




"""simple docstring"""




from typing import Dict, Optional, Tuple

import torch







def       __UpperCAmelCase      (				__UpperCamelCase					):
			__lowercase	:       List[str]				=   boundaries[1] - boundaries[0]
			__lowercase	:       str				=   boundaries + step / 2
			__lowercase	:       Tuple				=   torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1					)]					,							dim=0					)
			return bin_centers







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							):
			__lowercase	:       str				=   _calculate_bin_centers(__UpperCamelCase					)
			return (
			    torch.sum(aligned_distance_error_probs * bin_centers					,							dim=-1					),
			    bin_centers[-1],
			)







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase = 31					,							__UpperCamelCase = 64					,							**__UpperCamelCase					,							):
			__lowercase	:       Any				=   torch.linspace(0					,							__UpperCamelCase					,							steps=(no_bins - 1)					,							device=logits.device					)

			__lowercase	:       Optional[int]				=   torch.nn.functional.softmax(__UpperCamelCase					,							dim=-1					)
			__lowercase	,__lowercase	:       str				=   _calculate_expected_aligned_error(
			    alignment_confidence_breaks=__UpperCamelCase					,							aligned_distance_error_probs=__UpperCamelCase					,							)

			return {
			    "aligned_confidence_probs": aligned_confidence_probs,
			    "predicted_aligned_error": predicted_aligned_error,
			    "max_predicted_aligned_error": max_predicted_aligned_error,
			}







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase = None					,							__UpperCamelCase = 31					,							__UpperCamelCase = 64					,							__UpperCamelCase = 1e-8					,							**__UpperCamelCase					,							):
			if residue_weights is None:
						__lowercase	:       List[str]				=   logits.new_ones(logits.shape[-2]					)

			__lowercase	:       str				=   torch.linspace(0					,							__UpperCamelCase					,							steps=(no_bins - 1)					,							device=logits.device					)

			__lowercase	:       str				=   _calculate_bin_centers(__UpperCamelCase					)
			torch.sum(__UpperCamelCase					)
			__lowercase	:       Any				=   logits.shape[-2]
			__lowercase	:       Dict				=   max(__UpperCamelCase					,							19					)

			__lowercase	:       Optional[int]				=   1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

			__lowercase	:       int				=   torch.nn.functional.softmax(__UpperCamelCase					,							dim=-1					)

			__lowercase	:       List[str]				=   1.0 / (1 + (bin_centers**2) / (da**2))
			__lowercase	:       str				=   torch.sum(probs * tm_per_bin					,							dim=-1					)

			__lowercase	:       Any				=   residue_weights / (eps + residue_weights.sum())
			__lowercase	:       Union[str, Any]				=   torch.sum(predicted_tm_term * normed_residue_mask					,							dim=-1					)

			__lowercase	:       int				=   per_alignment * residue_weights

			__lowercase	:       int				=   (weighted == torch.max(__UpperCamelCase					)).nonzero()[0]
			return per_alignment[tuple(__UpperCamelCase					)]









"""simple docstring"""




from collections.abc import Callable

a_            =   Callable[[float], float]  # type alias for a real -> real function







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							):
			__lowercase	:       str				=   float(__UpperCamelCase					)
			while True:
						try:
									__lowercase	:       Dict				=   prev_guess - function(__UpperCamelCase					) / derivative(__UpperCamelCase					)
						except ZeroDivisionError:
									raise ZeroDivisionError('''Could not find root'''					) from None
						if abs(prev_guess - next_guess					) < 10**-5:
									return next_guess
						__lowercase	:       List[Any]				=   next_guess







def       __UpperCAmelCase      (				__UpperCamelCase					):
			return (x**3) - (2 * x) - 5







def       __UpperCAmelCase      (				__UpperCamelCase					):
			return 3 * (x**2) - 2


if __name__ == "__main__":
			print(newton(f, fa, 3))



