code: def _remove_redundancy_svd(A, b):
      """
      Eliminates redundant equations from system of equations defined by Ax = b
      and identifies infeasibilities.
  
      Parameters
      ----------
      A : 2-D array
          An array representing the left-hand side of a system of equations
      b : 1-D array
          An array representing the right-hand side of a system of equations
  
      Returns
      -------
      A : 2-D array
          An array representing the left-hand side of a system of equations
      b : 1-D array
          An array representing the right-hand side of a system of equations
      status: int
          An integer indicating the status of the system
          0: No infeasibility identified
          2: Trivially infeasible
      message : str
          A string descriptor of the exit status of the optimization.
  
      References
      ----------
      .. [2] Andersen, Erling D. "Finding all linearly dependent rows in
             large-scale linear programming." Optimization Methods and Software
             6.3 (1995): 219-227.
  
      """
  
      A, b, status, message = _remove_zero_rows(A, b)
  
      if status != 0:
          return A, b, status, message
  
      U, s, Vh = svd(A)
      eps = np.finfo(float).eps
      tol = s.max() * max(A.shape) * eps
  
      m, n = A.shape
      s_min = s[-1] if m <= n else 0
  
      # this algorithm is faster than that of [2] when the nullspace is small
      # but it could probably be improvement by randomized algorithms and with
      # a sparse implementation.
      # it relies on repeated singular value decomposition to find linearly
      # dependent rows (as identified by columns of U that correspond with zero
      # singular values). Unfortunately, only one row can be removed per
      # decomposition (I tried otherwise; doing so can cause problems.)
      # It would be nice if we could do truncated SVD like sp.sparse.linalg.svds
      # but that function is unreliable at finding singular values near zero.
      # Finding max eigenvalue L of A A^T, then largest eigenvalue (and
      # associated eigenvector) of -A A^T + L I (I is identity) via power
      # iteration would also work in theory, but is only efficient if the
      # smallest nonzero eigenvalue of A A^T is close to the largest nonzero
      # eigenvalue.
  
      while abs(s_min) < tol:
          v = U[
              :, -1
          ]  # TODO: return these so user can eliminate from problem?
          # rows need to be represented in significant amount
          eligibleRows = np.abs(v) > tol * 10e6
          if not np.any(eligibleRows) or np.any(np.abs(v.dot(A)) > tol):
              status = 4
              message = (
                  "Due to numerical issues, redundant equality "
                  "constraints could not be removed automatically. "
                  "Try providing your constraint matrices as sparse "
                  "matrices to activate sparse presolve, try turning "
                  "off redundancy removal, or try turning off presolve "
                  "altogether."
              )
              break
          if np.any(
              np.abs(v.dot(b)) > tol * 100
          ):  # factor of 100 to fix 10038 and 10349
              status = 2
              message = (
                  "There is a linear combination of rows of A_eq that "
                  "results in zero, suggesting a redundant constraint. "
                  "However the same linear combination of b_eq is "
                  "nonzero, suggesting that the constraints conflict "
                  "and the problem is infeasible."
              )
              break
  
          i_remove = _get_densest(A, eligibleRows)
          A = np.delete(A, i_remove, axis=0)
          b = np.delete(b, i_remove)
          U, s, Vh = svd(A)
          m, n = A.shape
          s_min = s[-1] if m <= n else 0
  
      return A, b, status, message
  
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 7 for calling a global function with example usage: _remove_redundancy_svd(A, b) and returns: A,  b,  status,  message, A,  b,  status,  message