Optimized implementation for calculation and fast-update of Pfaffians installed to the open-source fermionic variational solver mVMC

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 6 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.本文提出了一种高性能、可移植且模板设计完善的实现方案，用于计算偶阶斜对称（反对称）矩阵的普法夫行列式（Pfaffian）及其逆矩阵，并支持快速更新。该方案依托帕利特-里德（Parlett-Reid）算法的斜对称分块变体，以及基于伍德伯里矩阵恒等式的分块更新策略得以实现。将此框架集成至基于双子波函数的多变量变分蒙特卡洛（mVMC）代码后，可在不改变马尔可夫链行为的前提下，将采样性能提升至6倍以上。本实现基于类BLAS实例化软件（BLIS）框架的扩展版本，该框架针对英特尔Skylake-X、AMD EPYC Rome及富士通A64FX等多款当前主流处理器优化了计算内核。