`scipy.optimize._nonlin:anderson`

Signature

   def     anderson (    F    ,    xin    ,    iter    =  None   ,    alpha    =  None   ,    w0    =  0.01   ,    M    =  5   ,    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      )

Summary

Find a root of a function, using (extended) Anderson mixing.

Extended Summary

The Jacobian is formed by for a 'best' solution in the space spanned by last M vectors. As a result, only a MxM matrix inversions and MxN multiplications are required. [Ey]

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
alpha : float, optional: Initial guess for the Jacobian is (-1/alpha).
M : float, optional: Number of previous vectors to retain. Defaults to 5.
w0 : float, optional: Regularization parameter for numerical stability. Compared to unity, good values of the order of 0.01.
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.

Examples

The following functions define a system of nonlinear equations

def fun(x):
    return [x[0]  + 0.5 * (x[0] - x[1])**3 - 1.0,
            0.5 * (x[1] - x[0])**3 + x[1]]

✓

A solution can be obtained as follows.

from scipy import optimize
sol = optimize.anderson(fun, [0, 0])

✓

sol

✗

Aliases

scipy.optimize.anderson