code: def minDCF(
      positive_scores,
      negative_scores,
      c_miss=1.0,
      c_fa=1.0,
      p_target=0.01,
  ):
      """Computes the minDCF metric normally used to evaluate speaker verification
      systems. The min_DCF is the minimum of the following C_det function computed
      within the defined threshold range:
  
      C_det =  c_miss * p_miss * p_target + c_fa * p_fa * (1 -p_target)
  
      where p_miss is the missing probability and p_fa is the probability of having
      a false alarm.
  
      Arguments
      ---------
      positive_scores : torch.tensor
          The scores from entries of the same class.
      negative_scores : torch.tensor
          The scores from entries of different classes.
      c_miss : float
           Cost assigned to a missing error (default 1.0).
      c_fa : float
          Cost assigned to a false alarm (default 1.0).
      p_target: float
          Prior probability of having a target (default 0.01).
  
  
      Example
      -------
      >>> positive_scores = torch.tensor([0.6, 0.7, 0.8, 0.5])
      >>> negative_scores = torch.tensor([0.4, 0.3, 0.2, 0.1])
      >>> val_minDCF, threshold = minDCF(positive_scores, negative_scores)
      >>> val_minDCF
      0.0
      """
  
      # Computing candidate thresholds
      thresholds, _ = torch.sort(
          torch.cat([positive_scores, negative_scores])
      )
      thresholds = torch.unique(thresholds)
  
      # Adding intermediate thresholds
      interm_thresholds = (thresholds[0:-1] + thresholds[1:]) / 2
      thresholds, _ = torch.sort(
          torch.cat([thresholds, interm_thresholds])
      )
  
      # Computing False Rejection Rate (miss detection)
      positive_scores = torch.cat(
          len(thresholds) * [positive_scores.unsqueeze(0)]
      )
      pos_scores_threshold = (
          positive_scores.transpose(0, 1) <= thresholds
      )
      p_miss = (
          pos_scores_threshold.sum(0)
      ).float() / positive_scores.shape[1]
      del positive_scores
      del pos_scores_threshold
  
      # Computing False Acceptance Rate (false alarm)
      negative_scores = torch.cat(
          len(thresholds) * [negative_scores.unsqueeze(0)]
      )
      neg_scores_threshold = (
          negative_scores.transpose(0, 1) > thresholds
      )
      p_fa = (
          neg_scores_threshold.sum(0)
      ).float() / negative_scores.shape[1]
      del negative_scores
      del neg_scores_threshold
  
      c_det = c_miss * p_miss * p_target + c_fa * p_fa * (1 - p_target)
      c_min, min_index = torch.min(c_det, dim=0)
  
      return float(c_min), float(thresholds[min_index])
  
imports: import torch
  from joblib import Parallel, delayed
  from speechbrain.utils.data_utils import undo_padding
  from speechbrain.utils.edit_distance import wer_summary, wer_details_for_batch
  from speechbrain.dataio.dataio import merge_char, split_word, extract_concepts_values
  from speechbrain.dataio.wer import print_wer_summary, print_alignments
label_desc: Use image node_id 4 for calling a global function with example usage: minDCF(positive_scores, negative_scores, c_miss, c_fa, p_target) and returns: float,  float