chaospy.quadrature.grid

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

Generate the quadrature abscissas and weights for simple grid.

Args:

order (int, numpy.ndarray):

Quadrature order.

domain (chaospy.distributions.baseclass.Distribution, numpy.ndarray):

Either distribution or bounding of interval to integrate over.

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]).

Example:

>>> abscissas, weights = chaospy.quadrature.grid(4, chaospy.Uniform(-1, 1))
>>> abscissas.round(4)
array([[-0.8, -0.4,  0. ,  0.4,  0.8]])
>>> weights.round(4)
array([0.2, 0.2, 0.2, 0.2, 0.2])
>>> abscissas, weights = chaospy.quadrature.grid([1, 1])
>>> abscissas.round(4)
array([[0.25, 0.25, 0.75, 0.75],
       [0.25, 0.75, 0.25, 0.75]])
>>> weights.round(4)
array([0.25, 0.25, 0.25, 0.25])