Vous êtes un professionnel et vous avez besoin d'une formation ? Mise en oeuvre d'IHM
avec Qt et PySide6 Voir le programme détaillé

Module « scipy.special »

Fonction ellip_harm - module scipy.special

Signature de la fonction ellip_harm

def ellip_harm(h2, k2, n, p, s, signm=1, signn=1) 

Description

help(scipy.special.ellip_harm)

Ellipsoidal harmonic functions E^p_n(l)

These are also known as Lame functions of the first kind, and are
solutions to the Lame equation:

.. math:: (s^2 - h^2)(s^2 - k^2)E''(s)
          + s(2s^2 - h^2 - k^2)E'(s) + (a - q s^2)E(s) = 0

where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
returned) corresponding to the solutions.

Parameters
----------
h2 : float
    ``h**2``
k2 : float
    ``k**2``; should be larger than ``h**2``
n : int
    Degree
s : float
    Coordinate
p : int
    Order, can range between [1,2n+1]
signm : {1, -1}, optional
    Sign of prefactor of functions. Can be +/-1. See Notes.
signn : {1, -1}, optional
    Sign of prefactor of functions. Can be +/-1. See Notes.

Returns
-------
E : float
    the harmonic :math:`E^p_n(s)`

See Also
--------
ellip_harm_2, ellip_normal

Notes
-----
The geometric interpretation of the ellipsoidal functions is
explained in [2]_, [3]_, [4]_. The `signm` and `signn` arguments control the
sign of prefactors for functions according to their type::

    K : +1
    L : signm
    M : signn
    N : signm*signn

.. versionadded:: 0.15.0

References
----------
.. [1] Digital Library of Mathematical Functions 29.12
   https://dlmf.nist.gov/29.12
.. [2] Bardhan and Knepley, "Computational science and
   re-discovery: open-source implementations of
   ellipsoidal harmonics for problems in potential theory",
   Comput. Sci. Disc. 5, 014006 (2012)
   :doi:`10.1088/1749-4699/5/1/014006`.
.. [3] David J.and Dechambre P, "Computation of Ellipsoidal
   Gravity Field Harmonics for small solar system bodies"
   pp. 30-36, 2000
.. [4] George Dassios, "Ellipsoidal Harmonics: Theory and Applications"
   pp. 418, 2012

Examples
--------
>>> from scipy.special import ellip_harm
>>> w = ellip_harm(5,8,1,1,2.5)
>>> w
2.5

Check that the functions indeed are solutions to the Lame equation:

>>> import numpy as np
>>> from scipy.interpolate import UnivariateSpline
>>> def eigenvalue(f, df, ddf):
...     r = (((s**2 - h**2) * (s**2 - k**2) * ddf
...           + s * (2*s**2 - h**2 - k**2) * df
...           - n * (n + 1)*s**2*f) / f)
...     return -r.mean(), r.std()
>>> s = np.linspace(0.1, 10, 200)
>>> k, h, n, p = 8.0, 2.2, 3, 2
>>> E = ellip_harm(h**2, k**2, n, p, s)
>>> E_spl = UnivariateSpline(s, E)
>>> a, a_err = eigenvalue(E_spl(s), E_spl(s,1), E_spl(s,2))
>>> a, a_err
(583.44366156701483, 6.4580890640310646e-11)

Vous êtes un professionnel et vous avez besoin d'une formation ? Deep Learning avec Python
et Keras et Tensorflow Voir le programme détaillé