





"""simple docstring"""



from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a_				=    20

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






class 	__snake_case      :





 """simple docstring"""


 def __init__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase = 1.0      ,		__lowerCamelCase = 1.0      ,		__lowerCamelCase = "blue"      ,		):



     '''simple docstring'''




     __A					:		Optional[Any]						=  position_x
     __A					:		Tuple						=  position_y
     __A					:		List[str]						=  velocity_x
     __A					:		Union[str, Any]						=  velocity_y
     __A					:		Optional[int]						=  mass
     __A					:		Optional[int]						=  size
     __A					:		int						=  color

 @property
 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     return self.position_x, self.position_y

 @property
 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     return self.velocity_x, self.velocity_y

 def       UpperCamelCase__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase      ,		__lowerCamelCase						):



     '''simple docstring'''




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







 def       UpperCamelCase__(					self      ,		__lowerCamelCase						):



     '''simple docstring'''




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






class 	__snake_case      :





 """simple docstring"""


 def __init__(					self      ,		__lowerCamelCase      ,		__lowerCamelCase = 1.0      ,		__lowerCamelCase = 1.0      ,		__lowerCamelCase = 0.0      ,		):



     '''simple docstring'''




     __A					:		List[str]						=  bodies
     __A					:		Dict						=  gravitation_constant
     __A					:		Any						=  time_factor
     __A					:		Dict						=  softening_factor

 def __len__(					self						):



     '''simple docstring'''




     return len(self.bodies						)







 def       UpperCamelCase__(					self      ,		__lowerCamelCase						):



     '''simple docstring'''




     for bodya in self.bodies:
         __A					:		List[str]						=  0.0
         __A					:		List[Any]						=  0.0
         for bodya in self.bodies:
             if bodya != bodya:
                 __A					:		Any						=  bodya.position_x - bodya.position_x
                 __A					:		Optional[int]						=  bodya.position_y - bodya.position_y

                 # Calculation of the distance using Pythagoras's theorem
                 # Extra factor due to the softening technique
                 __A					:		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(__lowerCamelCase      ,		__lowerCamelCase      ,		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 	__lowercase  (     snake_case_						:						BodySystem       ,snake_case_						:						float       ,snake_case_						:						list[plt.Circle]		)     ->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		):
        __A					:		Dict						=  (body.position_x, body.position_y)







def 	__lowercase  (     snake_case_						:						str       ,snake_case_						:						BodySystem       ,snake_case_						:						float = -1       ,snake_case_						:						float = 1       ,snake_case_						:						float = -1       ,snake_case_						:						float = 1       ,)     ->None:



    '''simple docstring'''







    __A					:		List[str]						=  plt.figure()
    fig.canvas.set_window_title(snake_case_		)
    __A					:		Optional[int]						=  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
    __A					:		Any						=  [
        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_						:						int		) -> list[plt.Circle]:
        update_step(snake_case_       ,snake_case_       ,snake_case_		)
        return patches

    __A					:		Union[str, Any]						=  animation.FuncAnimation(  # noqa: F841
        snake_case_       ,snake_case_       ,interval=snake_case_       ,blit=snake_case_		)

    plt.show()







def 	__lowercase  (     )     ->BodySystem:



    '''simple docstring'''







    __A					:		List[Any]						=  0.9_700_436
    __A					:		List[Any]						=  -0.24_308_753
    __A					:		Any						=  0.466_203_685
    __A					:		Union[str, Any]						=  0.43_236_573

    __A					:		Optional[int]						=  [
        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 	__lowercase  (     )     ->BodySystem:



    '''simple docstring'''







    __A					:		Tuple						=  7.3476e22
    __A					:		Any						=  5.972e24
    __A					:		List[str]						=  1022
    __A					:		Optional[int]						=  384399000
    __A					:		Tuple						=  6.674e-11

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

    __A					:		Optional[Any]						=  Body(-earth_moon_distance       ,0       ,0       ,snake_case_       ,snake_case_       ,10000000       ,'''grey'''		)
    __A					:		Optional[Any]						=  Body(0       ,0       ,0       ,snake_case_       ,snake_case_       ,50000000       ,'''blue'''		)
    return BodySystem([earth, moon]       ,snake_case_       ,time_factor=1000000		)







def 	__lowercase  (     )     ->BodySystem:



    '''simple docstring'''







    __A					:		List[str]						=  []
    for _ in range(10		):
        __A					:		List[Any]						=  random.uniform(-0.5       ,0.5		)
        __A					:		Union[str, Any]						=  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(),
           -430000000,
           430000000,
           -430000000,
           430000000,
       )
       plot("""Random system with many bodies""", example_a(), -1.5, 1.5, -1.5, 1.5)











"""simple docstring"""



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 	__lowercase  (     snake_case_						:						Dict=2       ,snake_case_						:						str=True       ,snake_case_						:						Tuple=False		)     ->Any:



    '''simple docstring'''







    __A					:		List[str]						=  Accelerator(step_scheduler_with_optimizer=snake_case_       ,split_batches=snake_case_		)
    __A					:		Dict						=  torch.nn.Linear(2       ,4		)
    __A					:		Tuple						=  torch.optim.AdamW(model.parameters()       ,lr=1.0		)
    __A					:		int						=  torch.optim.lr_scheduler.OneCycleLR(snake_case_       ,max_lr=0.01       ,steps_per_epoch=2       ,epochs=1		)
    __A				, __A				, __A					:		Optional[int]						=  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 	__lowercase  (     snake_case_						:						str=2       ,snake_case_						:						Dict=True       ,snake_case_						:						Tuple=False		)     ->List[Any]:



    '''simple docstring'''







    __A					:		int						=  Accelerator(step_scheduler_with_optimizer=snake_case_       ,split_batches=snake_case_		)
    __A					:		Any						=  torch.nn.Linear(2       ,4		)
    __A					:		Optional[int]						=  torch.optim.AdamW(model.parameters()       ,lr=1.0		)
    __A					:		Tuple						=  torch.optim.lr_scheduler.LambdaLR(snake_case_       ,lr_lambda=lambda snake_case_		: 1 - n / 10		)
    __A				, __A				, __A					:		Tuple						=  accelerator.prepare(snake_case_       ,snake_case_       ,snake_case_		)

    # Optimizer has stepped
    __A					:		List[Any]						=  False
    scheduler.step()
    __A					:		List[Any]						=  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
    __A					:		List[str]						=  True
    scheduler.step()
    if not step_scheduler_with_optimizer:
        __A					:		List[Any]						=  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 	__lowercase  (     snake_case_						:						int = 2		)     ->str:



    '''simple docstring'''







    from transformers import get_linear_schedule_with_warmup

    __A					:		Any						=  [1, 2, 4]
    for num_steps in steps:
        __A					:		Tuple						=  GradientAccumulationPlugin(num_steps=snake_case_       ,adjust_scheduler=num_steps > 1		)
        __A					:		Optional[Any]						=  Accelerator(gradient_accumulation_plugin=snake_case_		)
        __A					:		Optional[int]						=  torch.nn.Linear(2       ,4		)
        __A					:		Any						=  torch.optim.AdamW(model.parameters()       ,lr=10.0		)
        __A					:		Dict						=  get_linear_schedule_with_warmup(optimizer=snake_case_       ,num_warmup_steps=0       ,num_training_steps=20		)

        __A				, __A				, __A					:		Union[str, Any]						=  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 	__snake_case      (	unittest.TestCase  ):





 """simple docstring"""


 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1						)      ,		num_processes=1						)
     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1      ,		split_batches=__lowerCamelCase						)      ,		num_processes=1						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1						)      ,		num_processes=1						)
     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1      ,		split_batches=__lowerCamelCase						)      ,		num_processes=1						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1      ,		step_scheduler_with_optimizer=__lowerCamelCase						)      ,		num_processes=1						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1      ,		step_scheduler_with_optimizer=__lowerCamelCase						)      ,		num_processes=1						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     AcceleratorState._reset_state(__lowerCamelCase						)
     debug_launcher(__lowerCamelCase						)
     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1      ,		split_batches=__lowerCamelCase						)      ,		num_processes=1						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     AcceleratorState._reset_state(__lowerCamelCase						)
     debug_launcher(__lowerCamelCase						)
     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1      ,		split_batches=__lowerCamelCase						)      ,		num_processes=1						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     AcceleratorState._reset_state(__lowerCamelCase						)
     debug_launcher(partial(__lowerCamelCase      ,		step_scheduler_with_optimizer=__lowerCamelCase						)						)

 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     AcceleratorState._reset_state(__lowerCamelCase						)
     debug_launcher(partial(__lowerCamelCase      ,		step_scheduler_with_optimizer=__lowerCamelCase						)						)







 @require_huggingface_suite
 def       UpperCamelCase__(					self						):



     '''simple docstring'''




     AcceleratorState._reset_state(__lowerCamelCase						)
     debug_launcher(partial(__lowerCamelCase      ,		num_processes=1						)						)
     debug_launcher(__lowerCamelCase						)




