code: def test_expm_multiply_interval_vector(self):
      np.random.seed(1234)
      interval = {"start": 0.1, "stop": 3.2, "endpoint": True}
      for num, n in product([14, 13, 2], [1, 2, 5, 20, 40]):
          A = scipy.linalg.inv(np.random.randn(n, n))
          v = np.random.randn(n)
          samples = np.linspace(num=num, **interval)
          X = expm_multiply(A, v, num=num, **interval)
          for solution, t in zip(X, samples):
              assert_allclose(solution, sp_expm(t * A).dot(v))
          # test for linear operator with unknown trace -> estimate trace
          Xguess = estimated(expm_multiply)(
              aslinearoperator(A), v, num=num, **interval
          )
          # test for linear operator with given trace
          Xgiven = expm_multiply(
              aslinearoperator(A),
              v,
              num=num,
              **interval,
              traceA=np.trace(A),
          )
          # test robustness for linear operator with wrong trace
          Xwrong = expm_multiply(
              aslinearoperator(A),
              v,
              num=num,
              **interval,
              traceA=np.trace(A) * 5,
          )
          for sol_guess, sol_given, sol_wrong, t in zip(
              Xguess, Xgiven, Xwrong, samples
          ):
              correct = sp_expm(t * A).dot(v)
              assert_allclose(sol_guess, correct)
              assert_allclose(sol_given, correct)
              assert_allclose(sol_wrong, correct)
  
imports: from functools import partial
  from itertools import product
  import numpy
  import pytest
  from numpy.testing import assert_allclose, assert_, assert_equal, suppress_warnings
  from scipy.sparse import SparseEfficiencyWarning
  from scipy.sparse.linalg import aslinearoperator
  import scipy.linalg
  from scipy.sparse.linalg import expm
  from scipy.sparse.linalg._expm_multiply import _theta, _compute_p_max, _onenormest_matrix_power, expm_multiply, _expm_multiply_simple, _expm_multiply_interval
  from scipy._lib._util import np_long
label_desc: Use image node_id 2 for calling the TestExpmActionInterval obj's underlying member method code with example usage: obj.test_expm_multiply_interval_vector() without return types