code: def _approx_fprime_scalar(
      x, f, epsilon=None, args=(), kwargs={}, centered=False
  ):
      """
      Gradient of function vectorized for scalar parameter.
  
      This assumes that the function ``f`` is vectorized for a scalar parameter.
      The function value ``f(x)`` has then the same shape as the input ``x``.
      The derivative returned by this function also has the same shape as ``x``.
  
      Parameters
      ----------
      x : ndarray
          Parameters at which the derivative is evaluated.
      f : function
          `f(*((x,)+args), **kwargs)` returning either one value or 1d array
      epsilon : float, optional
          Stepsize, if None, optimal stepsize is used. This is EPS**(1/2)*x for
          `centered` == False and EPS**(1/3)*x for `centered` == True.
      args : tuple
          Tuple of additional arguments for function `f`.
      kwargs : dict
          Dictionary of additional keyword arguments for function `f`.
      centered : bool
          Whether central difference should be returned. If not, does forward
          differencing.
  
      Returns
      -------
      grad : ndarray
          Array of derivatives, gradient evaluated at parameters ``x``.
      """
      x = np.asarray(x)
      n = 1
  
      f0 = f(*((x,) + args), **kwargs)
      if not centered:
          eps = _get_epsilon(x, 2, epsilon, n)
          grad = (f(*((x + eps,) + args), **kwargs) - f0) / eps
      else:
          eps = _get_epsilon(x, 3, epsilon, n) / 2.0
          grad = (
              f(*((x + eps,) + args), **kwargs)
              - f(*((x - eps,) + args), **kwargs)
          ) / (2 * eps)
  
      return grad
  
file_path: statsmodels/statsmodels/tools/numdiff.py
imports: import numpy
  from statsmodels.compat.pandas import Appender, Substitution
label_desc: Use image node_id 3 for calling a global function with example usage: _approx_fprime_scalar(x, f, epsilon, args, kwargs, centered) and returns: grad