scipy.optimize.fixed_point(func, x0, args=(), xtol=1e-08, maxiter=500)[source]

Find the point where func(x) == x

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

Uses Steffensen’s Method using Aitken’s Del^2 convergence acceleration. See Burden, Faires, “Numerical Analysis”, 5th edition, pg. 80


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

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