chaospy.discretized_stieltjes

chaospy.discretized_stieltjes(order, dist, rule=None, tolerance=1e-16, scaling=3, n_max=5000)

Discretized Stieltjes’ method.

Examples:

>>> dist = chaospy.J(chaospy.Uniform(0, 1), chaospy.Beta(3, 4))
>>> (alpha, beta), orth, norms = chaospy.discretized_stieltjes(2, dist)
>>> alpha.round(5)
array([[0.5    , 0.5    , 0.5    ],
       [0.42857, 0.46032, 0.47475]])
>>> beta.round(5)
array([[1.     , 0.08333, 0.06667],
       [1.     , 0.03061, 0.04321]])
>>> orth[:, 2].round(5)
polynomial([q0**2-q0+0.16667, q1**2-0.88889*q1+0.16667])
>>> norms.round(5)
array([[1.     , 0.08333, 0.00556],
       [1.     , 0.03061, 0.00132]])