From data to probability densities without histograms

When one deals with data drawn from continuous variables, a histogram is often inadequate to display their probability density. It deals inefficiently with statistical noise, and binsizes are free parameters. In contrast to that, the empirical cumulative distribution function (obtained after sorting the data) is parameter free. But it is a step function, so that its differentiation does not give a smooth probability density. Based on Fourier series expansion and Kolmogorov tests, we introduce a simple method, which overcomes this problem. Error bars on the estimated probability density are calculated using a jackknife method. We give several examples and provide computer code reproducing them. You may want to look at the corresponding figures 4 to 9 first.

Program summary

Program title: cdf_to_pdCatalogue identifier: AEBC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBC_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.: 2758No. of bytes in distributed program, including test data, etc.: 18 594Distribution format: tar.gzProgramming language: Fortran 77Computer: Any capable of compiling and executing Fortran codeOperating system: Any capable of compiling and executing Fortran codeClassification: 4.14, 9Nature of problem: When one deals with data drawn from continuous variables, a histogram is often inadequate to display the probability density. It deals inefficiently with statistical noise, and binsizes are free parameters. In contrast to that, the empirical cumulative distribution function (obtained after sorting the data) is parameter free. But it is a step function, so that its differentiation does not give a smooth probability density.Solution method: Based on Fourier series expansion and Kolmogorov tests, we introduce a simple method, which overcomes this problem. Error bars on the estimated probability density are calculated using a jackknife method. Several examples are included in the distribution file.Running time: The test runs provided take only a few seconds to execute.     

Solution of few-body problems with the stochastic variational method II: Two-dimensional systems

A computational approach is presented for efficient solution of two-dimensional few-body problems, such as quantum dots or excitonic complexes, using the stochastic variational method. The computer program can be used to calculate the energies and wave functions of various two-dimensional systems.

Program summary

Program title: svm-2dCatalogue identifier: AEBE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBE_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.: 5091No. of bytes in distributed program, including test data, etc.: 130 963Distribution format: tar.gzProgramming language: Fortran 90Computer: The program should work on any system with a Fortran 90 compilerOperating system: The program should work on any system with a Fortran 90 compilerClassification: 7.3Nature of problem: Variational calculation of energies and wave functions using Correlated Gaussian basis.Solution method: Two-dimensional few-electron problems are solved by the variational method. The ground state wave function is expanded into Correlated Gaussian basis functions and the parameters of the basis states are optimized by a stochastic selection procedure. Accurate results can be obtained for 2-6 electron systems.Running time: A couple of hours for a typical system.     

Real-time Java simulations of multiple interference dielectric filters

An interactive Java applet for real-time simulation and visualization of the transmittance properties of multiple interference dielectric filters is presented. The most commonly used interference filters as well as the state-of-the-art ones are embedded in this platform-independent applet which can serve research and education purposes. The Transmittance applet can be freely downloaded from the site http://cpc.cs.qub.ac.uk.

Program summary

Program title: TransmittanceCatalogue identifier: AEBQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBQ_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.: 5778No. of bytes in distributed program, including test data, etc.: 90 474Distribution format: tar.gzProgramming language: JavaComputer: Developed on PC-Pentium platformOperating system: Any Java-enabled OS. Applet was tested on Windows ME, XP, Sun Solaris, Mac OSRAM: VariableClassification: 18Nature of problem: Sophisticated wavelength selective multiple interference filters can include some tens or even hundreds of dielectric layers. The spectral response of such a stack is not obvious. On the other hand, there is a strong demand from application designers and students to get a quick insight into the properties of a given filter.Solution method: A Java applet was developed for the computation and the visualization of the transmittance of multilayer interference filters. It is simple to use and the embedded filter library can serve educational purposes. Also, its ability to handle complex structures will be appreciated as a useful research and development tool.Running time: Real-time simulations     

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.     

Solving surface structures from normal incidence X-ray standing wave data

A program is provided to determine structural parameters of atoms in or adsorbed on surfaces by refinement of atomistic models towards experimentally determined data generated by the normal incidence X-ray standing wave (NIXSW) technique. The method employs a combination of Differential Evolution Genetic Algorithms and Steepest Descent Line Minimisations to provide a fast, reliable and user friendly tool for experimentalists to interpret complex multidimensional NIXSW data sets.

Program summary

Program title: NIXSW Planewave SolverCatalogue identifier: ADZE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZE_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.: 16 874No. of bytes in distributed program, including test data, etc.: 1 631 874Distribution format: tar.gzProgramming language: Borland C++ Builder 5Computer: Any Windows CompatibleOperating system: Windows 2000 and XPRAM: <10 MBClassification: 7.4Nature of problem: Using NIXSW experimental data to calculate atomic positions of adsorbates.Restrictions: Data from substrates must have cubic, tetragonal or orthorhombic crystal structures i.e. with 90° between conventional cell axes.Running time: Seconds-minutes dependant on the number of plane waves and the number of atomic sites.     

JuNoLo - Jülich nonlocal code for parallel post-processing evaluation of vdW-DF correlation energy

Nowadays the state of the art Density Functional Theory (DFT) codes are based on local (LDA) or semilocal (GGA) energy functionals. Recently the theory of a truly nonlocal energy functional has been developed. It has been used mostly as a post-DFT calculation approach, i.e. by applying the functional to the charge density calculated using any standard DFT code, thus obtaining a new improved value for the total energy of the system. Nonlocal calculation is computationally quite expensive and scales as N² where N is the number of points in which the density is defined, and a massively parallel calculation is welcome for a wider applicability of the new approach. In this article we present a code which accomplishes this goal.

Program summary

Program title: JuNoLoCatalogue identifier: AEFM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFM_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.: 176 980No. of bytes in distributed program, including test data, etc.: 2 126 072Distribution format: tar.gzProgramming language: Fortran 90Computer: any architecture with a Fortran 90 compilerOperating system: Linux, AIXHas the code been vectorised or parallelized?: Yes, from 1 to 65536 processors may be used.RAM: depends strongly on the problem's size.Classification: 7.3External routines:• FFTW (http://www.tw.org/)• MPI (http://www.mcs.anl.gov/research/projects/mpich2/ or http://www.lam-mpi.org/)Nature of problem: Obtaining the value of the nonlocal vdW-DF energy based on the charge density distribution obtained from some Density Functional Theory code.Solution method: Numerical calculation of the double sum is implemented in a parallel F90 code. Calculation of this sum yields the required nonlocal vdW-DF energy.Unusual features: Binds to virtually any DFT program.Additional comments: Excellent parallelization features.Running time: Depends strongly on the size of the problem and the number of CPUs used.     

PETAG01: A program for the direct simulation of a pellet target

We describe a numerical model of an internal pellet target to study the beam dynamics in storage rings, where the nuclear experiments with such type of target are planned. In this model the Monte Carlo algorithm is applied to evaluate the particle coordinates and momentum deviation depending on time and parameters of the target. One has to mention that due to statistical character of the pellet distribution in the target the analytical techniques are not applicable. This is also true for the particle distribution in the stored beam, which is influenced by various effects (such as a cooling process, intra-beam scattering, betatron oscillation, space charge effect). In this case only the Monte Carlo technique to model energy straggling in combination with the pellet distribution in the target should be considered.

Program summary

Program title: PETAG01Catalogue identifier: ADZV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZV_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.: 1068No. of bytes in distributed program, including test data, etc.: 11 314Distribution format: tar.gzProgramming language: Fortran 77, C/C++Computer: Platform independentOperating system: MS Windows 95/2000/XP, Linux (Unix)RAM: 128 MBClassification: 11.10Nature of problem: Particle beam dynamics with use of the pellet target.Solution method: Monte Carlo with analytical approximation.Running time: dozens of seconds     

Resolution of singularities for multi-loop integrals

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program.

Program summary

Program title: sector_decompositionCatalogue identifier: AEAG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAG_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.: 47 506No. of bytes in distributed program, including test data, etc.: 328 485Distribution format: tar.gzProgramming language: C++Computer: allOperating system: UnixRAM: Depending on the complexity of the problemClassification: 4.4External routines: GiNaC, available from http://www.ginac.de, GNU scientific library, available from http://www.gnu.org/software/gslNature of problem: Computation of divergent multi-loop integrals.Solution method: Sector decomposition.Restrictions: Only limited by the available memory and CPU time.Running time: Depending on the complexity of the problem.     

Monte Carlo event generator for black hole production and decay in proton-proton collisions - QBH version 1.02

We describe the Monte Carlo event generator for black hole production and decay in proton-proton collisions - QBH version 1.02. The generator implements a model for quantum black hole production and decay based on the conservation of local gauge symmetries and democratic decays. The code in written entirely in C++ and interfaces to the PYTHIA 8 Monte Carlo code for fragmentation and decays.

Program summary

Program title: QBHCatalogue identifier: AEGU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGU_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.: 10 048No. of bytes in distributed program, including test data, etc.: 118 420Distribution format: tar.gzProgramming language: C++Computer: x86Operating system: Scientific Linux, Mac OS XRAM: 1 GBClassification: 11.6External routines: PYTHIA 8130 (http://home.thep.lu.se/~torbjorn/pythiaaux/present.html) and LHAPDF (http://projects.hepforge.org/lhapdf/)Nature of problem: Simulate black hole production and decay in proton-proton collision.Solution method: Monte Carlo simulation using importance sampling.Running time: Eight events per second.     

SUSY Les Houches Accord 2 I/O made easy

A library for reading and writing data in the SUSY Les Houches Accord 2 format is presented. The implementation is in native Fortran 77. The data are contained in a single array conveniently indexed by preprocessor statements.

Program summary

Program title: SLHA2LibCatalogue identifier: AEDY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDY_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.: 7550No. of bytes in distributed program, including test data, etc.: 160 123Distribution format: tar.gzProgramming language: FortranComputer: For the build process, a Fortran 77 compiler in a Unixish environment (make, shell) are requiredOperating system: Linux, Mac OS, Windows (Cygwin), Tru64 UnixRAM: The SLHA Record is currently 88 944 bytes longClassification: 4.14, 11.6Nature of problem: Exchange of SUSY parameters and decay information in an ASCII file format.Solution method: The SLHA2Lib provides routines for reading and writing files in the SUSY Les Houches Accord 2 format, a common interchange format for SUSY parameters and decay data.Restrictions: The fixed-sized array that holds the SLHA2 data necessarily limits the amount of decay data that can be stored. This limit can be enlarged by editing and re-running the SLHA2.m program.Unusual features: Data are transported in a single “double complex” array in Fortran, indexed through preprocessor macros. This is about the simplest conceivable container and needs neither dynamic memory allocation nor Fortran extension like structures.Running time: Both reading and writing a SLHA file are typically in the range of a few milliseconds.     

Gauss-Legendre and Chebyshev quadratures for singular integrals

Exact expressions are presented for efficient computation of the weights in Gauss-Legendre and Chebyshev quadratures for selected singular integrands. The singularities may be of Cauchy type, logarithmic type or algebraic-logarithmic end-point branching points. We provide Fortran 90 routines for computing the weights for both the Gauss-Legendre and the Chebyshev (Fejér-1) meshes whose size can be set by the user.

New program summary

Program title: SINGQUADCatalogue identifier: AEBR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBR_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.: 4128No. of bytes in distributed program, including test data, etc.: 25 815Distribution format: tar.gzProgramming language: Fortran 90Computer: Any with a Fortran 90 compilerOperating system: Linux, Windows, MacRAM: Depending on the complexity of the problemClassification: 4.11Nature of problem: Program provides Gauss-Legendre and Chebyshev (Fejér-1) weights for various singular integrands.Solution method: The weights are obtained from the condition that the quadrature of order N must be exact for a polynomial of degree?(N−1). The weights are expressed as moments of the singular kernels associated with Legendre or Chebyshev polynomials. These moments are obtained in analytic form amenable for computation.Additional comments: If the NAGWare f95 compiler is used, the option, “-kind = byte”, must be included in the compile command lines of the Makefile.Running time: The test run supplied with the distribution takes a couple of seconds to execute.     

Object-oriented design patterns in Fortran 90/95: mazev1, mazev2 and mazev3

This paper discusses the concept, application, and usefulness of software design patterns for scientific programming in Fortran 90/95. An example from the discipline of object-oriented design patterns, that of a game based on navigation through a maze, is used to describe how some important patterns can be implemented in Fortran 90/95 and how the progressive introduction of design patterns can usefully restructure Fortran software as it evolves. This example is complemented by a discussion of how design patterns have been used in a real-life simulation of Particle-in-Cell plasma physics. The following patterns are mentioned in this paper: Factory, Strategy, Template, Abstract Factory and Facade.

Program summary

Program title: mazev1, mazev2, mazev3Catalogue identifier: AEAI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAI_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.: 1958No. of bytes in distributed program, including test data, etc.: 17 100Distribution format: tar.gzProgramming language: Fortran 95Computer: PC/MacOperating system: Unix/Linux/Mac (FreeBSD)/Windows (Cygwin)RAM: These are interactive programs with small (KB) memory requirementsClassification: 6.5, 20Nature of problem: A sequence of programs which demonstrate the use of object oriented design patterns for the restructuring of Fortran 90/95 software. The programs implement a simple maze game similar to that described in [1].Solution method: Restructuring uses versions of the Template, Strategy and Factory design patterns.Running time: Interactive.References:

[1] 

E. Gamma, R. Helm, R. Johnson, J. Vlissides, Design Patterns: Elements of Reusable Object Oriented Software, Addison-Wesley, 1995, ISBN 0201633612.

     

Generating relativistic pseudo-potentials with explicit incorporation of semi-core states using APE, the Atomic Pseudo-potentials Engine

We present a computer package designed to generate and test norm-conserving pseudo-potentials within Density Functional Theory. The generated pseudo-potentials can be either non-relativistic, scalar relativistic or fully relativistic and can explicitly include semi-core states. A wide range of exchange-correlation functionals is included.

Program summary

Program title: Atomic Pseudo-potentials Engine (APE)Catalogue identifier: AEAC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAC_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.: 88 287No. of bytes in distributed program, including test data, etc.: 649 959Distribution format: tar.gzProgramming language: Fortran 90, CComputer: any computer architecture, running any flavor of UNIXOperating system: GNU/LinuxRAM: <5 MbClassification: 7.3External routines: GSL (http://www.gnu.org/software/gsl/)Nature of problem: Determination of atomic eigenvalues and wave-functions using relativistic and nonrelativistic Density-Functional Theory. Construction of pseudo-potentials for use in ab-initio simulations.Solution method: Grid-based integration of the Kohn-Sham equations.Restrictions: Relativistic spin-polarized calculations are not possible. The set of exchange-correlation functionals implemented in the code does not include orbital-dependent functionals.Unusual features: The program creates pseudo-potential files suitable for the most widely used ab-initio packages and, besides the standard non-relativistic Hamann and Troullier-Martins potentials, it can generate pseudo-potentials using the relativistic and semi-core extensions to the Troullier-Martins scheme. APE also has a very sophisticated and user-friendly input system.Running time: The example given in this paper (Si) takes 10 s to run on a Pentium IV machine clocked at 2 GHz.     

LanHEP—a package for the automatic generation of Feynman rules in field theory. Version 3.0

The LanHEP program version 3.0 for Feynman rules generation from the Lagrangian is described. It reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric theories can be described using the superpotential formalism and the 2-component fermion notation. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as LaTeX table. One-loop counterterms can be generated in FeynArts format.

Program summary

Program title: LanHEPCatalogue identifier: ADZV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECH_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.: 83 041No. of bytes in distributed program, including test data, etc.: 1 090 931Distribution format: tar.gzProgramming language: CComputer: PCOperating system: LinuxRAM: 2 MB (SM), 12 MB (MSSM), 120 MB (MSSM with counterterms)Classification: 4.4Nature of problem: Deriving Feynman rules from the LagrangianSolution method: The program reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Tools for checking the correctness of the model, and for simplifying the output expressions are provided. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as a LaTeX table.Running time: 1 sec (SM), 8 sec (MSSM), 8 min (MSSM with counterterms)     

Moment distributions of clusters and molecules in the adiabatic rotor model

We present a Fortran program to compute the distribution of dipole moments of free particles for use in analyzing molecular beams experiments that measure moments by deflection in an inhomogeneous field. The theory is the same for magnetic and electric dipole moments, and is based on a thermal ensemble of classical particles that are free to rotate and that have moment vectors aligned along a principal axis of rotation. The theory has two parameters, the ratio of the magnetic (or electric) dipole energy to the thermal energy, and the ratio of moments of inertia of the rotor.

Program summary

Program title:AdiabaticRotorCatalogue identifier:ADZO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZO_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.:479No. of bytes in distributed program, including test data, etc.:4853Distribution format:tar.gzProgramming language:Fortran 90Computer:Pentium-IV, Macintosh Power PC G4Operating system:Linux, Mac OS XRAM:600 KbytesWord size:64 bitsClassification:2.3Nature of problem:The system considered is a thermal ensemble of rotors having a magnetic or electric moment aligned along one of the principal axes. The ensemble is placed in an external field which is turned on adiabatically. The problem is to find the distribution of moments in the presence of the external field.Solution method:There are three adiabatic invariants. The only nontrivial one is the action associated with the polar angle of the rotor axis with respect to external field. It is found by Newton's method.Running time:3 min on a 3 GHz Pentium IV processor.     

BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.

Program summary

Program title: BOKASUNCatalogue identifier: AECG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_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.: 9404No. of bytes in distributed program, including test data, etc.: 104 123Distribution format: tar.gzProgramming language: FORTRAN77Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUXOperating system: LINUXRAM: 120 kbytesClassification: 4.4Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum.Solution method: The integrals depend on three internal masses and the external momentum squared p². The method is a combination of an accelerated expansion in 1/p² in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations.Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending on the required accuracy and the values of the physical parameters).