






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a_							=      20

# Time between time steps in seconds
a_							=      INTERVAL / 1000


class        lowercase__       :

	def __init__(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase = 1.0						,      __UpperCAmelCase = 1.0						,      __UpperCAmelCase = "blue"						,      )->   None:







							'''simple docstring'''





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

	@property
	def 						UpperCAmelCase					(							self    )->   tuple[float, float]:







							'''simple docstring'''





							return self.position_x, self.position_y

	@property
	def 						UpperCAmelCase					(							self    )->   tuple[float, float]:







							'''simple docstring'''





							return self.velocity_x, self.velocity_y

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase						,      __UpperCAmelCase						,      __UpperCAmelCase    )->   None:







							'''simple docstring'''





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


	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase    )->   None:







							'''simple docstring'''





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





class        lowercase__       :

	def __init__(							self						,      __UpperCAmelCase						,      __UpperCAmelCase = 1.0						,      __UpperCAmelCase = 1.0						,      __UpperCAmelCase = 0.0						,      )->   None:







							'''simple docstring'''





							lowerCAmelCase__	 =  bodies
							lowerCAmelCase__	 =  gravitation_constant
							lowerCAmelCase__	 =  time_factor
							lowerCAmelCase__	 =  softening_factor

	def __len__(							self    )->   int:







							'''simple docstring'''





							return len(self.bodies    )


	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase    )->   None:







							'''simple docstring'''





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

																									# Calculation of the distance using Pythagoras's theorem
																									# Extra factor due to the softening technique
																									lowerCAmelCase__	 =  (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     _a					(       UpperCamelCase_   :			BodySystem      ,				UpperCamelCase_   :			float      ,				UpperCamelCase_   :			list[plt.Circle]				)	->				None:
						"""simple docstring"""







						body_system.update_system(UpperCamelCase_				)

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


def     _a					(       UpperCamelCase_   :			str      ,				UpperCamelCase_   :			BodySystem      ,				UpperCamelCase_   :			float = -1      ,				UpperCamelCase_   :			float = 1      ,				UpperCamelCase_   :			float = -1      ,				UpperCamelCase_   :			float = 1      ,				)	->				None:
						"""simple docstring"""







						lowerCAmelCase__	 =  plt.figure()
						fig.canvas.set_window_title(UpperCamelCase_				)
						lowerCAmelCase__	 =  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__	 =  [
						    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(UpperCamelCase_				)

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

						lowerCAmelCase__	 =  animation.FuncAnimation(  # noqa: F841
						    UpperCamelCase_      ,				UpperCamelCase_      ,				interval=UpperCamelCase_      ,				blit=UpperCamelCase_				)

						plt.show()


def     _a					(       )	->				BodySystem:
						"""simple docstring"""







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

						lowerCAmelCase__	 =  [
						    Body(UpperCamelCase_      ,				UpperCamelCase_      ,				UpperCamelCase_      ,				UpperCamelCase_      ,				size=0.2      ,				color="red"				),
						    Body(-position_x      ,				-position_y      ,				UpperCamelCase_      ,				UpperCamelCase_      ,				size=0.2      ,				color="green"				),
						    Body(0      ,				0      ,				-2 * velocity_x      ,				-2 * velocity_y      ,				size=0.2      ,				color="blue"				),
						]
						return BodySystem(UpperCamelCase_      ,				time_factor=3				)


def     _a					(       )	->				BodySystem:
						"""simple docstring"""







						lowerCAmelCase__	 =  7.3_4_7_6e2_2
						lowerCAmelCase__	 =  5.9_7_2e2_4
						lowerCAmelCase__	 =  1_022
						lowerCAmelCase__	 =  384_399_000
						lowerCAmelCase__	 =  6.6_7_4e-1_1

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

						lowerCAmelCase__	 =  Body(-earth_moon_distance      ,				0      ,				0      ,				UpperCamelCase_      ,				UpperCamelCase_      ,				10_000_000      ,				"grey"				)
						lowerCAmelCase__	 =  Body(0      ,				0      ,				0      ,				UpperCamelCase_      ,				UpperCamelCase_      ,				50_000_000      ,				"blue"				)
						return BodySystem([earth, moon]      ,				UpperCamelCase_      ,				time_factor=1_000_000				)


def     _a					(       )	->				BodySystem:
						"""simple docstring"""







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














import unittest

import numpy as np
import PIL
import torch

from diffusers.image_processor import VaeImageProcessor


class        lowercase__       (     unittest.TestCase		):

	@property
	def 						UpperCAmelCase					(							self    )->   List[str]:







							'''simple docstring'''





							lowerCAmelCase__	 =  1
							lowerCAmelCase__	 =  3
							lowerCAmelCase__	 =  8
							lowerCAmelCase__	 =  8

							lowerCAmelCase__	 =  torch.rand((batch_size, num_channels, height, width)    )

							return sample

	def 						UpperCAmelCase					(							self						,      __UpperCAmelCase    )->   Dict:







							'''simple docstring'''





							if isinstance(image[0]						,      PIL.Image.Image    ):
													return np.stack([np.array(__UpperCAmelCase    ) for i in image]						,      axis=0    )
							elif isinstance(__UpperCAmelCase						,      torch.Tensor    ):
													return image.cpu().numpy().transpose(0						,      2						,      3						,      1    )
							return image

	def 						UpperCAmelCase					(							self    )->   Optional[int]:







							'''simple docstring'''





							lowerCAmelCase__	 =  VaeImageProcessor(do_resize=__UpperCAmelCase						,      do_normalize=__UpperCAmelCase    )

							lowerCAmelCase__	 =  self.dummy_sample
							lowerCAmelCase__	 =  self.to_np(__UpperCAmelCase    )

							for output_type in ["pt", "np", "pil"]:
													lowerCAmelCase__	 =  image_processor.postprocess(
													    image_processor.preprocess(__UpperCAmelCase    )						,      output_type=__UpperCAmelCase						,      )
													lowerCAmelCase__	 =  self.to_np(__UpperCAmelCase    )
													lowerCAmelCase__	 =  (input_np * 255).round() if output_type == "pil" else input_np
													assert (
													    np.abs(in_np - out_np    ).max() < 1E-6
													), F"decoded output does not match input for output_type {output_type}"

	def 						UpperCAmelCase					(							self    )->   int:







							'''simple docstring'''





							lowerCAmelCase__	 =  VaeImageProcessor(do_resize=__UpperCAmelCase						,      do_normalize=__UpperCAmelCase    )
							lowerCAmelCase__	 =  self.dummy_sample.cpu().numpy().transpose(0						,      2						,      3						,      1    )

							for output_type in ["pt", "np", "pil"]:
													lowerCAmelCase__	 =  image_processor.postprocess(image_processor.preprocess(__UpperCAmelCase    )						,      output_type=__UpperCAmelCase    )

													lowerCAmelCase__	 =  self.to_np(__UpperCAmelCase    )
													lowerCAmelCase__	 =  (input_np * 255).round() if output_type == "pil" else input_np
													assert (
													    np.abs(in_np - out_np    ).max() < 1E-6
													), F"decoded output does not match input for output_type {output_type}"

	def 						UpperCAmelCase					(							self    )->   Any:







							'''simple docstring'''





							lowerCAmelCase__	 =  VaeImageProcessor(do_resize=__UpperCAmelCase						,      do_normalize=__UpperCAmelCase    )

							lowerCAmelCase__	 =  self.dummy_sample.cpu().numpy().transpose(0						,      2						,      3						,      1    )
							lowerCAmelCase__	 =  image_processor.numpy_to_pil(__UpperCAmelCase    )

							for output_type in ["pt", "np", "pil"]:
													lowerCAmelCase__	 =  image_processor.postprocess(image_processor.preprocess(__UpperCAmelCase    )						,      output_type=__UpperCAmelCase    )
													for i, o in zip(__UpperCAmelCase						,      __UpperCAmelCase    ):
																			lowerCAmelCase__	 =  np.array(__UpperCAmelCase    )
																			lowerCAmelCase__	 =  self.to_np(__UpperCAmelCase    ) if output_type == "pil" else (self.to_np(__UpperCAmelCase    ) * 255).round()
																			assert (
																			    np.abs(in_np - out_np    ).max() < 1E-6
																			), F"decoded output does not match input for output_type {output_type}"

	def 						UpperCAmelCase					(							self    )->   Union[str, Any]:







							'''simple docstring'''





							lowerCAmelCase__	 =  VaeImageProcessor(do_resize=__UpperCAmelCase						,      do_normalize=__UpperCAmelCase    )

							lowerCAmelCase__	 =  self.dummy_sample
							lowerCAmelCase__	 =  input_pt_ad.squeeze(0    )

							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )
							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )

							lowerCAmelCase__	 =  self.to_np(self.dummy_sample    )
							lowerCAmelCase__	 =  input_np_ad.squeeze(0    )

							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )
							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )

							assert np.abs(out_pt_ad - out_pt_ad    ).max() < 1E-6
							assert np.abs(out_np_ad - out_np_ad    ).max() < 1E-6


	def 						UpperCAmelCase					(							self    )->   List[Any]:







							'''simple docstring'''





							lowerCAmelCase__	 =  VaeImageProcessor(do_resize=__UpperCAmelCase						,      do_normalize=__UpperCAmelCase    )

							lowerCAmelCase__	 =  self.dummy_sample
							lowerCAmelCase__	 =  list(__UpperCAmelCase    )

							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )

							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )

							lowerCAmelCase__	 =  self.to_np(self.dummy_sample    )
							list(__UpperCAmelCase    )

							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )

							lowerCAmelCase__	 =  image_processor.postprocess(
							    image_processor.preprocess(__UpperCAmelCase    )						,      output_type="np"						,      )

							assert np.abs(out_pt_ad - out_pt_list    ).max() < 1E-6
							assert np.abs(out_np_ad - out_np_list    ).max() < 1E-6






