Module « scipy.optimize »

Fonction approx_fprime - module scipy.optimize

Signature de la fonction approx_fprime

def approx_fprime(xk, f, epsilon, *args) 

Description

approx_fprime.__doc__

Finite-difference approximation of the gradient of a scalar function.

    Parameters
    ----------
    xk : array_like
        The coordinate vector at which to determine the gradient of `f`.
    f : callable
        The function of which to determine the gradient (partial derivatives).
        Should take `xk` as first argument, other arguments to `f` can be
        supplied in ``*args``. Should return a scalar, the value of the
        function at `xk`.
    epsilon : array_like
        Increment to `xk` to use for determining the function gradient.
        If a scalar, uses the same finite difference delta for all partial
        derivatives. If an array, should contain one value per element of
        `xk`.
    \*args : args, optional
        Any other arguments that are to be passed to `f`.

    Returns
    -------
    grad : ndarray
        The partial derivatives of `f` to `xk`.

    See Also
    --------
    check_grad : Check correctness of gradient function against approx_fprime.

    Notes
    -----
    The function gradient is determined by the forward finite difference
    formula::

                 f(xk[i] + epsilon[i]) - f(xk[i])
        f'[i] = ---------------------------------
                            epsilon[i]

    The main use of `approx_fprime` is in scalar function optimizers like
    `fmin_bfgs`, to determine numerically the Jacobian of a function.

    Examples
    --------
    >>> from scipy import optimize
    >>> def func(x, c0, c1):
    ...     "Coordinate vector `x` should be an array of size two."
    ...     return c0 * x[0]**2 + c1*x[1]**2

    >>> x = np.ones(2)
    >>> c0, c1 = (1, 200)
    >>> eps = np.sqrt(np.finfo(float).eps)
    >>> optimize.approx_fprime(x, func, [eps, np.sqrt(200) * eps], c0, c1)
    array([   2.        ,  400.00004198])