pub fn default_sampling_points(
u: &PiecewiseLegendrePolyVector,
l: usize,
) -> Vec<f64>Expand description
Get default sampling points in [-1, 1]
C++ implementation: libsparseir/include/sparseir/basis.hpp:287-310
For orthogonal polynomials (the high-T limit of IR), we know that the ideal sampling points for a basis of size L are the roots of the L-th polynomial. We empirically find that these stay good sampling points for our kernels (probably because the kernels are totally positive).
If we do not have enough polynomials in the basis, we approximate the roots of the L’th polynomial by the extrema of the last basis function, which is sensible due to the strong interleaving property of these functions’ roots.