code: def test_for_very_close_to_zero(self):
      H = np.array(
          [
              [
                  0.88547534,
                  2.90692271,
                  0.98440885,
                  -0.78911503,
                  -0.28035809,
              ],
              [
                  2.90692271,
                  -0.04618819,
                  0.32867263,
                  -0.83737945,
                  0.17116396,
              ],
              [
                  0.98440885,
                  0.32867263,
                  -0.87355957,
                  -0.06521957,
                  -1.43030957,
              ],
              [
                  -0.78911503,
                  -0.83737945,
                  -0.06521957,
                  -1.645709,
                  -0.33887298,
              ],
              [
                  -0.28035809,
                  0.17116396,
                  -1.43030957,
                  -0.33887298,
                  -1.68586978,
              ],
          ]
      )
      g = np.array([0, 0, 0, 0, 1e-6])
      trust_radius = 1.1
  
      # Solve Subproblem
      subprob = KrylovQP(
          x=0,
          fun=lambda x: 0,
          jac=lambda x: g,
          hess=lambda x: None,
          hessp=lambda x, y: H.dot(y),
      )
      p, hits_boundary = subprob.solve(trust_radius)
  
      # check kkt satisfaction
      assert_almost_equal(
          np.linalg.norm(H.dot(p) + subprob.lam * p + g), 0.0
      )
      # check trust region constraint
      assert_almost_equal(np.linalg.norm(p), trust_radius)
  
      assert_array_almost_equal(
          p,
          [
              0.06910534,
              -0.01432721,
              -0.65311947,
              -0.23815972,
              -0.84954934,
          ],
      )
      assert_array_almost_equal(hits_boundary, True)
  
file_path: catboost/contrib/python/scipy/py3/scipy/optimize/tests/test_trustregion_krylov.py
imports: import numpy
  from scipy.optimize._trlib import get_trlib_quadratic_subproblem
  from numpy.testing import assert_, assert_almost_equal, assert_equal, assert_array_almost_equal
label_desc: Use image node_id 4 for calling the TestKrylovQuadraticSubproblem obj's underlying member method code with example usage: obj.test_for_very_close_to_zero() without return types