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)#

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:

Ffunction(x) -> f: Function whose root to find; should take and return an array-like object.
xinarray_like: Initial guess for the solution
alphafloat, optional: Initial Jacobian approximation is (-1/alpha).
alphamaxfloat, optional: The entries of the diagonal Jacobian are kept in the range [alpha, alphamax].
iterint, optional: Number of iterations to make. If omitted (default), make as many as required to meet tolerances.
verbosebool, 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.
f_tolfloat, optional: Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.
f_rtolfloat, optional: Relative tolerance for the residual. If omitted, not used.
x_tolfloat, 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_rtolfloat, optional: Relative minimum step size. 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’.
callbackfunction, 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:

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

Raises:

NoConvergence: When a solution was not found.