+
    Y°³jÅ  ã                   óP   € ^ RI HtHt ^ RIHt ^ RIHt ^RIHt  ! R R]4      t	R# )é    )Úarray_namespaceÚ	np_compat)Úcached_property)Úroots_legendre)Ú	FixedRulec                   ó>   a € ] tR t^
t o RtRR lt]R 4       tRtV t	R# )ÚGaussLegendreQuadraturea  
Gauss-Legendre quadrature.

Parameters
----------
npoints : int
    Number of nodes for the higher-order rule.

xp : array_namespace, optional
    The namespace for the node and weight arrays. Default is None, where NumPy is
    used.

Examples
--------
Evaluate a 1D integral. Note in this example that ``f`` returns an array, so the
estimates will also be arrays.

>>> import numpy as np
>>> from scipy.integrate import cubature
>>> from scipy.integrate._rules import GaussLegendreQuadrature
>>> def f(x):
...     return np.cos(x)
>>> rule = GaussLegendreQuadrature(21) # Use 21-point GaussLegendre
>>> a, b = np.array([0]), np.array([1])
>>> rule.estimate(f, a, b) # True value sin(1), approximately 0.84147
 array([0.84147098])
>>> rule.estimate_error(f, a, b)
 array([1.11022302e-16])
Nc                óˆ   € V^8  d   \        R4      hWn        Vf   \        p\        VP	                  ^ 4      4      V n        R# )é   z5At least 2 nodes required for Gauss-Legendre cubatureN)Ú
ValueErrorÚnpointsr   r   ÚemptyÚxp)Úselfr   r   s   &&&Úg/home/luca/screen-checking/.venv/lib/python3.14/site-packages/scipy/integrate/_rules/_gauss_legendre.pyÚ__init__Ú GaussLegendreQuadrature.__init__)   s>   € Ø�QŒ;ÜØGóð ð ŒàŠ:ÜˆBä! "§(¡(¨1£+Ó.ˆŽó    c                óð   € \        V P                  4      w  rV P                  P                  WP                  P                  R 7      V P                  P                  W P                  P                  R 7      3# ))Údtype)r   r   r   ÚasarrayÚfloat64)r   ÚnodesÚweightss   &  r   Únodes_and_weightsÚ)GaussLegendreQuadrature.nodes_and_weights6   sT   € ô (¨¯©Ó5‰ˆð �G‰G�O‰O˜E¯©¯©ˆOÓ9Ø�G‰G�O‰O˜G¯7©7¯?©?ˆOÓ;ð
ð 	
r   )r   r   )N)
Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__r   r   r   Ú__static_attributes__Ú__classdictcell__)Ú__classdict__s   @r   r	   r	   
   s#   ø‡ € ñô</ð ñ
ó ö
r   r	   N)
Úscipy._lib._array_apir   r   Ú	functoolsr   Úscipy.specialr   Ú_baser   r	   © r   r   Ú<module>r*      s   ðß <å %å (å ô4
˜iö 4
r   