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# scipy.optimize.fixed_point

`scipy.optimize.``fixed_point`(func, x0, args=(), xtol=1e-08, maxiter=500, method='del2')

  Find a fixed point of the function.

  Given a function of one or more variables and a starting point, find a fixed-point of the function: i.e. where `func(x0) == x0`.

  Parameters:

  func : function

  > Function to evaluate.

  x0 : array_like

  > Fixed point of function.

  args : tuple, optional

  > Extra arguments to func.

  xtol : float, optional

  > Convergence tolerance, defaults to 1e-08.

  maxiter : int, optional

  > Maximum number of iterations, defaults to 500.

  method : {“del2”, “iteration”}, optional

  > Method of finding the fixed-point, defaults to “del2” which uses Steffensen’s Method with Aitken’s `Del^2` convergence acceleration [R143]. The “iteration” method simply iterates the function until convergence is detected, without attempting to accelerate the convergence.

  References

  [R143] | (1, 2) Burden, Faires, “Numerical Analysis”, 5th edition, pg. 80

  Examples

      >>> from scipy import optimize
      >>> def func(x, c1, c2):
      ...    return np.sqrt(c1/(x+c2))
      >>> c1 = np.array([10,12.])
      >>> c2 = np.array([3, 5.])
      >>> optimize.fixed_point(func, [1.2, 1.3], args=(c1,c2))
      array([ 1.4920333 ,  1.37228132])