GYutsis: heuristic based calculation of general recoupling coefficients

General angular momentum recoupling coefficients can be expressed as a summation formula over products of 6-j coefficients. Yutsis, Levinson and Vanagas developed graphical techniques for representing the general recoupling coefficient as a cubic graph and they describe a set of reduction rules allowing a stepwise generation of the corresponding summation formula. This paper is a follow up to Van Dyck and Fack, Comput. Phys. Comm. 151 (2003) 353-368] where we described a heuristic algorithm based on these techniques. In this article we separate the heuristic from the algorithm and describe some new heuristic approaches which can be plugged into the generic algorithm. We show that these new heuristics lead to good results: in many cases we get a more efficient summation formula than our previous approach, in particular for problems of higher order. In addition the new features and the use of our program GYutsis, which implements these techniques, is described both for end users and application programmers.

Program summary

Title of program: CycleCostAlgorithm, GYutsisCatalogue number: ADSAProgram Summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSAProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland. Users may obtain the program also by downloading either the compressed tar file gyutsis.tgz (for Unix and Linux) or the zip file gyutsis.zip (for Windows) from our website (http://caagt.rug.ac.be/yutsis/). An applet version of the program is also available on our website and can be run in a web browser from the URL http://caagt.rug.ac.be/yutsis/GYutsisApplet.html.Licensing provisions: noneComputers for which the program is designed: any computer with Sun's Java Runtime Environment 1.4 or higher installed.Programming language used: Java 1.2 (Compiler: Sun's SDK 1.4.0)No. of lines in program: approximately 9400No. of bytes in distributed program, including test data, etc.: 544 117Distribution format: tar gzip fileNature of physical problem: A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta can be expressed as a formula consisting of products of 6-j coefficients summed over a certain number of variables. Such a formula can be generated using the program GYutsis (with a graphical user front end) or CycleCostAlgorithm (with a text-mode user front end).Method of solution: Using the graphical techniques of Yutsis, Levinson and Vanagas (1962) a summation formula for a general recoupling coefficient is obtained by representing the coefficient as a Yutsis graph and by performing a selection of reduction rules valid for such graphs. Each reduction rule contributes to the final summation formula by a numerical factor or by an additional summation variable. Whereas an optimal summation formula (i.e. with a minimum number of summation variables) is hard to obtain, we present here some new heuristic approaches for selecting an edge from a k-cycle in order to transform it into an (k−1)-cycle (k>3) in such a way that a ‘good’ summation formula is obtained.Typical running time: From instantaneously for the typical problems to 30 s for the heaviest problems on a Pentium II-350 Linux-system with 256 MB RAM.