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

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_k` parameter, 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 > 0` and `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]
1. La Cruz, Opt. Meth. Software, 29, 24 (2014).

[3]
1. Cheng, D.-H. Li. IMA J. Numer. Anal. 29, 814 (2009).