code: def test_carlson_rf():
      # Define inputs that we know the outputs from:
      # Carlson, B.C., 1994. Numerical computation of real or complex
      # elliptic integrals. arXiv:math/9409227 [math.CA]
  
      # Real values (test in 2D format)
      x = np.array([[1.0, 0.5], [2.0, 2.0]])
      y = np.array([[2.0, 1.0], [3.0, 3.0]])
      z = np.array([[0.0, 0.0], [4.0, 4.0]])
  
      # Define reference outputs
      RF_ref = np.array(
          [
              [1.3110287771461, 1.8540746773014],
              [0.58408284167715, 0.58408284167715],
          ]
      )
  
      # Compute integrals
      RF = carlson_rf(x, y, z)
  
      # Compare
      assert_array_almost_equal(RF, RF_ref)
  
      # Complex values
      x = np.array([1j, 1j - 1, 1j, 1j - 1])
      y = np.array([-1j, 1j, -1j, 1j])
      z = np.array([0.0, 0.0, 2, 1 - 1j])
  
      # Define reference outputs
      RF_ref = np.array(
          [
              1.8540746773014,
              0.79612586584234 - 1.2138566698365j,
              1.0441445654064,
              0.93912050218619 - 0.53296252018635j,
          ]
      )
      # Compute integrals
      RF = carlson_rf(x, y, z, errtol=3e-5)
  
      # Compare
      assert_array_almost_equal(RF, RF_ref)
  
imports: import numpy
  import random
  import dipy.reconst.dki
  import dipy.reconst.dti
  from numpy.testing import assert_array_almost_equal, assert_array_equal, assert_almost_equal, assert_raises
  from dipy.sims.voxel import multi_tensor_dki
  from dipy.io.gradients import read_bvals_bvecs
  from dipy.core.gradients import gradient_table
  from dipy.data import get_fnames
  from dipy.reconst.dti import from_lower_triangular, decompose_tensor
  from dipy.reconst.dki import mean_kurtosis, carlson_rf, carlson_rd, axial_kurtosis, radial_kurtosis, mean_kurtosis_tensor, _positive_evals, lower_triangular, kurtosis_fractional_anisotropy
  from dipy.core.sphere import Sphere
  from dipy.data import default_sphere
  from dipy.core.geometry import sphere2cart
  from dipy.utils.optpkg import optional_package
  from dipy.utils.tripwire import TripWireError
label_desc: Use image node_id 8 for calling a global function with example usage: test_carlson_rf() without return types