docstr: Compute the value, 1st derivative, second derivative (Hessian) of
  a dissimilarity constraint function gF(sum_ij distance(d_ij A d_ij))
  where A is a diagonal matrix (in the form of a column vector 'w').
docstr_tok: ["Compute","the","value",",","1st","derivative",",","second","derivative","(","Hessian",")","of","a","dissimilarity","constraint","function","gF","(","sum_ij","distance","(","d_ij","A","d_ij",")",")","where","A","is","a","diagonal","matrix","(","in","the","form","of","a","column","vector","'","w","'",")","."]
code: def _D_constraint(self, neg_pairs, w):
      """Compute the value, 1st derivative, second derivative (Hessian) of
      a dissimilarity constraint function gF(sum_ij distance(d_ij A d_ij))
      where A is a diagonal matrix (in the form of a column vector 'w').
      """
      diff = neg_pairs[:, 0, :] - neg_pairs[:, 1, :]
      diff_sq = diff * diff
      dist = np.sqrt(diff_sq.dot(w))
      sum_deri1 = np.einsum(
          "ij,i", diff_sq, 0.5 / np.maximum(dist, 1e-6)
      )
      sum_deri2 = np.einsum(
          "ij,ik->jk",
          diff_sq,
          diff_sq / (-4 * np.maximum(1e-6, dist**3))[:, None],
      )
      sum_dist = dist.sum()
      return (
          np.log(sum_dist),
          sum_deri1 / sum_dist,
          sum_deri2 / sum_dist
          - np.outer(sum_deri1, sum_deri1) / (sum_dist * sum_dist),
      )
  
imports: import numpy
  from sklearn.base import TransformerMixin
  from sklearn.utils.validation import assert_all_finite
  from .base_metric import _PairsClassifierMixin, MahalanobisMixin
  from .constraints import Constraints, wrap_pairs
  from ._util import components_from_metric, _initialize_metric_mahalanobis
  import warnings
label_desc: Use image node_id 10 for calling the _BaseMMC obj's underlying member method code with example usage: obj._D_constraint(neg_pairs, w) and returns: np,  unknown,  unknown