


from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
UpperCAmelCase__     			=							20

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







class    lowerCamelCase__     :





					def __init__(self	,  UpperCAmelCase	,  UpperCAmelCase	,  UpperCAmelCase	,  UpperCAmelCase	,  UpperCAmelCase = 1.0	,  UpperCAmelCase = 1.0	,  UpperCAmelCase = "blue"	,  )  ->     None:
						_lowercase							   =position_x
						_lowercase							   =position_y
						_lowercase							   =velocity_x
						_lowercase							   =velocity_y
						_lowercase							   =mass
						_lowercase							   =size
						_lowercase							   =color





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





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





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





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







class    lowerCamelCase__     :





					def __init__(self	,  UpperCAmelCase	,  UpperCAmelCase = 1.0	,  UpperCAmelCase = 1.0	,  UpperCAmelCase = 0.0	,  )  ->     None:
						_lowercase							   =bodies
						_lowercase							   =gravitation_constant
						_lowercase							   =time_factor
						_lowercase							   =softening_factor





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





					def   __A      (self	,  UpperCAmelCase )  ->     None:
						for bodya in self.bodies:
							_lowercase							   =0.0
							_lowercase							   =0.0
							for bodya in self.bodies:
								if bodya != bodya:
									_lowercase							   =bodya.position_x - bodya.position_x
									_lowercase							   =bodya.position_y - bodya.position_y

									# Calculation of the distance using Pythagoras's theorem
									# Extra factor due to the softening technique
									_lowercase							   =(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(SCREAMING_SNAKE_CASE_	,  SCREAMING_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_      (							__snake_case  ,		__snake_case  ,		__snake_case		)  ->    None:







	"""simple docstring"""


	body_system.update_system(snake_case__		)

	# Update the positions of the patches
	for patch, body in zip(snake_case__  ,		body_system.bodies		):
		_lowercase							   =(body.position_x, body.position_y)
def        UpperCAmelCase_      (							__snake_case  ,		__snake_case  ,		__snake_case = -1  ,		__snake_case = 1  ,		__snake_case = -1  ,		__snake_case = 1  ,		)  ->    None:







	"""simple docstring"""


	_lowercase							   =plt.figure()
	fig.canvas.set_window_title(snake_case__		)
	_lowercase							   =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
	_lowercase							   =[
	    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		) -> list[plt.Circle]:
		update_step(snake_case__  ,		snake_case__  ,		snake_case__		)
		return patches

	_lowercase							   =animation.FuncAnimation(  # noqa: F841
	    snake_case__  ,		snake_case__  ,		interval=snake_case__  ,		blit=snake_case__		)

	plt.show()
def        UpperCAmelCase_      (							)  ->    BodySystem:







	"""simple docstring"""


	_lowercase							   =0.9_70_04_36
	_lowercase							   =-0.24_30_87_53
	_lowercase							   =0.4_66_20_36_85
	_lowercase							   =0.43_23_65_73

	_lowercase							   =[
	    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_      (							)  ->    BodySystem:







	"""simple docstring"""


	_lowercase							   =7.3_4_7_6e2_2
	_lowercase							   =5.9_7_2e2_4
	_lowercase							   =1022
	_lowercase							   =384399000
	_lowercase							   =6.6_7_4e-1_1

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

	_lowercase							   =Body(-earth_moon_distance  ,		0  ,		0  ,		snake_case__  ,		snake_case__  ,		10000000  ,		'''grey'''		)
	_lowercase							   =Body(0  ,		0  ,		0  ,		snake_case__  ,		snake_case__  ,		50000000  ,		'''blue'''		)
	return BodySystem([earth, moon]  ,		snake_case__  ,		time_factor=1000000		)
def        UpperCAmelCase_      (							)  ->    BodySystem:







	"""simple docstring"""


	_lowercase							   =[]
	for _ in range(10		):
		_lowercase							   =random.uniform(-0.5  ,		0.5		)
		_lowercase							   =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  ,		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_3000_0000,
		    4_3000_0000,
		    -4_3000_0000,
		    4_3000_0000,
		)
		plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)





import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin
def        UpperCAmelCase_      (							__snake_case=2  ,		__snake_case=True  ,		__snake_case=False		)  ->    Dict:







 """simple docstring"""


 _lowercase							   =Accelerator(step_scheduler_with_optimizer=__snake_case  ,		split_batches=__snake_case		)
 _lowercase							   =torch.nn.Linear(2  ,		4		)
 _lowercase							   =torch.optim.AdamW(model.parameters()  ,		lr=1.0		)
 _lowercase							   =torch.optim.lr_scheduler.OneCycleLR(__snake_case  ,		max_lr=0.01  ,		steps_per_epoch=2  ,		epochs=1		)
 _lowercase   ,					_lowercase   ,					_lowercase							   =accelerator.prepare(__snake_case  ,		__snake_case  ,		__snake_case		)

 # Optimizer has stepped
 scheduler.step()
 if step_scheduler_with_optimizer or (num_processes == 1):
  assert (
      scheduler.scheduler.last_epoch == num_processes
  ), F"Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})"
 else:
  assert (
      scheduler.scheduler.last_epoch != num_processes
  ), F"Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})"
def        UpperCAmelCase_      (							__snake_case=2  ,		__snake_case=True  ,		__snake_case=False		)  ->    Optional[int]:







 """simple docstring"""


 _lowercase							   =Accelerator(step_scheduler_with_optimizer=__snake_case  ,		split_batches=__snake_case		)
 _lowercase							   =torch.nn.Linear(2  ,		4		)
 _lowercase							   =torch.optim.AdamW(model.parameters()  ,		lr=1.0		)
 _lowercase							   =torch.optim.lr_scheduler.LambdaLR(__snake_case  ,		lr_lambda=lambda __snake_case		: 1 - n / 10		)
 _lowercase   ,					_lowercase   ,					_lowercase							   =accelerator.prepare(__snake_case  ,		__snake_case  ,		__snake_case		)

 # Optimizer has stepped
 _lowercase							   =False
 scheduler.step()
 _lowercase							   =1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
 assert (
     scheduler.get_last_lr()[0] == expected_lr
 ), F"Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}"

 # Optimizer has not stepped
 _lowercase							   =True
 scheduler.step()
 if not step_scheduler_with_optimizer:
  _lowercase							   =1 - 2 / 10
 assert (
     scheduler.get_last_lr()[0] == expected_lr
 ), F"Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}"
def        UpperCAmelCase_      (							__snake_case = 2		)  ->    Optional[int]:







 """simple docstring"""


 from transformers import get_linear_schedule_with_warmup

 _lowercase							   =[1, 2, 4]
 for num_steps in steps:
  _lowercase							   =GradientAccumulationPlugin(num_steps=__snake_case  ,		adjust_scheduler=num_steps > 1		)
  _lowercase							   =Accelerator(gradient_accumulation_plugin=__snake_case		)
  _lowercase							   =torch.nn.Linear(2  ,		4		)
  _lowercase							   =torch.optim.AdamW(model.parameters()  ,		lr=10.0		)
  _lowercase							   =get_linear_schedule_with_warmup(optimizer=__snake_case  ,		num_warmup_steps=0  ,		num_training_steps=20		)

  _lowercase   ,					_lowercase   ,					_lowercase							   =accelerator.prepare(__snake_case  ,		__snake_case  ,		__snake_case		)

  for i in range(10 * num_steps		):
   with accelerator.accumulate(__snake_case		):
    optimizer.step()
    scheduler.step()

   if i == (10 * num_steps - 2):
    assert (
        scheduler.get_last_lr()[0] != 0
    ), F"Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}"
  assert (
      scheduler.get_last_lr()[0] == 0
  ), F"Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}"
  GradientState._reset_state()







@require_cpu
class    lowerCamelCase__     ( unittest.TestCase):





     def   __A      (self )  ->     Optional[Any]:
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1 )	,  num_processes=1 )
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1	,  split_batches=UpperCAmelCase )	,  num_processes=1 )





     def   __A      (self )  ->     Any:
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1 )	,  num_processes=1 )
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1	,  split_batches=UpperCAmelCase )	,  num_processes=1 )





     def   __A      (self )  ->     Union[str, Any]:
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1	,  step_scheduler_with_optimizer=UpperCAmelCase )	,  num_processes=1 )





     def   __A      (self )  ->     Dict:
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1	,  step_scheduler_with_optimizer=UpperCAmelCase )	,  num_processes=1 )





     def   __A      (self )  ->     int:
      AcceleratorState._reset_state(UpperCAmelCase )
      debug_launcher(UpperCAmelCase )
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1	,  split_batches=UpperCAmelCase )	,  num_processes=1 )





     def   __A      (self )  ->     Optional[Any]:
      AcceleratorState._reset_state(UpperCAmelCase )
      debug_launcher(UpperCAmelCase )
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1	,  split_batches=UpperCAmelCase )	,  num_processes=1 )





     def   __A      (self )  ->     List[str]:
      AcceleratorState._reset_state(UpperCAmelCase )
      debug_launcher(partial(UpperCAmelCase	,  step_scheduler_with_optimizer=UpperCAmelCase ) )





     def   __A      (self )  ->     Union[str, Any]:
      AcceleratorState._reset_state(UpperCAmelCase )
      debug_launcher(partial(UpperCAmelCase	,  step_scheduler_with_optimizer=UpperCAmelCase ) )





     @require_huggingface_suite
     def   __A      (self )  ->     int:
      AcceleratorState._reset_state(UpperCAmelCase )
      debug_launcher(partial(UpperCAmelCase	,  num_processes=1 ) )
      debug_launcher(UpperCAmelCase )

