The program LOPT for least-squares optimization of energy levels
The program LOPT for least-squares optimization of energy levels
复制标题
DOI：
10.1016/j.cpc.2010.09.019
复制
发表时间：
2011-02-01
影响因子：
6.3
通讯作者：
Kramida, A. E.
中科院分区：
文献类型：
--
作者：
Kramida, A. E.
这篇文章描述了一个解决最小二乘优化问题的程序，该程序基于一组测量的能量分离或这些能级之间的跃迁波长，以及确定跃迁的里兹波长及其不确定性，来求出量子力学系统的能级。能级通过求解问题的矩阵方程来确定，而里兹波数的不确定性则由问题的协方差矩阵来确定。计划摘要计划标题：LOPT目录标识符：AEHM_v1_0计划摘要URL：http://cpc.cs.qub.ac.uk/summaries/AEHM_v1_0.htmlProgram可从：爱尔兰贝尔法斯特女王大学CPC程序图书馆获得。许可条款：标准CPC许可证，http://cpc.cs.qub.ac.uk/licence/licence.htmlNo.分布式程序的行数，包括测试数据等：19254No.分布式程序的字节数，包括测试数据等：427 839分布格式：tar.gz编程语言：PERT v.5计算机：PC、Mac、Unix工作站操作系统：MS Windows(XP.Vista，7)，Mac OS X，Linux，Unix(AIX)RAM：3 Mword或更多字大小：32或64分类：2.2问题的性质：最小二乘能级优化问题，即找到一组最适合给定过渡区间的能级值。解决方法：最小二乘问题的解通过求解相应的线性矩阵方程来找到，其中矩阵是使用具有变量替换的新方法构造的。限制：由执行时间对问题N的大小施加实际限制，不寻常的特点：适当地对结果数据进行舍入，并以适合于使用电子表格编辑软件查看的格式来格式化输出。估计由于机器精度有限而产生的数值误差。在典型的PC上，运行时间：1 S(N=100)或60 S(N=400)。(C)201 0爱思唯尔B.V.保留所有权利。
The article describes a program that solves the least-squares optimization problem for finding the energy levels of a quantum-mechanical system based on a set of measured energy separations or wavelengths of transitions between those energy levels, as well as determining the Ritz wavelengths of transitions and their uncertainties. The energy levels are determined by solving the matrix equation of the problem, and the uncertainties of the Ritz wavenumbers are determined from the covariance matrix of the problem.Program summaryProgram title: LOPTCatalogue identifier: AEHM_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 19254No. of bytes in distributed program, including test data, etc.: 427 839Distribution format: tar.gzProgramming language: Pert v.5Computer: PC, Mac, Unix workstationsOperating system: MS Windows (XP. Vista, 7), Mac OS X, Linux, Unix (AIX)RAM: 3 Mwords or moreWord size: 32 or 64Classification: 2.2Nature of problem: The least-squares energy-level optimization problem, i.e., finding a set of energy level values that best fits the given set of transition intervals.Solution method: The solution of the least-squares problem is found by solving the corresponding linear matrix equation, where the matrix is constructed using a new method with variable substitution.Restrictions: A practical limitation on the size of the problem N is imposed by the execution time, which scales as N-3 and depends on the computer.Unusual features: Properly rounds the resulting data and formats the output in a format suitable for viewing with spreadsheet editing software. Estimates numerical errors resulting from the limited machine precision.Running time: 1 s for N = 100, or 60 s for N = 400 on a typical PC. (c) 201 0 Elsevier B.V. All rights reserved.