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Module « scipy.special »

Fonction kve - module scipy.special

Signature de la fonction kve

def kve(*args, **kwargs) 

Description

help(scipy.special.kve)

kve(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    kve(v, z, out=None)

    Exponentially scaled modified Bessel function of the second kind.

    Returns the exponentially scaled, modified Bessel function of the
    second kind (sometimes called the third kind) for real order `v` at
    complex `z`::

        kve(v, z) = kv(v, z) * exp(z)

    Parameters
    ----------
    v : array_like of float
        Order of Bessel functions
    z : array_like of complex
        Argument at which to evaluate the Bessel functions
    out : ndarray, optional
        Optional output array for the function results

    Returns
    -------
    scalar or ndarray
        The exponentially scaled modified Bessel function of the second kind.

    See Also
    --------
    kv : This function without exponential scaling.
    k0e : Faster version of this function for order 0.
    k1e : Faster version of this function for order 1.

    Notes
    -----
    Wrapper for AMOS [1]_ routine `zbesk`.  For a discussion of the
    algorithm used, see [2]_ and the references therein.

    References
    ----------
    .. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
           of a Complex Argument and Nonnegative Order",
           http://netlib.org/amos/
    .. [2] Donald E. Amos, "Algorithm 644: A portable package for Bessel
           functions of a complex argument and nonnegative order", ACM
           TOMS Vol. 12 Issue 3, Sept. 1986, p. 265

    Examples
    --------
    In the following example `kv` returns 0 whereas `kve` still returns
    a useful finite number.

    >>> import numpy as np
    >>> from scipy.special import kv, kve
    >>> import matplotlib.pyplot as plt
    >>> kv(3, 1000.), kve(3, 1000.)
    (0.0, 0.03980696128440973)

    Evaluate the function at one point for different orders by
    providing a list or NumPy array as argument for the `v` parameter:

    >>> kve([0, 1, 1.5], 1.)
    array([1.14446308, 1.63615349, 2.50662827])

    Evaluate the function at several points for order 0 by providing an
    array for `z`.

    >>> points = np.array([1., 3., 10.])
    >>> kve(0, points)
    array([1.14446308, 0.6977616 , 0.39163193])

    Evaluate the function at several points for different orders by
    providing arrays for both `v` for `z`. Both arrays have to be
    broadcastable to the correct shape. To calculate the orders 0, 1
    and 2 for a 1D array of points:

    >>> kve([[0], [1], [2]], points)
    array([[1.14446308, 0.6977616 , 0.39163193],
           [1.63615349, 0.80656348, 0.41076657],
           [4.41677005, 1.23547058, 0.47378525]])

    Plot the functions of order 0 to 3 from 0 to 5.

    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(0., 5., 1000)
    >>> for i in range(4):
    ...     ax.plot(x, kve(i, x), label=fr'$K_{i!r}(z)\cdot e^z$')
    >>> ax.legend()
    >>> ax.set_xlabel(r"$z$")
    >>> ax.set_ylim(0, 4)
    >>> ax.set_xlim(0, 5)
    >>> plt.show()
    

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