code: def forecast_error_func(x, b_unique, E):
      r"""Calculates the difference between the mean signal calculated using
      the parameter vector x and the average signal E using FORECAST and SMT
      """
      d_par = np.cos(x[0]) ** 2 * 3e-03
      d_perp = np.cos(x[1]) ** 2 * 3e-03
  
      if d_perp >= d_par:
          d_par, d_perp = d_perp, d_par
  
      E_reconst = (
          0.5
          * np.exp(-b_unique * d_perp)
          * psi_l(0, (b_unique * (d_par - d_perp)))
      )
  
      v = E - E_reconst
      return v
  
imports: from warnings import warn
  import numpy
  from dipy.reconst.cache import Cache
  from dipy.reconst.multi_voxel import multi_voxel_fit
  from dipy.reconst.csdeconv import csdeconv
  from dipy.reconst.shm import real_sh_descoteaux_from_index
  from scipy.special import gamma, hyp1f1
  from dipy.core.geometry import cart2sphere
  from dipy.data import default_sphere
  from dipy.reconst.odf import OdfModel, OdfFit
  from scipy.optimize import leastsq
  from dipy.utils.optpkg import optional_package
label_desc: Use image node_id 2 for calling a global function with example usage: forecast_error_func(x, b_unique, E) and returns: v