
from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
UpperCAmelCase__				:   str   							=			2_0

# Time between time steps in seconds
UpperCAmelCase__				:   Optional[int]   							=			INTERVAL / 1_0_0_0



class      lowerCAmelCase_						:


				"""simple docstring"""



				def __init__(self       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__ = 1.0       ,	SCREAMING_SNAKE_CASE__ = 1.0       ,	SCREAMING_SNAKE_CASE__ = "blue"       ,	) ->		None:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:	Any									=       position_x
											SCREAMING_SNAKE_CASE__						:	Tuple									=       position_y
											SCREAMING_SNAKE_CASE__						:	List[str]									=       velocity_x
											SCREAMING_SNAKE_CASE__						:	str									=       velocity_y
											SCREAMING_SNAKE_CASE__						:	Dict									=       mass
											SCREAMING_SNAKE_CASE__						:	Optional[Any]									=       size
											SCREAMING_SNAKE_CASE__						:	Any									=       color



				@property
				def      __magic_name__   (self   ) ->		tuple[float, float]:



											"""simple docstring"""




											return self.position_x, self.position_y



				@property
				def      __magic_name__   (self   ) ->		tuple[float, float]:



											"""simple docstring"""




											return self.velocity_x, self.velocity_y



				def      __magic_name__   (self       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__   ) ->		None:



											"""simple docstring"""




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



				def      __magic_name__   (self       ,	SCREAMING_SNAKE_CASE__   ) ->		None:



											"""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       ,	SCREAMING_SNAKE_CASE__       ,	SCREAMING_SNAKE_CASE__ = 1.0       ,	SCREAMING_SNAKE_CASE__ = 1.0       ,	SCREAMING_SNAKE_CASE__ = 0.0       ,	) ->		None:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:	Dict									=       bodies
											SCREAMING_SNAKE_CASE__						:	int									=       gravitation_constant
											SCREAMING_SNAKE_CASE__						:	int									=       time_factor
											SCREAMING_SNAKE_CASE__						:	str									=       softening_factor



				def __len__(self   ) ->		int:



											"""simple docstring"""




											return len(self.bodies   )



				def      __magic_name__   (self       ,	SCREAMING_SNAKE_CASE__   ) ->		None:



											"""simple docstring"""




											for bodya in self.bodies:
																		SCREAMING_SNAKE_CASE__						:	Any									=       0.0
																		SCREAMING_SNAKE_CASE__						:	Optional[Any]									=       0.0
																		for bodya in self.bodies:
																									if bodya != bodya:
																																SCREAMING_SNAKE_CASE__						:	Optional[int]									=       bodya.position_x - bodya.position_x
																																SCREAMING_SNAKE_CASE__						:	Any									=       bodya.position_y - bodya.position_y

																																# Calculation of the distance using Pythagoras's theorem
																																# Extra factor due to the softening technique
																																SCREAMING_SNAKE_CASE__						:	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 lowercase_  (       _snake_case       ,_snake_case       ,_snake_case						):
							body_system.update_system(snake_case__						)

							# Update the positions of the patches
							for patch, body in zip(snake_case__       ,body_system.bodies						):
														SCREAMING_SNAKE_CASE__						:	List[str]									=       (body.position_x, body.position_y)

def lowercase_  (       _snake_case       ,_snake_case       ,_snake_case = -1       ,_snake_case = 1       ,_snake_case = -1       ,_snake_case = 1       ,):
							SCREAMING_SNAKE_CASE__						:	Any									=       plt.figure()
							fig.canvas.set_window_title(snake_case__						)
							SCREAMING_SNAKE_CASE__						:	Optional[Any]									=       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
							SCREAMING_SNAKE_CASE__						:	Optional[int]									=       [
							    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(snake_case__						)

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

							SCREAMING_SNAKE_CASE__						:	List[Any]									=       animation.FuncAnimation(  # noqa: F841
							    snake_case__       ,snake_case__       ,interval=snake_case__       ,blit=snake_case__						)

							plt.show()

def lowercase_  (       ):
							SCREAMING_SNAKE_CASE__						:	List[Any]									=       0.9700436
							SCREAMING_SNAKE_CASE__						:	Union[str, Any]									=       -0.24308753
							SCREAMING_SNAKE_CASE__						:	List[str]									=       0.466203685
							SCREAMING_SNAKE_CASE__						:	List[Any]									=       0.43236573

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

def lowercase_  (       ):
							SCREAMING_SNAKE_CASE__						:	int									=       7.34_76E22
							SCREAMING_SNAKE_CASE__						:	List[Any]									=       5.9_72E24
							SCREAMING_SNAKE_CASE__						:	Optional[Any]									=       1_022
							SCREAMING_SNAKE_CASE__						:	Tuple									=       384_399_000
							SCREAMING_SNAKE_CASE__						:	str									=       6.6_74E-11

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

							SCREAMING_SNAKE_CASE__						:	Optional[int]									=       Body(-earth_moon_distance       ,0       ,0       ,snake_case__       ,snake_case__       ,10_000_000       ,"""grey"""						)
							SCREAMING_SNAKE_CASE__						:	int									=       Body(0       ,0       ,0       ,snake_case__       ,snake_case__       ,50_000_000       ,"""blue"""						)
							return BodySystem([earth, moon]       ,snake_case__       ,time_factor=1_000_000						)

def lowercase_  (       ):
							SCREAMING_SNAKE_CASE__						:	Any									=       []
							for _ in range(10						):
														SCREAMING_SNAKE_CASE__						:	Optional[int]									=       random.uniform(-0.5       ,0.5						)
														SCREAMING_SNAKE_CASE__						:	List[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						)       ,snake_case__       ,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(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_3_0_0_0_0_0_0_0,
					    4_3_0_0_0_0_0_0_0,
					    -4_3_0_0_0_0_0_0_0,
					    4_3_0_0_0_0_0_0_0,
					)
					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


UpperCAmelCase__				:   Optional[Any]   							=			{'configuration_umt5': ['UMT5Config', 'UMT5OnnxConfig']}


try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCAmelCase__				:   Tuple   							=			[
					    'UMT5EncoderModel',
					    'UMT5ForConditionalGeneration',
					    'UMT5ForQuestionAnswering',
					    'UMT5Model',
					    'UMT5PreTrainedModel',
					]

if TYPE_CHECKING:
					from .configuration_umta import UMTaConfig, UMTaOnnxConfig

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_umta import (
										    UMTaEncoderModel,
										    UMTaForConditionalGeneration,
										    UMTaForQuestionAnswering,
										    UMTaModel,
										    UMTaPreTrainedModel,
										)
else:
					import sys

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




