


'''simple docstring'''

from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
_UpperCAmelCase					:			Tuple				     =					2_0

# Time between time steps in seconds
_UpperCAmelCase					:			Optional[int]				     =					INTERVAL / 1_0_0_0


class    a__					:







				"""simple docstring"""



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




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




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




				def        _snake_case	(self							,      __lowercase							,      __lowercase							,      __lowercase		):
										self.velocity_x += force_x * delta_time
										self.velocity_y += force_y * delta_time




				def        _snake_case	(self							,      __lowercase		):
										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							,      ):
										__lowerCAmelCase											=					bodies
										__lowerCAmelCase											=					gravitation_constant
										__lowerCAmelCase											=					time_factor
										__lowerCAmelCase											=					softening_factor




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




				def        _snake_case	(self							,      __lowercase		):
										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(__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 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase):
						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 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase = -1,					lowerCamelCase = 1,					lowerCamelCase = -1,					lowerCamelCase = 1,					):
						__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 				__magic_name__(    ):
						__lowerCAmelCase											=					0.9_70_04_36
						__lowerCAmelCase											=					-0.24_30_87_53
						__lowerCAmelCase											=					0.4_66_20_36_85
						__lowerCAmelCase											=					0.43_23_65_73

						__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 				__magic_name__(    ):
						__lowerCAmelCase											=					7.34_76E22
						__lowerCAmelCase											=					5.9_72E24
						__lowerCAmelCase											=					1_0_2_2
						__lowerCAmelCase											=					3_8_4_3_9_9_0_0_0
						__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,					1_0_0_0_0_0_0_0,					'''grey''')
						__lowerCAmelCase											=					Body(0,					0,					0,					lowerCamelCase,					lowerCamelCase,					5_0_0_0_0_0_0_0,					'''blue''')
						return BodySystem([earth, moon],					lowerCamelCase,					time_factor=1_0_0_0_0_0_0)

def 				__magic_name__(    ):
						__lowerCAmelCase											=					[]
						for _ in range(1_0):
												__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,					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(),
	    -4_3_0_0_0_0_0_0_0,
	    4_3_0_0_0_0_0_0_0,
	    -4_3_0_0_0_0_0_0_0,
	    4_3_0_0_0_0_0_0_0,
	)
	plot("""Random system with many bodies""", example_a(), -1.5, 1.5, -1.5, 1.5)





'''simple docstring'''

import logging

import torch
from torch import nn
from torch.nn import CrossEntropyLoss, MSELoss

from transformers.file_utils import add_start_docstrings, add_start_docstrings_to_model_forward
from transformers.models.albert.modeling_albert import (
    ALBERT_INPUTS_DOCSTRING,
    ALBERT_START_DOCSTRING,
    AlbertModel,
    AlbertPreTrainedModel,
    AlbertTransformer,
)


_UpperCAmelCase					:			List[str]				     =					logging.getLogger(__name__)


class    a__					(			__A   ):







				"""simple docstring"""



				def        _snake_case	(self							,      __lowercase							,      __lowercase							,      __lowercase=None							,      __lowercase=None		):
										if current_layer == 0:
																__lowerCAmelCase											=					self.embedding_hidden_mapping_in(__lowercase		)
										else:
																__lowerCAmelCase											=					hidden_states[0]

										__lowerCAmelCase											=					int(self.config.num_hidden_layers / self.config.num_hidden_groups		)

										# Index of the hidden group
										__lowerCAmelCase											=					int(current_layer / (self.config.num_hidden_layers / self.config.num_hidden_groups)		)

										__lowerCAmelCase											=					self.albert_layer_groups[group_idx](
										    __lowercase							,      __lowercase							,      head_mask[group_idx * layers_per_group : (group_idx + 1) * layers_per_group]							,      )
										__lowerCAmelCase											=					layer_group_output[0]

										return (hidden_states,)


@add_start_docstrings(
    'The bare ALBERT Model transformer with PABEE outputting raw hidden-states without any specific head on top.'				,    __A				,    )
class    a__					(			__A   ):







				"""simple docstring"""



				def __init__(self							,      __lowercase		):
										super().__init__(__lowercase		)

										__lowerCAmelCase											=					AlbertTransformerWithPabee(__lowercase		)

										self.init_weights()
										__lowerCAmelCase											=					0
										__lowerCAmelCase											=					0
										__lowerCAmelCase											=					0

										__lowerCAmelCase											=					0




				def        _snake_case	(self							,      __lowercase		):
										__lowerCAmelCase											=					threshold




				def        _snake_case	(self							,      __lowercase		):
										__lowerCAmelCase											=					patience




				def        _snake_case	(self		):
										__lowerCAmelCase											=					0
										__lowerCAmelCase											=					0




				def        _snake_case	(self		):
										__lowerCAmelCase											=					self.inference_layers_num / self.inference_instances_num
										__lowerCAmelCase											=					(
										    F"""*** Patience = {self.patience} Avg. Inference Layers = {avg_inf_layers:.2f} Speed Up ="""
										    F""" {1 - avg_inf_layers / self.config.num_hidden_layers:.2f} ***"""
										)
										print(__lowercase		)




				@add_start_docstrings_to_model_forward(__lowercase		)
				def        _snake_case	(self							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=False							,      ):

										if input_ids is not None and inputs_embeds is not None:
																raise ValueError('''You cannot specify both input_ids and inputs_embeds at the same time'''		)
										elif input_ids is not None:
																__lowerCAmelCase											=					input_ids.size()
										elif inputs_embeds is not None:
																__lowerCAmelCase											=					inputs_embeds.size()[:-1]
										else:
																raise ValueError('''You have to specify either input_ids or inputs_embeds'''		)

										__lowerCAmelCase											=					input_ids.device if input_ids is not None else inputs_embeds.device

										if attention_mask is None:
																__lowerCAmelCase											=					torch.ones(__lowercase							,      device=__lowercase		)
										if token_type_ids is None:
																__lowerCAmelCase											=					torch.zeros(__lowercase							,      dtype=torch.long							,      device=__lowercase		)

										__lowerCAmelCase											=					attention_mask.unsqueeze(1		).unsqueeze(2		)
										__lowerCAmelCase											=					extended_attention_mask.to(dtype=self.dtype		)  # fp16 compatibility
										__lowerCAmelCase											=					(1.0 - extended_attention_mask) * -1_0_0_0_0.0
										__lowerCAmelCase											=					self.get_head_mask(__lowercase							,      self.config.num_hidden_layers		)

										__lowerCAmelCase											=					self.embeddings(
										    __lowercase							,      position_ids=__lowercase							,      token_type_ids=__lowercase							,      inputs_embeds=__lowercase		)
										__lowerCAmelCase											=					embedding_output

										if self.training:
																__lowerCAmelCase											=					[]
																for i in range(self.config.num_hidden_layers		):
																						__lowerCAmelCase											=					self.encoder.adaptive_forward(
																						    __lowercase							,      current_layer=__lowercase							,      attention_mask=__lowercase							,      head_mask=__lowercase							,      )

																						__lowerCAmelCase											=					self.pooler_activation(self.pooler(encoder_outputs[0][:, 0]		)		)
																						__lowerCAmelCase											=					output_layers[i](output_dropout(__lowercase		)		)
																						res.append(__lowercase		)
										elif self.patience == 0:  # Use all layers for inference
																__lowerCAmelCase											=					self.encoder(__lowercase							,      __lowercase							,      head_mask=__lowercase		)
																__lowerCAmelCase											=					self.pooler_activation(self.pooler(encoder_outputs[0][:, 0]		)		)
																__lowerCAmelCase											=					[output_layers[self.config.num_hidden_layers - 1](__lowercase		)]
										else:
																__lowerCAmelCase											=					0
																__lowerCAmelCase											=					None
																__lowerCAmelCase											=					0
																for i in range(self.config.num_hidden_layers		):
																						calculated_layer_num += 1
																						__lowerCAmelCase											=					self.encoder.adaptive_forward(
																						    __lowercase							,      current_layer=__lowercase							,      attention_mask=__lowercase							,      head_mask=__lowercase							,      )

																						__lowerCAmelCase											=					self.pooler_activation(self.pooler(encoder_outputs[0][:, 0]		)		)
																						__lowerCAmelCase											=					output_layers[i](__lowercase		)
																						if regression:
																												__lowerCAmelCase											=					logits.detach()
																												if patient_result is not None:
																																		__lowerCAmelCase											=					patient_result.detach()
																												if (patient_result is not None) and torch.abs(patient_result - labels		) < self.regression_threshold:
																																		patient_counter += 1
																												else:
																																		__lowerCAmelCase											=					0
																						else:
																												__lowerCAmelCase											=					logits.detach().argmax(dim=1		)
																												if patient_result is not None:
																																		__lowerCAmelCase											=					patient_result.detach().argmax(dim=1		)
																												if (patient_result is not None) and torch.all(labels.eq(__lowercase		)		):
																																		patient_counter += 1
																												else:
																																		__lowerCAmelCase											=					0

																						__lowerCAmelCase											=					logits
																						if patient_counter == self.patience:
																												break
																__lowerCAmelCase											=					[patient_result]
																self.inference_layers_num += calculated_layer_num
																self.inference_instances_num += 1

										return res


@add_start_docstrings(
    'Albert Model transformer with PABEE and a sequence classification/regression head on top (a linear layer on top of\n    the pooled output) e.g. for GLUE tasks. '				,    __A				,    )
class    a__					(			__A   ):







				"""simple docstring"""



				def __init__(self							,      __lowercase		):
										super().__init__(__lowercase		)
										__lowerCAmelCase											=					config.num_labels

										__lowerCAmelCase											=					AlbertModelWithPabee(__lowercase		)
										__lowerCAmelCase											=					nn.Dropout(config.classifier_dropout_prob		)
										__lowerCAmelCase											=					nn.ModuleList(
										    [nn.Linear(config.hidden_size							,      self.config.num_labels		) for _ in range(config.num_hidden_layers		)]		)

										self.init_weights()




				@add_start_docstrings_to_model_forward(__lowercase		)
				def        _snake_case	(self							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      __lowercase=None							,      ):
										__lowerCAmelCase											=					self.albert(
										    input_ids=__lowercase							,      attention_mask=__lowercase							,      token_type_ids=__lowercase							,      position_ids=__lowercase							,      head_mask=__lowercase							,      inputs_embeds=__lowercase							,      output_dropout=self.dropout							,      output_layers=self.classifiers							,      regression=self.num_labels == 1							,      )

										__lowerCAmelCase											=					(logits[-1],)

										if labels is not None:
																__lowerCAmelCase											=					None
																__lowerCAmelCase											=					0
																for ix, logits_item in enumerate(__lowercase		):
																						if self.num_labels == 1:
																												#  We are doing regression
																												__lowerCAmelCase											=					MSELoss()
																												__lowerCAmelCase											=					loss_fct(logits_item.view(-1		)							,      labels.view(-1		)		)
																						else:
																												__lowerCAmelCase											=					CrossEntropyLoss()
																												__lowerCAmelCase											=					loss_fct(logits_item.view(-1							,      self.num_labels		)							,      labels.view(-1		)		)
																						if total_loss is None:
																												__lowerCAmelCase											=					loss
																						else:
																												total_loss += loss * (ix + 1)
																						total_weights += ix + 1
																__lowerCAmelCase											=					(total_loss / total_weights,) + outputs

										return outputs

