Module « scipy.optimize »

Fonction fmin_ncg - module scipy.optimize

Signature de la fonction fmin_ncg

def fmin_ncg(f, x0, fprime, fhess_p=None, fhess=None, args=(), avextol=1e-05, epsilon=1.4901161193847656e-08, maxiter=None, full_output=0, disp=1, retall=0, callback=None) 

Description

fmin_ncg.__doc__

    Unconstrained minimization of a function using the Newton-CG method.

    Parameters
    ----------
    f : callable ``f(x, *args)``
        Objective function to be minimized.
    x0 : ndarray
        Initial guess.
    fprime : callable ``f'(x, *args)``
        Gradient of f.
    fhess_p : callable ``fhess_p(x, p, *args)``, optional
        Function which computes the Hessian of f times an
        arbitrary vector, p.
    fhess : callable ``fhess(x, *args)``, optional
        Function to compute the Hessian matrix of f.
    args : tuple, optional
        Extra arguments passed to f, fprime, fhess_p, and fhess
        (the same set of extra arguments is supplied to all of
        these functions).
    epsilon : float or ndarray, optional
        If fhess is approximated, use this value for the step size.
    callback : callable, optional
        An optional user-supplied function which is called after
        each iteration. Called as callback(xk), where xk is the
        current parameter vector.
    avextol : float, optional
        Convergence is assumed when the average relative error in
        the minimizer falls below this amount.
    maxiter : int, optional
        Maximum number of iterations to perform.
    full_output : bool, optional
        If True, return the optional outputs.
    disp : bool, optional
        If True, print convergence message.
    retall : bool, optional
        If True, return a list of results at each iteration.

    Returns
    -------
    xopt : ndarray
        Parameters which minimize f, i.e., ``f(xopt) == fopt``.
    fopt : float
        Value of the function at xopt, i.e., ``fopt = f(xopt)``.
    fcalls : int
        Number of function calls made.
    gcalls : int
        Number of gradient calls made.
    hcalls : int
        Number of Hessian calls made.
    warnflag : int
        Warnings generated by the algorithm.
        1 : Maximum number of iterations exceeded.
        2 : Line search failure (precision loss).
        3 : NaN result encountered.
    allvecs : list
        The result at each iteration, if retall is True (see below).

    See also
    --------
    minimize: Interface to minimization algorithms for multivariate
        functions. See the 'Newton-CG' `method` in particular.

    Notes
    -----
    Only one of `fhess_p` or `fhess` need to be given.  If `fhess`
    is provided, then `fhess_p` will be ignored. If neither `fhess`
    nor `fhess_p` is provided, then the hessian product will be
    approximated using finite differences on `fprime`. `fhess_p`
    must compute the hessian times an arbitrary vector. If it is not
    given, finite-differences on `fprime` are used to compute
    it.

    Newton-CG methods are also called truncated Newton methods. This
    function differs from scipy.optimize.fmin_tnc because

    1. scipy.optimize.fmin_ncg is written purely in Python using NumPy
        and scipy while scipy.optimize.fmin_tnc calls a C function.
    2. scipy.optimize.fmin_ncg is only for unconstrained minimization
        while scipy.optimize.fmin_tnc is for unconstrained minimization
        or box constrained minimization. (Box constraints give
        lower and upper bounds for each variable separately.)

    References
    ----------
    Wright & Nocedal, 'Numerical Optimization', 1999, p. 140.