The program LOPT for least-squares optimization of energy levels

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.: 19 254No. of bytes in distributed program, including test data, etc.: 427 839Distribution format: tar.gzProgramming language: Perl 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 N3N3 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=100N=100, or 60 s for N=400N=400 on a typical PC.