code: def test_big_problem_with_parameters():
      n = 30
      x = np.linspace(0, np.pi, 5)
      x_test = np.linspace(0, np.pi, 100)
      y = np.ones((2 * n, x.size))
  
      for fun_jac in [None, big_fun_with_parameters_jac]:
          for bc_jac in [None, big_bc_with_parameters_jac]:
              sol = solve_bvp(
                  big_fun_with_parameters,
                  big_bc_with_parameters,
                  x,
                  y,
                  p=[0.5, 0.5],
                  fun_jac=fun_jac,
                  bc_jac=bc_jac,
              )
  
              assert_equal(sol.status, 0)
              assert_(sol.success)
  
              assert_allclose(sol.p, [1, 1], rtol=1e-4)
  
              sol_test = sol.sol(x_test)
  
              for isol in range(0, n, 4):
                  assert_allclose(
                      sol_test[isol],
                      big_sol_with_parameters(x_test, [1, 1])[0],
                      rtol=1e-4,
                      atol=1e-4,
                  )
                  assert_allclose(
                      sol_test[isol + 2],
                      big_sol_with_parameters(x_test, [1, 1])[1],
                      rtol=1e-4,
                      atol=1e-4,
                  )
  
              f_test = big_fun_with_parameters(x_test, sol_test, [1, 1])
              r = sol.sol(x_test, 1) - f_test
              rel_res = r / (1 + np.abs(f_test))
              norm_res = np.sum(rel_res**2, axis=0) ** 0.5
              assert_(np.all(norm_res < 1e-3))
  
              assert_(np.all(sol.rms_residuals < 1e-3))
              assert_allclose(
                  sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10
              )
              assert_allclose(
                  sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10
              )
  
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 45 for calling a global function with example usage: test_big_problem_with_parameters() without return types