code: def bg_update_dense(plu, perm_r, v, j):
      LU, p = plu
  
      vperm = v[perm_r]
      u = dtrsm(1, LU, vperm, lower=1, diag=1)
      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/py3/scipy/optimize/_remove_redundancy.py
imports: import numpy
  from scipy.linalg import svd
  from scipy.linalg.interpolative import interp_decomp
  import scipy
  from scipy.linalg.blas import dtrsm
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