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Module « scipy.special »

Fonction mathieu_cem - module scipy.special

Signature de la fonction mathieu_cem

def mathieu_cem(*args, **kwargs) 

Description

help(scipy.special.mathieu_cem)

mathieu_cem(x1, x2, x3[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    mathieu_cem(m, q, x, out=None)

    Even Mathieu function and its derivative

    Returns the even Mathieu function, ``ce_m(x, q)``, of order `m` and
    parameter `q` evaluated at `x` (given in degrees).  Also returns the
    derivative with respect to `x` of ce_m(x, q)

    Parameters
    ----------
    m : array_like
        Order of the function
    q : array_like
        Parameter of the function
    x : array_like
        Argument of the function, *given in degrees, not radians*
    out : tuple of ndarray, optional
        Optional output arrays for the function results

    Returns
    -------
    y : scalar or ndarray
        Value of the function
    yp : scalar or ndarray
        Value of the derivative vs x

    See Also
    --------
    mathieu_a, mathieu_b, mathieu_sem

    Notes
    -----
    The even Mathieu functions are the solutions to Mathieu's differential equation

    .. math::

        \frac{d^2y}{dx^2} + (a_m - 2q \cos(2x))y = 0

    for which the characteristic number :math:`a_m` (calculated with `mathieu_a`)
    results in an odd, periodic solution :math:`y(x)` with period 180 degrees
    (for even :math:`m`) or 360 degrees (for odd :math:`m`).

    References
    ----------
    .. [1] 'Mathieu function'. *Wikipedia*.
           https://en.wikipedia.org/wiki/Mathieu_function

    Examples
    --------
    Plot even Mathieu functions of orders ``2`` and ``4``.

    >>> import numpy as np
    >>> from scipy import special
    >>> import matplotlib.pyplot as plt
    >>> m = np.asarray([2, 4])
    >>> q = 50
    >>> x = np.linspace(-180, 180, 300)[:, np.newaxis]
    >>> y, _ = special.mathieu_cem(m, q, x)
    >>> plt.plot(x, y)
    >>> plt.xlabel('x (degrees)')
    >>> plt.ylabel('y')
    >>> plt.legend(('m = 2', 'm = 4'))

    Because the orders ``2`` and
    ``4`` are even, the period of each function is 180 degrees.

    

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