root(method=’krylov’)¶

scipy.optimize.root(fun, x0, args=(), method='krylov', tol=None, callback=None, options={})

See also

For documentation for the rest of the parameters, see scipy.optimize.root

Options:

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 : {‘lgmres’, ‘gmres’, ‘bicgstab’, ‘cgs’, ‘minres’} or function 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`. 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.

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 : {‘lgmres’, ‘gmres’, ‘bicgstab’, ‘cgs’, ‘minres’} or function

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.

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.

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