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Module « scipy.special »

Fonction itairy - module scipy.special

Signature de la fonction itairy

def itairy(*args, **kwargs) 

Description

help(scipy.special.itairy)

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


    itairy(x, out=None)

    Integrals of Airy functions

    Calculates the integrals of Airy functions from 0 to `x`.

    Parameters
    ----------

    x : array_like
        Upper limit of integration (float).
    out : tuple of ndarray, optional
        Optional output arrays for the function values

    Returns
    -------
    Apt : scalar or ndarray
        Integral of Ai(t) from 0 to x.
    Bpt : scalar or ndarray
        Integral of Bi(t) from 0 to x.
    Ant : scalar or ndarray
        Integral of Ai(-t) from 0 to x.
    Bnt : scalar or ndarray
        Integral of Bi(-t) from 0 to x.

    Notes
    -----

    Wrapper for a Fortran routine created by Shanjie Zhang and Jianming
    Jin [1]_.

    References
    ----------

    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
           Functions", John Wiley and Sons, 1996.
           https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html

    Examples
    --------
    Compute the functions at ``x=1.``.

    >>> import numpy as np
    >>> from scipy.special import itairy
    >>> import matplotlib.pyplot as plt
    >>> apt, bpt, ant, bnt = itairy(1.)
    >>> apt, bpt, ant, bnt
    (0.23631734191710949,
     0.8727691167380077,
     0.46567398346706845,
     0.3730050096342943)

    Compute the functions at several points by providing a NumPy array for `x`.

    >>> x = np.array([1., 1.5, 2.5, 5])
    >>> apt, bpt, ant, bnt = itairy(x)
    >>> apt, bpt, ant, bnt
    (array([0.23631734, 0.28678675, 0.324638  , 0.33328759]),
     array([  0.87276912,   1.62470809,   5.20906691, 321.47831857]),
     array([0.46567398, 0.72232876, 0.93187776, 0.7178822 ]),
     array([ 0.37300501,  0.35038814, -0.02812939,  0.15873094]))

    Plot the functions from -10 to 10.

    >>> x = np.linspace(-10, 10, 500)
    >>> apt, bpt, ant, bnt = itairy(x)
    >>> fig, ax = plt.subplots(figsize=(6, 5))
    >>> ax.plot(x, apt, label=r"$\int_0^x\, Ai(t)\, dt$")
    >>> ax.plot(x, bpt, ls="dashed", label=r"$\int_0^x\, Bi(t)\, dt$")
    >>> ax.plot(x, ant, ls="dashdot", label=r"$\int_0^x\, Ai(-t)\, dt$")
    >>> ax.plot(x, bnt, ls="dotted", label=r"$\int_0^x\, Bi(-t)\, dt$")
    >>> ax.set_ylim(-2, 1.5)
    >>> ax.legend(loc="lower right")
    >>> plt.show()
    

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