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.

     

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     

ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation

We describe a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom. While the field-free Hamiltonian and the dipole matrices may be generated using an arbitrary primitive basis, they are assumed to have been transformed to the eigenbasis of the problem before the solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. Probabilities for survival of the ground state, excitation, and single ionization can be extracted from the propagated wavefunction.

Program summary

Program title: ALTDSECatalogue identifier: AEDM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDM_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.: 2154No. of bytes in distributed program, including test data, etc.: 30 827Distribution format: tar.gzProgramming language: Fortran 95. [A Fortran 2003 call to “flush” is used to simplify monitoring the output file during execution. If this function is not available, these statements should be commented out.].Computer: Shared-memory machinesOperating system: Linux, OpenMPHas the code been vectorized or parallelized?: YesRAM: Several Gb, depending on matrix size and number of processorsSupplementary material: To facilitate the execution of the program, Hamiltonian field-free and dipole matrix files are provided.Classification: 2.5External routines: LAPACK, BLASNature of problem: We describe a computer program for a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom [1,2]. The probabilities for survival of the initial state, excitation of discrete states, and single ionization due to multi-photon processes can be obtained.Solution method: The solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. The field-free Hamiltonian and the dipole matrices, originally generated in an arbitrary basis (e.g., the flexible B-spline R-matrix (BSR) method with non-orthogonal orbitals [3]), must be provided in the eigenbasis of the problem as input.Restrictions: The present program is restricted to a ¹S^e initial state and linearly polarized light. This is the most common situation experimentally, but a generalization is straightforward.Running time: Several hours, depending on the number of threads used.References: [1] X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76 (2007) 053411. [2] X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78 (2008) 053402. [3] O. Zatsarinny, Comput. Phys. Comm. 174 (2006) 273.     

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.     

Classifying species of individual trees by intensity and structure features derived from airborne laser scanner data

The objective of this study was to identify candidate features derived from airborne laser scanner (ALS) data suitable to discriminate between coniferous and deciduous tree species. Both features related to structure and intensity were considered. The study was conducted on 197 Norway spruce and 180 birch trees (leaves on conditions) in a boreal forest reserve in Norway. The ALS sensor used was capable of recording multiple echoes. The point density was 6.6 m^− 2. Laser echoes located within the vertical projection of the tree crowns, which were assumed to be circular and defined according to field measurements, were attributed to three categories: “first echoes of many”, “single echoes”, or “last echoes of many echoes”. They were denoted FIRST, SINGLE, and LAST, respectively. In tree species classification using ALS data features should be independent of tree heights. We found that many features were dependent on tree height and that this dependency influenced selection of candidate features. When we accounted for this dependency, it was revealed that FIRST and SINGLE echoes were located higher and LAST echoes lower in the birch crowns than in spruce crowns. The intensity features of the FIRST echoes differed more between species than corresponding features of the other echo categories. For the FIRST echoes the intensity values tended to be higher for birch than spruce. When using the various features for species classification, maximum overall classification accuracies of 77% and 73% were obtained for structural and intensity features, respectively. Combining candidate features related to structure and intensity resulted in an overall classification accuracy of 88%.     

A Visualization Based Approach for Digital Signature Authentication

We propose a visualization based approach for digital signature authentication. Using our method, the speed and pressure aspects of a digital signature process can be clearly and intuitively conveyed to the user for digital signature authentication. Our design takes into account both the expressiveness and aesthetics of the derived visual patterns. With the visual aid provided by our method, digital signatures can be authenticated with better accuracy than using existing methods—even novices can examine the authenticity of a digital signature in most situations using our method. To validate the effectiveness of our method, we conducted a comprehensive user study which confirms positively the advantages of our approach. Our method can be employed as a new security enhancement measure for a range of business and legal applications in reality which involve digital signature authorization and authentication.     

SecondSkin: An interactive method for appearance transfer

SecondSkin estimates an appearance model for an object visible in a video sequence, without the need for complex interaction or any calibration apparatus. This model can then be transferred to other objects, allowing a non‐expert user to insert a synthetic object into a real video sequence so that its appearance matches that of an existing object, and changes appropriately throughout the sequence. As the method does not require any prior knowledge about the scene, the lighting conditions, or the camera, it is applicable to video which was not captured with this purpose in mind. However, this lack of prior knowledge precludes the recovery of separate lighting and surface reflectance information. The SecondSkin appearance model therefore combines these factors. The appearance model does require a dominant light‐source direction, which we estimate via a novel process involving a small amount of user interaction. The resulting model estimate provides exactly the information required to transfer the appearance of the original object to new geometry composited into the same video sequence.     

Linkless Octree Using Multi‐Level Perfect Hashing

The standard C/C++ implementation of a spatial partitioning data structure, such as octree and quadtree, is often inefficient in terms of storage requirements particularly when the memory overhead for maintaining parent‐to‐child pointers is significant with respect to the amount of actual data in each tree node. In this work, we present a novel data structure that implements uniform spatial partitioning without storing explicit parent‐to‐child pointer links. Our linkless tree encodes the storage locations of subdivided nodes using perfect hashing while retaining important properties of uniform spatial partitioning trees, such as coarse‐to‐fine hierarchical representation, efficient storage usage, and efficient random accessibility. We demonstrate the performance of our linkless trees using image compression and path planning examples.