A global collisionless PIC code in magnetic coordinates

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), δf scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-line magnetic coordinates and a field-aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Another feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 10⁹ marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests.     

BOUT++: A framework for parallel plasma fluid simulations

A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak x-point geometry, the code is able to simulate a wide range of fluid models (magnetised and unmagnetised) involving an arbitrary number of scalar and vector fields, in a wide range of geometries. Time evolution is fully implicit, and 3rd-order WENO schemes are implemented. Benchmarks are presented for linear and non-linear problems (the Orszag-Tang vortex) showing good agreement. Performance of the code is tested by scaling with problem size and processor number, showing efficient scaling to thousands of processors.Linear initial-value simulations of ELMs using reduced ideal MHD are presented, and the results compared to the ELITE linear MHD eigenvalue code. The resulting mode-structures and growth-rate are found to be in good agreement (γBOUT++=0.245ωA, γELITE=0.239ωA, with Alfvénic timescale 1/ωA=R/VA). To our knowledge, this is the first time dissipationless, initial-value simulations of ELMs have been successfully demonstrated.     

A semi-Lagrangian code for nonlinear global simulations of electrostatic drift-kinetic ITG modes

A semi-Lagrangian code for the solution of the electrostatic drift-kinetic equations in straight cylinder configuration is presented. The code, CYGNE, is part of a project with the long term aim of studying microturbulence in fusion devices. The code has been constructed in such a way as to preserve a good control of the constants of motion, possessed by the drift-kinetic equations, until the nonlinear saturation of the ion-temperature-gradient modes occurs. Studies of convergence with phase space resolution and time-step are presented and discussed. The code is benchmarked against electrostatic Particle-in-Cell codes.     

Conservative global gyrokinetic toroidal full-f five-dimensional Vlasov simulation

A new conservative global gyrokinetic toroidal full-f five-dimensional Vlasov simulation (GT5D) is developed using a novel non-dissipative conservative finite difference scheme. The scheme guarantees numerical stability by satisfying relevant first principles in the modern gyrokinetic theory, and enables robust and accurate simulations of tokamak micro-turbulence. GT5D is verified through comparisons of zonal flow damping tests, linear analyses of ion temperature gradient driven (ITG) modes, and nonlinear ITG turbulence simulations against a global gyrokinetic toroidal δf particle code. In the comparison, global solutions of the ITG turbulence are identified quantitatively by using two gyrokinetic codes based on particle and mesh approaches.     

Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection

A detailed procedure of full-electromagnetic Vlasov simulation technique is presented. Our new unsplitting conservative scheme exactly satisfies the continuity equation for charge. The implicit Finite Difference Time Domain method is also adopted for computation of electromagnetic fields, which is not restricted by the CFL condition for light. The Geospace Environment Modeling magnetic reconnection challenge problem is adopted as a benchmark test. The characteristics of the present Vlasov code are studied by varying the resolution in configuration space.     

Charge conservation in electromagnetic PIC codes; spectral comparison of Boris/DADI and Langdon-Marder methods

Non-charge conserving current collection algorithms for electromagnetic PIC plasma simulations may cause errors in Gauss's law. These errors arise from violations of the charge continuity equation, ∇ · J = −?π/?t, which is turn cause errors in the irrotational part of E.Two techniques for reducing these errors are examined and compared: a modified Marder correction which corrects electric fields locally and primarily affects short wavelengths, and a Boris divergence correction, which solves Poisson's equation to correct the electric fields so that Gauss's law is enforced globally. The effect of each method on the spectrum of the error is examined. Computational efficiency and accuracy of the two techniques are compared: neither method is clearly superior.Cases examined include corrections in electromagnetic relativistic beam simulations, and a hot thermal plasma. In addition, the spectral comparison provides insight into the behavior of the schemes applied.     

Plato: A localised orbital based density functional theory code

The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation.

Program summary

Program title: PlatoCatalogue identifier: AEFC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_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.: 219 974No. of bytes in distributed program, including test data, etc.: 1 821 493Distribution format: tar.gzProgramming language: C/MPI and PERLComputer: Apple Macintosh, PC, Unix machinesOperating system: Unix, Linux and Mac OS XHas the code been vectorised or parallelised?: Yes, up to 256 processors testedRAM: Up to 2 Gbytes per processorClassification: 7.3External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTWNature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces.Solution method: Localised orbital based density functional theory.Restrictions: Tight-binding and density functional theory only, no exact exchange.Unusual features: Both atom centred and uniform meshes available. Can deal with arbitrary angular momenta for orbitals, whilst still retaining Slater–Koster tables for accuracy.Running time: Test cases will run in a few minutes, large calculations may run for several days.     

The BAGEL assembler generation library

This paper presents two coupled software packages which receive widespread use in the field of numerical simulations of Quantum Chromo-Dynamics. These consist of the BAGEL library and the BAGEL fermion sparse-matrix library, BFM.The Bagel library can generate assembly code for a number of architectures and is configurable – supporting several precision and memory pattern options to allow architecture specific optimisation. It provides high performance on the QCDOC, BlueGene/L and BlueGene/P parallel computer architectures that are popular in the field of lattice QCD. The code includes a complete conjugate gradient implementation for the Wilson and domain wall fermion actions, making it easy to use for third party codes including the Jefferson Laboratory's CHROMA, UKQCD's UKhadron, and the Riken–Brookhaven–Columbia Collaboration's CPS packages.

Program summary

Program title: BagelCatalogue identifier: AEFE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU Public License V2No. of lines in distributed program, including test data, etc.: 109 576No. of bytes in distributed program, including test data, etc.: 892 841Distribution format: tar.gzProgramming language: C++, assemblerComputer: Massively parallel message passing. BlueGene/QCDOC/others.Operating system: POSIX, Linux and compatible.Has the code been vectorised or parallelized?: Yes. 16 384 processors used.Classification: 11.5External routines: QMP, QDP++Nature of problem: Quantum Chromo-Dynamics sparse matrix inversion for Wilson and domain wall fermion formulations.Solution method: Optimised Krylov linear solver.Unusual features: Domain specific compiler generates optimised assembly code.Running time: 1 h per matrix inversion; multi-year simulations.     

2DRMP: A suite of two-dimensional R-matrix propagation codes

The R-matrix method has proved to be a remarkably stable, robust and efficient technique for solving the close-coupling equations that arise in electron and photon collisions with atoms, ions and molecules. During the last thirty-four years a series of related R-matrix program packages have been published periodically in CPC. These packages are primarily concerned with low-energy scattering where the incident energy is insufficient to ionise the target. In this paper we describe 2DRMP, a suite of two-dimensional R-matrix propagation programs aimed at creating virtual experiments on high performance and grid architectures to enable the study of electron scattering from H-like atoms and ions at intermediate energies.

Program summary

Program title: 2DRMPCatalogue identifier: AEEA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEA_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.: 196 717No. of bytes in distributed program, including test data, etc.: 3 819 727Distribution format: tar.gzProgramming language: Fortran 95, MPIComputer: Tested on CRAY XT4 [1]; IBM eServer 575 [2]; Itanium II cluster [3]Operating system: Tested on UNICOS/lc [1]; IBM AIX [2]; Red Hat Linux Enterprise AS [3]Has the code been vectorised or parallelised?: Yes. 16 cores were used for small test runClassification: 2.4External routines: BLAS, LAPACK, PBLAS, ScaLAPACKSubprograms used: ADAZ_v1_1Nature of problem: 2DRMP is a suite of programs aimed at creating virtual experiments on high performance architectures to enable the study of electron scattering from H-like atoms and ions at intermediate energies.Solution method: Two-dimensional R-matrix propagation theory. The (r₁,r₂) space of the internal region is subdivided into a number of subregions. Local R-matrices are constructed within each subregion and used to propagate a global R-matrix, ℜ, across the internal region. On the boundary of the internal region ℜ is transformed onto the IERM target state basis. Thus, the two-dimensional R-matrix propagation technique transforms an intractable problem into a series of tractable problems enabling the internal region to be extended far beyond that which is possible with the standard one-sector codes. A distinctive feature of the method is that both electrons are treated identically and the R-matrix basis states are constructed to allow for both electrons to be in the continuum. The subregion size is flexible and can be adjusted to accommodate the number of cores available.Restrictions: The implementation is currently restricted to electron scattering from H-like atoms and ions.Additional comments: The programs have been designed to operate on serial computers and to exploit the distributed memory parallelism found on tightly coupled high performance clusters and supercomputers. 2DRMP has been systematically and comprehensively documented using ROBODoc [4] which is an API documentation tool that works by extracting specially formatted headers from the program source code and writing them to documentation files.Running time: The wall clock running time for the small test run using 16 cores and performed on [3] is as follows: bp (7 s); rint2 (34 s); newrd (32 s); diag (21 s); amps (11 s); prop (24 s).References:

• [1] 

  HECToR, CRAY XT4 running UNICOS/lc, http://www.hector.ac.uk/, accessed 22 July, 2009.

• [2] 

  HPCx, IBM eServer 575 running IBM AIX, http://www.hpcx.ac.uk/, accessed 22 July, 2009.

• [3] 

  HP Cluster, Itanium II cluster running Red Hat Linux Enterprise AS, Queen s University Belfast, http://www.qub.ac.uk/directorates/InformationServices/Research/HighPerformanceComputing/Services/Hardware/HPResearch/, accessed 22 July, 2009.

• [4] 

  Automating Software Documentation with ROBODoc, http://www.xs4all.nl/~rfsber/Robo/, accessed 22 July, 2009.

     

Accelerating scientific computations with mixed precision algorithms

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented.

Program summary

Program title: ITER-REFCatalogue identifier: AECO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_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.: 7211No. of bytes in distributed program, including test data, etc.: 41 862Distribution format: tar.gzProgramming language: FORTRAN 77Computer: desktop, serverOperating system: Unix/LinuxRAM: 512 MbytesClassification: 4.8External routines: BLAS (optional)Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution.Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision.Running time: seconds/minutes     

Simulation of electron spin resonance spectroscopy in diverse environments: An integrated approach

We discuss in this work a new software tool, named E-SpiReS (Electron Spin Resonance Simulations), aimed at the interpretation of dynamical properties of molecules in fluids from electron spin resonance (ESR) measurements. The code implements an integrated computational approach (ICA) for the calculation of relevant molecular properties that are needed in order to obtain spectral lines. The protocol encompasses information from atomistic level (quantum mechanical) to coarse grained level (hydrodynamical), and evaluates ESR spectra for rigid or flexible single or multi-labeled paramagnetic molecules in isotropic and ordered phases, based on a numerical solution of a stochastic Liouville equation.E-SpiReS automatically interfaces all the computational methodologies scheduled in the ICA in a way completely transparent for the user, who controls the whole calculation flow via a graphical interface.Parallelized algorithms are employed in order to allow running on calculation clusters, and a web applet Java has been developed with which it is possible to work from any operating system, avoiding the problems of recompilation.E-SpiReS has been used in the study of a number of different systems and two relevant cases are reported to underline the promising applicability of the ICA to complex systems and the importance of similar software tools in handling a laborious protocol.

Program summary

Program title: E-SpiReSCatalogue identifier: AEEM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPL v2.0No. of lines in distributed program, including test data, etc.: 311 761No. of bytes in distributed program, including test data, etc.: 10 039 531Distribution format: tar.gzProgramming language: C (core programs) and Java (graphical interface)Computer: PC and MacintoshOperating system: Unix and WindowsHas the code been vectorized or parallelized?: YesRAM: 2 048 000 000Classification: 7.2External routines: Babel-1.1, CLAPACK, BLAS, CBLAS, SPARSEBLAS, CQUADPACK, LEVMARNature of problem:Ab initio simulation of cw-ESR spectra of radicals in solutionSolution method: E-SpiReS uses an hydrodynamic approach to calculate the diffusion tensor of the molecule, DFT methodologies to evaluate magnetic tensors and linear algebra techniques to solve numerically the stochastic Liouville equation to obtain an ESR spectrum.Running time: Variable depending on the task. It takes seconds for small molecules in the fast motional regime to hours for big molecules in viscous and/or ordered media.     

FARM_2DRMP: A version of FARM for use with 2DRMP

To complete the 2DRMP package an asymptotic program, such as FARM, is needed. The original version of FARM is designed to construct the physical R-matrix, R, from surface amplitudes contained in the H-file. However, in 2DRMP, R has already been constructed for each scattering energy during propagation. Therefore, this modified version of FARM, known as FARM_2DRMP, has been developed solely for use with 2DRMP.

New version program summary

Program title: FARM_2DRMPCatalogue identifier: ADAZ_v1_1Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADAZ_v1_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.: 13 806No. of bytes in distributed program, including test data, etc.: 134 462Distribution format: tar.gzProgramming language: Fortran 95 and MPIComputer: Tested on CRAY XT4 [1]; IBM eServer 575 [2]; Itanium II cluster [3]Operating system: Tested on UNICOS/lc [1]; IBM AIX [2]; Red Hat Linux Enterprise AS [3]Has the code been vectorized or parallelized?: Yes. 16 cores were used for the small test runClassification: 2.4External routines: BLAS, LAPACKDoes the new version supersede the previous version?: NoNature of problem: The program solves the scattering problem in the asymptotic region of R-matrix theory where exchange is negligible.Solution method: A radius is determined at which the wave function, calculated as a Gailitis expansion [4] with accelerated summing [5] over terms, converges. The R-matrix is propagated from the boundary of the internal region to this radius and the K-matrix calculated. Collision strengths or cross sections may be calculated.Reasons for new version: To complete the 2DRMP package [6] an asymptotic program, such as FARM [7], is needed. The original version of FARM is designed to construct the physical R-matrix, R, from surface amplitudes contained in the H-file. However, in 2DRMP, R, has already been constructed for each scattering energy during propagation and each R is stored in one of the RmatT files described in Fig. 8 of [6]. Therefore, this modified version of FARM, known as FARM_2DRMP, has been developed solely for use with 2DRMP. Instructions on its use and corresponding test data is provided with 2DRMP [6].Summary of revisions: FARM_2DRMP contains two codes, farm.f and farm_par.f90. The former is a serial code while the latter is a parallel F95 code that employs an MPI harness to enable the nenergy energies to be computed simultaneously across ncore cores, with each core processing either ⌊nenergy/ncore⌋ or ⌈nenergy/ncore⌉ energies. The input files, input.d and H, and the output file farm.out are as described in [7]. Both codes read R directly from RmatT.Restrictions: FARM_2DRMP is for use solely with 2DRMP and for a specified L,S and Π combination. The energy range specified in input.d must match that specified in energies.data.Running time: The wall clock running time for the small test run using 16 cores and performed on [3] is 9 secs.References:

• [1] 

  HECToR, CRAY XT4 running UNICOS/lc, http://www.hector.ac.uk/, visited 22 July, 2009.

• [2] 

  HPCx, IBM eServer 575 running IBM AIX, http://www.hpcx.ac.uk/, visited 22 July, 2009.

• [3] 

  HP Cluster, Itanium II cluster running Red Hat Linux Enterprise AS, Queen's University Belfast, http://www.qub.ac.uk/directorates/InformationServices/Research/HighPerformanceComputing/Services/Hardware/HPResearch/, visited 22 July, 2009.

• [4] 

  M. Gailitis, J. Phys. B 9 (1976) 843.

• [5] 

  C.J. Noble, R.K. Nesbet, Comput. Phys. Comm. 33 (1984) 399.

• [6] 

  N.S. Scott, M.P. Scott, P.G. Burke, T. Stitt, V. Faro-Maza, C. Denis, A. Maniopoulou, Comput. Phys. Comm. 180 (12) (2009) 2424–2449, this issue.

• [7] 

  V.M. Burke, C.J. Noble, Comput. Phys. Comm. 85 (1995) 471.

     

Automated generation of lattice QCD Feynman rules

The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams.

Program summary

Program title: HiPPY, HPsrcCatalogue identifier: AEDX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPLv2 (see Additional comments below)No. of lines in distributed program, including test data, etc.: 513 426No. of bytes in distributed program, including test data, etc.: 4 893 707Distribution format: tar.gzProgramming language: Python, Fortran95Computer: HiPPy: Single-processor workstations. HPsrc: Single-processor workstations and MPI-enabled multi-processor systemsOperating system: HiPPy: Any for which Python v2.5.x is available. HPsrc: Any for which a standards-compliant Fortran95 compiler is availableHas the code been vectorised or parallelised?: YesRAM: Problem specific, typically less than 1 GB for either codeClassification: 4.4, 11.5Nature of problem: Derivation and use of perturbative Feynman rules for complicated lattice QCD actions.Solution method: An automated expansion method implemented in Python (HiPPy) and code to use expansions to generate Feynman rules in Fortran95 (HPsrc).Restrictions: No general restrictions. Specific restrictions are discussed in the text.Additional comments: The HiPPy and HPsrc codes are released under the second version of the GNU General Public Licence (GPL v2). Therefore anyone is free to use or modify the code for their own calculations. As part of the licensing, we ask that any publications including results from the use of this code or of modifications of it cite Refs. [1,2] as well as this paper. Finally, we also ask that details of these publications, as well as of any bugs or required or useful improvements of this core code, would be communicated to us.Running time: Very problem specific, depending on the complexity of the Feynman rules and the number of integration points. Typically between a few minutes and several weeks. The installation tests provided with the program code take only a few seconds to run.References:

• [1] 

  A. Hart, G.M. von Hippel, R.R. Horgan, L.C. Storoni, Automatically generating Feynman rules for improved lattice eld theories, J. Comput. Phys. 209 (2005) 340–353, doi:10.1016/j.jcp.2005.03.010, arXiv:hep-lat/0411026.

• [2] 

  M. Lüscher, P. Weisz, Efficient Numerical Techniques for Perturbative Lattice Gauge Theory Computations, Nucl. Phys. B 266 (1986) 309, doi:10.1016/0550-3213(86)90094-5.

     

A numerical Hartree-Fock program for diatomic molecules

This paper describes an algorithm and a computer program which solves numerically (virtually exactly) equations of the restricted open-shell Hartree-Fock and Hartree-Fock-Slater model for diatomic molecules     

PHON: A program to calculate phonons using the small displacement method

The program phon calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like the Helmholtz free energy, the entropy, the specific heat and the internal energy of the harmonic crystal. The procedure is based on the small displacement method, and can be used in combination with any program capable to calculate forces on the atoms of the crystal. In order to examine the usability of the method, I present here two examples: metallic Al and insulating MgO. The phonons of these two materials are calculated using density functional theory. The small displacement method results are compared with those obtained using the linear response method. In the case of Al the method provides accurate phonon frequencies everywhere in the Brillouin Zone (BZ). In the case of MgO the longitudinal branch of the optical phonons near the centre of the BZ is incorrectly described as degenerate with the two transverse branches, because the non-analytical part of the dynamical matrix is ignored here; however, thermodynamic properties like the Helmholtz free are essentially unaffected.

Program summary

Program title: PHONCatalogue identifier: AEDP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDP_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.: 19 580No. of bytes in distributed program, including test data, etc.: 612 193Distribution format: tar.gzProgramming language: Fortran 90Computer: Any Unix, LinuxOperating system: UnixRAM: Depends on super-cell size, but usually negligibleClassification: 7.8External routines: Subprograms ZHEEV and DSYEV (Lapack); needs BLAS. A tutorial is provided with the distribution which requires the installation of the quantum-espresso package (http://www.quantum-espresso.org)Nature of problem: Stable crystals at low temperature can be well described by expanding the potential energy around the atomic equilibrium positions. The movements of the atoms around their equilibrium positions can then be described using harmonic theory, and is characterised by global vibrations called phonons, which can be identified by vectors in the Brillouin zone of the crystal, and there are 3 phonon branches for each atom in the primitive cell. The problem is to calculate the frequencies of these phonons for any arbitrary choice of q-vector in the Brillouin zone.Solution method: The small displacement method: each atom in the primitive cell is displaced by a small amount, and the forces induced on all the other atoms in the crystal are calculated and used to construct the force constant matrix. Supercells of ∼100 atoms are usually large enough to describe the force constant matrix up to the range where its elements have fallen to negligibly small values. The force constant matrix is then used to compute the dynamical matrix at any chosen q-vector in the Brillouin zone, and the diagonalisation of the dynamical matrix provides the squares of the phonon frequencies. The PHON code needs external programs to calculate these forces, and it can be used with any program capable of calculating forces in crystals. The most useful applications are obtained with codes based on density functional theory, but there is no restriction on what can be used.Running time: Negligible, typically a few seconds (or at most a few minutes) on a PC. It can take longer if very dense meshes of q-points are needed, for example, to compute very accurate phonon density of states.     

An iterative nonlinear discriminant analysis program: IDA 1.0

A Fortran 77 package of an iterated discriminant analysis multi-background and signal recognition, IDA 1.0, is presented. The primary target is the high energy physics community, but it is general enough to be used in many classification application areas. The package can easily be used as is or may readily be modified for alternative purposes and optimizations.