code: def bg_update_dense(plu, perm_r, v, j):
      LU, p = plu
  
      u = scipy.linalg.solve_triangular(
          LU, v[perm_r], lower=True, unit_diagonal=True
      )
      LU[: j + 1, j] = u[: j + 1]
      l = u[j + 1 :]
      piv = LU[j, j]
      LU[j + 1 :, j] += l / piv
      return LU, p
  
file_path: catboost/contrib/python/scipy/py2/scipy/optimize/_remove_redundancy.py
imports: from __future__ import division, print_function, absolute_import
  import numpy
  from scipy.linalg import svd
  import scipy
label_desc: Use image node_id 4 for calling a global function with example usage: bg_update_dense(plu, perm_r, v, j) and returns: LU,  p