Vous êtes un professionnel et vous avez besoin d'une formation ? Sensibilisation à
l'Intelligence Artificielle Voir le programme détaillé

Module « scipy.special »

Fonction airy - module scipy.special

Signature de la fonction airy

def airy(*args, **kwargs) 

Description

help(scipy.special.airy)

airy(x[, out1, out2, out3, out4], / [, out=(None, None, None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    airy(z, out=None)

    Airy functions and their derivatives.

    Parameters
    ----------
    z : array_like
        Real or complex argument.
    out : tuple of ndarray, optional
        Optional output arrays for the function values

    Returns
    -------
    Ai, Aip, Bi, Bip : 4-tuple of scalar or ndarray
        Airy functions Ai and Bi, and their derivatives Aip and Bip.

    See Also
    --------
    airye : exponentially scaled Airy functions.

    Notes
    -----
    The Airy functions Ai and Bi are two independent solutions of

    .. math:: y''(x) = x y(x).

    For real `z` in [-10, 10], the computation is carried out by calling
    the Cephes [1]_ `airy` routine, which uses power series summation
    for small `z` and rational minimax approximations for large `z`.

    Outside this range, the AMOS [2]_ `zairy` and `zbiry` routines are
    employed.  They are computed using power series for :math:`|z| < 1` and
    the following relations to modified Bessel functions for larger `z`
    (where :math:`t \equiv 2 z^{3/2}/3`):

    .. math::

        Ai(z) = \frac{1}{\pi \sqrt{3}} K_{1/3}(t)

        Ai'(z) = -\frac{z}{\pi \sqrt{3}} K_{2/3}(t)

        Bi(z) = \sqrt{\frac{z}{3}} \left(I_{-1/3}(t) + I_{1/3}(t) \right)

        Bi'(z) = \frac{z}{\sqrt{3}} \left(I_{-2/3}(t) + I_{2/3}(t)\right)

    References
    ----------
    .. [1] Cephes Mathematical Functions Library,
           http://www.netlib.org/cephes/
    .. [2] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
           of a Complex Argument and Nonnegative Order",
           http://netlib.org/amos/

    Examples
    --------
    Compute the Airy functions on the interval [-15, 5].

    >>> import numpy as np
    >>> from scipy import special
    >>> x = np.linspace(-15, 5, 201)
    >>> ai, aip, bi, bip = special.airy(x)

    Plot Ai(x) and Bi(x).

    >>> import matplotlib.pyplot as plt
    >>> plt.plot(x, ai, 'r', label='Ai(x)')
    >>> plt.plot(x, bi, 'b--', label='Bi(x)')
    >>> plt.ylim(-0.5, 1.0)
    >>> plt.grid()
    >>> plt.legend(loc='upper left')
    >>> plt.show()

    

Vous êtes un professionnel et vous avez besoin d'une formation ? Deep Learning avec Python
et Keras et Tensorflow Voir le programme détaillé