num::gauss_legendre

Defined in header <quadrature/quadrature.hpp>

template <typename Float = double, std::invocable<Float> Func = scalar_fn>
Float gauss_legendre(Func &&f, Float a, Float b, idx p = 5);

Gauss–Legendre quadrature with \(p \in [1, 5]\) optimal nodes.

Exact for all polynomials up to degree \(2p - 1\) using precomputed roots and weights of Legendre polynomials.

Template parameters

• Float: Floating point scalar type.
• Func: Integrand callable.

Parameters

• f: Integrand function.
• a: Lower integration limit.
• b: Upper integration limit.
• p: Number of quadrature nodes (\(1 \le p \le 5\), default: 5).

Return value

Exact or high-precision approximation of the integral.

Exceptions

• std::invalid_argument: If p is not in range \([1, 5]\).