An algorithm is presented to extract the distance list from atomic pair distribution functions in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Because of the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.

中文翻译：

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从对分布函数中提取距离列表的算法

提出了一种以高度自动化的方式从原子对分布函数中提取距离列表的算法。该算法是通过基于德拜散射方程模型的曲线拟合构建的。由于所产生的优化问题的非凸性质，开发了许多技术来克服各种计算困难。一个关键要素是一种根据数学模型的理论特性获得合理初始猜测的新方法。对各种纳米结构样品的测试表明了初始猜测的有效性以及提取算法的准确性和整体良好性能。这种方法可以扩展到任何近似为高斯函数之和的频谱。