# AutoSymPTR.jl

`AutoSymPTR`

— ModuleA package implementing the automatic symmetrized periodic trapezoidal rule (PTR) for spectrally-accurate integration of periodic functions with the algorithm described by Kaye et al.. The main routine is `autosymptr`

, which computes the integral of a periodic function to within a requested error tolerance. If nontrivial symmetries are provided, the routines return the integral on the symmetry-reduced domain, since it is generally up to the caller to implement the mapping back to the full domain, which is nontrivial in cases with non-scalar integrands. A simple example is

```
using LinearAlgebra, AutoSymPTR
autosymptr(x -> 1 + mapreduce(y -> cospi(2y), +, x), I(3))[1] ≈ 1
```