code: 
  
  from __future__ import annotations
  
  import random
  
  from matplotlib import animation
  from matplotlib import pyplot as plt
  
  # Frame rate of the animation
  A_		:			str										=   20
  
  # Time between time steps in seconds
  A_		:			Dict										=   INTERVAL / 1000
  class 					A_   :
  
  
      '''simple docstring'''
  
  
  
  
  
  
      def __init__(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__ = 1.0     ,      lowercase__ = 1.0     ,      lowercase__ = "blue"     ,      )     ->      Union[str, Any]:
          __UpperCAmelCase									=			position_x
          __UpperCAmelCase									=			position_y
          __UpperCAmelCase									=			velocity_x
          __UpperCAmelCase									=			velocity_y
          __UpperCAmelCase									=			mass
          __UpperCAmelCase									=			size
          __UpperCAmelCase									=			color
  
  
      @property
      def      lowerCAmelCase_						(self  )     ->      Dict:
          return self.position_x, self.position_y
  
  
      @property
      def      lowerCAmelCase_						(self  )     ->      Union[str, Any]:
          return self.velocity_x, self.velocity_y
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      Tuple:
          self.velocity_x += force_x * delta_time
          self.velocity_y += force_y * delta_time
  
  
  
  
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__  )     ->      Tuple:
          self.position_x += self.velocity_x * delta_time
          self.position_y += self.velocity_y * delta_time
  
  
  
  
  
  
  class 					A_   :
  
  
      '''simple docstring'''
  
  
  
  
  
  
      def __init__(self     ,      lowercase__     ,      lowercase__ = 1.0     ,      lowercase__ = 1.0     ,      lowercase__ = 0.0     ,      )     ->      Dict:
          __UpperCAmelCase									=			bodies
          __UpperCAmelCase									=			gravitation_constant
          __UpperCAmelCase									=			time_factor
          __UpperCAmelCase									=			softening_factor
  
  
      def __len__(self  )     ->      Tuple:
          return len(self.bodies  )
  
  
  
  
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__  )     ->      Any:
  
  
  
  
  
  
  
          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(lowercase__     ,      lowercase__     ,      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       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )      ->     str:
  
  
  
  
  
  
      '''simple docstring'''
      body_system.update_system(lowercase__      )
  
      # Update the positions of the patches
      for patch, body in zip(lowercase__       ,   body_system.bodies      ):
          __UpperCAmelCase									=			(body.position_x, body.position_y)
  
  
  def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE = -1       ,   SCREAMING_SNAKE_CASE = 1       ,   SCREAMING_SNAKE_CASE = -1       ,   SCREAMING_SNAKE_CASE = 1       ,   )      ->     Tuple:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			plt.figure()
      fig.canvas.set_window_title(lowercase__      )
      __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(lowercase__      )
  
      # Function called at each step of the animation
      def update(SCREAMING_SNAKE_CASE      ) -> list[plt.Circle]:
          update_step(lowercase__       ,   lowercase__       ,   lowercase__      )
          return patches
  
      __UpperCAmelCase									=			animation.FuncAnimation(  # noqa: F841
          lowercase__       ,   lowercase__       ,   interval=lowercase__       ,   blit=lowercase__      )
  
      plt.show()
  
  
  def       __a       (   )      ->     Any:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			0.9700436
      __UpperCAmelCase									=			-0.24308753
      __UpperCAmelCase									=			0.466203685
      __UpperCAmelCase									=			0.43236573
  
      __UpperCAmelCase									=			[
          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       (   )      ->     Optional[int]:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			7.3476e22
      __UpperCAmelCase									=			5.972e24
      __UpperCAmelCase									=			1_0_2_2
      __UpperCAmelCase									=			3_8_4_3_9_9_0_0_0
      __UpperCAmelCase									=			6.674e-11
  
      # 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       ,   lowercase__       ,   lowercase__       ,   1_0_0_0_0_0_0_0       ,   '''grey'''      )
      __UpperCAmelCase									=			Body(0       ,   0       ,   0       ,   lowercase__       ,   lowercase__       ,   5_0_0_0_0_0_0_0       ,   '''blue'''      )
      return BodySystem([earth, moon]       ,   lowercase__       ,   time_factor=1_0_0_0_0_0_0      )
  
  
  def       __a       (   )      ->     Optional[int]:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase									=			[]
      for _ in range(1_0      ):
          __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      )       ,   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       ,   1_0       ,   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)
  
  
  
  
  
  
style_context: 
  
  from __future__ import annotations
  
  import unittest
  
  from transformers import MPNetConfig, is_tf_available
  from transformers.testing_utils import require_tf, slow
  
  from ...test_configuration_common import ConfigTester
  from ...test_modeling_tf_common import TFModelTesterMixin, ids_tensor, random_attention_mask
  from ...test_pipeline_mixin import PipelineTesterMixin
  
  
  if is_tf_available():
         import tensorflow as tf
  
         from transformers.models.mpnet.modeling_tf_mpnet import (
             TFMPNetForMaskedLM,
             TFMPNetForMultipleChoice,
             TFMPNetForQuestionAnswering,
             TFMPNetForSequenceClassification,
             TFMPNetForTokenClassification,
             TFMPNetModel,
         )
  class 					A_   :
  
  
      '''simple docstring'''
  
  
  
  
  
  
      def __init__(self     ,      lowercase__     ,      lowercase__=13     ,      lowercase__=7     ,      lowercase__=True     ,      lowercase__=True     ,      lowercase__=False     ,      lowercase__=True     ,      lowercase__=99     ,      lowercase__=64     ,      lowercase__=2     ,      lowercase__=4     ,      lowercase__=64     ,      lowercase__="gelu"     ,      lowercase__=0.1     ,      lowercase__=0.1     ,      lowercase__=512     ,      lowercase__=16     ,      lowercase__=2     ,      lowercase__=0.02     ,      lowercase__=3     ,      lowercase__=4     ,      lowercase__=None     ,      )     ->      Tuple:
          __UpperCAmelCase									=			parent
          __UpperCAmelCase									=			batch_size
          __UpperCAmelCase									=			seq_length
          __UpperCAmelCase									=			is_training
          __UpperCAmelCase									=			use_input_mask
          __UpperCAmelCase									=			use_token_type_ids
          __UpperCAmelCase									=			use_labels
          __UpperCAmelCase									=			vocab_size
          __UpperCAmelCase									=			hidden_size
          __UpperCAmelCase									=			num_hidden_layers
          __UpperCAmelCase									=			num_attention_heads
          __UpperCAmelCase									=			intermediate_size
          __UpperCAmelCase									=			hidden_act
          __UpperCAmelCase									=			hidden_dropout_prob
          __UpperCAmelCase									=			attention_probs_dropout_prob
          __UpperCAmelCase									=			max_position_embeddings
          __UpperCAmelCase									=			type_vocab_size
          __UpperCAmelCase									=			type_sequence_label_size
          __UpperCAmelCase									=			initializer_range
          __UpperCAmelCase									=			num_labels
          __UpperCAmelCase									=			num_choices
          __UpperCAmelCase									=			scope
  
  
      def      lowerCAmelCase_						(self  )     ->      str:
          __UpperCAmelCase									=			ids_tensor([self.batch_size, self.seq_length]     ,      self.vocab_size  )
  
          __UpperCAmelCase									=			None
          if self.use_input_mask:
              __UpperCAmelCase									=			random_attention_mask([self.batch_size, self.seq_length]  )
  
          __UpperCAmelCase									=			None
          __UpperCAmelCase									=			None
          __UpperCAmelCase									=			None
          if self.use_labels:
              __UpperCAmelCase									=			ids_tensor([self.batch_size]     ,      self.type_sequence_label_size  )
              __UpperCAmelCase									=			ids_tensor([self.batch_size, self.seq_length]     ,      self.num_labels  )
              __UpperCAmelCase									=			ids_tensor([self.batch_size]     ,      self.num_choices  )
  
          __UpperCAmelCase									=			MPNetConfig(
              vocab_size=self.vocab_size     ,      hidden_size=self.hidden_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     ,      initializer_range=self.initializer_range     ,      )
          return config, input_ids, input_mask, sequence_labels, token_labels, choice_labels
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      List[Any]:
          __UpperCAmelCase									=			TFMPNetModel(config=lowercase__  )
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''attention_mask''': input_mask}
          __UpperCAmelCase									=			model(lowercase__  )
          __UpperCAmelCase									=			[input_ids, input_mask]
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.last_hidden_state.shape     ,      (self.batch_size, self.seq_length, self.hidden_size)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      Dict:
          __UpperCAmelCase									=			TFMPNetForMaskedLM(config=lowercase__  )
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''attention_mask''': input_mask}
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.seq_length, self.vocab_size)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      List[Any]:
          __UpperCAmelCase									=			TFMPNetForQuestionAnswering(config=lowercase__  )
          __UpperCAmelCase									=			{
              '''input_ids''': input_ids,
              '''attention_mask''': input_mask,
          }
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.start_logits.shape     ,      (self.batch_size, self.seq_length)  )
          self.parent.assertEqual(result.end_logits.shape     ,      (self.batch_size, self.seq_length)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      str:
          __UpperCAmelCase									=			self.num_labels
          __UpperCAmelCase									=			TFMPNetForSequenceClassification(lowercase__  )
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''attention_mask''': input_mask}
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.num_labels)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      str:
          __UpperCAmelCase									=			self.num_choices
          __UpperCAmelCase									=			TFMPNetForMultipleChoice(lowercase__  )
          __UpperCAmelCase									=			tf.tile(tf.expand_dims(lowercase__     ,      1  )     ,      (1, self.num_choices, 1)  )
          __UpperCAmelCase									=			tf.tile(tf.expand_dims(lowercase__     ,      1  )     ,      (1, self.num_choices, 1)  )
          __UpperCAmelCase									=			{
              '''input_ids''': multiple_choice_inputs_ids,
              '''attention_mask''': multiple_choice_input_mask,
          }
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.num_choices)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      List[str]:
          __UpperCAmelCase									=			self.num_labels
          __UpperCAmelCase									=			TFMPNetForTokenClassification(lowercase__  )
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''attention_mask''': input_mask}
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.seq_length, self.num_labels)  )
  
  
  
  
  
  
      def      lowerCAmelCase_						(self  )     ->      Optional[Any]:
          __UpperCAmelCase									=			self.prepare_config_and_inputs()
          ((__UpperCAmelCase)					,     (__UpperCAmelCase)					,     (__UpperCAmelCase)					,     (__UpperCAmelCase)					,     (__UpperCAmelCase)					,     (__UpperCAmelCase))									=			config_and_inputs
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''attention_mask''': input_mask}
          return config, inputs_dict
  
  
  
  
  
  
  @require_tf
  class 					A_   (      _a ,     _a ,     unittest.TestCase						):
  
  
      '''simple docstring'''
  
  
  
  
  
  
      a__     							=       (
          (
              TFMPNetForMaskedLM,
              TFMPNetForMultipleChoice,
              TFMPNetForQuestionAnswering,
              TFMPNetForSequenceClassification,
              TFMPNetForTokenClassification,
              TFMPNetModel,
          )
          if is_tf_available()
          else ()
      )
      a__     							=       (
          {
              "feature-extraction": TFMPNetModel,
              "fill-mask": TFMPNetForMaskedLM,
              "question-answering": TFMPNetForQuestionAnswering,
              "text-classification": TFMPNetForSequenceClassification,
              "token-classification": TFMPNetForTokenClassification,
              "zero-shot": TFMPNetForSequenceClassification,
          }
          if is_tf_available()
          else {}
      )
      a__     							=       False
      a__     							=       False
  
  
      def      lowerCAmelCase_						(self  )     ->      int:
          __UpperCAmelCase									=			TFMPNetModelTester(self  )
          __UpperCAmelCase									=			ConfigTester(self     ,      config_class=lowercase__     ,      hidden_size=37  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Optional[int]:
          self.config_tester.run_common_tests()
  
  
      def      lowerCAmelCase_						(self  )     ->      Dict:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_mpnet_model(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Any:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_mpnet_for_masked_lm(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      int:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_mpnet_for_question_answering(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Optional[int]:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_mpnet_for_sequence_classification(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      str:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_mpnet_for_multiple_choice(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      str:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_mpnet_for_token_classification(*lowercase__  )
  
  
  
  
  
  
      @slow
      def      lowerCAmelCase_						(self  )     ->      List[str]:
          for model_name in ["microsoft/mpnet-base"]:
              __UpperCAmelCase									=			TFMPNetModel.from_pretrained(lowercase__  )
              self.assertIsNotNone(lowercase__  )
  
  
  
  
  
  
  @require_tf
  class 					A_   (      unittest.TestCase						):
  
  
      '''simple docstring'''
  
  
  
  
  
  
      @slow
      def      lowerCAmelCase_						(self  )     ->      Any:
          __UpperCAmelCase									=			TFMPNetModel.from_pretrained('''microsoft/mpnet-base'''  )
          __UpperCAmelCase									=			tf.constant([[0, 1, 2, 3, 4, 5]]  )
          __UpperCAmelCase									=			model(lowercase__  )[0]
  
          __UpperCAmelCase									=			[1, 6, 768]
          self.assertEqual(output.shape     ,      lowercase__  )
  
          __UpperCAmelCase									=			tf.constant(
              [
                  [
                      [-0.1067172, 0.08216473, 0.0024543],
                      [-0.03465879, 0.8354118, -0.03252288],
                      [-0.06569476, -0.12424111, -0.0494436],
                  ]
              ]  )
          tf.debugging.assert_near(output[:, :3, :3]     ,      lowercase__     ,      atol=1E-4  )
  
  
  
  
  