





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




def     A_      (	lowercase_   ,		lowercase_   ,		lowercase_ = "x"   ,		lowercase_ = 10**-10   ,		lowercase_ = 1   ,		)      ->    List[Any]:
       _snake_case   :				str  					=    symbols(_A	)
       _snake_case   :				Any  					=    lambdify(_A   ,		_A	)
       _snake_case   :				Dict  					=    lambdify(_A   ,		diff(_A   ,		_A	)	)

       _snake_case   :				Tuple  					=    starting_point

       while True:
              if diff_function(_A	) != 0:
                     _snake_case   :				List[str]  					=    prev_guess - multiplicity * func(_A	) / diff_function(
                         _A	)
              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

              _snake_case   :				List[str]  					=    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", 1_0, precision=0.0_0_5)}""",
   )

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







'''simple docstring'''

import os
import sys
import tempfile

import torch

from .state import AcceleratorState
from .utils import PrecisionType, PrepareForLaunch, is_mps_available, patch_environment







def __UpperCamelCase( _A       :					Any	,      _A       :					List[str]=()	,      _A       :					List[str]=None	,      _A       :					Dict="no"	,      _A       :					List[str]="29500"     ):
   '''simple docstring'''
   UpperCAmelCase__				:					int 					=	False
   UpperCAmelCase__				:					List[str] 					=	False
   if any(key.startswith('''KAGGLE'''     ) for key in os.environ.keys()     ):
      UpperCAmelCase__				:					List[str] 					=	True
   elif "IPython" in sys.modules:
      UpperCAmelCase__				:					List[Any] 					=	'''google.colab''' in str(sys.modules['''IPython'''].get_ipython()     )

   try:
      UpperCAmelCase__				:					Tuple 					=	PrecisionType(mixed_precision.lower()     )
   except ValueError:
      raise ValueError(
          F'''Unknown mixed_precision mode: {args.mixed_precision.lower()}. Choose between {PrecisionType.list()}.'''     )

   if (in_colab or in_kaggle) and (os.environ.get('''TPU_NAME'''	,      _A     ) is not None):
      # TPU launch
      import torch_xla.distributed.xla_multiprocessing as xmp

      if len(AcceleratorState._shared_state     ) > 0:
         raise ValueError(
             '''To train on TPU in Colab or Kaggle Kernel, the `Accelerator` should only be initialized inside '''
             '''your training function. Restart your notebook and make sure no cells initializes an '''
             '''`Accelerator`.'''     )
      if num_processes is None:
         UpperCAmelCase__				:					Tuple 					=	8

      UpperCAmelCase__				:					Optional[Any] 					=	PrepareForLaunch(_A	,      distributed_type='''TPU'''     )
      print(F'''Launching a training on {num_processes} TPU cores.'''     )
      xmp.spawn(_A	,      args=_A	,      nprocs=_A	,      start_method='''fork'''     )
   elif in_colab:
      # No need for a distributed launch otherwise as it's either CPU or one GPU.
      if torch.cuda.is_available():
         print('''Launching training on one GPU.'''     )
      else:
         print('''Launching training on one CPU.'''     )
      function(*_A     )
   else:
      if num_processes is None:
         raise ValueError(
             '''You have to specify the number of GPUs you would like to use, add `num_processes=...` to your call.'''     )

      if num_processes > 1:
         # Multi-GPU launch
         from torch.multiprocessing import start_processes
         from torch.multiprocessing.spawn import ProcessRaisedException

         if len(AcceleratorState._shared_state     ) > 0:
            raise ValueError(
                '''To launch a multi-GPU training from your notebook, the `Accelerator` should only be initialized '''
                '''inside your training function. Restart your notebook and make sure no cells initializes an '''
                '''`Accelerator`.'''     )

         if torch.cuda.is_initialized():
            raise ValueError(
                '''To launch a multi-GPU training from your notebook, you need to avoid running any instruction '''
                '''using `torch.cuda` in any cell. Restart your notebook and make sure no cells use any CUDA '''
                '''function.'''     )

         # torch.distributed will expect a few environment variable to be here. We set the ones common to each
         # process here (the other ones will be set be the launcher).
         with patch_environment(
             world_size=_A	,      master_addr='''127.0.01'''	,      master_port=_A	,      mixed_precision=_A     ):
            UpperCAmelCase__				:					str 					=	PrepareForLaunch(_A	,      distributed_type='''MULTI_GPU'''     )
            print(F'''Launching training on {num_processes} GPUs.'''     )
            try:
               start_processes(_A	,      args=_A	,      nprocs=_A	,      start_method='''fork'''     )
            except ProcessRaisedException as e:
               if "Cannot re-initialize CUDA in forked subprocess" in e.args[0]:
                  raise RuntimeError(
                      '''CUDA has been initialized before the `notebook_launcher` could create a forked subprocess. '''
                      '''This likely stems from an outside import causing issues once the `notebook_launcher()` is called. '''
                      '''Please review your imports and test them when running the `notebook_launcher()` to identify '''
                      '''which one is problematic.'''     ) from e

      else:
         # No need for a distributed launch otherwise as it's either CPU, GPU or MPS.
         if is_mps_available():
            UpperCAmelCase__				:					Union[str, Any] 					=	'''1'''
            print('''Launching training on MPS.'''     )
         elif torch.cuda.is_available():
            print('''Launching training on one GPU.'''     )
         else:
            print('''Launching training on CPU.'''     )
         function(*_A     )







def __UpperCamelCase( _A       :					List[str]	,      _A       :					Optional[Any]=()	,      _A       :					str=2     ):
   '''simple docstring'''
   from torch.multiprocessing import start_processes

   with tempfile.NamedTemporaryFile() as tmp_file:
      # torch.distributed will expect a few environment variable to be here. We set the ones common to each
      # process here (the other ones will be set be the launcher).
      with patch_environment(
          world_size=_A	,      master_addr='''127.0.01'''	,      master_port='''29500'''	,      accelerate_mixed_precision='''no'''	,      accelerate_debug_rdv_file=tmp_file.name	,      accelerate_use_cpu='''yes'''	,      ):
         UpperCAmelCase__				:					Optional[int] 					=	PrepareForLaunch(_A	,      debug=_A     )
         start_processes(_A	,      args=_A	,      nprocs=_A	,      start_method='''fork'''     )




