




"""simple docstring"""

import tempfile
import unittest

import transformers
from transformers import XGLMConfig, XGLMTokenizer, is_flax_available, is_torch_available
from transformers.testing_utils import is_pt_flax_cross_test, require_flax, require_sentencepiece, slow

from ...generation.test_flax_utils import FlaxGenerationTesterMixin
from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_flax_available():
		import jax
		import jax.numpy as jnp
		import numpy as np

		from transformers.modeling_flax_pytorch_utils import (
		    convert_pytorch_state_dict_to_flax,
		    load_flax_weights_in_pytorch_model,
		)
		from transformers.models.xglm.modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel


if is_torch_available():
		import torch

@require_flax
class 							lowercase   :







				def __init__(				self :       List[str]   ,  _lowerCamelCase :       str   ,  _lowerCamelCase :       List[str]=14   ,  _lowerCamelCase :       List[str]=7   ,  _lowerCamelCase :       List[Any]=True   ,  _lowerCamelCase :       Dict=True   ,  _lowerCamelCase :       Tuple=True   ,  _lowerCamelCase :       Optional[int]=99   ,  _lowerCamelCase :       List[Any]=32   ,  _lowerCamelCase :       Tuple=5   ,  _lowerCamelCase :       Dict=4   ,  _lowerCamelCase :       Optional[Any]=37   ,  _lowerCamelCase :       str="gelu"   ,  _lowerCamelCase :       Any=0.1   ,  _lowerCamelCase :       List[str]=0.1   ,  _lowerCamelCase :       int=5_12   ,  _lowerCamelCase :       Optional[Any]=0.02   ,  _lowerCamelCase :       List[str]=None   ,  ):



					"""simple docstring"""

					A_	:					List[Any]						 =		parent
					A_	:					str						 =		batch_size
					A_	:					Tuple						 =		seq_length
					A_	:					Optional[Any]						 =		is_training
					A_	:					List[Any]						 =		use_input_mask
					A_	:					Optional[int]						 =		use_labels
					A_	:					Optional[Any]						 =		vocab_size
					A_	:					str						 =		d_model
					A_	:					List[Any]						 =		num_hidden_layers
					A_	:					Optional[Any]						 =		num_attention_heads
					A_	:					List[Any]						 =		ffn_dim
					A_	:					List[str]						 =		activation_function
					A_	:					Tuple						 =		activation_dropout
					A_	:					int						 =		attention_dropout
					A_	:					Optional[Any]						 =		max_position_embeddings
					A_	:					List[Any]						 =		initializer_range
					A_	:					List[Any]						 =		None
					A_	:					Optional[Any]						 =		0
					A_	:					List[str]						 =		2
					A_	:					Optional[Any]						 =		1







				def        a_	(				self :       Dict							):



					"""simple docstring"""

					A_	:					Tuple						 =		np.clip(ids_tensor([self.batch_size, self.seq_length]   ,  self.vocab_size							)   ,  3   ,  self.vocab_size							)

					A_	:					Tuple						 =		None
					if self.use_input_mask:
						A_	:					str						 =		random_attention_mask([self.batch_size, self.seq_length]							)

					A_	:					int						 =		XGLMConfig(
					    vocab_size=self.vocab_size   ,  d_model=self.hidden_size   ,  num_layers=self.num_hidden_layers   ,  attention_heads=self.num_attention_heads   ,  ffn_dim=self.ffn_dim   ,  activation_function=self.activation_function   ,  activation_dropout=self.activation_dropout   ,  attention_dropout=self.attention_dropout   ,  max_position_embeddings=self.max_position_embeddings   ,  initializer_range=self.initializer_range   ,  use_cache=_lowerCamelCase   ,  bos_token_id=self.bos_token_id   ,  eos_token_id=self.eos_token_id   ,  pad_token_id=self.pad_token_id   ,  )

					return (config, input_ids, input_mask)







				def        a_	(				self :       Optional[Any]							):



					"""simple docstring"""

					A_	:					Optional[int]						 =		self.prepare_config_and_inputs()
					A_ ,			A_ ,			A_	:					Tuple						 =		config_and_inputs
					A_	:					Tuple						 =		{'''input_ids''': input_ids, '''attention_mask''': attention_mask}
					return config, inputs_dict







				def        a_	(				self :       Union[str, Any]							):



					"""simple docstring"""

					A_ ,			A_ ,			A_	:					int						 =		self.prepare_config_and_inputs()

					A_	:					Optional[int]						 =		floats_tensor([self.batch_size, self.seq_length, self.hidden_size]							)
					A_	:					Tuple						 =		ids_tensor([self.batch_size, self.seq_length]   ,  vocab_size=2							)

					return (
					    config,
					    input_ids,
					    attention_mask,
					    encoder_hidden_states,
					    encoder_attention_mask,
					)







				def        a_	(				self :       Optional[Any]   ,  _lowerCamelCase :       List[Any]   ,  _lowerCamelCase :       Dict   ,  _lowerCamelCase :       List[Any]   ,  _lowerCamelCase :       List[Any]							):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		20
					A_	:					List[str]						 =		model_class_name(_lowerCamelCase							)

					A_	:					Optional[Any]						 =		model.init_cache(input_ids.shape[0]   ,  _lowerCamelCase							)
					A_	:					int						 =		jnp.ones((input_ids.shape[0], max_decoder_length)   ,  dtype='''i4'''							)

					A_	:					Any						 =		jnp.broadcast_to(
					    jnp.arange(input_ids.shape[-1] - 1							)[None, :]   ,  (input_ids.shape[0], input_ids.shape[-1] - 1)							)
					A_	:					Optional[int]						 =		model(
					    input_ids[:, :-1]   ,  attention_mask=_lowerCamelCase   ,  past_key_values=_lowerCamelCase   ,  position_ids=_lowerCamelCase   ,  )

					A_	:					Tuple						 =		jnp.array(input_ids.shape[0] * [[input_ids.shape[-1] - 1]]   ,  dtype='''i4'''							)
					A_	:					int						 =		model(
					    input_ids[:, -1:]   ,  attention_mask=_lowerCamelCase   ,  past_key_values=outputs_cache.past_key_values   ,  position_ids=_lowerCamelCase   ,  )

					A_	:					Tuple						 =		model(_lowerCamelCase							)

					A_	:					Union[str, Any]						 =		np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])							)							)
					self.parent.assertTrue(diff < 1E-3   ,  msg=F"""Max diff is {diff}"""							)







				def        a_	(				self :       Dict   ,  _lowerCamelCase :       Any   ,  _lowerCamelCase :       Optional[Any]   ,  _lowerCamelCase :       Optional[int]   ,  _lowerCamelCase :       List[Any]							):



					"""simple docstring"""

					A_	:					Dict						 =		20
					A_	:					List[Any]						 =		model_class_name(_lowerCamelCase							)

					A_	:					int						 =		jnp.concatenate(
					    [attention_mask, jnp.zeros((attention_mask.shape[0], max_decoder_length - attention_mask.shape[1])							)]   ,  axis=-1   ,  )

					A_	:					Optional[int]						 =		model.init_cache(input_ids.shape[0]   ,  _lowerCamelCase							)
					A_	:					Tuple						 =		jnp.broadcast_to(
					    jnp.arange(input_ids.shape[-1] - 1							)[None, :]   ,  (input_ids.shape[0], input_ids.shape[-1] - 1)							)

					A_	:					int						 =		model(
					    input_ids[:, :-1]   ,  attention_mask=_lowerCamelCase   ,  past_key_values=_lowerCamelCase   ,  position_ids=_lowerCamelCase   ,  )
					A_	:					Any						 =		jnp.array(input_ids.shape[0] * [[input_ids.shape[-1] - 1]]   ,  dtype='''i4'''							)
					A_	:					Union[str, Any]						 =		model(
					    input_ids[:, -1:]   ,  past_key_values=outputs_cache.past_key_values   ,  attention_mask=_lowerCamelCase   ,  position_ids=_lowerCamelCase   ,  )

					A_	:					Tuple						 =		model(_lowerCamelCase   ,  attention_mask=_lowerCamelCase							)
					A_	:					List[str]						 =		np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])							)							)
					self.parent.assertTrue(diff < 1E-3   ,  msg=F"""Max diff is {diff}"""							)

@require_sentencepiece
@require_flax
class 							lowercase   (     __UpperCAmelCase  ,						__UpperCAmelCase  ,						unittest.TestCase):
				__lowerCAmelCase     :     List[Any]								= (FlaxXGLMModel, FlaxXGLMForCausalLM) if is_flax_available() else ()
				__lowerCAmelCase     :     Optional[int]								= (FlaxXGLMForCausalLM,) if is_flax_available() else ()







				def        a_	(				self :       List[Any]							):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		FlaxXGLMModelTester(self							)







				def        a_	(				self :       List[Any]							):



					"""simple docstring"""

					for model_class_name in self.all_model_classes:
						A_ ,			A_ ,			A_	:					Optional[int]						 =		self.model_tester.prepare_config_and_inputs()
						self.model_tester.check_use_cache_forward(_lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase							)







				def        a_	(				self :       List[Any]							):



					"""simple docstring"""

					for model_class_name in self.all_model_classes:
						A_ ,			A_ ,			A_	:					Dict						 =		self.model_tester.prepare_config_and_inputs()
						self.model_tester.check_use_cache_forward_with_attn_mask(
						    _lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase							)







				@slow
				def        a_	(				self :       List[str]							):



					"""simple docstring"""

					A_	:					Dict						 =		XGLMTokenizer.from_pretrained('''XGLM'''   ,  padding_side='''left'''							)
					A_	:					str						 =		tokenizer(['''Hello this is a long string''', '''Hey''']   ,  return_tensors='''np'''   ,  padding=_lowerCamelCase   ,  truncation=_lowerCamelCase							)

					A_	:					Union[str, Any]						 =		FlaxXGLMForCausalLM.from_pretrained('''facebook/xglm-564M'''							)
					A_	:					List[Any]						 =		1
					A_	:					List[Any]						 =		False

					A_	:					Union[str, Any]						 =		jax.jit(model.generate							)

					A_	:					Optional[int]						 =		jit_generate(inputs['''input_ids''']   ,  attention_mask=inputs['''attention_mask''']							).sequences

					A_	:					Union[str, Any]						 =		tokenizer.batch_decode(_lowerCamelCase   ,  skip_special_tokens=_lowerCamelCase							)

					A_	:					List[Any]						 =		[
					    '''Hello this is a long string of questions, but I\'m not sure if I\'m''',
					    '''Hey, I\'m a newbie to the forum and I\'''',
					]

					self.assertListEqual(_lowerCamelCase   ,  _lowerCamelCase							)







				@is_pt_flax_cross_test
				def        a_	(				self :       Tuple							):



					"""simple docstring"""

					A_ ,			A_	:					str						 =		self.model_tester.prepare_config_and_inputs_for_common()

					for model_class in self.all_model_classes:
						with self.subTest(model_class.__name__							):
							# prepare inputs
							A_	:					int						 =		self._prepare_for_class(_lowerCamelCase   ,  _lowerCamelCase							)
							A_	:					int						 =		{k: torch.tensor(v.tolist()							) for k, v in prepared_inputs_dict.items()}

							# load corresponding PyTorch class
							A_	:					Union[str, Any]						 =		model_class.__name__[4:]  # Skip the "Flax" at the beginning
							A_	:					Union[str, Any]						 =		getattr(_lowerCamelCase   ,  _lowerCamelCase							)

							A_ ,			A_	:					List[Any]						 =		pt_inputs['''input_ids'''].shape
							A_	:					Optional[int]						 =		np.random.randint(0   ,  seq_length - 1   ,  size=(batch_size,)							)
							for batch_idx, start_index in enumerate(_lowerCamelCase							):
								A_	:					List[Any]						 =		0
								A_	:					Optional[int]						 =		1
								A_	:					Optional[Any]						 =		0
								A_	:					str						 =		1
							A_	:					Optional[Any]						 =		pt_model_class(_lowerCamelCase							).eval()
							# Flax models don't use the `use_cache` option and cache is not returned as a default.
							# So we disable `use_cache` here for PyTorch model.
							A_	:					Optional[int]						 =		False
							A_	:					Optional[Any]						 =		model_class(_lowerCamelCase   ,  dtype=jnp.floataa							)
							A_	:					Optional[Any]						 =		convert_pytorch_state_dict_to_flax(pt_model.state_dict()   ,  _lowerCamelCase							)
							A_	:					Optional[Any]						 =		fx_state

							with torch.no_grad():
								A_	:					int						 =		pt_model(**_lowerCamelCase							).to_tuple()

							A_	:					int						 =		fx_model(**_lowerCamelCase							).to_tuple()
							self.assertEqual(len(_lowerCamelCase							)   ,  len(_lowerCamelCase							)   ,  '''Output lengths differ between Flax and PyTorch'''							)
							for fx_output, pt_output in zip(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assert_almost_equals(fx_output[:, -1]   ,  pt_output[:, -1].numpy()   ,  4E-2							)

							with tempfile.TemporaryDirectory() as tmpdirname:
								pt_model.save_pretrained(_lowerCamelCase							)
								A_	:					Optional[Any]						 =		model_class.from_pretrained(_lowerCamelCase   ,  from_pt=_lowerCamelCase							)

							A_	:					Union[str, Any]						 =		fx_model_loaded(**_lowerCamelCase							).to_tuple()
							self.assertEqual(
							    len(_lowerCamelCase							)   ,  len(_lowerCamelCase							)   ,  '''Output lengths differ between Flax and PyTorch'''							)
							for fx_output_loaded, pt_output in zip(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assert_almost_equals(fx_output_loaded[:, -1]   ,  pt_output[:, -1].numpy()   ,  4E-2							)







				@is_pt_flax_cross_test
				def        a_	(				self :       int							):



					"""simple docstring"""

					A_ ,			A_	:					Optional[int]						 =		self.model_tester.prepare_config_and_inputs_for_common()
					for model_class in self.all_model_classes:
						with self.subTest(model_class.__name__							):
							# prepare inputs
							A_	:					List[Any]						 =		self._prepare_for_class(_lowerCamelCase   ,  _lowerCamelCase							)
							A_	:					List[Any]						 =		{k: torch.tensor(v.tolist()							) for k, v in prepared_inputs_dict.items()}

							# load corresponding PyTorch class
							A_	:					Dict						 =		model_class.__name__[4:]  # Skip the "Flax" at the beginning
							A_	:					Tuple						 =		getattr(_lowerCamelCase   ,  _lowerCamelCase							)

							A_	:					Optional[Any]						 =		pt_model_class(_lowerCamelCase							).eval()
							A_	:					Union[str, Any]						 =		False
							A_	:					Union[str, Any]						 =		model_class(_lowerCamelCase   ,  dtype=jnp.floataa							)

							A_	:					Optional[Any]						 =		load_flax_weights_in_pytorch_model(_lowerCamelCase   ,  fx_model.params							)
							A_ ,			A_	:					Any						 =		pt_inputs['''input_ids'''].shape
							A_	:					Union[str, Any]						 =		np.random.randint(0   ,  seq_length - 1   ,  size=(batch_size,)							)
							for batch_idx, start_index in enumerate(_lowerCamelCase							):
								A_	:					List[str]						 =		0
								A_	:					str						 =		1
								A_	:					List[str]						 =		0
								A_	:					List[Any]						 =		1

							# make sure weights are tied in PyTorch
							pt_model.tie_weights()

							with torch.no_grad():
								A_	:					Tuple						 =		pt_model(**_lowerCamelCase							).to_tuple()

							A_	:					Optional[int]						 =		fx_model(**_lowerCamelCase							).to_tuple()
							self.assertEqual(len(_lowerCamelCase							)   ,  len(_lowerCamelCase							)   ,  '''Output lengths differ between Flax and PyTorch'''							)
							for fx_output, pt_output in zip(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assert_almost_equals(fx_output[:, -1]   ,  pt_output[:, -1].numpy()   ,  4E-2							)

							with tempfile.TemporaryDirectory() as tmpdirname:
								fx_model.save_pretrained(_lowerCamelCase							)
								A_	:					Optional[int]						 =		pt_model_class.from_pretrained(_lowerCamelCase   ,  from_flax=_lowerCamelCase							)

							with torch.no_grad():
								A_	:					Optional[Any]						 =		pt_model_loaded(**_lowerCamelCase							).to_tuple()

							self.assertEqual(
							    len(_lowerCamelCase							)   ,  len(_lowerCamelCase							)   ,  '''Output lengths differ between Flax and PyTorch'''							)
							for fx_output, pt_output in zip(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assert_almost_equals(fx_output[:, -1]   ,  pt_output[:, -1].numpy()   ,  4E-2							)







				@slow
				def        a_	(				self :       List[str]							):



					"""simple docstring"""

					for model_class_name in self.all_model_classes:
						A_	:					List[str]						 =		model_class_name.from_pretrained('''facebook/xglm-564M'''							)
						A_	:					Optional[int]						 =		model(np.ones((1, 1)							)							)
						self.assertIsNotNone(_lowerCamelCase							)











"""simple docstring"""

from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
_lowerCamelCase	:      int   =							20

# Time between time steps in seconds
_lowerCamelCase	:      Union[str, Any]   =							INTERVAL / 1000

class 							lowercase   :







				def __init__(				self :       Union[str, Any]   ,  _lowerCamelCase :       float   ,  _lowerCamelCase :       float   ,  _lowerCamelCase :       float   ,  _lowerCamelCase :       float   ,  _lowerCamelCase :       float = 1.0   ,  _lowerCamelCase :       float = 1.0   ,  _lowerCamelCase :       str = "blue"   ,  ):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		position_x
					A_	:					Optional[int]						 =		position_y
					A_	:					List[str]						 =		velocity_x
					A_	:					List[Any]						 =		velocity_y
					A_	:					Dict						 =		mass
					A_	:					Optional[Any]						 =		size
					A_	:					Any						 =		color







				@property
				def        a_	(				self :       Any							):



					"""simple docstring"""

					return self.position_x, self.position_y







				@property
				def        a_	(				self :       int							):



					"""simple docstring"""

					return self.velocity_x, self.velocity_y







				def        a_	(				self :       Dict   ,  _lowerCamelCase :       float   ,  _lowerCamelCase :       float   ,  _lowerCamelCase :       float							):



					"""simple docstring"""

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







				def        a_	(				self :       int   ,  _lowerCamelCase :       float							):



					"""simple docstring"""

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

class 							lowercase   :







				def __init__(				self :       Optional[Any]   ,  _lowerCamelCase :       list[Body]   ,  _lowerCamelCase :       float = 1.0   ,  _lowerCamelCase :       float = 1.0   ,  _lowerCamelCase :       float = 0.0   ,  ):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		bodies
					A_	:					Union[str, Any]						 =		gravitation_constant
					A_	:					str						 =		time_factor
					A_	:					str						 =		softening_factor







				def __len__(				self :       Dict							):



					"""simple docstring"""

					return len(self.bodies							)







				def        a_	(				self :       Dict   ,  _lowerCamelCase :       float							):



					"""simple docstring"""

					for bodya in self.bodies:
						A_	:					Tuple						 =		0.0
						A_	:					int						 =		0.0
						for bodya in self.bodies:
							if bodya != bodya:
								A_	:					Any						 =		bodya.position_x - bodya.position_x
								A_	:					Optional[int]						 =		bodya.position_y - bodya.position_y

								# Calculation of the distance using Pythagoras's theorem
								# Extra factor due to the softening technique
								A_	:					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(_lowerCamelCase   ,  _lowerCamelCase   ,  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 		lowercase_   (		_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase						):




	"""simple docstring"""






	body_system.update_system(_UpperCAmelCase						)

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

def 		lowercase_   (		_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase = -1	,   _UpperCAmelCase = 1	,   _UpperCAmelCase = -1	,   _UpperCAmelCase = 1	,   ):




	"""simple docstring"""






	A_	:					Optional[Any]						 =		plt.figure()
	fig.canvas.set_window_title(_UpperCAmelCase						)
	A_	:					Union[str, 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
	A_	:					List[str]						 =		[
	    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						) -> list[plt.Circle]:
		update_step(_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase						)
		return patches

	A_	:					str						 =		animation.FuncAnimation(  # noqa: F841
	    _UpperCAmelCase	,   _UpperCAmelCase	,   interval=_UpperCAmelCase	,   blit=_UpperCAmelCase						)

	plt.show()

def 		lowercase_   (		):




	"""simple docstring"""






	A_	:					Optional[int]						 =		0.970_0436
	A_	:					Any						 =		-0.2430_8753
	A_	:					Tuple						 =		0.4_6620_3685
	A_	:					Any						 =		0.4323_6573

	A_	:					Dict						 =		[
	    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 		lowercase_   (		):




	"""simple docstring"""






	A_	:					int						 =		7.3476E22
	A_	:					Optional[Any]						 =		5.972E24
	A_	:					List[Any]						 =		1022
	A_	:					Optional[int]						 =		3_8439_9000
	A_	:					Tuple						 =		6.674E-11

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

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

def 		lowercase_   (		):




	"""simple docstring"""






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





