chaospy.quadrature.genz_keister_16¶

chaospy.quadrature.genz_keister_16(order, dist=None)[source]¶

Create Genz-Keister variant 16 quadrature nodes and weights.

Args:

order (int, Sequence[int]):: The order of the quadrature.
dist (Optional[chaospy.Distribution]):: The distribution which density will be used as weight function. If omitted, standard Gaussian is assumed.

Returns:

(numpy.ndarray, numpy.ndarray):: Genz-Keister quadrature abscissas and weights.

Examples:

>>> nodes, weights = genz_keister_16(4)
>>> nodes.round(2)
array([[-6.36, -5.19, -4.18, -2.86, -2.6 , -1.73, -1.23, -0.74,  0.  ,
         0.74,  1.23,  1.73,  2.6 ,  2.86,  4.18,  5.19,  6.36]])
>>> weights.round(8)
array([ 2.0000000e-08, -8.2000000e-07,  1.0564000e-04,  7.0334800e-03,
        1.9656800e-03,  8.8681000e-02,  1.4192650e-02,  2.5456123e-01,
        2.6692223e-01,  2.5456123e-01,  1.4192650e-02,  8.8681000e-02,
        1.9656800e-03,  7.0334800e-03,  1.0564000e-04, -8.2000000e-07,
        2.0000000e-08])