UiVddlmZmZddlmZddlmZddlmZGddeZ dS) )array_namespace np_compat)cached_property)roots_legendre) FixedRulec0eZdZdZddZedZdS)GaussLegendreQuadratureaw 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|dkrtd||_|t}t|d|_dS)Nz5At least 2 nodes required for Gauss-Legendre cubaturer) ValueErrornpointsrremptyxp)selfrrs ~/var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/scipy/integrate/_rules/_gauss_legendre.py__init__z GaussLegendreQuadrature.__init__)sP Q;;G  :B!"((1++..ct|j\}}|j||jj|j||jjfS)N)dtype)rrrasarrayfloat64)rnodesweightss rnodes_and_weightsz)GaussLegendreQuadrature.nodes_and_weights6sU( 55w GOOEO 9 9 GOOG47?O ; ;  r)N)__name__ __module__ __qualname____doc__rrrrrr r sM< / / / /  _   rr N) scipy._lib._array_apirr functoolsr scipy.specialr_baserr r rrr%s<<<<<<<<%%%%%%((((((4 4 4 4 4 i4 4 4 4 4 r