

from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
_a			=       2_0

# Time between time steps in seconds
_a			=       INTERVAL / 1_0_0_0






class 							A_			:


     def __init__(							self      :		Union[str, Any]      ,  UpperCAmelCase      :		float      ,  UpperCAmelCase      :		float      ,  UpperCAmelCase      :		float      ,  UpperCAmelCase      :		float      ,  UpperCAmelCase      :		float = 1.0      ,  UpperCAmelCase      :		float = 1.0      ,  UpperCAmelCase      :		str = "blue"      ,  )							->     None:
      __lowerCAmelCase:       Dict            =				position_x
      __lowerCAmelCase:       int            =				position_y
      __lowerCAmelCase:       Dict            =				velocity_x
      __lowerCAmelCase:       str            =				velocity_y
      __lowerCAmelCase:       int            =				mass
      __lowerCAmelCase:       Tuple            =				size
      __lowerCAmelCase:       Optional[Any]            =				color


     @property
     def   UpperCAmelCase  (							self      :		Union[str, Any] )							->     tuple[float, float]:
      return self.position_x, self.position_y


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


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


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







class 							A_			:


     def __init__(							self      :		Union[str, Any]      ,  UpperCAmelCase      :		list[Body]      ,  UpperCAmelCase      :		float = 1.0      ,  UpperCAmelCase      :		float = 1.0      ,  UpperCAmelCase      :		float = 0.0      ,  )							->     None:
      __lowerCAmelCase:       Union[str, Any]            =				bodies
      __lowerCAmelCase:       List[str]            =				gravitation_constant
      __lowerCAmelCase:       Optional[int]            =				time_factor
      __lowerCAmelCase:       str            =				softening_factor


     def __len__(							self      :		Optional[Any] )							->     int:
      return len(self.bodies )


     def   UpperCAmelCase  (							self      :		int      ,  UpperCAmelCase      :		float )							->     None:
      for bodya in self.bodies:
       __lowerCAmelCase:       Optional[Any]            =				0.0
       __lowerCAmelCase:       int            =				0.0
       for bodya in self.bodies:
        if bodya != bodya:
         __lowerCAmelCase:       Tuple            =				bodya.position_x - bodya.position_x
         __lowerCAmelCase:       Tuple            =				bodya.position_y - bodya.position_y

         # Calculation of the distance using Pythagoras's theorem
         # Extra factor due to the softening technique
         __lowerCAmelCase:       List[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(UpperCAmelCase      ,  UpperCAmelCase      ,  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 _a			(	SCREAMING_SNAKE_CASE		:      BodySystem   , SCREAMING_SNAKE_CASE		:      float   , SCREAMING_SNAKE_CASE		:      list[plt.Circle]		)   ->   None:

 """simple docstring"""






 body_system.update_system(SCREAMING_SNAKE_CASE		)

 # Update the positions of the patches
 for patch, body in zip(SCREAMING_SNAKE_CASE   , body_system.bodies		):
  __lowerCAmelCase:       List[Any]            =				(body.position_x, body.position_y)







def _a			(	SCREAMING_SNAKE_CASE		:      str   , SCREAMING_SNAKE_CASE		:      BodySystem   , SCREAMING_SNAKE_CASE		:      float = -1   , SCREAMING_SNAKE_CASE		:      float = 1   , SCREAMING_SNAKE_CASE		:      float = -1   , SCREAMING_SNAKE_CASE		:      float = 1   , )   ->   None:

 """simple docstring"""






 __lowerCAmelCase:       str            =				plt.figure()
 fig.canvas.set_window_title(SCREAMING_SNAKE_CASE		)
 __lowerCAmelCase:       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
 __lowerCAmelCase:       Optional[int]            =				[
     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(SCREAMING_SNAKE_CASE		)

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

 __lowerCAmelCase:       int            =				animation.FuncAnimation(  # noqa: F841
     SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , interval=SCREAMING_SNAKE_CASE   , blit=SCREAMING_SNAKE_CASE		)

 plt.show()







def _a			(	)   ->   BodySystem:

 """simple docstring"""






 __lowerCAmelCase:       List[Any]            =				0.9_7_0_0_4_3_6
 __lowerCAmelCase:       List[str]            =				-0.2_4_3_0_8_7_5_3
 __lowerCAmelCase:       List[Any]            =				0.4_6_6_2_0_3_6_8_5
 __lowerCAmelCase:       Union[str, Any]            =				0.4_3_2_3_6_5_7_3

 __lowerCAmelCase:       Any            =				[
     Body(SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , size=0.2   , color='red'		),
     Body(-position_x   , -position_y   , SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , size=0.2   , color='green'		),
     Body(0   , 0   , -2 * velocity_x   , -2 * velocity_y   , size=0.2   , color='blue'		),
 ]
 return BodySystem(SCREAMING_SNAKE_CASE   , time_factor=3		)







def _a			(	)   ->   BodySystem:

 """simple docstring"""






 __lowerCAmelCase:       Any            =				7.3476E22
 __lowerCAmelCase:       Union[str, Any]            =				5.972E24
 __lowerCAmelCase:       Optional[Any]            =				10_22
 __lowerCAmelCase:       Dict            =				3_84_39_90_00
 __lowerCAmelCase:       Optional[int]            =				6.674E-11

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

 __lowerCAmelCase:       List[str]            =				Body(-earth_moon_distance   , 0   , 0   , SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , 10_00_00_00   , 'grey'		)
 __lowerCAmelCase:       Tuple            =				Body(0   , 0   , 0   , SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , 50_00_00_00   , 'blue'		)
 return BodySystem([earth, moon]   , SCREAMING_SNAKE_CASE   , time_factor=1_00_00_00		)







def _a			(	)   ->   BodySystem:

 """simple docstring"""






 __lowerCAmelCase:       int            =				[]
 for _ in range(10		):
  __lowerCAmelCase:       Union[str, Any]            =				random.uniform(-0.5   , 0.5		)
  __lowerCAmelCase:       Optional[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		)   , SCREAMING_SNAKE_CASE   , SCREAMING_SNAKE_CASE   , size=0.0_5   , )		)
  bodies.append(
      Body(
          random.uniform(-0.5   , 0.5		)   , random.uniform(-0.5   , 0.5		)   , -velocity_x   , -velocity_y   , size=0.0_5   , )		)
 return BodySystem(SCREAMING_SNAKE_CASE   , 0.0_1   , 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_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)








import json
import os
from dataclasses import dataclass

import numpy as np
import pyarrow as pa

import datasets
from utils import get_duration


_a			=       1_0_0_0_0_0_0_0_0_0_0_0
_a			=       1_0_0_0_0

_a	,     _a			=       os.path.split(__file__)
_a			=       os.path.join(RESULTS_BASEPATH, '''results''', RESULTS_FILENAME.replace('''.py''', '''.json'''))







def _a			(	SCREAMING_SNAKE_CASE		:      int   , SCREAMING_SNAKE_CASE		:      int		)   ->   datasets.Dataset:

 """simple docstring"""






 __lowerCAmelCase:       List[Any]            =				pa.Table.from_pydict({'col': [0] * chunk_size}		)
 __lowerCAmelCase:       Dict            =				pa.concat_tables([table] * (num_examples // chunk_size)		)
 return datasets.Dataset(SCREAMING_SNAKE_CASE   , fingerprint='table_100B'		)






@dataclass
class 							A_			:
     _lowercase      :					int
     _lowercase      :					int
     _lowercase      :					int
     _lowercase      :					int


     def   UpperCAmelCase  (							self      :		Optional[Any] )							->     Dict:
      __lowerCAmelCase:       Dict            =				np.random.default_rng(self.seed )
      __lowerCAmelCase:       List[Any]            =				rng.integers(low=self.low      ,  high=self.high      ,  size=self.size ).tolist()


     def __iter__(							self      :		Any )							->     Optional[int]:
      return iter(self._sampled_values )


     def __len__(							self      :		Union[str, Any] )							->     Dict:
      return self.size







@get_duration
def _a			(	SCREAMING_SNAKE_CASE		:      datasets.Dataset		)   ->   List[str]:

 """simple docstring"""






 __lowerCAmelCase:       List[Any]            =				dataset[0]







@get_duration
def _a			(	SCREAMING_SNAKE_CASE		:      datasets.Dataset		)   ->   Dict:

 """simple docstring"""






 __lowerCAmelCase:       Dict            =				dataset[-1]







@get_duration
def _a			(	SCREAMING_SNAKE_CASE		:      datasets.Dataset		)   ->   Any:

 """simple docstring"""






 __lowerCAmelCase:       Union[str, Any]            =				dataset[range(len(SCREAMING_SNAKE_CASE		) // 2   , len(SCREAMING_SNAKE_CASE		) // 2 + 10_24		)]







@get_duration
def _a			(	SCREAMING_SNAKE_CASE		:      datasets.Dataset		)   ->   Optional[Any]:

 """simple docstring"""






 __lowerCAmelCase:       int            =				dataset[RandIter(0   , len(SCREAMING_SNAKE_CASE		)   , 10_24   , seed=42		)]







def _a			(	)   ->   Tuple:

 """simple docstring"""






 __lowerCAmelCase:       str            =				{'num examples': SPEED_TEST_N_EXAMPLES}
 __lowerCAmelCase:       Tuple            =				(get_first_row, get_last_row, get_batch_of_aaaa_rows, get_batch_of_aaaa_random_rows)
 print('generating dataset'		)
 __lowerCAmelCase:       str            =				generate_100B_dataset(num_examples=SCREAMING_SNAKE_CASE   , chunk_size=SCREAMING_SNAKE_CASE		)
 print('Functions'		)
 for func in functions:
  print(func.__name__		)
  __lowerCAmelCase:       Dict            =				func(SCREAMING_SNAKE_CASE		)

 with open(SCREAMING_SNAKE_CASE   , 'wb'		) as f:
  f.write(json.dumps(SCREAMING_SNAKE_CASE		).encode('utf-8'		)		)


if __name__ == "__main__":  # useful to run the profiler
  benchmark_table_100B()





