





import math as m



def 							lowerCAmelCase_				(    A_  ,A_  ,A_=0.001):
    return (f(a + h) - f(a - h)) / (2 * h)



def 							lowerCAmelCase_				(    A_  ,A_=0  ,A_=1_00  ,A_=0.0001  ,A_=1e-6  ,A_=False):
    UpperCamelCase__:					int												=      xa  # set the initial guess
    UpperCamelCase__:					Dict												=      [a]
    UpperCamelCase__:					Dict												=      abs(f(A_))
    UpperCamelCase__:					List[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")
        UpperCamelCase__:					str												=      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

   A__:  str       					=					lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
   A__					,						A__					,						A__:  Any       					=					newton_raphson(
       f, xa=10, maxiter=1000, 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}}}")








from .chunk_utils import chunk_layer
from .data_transforms import make_atomaa_masks
from .feats import atomaa_to_atomaa, frames_and_literature_positions_to_atomaa_pos, torsion_angles_to_frames
from .loss import compute_predicted_aligned_error, compute_tm
from .protein import Protein as OFProtein
from .protein import to_pdb
from .rigid_utils import Rigid, Rotation
from .tensor_utils import dict_multimap, flatten_final_dims, permute_final_dims

