anderson#
- scipy.optimize.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)#
- Find a root of a function, using (extended) Anderson mixing. - 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:
- 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 guess for the Jacobian is (-1/alpha). 
- Mfloat, optional
- Number of previous vectors to retain. Defaults to 5. 
- w0float, optional
- Regularization parameter for numerical stability. Compared to unity, good values of the order of 0.01. 
- 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, - NoConvergenceis 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. 
 
 - See also - root
- Interface to root finding algorithms for multivariate functions. See - method='anderson'in particular.
 - References [Ey]- Eyert, J. Comp. Phys., 124, 271 (1996). 
 - 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 array([0.84116588, 0.15883789])