

from typing import Dict, Optional, Tuple

import torch



def    snake_case_(_UpperCamelCase  )							->			torch.Tensor:



  """simple docstring"""






  _snake_case		=							boundaries[1] - boundaries[0]
  _snake_case		=							boundaries + step / 2
  _snake_case		=							torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1  )]				, dim=0  )
  return bin_centers



def    snake_case_(_UpperCamelCase				, _UpperCamelCase				, )							->			Tuple[torch.Tensor, torch.Tensor]:



  """simple docstring"""






  _snake_case		=							_calculate_bin_centers(_UpperCamelCase  )
  return (
      torch.sum(aligned_distance_error_probs * bin_centers				, dim=-1  ),
      bin_centers[-1],
  )



def    snake_case_(_UpperCamelCase				, _UpperCamelCase = 31				, _UpperCamelCase = 64				, **_UpperCamelCase				, )							->			Dict[str, torch.Tensor]:



  """simple docstring"""






  _snake_case		=							torch.linspace(0				, _UpperCamelCase				, steps=(no_bins - 1)				, device=logits.device  )

  _snake_case		=							torch.nn.functional.softmax(_UpperCamelCase				, dim=-1  )
  _snake_case,  _snake_case		=							_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    snake_case_(_UpperCamelCase				, _UpperCamelCase = None				, _UpperCamelCase = 31				, _UpperCamelCase = 64				, _UpperCamelCase = 1E-8				, **_UpperCamelCase				, )							->			torch.Tensor:



  """simple docstring"""






  if residue_weights is None:
    _snake_case		=							logits.new_ones(logits.shape[-2]  )

  _snake_case		=							torch.linspace(0				, _UpperCamelCase				, steps=(no_bins - 1)				, device=logits.device  )

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

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

  _snake_case		=							torch.nn.functional.softmax(_UpperCamelCase				, dim=-1  )

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

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

  _snake_case		=							per_alignment * residue_weights

  _snake_case		=							(weighted == torch.max(_UpperCamelCase  )).nonzero()[0]
  return per_alignment[tuple(_UpperCamelCase  )]




__A    	=			{
    '''+''': lambda x, y: x + y,
    '''-''': lambda x, y: x - y,
    '''*''': lambda x, y: x * y,
    '''/''': lambda x, y: x / y,
}



def    snake_case_(_UpperCamelCase  )							->			str:



  """simple docstring"""






  return c.isdigit()



def    snake_case_(_UpperCamelCase  )							->			str:



  """simple docstring"""






  _snake_case		=							[]

  # iterate over the string in reverse order
  for c in expression.split()[::-1]:
    # push operand to stack
    if is_operand(_UpperCamelCase  ):
      stack.append(int(_UpperCamelCase  )  )

    else:
      # pop values from stack can calculate the result
      # push the result onto the stack again
      _snake_case		=							stack.pop()
      _snake_case		=							stack.pop()
      stack.append(calc[c](_UpperCamelCase				, _UpperCamelCase  )  )

  return stack.pop()


# Driver code
if __name__ == "__main__":
 __A    	=			'''+ 9 * 2 6'''
 print(evaluate(test_expression))

 __A    	=			'''/ * 10 2 + 4 1 '''
 print(evaluate(test_expression))

