chaospy.quadrature.laguerre

chaospy.quadrature.laguerre(order, alpha=0.0, physicist=False)

Generalized Gauss-Laguerre quadrature rule.

Compute the sample points and weights for Gauss-Laguerre quadrature. The sample points are the roots of the nth degree Laguerre polynomial. These sample points and weights correctly integrate polynomials of degree \(2N-1\) or less.

Gaussian quadrature come in two variants: physicist and probabilist. For Gauss-Laguerre physicist means a weight function \(x^\alpha e^{-x}\) and weights that sum to :math`Gamma(alpha+1)`, and probabilist means a weight function is \(x^\alpha e^{-x}\) and sum to 1.

Args:

order (int):

The quadrature order.

alpha (float):

Shape parameter. Defaults to non-generalized Laguerre if 0.

physicist (bool):

Use physicist weights instead of probabilist.

Returns:

abscissas (numpy.ndarray):

The order+1 quadrature points for where to evaluate the model function with.

weights (numpy.ndarray):

The quadrature weights associated with each abscissas.

Examples:

>>> abscissas, weights = chaospy.quadrature.laguerre(2)
>>> abscissas
array([[0.41577456, 2.29428036, 6.28994508]])
>>> weights
array([0.71109301, 0.27851773, 0.01038926])

See also:

chaospy.quadrature.gaussian()