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Module « scipy.special »

Fonction modstruve - module scipy.special

Signature de la fonction modstruve

def modstruve(*args, **kwargs) 

Description

help(scipy.special.modstruve)

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


    modstruve(v, x, out=None)

    Modified Struve function.

    Return the value of the modified Struve function of order `v` at `x`.  The
    modified Struve function is defined as,

    .. math::
        L_v(x) = -\imath \exp(-\pi\imath v/2) H_v(\imath x),

    where :math:`H_v` is the Struve function.

    Parameters
    ----------
    v : array_like
        Order of the modified Struve function (float).
    x : array_like
        Argument of the Struve function (float; must be positive unless `v` is
        an integer).
    out : ndarray, optional
        Optional output array for the function results

    Returns
    -------
    L : scalar or ndarray
        Value of the modified Struve function of order `v` at `x`.

    See Also
    --------
    struve

    Notes
    -----
    Three methods discussed in [1]_ are used to evaluate the function:

    - power series
    - expansion in Bessel functions (if :math:`|x| < |v| + 20`)
    - asymptotic large-x expansion (if :math:`x \geq 0.7v + 12`)

    Rounding errors are estimated based on the largest terms in the sums, and
    the result associated with the smallest error is returned.

    References
    ----------
    .. [1] NIST Digital Library of Mathematical Functions
           https://dlmf.nist.gov/11

    Examples
    --------
    Calculate the modified Struve function of order 1 at 2.

    >>> import numpy as np
    >>> from scipy.special import modstruve
    >>> import matplotlib.pyplot as plt
    >>> modstruve(1, 2.)
    1.102759787367716

    Calculate the modified Struve function at 2 for orders 1, 2 and 3 by
    providing a list for the order parameter `v`.

    >>> modstruve([1, 2, 3], 2.)
    array([1.10275979, 0.41026079, 0.11247294])

    Calculate the modified Struve function of order 1 for several points
    by providing an array for `x`.

    >>> points = np.array([2., 5., 8.])
    >>> modstruve(1, points)
    array([  1.10275979,  23.72821578, 399.24709139])

    Compute the modified Struve function for several orders at several
    points by providing arrays for `v` and `z`. The arrays have to be
    broadcastable to the correct shapes.

    >>> orders = np.array([[1], [2], [3]])
    >>> points.shape, orders.shape
    ((3,), (3, 1))

    >>> modstruve(orders, points)
    array([[1.10275979e+00, 2.37282158e+01, 3.99247091e+02],
           [4.10260789e-01, 1.65535979e+01, 3.25973609e+02],
           [1.12472937e-01, 9.42430454e+00, 2.33544042e+02]])

    Plot the modified Struve 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, modstruve(i, x), label=f'$L_{i!r}$')
    >>> ax.legend(ncol=2)
    >>> ax.set_xlim(-5, 5)
    >>> ax.set_title(r"Modified Struve functions $L_{\nu}$")
    >>> plt.show()
    

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