Is anyone aware of a package that is able to do a Fast Legendre Transform similar to the one in chebfun (The fast discrete Legendre transform » Chebfun).
The closest that I could find was something in FastTransform, where from the chebysheb mesh you generate (fast), the legendre coefficient. But that’s not quite what I need.
You can use the inverse nonuniform FFT (Home · FastTransforms.jl) to convert Legendre samples to a Chebyshev series, then call cheb2leg.
Edit: The Gauss–Legendre points live in GitHub - JuliaApproximation/FastGaussQuadrature.jl: Julia package for Gaussian quadrature
Ok so I had read about the existence of an algorithm NlogN for the Legendre Transform, however it seems that it only is worth using for N > 1000 or something like (in comparison to just use the Matrix multiplication strategy) and most likely if you need that many points, then the legendre polynomials where not a good basis to start from.