code: def modified_lu(q):
      """Perform a modified LU decomposition of a matrix.
  
      This takes a matrix q with orthonormal columns, returns l, u, s such that
      q - s = l * u.
  
      Args:
          q: A two dimensional orthonormal matrix q.
  
      Returns:
          A tuple of a lower triangular matrix l, an upper triangular matrix u,
              and a a vector representing a diagonal matrix s such that
              q - s = l * u.
      """
      q = q.assemble()
      m, b = q.shape[0], q.shape[1]
      S = np.zeros(b)
  
      q_work = np.copy(q)
  
      for i in range(b):
          S[i] = -1 * np.sign(q_work[i, i])
          q_work[i, i] -= S[i]
          # Scale ith column of L by diagonal element.
          q_work[(i + 1) : m, i] /= q_work[i, i]
          # Perform Schur complement update.
          q_work[(i + 1) : m, (i + 1) : b] -= np.outer(
              q_work[(i + 1) : m, i], q_work[i, (i + 1) : b]
          )
  
      L = np.tril(q_work)
      for i in range(b):
          L[i, i] = 1
      U = np.triu(q_work)[:b, :]
      # TODO(rkn): Get rid of the put below.
      return ray.get(core.numpy_to_dist.remote(ray.put(L))), U, S
  
file_path: ray/python/ray/experimental/array/distributed/linalg.py
imports: import numpy
  import ray
  import ray.experimental.array.remote
  from .None import core
label_desc: Use image node_id 2 for calling a global function with example usage: modified_lu(q) and returns: ray,  U,  S