





'''simple docstring'''






from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
A_		:  Optional[Any]		 =						299792458

# Symbols
A_		:  Optional[Any]		 =						symbols("ct x y z")



def        UpperCamelCase__		(						__magic_name__  :   Union[str, Any]      )				->			float:
 '''simple docstring'''






 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__		(						__magic_name__  :   Optional[Any]      )				->			float:
 '''simple docstring'''






 return 1 / sqrt(1 - beta(__magic_name__      ) ** 2      )



def        UpperCamelCase__		(						__magic_name__  :   Tuple      )				->			np.ndarray:
 '''simple docstring'''






 return np.array(
     [
         [gamma(__magic_name__      ), -gamma(__magic_name__      ) * beta(__magic_name__      ), 0, 0],
         [-gamma(__magic_name__      ) * beta(__magic_name__      ), gamma(__magic_name__      ), 0, 0],
         [0, 0, 1, 0],
         [0, 0, 0, 1],
     ]      )



def        UpperCamelCase__		(						__magic_name__  :   Tuple		,       __magic_name__  :   Any = None      )				->			np.ndarray:
 '''simple docstring'''






 if event is None:
  snake_case__     :					List[Any]    =  np.array([ct, x, y, z]      )  # Symbolic four vector
 else:
  event[0] *= c  # x0 is ct (speed of light * time)

 return transformation_matrix(__magic_name__      ) @ event


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # Example of symbolic vector:
    A_		:  Optional[Any]		 =						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
    A_		:  List[Any]		 =						{ct: c, x: 1, y: 1, z: 1}
    A_		:  int		 =						[four_vector[i].subs(sub_dict) for i in range(4)]

    print(F'\n{numerical_vector}')








'''simple docstring'''

# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
 import torch
class     __lowerCAmelCase		(TensorFormatter[Mapping, """torch.Tensor""", Mapping]	):





      '''simple docstring'''






      def __init__(self       :       Optional[Any]  ,		UpperCamelCase       :       Tuple=None  ,		**UpperCamelCase       :       List[str]					):

             '''simple docstring'''







             super().__init__(features=UpperCamelCase					)
             lowercase__      =					torch_tensor_kwargs
             import torch  # noqa import torch at initialization



      def  UpperCamelCase__						(self       :       List[str]  ,		UpperCamelCase       :       Union[str, Any]					):

             '''simple docstring'''







             import torch

             if isinstance(UpperCamelCase  ,		UpperCamelCase					) and column:
                    if all(
                        isinstance(UpperCamelCase  ,		torch.Tensor					) and x.shape == column[0].shape and x.dtype == column[0].dtype
                        for x in column					):
                           return torch.stack(UpperCamelCase					)
             return column



      def  UpperCamelCase__						(self       :       List[Any]  ,		UpperCamelCase       :       Optional[Any]					):

             '''simple docstring'''







             import torch

             if isinstance(UpperCamelCase  ,		(str, bytes, type(UpperCamelCase					))					):
                    return value
             elif isinstance(UpperCamelCase  ,		(np.character, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.character					):
                    return value.tolist()

             lowercase__      =					{}

             if isinstance(UpperCamelCase  ,		(np.number, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.integer					):
                    lowercase__      =					{'''dtype''': torch.intaa}
             elif isinstance(UpperCamelCase  ,		(np.number, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.floating					):
                    lowercase__      =					{'''dtype''': torch.floataa}
             elif config.PIL_AVAILABLE and "PIL" in sys.modules:
                    import PIL.Image

                    if isinstance(UpperCamelCase  ,		PIL.Image.Image					):
                           lowercase__      =					np.asarray(UpperCamelCase					)
             return torch.tensor(UpperCamelCase  ,		**{**default_dtype, **self.torch_tensor_kwargs}					)



      def  UpperCamelCase__						(self       :       Optional[int]  ,		UpperCamelCase       :       Dict					):

             '''simple docstring'''







             import torch

             # support for torch, tf, jax etc.
             if hasattr(UpperCamelCase  ,		'''__array__'''					) and not isinstance(UpperCamelCase  ,		torch.Tensor					):
                    lowercase__      =					data_struct.__array__()
             # support for nested types like struct of list of struct
             if isinstance(UpperCamelCase  ,		np.ndarray					):
                    if data_struct.dtype == object:  # torch tensors cannot be instantied from an array of objects
                           return self._consolidate([self.recursive_tensorize(UpperCamelCase					) for substruct in data_struct]					)
             elif isinstance(UpperCamelCase  ,		(list, tuple)					):
                    return self._consolidate([self.recursive_tensorize(UpperCamelCase					) for substruct in data_struct]					)
             return self._tensorize(UpperCamelCase					)



      def  UpperCamelCase__						(self       :       List[str]  ,		UpperCamelCase       :       dict					):

             '''simple docstring'''







             return map_nested(self._recursive_tensorize  ,		UpperCamelCase  ,		map_list=UpperCamelCase					)



      def  UpperCamelCase__						(self       :       Dict  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_row(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_row(UpperCamelCase					)
             return self.recursive_tensorize(UpperCamelCase					)



      def  UpperCamelCase__						(self       :       List[Any]  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_column(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_column(UpperCamelCase  ,		pa_table.column_names[0]					)
             lowercase__      =					self.recursive_tensorize(UpperCamelCase					)
             lowercase__      =					self._consolidate(UpperCamelCase					)
             return column






      def  UpperCamelCase__						(self       :       Tuple  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_batch(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_batch(UpperCamelCase					)
             lowercase__      =					self.recursive_tensorize(UpperCamelCase					)
             for column_name in batch:
                    lowercase__      =					self._consolidate(batch[column_name]					)
             return batch




