statsmodels.tools.numdiff.approx_fprime(x, f, epsilon=None, args=(), kwargs={}, centered=False) [source]

Gradient of function, or Jacobian if function f returns 1d array

  • x (array) – 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.

grad – gradient or Jacobian

Return type:



If f returns a 1d array, it returns a Jacobian. If a 2d array is returned by f (e.g., with a value for each observation), it returns a 3d array with the Jacobian of each observation with shape xk x nobs x xk. I.e., the Jacobian of the first observation would be [:, 0, :]

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© 2006 Jonathan E. Taylor
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