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

nitint, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

dispbool, optional

Print status to stdout on every iteration.

maxiterint, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftolfloat, optional

Relative tolerance for the residual. If omitted, not used.

fatolfloat, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtolfloat, optional

Relative minimum step size. If omitted, not used.

xatolfloat, 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_normfunction(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_optionsdict, optional

Options for the respective Jacobian approximation.

rdifffloat, 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_MLinearOperator 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_kint, optional

Size of the subspace kept across LGMRES nonlinear iterations.

See scipy.sparse.linalg.lgmres for details.