root(method=’df-sane’)#
- scipy.optimize.root(fun, x0, args=(), method='hybr', jac=None, tol=None, callback=None, options=None)
- Solve nonlinear equation with the DF-SANE method - See also - For documentation for the rest of the parameters, see - scipy.optimize.root- Options:
- ——-
- ftolfloat, optional
- Relative norm tolerance. 
- fatolfloat, optional
- Absolute norm tolerance. Algorithm terminates when - ||func(x)|| < fatol + ftol ||func(x_0)||.
- fnormcallable, optional
- Norm to use in the convergence check. If None, 2-norm is used. 
- maxfevint, optional
- Maximum number of function evaluations. 
- dispbool, optional
- Whether to print convergence process to stdout. 
- eta_strategycallable, optional
- Choice of the - eta_kparameter, which gives slack for growth of- ||F||**2. Called as- eta_k = eta_strategy(k, x, F)with k the iteration number, x the current iterate and F the current residual. Should satisfy- eta_k > 0and- sum(eta, k=0..inf) < inf. Default:- ||F||**2 / (1 + k)**2.
- sigma_epsfloat, optional
- The spectral coefficient is constrained to - sigma_eps < sigma < 1/sigma_eps. Default: 1e-10
- sigma_0float, optional
- Initial spectral coefficient. Default: 1.0 
- Mint, 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 [1]- “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). [2]- La Cruz, Opt. Meth. Software, 29, 24 (2014). 
 [3]- Cheng, D.-H. Li. IMA J. Numer. Anal. 29, 814 (2009).