code: def test_for_first_element_equal_to_zero(self):
      # Define test matrix A.
      # Note that the leading 2x2 submatrix is singular.
      A = np.array([[0, 3, 11], [3, 12, 5], [11, 5, 6]])
  
      # Get Cholesky from lapack functions
      (cholesky,) = get_lapack_funcs(("potrf",), (A,))
  
      # Compute Cholesky Decomposition
      c, k = cholesky(A, lower=False, overwrite_a=False, clean=True)
  
      delta, v = singular_leading_submatrix(A, c, k)
  
      A[k - 1, k - 1] += delta
  
      # Check if the leading submatrix is singular
      assert_array_almost_equal(det(A[:k, :k]), 0)
  
      # Check if `v` fullfil the specified properties
      quadratic_term = np.dot(v, np.dot(A, v))
      assert_array_almost_equal(quadratic_term, 0)
  
imports: from __future__ import division, print_function, absolute_import
  import numpy
  from scipy.optimize._trustregion_exact import estimate_smallest_singular_value, singular_leading_submatrix, IterativeSubproblem
  from scipy.linalg import svd, get_lapack_funcs, det, cho_factor, cho_solve, qr, eigvalsh, eig, norm
  from numpy.testing import assert_, assert_array_equal, assert_equal, assert_array_almost_equal, assert_array_less
label_desc: Use image node_id 3 for calling the TestSingularLeadingSubmatrix obj's underlying member method code with example usage: obj.test_for_first_element_equal_to_zero() without return types