


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 	a__						:

       def __init__( self   :  Tuple   ,				lowerCamelCase_   :  float   ,				lowerCamelCase_   :  float   ,				lowerCamelCase_   :  float   ,				lowerCamelCase_   :  float   ,				lowerCamelCase_   :  float = 1.0   ,				lowerCamelCase_   :  float = 1.0   ,				lowerCamelCase_   :  str = "blue"   ,				):
            a_     :  Any				      =     position_x
            a_     :  Optional[int]				      =     position_y
            a_     :  Dict				      =     velocity_x
            a_     :  Dict				      =     velocity_y
            a_     :  Dict				      =     mass
            a_     :  List[str]				      =     size
            a_     :  Any				      =     color

       @property
       def     UpperCAmelCase( self   :  str     ):
            return self.position_x, self.position_y

       @property
       def     UpperCAmelCase( self   :  List[Any]     ):
            return self.velocity_x, self.velocity_y

       def     UpperCAmelCase( self   :  Optional[int]   ,				lowerCamelCase_   :  float   ,				lowerCamelCase_   :  float   ,				lowerCamelCase_   :  float     ):
            self.velocity_x += force_x * delta_time
            self.velocity_y += force_y * delta_time

       def     UpperCAmelCase( self   :  Optional[int]   ,				lowerCamelCase_   :  float     ):
            self.position_x += self.velocity_x * delta_time
            self.position_y += self.velocity_y * delta_time


class 	a__						:

       def __init__( self   :  List[str]   ,				lowerCamelCase_   :  list[Body]   ,				lowerCamelCase_   :  float = 1.0   ,				lowerCamelCase_   :  float = 1.0   ,				lowerCamelCase_   :  float = 0.0   ,				):
            a_     :  int				      =     bodies
            a_     :  Optional[Any]				      =     gravitation_constant
            a_     :  Tuple				      =     time_factor
            a_     :  Union[str, Any]				      =     softening_factor

       def __len__( self   :  Union[str, Any]     ):
            return len(self.bodies     )

       def     UpperCAmelCase( self   :  List[str]   ,				lowerCamelCase_   :  float     ):
            for bodya in self.bodies:
                 a_     :  Optional[Any]				      =     0.0
                 a_     :  Optional[Any]				      =     0.0
                 for bodya in self.bodies:
                      if bodya != bodya:
                           a_     :  Optional[Any]				      =     bodya.position_x - bodya.position_x
                           a_     :  Any				      =     bodya.position_y - bodya.position_y

                           # Calculation of the distance using Pythagoras's theorem
                           # Extra factor due to the softening technique
                           a_     :  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(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 			_a      (    __UpperCamelCase	,	__UpperCamelCase	,	__UpperCamelCase			):
     body_system.update_system(UpperCAmelCase__			)

     # Update the positions of the patches
     for patch, body in zip(UpperCAmelCase__	,	body_system.bodies			):
          a_     :  Optional[int]				      =     (body.position_x, body.position_y)



def 			_a      (    __UpperCamelCase	,	__UpperCamelCase	,	__UpperCamelCase = -1	,	__UpperCamelCase = 1	,	__UpperCamelCase = -1	,	__UpperCamelCase = 1	,	):
     a_     :  Dict				      =     plt.figure()
     fig.canvas.set_window_title(UpperCAmelCase__			)
     a_     :  Dict				      =     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_     :  Optional[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(UpperCAmelCase__			)

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

     a_     :  Dict				      =     animation.FuncAnimation(  # noqa: F841
         UpperCAmelCase__	,	UpperCAmelCase__	,	interval=UpperCAmelCase__	,	blit=UpperCAmelCase__			)

     plt.show()



def 			_a      (    ):
     a_     :  List[Any]				      =     0.9_70_04_36
     a_     :  Any				      =     -0.24_30_87_53
     a_     :  Tuple				      =     0.4_66_20_36_85
     a_     :  Optional[int]				      =     0.43_23_65_73

     a_     :  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 			_a      (    ):
     a_     :  Dict				      =     7.3476E22
     a_     :  str				      =     5.972E24
     a_     :  str				      =     1_0_2_2
     a_     :  Tuple				      =     3_8_4_3_9_9_0_0_0
     a_     :  Optional[Any]				      =     6.674E-11

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

     a_     :  Optional[Any]				      =     Body(-earth_moon_distance	,	0	,	0	,	UpperCAmelCase__	,	UpperCAmelCase__	,	1_0_0_0_0_0_0_0	,	"""grey"""			)
     a_     :  Optional[int]				      =     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 			_a      (    ):
     a_     :  List[str]				      =     []
     for _ in range(1_0			):
          a_     :  int				      =     random.uniform(-0.5	,	0.5			)
          a_     :  str				      =     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 os
import tempfile
from pathlib import Path
from unittest import TestCase

import pyarrow as pa
import pytest

from datasets.arrow_dataset import Dataset
from datasets.arrow_reader import ArrowReader, BaseReader, FileInstructions, ReadInstruction, make_file_instructions
from datasets.info import DatasetInfo
from datasets.splits import NamedSplit, Split, SplitDict, SplitInfo

from .utils import assert_arrow_memory_doesnt_increase, assert_arrow_memory_increases





class        __magic_name__		(       _UpperCAmelCase):







			def       SCREAMING_SNAKE_CASE_	(      self							:    Any							,     lowercase_							:    Dict							,     lowercase_							:    List[str]=False       ):
										lowercase_		,		lowercase_		,		lowercase_   :     str									=			(
										    filename_skip_take["""filename"""],
										    filename_skip_take["""skip"""] if """skip""" in filename_skip_take else None,
										    filename_skip_take["""take"""] if """take""" in filename_skip_take else None,
										)
										open(os.path.join(lowercase_       )							,     """wb"""       ).close()
										lowercase_   :     Union[str, Any]									=			pa.Table.from_pydict({"""filename""": [Path(lowercase_       ).name] * 100}       )
										if take == -1:
																	lowercase_   :     Optional[int]									=			len(lowercase_       ) - skip
										if skip is not None and take is not None:
																	lowercase_   :     Any									=			pa_table.slice(lowercase_							,     lowercase_       )
										return pa_table





class        __magic_name__		(       _UpperCAmelCase):







			def       SCREAMING_SNAKE_CASE_	(      self							:    int       ):
										lowercase_   :     Union[str, Any]									=			"""my_name"""
										lowercase_   :     Optional[Any]									=			SplitInfo(name="""train"""							,     num_examples=100       )
										lowercase_   :     Dict									=			SplitInfo(name="""test"""							,     num_examples=100       )
										lowercase_   :     str									=			[train_info, test_info]
										lowercase_   :     Any									=			SplitDict()
										split_dict.add(lowercase_       )
										split_dict.add(lowercase_       )
										lowercase_   :     Union[str, Any]									=			DatasetInfo(splits=lowercase_       )

										with tempfile.TemporaryDirectory() as tmp_dir:
																	lowercase_   :     Tuple									=			ReaderTest(lowercase_							,     lowercase_       )

																	lowercase_   :     Optional[Any]									=			"""test[:33%]"""
																	lowercase_   :     List[Any]									=			Dataset(**reader.read(lowercase_							,     lowercase_							,     lowercase_       )       )
																	self.assertEqual(dset["""filename"""][0]							,     f'''{name}-test'''       )
																	self.assertEqual(dset.num_rows							,     33       )
																	self.assertEqual(dset.num_columns							,     1       )

																	lowercase_   :     str									=			["""train""", """test[:33%]"""]
																	lowercase_   :     Any									=			[Split.TRAIN, ReadInstruction.from_spec("""test[:33%]"""       )]
																	for instructions in [instructionsa, instructionsa]:
																								lowercase_   :     Dict									=			[reader.read(lowercase_							,     lowercase_							,     lowercase_       ) for instr in instructions]
																								lowercase_		,		lowercase_   :     List[Any]									=			(Dataset(**lowercase_       ) for dataset_kwargs in datasets_kwargs)
																								self.assertEqual(train_dset["""filename"""][0]							,     f'''{name}-train'''       )
																								self.assertEqual(train_dset.num_rows							,     100       )
																								self.assertEqual(train_dset.num_columns							,     1       )
																								self.assertIsInstance(train_dset.split							,     lowercase_       )
																								self.assertEqual(str(train_dset.split       )							,     """train"""       )
																								self.assertEqual(test_dset["""filename"""][0]							,     f'''{name}-test'''       )
																								self.assertEqual(test_dset.num_rows							,     33       )
																								self.assertEqual(test_dset.num_columns							,     1       )
																								self.assertIsInstance(test_dset.split							,     lowercase_       )
																								self.assertEqual(str(test_dset.split       )							,     """test[:33%]"""       )
																								del train_dset, test_dset







			def       SCREAMING_SNAKE_CASE_	(      self							:    Dict       ):
										lowercase_   :     List[Any]									=			"""my_name"""
										lowercase_   :     int									=			SplitInfo(name="""train"""							,     num_examples=1000							,     shard_lengths=[100] * 10       )
										lowercase_   :     Tuple									=			[train_info]
										lowercase_   :     Any									=			SplitDict()
										split_dict.add(lowercase_       )
										lowercase_   :     Union[str, Any]									=			DatasetInfo(splits=lowercase_       )

										with tempfile.TemporaryDirectory() as tmp_dir:
																	lowercase_   :     Optional[int]									=			ReaderTest(lowercase_							,     lowercase_       )

																	lowercase_   :     Optional[int]									=			"""train[:33%]"""
																	lowercase_   :     int									=			Dataset(**reader.read(lowercase_							,     lowercase_							,     lowercase_       )       )
																	self.assertEqual(dset["""filename"""][0]							,     f'''{name}-train-00000-of-00010'''       )
																	self.assertEqual(dset["""filename"""][-1]							,     f'''{name}-train-00003-of-00010'''       )
																	self.assertEqual(dset.num_rows							,     330       )
																	self.assertEqual(dset.num_columns							,     1       )







			def       SCREAMING_SNAKE_CASE_	(      self							:    Any       ):
										lowercase_   :     Any									=			SplitInfo(name="""train"""							,     num_examples=100       )
										lowercase_   :     Optional[int]									=			SplitInfo(name="""test"""							,     num_examples=100       )
										lowercase_   :     Union[str, Any]									=			SplitDict()
										split_dict.add(lowercase_       )
										split_dict.add(lowercase_       )
										lowercase_   :     Tuple									=			DatasetInfo(splits=lowercase_       )

										with tempfile.TemporaryDirectory() as tmp_dir:
																	lowercase_   :     Tuple									=			ReaderTest(lowercase_							,     lowercase_       )

																	lowercase_   :     List[str]									=			[
																	    {"""filename""": os.path.join(lowercase_							,     """train"""       )},
																	    {"""filename""": os.path.join(lowercase_							,     """test"""       ), """skip""": 10, """take""": 10},
																	]
																	lowercase_   :     int									=			Dataset(**reader.read_files(lowercase_							,     original_instructions="""train+test[10:20]"""       )       )
																	self.assertEqual(dset.num_rows							,     110       )
																	self.assertEqual(dset.num_columns							,     1       )
																	del dset




@pytest.mark.parametrize("""in_memory""" , [False, True]					)
def 				lowerCamelCase      ( UpperCAmelCase__			:   List[Any] , UpperCAmelCase__			:   int , UpperCAmelCase__			:   Union[str, Any]					)     -> Union[str, Any]:
							lowercase_   :     str									=			arrow_file
							with assert_arrow_memory_increases() if in_memory else assert_arrow_memory_doesnt_increase():
														lowercase_   :     Optional[Any]									=			ArrowReader.read_table(UpperCAmelCase__ , in_memory=UpperCAmelCase__					)
							assert table.shape == dataset.data.shape
							assert set(table.column_names					) == set(dataset.data.column_names					)
							assert dict(table.to_pydict()					) == dict(dataset.data.to_pydict()					)  # to_pydict returns OrderedDict




@pytest.mark.parametrize("""in_memory""" , [False, True]					)
def 				lowerCamelCase      ( UpperCAmelCase__			:   Tuple , UpperCAmelCase__			:   int , UpperCAmelCase__			:   Optional[int]					)     -> Any:
							lowercase_   :     Tuple									=			arrow_file
							lowercase_   :     Optional[Any]									=			ArrowReader("""""" , UpperCAmelCase__					)
							with assert_arrow_memory_increases() if in_memory else assert_arrow_memory_doesnt_increase():
														lowercase_   :     Dict									=			reader.read_files([{"""filename""": filename}] , in_memory=UpperCAmelCase__					)
							assert dataset_kwargs.keys() == {"arrow_table", "info", "split"}
							lowercase_   :     Optional[int]									=			dataset_kwargs["""arrow_table"""]
							assert table.shape == dataset.data.shape
							assert set(table.column_names					) == set(dataset.data.column_names					)
							assert dict(table.to_pydict()					) == dict(dataset.data.to_pydict()					)  # to_pydict returns OrderedDict




def 				lowerCamelCase      ( )     -> Optional[Any]:
							assert ReadInstruction("""train""" , to=10 , unit="""abs"""					).to_spec() == "train[:10]"
							assert ReadInstruction("""train""" , from_=-80 , to=10 , unit="""%"""					).to_spec() == "train[-80%:10%]"

							lowercase_   :     Tuple									=			"""train+test"""
							assert ReadInstruction.from_spec(UpperCAmelCase__					).to_spec() == spec_train_test

							lowercase_   :     List[Any]									=			"""train[2:10]"""
							assert ReadInstruction.from_spec(UpperCAmelCase__					).to_spec() == spec_train_abs

							lowercase_   :     Any									=			"""train[15%:-20%]"""
							assert ReadInstruction.from_spec(UpperCAmelCase__					).to_spec() == spec_train_pct

							lowercase_   :     Optional[int]									=			"""train[:10%](closest)"""
							assert ReadInstruction.from_spec(UpperCAmelCase__					).to_spec() == "train[:10%]"

							lowercase_   :     List[Any]									=			"""train[:10%](pct1_dropremainder)"""
							assert ReadInstruction.from_spec(UpperCAmelCase__					).to_spec() == spec_train_pct_rounding

							lowercase_   :     Union[str, Any]									=			"""train[:10%](pct1_dropremainder)+test[-10%:](pct1_dropremainder)"""
							assert ReadInstruction.from_spec(UpperCAmelCase__					).to_spec() == spec_train_test_pct_rounding




def 				lowerCamelCase      ( )     -> int:
							lowercase_   :     Optional[int]									=			"""dummy"""
							lowercase_   :     Union[str, Any]									=			[SplitInfo(name="""train""" , num_examples=100					)]
							lowercase_   :     Optional[int]									=			"""train[:33%]"""
							lowercase_   :     Dict									=			"""arrow"""
							lowercase_   :     int									=			"""prefix"""

							lowercase_   :     int									=			make_file_instructions(UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__					)
							assert isinstance(UpperCAmelCase__ , UpperCAmelCase__					)
							assert file_instructions.num_examples == 33
							assert file_instructions.file_instructions == [
							    {"filename": os.path.join(UpperCAmelCase__ , F'''{name}-train.arrow'''					), "skip": 0, "take": 33}
							]

							lowercase_   :     Dict									=			[SplitInfo(name="""train""" , num_examples=100 , shard_lengths=[10] * 10					)]
							lowercase_   :     Dict									=			make_file_instructions(UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__					)
							assert isinstance(UpperCAmelCase__ , UpperCAmelCase__					)
							assert file_instructions.num_examples == 33
							assert file_instructions.file_instructions == [
							    {"filename": os.path.join(UpperCAmelCase__ , F'''{name}-train-00000-of-00010.arrow'''					), "skip": 0, "take": -1},
							    {"filename": os.path.join(UpperCAmelCase__ , F'''{name}-train-00001-of-00010.arrow'''					), "skip": 0, "take": -1},
							    {"filename": os.path.join(UpperCAmelCase__ , F'''{name}-train-00002-of-00010.arrow'''					), "skip": 0, "take": -1},
							    {"filename": os.path.join(UpperCAmelCase__ , F'''{name}-train-00003-of-00010.arrow'''					), "skip": 0, "take": 3},
							]




@pytest.mark.parametrize("""name, expected_exception""" , [(None, TypeError), ("""""", ValueError)]					)
def 				lowerCamelCase      ( UpperCAmelCase__			:   List[Any] , UpperCAmelCase__			:   Any					)     -> List[str]:
							lowercase_   :     str									=			[SplitInfo(name="""train""" , num_examples=100					)]
							lowercase_   :     Any									=			"""train"""
							lowercase_   :     Optional[int]									=			"""arrow"""
							lowercase_   :     str									=			"""prefix_path"""
							with pytest.raises(UpperCAmelCase__					):
														lowercase_   :     List[str]									=			make_file_instructions(UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__					)





