





from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
UpperCAmelCase_       : Tuple							=    20

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





class   lowercase__     :







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







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







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







  def 						UpperCAmelCase__		(						self     ,    _lowercase     ,    _lowercase     ,    _lowercase    ):
       self.velocity_x += force_x * delta_time
       self.velocity_y += force_y * delta_time







  def 						UpperCAmelCase__		(						self     ,    _lowercase    ):
       self.position_x += self.velocity_x * delta_time
       self.position_y += self.velocity_y * delta_time





class   lowercase__     :







  def __init__(						self     ,    _lowercase     ,    _lowercase = 1.0     ,    _lowercase = 1.0     ,    _lowercase = 0.0     ,    ):
       lowerCAmelCase_       :							int			 =		bodies
       lowerCAmelCase_       :							Optional[int]			 =		gravitation_constant
       lowerCAmelCase_       :							List[Any]			 =		time_factor
       lowerCAmelCase_       :							Any			 =		softening_factor







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







  def 						UpperCAmelCase__		(						self     ,    _lowercase    ):
       for bodya in self.bodies:
            lowerCAmelCase_       :							Dict			 =		0.0
            lowerCAmelCase_       :							List[Any]			 =		0.0
            for bodya in self.bodies:
                 if bodya != bodya:
                      lowerCAmelCase_       :							Any			 =		bodya.position_x - bodya.position_x
                      lowerCAmelCase_       :							str			 =		bodya.position_y - bodya.position_y

                      # Calculation of the distance using Pythagoras's theorem
                      # Extra factor due to the softening technique
                      lowerCAmelCase_       :							Union[str, 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(_lowercase     ,    _lowercase     ,    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			(	_a :       BodySystem       , _a :       float       , _a :       list[plt.Circle]      )						->      None:
     body_system.update_system(_a      )

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






def 				_lowerCAmelCase			(	_a :       str       , _a :       BodySystem       , _a :       float = -1       , _a :       float = 1       , _a :       float = -1       , _a :       float = 1       , )						->      None:
     lowerCAmelCase_       :							Optional[int]			 =		plt.figure()
     fig.canvas.set_window_title(_a      )
     lowerCAmelCase_       :							Tuple			 =		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
     lowerCAmelCase_       :							List[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(_a      )

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

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

     plt.show()






def 				_lowerCAmelCase			(	)						->      BodySystem:
     lowerCAmelCase_       :							str			 =		0.9_700_436
     lowerCAmelCase_       :							int			 =		-0.24_308_753
     lowerCAmelCase_       :							str			 =		0.466_203_685
     lowerCAmelCase_       :							Any			 =		0.43_236_573

     lowerCAmelCase_       :							Any			 =		[
         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 				_lowerCAmelCase			(	)						->      BodySystem:
     lowerCAmelCase_       :							Any			 =		7.3476E22
     lowerCAmelCase_       :							Dict			 =		5.972E24
     lowerCAmelCase_       :							Optional[Any]			 =		10_22
     lowerCAmelCase_       :							Optional[int]			 =		3_84_39_90_00
     lowerCAmelCase_       :							int			 =		6.674E-11

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

     lowerCAmelCase_       :							Union[str, Any]			 =		Body(-earth_moon_distance       , 0       , 0       , _a       , _a       , 10_00_00_00       , """grey"""      )
     lowerCAmelCase_       :							Optional[int]			 =		Body(0       , 0       , 0       , _a       , _a       , 50_00_00_00       , """blue"""      )
     return BodySystem([earth, moon]       , _a       , time_factor=1_00_00_00      )






def 				_lowerCAmelCase			(	)						->      BodySystem:
     lowerCAmelCase_       :							List[Any]			 =		[]
     for _ in range(10      ):
          lowerCAmelCase_       :							Tuple			 =		random.uniform(-0.5       , 0.5      )
          lowerCAmelCase_       :							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      )       , _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(),
          -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_tokenizers_available, is_torch_available


UpperCAmelCase_       : List[Any]							=    {
    """configuration_retribert""": ["""RETRIBERT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """RetriBertConfig"""],
    """tokenization_retribert""": ["""RetriBertTokenizer"""],
}

try:
      if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      UpperCAmelCase_       : str							=    ["""RetriBertTokenizerFast"""]

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      UpperCAmelCase_       : Optional[Any]							=    [
          """RETRIBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
          """RetriBertModel""",
          """RetriBertPreTrainedModel""",
      ]


if TYPE_CHECKING:
      from .configuration_retribert import RETRIBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, RetriBertConfig
      from .tokenization_retribert import RetriBertTokenizer

      try:
            if not is_tokenizers_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_retribert_fast import RetriBertTokenizerFast

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_retribert import (
                RETRIBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
                RetriBertModel,
                RetriBertPreTrainedModel,
            )

else:
      import sys

      UpperCAmelCase_       : Tuple							=    _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
