code: def TLS_logL(v, X, dX):
      """Compute the total least squares log-likelihood
  
      This uses Hogg et al eq. 29-32
  
      Parameters
      ----------
      v : ndarray
          The normal vector to the linear best fit.  shape=(D,).
          Note that the magnitude |v| is a stand-in for the intercept.
      X : ndarray
          The input data.  shape = [N, D]
      dX : ndarray
          The covariance of the errors for each point.
          For diagonal errors, the shape = (N, D) and the entries are
          dX[i] = [sigma_x1, sigma_x2 ... sigma_xD]
          For full covariance, the shape = (N, D, D) and the entries are
          dX[i] = Cov(X[i], X[i]), the full error covariance.
  
      Returns
      -------
      logL : float
          The log-likelihood of the model v given the data.
  
      Notes
      -----
      This implementation follows Hogg 2010, arXiv 1008.4686
      """
      # check inputs
      X, dX, v = map(np.asarray, (X, dX, v))
      N, D = X.shape
      assert v.shape == (D,)
      assert dX.shape in ((N, D), (N, D, D))
  
      v_norm = np.linalg.norm(v)
      v_hat = v / v_norm
  
      # eq. 30
      Delta = np.dot(X, v_hat) - v_norm
  
      # eq. 31
      if dX.ndim == 2:
          # diagonal covariance
          Sig2 = np.sum(dX * v_hat**2, 1)
      else:
          # full covariance
          Sig2 = np.dot(np.dot(v_hat, dX), v_hat)
  
      return -0.5 * np.sum(np.log(2 * np.pi * Sig2)) - np.sum(
          0.5 * Delta**2 / Sig2
      )
  
label_desc: Use image node_id 1 for calling a global function with example usage: TLS_logL(v, X, dX) and returns: unknown