Weingarten Calculus and the IntHaar Package for Integrals over Compact Matrix Groups. In this paper, we present a uniform formula for the integration of polynomials over the unitary, orthogonal, and symplectic groups using Weingarten calculus. From this description, we further simplify the integration formulas and give several optimizations for various cases. We implemented the optimized Weingarten calculus in Maple in a package called IntHaar for all three compact groups. Here we will discuss its functions, provide instructions for the package, and produce some examples of computed integrals.
Keywords for this software
References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Ginory, Alejandro; Kim, Jongwon: Weingarten calculus and the IntHaar package for integrals over compact matrix groups (2021)
- Motohisa Fukuda, Robert Koenig, Ion Nechita: RTNI - A symbolic integrator for Haar-random tensor networks (2019) arXiv
- Alejandro Ginory, Jongwon Kim: Weingarten Calculus and the IntHaar Package for Integrals over Compact Matrix Groups (2016) arXiv