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d }t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d	}
d
}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d}t          d|||||          \  }}
d}
d }t          d|||||          \  }}
d!}
d"}t          d|||||          \  }}
d#}
d$}t          d|||||          \  }}
d%}
d&}t          d|||||          \  }}
d'}
d(}t          d|||||          \  }}
d)}
d*}t          d|||||          \  }}
d+}
d,}
d-}t          d|||||          \  }}
d.}
d/}
d0}t          d|||||          \  }}
d1}
d2}
d3}t          d|||||          \  }}
d4}
d5}
d6}t          d|||||          \  }}
d7}
d8}
d9}t          d|||||          \  }}
d:}
d;}
d<}t          d|||||          \  }}
d=}
d>}
d?}t          d|||||          \  }}
d@}
dA}
dB}t          d|||||          \  }}
dC}
dD}
dE}t          d|||||          \  }}
dF}
dG}
dH}t          d|||||          \  }}
dI}
dJ}
dK}t          d|||||          \  }}
dL}
dM}
dN}t          d|||||          \  }}
dO}
dP}
dQ}t          d|||||          \  }}
dR}
dS}
dT}t          d|||||          \  }}
dU}
dV}
dW}t          d|||||          \  }}
dX}
dY}
dZ}t          d|||||          \  }}
d[}
d\}
d]}t          d|||||          \  }}
d^}
d_}
d`}t          d|||||          \  }}
da}
db}
dc}t          d|||||          \  }}
dd}
de}
df}t          d|||||          \  }}
dg}
dh}
di}t          d|||||          \  }}
dj}
dk}
dl}t          d|||||          \  }}
dm}
dn}
do}t          d|||||          \  }}
dp}
dq}
dr}t          d|||||          \  }}
ds}
dt}
du}t          d|||||          \  }}
dv}
dw}
dx}t          d|||||          \  }}
dy}
dz}
d{}t          d|||||          \  }}
d|}
d}}
d~}t          d|||||          \  }}
d}
d}
d}t          d|||||          \  }}
d}
d}
d}t          d|||||          \  }}
d}
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__module____qualname__xyzw     X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/integrate/_lebedev.pyLebr	   [   s        +
1ar   r   r              gWUUUUU?      g?g333333?      gaa?g88?   gPuPu?&   g88?gk?gAA?   2   g?g3V?g?g%h=K?gߋQ?   J   gK`@?gi? ?gwKgo?w?g6?g޷4?glN 0?V   g^ c?gGWv?g܁?gNV!?g%8?gW5R?gi?gYD1?n   gnw\o?g2?gVޱ?gᘸPр?g?geM\?g?dR?g\ʦ?gǷ!?g'wbڃ?   g|8C?g5g&3~?gǋň}?gg?g4 !
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MG8?gXR9 wM?  g'a
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]G?gM\Fs?gɅ~ӻ?g?UVF?g[YL1 #?g<W?gID?g$͵V?gUh?gUH?g'ߟpC?g0?ge#H?gXN?gnٳ0?g쟯	H?gLFjh?g_]"?gUfLG?g[խ??gGlͽ?gyRH?gAw?g<?gTH?  gp?gED?giD?gK?gJl"-?gd}E-H?g2re6?gJ0?gYU<?gHA?gqÔSP@?gS>?gwl,$=A?gM$?g<xB?g%dD?gt+C?gz	b]?g51D?gEjN?gv=uZD?gVh?giD?g#.&?g[iD?g?g dmD?g}yu?gvD?g{n?gUkD?gF^f?g[-%%D?gb[?g	y+D?gl14c?gFB~4?gmϚ=?gx#m>?gyϿ?g֞N&B?gY?g`:0QyC?g3;D?g5D?g#?gܚ?gͷ̺:?gx]0?g(=?g;6s1??gʅܪK?g^?gg2Q>CA?g{ p+?g_ gn?g}Kks}B?g1e?g~i`,ϖ?gOoqaC?g ɗ?g3*I8?grF D?gBHat?gR?gv7PjD?gّ
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     z  |z  |j        |dz   <   |d	z   }nxdk    r t          d
          }d|j         |<   ||j        |<   ||j        |<   dt          z  |z  |j        |<   d|j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   d|j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   d|j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |d	z   <   d|j        |d	z   <   ||j        |d	z   <   dt          z  |z  |j        |d	z   <   | |j         |dz   <   d|j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   |dz   }nxdk    r t          d          }||j         |<   ||j        |<   ||j        |<   dt          z  |z  |j        |<   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |d	z   <   ||j        |d	z   <   | |j        |d	z   <   dt          z  |z  |j        |d	z   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   |dz   }nxdk    r  t          dd|z  |z  z
            }||j         |<   ||j        |<   ||j        |<   dt          z  |z  |j        |<   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |d	z   <   | |j        |d	z   <   | |j        |d	z   <   dt          z  |z  |j        |d	z   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   |dz   }n[xdk    r t          d||z  z
            }||j         |<   ||j        |<   d|j        |<   dt          z  |z  |j        |<   | |j         |dz   <   ||j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |d	z   <   | |j        |d	z   <   d|j        |d	z   <   dt          z  |z  |j        |d	z   <   | |j         |dz   <   | |j        |dz   <   d|j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   d|j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   d|j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   d|j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   d|j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   d|j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   d|j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   d|j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   d|j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   d|j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   |dz   }nCd	k    r-t          d||z  z
  ||z  z
            }||j         |<   ||j        |<   ||j        |<   dt          z  |z  |j        |<   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |d	z   <   ||j        |d	z   <   | |j        |d	z   <   dt          z  |z  |j        |d	z   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   | |j        |dz   <   | |j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   | |j         |dz   <   ||j        |dz   <   ||j        |dz   <   dt          z  |z  |j        |dz   <   ||j         |d z   <   | |j        |d z   <   ||j        |d z   <   dt          z  |z  |j        |d z   <   ||j         |d!z   <   ||j        |d!z   <   | |j        |d!z   <   dt          z  |z  |j        |d!z   <   | |j         |d"z   <   | |j        |d"z   <   ||j        |d"z   <   dt          z  |z  |j        |d"z   <   ||j         |d#z   <   | |j        |d#z   <   | |j        |d#z   <   dt          z  |z  |j        |d#z   <   | |j         |d$z   <   ||j        |d$z   <   | |j        |d$z   <   dt          z  |z  |j        |d$z   <   | |j         |d%z   <   | |j        |d%z   <   | |j        |d%z   <   dt          z  |z  |j        |d%z   <   ||j         |d&z   <   ||j        |d&z   <   ||j        |d&z   <   dt          z  |z  |j        |d&z   <   | |j         |d'z   <   ||j        |d'z   <   ||j        |d'z   <   dt          z  |z  |j        |d'z   <   ||j         |d(z   <   | |j        |d(z   <   ||j        |d(z   <   dt          z  |z  |j        |d(z   <   ||j         |d)z   <   ||j        |d)z   <   | |j        |d)z   <   dt          z  |z  |j        |d)z   <   | |j         |d*z   <   | |j        |d*z   <   ||j        |d*z   <   dt          z  |z  |j        |d*z   <   ||j         |d+z   <   | |j        |d+z   <   | |j        |d+z   <   dt          z  |z  |j        |d+z   <   | |j         |d,z   <   ||j        |d,z   <   | |j        |d,z   <   dt          z  |z  |j        |d,z   <   | |j         |d-z   <   | |j        |d-z   <   | |j        |d-z   <   dt          z  |z  |j        |d-z   <   ||j         |d.z   <   ||j        |d.z   <   ||j        |d.z   <   dt          z  |z  |j        |d.z   <   | |j         |d/z   <   ||j        |d/z   <   ||j        |d/z   <   dt          z  |z  |j        |d/z   <   ||j         |d0z   <   | |j        |d0z   <   ||j        |d0z   <   dt          z  |z  |j        |d0z   <   ||j         |d1z   <   ||j        |d1z   <   | |j        |d1z   <   dt          z  |z  |j        |d1z   <   | |j         |d2z   <   | |j        |d2z   <   ||j        |d2z   <   dt          z  |z  |j        |d2z   <   ||j         |d3z   <   | |j        |d3z   <   | |j        |d3z   <   dt          z  |z  |j        |d3z   <   | |j         |d4z   <   ||j        |d4z   <   | |j        |d4z   <   dt          z  |z  |j        |d4z   <   | |j         |d5z   <   | |j        |d5z   <   | |j        |d5z   <   dt          z  |z  |j        |d5z   <   |d6z   }n	 t          d7          ||fS )8Nr   r   g      ?g      @r   r   r   r   r   g      ?      	   
         gUUUUUU?g       @   r                                    r                      !   "   #   $   %   r   '   (   )   *   +   ,   -   .   /   0   zBad grid order)r   r   r   r   r   r   r<   )type_r@   rA   rB   rC   lebcs          r   r;   r;   k  s($   A
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  Lebedev quadrature.

    Compute the sample points and weights for Lebedev quadrature [1]_
    for integration of a function over the surface of a unit sphere.

    Parameters
    ----------
    n : int
        Quadrature order. See Notes for supported values.

    Returns
    -------
    x : ndarray of shape ``(3, m)``
        Sample points on the unit sphere in Cartesian coordinates.
        ``m`` is the "degree" corresponding with the specified order; see Notes.
    w : ndarray of shape ``(m,)``
        Weights

    Notes
    -----
    Implemented by translating the Matlab code of [2]_ to Python.

    The available orders (argument `n`) are::

        3, 5, 7, 9, 11, 13, 15, 17,
        19, 21, 23, 25, 27, 29, 31, 35,
        41, 47, 53, 59, 65, 71, 77, 83,
        89, 95, 101, 107, 113, 119, 125, 131

    The corresponding degrees ``m`` are::

        6, 14, 26, 38, 50, 74, 86, 110,
        146, 170, 194, 230, 266, 302, 350, 434,
        590, 770, 974, 1202, 1454, 1730, 2030, 2354,
        2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810

    References
    ----------
    .. [1] V.I. Lebedev, and D.N. Laikov. "A quadrature formula for the sphere of
           the 131st algebraic order of accuracy". Doklady Mathematics, Vol. 59,
           No. 3, 1999, pp. 477-481.
    .. [2] R. Parrish. ``getLebedevSphere``. Matlab Central File Exchange.
           https://www.mathworks.com/matlabcentral/fileexchange/27097-getlebedevsphere.
    .. [3] Bellet, Jean-Baptiste, Matthieu Brachet, and Jean-Pierre Croisille.
           "Quadrature and symmetry on the Cubed Sphere." Journal of Computational and
           Applied Mathematics 409 (2022): 114142. :doi:`10.1016/j.cam.2022.114142`.

    Examples
    --------
    An example given in [3]_ is integration of :math:`f(x, y, z) = \exp(x)` over a
    sphere of radius :math:`1`; the reference there is ``14.7680137457653``.
    Show the convergence to the expected result as the order increases:

    >>> import matplotlib.pyplot as plt
    >>> import numpy as np
    >>> from scipy.integrate import lebedev_rule
    >>>
    >>> def f(x):
    ...     return np.exp(x[0])
    >>>
    >>> res = []
    >>> orders = np.arange(3, 20, 2)
    >>> for n in orders:
    ...     x, w = lebedev_rule(n)
    ...     res.append(w @ f(x))
    >>>
    >>> ref = np.full_like(res, 14.7680137457653)
    >>> err = abs(res - ref)/abs(ref)
    >>> plt.semilogy(orders, err)
    >>> plt.xlabel('order $n$')
    >>> plt.ylabel('relative error')
    >>> plt.title(r'Convergence for $f(x, y, z) = \exp(x)$')
    >>> plt.show()

    ) r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   ) r   r   rF   rH   rJ   rL   rM   rO   rQ   rS   rU   rW   rX   rZ   r\   r`   re   rk   5   ;   A   G   M   S   Y   _   e   k   q   w   }      zOrder n=z% not available. Available orders are .)
dictzipNotImplementedErrorrD   npstackr   r   r   r   )r=   r>   orderorder_degree_mapmessageresr   r   s           r   r   r     s    X, , ,FK K KECv..//   L1LLELLL!'***a F
V
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