code: def test_integration_sparse_difference():
      n = 200
      t_span = [0, 20]
      y0 = np.zeros(2 * n)
      y0[1::2] = 1
      sparsity = medazko_sparsity(n)
  
      for method in ["BDF", "Radau"]:
          res = solve_ivp(
              fun_medazko,
              t_span,
              y0,
              method=method,
              jac_sparsity=sparsity,
          )
  
          assert_equal(res.t[0], t_span[0])
          assert_(res.t_events is None)
          assert_(res.y_events is None)
          assert_(res.success)
          assert_equal(res.status, 0)
  
          assert_allclose(res.y[78, -1], 0.233994e-3, rtol=1e-2)
          assert_allclose(res.y[79, -1], 0, atol=1e-3)
          assert_allclose(res.y[148, -1], 0.359561e-3, rtol=1e-2)
          assert_allclose(res.y[149, -1], 0, atol=1e-3)
          assert_allclose(res.y[198, -1], 0.117374129e-3, rtol=1e-2)
          assert_allclose(res.y[199, -1], 0.6190807e-5, atol=1e-3)
          assert_allclose(res.y[238, -1], 0, atol=1e-3)
          assert_allclose(res.y[239, -1], 0.9999997, rtol=1e-2)
  
imports: from itertools import product
  from numpy.testing import assert_, assert_allclose, assert_array_less, assert_equal, assert_no_warnings, suppress_warnings
  import pytest
  from pytest import raises
  import numpy
  from scipy.optimize._numdiff import group_columns
  from scipy.integrate import solve_ivp, RK23, RK45, DOP853, Radau, BDF, LSODA
  from scipy.integrate import OdeSolution
  from scipy.integrate._ivp.common import num_jac
  from scipy.integrate._ivp.base import ConstantDenseOutput
  from scipy.sparse import coo_matrix, csc_matrix
label_desc: Use image node_id 22 for calling a global function with example usage: test_integration_sparse_difference() without return types