SciPy

scipy.optimize.excitingmixing

scipy.optimize.excitingmixing(F, xin, iter=None, alpha=None, alphamax=1.0, verbose=False, maxiter=None, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None, tol_norm=None, line_search='armijo', callback=None, **kw)[source]

Find a root of a function, using a tuned diagonal Jacobian approximation.

The Jacobian matrix is diagonal and is tuned on each iteration.

Warning

This algorithm may be useful for specific problems, but whether it will work may depend strongly on the problem.

Parameters :

F : function(x) -> f

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

x0 : array_like

Initial guess for the solution

alpha : float, optional

Initial Jacobian approximation is (-1/alpha).

alphamax : float, optional

The entries of the diagonal Jacobian are kept in the range [alpha, alphamax].

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.

Returns :

sol : ndarray

An array (of similar array type as x0) containing the final solution.

Raises :

NoConvergence :

When a solution was not found.