code: def qti_signal(gtab, D, C, S0=1):
      """Generate signals using the covariance tensor signal representation.
  
      Parameters
      ----------
      gtab : dipy.core.gradients.GradientTable
          Gradient table with b-tensors.
      D : numpy.ndarray
          Diffusion tensors of shape (..., 3, 3), (..., 6, 1), or (..., 6).
      C : numpy.ndarray
          Covariance tensors of shape (..., 6, 6), (..., 21, 1), or (..., 21).
      S0 : numpy.ndarray, optional
          Signal magnitudes without diffusion-weighting. Must be a single number
          or an array of same shape as D and C without the last two dimensions.
  
      Returns
      -------
      S : numpy.ndarray
          Simulated signals.
  
      Notes
      -----
      The signal is generated according to
  
          .. math::
  
              S = S_0 \exp \left(- \mathbf{b} : \langle \mathbf{D} \rangle
              + \frac{1}{2}(\mathbf{b} \otimes \mathbf{b}) : \mathbb{C} \right)
      """
  
      # Validate input and convert to Voigt notation if necessary
      if gtab.btens is None:
          raise ValueError(
              "QTI requires b-tensors to be defined in the gradient table."
          )
      if D.shape[-2::] != (6, 1):
          if D.shape[-2::] == (3, 3):
              D = from_3x3_to_6x1(D)
          elif D.shape[-1] == 6:
              D = D[..., np.newaxis]
          else:
              raise ValueError(
                  "The shape of D must be (..., 3, 3), (..., 6, 1) or (..., 6)."
              )
      if C.shape[-2::] != (21, 1):
          if C.shape[-2::] == (6, 6):
              C = from_6x6_to_21x1(C)
          elif C.shape[-1] == 21:
              C = C[..., np.newaxis]
          else:
              raise ValueError(
                  "The shape of C must be (..., 6, 6), (..., 21, 1), or "
                  + "(..., 21)."
              )
      if D.shape[0:-2] != C.shape[0:-2]:
          raise ValueError("The shapes of C and D are not compatible")
      if not isinstance(S0, (int, float)):
          if S0.shape != (1,) and S0.shape != D.shape[0:-2]:
              raise ValueError(
                  "S0 must be a single number or an array of the same shape "
                  + " compatible with D and C."
              )
  
      # Generate signals
      S = np.zeros(D.shape[0:-2] + (gtab.btens.shape[0],))
      for i, bten in enumerate(gtab.btens):
          b = from_3x3_to_6x1(bten)
          b_sq = from_6x6_to_21x1(b @ np.swapaxes(b, -2, -1))
          S[..., i] = (
              S0
              * np.exp(
                  -np.swapaxes(b, -2, -1) @ D
                  + 0.5 * np.swapaxes(b_sq, -2, -1) @ C
              )[..., 0, 0]
          )
      return S
  
imports: from warnings import warn
  import numpy
  from dipy.reconst.base import ReconstModel
  from dipy.reconst.dti import auto_attr
  from dipy.utils.optpkg import optional_package
label_desc: Use image node_id 8 for calling a global function with example usage: qti_signal(gtab, D, C, S0) and returns: S