




'''simple docstring'''






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowercase						:   Dict      						=							20

# Time between time steps in seconds
lowercase						:   List[Any]      						=							INTERVAL / 1000

class 	SCREAMING_SNAKE_CASE_		:



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






        '''simple docstring'''




        lowercase	:		Union[str, Any]    =   position_x
        lowercase	:		Tuple    =   position_y
        lowercase	:		Union[str, Any]    =   velocity_x
        lowercase	:		int    =   velocity_y
        lowercase	:		Dict    =   mass
        lowercase	:		Any    =   size
        lowercase	:		Any    =   color



 @property
 def  SCREAMING_SNAKE_CASE(	self			):






        '''simple docstring'''




        return self.position_x, self.position_y



 @property
 def  SCREAMING_SNAKE_CASE(	self			):






        '''simple docstring'''




        return self.velocity_x, self.velocity_y



 def  SCREAMING_SNAKE_CASE(	self ,		A ,		A ,		A			):






        '''simple docstring'''




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





 def  SCREAMING_SNAKE_CASE(	self ,		A			):






        '''simple docstring'''




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






class 	SCREAMING_SNAKE_CASE_		:



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






        '''simple docstring'''




        lowercase	:		Any    =   bodies
        lowercase	:		str    =   gravitation_constant
        lowercase	:		Any    =   time_factor
        lowercase	:		int    =   softening_factor



 def __len__(	self			):






        '''simple docstring'''




        return len(self.bodies			)





 def  SCREAMING_SNAKE_CASE(	self ,		A			):






        '''simple docstring'''




        for bodya in self.bodies:
               lowercase	:		Tuple    =   0.0
               lowercase	:		Any    =   0.0
               for bodya in self.bodies:
                      if bodya != bodya:
                             lowercase	:		Any    =   bodya.position_x - bodya.position_x
                             lowercase	:		Any    =   bodya.position_y - bodya.position_y

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






       '''simple docstring'''




       body_system.update_system(lowerCamelCase   )

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




def 		a_(			lowerCamelCase ,					lowerCamelCase ,					lowerCamelCase = -1 ,					lowerCamelCase = 1 ,					lowerCamelCase = -1 ,					lowerCamelCase = 1 ,					)					->None:






       '''simple docstring'''




       lowercase	:		Any    =   plt.figure()
       fig.canvas.set_window_title(lowerCamelCase   )
       lowercase	:		List[str]    =   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	:		Dict    =   [
           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   ) -> list[plt.Circle]:
              update_step(lowerCamelCase ,					lowerCamelCase ,					lowerCamelCase   )
              return patches

       lowercase	:		str    =   animation.FuncAnimation(  # noqa: F841
           lowerCamelCase ,					lowerCamelCase ,					interval=lowerCamelCase ,					blit=lowerCamelCase   )

       plt.show()




def 		a_(			)					->BodySystem:






       '''simple docstring'''




       lowercase	:		List[str]    =   0.9_70_04_36
       lowercase	:		Union[str, Any]    =   -0.24_30_87_53
       lowercase	:		Union[str, Any]    =   0.4_66_20_36_85
       lowercase	:		Optional[Any]    =   0.43_23_65_73

       lowercase	:		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 		a_(			)					->BodySystem:






       '''simple docstring'''




       lowercase	:		Optional[Any]    =   7.3476E22
       lowercase	:		int    =   5.972E24
       lowercase	:		int    =   1022
       lowercase	:		Dict    =   3_8439_9000
       lowercase	:		str    =   6.674E-11

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

       lowercase	:		Tuple    =   Body(-earth_moon_distance ,					0 ,					0 ,					lowerCamelCase ,					lowerCamelCase ,					1000_0000 ,					'''grey'''   )
       lowercase	:		Optional[Any]    =   Body(0 ,					0 ,					0 ,					lowerCamelCase ,					lowerCamelCase ,					5000_0000 ,					'''blue'''   )
       return BodySystem([earth, moon] ,					lowerCamelCase ,					time_factor=100_0000   )




def 		a_(			)					->BodySystem:






       '''simple docstring'''




       lowercase	:		Optional[Any]    =   []
       for _ in range(10   ):
              lowercase	:		Any    =   random.uniform(-0.5 ,					0.5   )
              lowercase	:		List[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=0.05 ,					)   )
              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(),
          -430000000,
          430000000,
          -430000000,
          430000000,
      )
      plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)










'''simple docstring'''






import os

from packaging import version

from .. import __version__
from .accelerate_utils import apply_forward_hook
from .constants import (
    CONFIG_NAME,
    DEPRECATED_REVISION_ARGS,
    DIFFUSERS_CACHE,
    DIFFUSERS_DYNAMIC_MODULE_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    ONNX_EXTERNAL_WEIGHTS_NAME,
    ONNX_WEIGHTS_NAME,
    SAFETENSORS_WEIGHTS_NAME,
    TEXT_ENCODER_ATTN_MODULE,
    WEIGHTS_NAME,
)
from .deprecation_utils import deprecate
from .doc_utils import replace_example_docstring
from .dynamic_modules_utils import get_class_from_dynamic_module
from .hub_utils import (
    HF_HUB_OFFLINE,
    _add_variant,
    _get_model_file,
    extract_commit_hash,
    http_user_agent,
)
from .import_utils import (
    BACKENDS_MAPPING,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    DummyObject,
    OptionalDependencyNotAvailable,
    is_accelerate_available,
    is_accelerate_version,
    is_bsa_available,
    is_flax_available,
    is_ftfy_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_omegaconf_available,
    is_onnx_available,
    is_safetensors_available,
    is_scipy_available,
    is_tensorboard_available,
    is_tf_available,
    is_torch_available,
    is_torch_version,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    is_wandb_available,
    is_xformers_available,
    requires_backends,
)
from .logging import get_logger
from .outputs import BaseOutput
from .pil_utils import PIL_INTERPOLATION, numpy_to_pil, pt_to_pil
from .torch_utils import is_compiled_module, randn_tensor


if is_torch_available():
      from .testing_utils import (
          floats_tensor,
          load_hf_numpy,
          load_image,
          load_numpy,
          load_pt,
          nightly,
          parse_flag_from_env,
          print_tensor_test,
          require_torch_a,
          require_torch_gpu,
          skip_mps,
          slow,
          torch_all_close,
          torch_device,
      )
      from .torch_utils import maybe_allow_in_graph

from .testing_utils import export_to_gif, export_to_video


lowercase						:   Tuple      						=							get_logger(__name__)




def 		a_(			lowerCamelCase   )					->Any:






       '''simple docstring'''




       if version.parse(lowerCamelCase   ) < version.parse(lowerCamelCase   ):
              if "dev" in min_version:
                     lowercase	:		str    =   (
                         '''This example requires a source install from HuggingFace diffusers (see '''
                         '''`https://huggingface.co/docs/diffusers/installation#install-from-source`),'''
                     )
              else:
                     lowercase	:		List[str]    =   f"""This example requires a minimum version of {min_version},"""
              error_message += f""" but the version found is {__version__}.\n"""
              raise ImportError(lowerCamelCase   )




