code: def test_compute_bc_jac():
      ya = np.array([-1.0, 2])
      yb = np.array([0.5, 3])
      p = np.array([])
      dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(
          lambda ya, yb, p: exp_bc(ya, yb), ya, yb, p
      )
      dbc_dya_an, dbc_dyb_an = exp_bc_jac(ya, yb)
      assert_allclose(dbc_dya, dbc_dya_an)
      assert_allclose(dbc_dyb, dbc_dyb_an)
      assert_(dbc_dp is None)
  
      ya = np.array([0.0, 1])
      yb = np.array([0.0, -1])
      p = np.array([0.5])
      dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(sl_bc, ya, yb, p)
      dbc_dya_an, dbc_dyb_an, dbc_dp_an = sl_bc_jac(ya, yb, p)
      assert_allclose(dbc_dya, dbc_dya_an)
      assert_allclose(dbc_dyb, dbc_dyb_an)
      assert_allclose(dbc_dp, dbc_dp_an)
  
      ya = np.array([0.5, 100])
      yb = np.array([-1000, 10.5])
      p = np.array([])
      dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(
          lambda ya, yb, p: emden_bc(ya, yb), ya, yb, p
      )
      dbc_dya_an, dbc_dyb_an = emden_bc_jac(ya, yb)
      assert_allclose(dbc_dya, dbc_dya_an)
      assert_allclose(dbc_dyb, dbc_dyb_an)
      assert_(dbc_dp is None)
  
imports: import sys
  import numpy
  from numpy.testing import assert_, assert_array_equal, assert_allclose, assert_equal
  from pytest import raises
  from scipy.sparse import coo_matrix
  from scipy.special import erf
  from scipy.integrate._bvp import modify_mesh, estimate_fun_jac, estimate_bc_jac, compute_jac_indices, construct_global_jac, solve_bvp
label_desc: Use image node_id 35 for calling a global function with example usage: test_compute_bc_jac() without return types