code: def cylinders_and_ball_soderman(
      gtab,
      tau,
      radii=(5e-3, 5e-3),
      D=0.7e-3,
      S0=1.0,
      angles=((0, 0), (90, 0)),
      fractions=(35, 35),
      snr=20,
  ):
      r"""Calculates the three-dimensional signal attenuation E(q) originating
      from within a cylinder of radius R using the Soderman approximation [1]_.
      The diffusion signal is assumed to be separable perpendicular and parallel
      to the cylinder axis [2]_.
      This function is basically an extension of the ball and stick model.
      Setting the radius to zero makes them equivalent.
  
      Parameters
      ----------
      gtab : GradientTable
          Signal measurement directions.
      tau : float
          diffusion time in s
      radii : array-like, optional
          cylinder radius in mm
      D : float, optional
          diffusion constant
      S0 : float, optional
          Unweighted signal value.
      angles : array (K, 2) or (K, 3), optional
          List of K polar angles (in degrees) for the sticks or array of K
          sticks as unit vectors.
      fractions : array-like, optional
          Percentage of each stick.  Remainder to 100 specifies isotropic
          component.
      snr : float, optional
          Signal to noise ratio, assuming Rician noise.  If set to None, no
          noise is added.
  
      Returns
      -------
      E : array, shape (N,)
          signal attenuation
  
      References
      ----------
      .. [1] Söderman, Olle, and Bengt Jönsson. "Restricted diffusion in
             cylindrical geometry." Journal of Magnetic Resonance, Series A
             117.1 (1995): 94-97.
      .. [2] Assaf, Yaniv, et al. "New modeling and experimental framework to
             characterize hindered and restricted water diffusion in brain white
             matter." Magnetic Resonance in Medicine 52.5 (2004): 965-978.
  
      """
      qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi)
      qvecs = qvals[:, None] * gtab.bvecs
      q_norm = np.sqrt(np.einsum("ij,ij->i", qvecs, qvecs))
  
      fractions = [f / 100.0 for f in fractions]
      f0 = 1 - np.sum(fractions)
  
      S = np.zeros(len(gtab.bvals))
      sticks = _check_directions(angles)
  
      for i, f in enumerate(fractions):
          q_par = abs(np.dot(qvecs, sticks[i]))
          q_perp = np.sqrt(q_norm**2 - q_par**2)
          S_cylinder = callaghan_perpendicular(
              q_perp, radii[i]
          ) * gaussian_parallel(q_par, tau, D=D)
          S += f * S_cylinder
  
      S += f0 * np.exp(-gtab.bvals * D)
      S *= S0
      S[gtab.b0s_mask] = S0
      S = add_noise(S, snr, S0)
  
      return S, sticks
  
imports: import numpy
  from numpy import dot
  from dipy.core.geometry import sphere2cart
  from dipy.core.geometry import vec2vec_rotmat
  from dipy.core.gradients import GradientTable
  from dipy.reconst.utils import dki_design_matrix
  from scipy.special import jn
label_desc: Use image node_id 9 for calling a global function with example usage: cylinders_and_ball_soderman(gtab, tau, radii, D, S0, angles, fractions, snr) and returns: S,  sticks