Module « scipy.optimize »

Fonction minimize_scalar - module scipy.optimize

Signature de la fonction minimize_scalar

def minimize_scalar(fun, bracket=None, bounds=None, args=(), method='brent', tol=None, options=None) 

Description

minimize_scalar.__doc__

Minimization of scalar function of one variable.

    Parameters
    ----------
    fun : callable
        Objective function.
        Scalar function, must return a scalar.
    bracket : sequence, optional
        For methods 'brent' and 'golden', `bracket` defines the bracketing
        interval and can either have three items ``(a, b, c)`` so that
        ``a < b < c`` and ``fun(b) < fun(a), fun(c)`` or two items ``a`` and
        ``c`` which are assumed to be a starting interval for a downhill
        bracket search (see `bracket`); it doesn't always mean that the
        obtained solution will satisfy ``a <= x <= c``.
    bounds : sequence, optional
        For method 'bounded', `bounds` is mandatory and must have two items
        corresponding to the optimization bounds.
    args : tuple, optional
        Extra arguments passed to the objective function.
    method : str or callable, optional
        Type of solver.  Should be one of:

            - 'Brent'     :ref:`(see here) <optimize.minimize_scalar-brent>`
            - 'Bounded'   :ref:`(see here) <optimize.minimize_scalar-bounded>`
            - 'Golden'    :ref:`(see here) <optimize.minimize_scalar-golden>`
            - custom - a callable object (added in version 0.14.0), see below

    tol : float, optional
        Tolerance for termination. For detailed control, use solver-specific
        options.
    options : dict, optional
        A dictionary of solver options.

            maxiter : int
                Maximum number of iterations to perform.
            disp : bool
                Set to True to print convergence messages.

        See :func:`show_options()` for solver-specific options.

    Returns
    -------
    res : OptimizeResult
        The optimization result represented as a ``OptimizeResult`` object.
        Important attributes are: ``x`` the solution array, ``success`` a
        Boolean flag indicating if the optimizer exited successfully and
        ``message`` which describes the cause of the termination. See
        `OptimizeResult` for a description of other attributes.

    See also
    --------
    minimize : Interface to minimization algorithms for scalar multivariate
        functions
    show_options : Additional options accepted by the solvers

    Notes
    -----
    This section describes the available solvers that can be selected by the
    'method' parameter. The default method is *Brent*.

    Method :ref:`Brent <optimize.minimize_scalar-brent>` uses Brent's
    algorithm to find a local minimum.  The algorithm uses inverse
    parabolic interpolation when possible to speed up convergence of
    the golden section method.

    Method :ref:`Golden <optimize.minimize_scalar-golden>` uses the
    golden section search technique. It uses analog of the bisection
    method to decrease the bracketed interval. It is usually
    preferable to use the *Brent* method.

    Method :ref:`Bounded <optimize.minimize_scalar-bounded>` can
    perform bounded minimization. It uses the Brent method to find a
    local minimum in the interval x1 < xopt < x2.

    **Custom minimizers**

    It may be useful to pass a custom minimization method, for example
    when using some library frontend to minimize_scalar. You can simply
    pass a callable as the ``method`` parameter.

    The callable is called as ``method(fun, args, **kwargs, **options)``
    where ``kwargs`` corresponds to any other parameters passed to `minimize`
    (such as `bracket`, `tol`, etc.), except the `options` dict, which has
    its contents also passed as `method` parameters pair by pair.  The method
    shall return an `OptimizeResult` object.

    The provided `method` callable must be able to accept (and possibly ignore)
    arbitrary parameters; the set of parameters accepted by `minimize` may
    expand in future versions and then these parameters will be passed to
    the method. You can find an example in the scipy.optimize tutorial.

    .. versionadded:: 0.11.0

    Examples
    --------
    Consider the problem of minimizing the following function.

    >>> def f(x):
    ...     return (x - 2) * x * (x + 2)**2

    Using the *Brent* method, we find the local minimum as:

    >>> from scipy.optimize import minimize_scalar
    >>> res = minimize_scalar(f)
    >>> res.x
    1.28077640403

    Using the *Bounded* method, we find a local minimum with specified
    bounds as:

    >>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded')
    >>> res.x
    -2.0000002026