code: def _root_krylov_doc():
      """
      Options
      -------
      nit : int, optional
          Number of iterations to make. If omitted (default), make as many
          as required to meet tolerances.
      disp : bool, optional
          Print status to stdout on every iteration.
      maxiter : int, optional
          Maximum number of iterations to make. If more are needed to
          meet convergence, `NoConvergence` is raised.
      ftol : float, optional
          Relative tolerance for the residual. If omitted, not used.
      fatol : float, optional
          Absolute tolerance (in max-norm) for the residual.
          If omitted, default is 6e-6.
      xtol : float, optional
          Relative minimum step size. If omitted, not used.
      xatol : float, optional
          Absolute minimum step size, as determined from the Jacobian
          approximation. If the step size is smaller than this, optimization
          is terminated as successful. If omitted, not used.
      tol_norm : function(vector) -> scalar, optional
          Norm to use in convergence check. Default is the maximum norm.
      line_search : {None, 'armijo' (default), 'wolfe'}, optional
          Which type of a line search to use to determine the step size in
          the direction given by the Jacobian approximation. Defaults to
          'armijo'.
      jac_options : dict, optional
          Options for the respective Jacobian approximation.
  
          rdiff : float, optional
              Relative step size to use in numerical differentiation.
          method : str or callable, optional
              Krylov method to use to approximate the Jacobian.  Can be a string,
              or a function implementing the same interface as the iterative
              solvers in `scipy.sparse.linalg`. If a string, needs to be one of:
              ``'lgmres'``, ``'gmres'``, ``'bicgstab'``, ``'cgs'``, ``'minres'``,
              ``'tfqmr'``.
  
              The default is `scipy.sparse.linalg.lgmres`.
          inner_M : LinearOperator or InverseJacobian
              Preconditioner for the inner Krylov iteration.
              Note that you can use also inverse Jacobians as (adaptive)
              preconditioners. For example,
  
              >>> jac = BroydenFirst()
              >>> kjac = KrylovJacobian(inner_M=jac.inverse).
  
              If the preconditioner has a method named 'update', it will
              be called as ``update(x, f)`` after each nonlinear step,
              with ``x`` giving the current point, and ``f`` the current
              function value.
          inner_tol, inner_maxiter, ...
              Parameters to pass on to the "inner" Krylov solver.
              See `scipy.sparse.linalg.gmres` for details.
          outer_k : int, optional
              Size of the subspace kept across LGMRES nonlinear
              iterations.
  
              See `scipy.sparse.linalg.lgmres` for details.
      """
      pass
  
file_path: scipy/scipy/optimize/_root.py
imports: import numpy
  from warnings import warn
  from ._optimize import MemoizeJac, OptimizeResult, _check_unknown_options
  from ._minpack_py import _root_hybr, leastsq
  from ._spectral import _root_df_sane
  from .None import _nonlin
label_desc: Use image node_id 11 for calling a global function with example usage: _root_krylov_doc() without return types