chaospy.quadrature.discrete

chaospy.quadrature.discrete(order, domain=(0, 1), growth=False)

Generate quadrature abscissas and weights for discrete distributions.

A specialized quadrature designed for discrete distributions. It is defined as an evenly spaced grid on the domain, rounded to nearest integer. Rule will converge to where all integer values on the domain is covered. This ensure that only necessary samples are evaluated.

Args:

order (int, numpy.ndarray):

Quadrature order.

domain (chaospy.Distribution, numpy.ndarray):

Either distribution or bounding of interval to integrate over.

growth (bool):

if true sets the growth rule for the quadrature rule to only include orders that enhances nested samples.

Returns:

(numpy.ndarray, numpy.ndarray):

The quadrature points and weights. The points are equi-spaced grid on the interior of the domain bounds. The weights are all equal to 1/len(weights[0]). Either distribution or bounding of interval to integrate over.

Examples:

>>> distribution = chaospy.Binomial(6, 0.4)
>>> abscissas, weights = chaospy.quadrature.discrete(4, distribution)
>>> abscissas
array([[0., 2., 3., 4., 6.]])
>>> weights.round(4)
array([0.0601, 0.4006, 0.3561, 0.178 , 0.0053])
>>> abscissas, weights = chaospy.quadrature.discrete(10, distribution)
>>> abscissas
array([[0., 1., 2., 3., 4., 5., 6.]])
>>> weights.round(4)
array([0.0467, 0.1866, 0.311 , 0.2765, 0.1382, 0.0369, 0.0041])