scipy.optimize.linearmixing¶

scipy.optimize.linearmixing(F, xin, iter=None, alpha=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, **kw)[source]¶

Find a root of a function, using a scalar Jacobian approximation.

Warning

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

Parameters:

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 The Jacobian approximation is (-1/alpha). 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.

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

The Jacobian approximation is (-1/alpha).

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.