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bundles / scipy 2.0.0.dev0+git20260907.41eeb59 / scipy / optimize / _nonlin / diagbroyden

function

scipy.optimize._nonlin:diagbroyden

Signature

def diagbroyden(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)

Summary

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

Extended Summary

The Jacobian approximation is derived from previous iterations, by retaining only the diagonal of Broyden matrices.

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).

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.diagbroyden(fun, [0, 0])
✓
sol
✗
array([0.841, 0.159])

See also

root

Interface to root finding algorithms for multivariate functions. See method='diagbroyden' in particular.

Aliases

  • scipy.optimize.diagbroyden