'''simple docstring'''


from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
snake_case__     :			int      			=  20

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






class      __SCREAMING_SNAKE_CASE						:







  '''simple docstring'''






  def __init__( self      ,		snake_case_      ,		snake_case_      ,		snake_case_      ,		snake_case_      ,		snake_case_ = 1.0      ,		snake_case_ = 1.0      ,		snake_case_ = "blue"      ,		):




       '''simple docstring'''

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


  @property
  def _UpperCamelCase     ( self						):




       '''simple docstring'''

       return self.position_x, self.position_y


  @property
  def _UpperCamelCase     ( self						):




       '''simple docstring'''

       return self.velocity_x, self.velocity_y


  def _UpperCamelCase     ( self      ,		snake_case_      ,		snake_case_      ,		snake_case_						):




       '''simple docstring'''

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






  def _UpperCamelCase     ( self      ,		snake_case_						):




       '''simple docstring'''

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







class      __SCREAMING_SNAKE_CASE						:







  '''simple docstring'''






  def __init__( self      ,		snake_case_      ,		snake_case_ = 1.0      ,		snake_case_ = 1.0      ,		snake_case_ = 0.0      ,		):




       '''simple docstring'''

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


  def __len__( self						):




       '''simple docstring'''

       return len(self.bodies						)






  def _UpperCamelCase     ( self      ,		snake_case_						):




       '''simple docstring'''

       for bodya in self.bodies:
            UpperCAmelCase_							:   Optional[Any]   =      0.0
            UpperCAmelCase_							:   Tuple   =      0.0
            for bodya in self.bodies:
                 if bodya != bodya:
                      UpperCAmelCase_							:   str   =      bodya.position_x - bodya.position_x
                      UpperCAmelCase_							:   str   =      bodya.position_y - bodya.position_y

                      # Calculation of the distance using Pythagoras's theorem
                      # Extra factor due to the softening technique
                      UpperCAmelCase_							:   int   =      (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(snake_case_      ,		snake_case_      ,		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    (      lowerCamelCase_					:							BodySystem	,     lowerCamelCase_					:							float	,     lowerCamelCase_					:							list[plt.Circle]   ):



     """simple docstring"""





     body_system.update_system(lowerCamelCase_   )

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


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



     """simple docstring"""





     UpperCAmelCase_							:   int   =      plt.figure()
     fig.canvas.set_window_title(lowerCamelCase_   )
     UpperCAmelCase_							:   Dict   =      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_							:   str   =      [
         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(lowerCamelCase_   )

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

     UpperCAmelCase_							:   Optional[int]   =      animation.FuncAnimation(  # noqa: F841
         lowerCamelCase_	,     lowerCamelCase_	,     interval=lowerCamelCase_	,     blit=lowerCamelCase_   )

     plt.show()


def 					_lowerCamelCase    (      ):



     """simple docstring"""





     UpperCAmelCase_							:   Union[str, Any]   =      0.970_0436
     UpperCAmelCase_							:   int   =      -0.2430_8753
     UpperCAmelCase_							:   str   =      0.4_6620_3685
     UpperCAmelCase_							:   int   =      0.4323_6573

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


def 					_lowerCamelCase    (      ):



     """simple docstring"""





     UpperCAmelCase_							:   Tuple   =      7.3_476e22
     UpperCAmelCase_							:   Dict   =      5.972e24
     UpperCAmelCase_							:   Tuple   =      1022
     UpperCAmelCase_							:   str   =      384399000
     UpperCAmelCase_							:   int   =      6.674e-11

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

     UpperCAmelCase_							:   Union[str, Any]   =      Body(-earth_moon_distance	,     0	,     0	,     lowerCamelCase_	,     lowerCamelCase_	,     10000000	,     'grey'   )
     UpperCAmelCase_							:   List[Any]   =      Body(0	,     0	,     0	,     lowerCamelCase_	,     lowerCamelCase_	,     50000000	,     'blue'   )
     return BodySystem([earth, moon]	,     lowerCamelCase_	,     time_factor=1000000   )


def 					_lowerCamelCase    (      ):



     """simple docstring"""





     UpperCAmelCase_							:   List[str]   =      []
     for _ in range(10   ):
          UpperCAmelCase_							:   int   =      random.uniform(-0.5	,     0.5   )
          UpperCAmelCase_							:   Tuple   =      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   )	,     lowerCamelCase_	,     lowerCamelCase_	,     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(lowerCamelCase_	,     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_3000_0000,
     4_3000_0000,
     -4_3000_0000,
     4_3000_0000,
 )
 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


snake_case__     :			Optional[Any]      			=  {'''configuration_nat''': ['''NAT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''NatConfig''']}


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 snake_case__     :			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

 snake_case__     :			int      			=  _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)






