orthax.orthgauss

orthax.orthgauss(deg, rec, x0=None, x1=None)Source

Compute Gaussian quadrature nodes and weights for given orthogonal polynomials.

Can optionally compute Gauss-Radau or Gauss-Lobatto points if x0 and/or x1 are given.

Parameters:

  • deg (int) – Number of sample points and weights. It must be >= 1.

  • rec (AbstractRecurrenceRelation) – Recurrence relation for the family of orthogonal polynomials

  • x0 (float, optional) – Optional points to include in the nodes, for Gauss-Radau (if x0 is given) or Gauss-Lobatto (if x0 and x1 given). Generally taken to be the start and/or end points of the interval of integration.

  • x1 (float, optional) – Optional points to include in the nodes, for Gauss-Radau (if x0 is given) or Gauss-Lobatto (if x0 and x1 given). Generally taken to be the start and/or end points of the interval of integration.

Returns:

x, w (jax.Array, shape(n,)) – Nodes and weights for n point quadrature rule.