






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a		:	str      					=			20

# Time between time steps in seconds
a		:	Optional[Any]      					=			INTERVAL / 1_000
class    a   :



      """simple docstring"""


      def __init__(				self :      Optional[int]		,				__lowercase :      float		,				__lowercase :      float		,				__lowercase :      float		,				__lowercase :      float		,				__lowercase :      float = 1.0		,				__lowercase :      float = 1.0		,				__lowercase :      str = "blue"		,				)							->				None:
        __UpperCAmelCase							:     Union[str, Any]									=  position_x
        __UpperCAmelCase							:     Union[str, Any]									=  position_y
        __UpperCAmelCase							:     List[Any]									=  velocity_x
        __UpperCAmelCase							:     Optional[Any]									=  velocity_y
        __UpperCAmelCase							:     Optional[int]									=  mass
        __UpperCAmelCase							:     Optional[Any]									=  size
        __UpperCAmelCase							:     int									=  color
      @property
      def      UpperCAmelCase				(				self :      Any )							->				tuple[float, float]:
        return self.position_x, self.position_y
      @property
      def      UpperCAmelCase				(				self :      Tuple )							->				tuple[float, float]:
        return self.velocity_x, self.velocity_y
      def      UpperCAmelCase				(				self :      int		,				__lowercase :      float		,				__lowercase :      float		,				__lowercase :      float )							->				None:
        self.velocity_x += force_x * delta_time
        self.velocity_y += force_y * delta_time




      def      UpperCAmelCase				(				self :      int		,				__lowercase :      float )							->				None:
        self.position_x += self.velocity_x * delta_time
        self.position_y += self.velocity_y * delta_time


class    a   :



      """simple docstring"""


      def __init__(				self :      Tuple		,				__lowercase :      list[Body]		,				__lowercase :      float = 1.0		,				__lowercase :      float = 1.0		,				__lowercase :      float = 0.0		,				)							->				None:
        __UpperCAmelCase							:     Union[str, Any]									=  bodies
        __UpperCAmelCase							:     int									=  gravitation_constant
        __UpperCAmelCase							:     List[str]									=  time_factor
        __UpperCAmelCase							:     List[Any]									=  softening_factor
      def __len__(				self :      Optional[Any] )							->				int:
        return len(self.bodies )




      def      UpperCAmelCase				(				self :      Optional[Any]		,				__lowercase :      float )							->				None:
        for bodya in self.bodies:
          __UpperCAmelCase							:     List[Any]									=  0.0
          __UpperCAmelCase							:     List[str]									=  0.0
          for bodya in self.bodies:
            if bodya != bodya:
              __UpperCAmelCase							:     Optional[int]									=  bodya.position_x - bodya.position_x
              __UpperCAmelCase							:     Optional[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(__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__				(   __lowerCamelCase      :					BodySystem  ,		__lowerCamelCase      :					float  ,		__lowerCamelCase      :					list[plt.Circle]		):
  body_system.update_system(__lowerCamelCase		)

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






def     lowerCamelCase__				(   __lowerCamelCase      :					str  ,		__lowerCamelCase      :					BodySystem  ,		__lowerCamelCase      :					float = -1  ,		__lowerCamelCase      :					float = 1  ,		__lowerCamelCase      :					float = -1  ,		__lowerCamelCase      :					float = 1  ,		):
  __UpperCAmelCase							:     Tuple									=  plt.figure()
  fig.canvas.set_window_title(__lowerCamelCase		)
  __UpperCAmelCase							:     List[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
  __UpperCAmelCase							:     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(__lowerCamelCase		)

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

  __UpperCAmelCase							:     str									=  animation.FuncAnimation(  # noqa: F841
      __lowerCamelCase  ,		__lowerCamelCase  ,		interval=__lowerCamelCase  ,		blit=__lowerCamelCase		)

  plt.show()






def     lowerCamelCase__				(   ):
  __UpperCAmelCase							:     Optional[int]									=  0.9_7_0_0_4_3_6
  __UpperCAmelCase							:     Optional[int]									=  -0.2_4_3_0_8_7_5_3
  __UpperCAmelCase							:     Optional[Any]									=  0.4_6_6_2_0_3_6_8_5
  __UpperCAmelCase							:     List[Any]									=  0.4_3_2_3_6_5_7_3

  __UpperCAmelCase							:     str									=  [
      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__				(   ):
  __UpperCAmelCase							:     List[Any]									=  7.3476E22
  __UpperCAmelCase							:     Union[str, Any]									=  5.972E24
  __UpperCAmelCase							:     Union[str, Any]									=  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							:     Any									=  earth_mass * velocity_dif / (earth_mass + moon_mass)
  __UpperCAmelCase							:     Optional[Any]									=  moon_velocity - velocity_dif

  __UpperCAmelCase							:     Dict									=  Body(-earth_moon_distance  ,		0  ,		0  ,		__lowerCamelCase  ,		__lowerCamelCase  ,		10000000  ,		"""grey"""		)
  __UpperCAmelCase							:     Optional[Any]									=  Body(0  ,		0  ,		0  ,		__lowerCamelCase  ,		__lowerCamelCase  ,		50000000  ,		"""blue"""		)
  return BodySystem([earth, moon]  ,		__lowerCamelCase  ,		time_factor=1000000		)






def     lowerCamelCase__				(   ):
  __UpperCAmelCase							:     Tuple									=  []
  for _ in range(10		):
    __UpperCAmelCase							:     Dict									=  random.uniform(-0.5  ,		0.5		)
    __UpperCAmelCase							:     Optional[Any]									=  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=0.0_5  ,		)		)
    bodies.append(
        Body(
            random.uniform(-0.5  ,		0.5		)  ,		random.uniform(-0.5  ,		0.5		)  ,		-velocity_x  ,		-velocity_y  ,		size=0.0_5  ,		)		)
  return BodySystem(__lowerCamelCase  ,		0.0_1  ,		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)










import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import AutoConfig


a		:	Optional[Any]      					=			logging.get_logger(__name__)

a		:	int      					=			{
    "facebook/musicgen-small": "https://huggingface.co/facebook/musicgen-small/resolve/main/config.json",
    # See all Musicgen models at https://huggingface.co/models?filter=musicgen
}
class    a   (			lowercase__       ):



      """simple docstring"""


      a  :			Optional[int]								=     'musicgen_decoder'
      a  :			Optional[int]								=     ['past_key_values']
      def __init__(				self :      Optional[Any]		,				__lowercase :      str=2048		,				__lowercase :      Optional[int]=2048		,				__lowercase :      List[Any]=24		,				__lowercase :      Optional[Any]=4096		,				__lowercase :      Dict=16		,				__lowercase :      List[Any]=0.0		,				__lowercase :      Tuple=True		,				__lowercase :      List[Any]="gelu"		,				__lowercase :      Any=1024		,				__lowercase :      Optional[Any]=0.1		,				__lowercase :      List[Any]=0.0		,				__lowercase :      int=0.0		,				__lowercase :      List[str]=0.02		,				__lowercase :      Dict=False		,				__lowercase :      List[str]=4		,				__lowercase :      List[str]=2048		,				__lowercase :      List[Any]=2048		,				__lowercase :      Union[str, Any]=None		,				__lowercase :      List[str]=False		,				**__lowercase :      int		,				)							->				str:
        __UpperCAmelCase							:     Union[str, Any]									=  vocab_size
        __UpperCAmelCase							:     Dict									=  max_position_embeddings
        __UpperCAmelCase							:     str									=  hidden_size
        __UpperCAmelCase							:     Optional[Any]									=  ffn_dim
        __UpperCAmelCase							:     List[Any]									=  num_hidden_layers
        __UpperCAmelCase							:     Any									=  num_attention_heads
        __UpperCAmelCase							:     List[Any]									=  dropout
        __UpperCAmelCase							:     List[str]									=  attention_dropout
        __UpperCAmelCase							:     List[Any]									=  activation_dropout
        __UpperCAmelCase							:     int									=  activation_function
        __UpperCAmelCase							:     Optional[int]									=  initializer_factor
        __UpperCAmelCase							:     List[Any]									=  layerdrop
        __UpperCAmelCase							:     Tuple									=  use_cache
        __UpperCAmelCase							:     Tuple									=  scale_embedding  # scale factor will be sqrt(d_model) if True
        __UpperCAmelCase							:     int									=  num_codebooks
        super().__init__(
            pad_token_id=__lowercase		,				bos_token_id=__lowercase		,				eos_token_id=__lowercase		,				tie_word_embeddings=__lowercase		,				**__lowercase		,				)


class    a   (			lowercase__       ):



      """simple docstring"""


      a  :			Tuple								=     'musicgen'
      a  :			int								=     True
      def __init__(				self :      Any		,				**__lowercase :      Tuple )							->				Union[str, Any]:
        super().__init__(**__lowercase )
        if "text_encoder" not in kwargs or "audio_encoder" not in kwargs or "decoder" not in kwargs:
          raise ValueError("""Config has to be initialized with text_encoder, audio_encoder and decoder config""" )

        __UpperCAmelCase							:     int									=  kwargs.pop("""text_encoder""" )
        __UpperCAmelCase							:     str									=  text_encoder_config.pop("""model_type""" )

        __UpperCAmelCase							:     Tuple									=  kwargs.pop("""audio_encoder""" )
        __UpperCAmelCase							:     Optional[Any]									=  audio_encoder_config.pop("""model_type""" )

        __UpperCAmelCase							:     Optional[Any]									=  kwargs.pop("""decoder""" )

        __UpperCAmelCase							:     Any									=  AutoConfig.for_model(__lowercase		,				**__lowercase )
        __UpperCAmelCase							:     Dict									=  AutoConfig.for_model(__lowercase		,				**__lowercase )
        __UpperCAmelCase							:     Any									=  MusicgenDecoderConfig(**__lowercase )
        __UpperCAmelCase							:     int									=  True
      @classmethod
      def      UpperCAmelCase				(				cls :      Optional[Any]		,				__lowercase :      PretrainedConfig		,				__lowercase :      PretrainedConfig		,				__lowercase :      MusicgenDecoderConfig		,				**__lowercase :      List[Any]		,				)							->				List[str]:
        return cls(
            text_encoder=text_encoder_config.to_dict()		,				audio_encoder=audio_encoder_config.to_dict()		,				decoder=decoder_config.to_dict()		,				**__lowercase		,				)




      def      UpperCAmelCase				(				self :      Any )							->				int:
        __UpperCAmelCase							:     Optional[Any]									=  copy.deepcopy(self.__dict__ )
        __UpperCAmelCase							:     List[Any]									=  self.text_encoder.to_dict()
        __UpperCAmelCase							:     str									=  self.audio_encoder.to_dict()
        __UpperCAmelCase							:     List[str]									=  self.decoder.to_dict()
        __UpperCAmelCase							:     List[str]									=  self.__class__.model_type
        return output


