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nonlin_solve(F, x0, jacobian='krylov', iter=None, verbose=False, maxiter=None, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None, tol_norm=None, line_search='armijo', callback=None, full_output=False, raise_exception=True)

Notes

This algorithm implements the inexact Newton method, with backtracking or full line searches. Several Jacobian approximations are available, including Krylov and Quasi-Newton methods.

Parameters

F : function(x) -> f

Function whose root to find; should take and return an array-like object.

xin : array_like

Initial guess for the solution

jacobian : Jacobian

A Jacobian approximation: Jacobian object or something that asjacobian can transform to one. Alternatively, a string specifying which of the builtin Jacobian approximations to use:

krylov, broyden1, broyden2, anderson diagbroyden, linearmixing, excitingmixing

iter : int, optional

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

verbose : 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.

f_tol : float, optional

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

f_rtol : float, optional

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

x_tol : 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.

x_rtol : float, optional

Relative minimum step size. 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'.

callback : function, optional

Optional callback function. It is called on every iteration as callback(x, f) where x is the current solution and f the corresponding residual.

Raises

NoConvergence

When a solution was not found.

full_output : bool

If true, returns a dictionary :None:None:`info` containing convergence information.

raise_exception : bool

If True, a NoConvergence exception is raise if no solution is found.

Returns

sol : ndarray

An array (of similar array type as :None:None:`x0`) containing the final solution.

Find a root of a function, in a way suitable for large-scale problems.

See Also

Jacobian
asjacobian

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.optimize._nonlin._nonlin_wrapper

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GitHub : /scipy/optimize/_nonlin.py#115
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