code: def _gradient(self, metric, vab, vcd, prior_inv):
      dMetric = prior_inv - np.linalg.inv(metric)
      dabs = np.sum(vab.dot(metric) * vab, axis=1)
      dcds = np.sum(vcd.dot(metric) * vcd, axis=1)
      violations = dabs > dcds
      # TODO: vectorize
      for vab, dab, vcd, dcd in zip(
          vab[violations],
          dabs[violations],
          vcd[violations],
          dcds[violations],
      ):
          dMetric += (1 - np.sqrt(dcd / dab)) * np.outer(vab, vab) + (
              1 - np.sqrt(dab / dcd)
          ) * np.outer(vcd, vcd)
      return dMetric
  
imports: import numpy
  import scipy.linalg
  from sklearn.base import TransformerMixin
  from .base_metric import _QuadrupletsClassifierMixin, MahalanobisMixin
  from .constraints import Constraints
  from ._util import components_from_metric, _initialize_metric_mahalanobis
  import warnings
label_desc: Use image node_id 5 for calling the _BaseLSML obj's underlying member method code with example usage: obj._gradient(metric, vab, vcd, prior_inv) and returns: dMetric