Optimized Implementation for Calculation and Fast-Update of Pfaffians Installed to the Open-Source Fermionic Variational Solver mVMC
Abstract
In this article, we present a high performance, portable and well templated implementation for computing and fast-updating Pfaffian and inverse of an even-ranked skew-symmetric (antisymmetric) matrix. It is achieved with a skew-symmetric, blocked variant of the Parlett-Reid algorithm and a blocked update scheme based on the Woodbury matrix identity. Installation of this framework into the geminal-wavefunction-based many-variable Variational Monte Carlo (mVMC) code boosts sampling performance to up to more than times without changing Markov chain's behavior. The implementation is based on an extension of the BLAS-like instantiation software (BLIS) framework which has optimized kernel for many state-of-the-art processors including Intel Skylake-X, AMD EPYC Rome and Fujitsu A64FX.
Cite
@article{arxiv.2105.13098,
title = {Optimized Implementation for Calculation and Fast-Update of Pfaffians Installed to the Open-Source Fermionic Variational Solver mVMC},
author = {RuQing G. Xu and Tsuyoshi Okubo and Synge Todo and Masatoshi Imada},
journal= {arXiv preprint arXiv:2105.13098},
year = {2022}
}
Comments
18 pages, 3 figures and 3 tables. Source code presented in this work can be obtained from http://github.com/issp-center-dev/mVMC/tree/develop