fixed_point — SciPy v1.15.3 Manual (original) (raw)

scipy.optimize.

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

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:

funcfunction

Function to evaluate.

x0array_like

Fixed point of function.

argstuple, optional

Extra arguments to func.

xtolfloat, optional

Convergence tolerance, defaults to 1e-08.

maxiterint, 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^2convergence acceleration [1]. The “iteration” method simply iterates the function until convergence is detected, without attempting to accelerate the convergence.

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])