import math as m






def    __lowercase (       _A  ,      _A  ,      _A=0.001     )       ->  Optional[Any]:
      return (f(a + h     ) - f(a - h     )) / (2 * h)






def    __lowercase (       _A  ,      _A=0  ,      _A=100  ,      _A=0.0001  ,      _A=1e-6  ,      _A=False     )       ->  Tuple:
      SCREAMING_SNAKE_CASE	: List[Any]					       =				xa  # set the initial guess
      SCREAMING_SNAKE_CASE	: Tuple					       =				[a]
      SCREAMING_SNAKE_CASE	: Optional[int]					       =				abs(f(_A     )     )
      SCREAMING_SNAKE_CASE	: str					       =				lambda _A     : calc_derivative(_A  ,      _A  ,      h=_A     )  # noqa: E731  Derivative of f(x)
      for _ in range(_A     ):
            if fa(_A     ) == 0:
                  raise ValueError("""No converging solution found"""     )
            SCREAMING_SNAKE_CASE	: Dict					       =				a - f(_A     ) / fa(_A     )  # Calculate the next estimate
            if logsteps:
                  steps.append(_A     )
            if error < maxerror:
                  break
      else:
            raise ValueError("""Iteration limit reached, no converging solution found"""     )
      if logsteps:
            # If logstep is true, then log intermediate steps
            return a, error, steps
      return a, error


if __name__ == "__main__":
  from matplotlib import pyplot as plt

  UpperCAmelCase__	:       List[str]			      =      lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
  UpperCAmelCase__	:       str			      =      newton_raphson(
      f, xa=10, maxiter=1_000, step=1E-6, logsteps=True
  )
  plt.plot([abs(f(x)) for x in steps])
  plt.xlabel("""step""")
  plt.ylabel("""error""")
  plt.show()
  print(F"""solution = {{{solution:f}}}, error = {{{error:f}}}""")







import os
import unittest

import pytest
from parameterized import parameterized

from transformers.testing_utils import require_torch, require_torch_gpu, slow, torch_device


# skipping in unittest tests

UpperCAmelCase__	:       Dict			      =      [(1,)]






def    __lowercase (       )       ->  Tuple:
      SCREAMING_SNAKE_CASE	: Optional[Any]					       =				bool(os.getenv("""RUN_SLOW"""  ,      0     )     )
      if run_slow:
            assert True
      else:
            assert False, "should have been skipped"






def    __lowercase (       )       ->  Optional[Any]:
      SCREAMING_SNAKE_CASE	: Dict					       =				bool(os.getenv("""RUN_SLOW"""  ,      0     )     )
      if run_slow and torch_device == "cuda":
            assert True
      else:
            assert False, "should have been skipped"







@require_torch
class     a__    (				unittest.TestCase    ):







  """simple docstring"""




  @slow
  @require_torch_gpu
  def 	_lowercase (     self      :	Any						)   ->Optional[Any]:
        """simple docstring"""







        check_slow_torch_cuda()


  @require_torch_gpu
  @slow
  def 	_lowercase (     self      :	Optional[Any]						)   ->Any:
        """simple docstring"""







        check_slow_torch_cuda()




  @parameterized.expand(UpperCAmelCase__						)
  @slow
  def 	_lowercase (     self      :	Optional[int]			,			UpperCAmelCase__      :	Dict=None						)   ->Optional[Any]:
        """simple docstring"""







        check_slow()






@slow
@require_torch_gpu
def    __lowercase (       )       ->  Optional[int]:
      check_slow_torch_cuda()






@require_torch_gpu
@slow
def    __lowercase (       )       ->  int:
      check_slow_torch_cuda()






@slow
@pytest.mark.parametrize("""param"""  ,      [1]     )
def    __lowercase (       _A     )       ->  Optional[int]:
      check_slow()







@pytest.mark.parametrize("""param"""  ,      [1]     )
@slow
def    __lowercase (       _A     )       ->  str:
      check_slow()




