Module « scipy.optimize »

Fonction fmin_bfgs - module scipy.optimize

Signature de la fonction fmin_bfgs

def fmin_bfgs(f, x0, fprime=None, args=(), gtol=1e-05, norm=inf, epsilon=1.4901161193847656e-08, maxiter=None, full_output=0, disp=1, retall=0, callback=None) 

Description

fmin_bfgs.__doc__

    Minimize a function using the BFGS algorithm.

    Parameters
    ----------
    f : callable ``f(x,*args)``
        Objective function to be minimized.
    x0 : ndarray
        Initial guess.
    fprime : callable ``f'(x,*args)``, optional
        Gradient of f.
    args : tuple, optional
        Extra arguments passed to f and fprime.
    gtol : float, optional
        Gradient norm must be less than `gtol` before successful termination.
    norm : float, optional
        Order of norm (Inf is max, -Inf is min)
    epsilon : int or ndarray, optional
        If `fprime` is approximated, use this value for the step size.
    callback : callable, optional
        An optional user-supplied function to call after each
        iteration. Called as ``callback(xk)``, where ``xk`` is the
        current parameter vector.
    maxiter : int, optional
        Maximum number of iterations to perform.
    full_output : bool, optional
        If True, return ``fopt``, ``func_calls``, ``grad_calls``, and
        ``warnflag`` in addition to ``xopt``.
    disp : bool, optional
        Print convergence message if True.
    retall : bool, optional
        Return a list of results at each iteration if True.

    Returns
    -------
    xopt : ndarray
        Parameters which minimize f, i.e., ``f(xopt) == fopt``.
    fopt : float
        Minimum value.
    gopt : ndarray
        Value of gradient at minimum, f'(xopt), which should be near 0.
    Bopt : ndarray
        Value of 1/f''(xopt), i.e., the inverse Hessian matrix.
    func_calls : int
        Number of function_calls made.
    grad_calls : int
        Number of gradient calls made.
    warnflag : integer
        1 : Maximum number of iterations exceeded.
        2 : Gradient and/or function calls not changing.
        3 : NaN result encountered.
    allvecs : list
        The value of `xopt` at each iteration. Only returned if `retall` is
        True.

    Notes
    -----
    Optimize the function, `f`, whose gradient is given by `fprime`
    using the quasi-Newton method of Broyden, Fletcher, Goldfarb,
    and Shanno (BFGS).

    See Also
    --------
    minimize: Interface to minimization algorithms for multivariate
        functions. See ``method='BFGS'`` in particular.

    References
    ----------
    Wright, and Nocedal 'Numerical Optimization', 1999, p. 198.

    Examples
    --------
    >>> from scipy.optimize import fmin_bfgs
    >>> def quadratic_cost(x, Q):
    ...     return x @ Q @ x
    ...
    >>> x0 = np.array([-3, -4])
    >>> cost_weight =  np.diag([1., 10.])
    >>> # Note that a trailing comma is necessary for a tuple with single element
    >>> fmin_bfgs(quadratic_cost, x0, args=(cost_weight,))
    Optimization terminated successfully.
            Current function value: 0.000000
            Iterations: 7                   # may vary
            Function evaluations: 24        # may vary
            Gradient evaluations: 8         # may vary
    array([ 2.85169950e-06, -4.61820139e-07])

    >>> def quadratic_cost_grad(x, Q):
    ...     return 2 * Q @ x
    ...
    >>> fmin_bfgs(quadratic_cost, x0, quadratic_cost_grad, args=(cost_weight,))
    Optimization terminated successfully.
            Current function value: 0.000000
            Iterations: 7
            Function evaluations: 8
            Gradient evaluations: 8
    array([ 2.85916637e-06, -4.54371951e-07])