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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(xf) == xf`.

  Parameters:
    func function

      Function to evaluate.

    x0 array_like

      Guess of 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 [1]. The “iteration” method simply iterates the function until convergence is detected, without attempting to accelerate the convergence.

  Returns:
    xf array

      Fixed point of function.

  References

  [1]

  Burden, Faires, “Numerical Analysis”, 5th edition, pg. 80

  Examples

      >>> import numpy as np
      >>> 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])