
from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

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

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





class 		__lowerCamelCase     :



							def __init__(     self	,				__snake_case	,				__snake_case	,				__snake_case	,				__snake_case	,				__snake_case = 1.0	,				__snake_case = 1.0	,				__snake_case = "blue"	,				)						->     Tuple:






								"""simple docstring"""



								UpperCAmelCase:					Dict 						=     position_x
								UpperCAmelCase:					List[Any] 						=     position_y
								UpperCAmelCase:					Optional[Any] 						=     velocity_x
								UpperCAmelCase:					Dict 						=     velocity_y
								UpperCAmelCase:					Tuple 						=     mass
								UpperCAmelCase:					int 						=     size
								UpperCAmelCase:					List[Any] 						=     color



							@property
							def     A__ (     self							)						->     Optional[Any]:






								"""simple docstring"""



								return self.position_x, self.position_y



							@property
							def     A__ (     self							)						->     Optional[Any]:






								"""simple docstring"""



								return self.velocity_x, self.velocity_y



							def     A__ (     self	,				__snake_case	,				__snake_case	,				__snake_case							)						->     Union[str, Any]:






								"""simple docstring"""



								self.velocity_x += force_x * delta_time
								self.velocity_y += force_y * delta_time




							def     A__ (     self	,				__snake_case							)						->     Tuple:






								"""simple docstring"""



								self.position_x += self.velocity_x * delta_time
								self.position_y += self.velocity_y * delta_time





class 		__lowerCamelCase     :



							def __init__(     self	,				__snake_case	,				__snake_case = 1.0	,				__snake_case = 1.0	,				__snake_case = 0.0	,				)						->     Dict:






								"""simple docstring"""



								UpperCAmelCase:					str 						=     bodies
								UpperCAmelCase:					Dict 						=     gravitation_constant
								UpperCAmelCase:					str 						=     time_factor
								UpperCAmelCase:					List[str] 						=     softening_factor



							def __len__(     self							)						->     str:






								"""simple docstring"""



								return len(self.bodies							)




							def     A__ (     self	,				__snake_case							)						->     List[str]:






								"""simple docstring"""



								for bodya in self.bodies:
									UpperCAmelCase:					Tuple 						=     0.0
									UpperCAmelCase:					int 						=     0.0
									for bodya in self.bodies:
										if bodya != bodya:
											UpperCAmelCase:					Tuple 						=     bodya.position_x - bodya.position_x
											UpperCAmelCase:					List[Any] 						=     bodya.position_y - bodya.position_y

											# Calculation of the distance using Pythagoras's theorem
											# Extra factor due to the softening technique
											UpperCAmelCase:					Any 						=     (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      __UpperCAmelCase    (  snake_case_							:		Optional[int]				,					snake_case_							:		Any				,					snake_case_							:		Dict				):



	'''simple docstring'''



	body_system.update_system(snake_case_				)

	# Update the positions of the patches
	for patch, body in zip(snake_case_				,					body_system.bodies				):
		UpperCAmelCase:					Union[str, Any] 						=     (body.position_x, body.position_y)



def      __UpperCAmelCase    (  snake_case_							:		List[Any]				,					snake_case_							:		Any				,					snake_case_							:		int = -1				,					snake_case_							:		Dict = 1				,					snake_case_							:		List[Any] = -1				,					snake_case_							:		Optional[Any] = 1				,					):



	'''simple docstring'''



	UpperCAmelCase:					Union[str, Any] 						=     plt.figure()
	fig.canvas.set_window_title(snake_case_				)
	UpperCAmelCase:					List[str] 						=     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(snake_case_				)

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

	UpperCAmelCase:					List[Any] 						=     animation.FuncAnimation(  # noqa: F841
	    snake_case_				,					snake_case_				,					interval=snake_case_				,					blit=snake_case_				)

	plt.show()



def      __UpperCAmelCase    (  ):



	'''simple docstring'''



	UpperCAmelCase:					Any 						=     0.9700436
	UpperCAmelCase:					Tuple 						=     -0.24308753
	UpperCAmelCase:					List[Any] 						=     0.466203685
	UpperCAmelCase:					str 						=     0.43236573

	UpperCAmelCase:					List[Any] 						=     [
	    Body(snake_case_				,					snake_case_				,					snake_case_				,					snake_case_				,					size=0.2				,					color="red"				),
	    Body(-position_x				,					-position_y				,					snake_case_				,					snake_case_				,					size=0.2				,					color="green"				),
	    Body(0				,					0				,					-2 * velocity_x				,					-2 * velocity_y				,					size=0.2				,					color="blue"				),
	]
	return BodySystem(snake_case_				,					time_factor=3				)



def      __UpperCAmelCase    (  ):



	'''simple docstring'''



	UpperCAmelCase:					str 						=     7.3476e22
	UpperCAmelCase:					Union[str, Any] 						=     5.972e24
	UpperCAmelCase:					Optional[Any] 						=     1_0_2_2
	UpperCAmelCase:					str 						=     3_8_4_3_9_9_0_0_0
	UpperCAmelCase:					Dict 						=     6.674e-11

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

	UpperCAmelCase:					List[str] 						=     Body(-earth_moon_distance				,					0				,					0				,					snake_case_				,					snake_case_				,					1_0_0_0_0_0_0_0				,					"grey"				)
	UpperCAmelCase:					List[str] 						=     Body(0				,					0				,					0				,					snake_case_				,					snake_case_				,					5_0_0_0_0_0_0_0				,					"blue"				)
	return BodySystem([earth, moon]				,					snake_case_				,					time_factor=1_0_0_0_0_0_0				)



def      __UpperCAmelCase    (  ):



	'''simple docstring'''



	UpperCAmelCase:					List[str] 						=     []
	for _ in range(1_0				):
		UpperCAmelCase:					List[str] 						=     random.uniform(-0.5				,					0.5				)
		UpperCAmelCase:					Optional[int] 						=     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				)				,					snake_case_				,					snake_case_				,					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(snake_case_				,					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 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


_UpperCAmelCase					:			Optional[Any]				     =					[nn.LayerNorm]

_UpperCAmelCase					:			Dict				     =					logging.get_logger(__name__)

_UpperCAmelCase					:			Tuple				     =					version.parse(version.parse(torch.__version__).base_version)

_UpperCAmelCase					:			Optional[int]				     =					parsed_torch_version_base >= version.parse("""2.0""")
_UpperCAmelCase					:			Optional[int]				     =					parsed_torch_version_base >= version.parse("""1.12""")
_UpperCAmelCase					:			List[str]				     =					parsed_torch_version_base >= version.parse("""1.11""")
_UpperCAmelCase					:			Optional[int]				     =					parsed_torch_version_base < version.parse("""1.11""")

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					self):
						from torch import _softmax_backward_data

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

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase = 0):
						__lowerCAmelCase											=					index.to(layer.weight.device)
						__lowerCAmelCase											=					layer.weight.index_select(lowerCamelCase,					lowerCamelCase).clone().detach()
						if layer.bias is not None:
												if dim == 1:
																		__lowerCAmelCase											=					layer.bias.clone().detach()
												else:
																		__lowerCAmelCase											=					layer.bias[index].clone().detach()
						__lowerCAmelCase											=					list(layer.weight.size())
						__lowerCAmelCase											=					len(lowerCamelCase)
						__lowerCAmelCase											=					nn.Linear(new_size[1],					new_size[0],					bias=layer.bias is not None).to(layer.weight.device)
						__lowerCAmelCase											=					False
						new_layer.weight.copy_(W.contiguous())
						__lowerCAmelCase											=					True
						if layer.bias is not None:
												__lowerCAmelCase											=					False
												new_layer.bias.copy_(b.contiguous())
												__lowerCAmelCase											=					True
						return new_layer


class    a__					(			nn.Module   ):







				"""simple docstring"""



				def __init__(self							,      __lowercase							,      __lowercase		):
										super().__init__()
										__lowerCAmelCase											=					nf
										__lowerCAmelCase											=					nn.Parameter(torch.empty(__lowercase							,      __lowercase		)		)
										__lowerCAmelCase											=					nn.Parameter(torch.zeros(__lowercase		)		)
										nn.init.normal_(self.weight							,      std=0.0_2		)




				def        _snake_case	(self							,      __lowercase		):
										__lowerCAmelCase											=					x.size()[:-1] + (self.nf,)
										__lowerCAmelCase											=					torch.addmm(self.bias							,      x.view(-1							,      x.size(-1		)		)							,      self.weight		)
										__lowerCAmelCase											=					x.view(__lowercase		)
										return x

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase = 1):
						__lowerCAmelCase											=					index.to(layer.weight.device)
						__lowerCAmelCase											=					layer.weight.index_select(lowerCamelCase,					lowerCamelCase).clone().detach()
						if dim == 0:
												__lowerCAmelCase											=					layer.bias.clone().detach()
						else:
												__lowerCAmelCase											=					layer.bias[index].clone().detach()
						__lowerCAmelCase											=					list(layer.weight.size())
						__lowerCAmelCase											=					len(lowerCamelCase)
						__lowerCAmelCase											=					ConvaD(new_size[1],					new_size[0]).to(layer.weight.device)
						__lowerCAmelCase											=					False
						new_layer.weight.copy_(W.contiguous())
						__lowerCAmelCase											=					True
						__lowerCAmelCase											=					False
						new_layer.bias.copy_(b.contiguous())
						__lowerCAmelCase											=					True
						return new_layer

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase = None):
						if isinstance(lowerCamelCase,					nn.Linear):
												return prune_linear_layer(lowerCamelCase,					lowerCamelCase,					dim=0 if dim is None else dim)
						elif isinstance(lowerCamelCase,					lowerCamelCase):
												return prune_convad_layer(lowerCamelCase,					lowerCamelCase,					dim=1 if dim is None else dim)
						else:
												raise ValueError(F"""Can't prune layer of class {layer.__class__}""")

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					*lowerCamelCase):
						assert len(lowerCamelCase) > 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
						__lowerCAmelCase											=					len(inspect.signature(lowerCamelCase).parameters)
						if num_args_in_forward_chunk_fn != len(lowerCamelCase):
												raise ValueError(
												    F"""forward_chunk_fn expects {num_args_in_forward_chunk_fn} arguments, but only {len(lowerCamelCase)} input """
												    '''tensors are given''')

						if chunk_size > 0:
												__lowerCAmelCase											=					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}""")

												__lowerCAmelCase											=					input_tensors[0].shape[chunk_dim] // chunk_size

												# chunk input tensor into tuples
												__lowerCAmelCase											=					tuple(input_tensor.chunk(lowerCamelCase,					dim=lowerCamelCase) for input_tensor in input_tensors)
												# apply forward fn to every tuple
												__lowerCAmelCase											=					tuple(forward_fn(*lowerCamelCase) for input_tensors_chunk in zip(*lowerCamelCase))
												# concatenate output at same dimension
												return torch.cat(lowerCamelCase,					dim=lowerCamelCase)

						return forward_fn(*lowerCamelCase)

def 				__magic_name__(    lowerCamelCase,					lowerCamelCase,					lowerCamelCase,					lowerCamelCase):
						__lowerCAmelCase											=					torch.ones(lowerCamelCase,					lowerCamelCase)
						__lowerCAmelCase											=					set(lowerCamelCase) - 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
												__lowerCAmelCase											=					head - sum(1 if h < head else 0 for h in already_pruned_heads)
												__lowerCAmelCase											=					0
						__lowerCAmelCase											=					mask.view(-1).contiguous().eq(1)
						__lowerCAmelCase											=					torch.arange(len(lowerCamelCase))[mask].long()
						return heads, index

def 				__magic_name__(    *lowerCamelCase,					lowerCamelCase = None):
						return torch.meshgrid(*lowerCamelCase,					indexing=lowerCamelCase)




def 				__magic_name__(    lowerCamelCase):
						return tensor.device, storage_ptr(lowerCamelCase), storage_size(lowerCamelCase)

