code: def test_array_rtol():
      # solve_ivp had a bug with array_like `rtol`; see gh-15482
      # check that it's fixed
      def f(t, y):
          return y[0], y[1]
  
      # no warning (or error) when `rtol` is array_like
      sol = solve_ivp(f, (0, 1), [1.0, 1.0], rtol=[1e-1, 1e-1])
      err1 = np.abs(np.linalg.norm(sol.y[:, -1] - np.exp(1)))
  
      # warning when an element of `rtol` is too small
      with pytest.warns(UserWarning, match="At least one element..."):
          sol = solve_ivp(f, (0, 1), [1.0, 1.0], rtol=[1e-1, 1e-16])
          err2 = np.abs(np.linalg.norm(sol.y[:, -1] - np.exp(1)))
  
      # tighter rtol improves the error
      assert err2 < err1
  
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 41 for calling a global function with example usage: test_array_rtol() and returns: y,  y