





"""simple docstring"""




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
UpperCamelCase_           =20

# Time between time steps in seconds
UpperCamelCase_           =INTERVAL / 1_000




class  _a						:






				def __init__( self		:    Tuple, lowerCAmelCase__		:    float, lowerCAmelCase__		:    float, lowerCAmelCase__		:    float, lowerCAmelCase__		:    float, lowerCAmelCase__		:    float = 1.0, lowerCAmelCase__		:    float = 1.0, lowerCAmelCase__		:    str = "blue", )	->      None:




										'''simple docstring'''



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






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




										'''simple docstring'''



										return self.position_x, self.position_y






				@property
				def 				snake_case	( self		:    List[str]							)	->      tuple[float, float]:




										'''simple docstring'''



										return self.velocity_x, self.velocity_y






				def 				snake_case	( self		:    Optional[Any], lowerCAmelCase__		:    float, lowerCAmelCase__		:    float, lowerCAmelCase__		:    float							)	->      None:




										'''simple docstring'''



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






				def 				snake_case	( self		:    Any, lowerCAmelCase__		:    float							)	->      None:




										'''simple docstring'''



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




class  _a						:






				def __init__( self		:    str, lowerCAmelCase__		:    list[Body], lowerCAmelCase__		:    float = 1.0, lowerCAmelCase__		:    float = 1.0, lowerCAmelCase__		:    float = 0.0, )	->      None:




										'''simple docstring'''



										_UpperCamelCase			:					int     =    bodies
										_UpperCamelCase			:					Any     =    gravitation_constant
										_UpperCamelCase			:					str     =    time_factor
										_UpperCamelCase			:					List[Any]     =    softening_factor






				def __len__( self		:    Any							)	->      int:




										'''simple docstring'''



										return len(self.bodies							)






				def 				snake_case	( self		:    int, lowerCAmelCase__		:    float							)	->      None:




										'''simple docstring'''



										for bodya in self.bodies:
																_UpperCamelCase			:					str     =    0.0
																_UpperCamelCase			:					Any     =    0.0
																for bodya in self.bodies:
																						if bodya != bodya:
																												_UpperCamelCase			:					Optional[int]     =    bodya.position_x - bodya.position_x
																												_UpperCamelCase			:					List[str]     =    bodya.position_y - bodya.position_y

																												# Calculation of the distance using Pythagoras's theorem
																												# Extra factor due to the softening technique
																												_UpperCamelCase			:					Dict     =    (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        a_				(							_lowercase       ,						_lowercase       ,						_lowercase   ):
						body_system.update_system(_lowercase   )

						# Update the positions of the patches
						for patch, body in zip(_lowercase       ,						body_system.bodies   ):
												_UpperCamelCase			:					Optional[int]     =    (body.position_x, body.position_y)





def        a_				(							_lowercase       ,						_lowercase       ,						_lowercase = -1       ,						_lowercase = 1       ,						_lowercase = -1       ,						_lowercase = 1       ,						):
						_UpperCamelCase			:					Optional[int]     =    plt.figure()
						fig.canvas.set_window_title(_lowercase   )
						_UpperCamelCase			:					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
						_UpperCamelCase			:					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(_lowercase   )

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

						_UpperCamelCase			:					Tuple     =    animation.FuncAnimation(  # noqa: F841
						    _lowercase       ,						_lowercase       ,						interval=_lowercase       ,						blit=_lowercase   )

						plt.show()





def        a_				(							):
						_UpperCamelCase			:					str     =    0.9700436
						_UpperCamelCase			:					List[Any]     =    -0.24308753
						_UpperCamelCase			:					List[Any]     =    0.466203685
						_UpperCamelCase			:					Union[str, Any]     =    0.43236573

						_UpperCamelCase			:					Tuple     =    [
						    Body(_lowercase       ,						_lowercase       ,						_lowercase       ,						_lowercase       ,						size=0.2       ,						color='''red'''   ),
						    Body(-position_x       ,						-position_y       ,						_lowercase       ,						_lowercase       ,						size=0.2       ,						color='''green'''   ),
						    Body(0       ,						0       ,						-2 * velocity_x       ,						-2 * velocity_y       ,						size=0.2       ,						color='''blue'''   ),
						]
						return BodySystem(_lowercase       ,						time_factor=3   )





def        a_				(							):
						_UpperCamelCase			:					Dict     =    7.3476E22
						_UpperCamelCase			:					List[str]     =    5.972E24
						_UpperCamelCase			:					Dict     =    1022
						_UpperCamelCase			:					Union[str, Any]     =    3_8439_9000
						_UpperCamelCase			:					Any     =    6.674E-11

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

						_UpperCamelCase			:					str     =    Body(-earth_moon_distance       ,						0       ,						0       ,						_lowercase       ,						_lowercase       ,						1000_0000       ,						'''grey'''   )
						_UpperCamelCase			:					Dict     =    Body(0       ,						0       ,						0       ,						_lowercase       ,						_lowercase       ,						5000_0000       ,						'''blue'''   )
						return BodySystem([earth, moon]       ,						_lowercase       ,						time_factor=100_0000   )





def        a_				(							):
						_UpperCamelCase			:					str     =    []
						for _ in range(10   ):
												_UpperCamelCase			:					List[str]     =    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   )       ,						_lowercase       ,						_lowercase       ,						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(_lowercase       ,						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 unittest

import numpy as np

from transformers import ElectraConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor, random_attention_mask


if is_flax_available():
						from transformers.models.electra.modeling_flax_electra import (
						    FlaxElectraForCausalLM,
						    FlaxElectraForMaskedLM,
						    FlaxElectraForMultipleChoice,
						    FlaxElectraForPreTraining,
						    FlaxElectraForQuestionAnswering,
						    FlaxElectraForSequenceClassification,
						    FlaxElectraForTokenClassification,
						    FlaxElectraModel,
						)




class  _a						(      unittest.TestCase				):






				def __init__( self		:    str, lowerCAmelCase__		:    Tuple, lowerCAmelCase__		:    List[str]=1_3, lowerCAmelCase__		:    Optional[int]=7, lowerCAmelCase__		:    Optional[Any]=True, lowerCAmelCase__		:    Optional[int]=True, lowerCAmelCase__		:    Any=True, lowerCAmelCase__		:    str=True, lowerCAmelCase__		:    Any=9_9, lowerCAmelCase__		:    Union[str, Any]=2_4, lowerCAmelCase__		:    Optional[Any]=3_2, lowerCAmelCase__		:    Tuple=5, lowerCAmelCase__		:    int=4, lowerCAmelCase__		:    List[Any]=3_7, lowerCAmelCase__		:    Dict="gelu", lowerCAmelCase__		:    Any=0.1, lowerCAmelCase__		:    Any=0.1, lowerCAmelCase__		:    str=5_1_2, lowerCAmelCase__		:    Tuple=1_6, lowerCAmelCase__		:    int=2, lowerCAmelCase__		:    int=0.02, lowerCAmelCase__		:    Optional[int]=4, )	->      Union[str, Any]:




										'''simple docstring'''



										_UpperCamelCase			:					Dict     =    parent
										_UpperCamelCase			:					Tuple     =    batch_size
										_UpperCamelCase			:					str     =    seq_length
										_UpperCamelCase			:					Any     =    is_training
										_UpperCamelCase			:					Union[str, Any]     =    use_attention_mask
										_UpperCamelCase			:					List[Any]     =    use_token_type_ids
										_UpperCamelCase			:					str     =    use_labels
										_UpperCamelCase			:					Union[str, Any]     =    vocab_size
										_UpperCamelCase			:					int     =    hidden_size
										_UpperCamelCase			:					Optional[int]     =    embedding_size
										_UpperCamelCase			:					int     =    num_hidden_layers
										_UpperCamelCase			:					int     =    num_attention_heads
										_UpperCamelCase			:					Tuple     =    intermediate_size
										_UpperCamelCase			:					Optional[int]     =    hidden_act
										_UpperCamelCase			:					Any     =    hidden_dropout_prob
										_UpperCamelCase			:					Union[str, Any]     =    attention_probs_dropout_prob
										_UpperCamelCase			:					Any     =    max_position_embeddings
										_UpperCamelCase			:					List[str]     =    type_vocab_size
										_UpperCamelCase			:					Union[str, Any]     =    type_sequence_label_size
										_UpperCamelCase			:					str     =    initializer_range
										_UpperCamelCase			:					Union[str, Any]     =    num_choices






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




										'''simple docstring'''



										_UpperCamelCase			:					Optional[Any]     =    ids_tensor([self.batch_size, self.seq_length], self.vocab_size							)

										_UpperCamelCase			:					Dict     =    None
										if self.use_attention_mask:
																_UpperCamelCase			:					Union[str, Any]     =    random_attention_mask([self.batch_size, self.seq_length]							)

										_UpperCamelCase			:					Optional[Any]     =    None
										if self.use_token_type_ids:
																_UpperCamelCase			:					Union[str, Any]     =    ids_tensor([self.batch_size, self.seq_length], self.type_vocab_size							)

										_UpperCamelCase			:					Optional[Any]     =    ElectraConfig(
										    vocab_size=self.vocab_size, hidden_size=self.hidden_size, embedding_size=self.embedding_size, num_hidden_layers=self.num_hidden_layers, num_attention_heads=self.num_attention_heads, intermediate_size=self.intermediate_size, hidden_act=self.hidden_act, hidden_dropout_prob=self.hidden_dropout_prob, attention_probs_dropout_prob=self.attention_probs_dropout_prob, max_position_embeddings=self.max_position_embeddings, type_vocab_size=self.type_vocab_size, initializer_range=self.initializer_range, )

										return config, input_ids, token_type_ids, attention_mask






				def 				snake_case	( self		:    Any							)	->      Optional[int]:




										'''simple docstring'''



										_UpperCamelCase			:					Dict     =    self.prepare_config_and_inputs()
										_UpperCamelCase   ,							_UpperCamelCase   ,							_UpperCamelCase   ,							_UpperCamelCase			:					Tuple     =    config_and_inputs
										_UpperCamelCase			:					List[Any]     =    {'''input_ids''': input_ids, '''token_type_ids''': token_type_ids, '''attention_mask''': attention_mask}
										return config, inputs_dict




@require_flax
class  _a						(      _lowerCAmelCase	,				unittest.TestCase				):
				UpperCamelCase								=    True

				UpperCamelCase								=    (
				    (
				        FlaxElectraModel,
				        FlaxElectraForCausalLM,
				        FlaxElectraForMaskedLM,
				        FlaxElectraForPreTraining,
				        FlaxElectraForTokenClassification,
				        FlaxElectraForQuestionAnswering,
				        FlaxElectraForMultipleChoice,
				        FlaxElectraForSequenceClassification,
				    )
				    if is_flax_available()
				    else ()
				)






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




										'''simple docstring'''



										_UpperCamelCase			:					List[Any]     =    FlaxElectraModelTester(self							)






				@slow
				def 				snake_case	( self		:    Optional[Any]							)	->      str:




										'''simple docstring'''



										for model_class_name in self.all_model_classes:
																if model_class_name == FlaxElectraForMaskedLM:
																						_UpperCamelCase			:					int     =    model_class_name.from_pretrained('''google/electra-small-generator'''							)
																else:
																						_UpperCamelCase			:					Any     =    model_class_name.from_pretrained('''google/electra-small-discriminator'''							)
																_UpperCamelCase			:					List[str]     =    model(np.ones((1, 1)							)							)
																self.assertIsNotNone(lowerCAmelCase__							)



