
'''simple docstring'''



from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
snake_case_   :  Optional[Any]								=      20

# Time between time steps in seconds
snake_case_   :  Tuple								=      INTERVAL / 1000

class     A_ :

			'''simple docstring'''





			def __init__(					self			,     A_			,     A_			,     A_			,     A_			,     A_ = 1.0			,     A_ = 1.0			,     A_ = "blue"			,     ):
								_UpperCamelCase											=   position_x
								_UpperCamelCase											=   position_y
								_UpperCamelCase											=   velocity_x
								_UpperCamelCase											=   velocity_y
								_UpperCamelCase											=   mass
								_UpperCamelCase											=   size
								_UpperCamelCase											=   color




			@property
			def       a	(					self   ):
								return self.position_x, self.position_y




			@property
			def       a	(					self   ):
								return self.velocity_x, self.velocity_y




			def       a	(					self			,     A_			,     A_			,     A_   ):
								self.velocity_x += force_x * delta_time
								self.velocity_y += force_y * delta_time




			def       a	(					self			,     A_   ):
								self.position_x += self.velocity_x * delta_time
								self.position_y += self.velocity_y * delta_time




class     A_ :

			'''simple docstring'''





			def __init__(					self			,     A_			,     A_ = 1.0			,     A_ = 1.0			,     A_ = 0.0			,     ):
								_UpperCamelCase											=   bodies
								_UpperCamelCase											=   gravitation_constant
								_UpperCamelCase											=   time_factor
								_UpperCamelCase											=   softening_factor




			def __len__(					self   ):
								return len(self.bodies   )




			def       a	(					self			,     A_   ):
								for bodya in self.bodies:
													_UpperCamelCase											=   0.0
													_UpperCamelCase											=   0.0
													for bodya in self.bodies:
																		if bodya != bodya:
																							_UpperCamelCase											=   bodya.position_x - bodya.position_x
																							_UpperCamelCase											=   bodya.position_y - bodya.position_y

																							# Calculation of the distance using Pythagoras's theorem
																							# Extra factor due to the softening technique
																							_UpperCamelCase											=   (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  : List[Any] ,   _UpperCamelCase  : int ,   _UpperCamelCase  : Union[str, Any]				)->   List[str]:






					"""simple docstring"""

					body_system.update_system(_UpperCamelCase				)

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



def  lowercase__(		_UpperCamelCase  : List[Any] ,   _UpperCamelCase  : List[str] ,   _UpperCamelCase  : Tuple = -1 ,   _UpperCamelCase  : int = 1 ,   _UpperCamelCase  : Optional[Any] = -1 ,   _UpperCamelCase  : Tuple = 1 ,   )->   Optional[int]:






					"""simple docstring"""

					_UpperCamelCase											=   plt.figure()
					fig.canvas.set_window_title(_UpperCamelCase				)
					_UpperCamelCase											=   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											=   [
					    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

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

					plt.show()



def  lowercase__(		)->   int:






					"""simple docstring"""

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

					_UpperCamelCase											=   [
					    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__(		)->   List[str]:






					"""simple docstring"""

					_UpperCamelCase											=   7.3_4_7_6E2_2
					_UpperCamelCase											=   5.9_7_2E2_4
					_UpperCamelCase											=   1022
					_UpperCamelCase											=   384399000
					_UpperCamelCase											=   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
					_UpperCamelCase											=   earth_mass * velocity_dif / (earth_mass + moon_mass)
					_UpperCamelCase											=   moon_velocity - velocity_dif

					_UpperCamelCase											=   Body(-earth_moon_distance ,   0 ,   0 ,   _UpperCamelCase ,   _UpperCamelCase ,   10000000 ,   "grey"				)
					_UpperCamelCase											=   Body(0 ,   0 ,   0 ,   _UpperCamelCase ,   _UpperCamelCase ,   50000000 ,   "blue"				)
					return BodySystem([earth, moon] ,   _UpperCamelCase ,   time_factor=1000000				)



def  lowercase__(		)->   Optional[Any]:






					"""simple docstring"""

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










'''simple docstring'''



import os
from typing import List, Union

import tensorflow as tf
from tensorflow_text import BertTokenizer as BertTokenizerLayer
from tensorflow_text import FastBertTokenizer, ShrinkLongestTrimmer, case_fold_utfa, combine_segments, pad_model_inputs

from .tokenization_bert import BertTokenizer

class     A_ (  tf.keras.layers.Layer  ):

			'''simple docstring'''





			def __init__(					self			,     A_			,     A_			,     A_ = None			,     A_ = None			,     A_ = None			,     A_ = "longest"			,     A_ = True			,     A_ = 5_12			,     A_ = None			,     A_ = True			,     A_ = True			,     A_ = True			,     **A_			,     ):
								super().__init__()
								if use_fast_bert_tokenizer:
													_UpperCamelCase											=   FastBertTokenizer(
													    A_			,     token_out_type=tf.intaa			,     lower_case_nfd_strip_accents=A_			,     **A_   )
								else:
													_UpperCamelCase											=   tf.lookup.StaticVocabularyTable(
													    tf.lookup.KeyValueTensorInitializer(
													        keys=A_			,     key_dtype=tf.string			,     values=tf.range(tf.size(A_			,     out_type=tf.intaa   )			,     dtype=tf.intaa   )			,     value_dtype=tf.intaa			,     )			,     num_oov_buckets=1			,     )
													_UpperCamelCase											=   BertTokenizerLayer(
													    A_			,     token_out_type=tf.intaa			,     lower_case=A_			,     **A_   )

								_UpperCamelCase											=   vocab_list
								_UpperCamelCase											=   do_lower_case
								_UpperCamelCase											=   cls_token_id or vocab_list.index("[CLS]"   )
								_UpperCamelCase											=   sep_token_id or vocab_list.index("[SEP]"   )
								_UpperCamelCase											=   pad_token_id or vocab_list.index("[PAD]"   )
								_UpperCamelCase											=   ShrinkLongestTrimmer(max_length - 3			,     axis=1   )  # Allow room for special tokens
								_UpperCamelCase											=   max_length
								_UpperCamelCase											=   padding
								_UpperCamelCase											=   truncation
								_UpperCamelCase											=   pad_to_multiple_of
								_UpperCamelCase											=   return_token_type_ids
								_UpperCamelCase											=   return_attention_mask




			@classmethod
			def       a	(					cls			,     A_			,     **A_   ):  # noqa: F821
								_UpperCamelCase											=   kwargs.pop("do_lower_case"			,     A_   )
								_UpperCamelCase											=   tokenizer.do_lower_case if do_lower_case is None else do_lower_case
								_UpperCamelCase											=   kwargs.pop("cls_token_id"			,     A_   )
								_UpperCamelCase											=   tokenizer.cls_token_id if cls_token_id is None else cls_token_id
								_UpperCamelCase											=   kwargs.pop("sep_token_id"			,     A_   )
								_UpperCamelCase											=   tokenizer.sep_token_id if sep_token_id is None else sep_token_id
								_UpperCamelCase											=   kwargs.pop("pad_token_id"			,     A_   )
								_UpperCamelCase											=   tokenizer.pad_token_id if pad_token_id is None else pad_token_id

								_UpperCamelCase											=   tokenizer.get_vocab()
								_UpperCamelCase											=   sorted([(wordpiece, idx) for wordpiece, idx in vocab.items()]			,     key=lambda A_   : x[1]   )
								_UpperCamelCase											=   [entry[0] for entry in vocab]
								return cls(
								    vocab_list=A_			,     do_lower_case=A_			,     cls_token_id=A_			,     sep_token_id=A_			,     pad_token_id=A_			,     **A_			,     )




			@classmethod
			def       a	(					cls			,     A_			,     *A_			,     **A_   ):
								try:
													_UpperCamelCase											=   BertTokenizer.from_pretrained(A_			,     *A_			,     **A_   )
								except:  # noqa: E722
													from .tokenization_bert_fast import BertTokenizerFast

													_UpperCamelCase											=   BertTokenizerFast.from_pretrained(A_			,     *A_			,     **A_   )
								return cls.from_tokenizer(A_			,     **A_   )




			def       a	(					self			,     A_   ):
								if self.do_lower_case:
													_UpperCamelCase											=   case_fold_utfa(A_   )
								_UpperCamelCase											=   self.tf_tokenizer.tokenize(A_   )
								return tokens.merge_dims(1			,     -1   )




			def       a	(					self			,     A_			,     A_=None			,     A_=None			,     A_=None			,     A_=None			,     A_=None			,     A_=None			,     A_=None			,     ):
								if padding is None:
													_UpperCamelCase											=   self.padding
								if padding not in ("longest", "max_length"):
													raise ValueError("Padding must be either 'longest' or 'max_length'!"   )
								if max_length is not None and text_pair is not None:
													# Because we have to instantiate a Trimmer to do it properly
													raise ValueError("max_length cannot be overridden at call time when truncating paired texts!"   )
								if max_length is None:
													_UpperCamelCase											=   self.max_length
								if truncation is None:
													_UpperCamelCase											=   self.truncation
								if pad_to_multiple_of is None:
													_UpperCamelCase											=   self.pad_to_multiple_of
								if return_token_type_ids is None:
													_UpperCamelCase											=   self.return_token_type_ids
								if return_attention_mask is None:
													_UpperCamelCase											=   self.return_attention_mask
								if not isinstance(A_			,     tf.Tensor   ):
													_UpperCamelCase											=   tf.convert_to_tensor(A_   )
								if text_pair is not None and not isinstance(A_			,     tf.Tensor   ):
													_UpperCamelCase											=   tf.convert_to_tensor(A_   )
								if text_pair is not None:
													if text.shape.rank > 1:
																		raise ValueError("text argument should not be multidimensional when a text pair is supplied!"   )
													if text_pair.shape.rank > 1:
																		raise ValueError("text_pair should not be multidimensional!"   )
								if text.shape.rank == 2:
													_UpperCamelCase				,	_UpperCamelCase											=   text[:, 0], text[:, 1]
								_UpperCamelCase											=   self.unpaired_tokenize(A_   )
								if text_pair is None:  # Unpaired text
													if truncation:
																		_UpperCamelCase											=   text[:, : max_length - 2]  # Allow room for special tokens
													_UpperCamelCase				,	_UpperCamelCase											=   combine_segments(
													    (text,)			,     start_of_sequence_id=self.cls_token_id			,     end_of_segment_id=self.sep_token_id   )
								else:  # Paired text
													_UpperCamelCase											=   self.unpaired_tokenize(A_   )
													if truncation:
																		_UpperCamelCase				,	_UpperCamelCase											=   self.paired_trimmer.trim([text, text_pair]   )
													_UpperCamelCase				,	_UpperCamelCase											=   combine_segments(
													    (text, text_pair)			,     start_of_sequence_id=self.cls_token_id			,     end_of_segment_id=self.sep_token_id   )
								if padding == "longest":
													_UpperCamelCase											=   input_ids.bounding_shape(axis=1   )
													if pad_to_multiple_of is not None:
																		# No ceiling division in tensorflow, so we negate floordiv instead
																		_UpperCamelCase											=   pad_to_multiple_of * (-tf.math.floordiv(-pad_length			,     A_   ))
								else:
													_UpperCamelCase											=   max_length

								_UpperCamelCase				,	_UpperCamelCase											=   pad_model_inputs(A_			,     max_seq_length=A_			,     pad_value=self.pad_token_id   )
								_UpperCamelCase											=   {"input_ids": input_ids}
								if return_attention_mask:
													_UpperCamelCase											=   attention_mask
								if return_token_type_ids:
													_UpperCamelCase				,	_UpperCamelCase											=   pad_model_inputs(
													    A_			,     max_seq_length=A_			,     pad_value=self.pad_token_id   )
													_UpperCamelCase											=   token_type_ids
								return output




			def       a	(					self   ):
								return {
								    "vocab_list": self.vocab_list,
								    "do_lower_case": self.do_lower_case,
								    "cls_token_id": self.cls_token_id,
								    "sep_token_id": self.sep_token_id,
								    "pad_token_id": self.pad_token_id,
								}



