya.position_y

																																		# Calculation of the distance using Pythagoras's theorem
																																		# Extra factor due to the softening technique
																																		lowercase__				      =			(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 _SCREAMING_SNAKE_CASE				(A  ,			A  ,			A	)	->	None:






							"""simple docstring"""







							body_system.update_system(A	)

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

def _SCREAMING_SNAKE_CASE				(A  ,			A  ,			A = -1  ,			A = 1  ,			A = -1  ,			A = 1  ,			)	->	None:






							"""simple docstring"""







							lowercase__				      =			plt.figure()
							fig.canvas.set_window_title(A	)
							lowercase__				      =			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
							lowercase__				      =			[
							    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(A	)

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

							lowercase__				      =			animation.FuncAnimation(  # noqa: F841
							    A  ,			A  ,			interval=A  ,			blit=A	)

							plt.show()

def _SCREAMING_SNAKE_CASE				()	->	BodySystem:






							"""simple docstring"""







							lowercase__				      =			0.9_700_436
							lowercase__				      =			-0.24_308_753
							lowercase__				      =			0.466_203_685
							lowercase__				      =			0.43_236_573

							lowercase__				      =			[
							    Body(A  ,			A  ,			A  ,			A  ,			size=0.2  ,			color='''red'''	),
							    Body(-position_x  ,			-position_y  ,			A  ,			A  ,			size=0.2  ,			color='''green'''	),
							    Body(0  ,			0  ,			-2 * velocity_x  ,			-2 * velocity_y  ,			size=0.2  ,			color='''blue'''	),
							]
							return BodySystem(A  ,			time_factor=3	)

def _SCREAMING_SNAKE_CASE				()	->	BodySystem:






							"""simple docstring"""







							lowercase__				      =			7.3_476E22
							lowercase__				      =			5.972E24
							lowercase__				      =			1_022
							lowercase__				      =			384_399_000
							lowercase__				      =			6.674E-11

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

							lowercase__				      =			Body(-earth_moon_distance  ,			0  ,			0  ,			A  ,			A  ,			10_000_000  ,			'''grey'''	)
							lowercase__				      =			Body(0  ,			0  ,			0  ,			A  ,			A  ,			50_000_000  ,			'''blue'''	)
							return BodySystem([earth, moon]  ,			A  ,			time_factor=1_000_000	)

def _SCREAMING_SNAKE_CASE				()	->	BodySystem:






							"""simple docstring"""







							lowercase__				      =			[]
							for _ in range(10	):
														lowercase__				      =			random.uniform(-0.5  ,			0.5	)
														lowercase__				      =			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	)  ,			A  ,			A  ,			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(A  ,			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(),
	    -430_000_000,
	    430_000_000,
	    -430_000_000,
	    430_000_000,
	)
	plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)








'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCamelCase							:       str  						=     {'configuration_nat': ['NAT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'NatConfig']}


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCamelCase							:       Tuple  						=     [
     'NAT_PRETRAINED_MODEL_ARCHIVE_LIST',
     'NatForImageClassification',
     'NatModel',
     'NatPreTrainedModel',
     'NatBackbone',
 ]

if TYPE_CHECKING:
 from .configuration_nat import NAT_PRETRAINED_CONFIG_ARCHIVE_MAP, NatConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_nat import (
      NAT_PRETRAINED_MODEL_ARCHIVE_LIST,
      NatBackbone,
      NatForImageClassification,
      NatModel,
      NatPreTrainedModel,
  )

else:
 import sys

 lowerCamelCase							:       Optional[Any]  						=     _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




