





'''simple docstring'''






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

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

# Time between time steps in seconds
A__       :     Optional[Any]          =INTERVAL / 10_00




class 				UpperCAmelCase  :




						def __init__(    self    :				str    ,    __snake_case    :				float    ,    __snake_case    :				float    ,    __snake_case    :				float    ,    __snake_case    :				float    ,    __snake_case    :				float = 1.0    ,    __snake_case    :				float = 1.0    ,    __snake_case    :				str = "blue"    ,    )       ->   None:
												_lowerCAmelCase							  =							position_x
												_lowerCAmelCase							  =							position_y
												_lowerCAmelCase							  =							velocity_x
												_lowerCAmelCase							  =							velocity_y
												_lowerCAmelCase							  =							mass
												_lowerCAmelCase							  =							size
												_lowerCAmelCase							  =							color




						@property
						def        lowercase__					(    self    :				Tuple						)       ->   tuple[float, float]:
												return self.position_x, self.position_y




						@property
						def        lowercase__					(    self    :				List[str]						)       ->   tuple[float, float]:
												return self.velocity_x, self.velocity_y




						def        lowercase__					(    self    :				Optional[Any]    ,    __snake_case    :				float    ,    __snake_case    :				float    ,    __snake_case    :				float						)       ->   None:
												self.velocity_x += force_x * delta_time
												self.velocity_y += force_y * delta_time




						def        lowercase__					(    self    :				Tuple    ,    __snake_case    :				float						)       ->   None:
												self.position_x += self.velocity_x * delta_time
												self.position_y += self.velocity_y * delta_time




class 				UpperCAmelCase  :




						def __init__(    self    :				int    ,    __snake_case    :				list[Body]    ,    __snake_case    :				float = 1.0    ,    __snake_case    :				float = 1.0    ,    __snake_case    :				float = 0.0    ,    )       ->   None:
												_lowerCAmelCase							  =							bodies
												_lowerCAmelCase							  =							gravitation_constant
												_lowerCAmelCase							  =							time_factor
												_lowerCAmelCase							  =							softening_factor




						def __len__(    self    :				List[Any]						)       ->   int:
												return len(self.bodies						)




						def        lowercase__					(    self    :				Optional[int]    ,    __snake_case    :				float						)       ->   None:
												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(__snake_case    ,    __snake_case    ,    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      UpperCamelCase__   (	lowerCAmelCase							,			lowerCAmelCase							,			lowerCAmelCase						):





						"""simple docstring"""


						body_system.update_system(lowerCAmelCase						)

						# Update the positions of the patches
						for patch, body in zip(lowerCAmelCase							,			body_system.bodies						):
												_lowerCAmelCase							  =							(body.position_x, body.position_y)
def      UpperCamelCase__   (	lowerCAmelCase							,			lowerCAmelCase							,			lowerCAmelCase = -1							,			lowerCAmelCase = 1							,			lowerCAmelCase = -1							,			lowerCAmelCase = 1							,			):





						"""simple docstring"""


						_lowerCAmelCase							  =							plt.figure()
						fig.canvas.set_window_title(lowerCAmelCase						)
						_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(lowerCAmelCase						)

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

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

						plt.show()
def      UpperCamelCase__   (	):





						"""simple docstring"""


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

						_lowerCAmelCase							  =							[
						    Body(lowerCAmelCase							,			lowerCAmelCase							,			lowerCAmelCase							,			lowerCAmelCase							,			size=0.2							,			color="""red"""						),
						    Body(-position_x							,			-position_y							,			lowerCAmelCase							,			lowerCAmelCase							,			size=0.2							,			color="""green"""						),
						    Body(0							,			0							,			-2 * velocity_x							,			-2 * velocity_y							,			size=0.2							,			color="""blue"""						),
						]
						return BodySystem(lowerCAmelCase							,			time_factor=3						)
def      UpperCamelCase__   (	):





						"""simple docstring"""


						_lowerCAmelCase							  =							7.34_76e22
						_lowerCAmelCase							  =							5.9_72e24
						_lowerCAmelCase							  =							10_22
						_lowerCAmelCase							  =							3_84_39_90_00
						_lowerCAmelCase							  =							6.6_74e-11

						# 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							,			lowerCAmelCase							,			lowerCAmelCase							,			10_00_00_00							,			"""grey"""						)
						_lowerCAmelCase							  =							Body(0							,			0							,			0							,			lowerCAmelCase							,			lowerCAmelCase							,			50_00_00_00							,			"""blue"""						)
						return BodySystem([earth, moon]							,			lowerCAmelCase							,			time_factor=1_00_00_00						)
def      UpperCamelCase__   (	):





						"""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						)							,			lowerCAmelCase							,			lowerCAmelCase							,			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(lowerCAmelCase							,			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_30_00_00_00,
						    4_30_00_00_00,
						    -4_30_00_00_00,
						    4_30_00_00_00,
						)
						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 				UpperCAmelCase  (    unittest.TestCase     ):




      def __init__(    self    :				str    ,    __snake_case    :				str    ,    __snake_case    :				str=13    ,    __snake_case    :				Optional[Any]=7    ,    __snake_case    :				str=True    ,    __snake_case    :				Any=True    ,    __snake_case    :				List[str]=True    ,    __snake_case    :				Any=True    ,    __snake_case    :				List[str]=99    ,    __snake_case    :				Dict=24    ,    __snake_case    :				Any=32    ,    __snake_case    :				List[str]=5    ,    __snake_case    :				Any=4    ,    __snake_case    :				Optional[Any]=37    ,    __snake_case    :				Union[str, Any]="gelu"    ,    __snake_case    :				Dict=0.1    ,    __snake_case    :				int=0.1    ,    __snake_case    :				Dict=5_12    ,    __snake_case    :				List[Any]=16    ,    __snake_case    :				Dict=2    ,    __snake_case    :				str=0.02    ,    __snake_case    :				Any=4    ,    )       ->   Union[str, Any]:
            _lowerCAmelCase							  =							parent
            _lowerCAmelCase							  =							batch_size
            _lowerCAmelCase							  =							seq_length
            _lowerCAmelCase							  =							is_training
            _lowerCAmelCase							  =							use_attention_mask
            _lowerCAmelCase							  =							use_token_type_ids
            _lowerCAmelCase							  =							use_labels
            _lowerCAmelCase							  =							vocab_size
            _lowerCAmelCase							  =							hidden_size
            _lowerCAmelCase							  =							embedding_size
            _lowerCAmelCase							  =							num_hidden_layers
            _lowerCAmelCase							  =							num_attention_heads
            _lowerCAmelCase							  =							intermediate_size
            _lowerCAmelCase							  =							hidden_act
            _lowerCAmelCase							  =							hidden_dropout_prob
            _lowerCAmelCase							  =							attention_probs_dropout_prob
            _lowerCAmelCase							  =							max_position_embeddings
            _lowerCAmelCase							  =							type_vocab_size
            _lowerCAmelCase							  =							type_sequence_label_size
            _lowerCAmelCase							  =							initializer_range
            _lowerCAmelCase							  =							num_choices




      def        lowercase__					(    self    :				Optional[Any]						)       ->   Optional[Any]:
            _lowerCAmelCase							  =							ids_tensor([self.batch_size, self.seq_length]    ,    self.vocab_size						)

            _lowerCAmelCase							  =							None
            if self.use_attention_mask:
                  _lowerCAmelCase							  =							random_attention_mask([self.batch_size, self.seq_length]						)

            _lowerCAmelCase							  =							None
            if self.use_token_type_ids:
                  _lowerCAmelCase							  =							ids_tensor([self.batch_size, self.seq_length]    ,    self.type_vocab_size						)

            _lowerCAmelCase							  =							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        lowercase__					(    self    :				Any						)       ->   Optional[int]:
            _lowerCAmelCase							  =							self.prepare_config_and_inputs()
            _lowerCAmelCase  ,							_lowerCAmelCase  ,							_lowerCAmelCase  ,							_lowerCAmelCase							  =							config_and_inputs
            _lowerCAmelCase							  =							{"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """attention_mask""": attention_mask}
            return config, inputs_dict




@require_flax
class 				UpperCAmelCase  (    snake_case_							,	unittest.TestCase     ):
      _lowercase:    str		  =     True

      _lowercase:    Optional[Any]		  =     (
          (
              FlaxElectraModel,
              FlaxElectraForCausalLM,
              FlaxElectraForMaskedLM,
              FlaxElectraForPreTraining,
              FlaxElectraForTokenClassification,
              FlaxElectraForQuestionAnswering,
              FlaxElectraForMultipleChoice,
              FlaxElectraForSequenceClassification,
          )
          if is_flax_available()
          else ()
      )




      def        lowercase__					(    self    :				Tuple						)       ->   Optional[int]:
            _lowerCAmelCase							  =							FlaxElectraModelTester(self						)




      @slow
      def        lowercase__					(    self    :				List[Any]						)       ->   str:
            for model_class_name in self.all_model_classes:
                  if model_class_name == FlaxElectraForMaskedLM:
                        _lowerCAmelCase							  =							model_class_name.from_pretrained("""google/electra-small-generator"""						)
                  else:
                        _lowerCAmelCase							  =							model_class_name.from_pretrained("""google/electra-small-discriminator"""						)
                  _lowerCAmelCase							  =							model(np.ones((1, 1)						)						)
                  self.assertIsNotNone(__snake_case						)






