An object-oriented C++ implementation of Davidson method for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix

A C++ class named Davidson is presented for determining a few eigenpairs with lowest or alternatively highest values of a large, real, symmetric matrix. The algorithm described by Stathopoulos and Fischer is used. The exception mechanism is involved to report the errors. The class is written in ANSI C++, so it is fully portable. In addition a console program as well as a program with graphical user interface for Microsoft Windows is attached, which allow one to calculate the lowest eigenstates of time-independent Schrödinger equation for a given binding potential in one, two or three spatial dimensions. The package contains the classes providing often used potential functions (model atom potential, Coulomb potential, square well potential and Kramers-Henneberger well potential) as well as a possibility to use any potential stored in a file (then any dimensionality of the problem is allowed).The described code is the subject of M.Sc. thesis of T.D. prepared under the supervision of J.M.

Program summary

Program title: DavidsonCatalogue identifier: ADZM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZM_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.: 3 037 055No. of bytes in distributed program, including test data, etc.: 20 002 609Distribution format: tar.gzProgramming language: C++Computer: AllOperating system: AnyRAM: User's parameters dependentWord size: 32 and 64 bitsSupplementary material: Test results for the 2D and 3D cases is availableClassification: 4, 4.8Nature of problem: Finding a few extreme eigenpairs of a real, symmetric, sparse matrix. Examples in quantum optics (interaction of matter with a laser field).Solution method: Davidson algorithmRunning time: The test example included in the distribution package (1D matrix) takes approximately 30 minutes to run. 2D matrix calculations can take hours and 3D, days, to run.