

'''simple docstring'''


from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowerCAmelCase__      				=			20

# Time between time steps in seconds
lowerCAmelCase__      				=			INTERVAL / 1000



class        lowercase    :


							def __init__(      self     ,      _snake_case     ,      _snake_case     ,      _snake_case     ,      _snake_case     ,      _snake_case = 1.0     ,      _snake_case = 1.0     ,      _snake_case = "blue"     ,      )				->					None:
								UpperCAmelCase_		:   Optional[Any]													=       position_x
								UpperCAmelCase_		:   Optional[Any]													=       position_y
								UpperCAmelCase_		:   str													=       velocity_x
								UpperCAmelCase_		:   Optional[int]													=       velocity_y
								UpperCAmelCase_		:   Optional[int]													=       mass
								UpperCAmelCase_		:   Tuple													=       size
								UpperCAmelCase_		:   List[Any]													=       color


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


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


							def     _snake_case				(      self     ,      _snake_case     ,      _snake_case     ,      _snake_case)				->					None:
								self.velocity_x += force_x * delta_time
								self.velocity_y += force_y * delta_time





							def     _snake_case				(      self     ,      _snake_case)				->					None:
								self.position_x += self.velocity_x * delta_time
								self.position_y += self.velocity_y * delta_time



class        lowercase    :


							def __init__(      self     ,      _snake_case     ,      _snake_case = 1.0     ,      _snake_case = 1.0     ,      _snake_case = 0.0     ,      )				->					None:
								UpperCAmelCase_		:   List[Any]													=       bodies
								UpperCAmelCase_		:   Any													=       gravitation_constant
								UpperCAmelCase_		:   Tuple													=       time_factor
								UpperCAmelCase_		:   Tuple													=       softening_factor


							def __len__(      self)				->					int:
								return len(self.bodies)





							def     _snake_case				(      self     ,      _snake_case)				->					None:
								for bodya in self.bodies:
									UpperCAmelCase_		:   Optional[Any]													=       0.0
									UpperCAmelCase_		:   Dict													=       0.0
									for bodya in self.bodies:
										if bodya != bodya:
											UpperCAmelCase_		:   Union[str, Any]													=       bodya.position_x - bodya.position_x
											UpperCAmelCase_		:   Any													=       bodya.position_y - bodya.position_y

											# Calculation of the distance using Pythagoras's theorem
											# Extra factor due to the softening technique
											UpperCAmelCase_		:   Optional[int]													=       (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     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase	)     ->     None:
	body_system.update_system(UpperCamelCase	)

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







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = -1 ,UpperCamelCase = 1 ,UpperCamelCase = -1 ,UpperCamelCase = 1 ,)     ->     None:
	UpperCAmelCase_		:   int													=       plt.figure()
	fig.canvas.set_window_title(UpperCamelCase	)
	UpperCAmelCase_		:   List[Any]													=       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_		:   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(UpperCamelCase	)

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

	UpperCAmelCase_		:   Tuple													=       animation.FuncAnimation(  # noqa: F841
	    UpperCamelCase ,UpperCamelCase ,interval=UpperCamelCase ,blit=UpperCamelCase	)

	plt.show()







def     SCREAMING_SNAKE_CASE(	)     ->     BodySystem:
	UpperCAmelCase_		:   Tuple													=       0.970_0436
	UpperCAmelCase_		:   List[str]													=       -0.2430_8753
	UpperCAmelCase_		:   Optional[int]													=       0.4_6620_3685
	UpperCAmelCase_		:   str													=       0.4323_6573

	UpperCAmelCase_		:   Union[str, Any]													=       [
	    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     SCREAMING_SNAKE_CASE(	)     ->     BodySystem:
	UpperCAmelCase_		:   List[Any]													=       7.3476e22
	UpperCAmelCase_		:   str													=       5.972e24
	UpperCAmelCase_		:   Any													=       1_0_2_2
	UpperCAmelCase_		:   Tuple													=       3_8_4_3_9_9_0_0_0
	UpperCAmelCase_		:   Tuple													=       6.674e-11

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

	UpperCAmelCase_		:   Optional[Any]													=       Body(-earth_moon_distance ,0 ,0 ,UpperCamelCase ,UpperCamelCase ,1_0_0_0_0_0_0_0 ,'grey'	)
	UpperCAmelCase_		:   Tuple													=       Body(0 ,0 ,0 ,UpperCamelCase ,UpperCamelCase ,5_0_0_0_0_0_0_0 ,'blue'	)
	return BodySystem([earth, moon] ,UpperCamelCase ,time_factor=1_0_0_0_0_0_0	)







def     SCREAMING_SNAKE_CASE(	)     ->     BodySystem:
	UpperCAmelCase_		:   List[str]													=       []
	for _ in range(1_0	):
		UpperCAmelCase_		:   List[str]													=       random.uniform(-0.5 ,0.5	)
		UpperCAmelCase_		:   Dict													=       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 ,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)









'''simple docstring'''


import inspect
from typing import Callable, List, Optional, Set, Tuple, Union

import torch
from packaging import version
from safetensors.torch import storage_ptr, storage_size
from torch import nn

from .utils import logging


lowerCAmelCase__      				=			[nn.LayerNorm]

lowerCAmelCase__      				=			logging.get_logger(__name__)

lowerCAmelCase__      				=			version.parse(version.parse(torch.__version__).base_version)

lowerCAmelCase__      				=			parsed_torch_version_base >= version.parse("2.0")
lowerCAmelCase__      				=			parsed_torch_version_base >= version.parse("1.12")
lowerCAmelCase__      				=			parsed_torch_version_base >= version.parse("1.11")
lowerCAmelCase__      				=			parsed_torch_version_base < version.parse("1.11")







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,self	)     ->     List[Any]:
	from torch import _softmax_backward_data

	if is_torch_less_than_1_11:
		return _softmax_backward_data(UpperCamelCase ,UpperCamelCase ,parent.dim ,self	)
	else:
		return _softmax_backward_data(UpperCamelCase ,UpperCamelCase ,parent.dim ,self.dtype	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = 0	)     ->     nn.Linear:
	UpperCAmelCase_		:   Tuple													=       index.to(layer.weight.device	)
	UpperCAmelCase_		:   Tuple													=       layer.weight.index_select(UpperCamelCase ,UpperCamelCase	).clone().detach()
	if layer.bias is not None:
		if dim == 1:
			UpperCAmelCase_		:   List[Any]													=       layer.bias.clone().detach()
		else:
			UpperCAmelCase_		:   Tuple													=       layer.bias[index].clone().detach()
	UpperCAmelCase_		:   Optional[Any]													=       list(layer.weight.size()	)
	UpperCAmelCase_		:   int													=       len(UpperCamelCase	)
	UpperCAmelCase_		:   str													=       nn.Linear(new_size[1] ,new_size[0] ,bias=layer.bias is not None	).to(layer.weight.device	)
	UpperCAmelCase_		:   str													=       False
	new_layer.weight.copy_(W.contiguous()	)
	UpperCAmelCase_		:   Tuple													=       True
	if layer.bias is not None:
		UpperCAmelCase_		:   Union[str, Any]													=       False
		new_layer.bias.copy_(b.contiguous()	)
		UpperCAmelCase_		:   Any													=       True
	return new_layer



class        lowercase    (	nn.Module			):


							def __init__(      self     ,      _snake_case     ,      _snake_case)				->					int:
								super().__init__()
								UpperCAmelCase_		:   List[Any]													=       nf
								UpperCAmelCase_		:   List[Any]													=       nn.Parameter(torch.empty(_snake_case     ,      _snake_case))
								UpperCAmelCase_		:   List[Any]													=       nn.Parameter(torch.zeros(_snake_case))
								nn.init.normal_(self.weight     ,      std=0.02)





							def     _snake_case				(      self     ,      _snake_case)				->					Optional[int]:
								UpperCAmelCase_		:   Dict													=       x.size()[:-1] + (self.nf,)
								UpperCAmelCase_		:   Optional[Any]													=       torch.addmm(self.bias     ,      x.view(-1     ,      x.size(-1))     ,      self.weight)
								UpperCAmelCase_		:   List[str]													=       x.view(_snake_case)
								return x







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = 1	)     ->     ConvaD:
	UpperCAmelCase_		:   List[str]													=       index.to(layer.weight.device	)
	UpperCAmelCase_		:   Optional[Any]													=       layer.weight.index_select(UpperCamelCase ,UpperCamelCase	).clone().detach()
	if dim == 0:
		UpperCAmelCase_		:   Tuple													=       layer.bias.clone().detach()
	else:
		UpperCAmelCase_		:   str													=       layer.bias[index].clone().detach()
	UpperCAmelCase_		:   str													=       list(layer.weight.size()	)
	UpperCAmelCase_		:   List[str]													=       len(UpperCamelCase	)
	UpperCAmelCase_		:   List[Any]													=       ConvaD(new_size[1] ,new_size[0]	).to(layer.weight.device	)
	UpperCAmelCase_		:   Tuple													=       False
	new_layer.weight.copy_(W.contiguous()	)
	UpperCAmelCase_		:   Optional[Any]													=       True
	UpperCAmelCase_		:   Any													=       False
	new_layer.bias.copy_(b.contiguous()	)
	UpperCAmelCase_		:   Union[str, Any]													=       True
	return new_layer







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = None	)     ->     Union[nn.Linear, ConvaD]:
	if isinstance(UpperCamelCase ,nn.Linear	):
		return prune_linear_layer(UpperCamelCase ,UpperCamelCase ,dim=0 if dim is None else dim	)
	elif isinstance(UpperCamelCase ,UpperCamelCase	):
		return prune_convad_layer(UpperCamelCase ,UpperCamelCase ,dim=1 if dim is None else dim	)
	else:
		raise ValueError(f"""Can't prune layer of class {layer.__class__}"""	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,*UpperCamelCase	)     ->     torch.Tensor:
	assert len(UpperCamelCase	) > 0, f"""{input_tensors} has to be a tuple/list of tensors"""

	# inspect.signature exist since python 3.5 and is a python method -> no problem with backward compatibility
	UpperCAmelCase_		:   str													=       len(inspect.signature(UpperCamelCase	).parameters	)
	if num_args_in_forward_chunk_fn != len(UpperCamelCase	):
		raise ValueError(
		    f"""forward_chunk_fn expects {num_args_in_forward_chunk_fn} arguments, but only {len(UpperCamelCase	)} input """
		    'tensors are given'	)

	if chunk_size > 0:
		UpperCAmelCase_		:   Optional[int]													=       input_tensors[0].shape[chunk_dim]
		for input_tensor in input_tensors:
			if input_tensor.shape[chunk_dim] != tensor_shape:
				raise ValueError(
				    f"""All input tenors have to be of the same shape: {tensor_shape}, """
				    f"""found shape {input_tensor.shape[chunk_dim]}"""	)

		if input_tensors[0].shape[chunk_dim] % chunk_size != 0:
			raise ValueError(
			    f"""The dimension to be chunked {input_tensors[0].shape[chunk_dim]} has to be a multiple of the chunk """
			    f"""size {chunk_size}"""	)

		UpperCAmelCase_		:   Any													=       input_tensors[0].shape[chunk_dim] // chunk_size

		# chunk input tensor into tuples
		UpperCAmelCase_		:   int													=       tuple(input_tensor.chunk(UpperCamelCase ,dim=UpperCamelCase	) for input_tensor in input_tensors	)
		# apply forward fn to every tuple
		UpperCAmelCase_		:   List[str]													=       tuple(forward_fn(*UpperCamelCase	) for input_tensors_chunk in zip(*UpperCamelCase	)	)
		# concatenate output at same dimension
		return torch.cat(UpperCamelCase ,dim=UpperCamelCase	)

	return forward_fn(*UpperCamelCase	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase	)     ->     Tuple[Set[int], torch.LongTensor]:
	UpperCAmelCase_		:   List[Any]													=       torch.ones(UpperCamelCase ,UpperCamelCase	)
	UpperCAmelCase_		:   Optional[int]													=       set(UpperCamelCase	) - already_pruned_heads  # Convert to set and remove already pruned heads
	for head in heads:
		# Compute how many pruned heads are before the head and move the index accordingly
		UpperCAmelCase_		:   Any													=       head - sum(1 if h < head else 0 for h in already_pruned_heads	)
		UpperCAmelCase_		:   List[Any]													=       0
	UpperCAmelCase_		:   str													=       mask.view(-1	).contiguous().eq(1	)
	UpperCAmelCase_		:   torch.LongTensor													=       torch.arange(len(UpperCamelCase	)	)[mask].long()
	return heads, index







def     SCREAMING_SNAKE_CASE(	*UpperCamelCase ,UpperCamelCase = None	)     ->     Tuple[torch.Tensor, ...]:
	return torch.meshgrid(*UpperCamelCase ,indexing=UpperCamelCase	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     Tuple[torch.device, int, int]:
	return tensor.device, storage_ptr(UpperCamelCase	), storage_size(UpperCamelCase	)






