code: def test_burkardt_3(self):
      # This example is due to Laub.
      # This matrix is ill-suited for the Taylor series approach.
      # As powers of A are computed, the entries blow up too quickly.
      exp1 = np.exp(1)
      exp39 = np.exp(39)
      A = np.array(
          [
              [0, 1],
              [-39, -40],
          ],
          dtype=float,
      )
      desired = np.array(
          [
              [
                  39 / (38 * exp1) - 1 / (38 * exp39),
                  -np.expm1(-38) / (38 * exp1),
              ],
              [
                  39 * np.expm1(-38) / (38 * exp1),
                  -1 / (38 * exp1) + 39 / (38 * exp39),
              ],
          ],
          dtype=float,
      )
      actual = expm(A)
      assert_allclose(actual, desired)
  
imports: from __future__ import division, print_function, absolute_import
  import math
  import numpy
  from numpy import array, eye, exp, random
  from numpy.linalg import matrix_power
  from numpy.testing import assert_allclose, assert_, assert_array_almost_equal, assert_equal, assert_array_almost_equal_nulp
  from scipy._lib._numpy_compat import suppress_warnings
  from scipy.sparse import csc_matrix, SparseEfficiencyWarning
  from scipy.sparse.construct import eye
  from scipy.sparse.linalg.matfuncs import expm, _expm, ProductOperator, MatrixPowerOperator, _onenorm_matrix_power_nnm
  from scipy.sparse.sputils import matrix
  from scipy.linalg import logm
  from scipy.special import factorial, binom
  import scipy.sparse
  import scipy.sparse.linalg
label_desc: Use image node_id 16 for calling the TestExpM obj's underlying member method code with example usage: obj.test_burkardt_3() without return types