f90_quadratures

Modern Fortran modules to generate quadrature rules.

Functionality

Gauss-Legendre - this is via Golub-Welsh and Townsend-Hale. Golub-Welsch ok upto n ~ 10^3 [O(n^2) scaling] and Townsend-Hale ok for 10^3 < n <~ 10^9 [O(n) scaling]. Use cudabigquad for n ~> 10^6 as much faster.
Gauss-Jacobi - this is via Golub-Welsch with O(n^2) complexity which is quick upto n ~ 10^3
Gauss-Christofel - currently only polynomial weight functions are supported scaling is currently O(n^2), runtime is ~double that of Gauss-Legendre. Uses LAPACK Divide-and-conquer for n > 500, giving O(nlog(n)) scaling.
Clenshaw-Curtis - complexity O(n^2) but slower than Gauss-Legendre
Gauss-Kronrod - this is through Golub-Welsch and is agian O(n^2)
Others - Chebyshev,Gegenbauer, Gen' Laguerre, Gen' Hermite, Exponential and Rational (beta distribution weights) can also be calculated. These are accessable through the subroutine quad. (this is using code by S. Elhay, J. Kautsky and J. Burkardt which uses Golub-Welsch under the hood).