Function lagrange

pub fn lagrange<N: ComplexField + FromPrimitive + Copy>(
    xs: &[N],
    ys: &[N],
    tol: N::RealField,
) -> Result<Polynomial<N>, String>
where
    <N as ComplexField>::RealField: FromPrimitive + Copy,

Create a Lagrange interpolating polynomial.

Create an nth degree polynomial matching the n points (xs[i], ys[i]) using Neville’s iterated method for Lagrange polynomials. The result will match no derivatives.

Examples

use bacon_sci::interp::lagrange;
use bacon_sci::polynomial::Polynomial;
fn example() {
    let xs: Vec<_> = (0..10).map(|i| i as f64).collect();
    let ys: Vec<_> = xs.iter().map(|x| x.cos()).collect();
    let poly = lagrange(&xs, &ys, 1e-6).unwrap();
    for x in xs {
        assert!((x.cos() - poly.evaluate(x)).abs() < 0.00001);
    }
}