


import fcntl
import os
import socket

import torch
import torch.distributed as dist




def 	__lowercase		(  *_UpperCamelCase   )			->List[Any]:







      """simple docstring"""

      with open(__snake_case,			'''r'''   ) as fh:
            fcntl.flock(__snake_case,			fcntl.LOCK_EX   )
            try:
                  print(*__snake_case   )
            finally:
                  fcntl.flock(__snake_case,			fcntl.LOCK_UN   )


__a       =					int(os.environ['''LOCAL_RANK'''])
torch.cuda.set_device(local_rank)
__a       =					torch.device('''cuda''', local_rank)
__a       =					socket.gethostname()

__a       =					F'''[{hostname}-{local_rank}]'''

try:
  # test distributed
  dist.init_process_group('''nccl''')
  dist.all_reduce(torch.ones(1).to(device), op=dist.ReduceOp.SUM)
  dist.barrier()

  # test cuda is available and can allocate memory
  torch.cuda.is_available()
  torch.ones(1).cuda(local_rank)

  # global rank
  __a       =					dist.get_rank()
  __a       =					dist.get_world_size()

  printflock(F'''{gpu} is OK (global rank: {rank}/{world_size})''')

  dist.barrier()
  if rank == 0:
    printflock(F'''pt={torch.__version__}, cuda={torch.version.cuda}, nccl={torch.cuda.nccl.version()}''')

except Exception:
  printflock(F'''{gpu} is broken''')
  raise








'''simple docstring'''




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def        _lowerCAmelCase			(  __snake_case  : str ,							__snake_case  : complex ,							__snake_case  : str = "x" ,							__snake_case  : float = 10**-10 ,							__snake_case  : int = 1 ,							)     ->     complex:
     __A						: int      =       symbols(__snake_case			)
     __A						: Tuple      =       lambdify(__snake_case ,							__snake_case			)
     __A						: Any      =       lambdify(__snake_case ,							diff(__snake_case ,							__snake_case			)			)

     __A						: str      =       starting_point

     while True:
          if diff_function(__snake_case			) != 0:
               __A						: Optional[Any]      =       prev_guess - multiplicity * func(__snake_case			) / diff_function(
                   __snake_case			)
          else:
               raise ZeroDivisionError('Could not find root'			) from None

          # Precision is checked by comparing the difference of consecutive guesses
          if abs(next_guess - prev_guess			) < precision:
               return next_guess

          __A						: Dict      =       next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(f"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")

  # Find root of polynomial
  # Find fourth Root of 5
  print(f"""The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}""")

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      f"""{newton_raphson("log(y) - 1", 2, variable="y")}""",
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      f"""{newton_raphson("exp(x) - 1", 10, precision=0.005)}""",
  )

  # Find root of cos(x)
  print(f"""The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}""")