pystra.quadrature.quadratureRule#

quadratureRule(n, wfun=None, alpha=None, beta=None)[source]#

Compute Gauss-Legendre quadrature points and weights.

Returns n base points (abscissas) and corresponding weight factors for Gauss-Legendre quadrature on the interval [-1, 1]. An n-point rule integrates polynomials of degree up to 2*n* - 1 exactly.

The algorithm follows Davis and Rabinowitz, Methods of Numerical Integration, Academic Press, 1975, p. 365.

Parameters:

  • n (int) – Number of quadrature points.

  • wfun (int, optional) – Weight function selector (only 1 — Gauss-Legendre — is implemented).

  • alpha (float, optional) – Not used for Gauss-Legendre; must be > -1 if supplied.

  • beta (float, optional) – Not used for Gauss-Legendre; must be > -1 if supplied.

Returns:

  • bp (ndarray) – Base points (abscissas) in [-1, 1], length n.

  • wf (ndarray) – Corresponding weight factors, length n.