UNIVERSAL CRYSTALLOGRAPHIC FAST FOURIER TRANSFORM PACKAGE

该项目的长期目标是提供高性能的晶体学快速傅立叶变换，以纳入专门用于以原子分辨率可视化病毒或蛋白质结构的软件包中。具体而言，功率晶体对称傅立叶变换的新的数学公式将被探索作为主要的设计工具。预期的结果是一个高效的数学软件包，用于计算三维晶体傅立叶变换的3D数据样本，其边缘大小是一个素数的幂（特别是，2的幂）或素数的乘积（混合基数）。该程序包中的例程将避免计算中的冗余数据和晶体对称性引起的操作，并将适用于所有晶体对称性。新方法的实际准确性、适用性和效率将通过计算机实验和数学/算法修改的循环来实现。将选择几个测试问题，并在不同的计算机平台上测试软件原型。

The long-term objective of this project is to provide high-performance crystallographic fast Fourier transform for inclusion in software packages devoted to the visualization of virus or protein structures at atomic resolution. Specifically, the power of new mathematical formulation for crystal symmetric Fourier transformation will be explored as main design tool. The intended result is a highly-efficient mathematical software package for computing three-dimensional crystallographic Fourier transforms on 3D data-samples whose edge-size is a power of a prime (in particular, a power of two) or, product of primes (mixed radix). The routines in this package will avoid computing with redundant data and operations induced by the symmetries of the crystal, and will be applicable to all crystal symmetries. The actual accuracy, applicability, and efficiency of the new methods will be achieved through cycles of computer experimentation and mathematical/algorithmic modifications. Several test problems will be selected, and software prototypes will be tested on different computer platforms.