fgh, a code for the calculation of Coulomb radial wave functions from series expansions

The code fgh is an up-dated version of a code coulfg (see [Seaton, Comput. Phys. Comm. 25 (1982) 87]), used for the calculation of the Coulomb functions f and g, analytic in the energy, for attractive potentials. The new code works for attractive and repulsive potentials and also gives the functions h which have simple asymptotic forms. There is an option to use either the variables (?,r) customary in atomic physics, or (for positive energies) (η,ρ) customary in nuclear physics. When (η,ρ) are used, the code also gives the functions F_?(η,ρ) and G_?(η,ρ).Use of series solutions can lead to loss of accuracy due to cancellation effects. fgh provides an indication of the number of significant figures lost due to cancellations.     

Bandwidth on AT-free graphs

We study the classical Bandwidth problem from the viewpoint of parametrised algorithms. Given a graph G=(V,E) and a positive integer k, the Bandwidth problem asks whether there exists a bijective function β:{1,…,∣V∣}→V such that for every edge uv∈E, ∣β⁻¹(u)−β⁻¹(v)∣≤k. It is known that under standard complexity assumptions, no algorithm for Bandwidth with running time of the form f(k)n^O(1) exists, even when the input is restricted to trees. We initiate the search for classes of graphs where such algorithms do exist. We present an algorithm with running time n⋅2^O(klogk) for Bandwidth on AT-free graphs, a well-studied graph class that contains interval, permutation, and cocomparability graphs. Our result is the first non-trivial algorithm that shows fixed-parameter tractability of Bandwidth on a graph class on which the problem remains NP-complete.     

Revised and extended Utilities for the Ratip package

During the last years, the Ratip package has been found useful for calculating the excitation and decay properties of free atoms. Based on the (relativistic) multiconfiguration Dirac-Fock method, this program is used to obtain accurate predictions of atomic properties and to analyze many recent experiments. The daily work with this package made an extension of its Utilities [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] desirable in order to facilitate the data handling and interpretation of complex spectra. For this purpose, we make available an enlarged version of the Utilities which mainly supports the comparison with experiment as well as large Auger computations. Altogether 13 additional tasks have been appended to the program together with a new menu structure to improve the interactive control of the program.

Program summary

Title of program: RATIPCatalogue identifier: ADPD_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPD_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneReference in CPC to previous version: S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163Catalogue identifier of previous version: ADPDAuthors of previous version: S. Fritzsche, Department of Physics, University of Kassel, Heinrich-Plett-Strasse 40, D-34132 Kassel, GermanyDoes the new version supersede the original program?: yesComputer for which the new version is designed and others on which it has been tested: IBM RS 6000, PC Pentium II-IVInstallations: University of Kassel (Germany), University of Oulu (Finland)Operating systems: IBM AIX, Linux, UnixProgram language used in the new version: ANSI standard Fortran 90/95Memory required to execute with typical data: 300 kBNo. of bits in a word: All real variables are parameterized by a selected kind parameter and, thus, can be adapted to any required precision if supported by the compiler. Currently, the kind parameter is set to double precision (two 32-bit words) as used also for other components of the Ratip package [S. Fritzsche, C.F. Fischer, C.Z. Dong, Comput. Phys. Comm. 124 (2000) 341; G. Gaigalas, S. Fritzsche, Comput. Phys. Comm. 134 (2001) 86; S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163; S. Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155]No. of lines in distributed program, including test data, etc.:231 813No. of bytes in distributed program, including test data, etc.: 3 977 387Distribution format: tar.gzip fileNature of the physical problem: In order to describe atomic excitation and decay properties also quantitatively, large-scale computations are often needed. In the framework of the Ratip package, the Utilities support a variety of (small) tasks. For example, these tasks facilitate the file and data handling in large-scale applications or in the interpretation of complex spectra.Method of solution: The revised Utilities now support a total of 29 subtasks which are mainly concerned with the manipulation of output data as obtained from other components of the Ratip package. Each of these tasks are realized by one or several subprocedures which have access to the corresponding modules of the main components. While the main menu defines seven groups of subtasks for data manipulations and computations, a particular task is selected from one of these group menus. This allows to enlarge the program later if technical support for further tasks will become necessary. For each selected task, an interactive dialog about the required input and output data as well as a few additional information are printed during the execution of the program.Reasons for the new version: The requirement for enlarging the previous version of the Utilities [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] arose from the recent application of the Ratip package for large-scale radiative and Auger computations. A number of new subtasks now refer to the handling of Auger amplitudes and their proper combination in order to facilitate the interpretation of complex spectra. A few further tasks, such as the direct access to the one-electron matrix elements for some given set of orbital functions, have been found useful also in the analysis of data.Summary of revisions: extraction and handling of atomic data within the framework of Ratip. With the revised version, we now ‘add’ another 13 tasks which refer to the manipulation of data files, the generation and interpretation of Auger spectra, the computation of various one- and two-electron matrix elements as well as the evaluation of momentum densities and grid parameters. Owing to the rather large number of subtasks, the main menu has been divided into seven groups from which the individual tasks can be selected very similarly as before.Typical running time: The program responds promptly for most of the tasks. The responding time for some tasks, such as the generation of a relativistic momentum density, strongly depends on the size of the corresponding data files and the number of grid points.Unusual features of the program: A total of 29 different tasks are supported by the program. Starting from the main menu, the user is guided interactively through the program by a dialog and a few additional explanations. For each task, a short summary about its function is displayed before the program prompts for all the required input data.     

TiReX: Replica-exchange molecular dynamics using Tinker

We present a driver program for performing replica-exchange molecular dynamics simulations with the Tinker package. Parallelization is based on the Message Passing Interface, with every replica assigned to a separate process. The algorithm is not communication intensive, which makes the program suitable for running even on loosely coupled cluster systems. Particular attention is paid to the practical aspects of analyzing the program output.

Program summary

Program title: TiReXCatalogue identifier: AEEK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEK_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.: 43 385No. of bytes in distributed program, including test data, etc.: 502 262Distribution format: tar.gzProgramming language: Fortran 90/95Computer: Most UNIX machinesOperating system: LinuxHas the code been vectorized or parallelized?: parallelized with MPIClassification: 16.13External routines: TINKER version 4.2 or 5.0, built as a libraryNature of problem: Replica-exchange molecular dynamics.Solution method: Each replica is assigned to a separate process; temperatures are swapped between replicas at regular time intervals.Running time: The sample run may take up to a few minutes.     

auto_deriv: Tool for automatic differentiation of a Fortran code

auto_deriv is a module comprised of a set of fortran 95 procedures which can be used to calculate the first and second partial derivatives (mixed or not) of any continuous function with many independent variables. The mathematical function should be expressed as one or more fortran 77/90/95 procedures. A new type of variables is defined and the overloading mechanism of functions and operators provided by the fortran 95 language is extensively used to define the differentiation rules. Proper (standard complying) handling of floating-point exceptions is provided by using the IEEE_EXCEPTIONS intrinsic module (Technical Report 15580, incorporated in fortran 2003).

New version program summary

Program title: AUTO_DERIVCatalogue identifier: ADLS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADLS_v2_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.: 2963No. of bytes in distributed program, including test data, etc.: 10 314Distribution format: tar.gzProgramming language: Fortran 95 + (optionally) TR-15580 (Floating-point exception handling)Computer: all platforms with a Fortran 95 compilerOperating system: Linux, Windows, MacOSClassification: 4.12, 6.2Catalogue identifier of previous version: ADLS_v1_0Journal reference of previous version: Comput. Phys. Comm. 127 (2000) 343Does the new version supersede the previous version?: YesNature of problem: The need to calculate accurate derivatives of a multivariate function frequently arises in computational physics and chemistry. The most versatile approach to evaluate them by a computer, automatically and to machine precision, is via user-defined types and operator overloading. AUTO_DERIV is a Fortran 95 implementation of them, designed to evaluate the first and second derivatives of a function of many variables.Solution method: The mathematical rules for differentiation of sums, products, quotients, elementary functions in conjunction with the chain rule for compound functions are applied. The function should be expressed as one or more Fortran 77/90/95 procedures. A new type of variables is defined and the overloading mechanism of functions and operators provided by the Fortran 95 language is extensively used to implement the differentiation rules.Reasons for new version: The new version supports Fortran 95, handles properly the floating-point exceptions, and is faster due to internal reorganization. All discovered bugs are fixed.Summary of revisions:

•

The code was rewritten extensively to benefit from features introduced in Fortran 95. Additionally, there was a major internal reorganization of the code, resulting in faster execution. The user interface described in the original paper was not changed. The values that the user must or should specify before compilation (essentially, the number of independent variables) were moved into ad_types module.

•

There were many minor bug fixes. One important bug was found and fixed; the code did not handle correctly the overloading of in a∗∗λ when a=0.

•

The case of division by zero and the discontinuity of the function at the requested point are indicated by standard IEEE exceptions (IEEE_DIVIDE_BY_ZERO and IEEE_INVALID respectively). If the compiler does not support IEEE exceptions, a module with the appropriate name is provided, imitating the behavior of the ‘standard’ module in the sense that it raises the corresponding exceptions. It is up to the compiler (through certain flags probably) to detect them.

Restrictions: None imposed by the program. There are certain limitations that may appear mostly due to the specific implementation chosen in the user code. They can always be overcome by recoding parts of the routines developed by the user or by modifying AUTO_DERIV according to specific instructions given in [1]. The common restrictions of available memory and the capabilities of the compiler are the same as the original version.Additional comments: The program has been tested using the following compilers: Intel ifort, GNU gfortran, NAGWare f95, g95.Running time: The typical running time for the program depends on the compiler and the complexity of the differentiated function. A rough estimate is that AUTO_DERIV is ten times slower than the evaluation of the analytical (‘by hand’) function value and derivatives (if they are available).References:

[1]

S. Stamatiadis, R. Prosmiti, S.C. Farantos, AUTO_DERIV: tool for automatic differentiation of a Fortran code, Comput. Phys. Comm. 127 (2000) 343.

     

A combinatorial algorithm for max csp

We consider the problem max csp over multi-valued domains with variables ranging over sets of size s_i?s and constraints involving k_j?k variables. We study two algorithms with approximation ratios A and B, respectively, so we obtain a solution with approximation ratio max(A,B).The first algorithm is based on the linear programming algorithm of Serna, Trevisan, and Xhafa [Proc. 15th Annual Symp. on Theoret. Aspects of Comput. Sci., 1998, pp. 488-498] and gives ratio A which is bounded below by s^1−k. For k=2, our bound in terms of the individual set sizes is the minimum over all constraints involving two variables of , where s₁ and s₂ are the set sizes for the two variables.We then give a simple combinatorial algorithm which has approximation ratio B, with B>A/e. The bound is greater than s^1−k/e in general, and greater than s^1−k(1−(s−1)/2(k−1)) for s?k−1, thus close to the s^1−k linear programming bound for large k. For k=2, the bound is if s=2, 1/2(s−1) if s?3, and in general greater than the minimum of 1/4s₁+1/4s₂ over constraints with set sizes s₁ and s₂, thus within a factor of two of the linear programming bound.For the case of k=2 and s=2 we prove an integrality gap of . This shows that our analysis is tight for any method that uses the linear programming upper bound.     

Relativistic central-field Green's functions for the Ratip package

From perturbation theory, Green's functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green's functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green's functions also for atoms and ions other than the hydrogen-like ions, here we provide an extension to the Ratip program which supports the computation of relativistic (one-electron) Green's functions in an—arbitrarily given—central-field potential V(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green's functions for all bound-state energies E<0. In addition, care has been taken to provide a user-friendly component of the Ratip package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module-oriented design.

Program summary

Title of program:XgreensCatalogue number: ADWMProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWMProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:NoneComputer for which the new version has been tested: PC Pentium II, III, IV, AthlonInstallations: University of Kassel (Germany)Operating systems: SuSE Linux 8.2, SuSE Linux 9.0Program language used in the new version: ANSI standard Fortran 90/95Memory required to execute with typical data: On a standard grid (400 nodes), one central-field Green's function requires about 50 kBytes in RAM while approximately 3 MBytes are needed if saved as two-dimensional array on some external disc spaceNo. of bits in a word: Real variables of double- and quad-precision are usedPeripheral used: Disk for input/outputCPU time required to execute test data: 2 min on a 450 MHz Pentium III processorNo. of lines in distributed program, including test data etc.: 82 042No. of bytes in distributed program, including test data etc.: 814 096Distribution format: tar.gzNature of the physical problem: In atomic perturbation theory, Green's functions may help carry out the summation over the complete spectrum of atom and ions, including the (summation over the) bound states as well as an integration over the continuum [R.A. Swainson, G.W.F. Drake, J. Phys. A 24 (1991) 95]. Analytically, however, these functions are known only for free electrons (V(r)≡0) and for electrons in a pure Coulomb field (V(r)=−Z/r). For all other choices of the potential, in contrast, the Green's functions must be determined numerically.Method of solution: Relativistic Green's functions are generated for an arbitrary central-field potential V(r)=−Z(r)/r by using a piecewise linear approximation of the effective nuclear charge function Z(r) on some grid : Zi(r)=Z0i+Z1ir. Then, following McGuire's algorithm [E.J. McGuire, Phys. Rev. A 23 (1981) 186], the radial Green's functions are constructed from the (two) linear-independent solutions of the homogeneous equation [P. Morse, H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York 1953 (Part 1, p. 825)]. In the computation of these radial functions, the Kummer and Tricomi functions [J. Spanier, B. Keith, An Atlas of Functions, Springer, New York, 1987] are used extensively.Restrictions onto the complexity of the problem: The main restrictions of the program concern the shape of the effective nuclear charge Z(r)=−rV(r), i.e. the choice of the potential, and the allowed energies. Apart from obeying the proper boundary conditions for a point-like nucleus, namely, Z(r→0)=Znuc>0 and Z(r→∞)=Znuc−Nelectrons?0, the first derivative of the charge function Z(r) must be smaller than the (absolute value of the) energy of the Green's function, .Unusual features of the program:Xgreens has been designed as a part of the Ratip package [S. Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155] for the calculation of relativistic atomic transition and ionization properties. In a short dialog at the beginning of the execution, the user can specify the choice of the potential as well as the energies and the symmetries of the radial Green's functions to be calculated. Apart from central-field Green's functions, of course, the Coulomb Green's function [P. Koval, S. Fritzsche, Comput. Phys. Comm. 152 (2003) 191] can also be computed by selecting a constant nuclear charge Z(r)=Zeff. In order to test the generated Green's functions, moreover, we compare the two lowest bound-state orbitals which are calculated from the Green's functions with those as generated separately for the given potential. Like the other components of the Ratip package, Xgreens makes careful use of the Fortran 90/95 standard.     

Helac-Phegas: A generator for all parton level processes

The updated version of the Helac-Phegas¹ event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations using color connection representation. Phase-space generation is based on a multichannel approach, including optimization. Helac-Phegas generates parton level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders.

New version program summary

Program title: HELAC-PHEGASCatalogue identifier: ADMS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADMS_v2_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.: 35 986No. of bytes in distributed program, including test data, etc.: 380 214Distribution format: tar.gzProgramming language: FortranComputer: AllOperating system: LinuxClassification: 11.1, 11.2External routines: Optionally Les Houches Accord (LHA) PDF Interface library (http://projects.hepforge.org/lhapdf/)Catalogue identifier of previous version: ADMS_v1_0Journal reference of previous version: Comput. Phys. Comm. 132 (2000) 306Does the new version supersede the previous version?: Yes, partlyNature of problem: One of the most striking features of final states in current and future colliders is the large number of events with several jets. Being able to predict their features is essential. To achieve this, the calculations need to describe as accurately as possible the full matrix elements for the underlying hard processes. Even at leading order, perturbation theory based on Feynman graphs runs into computational problems, since the number of graphs contributing to the amplitude grows as n!.Solution method: Recursive algorithms based on Dyson-Schwinger equations have been developed recently in order to overcome the computational obstacles. The calculation of the amplitude, using Dyson-Schwinger recursive equations, results in a computational cost growing asymptotically as 3n, where n is the number of particles involved in the process. Off-shell subamplitudes are introduced, for which a recursion relation has been obtained allowing to express an n-particle amplitude in terms of subamplitudes, with 1-, 2-, …  up to (n−1) particles. The color connection representation is used in order to treat amplitudes involving colored particles. In the present version HELAC-PHEGAS can be used to efficiently obtain helicity amplitudes, total cross sections, parton-level event samples in LHA format, for arbitrary multiparticle processes in the Standard Model in leptonic, and pp collisions.Reasons for new version: Substantial improvements, major functionality upgrade.Summary of revisions: Color connection representation, efficient integration over PDF via the PARNI algorithm, interface to LHAPDF, parton level events generated in the most recent LHA format, k_⊥ reweighting for Parton Shower matching, numerical predictions for amplitudes for arbitrary processes for phase-space points provided by the user, new user interface and the possibility to run over computer clusters.Running time: Depending on the process studied. Usually from seconds to hours.References:

[1]

A. Kanaki, C.G. Papadopoulos, Comput. Phys. Comm. 132 (2000) 306.

[2]

C.G. Papadopoulos, Comput. Phys. Comm. 137 (2001) 247.

     

ASPIN: An all spin scattering code for atom-molecule rovibrationally inelastic cross sections

We present in this work a new computational code for the quantum calculation of integral cross sections for atom-molecule (linear) scattering processes. The atom is taken to be structureless while the molecule can be in its singlet, doublet, or triplet spin states and can be treated as either a rigid rotor or a rovibrational target. All the relevant state-to-state integral cross sections, and their sums over final states, can be calculated with the present code, for which we also describe in detail the various component routines.

Program summary

Program title: ASPINCatalogue identifier: AEBO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBO_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.: 99 596No. of bytes in distributed program, including test data, etc.: 1 267 615Distribution format: tar.gzProgramming language: Fortran/MPIComputer: AMD OPTERON COMPUTING SYSTEMS, model TYAN GX28 (B2882)Operating system: SuSE LINUX Professional 9RAM: 128 GBClassification: 2.6External routines: LAPACK/BLASNature of problem: Scattering of a diatomic molecule in its , , or spin states with an atom in its state. Partial and integral cross sections.Solution method: The coupled channel equations that describe the scattering process are solved through the propagation of the reactance K matrix employing a modification of the Variable Phase Method [1-3].Restrictions: Depending on the vib-rotational base used the problem may or may not fit into available RAM memory because all the runtime relevant quantities are stored on RAM memory instead of on disk.Additional comments: Both serial and parallel implementations of the program are provided. The CPC Librarian was not able to successfully run the parallel version.Running time: For simple and converged calculations a usual running time is in the order of a few minutes in the computer mentioned above, being shorter for the singlet and longer for the triplet.References:[1] F. Calogero, Variable Phase Approach to Potential Scattering, New York, 1967.[2] A. Degasperis, Il Nuovo Cimento 34 (1964) 1667.[3] C. Zemach, Il Nuovo Cimento 33 (1964) 939.     

One universal extra dimension in Pythia

The Universal Extra Dimensions model has been implemented in the Pythia generator from version 6.4.18 onwards, in its minimal formulation with one TeV⁻¹-sized extra dimension. The additional possibility of gravity-mediated decays, through a variable number of eV⁻¹-sized extra dimensions into which only gravity extends, is also available. The implementation covers the lowest lying Kaluza-Klein (KK) excitations of Standard Model particles, except for the excitations of the Higgs fields, with the mass spectrum calculated at one loop. 2→2 tree-level production cross sections and unpolarized KK number conserving 2-body decays are included. Mixing between iso-doublet and -singlet KK excitations is neglected thus far, and is expected to be negligible for all but the top sector.

New version summary

Program title: PYTHIA Version number: 6.420Catalogue identifier: ACTU_v2_1Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ACTU_v2_1.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.: 79 362No. of bytes in distributed program, including test data, etc.: 590 900Distribution format: tar.gzProgramming language: Fortran 77Computer: CERN lxplus and any other machine with a Fortran 77 compilerOperating system: Linux Red HatRAM: about 800 K wordsWord size: 32 bitsClassification: 11.2Catalogue identifier of previous version: ACTU_v2_0Journal reference of previous version: Comput. Phys. Comm. 135 (2001) 238Does the new version supersede the previous version?: YesNature of problem: At high energy collisions between elementary particles, physics beyond the Standard Model is searched for. Many models are being investigated, namely extra-dimensional models.Solution method: The Universal Extra Dimension model is implemented in the PYTHIA event generator.Reasons for new version: The Universal Extra Dimensions model has been implemented in the PYTHIA generator from version 6.4.18 onwards, in its minimal formulation with one TeV⁻¹-sized extra dimension. The additional possibility of gravity-mediated decays, through a variable number of eV⁻¹-sized extra dimensions into which only gravity extends, is also available. The implementation covers the lowest lying Kaluza-Klein (KK) excitations of Standard Model particles, except for the excitations of the Higgs fields, with the mass spectrum calculated at one loop. 2→2 tree-level production cross sections and unpolarized KK number conserving 2-body decays are included. Mixing between iso-doublet and -singlet KK excitations is neglected thus far, and is expected to be negligible for all but the top sector.Running time: 10-1000 events per second, depending on the process studied.     

Efficient evolution of unpolarized and polarized parton distributions with QCD-Pegasus

The Fortran package QCD-Pegasus is presented. This program provides fast, flexible and accurate solutions of the evolution equations for unpolarized and polarized parton distributions of hadrons in perturbative QCD. The evolution is performed using the symbolic moment-space solutions on a one-fits-all Mellin inversion contour. User options include the order of the evolution including the next-to-next-to-leading order in the unpolarized case, the type of the evolution including an emulation of brute-force solutions, the evolution with a fixed number nf of flavors or in the variable-nf scheme, and the evolution with a renormalization scale unequal to the factorization scale. The initial distributions are needed in a form facilitating the computation of the complex Mellin moments.

Program summary

Title of program: QCD-PegasusVersion: 1.0Catalogue identifier: ADVNProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVNProgram obtainable from: CPC Program Library Queen's University of Belfast, N. IrelandLicense: GNU Public LicenseComputers: allOperating systems: allProgram language:Fortran 77 (using the common compiler extension of procedure names with more than six characters)Memory required to execute: negligible (<1 MB)Other programs called: noneExternal files needed: noneNumber of lines in distributed program, including test data, etc.: 8157Number of bytes in distributed program, including test data, etc.: 240 578Distribution format: tar.gzNature of the physical problem: Solution of the evolution equations for the unpolarized and polarized parton distributions of hadrons at leading order (LO), next-to-leading order and next-to-next-to-leading order of perturbative QCD. Evolution performed either with a fixed number nf of effectively massless quark flavors or in the variable-nf scheme. The calculation of observables from the parton distributions is not part of the present package.Method of solution: Analytic solution in Mellin space (beyond LO in general by power-expansion around the lowest-order expansion) followed by a fast Mellin inversion to x-space using a fixed one-fits-all contour.Restrictions on complexity of the problem: The initial distributions for the evolution are required in a form facilitating an efficient calculation of their complex Mellin moments. The ratio of the renormalization and factorization scales μr/μ has to be a fixed number.Typical running time: One to ten seconds, on a PC with a 2.0 GHz Pentium-IV processor, for performing the evolution of 200 initial distributions to 500 (x,μ) points each. For more details see Section 6.     

-XSummer- Transcendental functions and symbolic summation in Form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.

Program summary

Title of program:XSummerCatalogue identifier:ADXQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0Program obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandLicense:GNU Public License and Form LicenseComputers:allOperating system:allProgram language:FormMemory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAMNo. of lines in distributed program, including test data, etc.:9854No. of bytes in distributed program, including test data, etc.:126 551Distribution format:tar.gzOther programs called:noneExternal files needed:noneNature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory.Method of solution:Algebraic manipulations of nested sums.Restrictions on complexity of the problem:Usually limited only by the available disk space.Typical running time:Dependent on the complexity of the problem.     

ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables

ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied to any FORTRAN 77/90/95 conforming code and requires minimal changes by the user. It provides a new derived data type that holds the value and derivatives and applies forward differencing by overloading all FORTRAN operators and intrinsic functions. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain over other available tools with operator overloading. This gain is especially pronounced for sparse systems with large number of independent variables. A wide class of numerical simulations, e.g., those employing implicit solvers, can profit from ADF95.

Program summary

Title of program:ADF95Catalogue identifier: ADVIProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVIProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed: all platforms with a FORTRAN 95 compilerProgramming language used:FORTRAN 95No. of lines in distributed program, including test data, etc.: 3103No. of bytes in distributed program, including test data, etc.: 9862Distribution format: tar.gzNature of problem: In many areas in the computational sciences first order partial derivatives for large and complex sets of equations are needed with machine precision accuracy. For example, any implicit or semi-implicit solver requires the computation of the Jacobian matrix, which contains the first derivatives with respect to the independent variables. ADF95 is a software module to facilitate the automatic computation of the first partial derivatives of any arbitrarily complex mathematical FORTRAN expression. The program exploits the sparsity inherited by many set of equations thereby enabling faster computations compared to alternate differentiation toolsSolution method: A class is constructed which applies the chain rule of differentiation to any FORTRAN expression, to compute the first derivatives by forward differencing. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain when sparsity can be exploited. From a users point of view, only minimal changes to his/her original code are needed in order to compute the first derivatives of any expression in the codeRestrictions: Processor and memory hardware may restrict both the possible number of independent variables and the computation timeUnusual features:ADF95 can operate on user code that makes use of the array features introduced in FORTRAN 90. A convenient extraction subroutine for the Jacobian matrix is also providedRunning time: In many realistic cases, the evaluation of the first order derivatives of a mathematical expression is only six times slower compared to the evaluation of analytically derived and hard-coded expressions. The actual factor depends on the underlying set of equations for which derivatives are to be calculated, the number of independent variables, the sparsity and on the FORTRAN 95 compiler     

TEA CO2 Laser Simulator: A software tool to predict the output pulse characteristics of TEA CO2 laser

“TEA CO₂ Laser Simulator” has been designed to simulate the dynamic emission processes of the TEA CO₂ laser based on the six-temperature model. The program predicts the behavior of the laser output pulse (power, energy, pulse duration, delay time, FWHM, etc.) depending on the physical and geometrical input parameters (pressure ratio of gas mixture, reflecting area of the output mirror, media length, losses, filling and decay factors, etc.).

Program summary

Title of program: TEA_CO2Catalogue identifier: ADVWProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVWProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: P.IV DELL PCSetup: Atomic Energy Commission of Syria, Scientific Services Department, Mathematics and Informatics DivisionOperating system: MS-Windows 9x, 2000, XPProgramming language: Delphi 6.0No. of lines in distributed program, including test data, etc.: 47 315No. of bytes in distributed program, including test data, etc.:7 681 109Distribution format:tar.gzClassification: 15 Laser PhysicsNature of the physical problem: “TEA CO₂ Laser Simulator” is a program that predicts the behavior of the laser output pulse by studying the effect of the physical and geometrical input parameters on the characteristics of the output laser pulse. The laser active medium consists of a CO₂-N₂-He gas mixture.Method of solution: Six-temperature model, for the dynamics emission of TEA CO₂ laser, has been adapted in order to predict the parameters of laser output pulses. A simulation of the laser electrical pumping was carried out using two approaches; empirical function equation (8) and differential equation (9).Typical running time: The program's running time mainly depends on both integration interval and step; for a 4 μs period of time and 0.001 μs integration step (defaults values used in the program), the running time will be about 4 seconds.Restrictions on the complexity: Using a very small integration step might leads to stop the program run due to the huge number of calculating points and to a small paging file size of the MS-Windows virtual memory. In such case, it is recommended to enlarge the paging file size to the appropriate size, or to use a bigger value of integration step.     

An integrated tool for loop calculations: aITALC

aITALC, a new tool for automating loop calculations in high energy physics, is described. The package creates Fortran code for two-fermion scattering processes automatically, starting from the generation and analysis of the Feynman graphs. We describe the modules of the tool, the intercommunication between them and illustrate its use with three examples.

Program summary

Title of the program:aITALC version 1.2.1 (9 August 2005)Catalogue identifier:ADWOProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWOProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandComputer:PC i386Operating system:GNU/Linux, tested on different distributions SuSE 8.2 to 9.3, Red Hat 7.2, Debian 3.0, Ubuntu 5.04. Also on SolarisProgramming language used:GNU Make, Diana, Form, Fortran77Additional programs/libraries used:Diana 2.35 (Qgraf 2.0), Form 3.1, LoopTools 2.1 (FF)Memory required to execute with typical data:Up to about 10 MBNo. of processors used:1No. of lines in distributed program, including test data, etc.:40 926No. of bytes in distributed program, including test data, etc.:371 424Distribution format:tar gzip fileHigh-speed storage required:from 1.5 to 30 MB, depending on modules present and unfolding of examplesNature of the physical problem:Calculation of differential cross sections for e⁺e⁻ annihilation in one-loop approximation.Method of solution:Generation and perturbative analysis of Feynman diagrams with later evaluation of matrix elements and form factors.Restriction of the complexity of the problem:The limit of application is, for the moment, the 2→2 particle reactions in the electro-weak standard model.Typical running time:Few minutes, being highly depending on the complexity of the process and the Fortran compiler.     

OneLOop: For the evaluation of one-loop scalar functions

OneLOop is a program to evaluate the one-loop scalar 1-point, 2-point, 3-point and 4-point functions, for all kinematical configurations relevant for collider-physics, and for any non-positive imaginary parts of the internal squared masses. It deals with all UV and IR divergences within dimensional regularization. Furthermore, it provides routines to evaluate these functions using straightforward numerical integration.

Program summary

Program title: OneLOopCatalogue identifier: AEJO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJO_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.: 12 061No. of bytes in distributed program, including test data, etc.: 74 163Distribution format: tar.gzProgramming language: FortranComputer: WorkstationsOperating system: Linux, UnixRAM: NegligibleClassification: 4.4, 11.1Nature of problem: In order to reach next-to-leading order precision in the calculation of cross sections of hard scattering processes, one-loop amplitudes have to be evaluated. This is done by expressing them as linear combination of one-loop scalar functions. In a concrete calculation, these functions eventually have to be evaluated. If the scattering process involves unstable particles, consistency requires the evaluation of these functions with complex internal masses.Solution method: Expressions for the one-loop scalar functions in terms of single-variable analytic functions existing in literature have been implemented.Restrictions: The applicability is restricted to the kinematics occurring in collider-physics.Running time: The evaluation of the most general 4-point function with 4 complex masses takes about 180 μs, and the evaluation of the 4-point function with 4 real masses takes about 18 μs on a 2.80 GHz Intel Xeon processor.     

On scheduling dag s for volatile computing platforms: Area-maximizing schedules

Many modern computing platforms—notably clouds and desktop grids—exhibit dynamic heterogeneity: the availability and computing power of their constituent resources can change unexpectedly and dynamically, even in the midst of a computation. We introduce a new quality metric, area, for schedules that execute computations having interdependent constituent chores (jobs, tasks, etc.) on such platforms. Area measures the average number of tasks that a schedule renders eligible for execution at each step of a computation. Even though the definition of area does not mention and properties of host platforms (such as volatility), intuition suggests that rendering tasks eligible at a faster rate will have a benign impact on the performance of volatile platforms—and we report on simulation experiments that support this intuition. We derive the basic properties of the area metric and show how to efficiently craft area-maximizing (A-M) schedules for several classes of significant computations. Simulations that compare A-M scheduling against heuristics ranging from lightweight ones (e.g., FIFO) to computationally intensive ones suggest that A-M schedules complete computations on volatile heterogeneous platforms faster than their competition, by percentages that vary with computation structure and platform behavior—but are often in the double digits.     

Concise: Compressed ‘n’ Composable Integer Set

Bit arrays, or bitmaps, are used to significantly speed up set operations in several areas, such as data warehousing, information retrieval, and data mining, to cite a few. However, bitmaps usually use a large storage space, thus requiring compression. Consequently, there is a space-time tradeoff among compression schemes. The Word Aligned Hybrid (WAH) bitmap compression trades some space to allow for bitwise operations without first decompressing bitmaps. WAH has been recognized as the most efficient scheme in terms of computation time. In this paper we present Concise (Compressed ‘n’ Composable Integer Set), a new scheme that enjoys significantly better performances than WAH. In particular, when compared to WAH our algorithm is able to reduce the required memory up to 50%, while having comparable computation time. Further, we show that Concise can be efficiently used to represent sets of integral numbers in lieu of well-known data structures such as arrays, lists, hashtables, and self-balancing binary search trees. Extensive experiments over synthetic data show the effectiveness of our proposal.