


def      _lowercase(				__a							:	Dict						,    __a							:	List[Any]    ):
							if len(str(__a    )    ) == 1 or len(str(__a    )    ) == 1:
														return a * b

							a__     						=max(len(str(__a    )    )						,    len(str(__a    )    )    )
							a__     						=ma // 2

							a__						,    a__     						=divmod(__a						,    10**ma    )
							a__						,    a__     						=divmod(__a						,    10**ma    )

							a__     						=karatsuba(__a						,    __a    )
							a__     						=karatsuba((aa + aa)						,    (ba + ba)    )
							a__     						=karatsuba(__a						,    __a    )

							return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)






def      _lowercase(				):
							print(karatsuba(1_5463						,    2_3489    )    )


if __name__ == "__main__":
	main()





from typing import Dict, Optional, Tuple

import torch






def      _lowercase(				__a							:	torch.Tensor    ):
							a__     						=boundaries[1] - boundaries[0]
							a__     						=boundaries + step / 2
							a__     						=torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1    )]						,    dim=0    )
							return bin_centers






def      _lowercase(				__a							:	torch.Tensor						,    __a							:	torch.Tensor						,    ):
							a__     						=_calculate_bin_centers(__a    )
							return (
							    torch.sum(aligned_distance_error_probs * bin_centers						,    dim=-1    ),
							    bin_centers[-1],
							)






def      _lowercase(				__a							:	torch.Tensor						,    __a							:	int = 31						,    __a							:	int = 64						,    **__a							:	List[str]						,    ):
							a__     						=torch.linspace(0						,    __a						,    steps=(no_bins - 1)						,    device=logits.device    )

							a__     						=torch.nn.functional.softmax(__a						,    dim=-1    )
							a__						,    a__     						=_calculate_expected_aligned_error(
							    alignment_confidence_breaks=__a						,    aligned_distance_error_probs=__a						,    )

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







def      _lowercase(				__a							:	torch.Tensor						,    __a							:	Optional[torch.Tensor] = None						,    __a							:	int = 31						,    __a							:	int = 64						,    __a							:	float = 1e-8						,    **__a							:	str						,    ):
							if residue_weights is None:
														a__     						=logits.new_ones(logits.shape[-2]    )

							a__     						=torch.linspace(0						,    __a						,    steps=(no_bins - 1)						,    device=logits.device    )

							a__     						=_calculate_bin_centers(__a    )
							torch.sum(__a    )
							a__     						=logits.shape[-2]
							a__     						=max(__a						,    19    )

							a__     						=1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

							a__     						=torch.nn.functional.softmax(__a						,    dim=-1    )

							a__     						=1.0 / (1 + (bin_centers**2) / (da**2))
							a__     						=torch.sum(probs * tm_per_bin						,    dim=-1    )

							a__     						=residue_weights / (eps + residue_weights.sum())
							a__     						=torch.sum(predicted_tm_term * normed_residue_mask						,    dim=-1    )

							a__     						=per_alignment * residue_weights

							a__     						=(weighted == torch.max(__a    )).nonzero()[0]
							return per_alignment[tuple(__a    )]

