# 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:
    ——-
    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 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_eps float, optional

      The spectral coefficient is constrained to `sigma_eps < sigma < 1/sigma_eps`. Default: 1e-10

    sigma_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

  [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]

  23. La Cruz, Opt. Meth. Software, 29, 24 (2014).

  [3]

  23. Cheng, D.-H. Li. IMA J. Numer. Anal. 29, 814 (2009).