VAMPyR——一个用于多小波表示中数学运算的高级Python库
VAMPyR -- A High-Level Python Library for Mathematical Operations in a Multiwavelets Representation
AI总结：
本文介绍Python库VAMPyR，它封装多小波C++计算功能，支持高精度求解Hartree-Fock、Poisson、Dirac及含时Schrödinger方程，缩小了理论形式与代码实现之间的差距。
摘要：
小波和多小波近年来已被引入量子化学领域，以克服两类主要基组——高斯型原子轨道和平面波——所带来的挑战。除了其数值优势（高精度、局域性、用于算子应用的快速算法、相对于体系规模的线性标度等）之外，它们还提供了一个框架，缩小了基本方程的理论形式与工作代码中的实际实现之间的差距。这一认识促使我们开发了名为VAMPyR（Very Accurate Multiresolution Python Routines，高精度多分辨Python例程）的Python库。VAMPyR封装了与用于多小波计算（代数、积分和微分算子应用）的C++库的绑定，并暴露了所需的功能，以便编写简单的Python代码来求解Hartree--Fock方程、广义Poisson方程、Dirac方程以及含时Schrödinger方程，且可达到任意预定义精度。在本文中，我们将概述使用多小波进行多分辨分析的主要特征，并描述代码的设计。几个示例将展示该代码的能力及其与其他软件平台的互操作性。
英文摘要：
Wavelets and Multiwavelets have lately been adopted in Quantum Chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few) they provide a framework which narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR, (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for Multiwavelet calculations (algebra, integral and differential operator application) and exposes the required functionality to write simple Python code to solve among others, the Hartree--Fock equations, the generalized Poisson Equation, the Dirac equation and the time-dependent Schrödinger equation up to any predefined precision. In this contribution we will outline the main features of Multiresolution Analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
