root(method=’df-sane’)¶
-
scipy.optimize.
root
(fun, x0, args=(), method='df-sane', tol=None, callback=None, options={'func': None, 'ftol': 1e-08, 'fatol': 1e-300, 'maxfev': 1000, 'fnorm': None, 'disp': False, 'M': 10, 'eta_strategy': None, 'sigma_eps': 1e-10, 'sigma_0': 1.0, 'line_search': 'cruz'}) Solve nonlinear equation with the DF-SANE method
See also
For documentation for the rest of the parameters, see
scipy.optimize.root
Options: ftol : float, optional
Relative norm tolerance.
fatol : float, optional
Absolute norm tolerance. Algorithm terminates when
||func(x)|| < fatol + ftol ||func(x_0)||
.fnorm : callable, optional
Norm to use in the convergence check. If None, 2-norm is used.
maxfev : int, optional
Maximum number of function evaluations.
disp : bool, optional
Whether to print convergence process to stdout.
eta_strategy : callable, optional
Choice of the
eta_k
parameter, which gives slack for growth of||F||**2
. Called aseta_k = eta_strategy(k, x, F)
with k the iteration number, x the current iterate and F the current residual. Should satisfyeta_k > 0
andsum(eta, k=0..inf) < inf
. Default:||F||**2 / (1 + k)**2
.sigma_eps : float, optional
The spectral coefficient is constrained to
sigma_eps < sigma < 1/sigma_eps
. Default: 1e-10sigma_0 : float, optional
Initial spectral coefficient. Default: 1.0
M : int, optional
Number of iterates to include in the nonmonotonic line search. Default: 10
line_search : {‘cruz’, ‘cheng’}
Type of line search to employ. ‘cruz’ is the original one defined in [Martinez & Raydan. Math. Comp. 75, 1429 (2006)], ‘cheng’ is a modified search defined in [Cheng & Li. IMA J. Numer. Anal. 29, 814 (2009)]. Default: ‘cruz’
References
[R879] “Spectral residual method without gradient information for solving large-scale nonlinear systems of equations.” W. La Cruz, J.M. Martinez, M. Raydan. Math. Comp. 75, 1429 (2006). [R880] - La Cruz, Opt. Meth. Software, 29, 24 (2014).
[R881] - Cheng, D.-H. Li. IMA J. Numer. Anal. 29, 814 (2009).