ACTest: A testing toolkit for analytic continuation methods and codes

TL;DR

ACTest is an open-source Julia toolkit for generating diverse spectral and Green's function datasets to benchmark and evaluate analytic continuation methods, supporting realistic noise and various spectral features.

Contribution

It introduces a comprehensive, automated dataset generation and testing framework for analytic continuation methods, integrated with the ACFlow toolkit for benchmarking.

Findings

Benchmark results for the maximum entropy method on ACT100 dataset.

Supports diverse spectral functions and Green's functions with realistic noise.

Facilitates evaluation of accuracy and efficiency of analytic continuation methods.

Abstract

ACTest is an open-source toolkit developed in the Julia language. Its central goal is to automatically establish analytic continuation testing datasets, which include a large number of spectral functions and the corresponding Green's functions. These datasets can be used to benchmark various analytic continuation methods and codes. In ACTest, the spectral functions are constructed by a superposition of randomly generated Gaussian, Lorentzian, $\delta$-like, rectangular, and Rise-And-Decay peaks. The spectra can be positive definite or non-positive definite. The corresponding energy grids can be linear or non-linear. ACTest supports both fermionic and bosonic Green's functions on either imaginary time or Matsubara frequency axes. Artificial noise can be superimposed on the synthetic Green's functions to simulate realistic Green's functions obtained by quantum Monte Carlo calculations. ACTest includes a standard testing dataset, namely ACT100. This built-in dataset contains 100 testing cases that cover representative analytic continuation scenarios. Now ACTest is fully integrated with the ACFlow toolkit. It can directly invoke the analytic continuation methods as implemented in the ACFlow toolkit for calculations, analyze calculated results, and evaluate computational efficiency and accuracy. ACTest comprises many examples and detailed documentation. The purpose of this paper is to introduce the major features and usages of the ACTest toolkit. The benchmark results on the ACT100 dataset for the maximum entropy method, which is probably the most popular analytic continuation method, are also presented.