New heuristic approach to the 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 on such a graph which allow a stepwise generation of the corresponding summation formula. In this paper we present a new heuristic approach to earlier reduction algorithms based on these techniques. In particular the heuristic tries in each step to make an ‘intelligent’ choice of which specific reduction rule to apply on which part of the graph. This approach leads to good results: in many cases we get a more efficient summation formula than the other algorithms. The program is written in Java and offers a platform-independent graphical user front end which allows user-friendly manipulation of recoupling coefficients as well as a detailed follow-up of the reduction process.     

FLY. A parallel tree N-body code for cosmological simulations

FLY is a parallel treecode which makes heavy use of the one-sided communication paradigm to handle the management of the tree structure. In its public version the code implements the equations for cosmological evolution, and can be run for different cosmological models.This reference guide describes the actual implementation of the algorithms of the public version of FLY, and suggests how to modify them to implement other types of equations (for instance, the Newtonian ones).

Program summary

Title of program:FLYCatalogue identifier: ADSCProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSCProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: Cray T3E, Sgi Origin 3000, IBM SPOperating systems or monitors under which the program has been tested: Unicos 2.0.5.40, Irix 6.5.14, Aix 4.3.3Programming language used: Fortran 90, CMemory required to execute with typical data: about 100 Mwords with 2 million-particlesNumber of bits in a word: 32Number of processors used: parallel program. The user can select the number of processors ?1Has the code been vectorized or parallelized?: parallelizedNumber of bytes in distributed program, including test data, etc.: 4 615 604Distribution format: tar gzip fileKeywords: Parallel tree N-body code for cosmological simulationsNature of physical problem:FLY is a parallel collisionless N-body code for the calculation of the gravitational force.Method of solution: It is based on the hierarchical oct-tree domain decomposition introduced by Barnes and Hut (1986).Restrictions on the complexity of the program: The program uses the leapfrog integrator schema, but could be changed by the user.Typical running time: 50 seconds for each time-step, running a 2-million-particles simulation on an Sgi Origin 3800 system with 8 processors having 512 Mbytes RAM for each processor.Unusual features of the program:FLY uses the one-side communications libraries: the SHMEM library on the Cray T3E system and Sgi Origin system, and the LAPI library on IBM SP system     

New efficient programs to calculate general recoupling coefficients: Part I: Generation of a summation formula

A program to generate a summation formula in terms of 6-j coefficients for a general angular momentum recoupling coefficient is described. This algorithms makes use of binary tree transformations as introduced by Burke [Comput. Phys. Commun. 1 (1970) 241] in the program NJSYM. Due attention is paid to finding an optimal summation formula with a minimal number of summation variables, thereby improving the results of NJSYM. The results obtained here are at least as good as (and often better than) the results of the alternative approach NJGRAF, introduced by Bar-Shalom and Klapisch [Comput. Phys. Commun. 50 (1998) 375], using more advanced graphical methods.     

Reduze - Feynman integral reduction in C++

Reduze is a computer program for reducing Feynman integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel.

Program summary

Program title:ReduzeCatalogue identifier: AEGE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:: yesNo. of lines in distributed program, including test data, etc.: 55 433No. of bytes in distributed program, including test data, etc.: 554 866Distribution format: tar.gzProgramming language: C++Computer: AllOperating system: Unix/LinuxNumber of processors used: The number of processors is problem dependent. More than one possible but not arbitrary many.RAM: Depends on the complexity of the system.Classification: 4.4, 5External routines: CLN (http://www.ginac.de/CLN/), GiNaC (http://www.ginac.de/)Nature of problem: Solving large systems of linear equations with Feynman integrals as unknowns and rational polynomials as prefactors.Solution method: Using a Gauss/Laporta algorithm to solve the system of equations.Restrictions: Limitations depend on the complexity of the system (number of equations, number of kinematic invariants).Running time: Depends on the complexity of the system.     

The tauola-photos-F environment for the TAUOLA and PHOTOS packages, release II

We present the system for maintaining the versions of two packages: the TAUOLA of τ-lepton decay and PHOTOS for radiative corrections in decays. The following features can be chosen in an automatic or semi-automatic way: (1) format of the common block HEPEVT; (2) version of the physics input (for TAUOLA): as published, as initialized by the CLEO collaboration, as initialized by the ALEPH collaboration (it is suggested to use this version only with the help of the collaboration advice), new optional parametrization of matrix elements in 4π decay channels; (3) type of application: stand-alone, universal interface based on the information stored in the HEPEVT common block including longitudinal spin effects in the elementary Z/γ^∗→τ⁺τ⁻ process, extended version of the standard universal interface including full spin effects in the H/A→τ⁺τ⁻ decay, interface for KKMC Monte Carlo, (4) random number generators; (5) compiler options. The last section of the paper contains documentation of the programs updates introduced over the last two years.

Program summary

Title of program:tauola-photos-F, release IICatalogue identifier:ADXO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXO_v1_0Programs obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: PC running GNU/Linux operating systemProgramming languages and tools used:CPP: standard C-language preprocessor, GNU Make builder tool, also FORTRAN compilerNo. of lines in distributed program, including test data, etc.: 194 118No. of bytes in distributed program, including test data, etc.:2 481 234Distribution format: tar.gzCatalogue identifier:ADXO_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXO_v2_0No. of lines in distributed program, including test data, etc.:308 235No. of bytes in distributed program, including test data, etc.:2 988 363Distribution format:tar.gzDoes the new version supersede the previous version:YesNature of the physical problem: The code of Monte Carlo generators often has to be tuned to the needs of large HEP Collaborations and experiments. Usually, these modifications do not introduce important changes in the algorithm, but rather modify the initialization and form of the hadronic current in τ decays. The format of the event record (HEPEVT common block) used to exchange information between building blocks of Monte Carlo systems often needs modification. Thus, there is a need to maintain various, slightly modified versions of the same code. The package presented here allows the production of ready-to-compile versions of TAUOLA [S. Jadach, Z. Wa?s, R. Decker, J.H. Kühn, Comput. Phys. Comm. 76 (1993) 361; A.E. Bondar, et al., Comput. Phys. Comm. 146 (2002) 139] and PHOTOS [E. Barberio, Z. Wa?s, Comput. Phys. Comm. 79 (1994) 291] Monte Carlo generators with appropriate demonstration programs. The new algorithm, universal interface of TAUOLA to work with the HEPEVT common block, is also documented here. Finally, minor technical improvements of TAUOLA and PHOTOS are also listed.Method of solution: The standard UNIX tool: the C-language preprocessor is used to produce a ready-to-distribute version of TAUOLA and PHOTOS code. The final FORTRAN code is produced from the library of ‘pre-code’ that is included in the package.Reasons for new version: The functionality of the version of TAUOLA and PHOTOS changed over the last two years. The changes, and their reasons, are documented in Section 9, and our new papers cited in this section.Additional comments: The updated version includes new features described in Section 9 of the paper. PHOTOS and TAUOLA were first submitted to the library as separate programs. Summary details of these previous programs are obtainable from the CPC Program Library.Typical running time: Depends on the speed of the computer used and the demonstration program chosen. Typically a few seconds.     

Spectroscopic LSJ notation for atomic levels obtained from relativistic calculations

Today, relativistic calculations are known to provide a very successful means in the study of open-shell atoms and ions. But although accurate atomic data are obtained from these computations, they are traditionally carried out in jj-coupling and, hence, do often not allow for a simple LSJ classification of the atomic levels as needed by experiment. In fact, this lack of providing a proper spectroscopic notation from relativistic structure calculations has recently hampered not only the spectroscopy of medium and heavy elements, but also the interpretation and analysis of inner-shell processes, for which the occurrence of additional vacancies usually leads to a very detailed fine structure.Therefore, in order to facilitate the classification of atomic levels from such computations, here we present a program (within the Ratip environment) which help transform the atomic wave functions from jj-coupled multiconfiguration Dirac-Fock computations into a LS-coupled representation. Beside of a proper LSJ assignment to the atomic levels, the program also supports the full transformation of the wave functions if required for (nonrelativistic) computations.

Program summary

Title of program:LsjCatalogue number: ADTLProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTLProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: NoneComputer for which the new version has been tested: IBM RS 6000, PC Pentium IIIInstallations: University of Kassel (Germany)Operating systems: IBM AIX 4.1.2+, Linux 7.1.+Program language used in the new version: ANSI standard Fortran 90/95Memory required to execute with typical data: Memory requirements depend on the shell structure and the size of the wave function expansion which is used to represent the atomic levelsNo. of bits in a word: All real variables are parametrized by a selected kind parameter and, thus, can easily be adapted to any required precision as supported by the compiler. Presently, the kind parameter is set to double precision (two 32-bit words) in the module rabs_constantNo. of lines in distributed program, including test data, etc.: 225 242No. of bytes in distributed program, including test data, etc.: 3 646 630CPU time required to execute test data: 5 s on a 1 GHz Pentium III processorDistribution format: tar gzip fileKeywords: Atomic, LSJ spectroscopic notation, LS−jj transformation, multiconfiguration Dirac-Fock, recoupling of angular momenta, relativisticNature of the physical problem: The spectroscopic LSJ notation is determined for atomic levels which were calculated previously in the framework of the jj-coupled multiconfiguration Dirac-Fock (MCDF) model. This notation is based on a complete jj−LS transformation of the leading jj-coupled configuration state functions (CSF) in the wave function representation of the selected levels.Restrictions onto the complexity of the problem: The jj→LS transformation of the (jj-coupled) CSF is supported for all shell structures including open s-, p-, d-, and f-shells. For shells with l>3 (i.e. beyond the f-subshells), however, a proper transformation of the antisymmetrized subshell states can be carried out only for the case of one or two equivalent electrons. This restriction also applies for the transformation of the and subshell states which are otherwise supported by the Ratip package [Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155]. The jj↔LS transformation matrices, which are applied internally by the program, are consistent with the definition of the (reduced) coefficients of fractional parentage [Gaigalas et al., At. Data Nucl. Data Tables 70 (1998) 1; Gaigalas et al., At. Data Nucl. Data Tables 76 (2000) 235] as published previously.Unusual features of the program: The Lsj program is designed as a part of the Ratip package [Fritzsche, Elec. Spec. Rel. Phen. 114-116 (2001) 1155] for the computation of (relativistic) atomic transition and ionization properties. This (new) component therefore supports the transformation of all atomic states which are generated either with Ratip or by means of the Grasp92 code [Parpia et al., Comput. Phys. Comm. 94 (1996) 249]. Moreover, the normalization of the transformed states is tested within the LSJ-coupled basis.     

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.     

MC-TESTER: a universal tool for comparisons of Monte Carlo predictions for particle decays in high energy physics

Theoretical predictions in high energy physics are routinely provided in the form of Monte Carlo generators. Comparisons of predictions from different programs and/or different initialization set-ups are often necessary. MC-TESTER can be used for such tests of decays of intermediate states (particles or resonances) in a semi-automated way. Our test consists of two steps. Different Monte Carlo programs are run; events with decays of a chosen particle are searched, decay trees are analyzed and appropriate information is stored. Then, at the analysis step, a list of all found decay modes is defined and branching ratios are calculated for both runs. Histograms of all scalar Lorentz-invariant masses constructed from the decay products are plotted and compared for each decay mode found in both runs. For each plot a measure of the difference of the distributions is calculated and its maximal value over all histograms for each decay channel is printed in a summary table. As an example of MC-TESTER application, we include a test with the τ lepton decay Monte Carlo generators, TAUOLA and PYTHIA. The HEPEVT (or LUJETS) common block is used as exclusive source of information on the generated events.

Program summary

Title of the program:MC-TESTER, version 1.1Catalogue identifier: ADSMProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSMProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: PC, two Intel Xeon 2.0 GHz processors, 512MB RAMOperating system: Linux Red Hat 6.1, 7.2, and also 8.0Programming language used:C++, FORTRAN77: gcc 2.96 or 2.95.2 (also 3.2) compiler suite with g++ and g77Size of the package: 7.3 MB directory including example programs (2 MB compressed distribution archive), without ROOT libraries (additional 43 MB).No. of bytes in distributed program, including test data, etc.: 2 024 425Distribution format: tar gzip fileAdditional disk space required: Depends on the analyzed particle: 40 MB in the case of τ lepton decays (30 decay channels, 594 histograms, 82-pages booklet).Keywords: particle physics, decay simulation, Monte Carlo methods, invariant mass distributions, programs comparisonNature of the physical problem: The decays of individual particles are well defined modules of a typical Monte Carlo program chain in high energy physics. A fast, semi-automatic way of comparing results from different programs is often desirable, for the development of new programs, to check correctness of the installations or for discussion of uncertainties.Method of solution: A typical HEP Monte Carlo program stores the generated events in the event records such as HEPEVT or PYJETS. MC-TESTER scans, event by event, the contents of the record and searches for the decays of the particle under study. The list of the found decay modes is successively incremented and histograms of all invariant masses which can be calculated from the momenta of the particle decay products are defined and filled. The outputs from the two runs of distinct programs can be later compared. A booklet of comparisons is created: for every decay channel, all histograms present in the two outputs are plotted and parameter quantifying shape difference is calculated. Its maximum over every decay channel is printed in the summary table.Restrictions on the complexity of the problem: For a list of limitations see Section 6.Typical running time: Varies substantially with the analyzed decay particle. On a PC/Linux with 2.0 GHz processors MC-TESTER increases the run time of the τ-lepton Monte Carlo program TAUOLA by 4.0 seconds for every 100000 analyzed events (generation itself takes 26 seconds). The analysis step takes 13 seconds; processing takes additionally 10 seconds. Generation step runs may be executed simultaneously on multi-processor machines.Accessibility: web page: http://cern.ch/Piotr.Golonka/MC/MC-TESTER e-mails: Piotr.Golonka@CERN.CH, T.Pierzchala@friend.phys.us.edu.pl, Zbigniew.Was@CERN.CH.     

Automatized analytic continuation of Mellin-Barnes integrals

This paper describe a package written in MATHEMATICA that automatizes typical operations performed during evaluation of Feynman graphs with Mellin-Barnes (MB) techniques. The main procedure allows to analytically continue a MB integral in a given parameter without any intervention from the user and thus to resolve the singularity structure in this parameter. The package can also perform numerical integrations at specified kinematic points, as long as the integrands have satisfactory convergence properties. It is demonstrated that, at least in the case of massive graphs in the physical region, the convergence may turn out to be poor, making naïve numerical integration of MB integrals unusable. Possible solutions to this problem are presented, but full automatization in such cases may not be achievable.

Program summary

Title of program: MBProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYG_v1_0Catalogue identifier: ADYG_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers: AllOperating systems: AllProgramming language used:MATHEMATICA, Fortran 77 for numerical evaluationMemory required to execute with typical data: Sufficient for a typical installation of MATHEMATICA.No. of lines in distributed program, including test data, etc.: 12 013No. of bytes in distributed program, including test data, etc.: 231 899Distribution format: tar.gzLibraries used:CUBA [T. Hahn, Comput. Phys. Commun. 168 (2005) 78] for numerical evaluation of multidimensional integrals and CERNlib [CERN Program Library, obtainable from: http://cernlib.web.cern.ch/cernlib/] for the implementation of Γ and ψ functions in Fortran.Nature of physical problem: Analytic continuation of Mellin-Barnes integrals in a parameter and subsequent numerical evaluation. This is necessary for evaluation of Feynman integrals from Mellin-Barnes representations.Method of solution: Recursive accumulation of residue terms occurring when singularities cross integration contours. Numerical integration of multidimensional integrals with the help of the CUBA library.Restrictions on the complexity of the problem: Limited by the size of the available storage space.Typical running time: Depending on the problem. Usually seconds for moderate dimensionality integrals.     

Slavnov-Taylor1.0: A Mathematica package for computation in BRST formalism

Slavnov-Taylor is a Mathematica package which allows us to perform automatic symbolic computation in BRST formalism. This article serves as a self-contained guide to prospective users, and indicates the conventions and approximations used.

Program summary

Title of program:Slavnov-TaylorCatalogue identifier:ADSSProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSSProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming Language: Mathematica 4.0Platform: Any platform supporting Mathematica 4.0Computers tested on: Pentium PCOperating systems under which the program has been tested: LinuxMemory required to execute: Minimal: 1.254.784 bytes, Standard: 1.281.248 bytesNo. of bytes in distributed program, including test data, etc.: 8368 bytesDistribution format: tar gzip fileKeywords: Slavnov-Taylor, BRST, MathematicaNature of physical problem: Symbolic computation in the Slavnov-Taylor formalism for gauge theories in 4-dimensional space-time based on a semi-simple compact Lie group for a general BRS transformations.Restrictions on the complexity of the problem: Only matter in the adjoint is allowed.Typical running time: less than one second     

HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters

We present the Mathematica package HypExp which allows to expand hypergeometric functions around integer parameters to arbitrary order. At this, we apply two methods, the first one being based on an integral representation, the second one on the nested sums approach. The expansion works for both symbolic argument z and unit argument. We also implemented new classes of integrals that appear in the first method and that are, in part, yet unknown to Mathematica.

Program summary

Title of program:HypExpCatalogue identifier:ADXF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXF_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicence:noneComputers:Computers running Mathematica under Linux or WindowsOperating system:Linux, WindowsProgram language:MathematicaNo. of bytes in distributed program, including test data, etc.:739 410No. of lines in distributed program, including test data, etc.:89 747Distribution format:tar.gzOther package needed:the package HPL, included in the distributionExternal file required:noneNature of the physical problem:Expansion of hypergeometric functions around integer-valued parameters. These are needed in the context of dimensional regularization for loop and phase space integrals.Method of solution:Algebraic manipulation of nested sums and integral representation.Restrictions on complexity of the problem:Limited by the memory availableTypical running time:Strongly depending on the problem and the availability of libraries.     

SuperIso Relic: A program for calculating relic density and flavor physics observables in Supersymmetry

We describe SuperIso Relic, a public program for evaluation of relic density and flavor physics observables in the minimal supersymmetric extension of the Standard Model (MSSM). SuperIso Relic is an extension of the SuperIso program which adds to the flavor observables of SuperIso the computation of all possible annihilation and coannihilation processes of the LSP which are required for the relic density calculation. All amplitudes have been generated at the tree level with FeynArts/FormCalc, and widths of the Higgs bosons are computed with FeynHiggs at the two-loop level. SuperIso Relic also provides the possibility to modify the assumptions of the cosmological model, and to study their consequences on the relic density.

Program summary

Program title: SuperIso RelicCatalogue identifier: AEGD_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGD_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: yesNo. of lines in distributed program, including test data, etc.: 2 274 720No. of bytes in distributed program, including test data, etc.: 6 735 649Distribution format: tar.gzProgramming language: C (C99 Standard compliant) and FortranComputer: 32- or 64-bit PC, MacOperating system: Linux, MacOSRAM: 100 MbClassification: 1.9, 11.6External routines: ISASUGRA/ISAJET and/or SOFTSUSY, FeynHiggsDoes the new version supersede the previous version?: No (AEAN_v2_0)Nature of problem: Calculation of the lightest supersymmetric particle relic density, as well as flavor physics observables, in order to derive constraints on the supersymmetric parameter space.Solution method: SuperIso Relic uses a SUSY Les Houches Accord file, which can be either generated automatically via a call to SOFTSUSY or ISAJET, or provided by the user. This file contains the masses and couplings of the supersymmetric particles. SuperIso Relic then computes the lightest supersymmetric particle relic density as well as the most constraining flavor physics observables. To do so, it calculates first the widths of the Higgs bosons with FeynHiggs, and then it evaluates the squared amplitudes of the diagrams needed for the relic density calculation. These thousands of diagrams have been previously generated with the FeynArts/FormCalc package. SuperIso Relic is able to perform the calculations in different supersymmetry breaking scenarios, such as mSUGRA, NUHM, AMSB and GMSB.Reasons for new version: This version incorporates the calculation of the relic density, which is often used to constrain Supersymmetry.Summary of revisions:

•

Addition of the relic density calculation

•

Replacement of "float" type by "double".

Unusual features: SuperIso Relic includes the possibility of altering the underlying cosmological model and testing the influence of the cosmological assumptions.Additional comments: This program is closely associated with the "SuperIso" program - CPC Program Library, Catalogue Id. AEAN.Running time:Compilation time: a couple of hours for the statically linked version, a few minutes for the dynamically linked version. Running time: about 1 second, or a few seconds if libraries need to be compiled on the fly.     

Maple procedures for the coupling of angular momenta. An up-date of the Racah module

An up-date of the Racah module is presented, adopted to Maple 11 and 12, which supports both, algebraic manipulations of expressions from Racah's algebra as well as numerical computations of many functions and symbols from the theory of angular momentum. The functions that are known to the program include the Wigner rotation matrices and n-j symbols, Clebsch-Gordan and Gaunt coefficients, spherical harmonics of various kinds as well as several others.

Program summary

Program title:RacahCatalogue identifier: ADFV_v10_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFV_v10_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.: 30 436No. of bytes in distributed program, including test data, etc.: 544 866Distribution format: tar.gzProgramming language: Maple 11 and 12Computer: All computers with a license for the computer algebra package Maple [1]Operating system: Suse Linux 10.2+ and Ubuntu 8.10Classification: 4.1, 5Catalogue identifier of previous version: ADFV_v9_0Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 616Does the new version supersede the previous version?: YesNature of problem: The theories of angular momentum and spherical tensor operators, sometimes known also as Racah's algebra, provide a powerful calculus for studying spin networks and (quantum) many-particle systems. For an efficient use of these theories, however, one requires not only a reliable handling of a large number of algebraic transformations and rules but, more often than not, also a fast access to their standard quantities, such as the Wigner n-j symbols, Clebsch-Gordan coefficients, spherical harmonics of various kinds, the rotation matrices, and many others.Solution method: A set of Maple procedures has been developed and maintained during the last decade which supports both, algebraic manipulations as well as fast computations of the standard expressions and symbols from the theory of angular momentum [2,3]. These procedures are based on a sizeable set of group-theoretical (and often rather sophisticated) relations which has been discussed and proven in the literature; see the monograph by Varshalovich et al. [4] for a comprehensive compilation. In particular the algebraic manipulation of complex (Racah) expressions may result in considerable simplifications, thus reducing the ‘numerical costs’, and often help obtain further insight into the behaviour of physical systems.Reasons for new version: A revision of the Racah module became necessary for mainly three reasons: (i) Since the last extension of the Racah procedures [5], which was developed within the framework of Maple 8, several updates of Maple were distributed by the vendors (currently Maple 13) and required a number of adaptations to the source code; (ii) the increasing size and program structure of the Racah module made it advisible to separate the (procedures for the treatment of the) atomic shell model from the manipulation and computation of Racah expressions. Therefore, the computation of angular coefficients for different coupling schemes, (grand) coefficients of fractional parentage as well as the matrix elements (of various irreducible tensors from the shell model) is to be maintained from now on independently within the Jucys module; (iii) a number of bugs and inconsistencies have been reported to us and corrected in the present version.Summary of revisions: In more detail, the following changes have been made:

1.

Since recent versions of Maple now support the automatic type checking of all incoming arguments and the definition of user-defined types; we have adapted most of the code to take advantage of these features, and especially those commands that are accessible by the user.

2.

In the computation of the Wigner n-j symbols and Clebsch-Gordan coefficients, we now return a ‘0’ in all cases in which the triangular rules are not fulfilled, for example, if δ(a,b,c)=0 for or . This change in the program saves the user making these tests on the quantum numbers explicitly everytime (in the summation over more complex expressions) that such a symbol or coefficient is invoked. The program still terminates with an error message if the (half-integer and integer) angular momentum quantum numbers appear in an inproper combination.

3.

While a recursive generation of the Wigner 3-j and 6-j symbols [6] may reduce the costs of some computations (and has thus been utilized in the past), it also makes the program rather sophisticated, especially if an algebraic evaluation or computations with a high number of Digits need to be supported by the same generic commands. The following procedures are therefore no longer supported by the Racah module:Racah_compute_w3j_jrange(), Racah_compute_w3j_mrange(),Racah_compute_w3j_recursive(), Racah_compute_w6j_range(), andRacah_compute_w6j_recursive().On most PCs, a sequential computation of all requested symbols is carried out within the same time basically.

4.

Because the module Jucys has grown to a size of about 35,000 lines of code and data, it appears helpful and necessary to maintain it independently. The procedures from the Jucys modules were designed to facilitate the computation of matrix elements of the unit tensors, the coefficients of fractional parentage (of various types) as well as transformation matrices between different coupling schemes [7] and are, thus, independent of the Racah module (although they typically require that the Racah code is available). The Jucys module is no longer distributed together with the present code.

5.

Apart from the Wigner n-j symbols (see above), some minor bugs have been reported and corrected in Racah_expand() and Racah_set().

6.

To facilitate the test of the installation and as a first tutorial on the module, we now provide the Maple worksheet Racah-tests-2009-maple12.mw in the Racah2009 root directory. This worksheet contains the examples and test cases from the previous versions. For the test of the installation, it is recommended that a ‘copy’ of this worksheet is saved and compared to the results from the re-run. It can be used also as a helpful source to define new examples in interactive work with the Racah module.

The Racah module is distributed in a tar file ADFV_v10_0.tar.gz from which the RACAH2009 root directory is (re-)generated by the command tar -zxvf ADFV_v10_0.tar.gz. This directory contains the source code libraries (tested for Maple 11 and 12), a Read.me for the installation of the program, the worksheet Racah-tests-2009-maple12.mw as well as the document Racah-commands-2009.pdf. This .pdf document serves as a Short Reference Manual and provides the definition of all the data structures of the Racah program together with an alphabetic list of all user relevant (and exported) commands. Although emphasis was placed on preserving the compatibility of the program with earlier releases of Maple, this cannot always be guaranteed due to changes in the Maple syntax. The Racah2009 root also contains an example of a .mapleinit file that can be modified and incorporated into the user's home directory to make the Racah module accessible like any other module of Maple. As mentioned above, the worksheet Racah-tests-2009-maple12.mw, help test the installation and may serve as a first tutorial.Restrictions: The (Racah) program is based on the concept of Racah expressions [cf. Fig. 1 in Ref. [4]] which, in principle, may contain any number of Wigner n-j symbols (n?9), Clebsch-Gordan coefficients, spherical harmonics and/or rotation matrices. In practise, of course, the required time and the success of an evaluation procedure depends on the complexity of the expressions and on the storage available, sometimes also on Maple's internal garbage treatment. In some cases, it is advisable to attempt first a simplification of the magnetic quantum numbers for a given expression before the summation over further 6-j and 9-j symbols should be taken into account. For all other quantities (that are compiled in Ref. [8], Tables 1 and 2, and explained in more detail in the Short Reference Manual, Racah-commands-2009.pdf), we currently just facilitate fast numerical computations by exploiting, as far as possible, Maple's hardware floating-point model. The program also supports simplifications on the Wigner rotation matrices. In integrals over the rotation matrices, products of up to three Wigner D-functions or reduced matrices (with the same angular arguments) are recognized; for the integration over a solid angle, however, the domain of integration must be specified explicitly for the Euler angles α and γ in order to force Maple to generate a constant of integration. In the course of the evaluation of Racah expressions, it is, in practice, often difficult to check internally whether all substructures of an expression are defined properly. Therefore, the user must ensure that all angular momenta (if given explicitly) must finally evaluate to integer and half-integer values and that they satisfy proper coupling conditions.Unusual features: The Racah program is designed for interactive use and for providing a quick and algebraic evaluation of (complex) expressions from Racah's algebra. In the evaluation, it exploits a large set of sum rules which are known from Racah's algebra and which may include (multiple) summations over dummy indices; see Varshalovich et al. [5] for a more detailed account of the theory. One strength of the program is that it recognizes automatically the symmetries of the symbols and functions, and that it applies also (some of) the graphical rules due to Yutsis and coworkers [9]. As before, the result of the evaluation process will be provided as Racah expressions, if a further simplification could be achieved, and may hence be used for further derivations and calculations within the given framework. In dealing with recoupling coefficients, these coefficients can be entered simply as a string of angular momenta (variables), separated by commas, and very similar to how they appear in mathematical texts. This is a crucial advantage of the program, compared with previous developments, for which the angular momenta and coupling coefficients had often to be given in a very detailed format. A Short Reference Manual to all procedures of the Racah program is provided by this distribution; it also contains the worksheet Racah-tests-2009-maple12.mw that contains the examples from all previous versions and may help test the installation. This worksheet can serve as a first tutorial to the Racah procedures. In the past, the Racah program has been utilized extensively in a number of applications including angular and polarization studies of heavy ions [10], angular distributions and correlation functions following photon-induced excitation processes [11], entanglement studies [12], in application of point-group symmetries and several others.Running time: The worksheet supplied with the distribution takes about 1 minute to run.References:

[1] Maple is a registered trademark of Waterloo Maple Inc.

[2] S. Fritzsche, Comp. Phys. Commun. 103 (1997) 51.

[3] S. Fritzsche, S. Varga, D. Geschke, B. Fricke, Comp. Phys. Commun. 111 (1998) 167;

T. Ingho, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 139 (2001) 297;

S. Fritzsche, T. Ingho, T. Bastug, M. Tomaselli, Comp. Phys. Commun. 139 (2001) 314.

[4] D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore a.o., 1988.

[5] J. Pagaran, S. Fritzsche, G. Gaigalas, Comp. Phys. Commun. 174 (2006) 616.

[6] K. Schulten, R.G. Gordon, Comp. Phys. Commun. 11 (1976) 269.

[7] G. Gaigalas, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 135 (2001) 219;

G. Gaigalas, S. Fritzsche, Comp. Phys. Commun. 149 (2002) 39;

G. Gaigalas, O. Scharf, S. Fritzsche, Comp. Phys. Commun. 166 (2005) 141.

[8] S. Fritzsche, T. Ingho, M. Tomaselli, Comp. Phys. Commun. 153 (2003) 424.

[9] A.P. Yutsis, I.B. Levinson, V.V. Vanagas, The Theory of Angular Momentum, Israel Program for Scientific Translation, Jerusalem, 1962.

[10] S. Fritzsche, P. Indelicato, T. Stöhlker, J. Phys. B 38 (2005) S707.

[11] M. Kitajima, M. Okamoto, M. Hoshino, et al., J. Phys. B 35 (2002) 3327;

N.M. Kabachnik, S. Fritzsche, A.N. Grum-Grzhimailo, et al., Phys. Reports 451 (2007) 155;

S. Fritzsche, A.N. Grum-Grzhimailo, E.V. Gryzlova, N.M. Kabachnik, J. Phys. B 41 (2008) 165601;

T. Radtke, et al., Phys. Rev. A 77 (2008) 022507.

[12] T. Radtke, S. Fritzsche, Comp. Phys. Commun. 175 (2006) 145.

     

TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95

We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula. TaylUR makes heavy use of operator overloading and other Fortran 95 features such as elemental functions.

Program summary

Program title: TaylURCatalogue identifier:ADXR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language:Fortran 95Computer:Any computer with a conforming Fortran 95 compilerOperating system:Any system with a conforming Fortran 95 compilerNo. of lines in distributed program, including test data, etc.:6286No. of bytes in distributed program, including test data, etc:14 994Distribution format:tar.gzNature of problem:Problems that require potentially high orders of derivatives with respect to some variables, such as e.g. expansions of Feynman diagrams in particle masses in perturbative Quantum Field Theory, and which cannot be treated using existing Fortran modules for automatic differentiation [C.W. Straka, ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables, Comput. Phys. Comm. 168 (2005) 123-139, arXiv:cs.MS/0503014; S. Stamatiadis, R. Prosmiti, S.C. Farantos, auto_deriv: Tool for automatic differentiation of a FORTRAN code, Comput. Phys. Comm. 127 (2000) 343-355].Solution method:Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula.Restrictions:Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders.Unusual features:No mixed higher-order derivatives are computed. The complex conjugation operation assumes all independent variables to be real.Running time:The running time of TaylUR operations depends linearly on the number of variables. Its dependence on the Taylor expansion order varies from linear (for linear operations) through quadratic (for multiplication) to exponential (for elementary function calls).     

DPEMC: A Monte Carlo for double diffraction

We extend the POMWIG Monte Carlo generator developed by B. Cox and J. Forshaw, to include new models of central production through inclusive and exclusive double Pomeron exchange in proton-proton collisions. Double photon exchange processes are described as well, both in proton-proton and heavy-ion collisions. In all contexts, various models have been implemented, allowing for comparisons and uncertainty evaluation and enabling detailed experimental simulations.

Program summary

Title of the program:DPEMC, version 2.4Catalogue identifier: ADVFProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVFProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: any computer with the FORTRAN 77 compiler under the UNIX or Linux operating systemsOperating system: UNIX; LinuxProgramming language used: FORTRAN 77High speed storage required:<25 MBNo. of lines in distributed program, including test data, etc.: 71 399No. of bytes in distributed program, including test data, etc.: 639 950Distribution format: tar.gzNature of the physical problem: Proton diffraction at hadron colliders can manifest itself in many forms, and a variety of models exist that attempt to describe it [A. Bialas, P.V. Landshoff, Phys. Lett. B 256 (1991) 540; A. Bialas, W. Szeremeta, Phys. Lett. B 296 (1992) 191; A. Bialas, R.A. Janik, Z. Phys. C 62 (1994) 487; M. Boonekamp, R. Peschanski, C. Royon, Phys. Rev. Lett. 87 (2001) 251806; Nucl. Phys. B 669 (2003) 277; R. Enberg, G. Ingelman, A. Kissavos, N. Timneanu, Phys. Rev. Lett. 89 (2002) 081801; R. Enberg, G. Ingelman, L. Motyka, Phys. Lett. B 524 (2002) 273; R. Enberg, G. Ingelman, N. Timneanu, Phys. Rev. D 67 (2003) 011301; B. Cox, J. Forshaw, Comput. Phys. Comm. 144 (2002) 104; B. Cox, J. Forshaw, B. Heinemann, Phys. Lett. B 540 (2002) 26; V. Khoze, A. Martin, M. Ryskin, Phys. Lett. B 401 (1997) 330; Eur. Phys. J. C 14 (2000) 525; Eur. Phys. J. C 19 (2001) 477; Erratum, Eur. Phys. J. C 20 (2001) 599; Eur. Phys. J. C 23 (2002) 311]. This program implements some of the more significant ones, enabling the simulation of central particle production through color singlet exchange between interacting protons or antiprotons.Method of solution: The Monte Carlo method is used to simulate all elementary 2→2 and 2→1 processes available in HERWIG. The color singlet exchanges implemented in DPEMC are implemented as functions reweighting the photon flux already present in HERWIG.Restriction on the complexity of the problem: The program relying extensively on HERWIG, the limitations are the same as in [G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, M.H. Seymour, L. Stanco, Comput. Phys. Comm. 67 (1992) 465; G. Corcella, I.G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. Seymour, B. Webber, JHEP 0101 (2001) 010].Typical running time: Approximate times on a 800 MHz Pentium III: 5-20 min per 10 000 unweighted events, depending on the process under consideration.     

A computer program for two-particle generalized coefficients of fractional parentage

We present a FORTRAN90 program GCFP for the calculation of the generalized coefficients of fractional parentage (generalized CFPs or GCFP). The approach is based on the observation that the multi-shell CFPs can be expressed in terms of single-shell CFPs, while the latter can be readily calculated employing a simple enumeration scheme of antisymmetric A-particle states and an efficient method of construction of the idempotent matrix eigenvectors. The program provides fast calculation of GCFPs for a given particle number and produces results possessing numerical uncertainties below the desired tolerance. A single j-shell is defined by four quantum numbers, (e,l,j,t).A supplemental C++ program parGCFP allows calculation to be done in batches and/or in parallel.

Program summary

Program title:GCFP, parGCFPCatalogue identifier: AEBI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBI_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.: 17 199No. of bytes in distributed program, including test data, etc.: 88 658Distribution format: tar.gzProgramming language: FORTRAN 77/90 (GCFP), C++ (parGCFP)Computer: Any computer with suitable compilers. The program GCFP requires a FORTRAN 77/90 compiler. The auxiliary program parGCFP requires GNU-C++ compatible compiler, while its parallel version additionally requires MPI-1 standard librariesOperating system: Linux (Ubuntu, Scientific) (all programs), also checked on Windows XP (GCFP, serial version of parGCFP)RAM: The memory demand depends on the computation and output mode. If this mode is not 4, the program GCFP demands the following amounts of memory on a computer with Linux operating system. It requires around 2 MB of RAM for the A=12 system at Ex?2. Computation of the A=50 particle system requires around 60 MB of RAM at Ex=0 and ∼70 MB at Ex=2 (note, however, that the calculation of this system will take a very long time). If the computation and output mode is set to 4, the memory demands by GCFP are significantly larger. Calculation of GCFPs of A=12 system at Ex=1 requires 145 MB. The program parGCFP requires additional 2.5 and 4.5 MB of memory for the serial and parallel version, respectively.Classification: 17.18Nature of problem: The program GCFP generates a list of two-particle coefficients of fractional parentage for several j-shells with isospin.Solution method: The method is based on the observation that multishell coefficients of fractional parentage can be expressed in terms of single-shell CFPs [1]. The latter are calculated using the algorithm [2,3] for a spectral decomposition of an antisymmetrization operator matrix Y. The coefficients of fractional parentage are those eigenvectors of the antisymmetrization operator matrix Y that correspond to unit eigenvalues. A computer code for these coefficients is available [4]. The program GCFP offers computation of two-particle multishell coefficients of fractional parentage. The program parGCFP allows a batch calculation using one input file. Sets of GCFPs are independent and can be calculated in parallel.Restrictions:A<86 when Ex=0 (due to the memory constraints); small numbers of particles allow significantly higher excitations, though the shell with j?11/2 cannot get full (it is the implementation constraint).Unusual features: Using the program GCFP it is possible to determine allowed particle configurations without the GCFP computation. The GCFPs can be calculated either for all particle configurations at once or for a specified particle configuration. The values of GCFPs can be printed out with a complete specification in either one file or with the parent and daughter configurations printed in separate files. The latter output mode requires additional time and RAM memory. It is possible to restrict the (J,T) values of the considered particle configurations. (Here J is the total angular momentum and T is the total isospin of the system.) The program parGCFP produces several result files the number of which equals to the number of particle configurations. To work correctly, the program GCFP needs to be compiled to read parameters from the standard input (the default setting).Running time: It depends on the size of the problem. The minimum time is required, if the computation and output mode (CompMode) is not 4, but the resulting file is larger. A system with A=12 particles at Ex=0 (all 9411 GCFPs) took around 1 sec on a Pentium4 2.8 GHz processor with 1 MB L2 cache. The program required about 14 min to calculate all 1.3×¹⁰⁶ GCFPs of Ex=1. The time for all 5.5×¹⁰⁷ GCFPs of Ex=2 was about 53 hours. For this number of particles, the calculation time of both Ex=0 and Ex=1 with CompMode = 1 and 4 is nearly the same, when no other processes are running. The case of Ex=2 could not be calculated with CompMode = 4, because the RAM memory was insufficient. In general, the latter CompMode requires a longer computation time, although the resulting files are smaller in size. The program parGCFP puts virtually no time overhead. Its parallel version speeds-up the calculation. However, the results need to be collected from several files created for each configuration.References:[1] J. Levinsonas, Works of Lithuanian SSR Academy of Sciences 4 (1957) 17.[2] A. Deveikis, A. Bon?kus, R. Kalinauskas, Lithuanian Phys. J. 41 (2001) 3.[3] A. Deveikis, R.K. Kalinauskas, B.R. Barrett, Ann. Phys. 296 (2002) 287.[4] A. Deveikis, Comput. Phys. Comm. 173 (2005) 186. (CPC Catalogue ID. ADWI_v1_0)