


from typing import List

import numpy as np






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  lowerCamelCase :					Any    =				{key: len(SCREAMING_SNAKE_CASE_	) for key, value in gen_kwargs.items() if isinstance(SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	)}
  if len(set(lists_lengths.values()	)	) > 1:
    raise RuntimeError(
        (
            "Sharding is ambiguous for this dataset: "
            + "we found several data sources lists of different lengths, and we don't know over which list we should parallelize:\n"
            + "\n".join(f"""\t- key {key} has length {length}""" for key, length in lists_lengths.items()	)
            + "\nTo fix this, check the 'gen_kwargs' and make sure to use lists only for data sources, "
            + "and use tuples otherwise. In the end there should only be one single list, or several lists with the same length."
        )	)
  lowerCamelCase :					Any    =				max(lists_lengths.values()      ,						default=0	)
  return max(1      ,						SCREAMING_SNAKE_CASE_	)






def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  lowerCamelCase :					List[str]    =				[]
  for group_idx in range(SCREAMING_SNAKE_CASE_	):
    lowerCamelCase :					Dict    =				num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
    if num_shards_to_add == 0:
      break
    lowerCamelCase :					str    =				shards_indices_per_group[-1].stop if shards_indices_per_group else 0
    lowerCamelCase :					List[str]    =				range(SCREAMING_SNAKE_CASE_      ,						start + num_shards_to_add	)
    shards_indices_per_group.append(SCREAMING_SNAKE_CASE_	)
  return shards_indices_per_group






def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  lowerCamelCase :					Dict    =				_number_of_shards_in_gen_kwargs(SCREAMING_SNAKE_CASE_	)
  if num_shards == 1:
    return [dict(SCREAMING_SNAKE_CASE_	)]
  else:
    lowerCamelCase :					Tuple    =				_distribute_shards(num_shards=SCREAMING_SNAKE_CASE_      ,						max_num_jobs=SCREAMING_SNAKE_CASE_	)
    return [
        {
            key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
            if isinstance(SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	)
            else value
            for key, value in gen_kwargs.items()
        }
        for group_idx in range(len(SCREAMING_SNAKE_CASE_	)	)
    ]






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  return {
      key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
      if isinstance(gen_kwargs_list[0][key]      ,						SCREAMING_SNAKE_CASE_	)
      else gen_kwargs_list[0][key]
      for key in gen_kwargs_list[0]
  }







def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  lowerCamelCase :					Optional[int]    =				{len(SCREAMING_SNAKE_CASE_	) for value in gen_kwargs.values() if isinstance(SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	)}
  lowerCamelCase :					List[str]    =				{}
  for size in list_sizes:
    lowerCamelCase :					Tuple    =				list(range(SCREAMING_SNAKE_CASE_	)	)
    rng.shuffle(indices_per_size[size]	)
  # Now let's copy the gen_kwargs and shuffle the lists based on their sizes
  lowerCamelCase :					Any    =				dict(SCREAMING_SNAKE_CASE_	)
  for key, value in shuffled_kwargs.items():
    if isinstance(SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	):
      lowerCamelCase :					Optional[int]    =				[value[i] for i in indices_per_size[len(SCREAMING_SNAKE_CASE_	)]]
  return shuffled_kwargs







from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_snake_case             =     2_99_79_24_58

# Symbols
_snake_case      ,       _snake_case      ,       _snake_case      ,       _snake_case             =     symbols('''ct x y z''')






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''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 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_ = None	):


  '''simple docstring'''

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

  return transformation_matrix(SCREAMING_SNAKE_CASE_	) @ event


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # Example of symbolic vector:
   _snake_case             =     transform(29_97_92_45)
   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
   _snake_case             =     {ct: c, x: 1, y: 1, z: 1}
   _snake_case             =     [four_vector[i].subs(sub_dict) for i in range(4)]

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



