

'''simple docstring'''

from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowercase__         =      299792458

# Symbols
lowercase__   ,  lowercase__   ,  lowercase__   ,  lowercase__         =      symbols("ct x y z")




def 				UpperCamelCase(					UpperCAmelCase_     ):
 if velocity > c:
  raise ValueError('Speed must not exceed light speed 299,792,458 [m/s]!'     )
 elif velocity < 1:
  # Usually the speed should be much higher than 1 (c order of magnitude)
  raise ValueError('Speed must be greater than or equal to 1!'     )

 return velocity / c




def 				UpperCamelCase(					UpperCAmelCase_     ):
 return 1 / sqrt(1 - beta(UpperCAmelCase_     ) ** 2     )




def 				UpperCamelCase(					UpperCAmelCase_     ):
 return np.array(
     [
         [gamma(UpperCAmelCase_     ), -gamma(UpperCAmelCase_     ) * beta(UpperCAmelCase_     ), 0, 0],
         [-gamma(UpperCAmelCase_     ) * beta(UpperCAmelCase_     ), gamma(UpperCAmelCase_     ), 0, 0],
         [0, 0, 1, 0],
         [0, 0, 0, 1],
     ]     )




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_ = None     ):
 # Ensure event is not empty
 if event is None:
  UpperCAmelCase	:     Optional[int]						 =			np.array([ct, x, y, z]     )  # Symbolic four vector
 else:
  event[0] *= c  # x0 is ct (speed of light * time)

 return transformation_matrix(UpperCAmelCase_     ) @ event


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # Example of symbolic vector:
 lowercase__         =      transform(29979245)
 print("Example of four vector: ")
 print(f'''ct\' = {four_vector[0]}''')
 print(f'''x\' = {four_vector[1]}''')
 print(f'''y\' = {four_vector[2]}''')
 print(f'''z\' = {four_vector[3]}''')

 # Substitute symbols with numerical values
 lowercase__         =      {ct: c, x: 1, y: 1, z: 1}
 lowercase__         =      [four_vector[i].subs(sub_dict) for i in range(4)]

 print(f'''\n{numerical_vector}''')







'''simple docstring'''

import pytest

from datasets import Dataset, DatasetDict, Features, NamedSplit, Value
from datasets.io.text import TextDatasetReader

from ..utils import assert_arrow_memory_doesnt_increase, assert_arrow_memory_increases




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_     ):
 assert isinstance(UpperCAmelCase_  ,	UpperCAmelCase_     )
 assert dataset.num_rows == 4
 assert dataset.num_columns == 1
 assert dataset.column_names == ["text"]
 for feature, expected_dtype in expected_features.items():
  assert dataset.features[feature].dtype == expected_dtype




@pytest.mark.parametrize('keep_in_memory'  ,	[False, True]     )
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     int						 =			tmp_path / 'cache'
 UpperCAmelCase	:     List[str]						 =			{'text': 'string'}
 with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
  UpperCAmelCase	:     Tuple						 =			TextDatasetReader(UpperCAmelCase_  ,	cache_dir=UpperCAmelCase_  ,	keep_in_memory=UpperCAmelCase_     ).read()
 _check_text_dataset(UpperCAmelCase_  ,	UpperCAmelCase_     )




@pytest.mark.parametrize(
    'features'  ,	[
        None,
        {'text': 'string'},
        {'text': 'int32'},
        {'text': 'float32'},
    ]  ,	)
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     Optional[int]						 =			tmp_path / 'cache'
 UpperCAmelCase	:     List[str]						 =			{'text': 'string'}
 UpperCAmelCase	:     Optional[int]						 =			features.copy() if features else default_expected_features
 UpperCAmelCase	:     int						 =			(
     Features({feature: Value(UpperCAmelCase_     ) for feature, dtype in features.items()}     ) if features is not None else None
 )
 UpperCAmelCase	:     Union[str, Any]						 =			TextDatasetReader(UpperCAmelCase_  ,	features=UpperCAmelCase_  ,	cache_dir=UpperCAmelCase_     ).read()
 _check_text_dataset(UpperCAmelCase_  ,	UpperCAmelCase_     )




@pytest.mark.parametrize('split'  ,	[None, NamedSplit('train'     ), 'train', 'test']     )
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     Optional[int]						 =			tmp_path / 'cache'
 UpperCAmelCase	:     Tuple						 =			{'text': 'string'}
 UpperCAmelCase	:     List[str]						 =			TextDatasetReader(UpperCAmelCase_  ,	cache_dir=UpperCAmelCase_  ,	split=UpperCAmelCase_     ).read()
 _check_text_dataset(UpperCAmelCase_  ,	UpperCAmelCase_     )
 assert dataset.split == split if split else "train"




@pytest.mark.parametrize('path_type'  ,	[str, list]     )
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 if issubclass(UpperCAmelCase_  ,	UpperCAmelCase_     ):
  UpperCAmelCase	:     Tuple						 =			text_path
 elif issubclass(UpperCAmelCase_  ,	UpperCAmelCase_     ):
  UpperCAmelCase	:     Optional[Any]						 =			[text_path]
 UpperCAmelCase	:     List[Any]						 =			tmp_path / 'cache'
 UpperCAmelCase	:     Union[str, Any]						 =			{'text': 'string'}
 UpperCAmelCase	:     List[Any]						 =			TextDatasetReader(UpperCAmelCase_  ,	cache_dir=UpperCAmelCase_     ).read()
 _check_text_dataset(UpperCAmelCase_  ,	UpperCAmelCase_     )




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_=("train",)     ):
 assert isinstance(UpperCAmelCase_  ,	UpperCAmelCase_     )
 for split in splits:
  UpperCAmelCase	:     Union[str, Any]						 =			dataset_dict[split]
  assert dataset.num_rows == 4
  assert dataset.num_columns == 1
  assert dataset.column_names == ["text"]
  for feature, expected_dtype in expected_features.items():
   assert dataset.features[feature].dtype == expected_dtype




@pytest.mark.parametrize('keep_in_memory'  ,	[False, True]     )
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     Any						 =			tmp_path / 'cache'
 UpperCAmelCase	:     List[str]						 =			{'text': 'string'}
 with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
  UpperCAmelCase	:     int						 =			TextDatasetReader({'train': text_path}  ,	cache_dir=UpperCAmelCase_  ,	keep_in_memory=UpperCAmelCase_     ).read()
 _check_text_datasetdict(UpperCAmelCase_  ,	UpperCAmelCase_     )




@pytest.mark.parametrize(
    'features'  ,	[
        None,
        {'text': 'string'},
        {'text': 'int32'},
        {'text': 'float32'},
    ]  ,	)
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     Union[str, Any]						 =			tmp_path / 'cache'
 # CSV file loses col_1 string dtype information: default now is "int64" instead of "string"
 UpperCAmelCase	:     Tuple						 =			{'text': 'string'}
 UpperCAmelCase	:     Union[str, Any]						 =			features.copy() if features else default_expected_features
 UpperCAmelCase	:     int						 =			(
     Features({feature: Value(UpperCAmelCase_     ) for feature, dtype in features.items()}     ) if features is not None else None
 )
 UpperCAmelCase	:     List[Any]						 =			TextDatasetReader({'train': text_path}  ,	features=UpperCAmelCase_  ,	cache_dir=UpperCAmelCase_     ).read()
 _check_text_datasetdict(UpperCAmelCase_  ,	UpperCAmelCase_     )




@pytest.mark.parametrize('split'  ,	[None, NamedSplit('train'     ), 'train', 'test']     )
def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 if split:
  UpperCAmelCase	:     int						 =			{split: text_path}
 else:
  UpperCAmelCase	:     int						 =			'train'
  UpperCAmelCase	:     Any						 =			{'train': text_path, 'test': text_path}
 UpperCAmelCase	:     Dict						 =			tmp_path / 'cache'
 UpperCAmelCase	:     Any						 =			{'text': 'string'}
 UpperCAmelCase	:     List[str]						 =			TextDatasetReader(UpperCAmelCase_  ,	cache_dir=UpperCAmelCase_     ).read()
 _check_text_datasetdict(UpperCAmelCase_  ,	UpperCAmelCase_  ,	splits=list(path.keys()     )     )
 assert all(dataset[split].split == split for split in path.keys()     )




