Vous êtes un professionnel et vous avez besoin d'une formation ? Calcul scientifique
avec Python Voir le programme détaillé

Module « scipy.special »

Fonction ive - module scipy.special

Signature de la fonction ive

def ive(*args, **kwargs) 

Description

help(scipy.special.ive)

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


    ive(v, z, out=None)

    Exponentially scaled modified Bessel function of the first kind.

    Defined as::

        ive(v, z) = iv(v, z) * exp(-abs(z.real))

    For imaginary numbers without a real part, returns the unscaled
    Bessel function of the first kind `iv`.

    Parameters
    ----------
    v : array_like of float
        Order.
    z : array_like of float or complex
        Argument.
    out : ndarray, optional
        Optional output array for the function values

    Returns
    -------
    scalar or ndarray
        Values of the exponentially scaled modified Bessel function.

    See Also
    --------
    iv: Modified Bessel function of the first kind
    i0e: Faster implementation of this function for order 0
    i1e: Faster implementation of this function for order 1

    Notes
    -----
    For positive `v`, the AMOS [1]_ `zbesi` routine is called. It uses a
    power series for small `z`, the asymptotic expansion for large
    `abs(z)`, the Miller algorithm normalized by the Wronskian and a
    Neumann series for intermediate magnitudes, and the uniform asymptotic
    expansions for :math:`I_v(z)` and :math:`J_v(z)` for large orders.
    Backward recurrence is used to generate sequences or reduce orders when
    necessary.

    The calculations above are done in the right half plane and continued
    into the left half plane by the formula,

    .. math:: I_v(z \exp(\pm\imath\pi)) = \exp(\pm\pi v) I_v(z)

    (valid when the real part of `z` is positive).  For negative `v`, the
    formula

    .. math:: I_{-v}(z) = I_v(z) + \frac{2}{\pi} \sin(\pi v) K_v(z)

    is used, where :math:`K_v(z)` is the modified Bessel function of the
    second kind, evaluated using the AMOS routine `zbesk`.

    `ive` is useful for large arguments `z`: for these, `iv` easily overflows,
    while `ive` does not due to the exponential scaling.

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

    Examples
    --------
    In the following example `iv` returns infinity whereas `ive` still returns
    a finite number.

    >>> from scipy.special import iv, ive
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> iv(3, 1000.), ive(3, 1000.)
    (inf, 0.01256056218254712)

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

    >>> ive([0, 1, 1.5], 1.)
    array([0.46575961, 0.20791042, 0.10798193])

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

    >>> points = np.array([-2., 0., 3.])
    >>> ive(0, points)
    array([0.30850832, 1.        , 0.24300035])

    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:

    >>> ive([[0], [1], [2]], points)
    array([[ 0.30850832,  1.        ,  0.24300035],
           [-0.21526929,  0.        ,  0.19682671],
           [ 0.09323903,  0.        ,  0.11178255]])

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

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

Vous êtes un professionnel et vous avez besoin d'une formation ? RAG (Retrieval-Augmented Generation)
et Fine Tuning d'un LLM Voir le programme détaillé