


'''simple docstring'''

from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowerCamelCase							:       List[str]  						=     20

# Time between time steps in seconds
lowerCamelCase							:       Tuple  						=     INTERVAL / 1_000
class   __lowerCAmelCase						:





      '''simple docstring'''






      def __init__(self   :   Optional[int]       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   str = "blue"       ,						):

             '''simple docstring'''







             lowercase__				      =			position_x
             lowercase__				      =			position_y
             lowercase__				      =			velocity_x
             lowercase__				      =			velocity_y
             lowercase__				      =			mass
             lowercase__				      =			size
             lowercase__				      =			color



      @property
      def 				UpperCamelCase__		(self   :   str			):

             '''simple docstring'''







             return self.position_x, self.position_y



      @property
      def 				UpperCamelCase__		(self   :   int			):

             '''simple docstring'''







             return self.velocity_x, self.velocity_y



      def 				UpperCamelCase__		(self   :   str       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float       ,						UpperCamelCase   :   float			):

             '''simple docstring'''







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






      def 				UpperCamelCase__		(self   :   Optional[int]       ,						UpperCamelCase   :   float			):

             '''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   :   int       ,						UpperCamelCase   :   list[Body]       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   float = 1.0       ,						UpperCamelCase   :   float = 0.0       ,						):

             '''simple docstring'''







             lowercase__				      =			bodies
             lowercase__				      =			gravitation_constant
             lowercase__				      =			time_factor
             lowercase__				      =			softening_factor



      def __len__(self   :   Any			):

             '''simple docstring'''







             return len(self.bodies			)






      def 				UpperCamelCase__		(self   :   Any       ,						UpperCamelCase   :   float			):

             '''simple docstring'''







             for bodya in self.bodies:
                    lowercase__				      =			0.0
                    lowercase__				      =			0.0
                    for bodya in self.bodies:
                           if bodya != bodya:
                                  lowercase__				      =			bodya.position_x - bodya.position_x
                                  lowercase__				      =			bodya.position_y - bodya.position_y

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






       """simple docstring"""







       body_system.update_system(A	)

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

def _SCREAMING_SNAKE_CASE				(A  ,			A  ,			A = -1  ,			A = 1  ,			A = -1  ,			A = 1  ,			)	->	None:






       """simple docstring"""







       lowercase__				      =			plt.figure()
       fig.canvas.set_window_title(A	)
       lowercase__				      =			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__				      =			[
           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	) -> list[plt.Circle]:
              update_step(A  ,			A  ,			A	)
              return patches

       lowercase__				      =			animation.FuncAnimation(  # noqa: F841
           A  ,			A  ,			interval=A  ,			blit=A	)

       plt.show()

def _SCREAMING_SNAKE_CASE				()	->	BodySystem:






       """simple docstring"""







       lowercase__				      =			0.9_700_436
       lowercase__				      =			-0.24_308_753
       lowercase__				      =			0.466_203_685
       lowercase__				      =			0.43_236_573

       lowercase__				      =			[
           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 _SCREAMING_SNAKE_CASE				()	->	BodySystem:






       """simple docstring"""







       lowercase__				      =			7.3_476E22
       lowercase__				      =			5.972E24
       lowercase__				      =			1_022
       lowercase__				      =			384_399_000
       lowercase__				      =			6.674E-11

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

       lowercase__				      =			Body(-earth_moon_distance  ,			0  ,			0  ,			A  ,			A  ,			10_000_000  ,			'''grey'''	)
       lowercase__				      =			Body(0  ,			0  ,			0  ,			A  ,			A  ,			50_000_000  ,			'''blue'''	)
       return BodySystem([earth, moon]  ,			A  ,			time_factor=1_000_000	)

def _SCREAMING_SNAKE_CASE				()	->	BodySystem:






       """simple docstring"""







       lowercase__				      =			[]
       for _ in range(10	):
              lowercase__				      =			random.uniform(-0.5  ,			0.5	)
              lowercase__				      =			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(),
     -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)








'''simple docstring'''

import random
import unittest

import torch

from diffusers import IFImgaImgPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import (
    TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS,
    TEXT_GUIDED_IMAGE_VARIATION_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin
@skip_mps
class   __lowerCAmelCase						(lowercase_  ,					lowercase_  ,					unittest.TestCase					):





      '''simple docstring'''






      lowerCAmelCase__ :					Dict   =							IFImgaImgPipeline
      lowerCAmelCase__ :					int   =							TEXT_GUIDED_IMAGE_VARIATION_PARAMS - {"""width""", """height"""}
      lowerCAmelCase__ :					Optional[int]   =							TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS
      lowerCAmelCase__ :					str   =							PipelineTesterMixin.required_optional_params - {"""latents"""}



      def 				UpperCamelCase__		(self   :   Dict			):

             '''simple docstring'''







             return self._get_dummy_components()



      def 				UpperCamelCase__		(self   :   Optional[Any]       ,						UpperCamelCase   :   List[Any]       ,						UpperCamelCase   :   Optional[Any]=0			):

             '''simple docstring'''







             if str(UpperCamelCase			).startswith('''mps'''			):
                    lowercase__				      =			torch.manual_seed(UpperCamelCase			)
             else:
                    lowercase__				      =			torch.Generator(device=UpperCamelCase			).manual_seed(UpperCamelCase			)

             lowercase__				      =			floats_tensor((1, 3, 32, 32)       ,						rng=random.Random(UpperCamelCase			)			).to(UpperCamelCase			)

             lowercase__				      =			{
                 '''prompt''': '''A painting of a squirrel eating a burger''',
                 '''image''': image,
                 '''generator''': generator,
                 '''num_inference_steps''': 2,
                 '''output_type''': '''numpy''',
             }

             return inputs



      def 				UpperCamelCase__		(self   :   int			):

             '''simple docstring'''







             self._test_save_load_optional_components()



      @unittest.skipIf(
          torch_device != '''cuda''' or not is_xformers_available()       ,						reason='''XFormers attention is only available with CUDA and `xformers` installed'''       ,						)
      def 				UpperCamelCase__		(self   :   Optional[Any]			):

             '''simple docstring'''







             self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3			)



      @unittest.skipIf(torch_device != '''cuda'''       ,						reason='''float16 requires CUDA'''			)
      def 				UpperCamelCase__		(self   :   Any			):

             '''simple docstring'''







             super().test_save_load_floataa(expected_max_diff=1E-1			)



      @unittest.skipIf(torch_device != '''cuda'''       ,						reason='''float16 requires CUDA'''			)
      def 				UpperCamelCase__		(self   :   Dict			):

             '''simple docstring'''







             super().test_floataa_inference(expected_max_diff=1E-1			)



      def 				UpperCamelCase__		(self   :   Optional[int]			):

             '''simple docstring'''







             self._test_attention_slicing_forward_pass(expected_max_diff=1E-2			)



      def 				UpperCamelCase__		(self   :   str			):

             '''simple docstring'''







             self._test_save_load_local()






      def 				UpperCamelCase__		(self   :   List[Any]			):

             '''simple docstring'''







             self._test_inference_batch_single_identical(
                 expected_max_diff=1E-2       ,						)




