OpenMP Architecture Review Board Research Articles

PAREMD: A parallel program for the evaluation of momentum space properties of atoms and molecules

The present work describes a code for evaluating the electron momentum density (EMD), its moments and the associated Shannon information entropy for a multi-electron molecular system. The code works specifically for electronic wave functions obtained from traditional electronic structure packages such as GAMESS and GAUSSIAN. For the momentum space orbitals, the general expression for Gaussian basis sets in position space is analytically Fourier transformed to momentum space Gaussian basis functions. The molecular orbital coefficients of the wave function are taken as an input from the output file of the electronic structure calculation. The analytic expressions of EMD are evaluated over a fine grid and the accuracy of the code is verified by a normalization check and a numerical kinetic energy evaluation which is compared with the analytic kinetic energy given by the electronic structure package. Apart from electron momentum density, electron density in position space has also been integrated into this package. The program is written in C++ and is executed through a Shell script. It is also tuned for multicore machines with shared memory through OpenMP. The program has been tested for a variety of molecules and correlated methods such as CISD, Møller–Plesset second order (MP2) theory and density functional methods. For correlated methods, the PAREMD program uses natural spin orbitals as an input. The program has been benchmarked for a variety of Gaussian basis sets for different molecules showing a linear speedup on a parallel architecture. Program summaryProgram Title: PAREMDProgram Files doi:http://dx.doi.org/10.17632/gcr9gmh6zv.1Licensing provisions: GPLv3Programming language: C, CshExternal routines/libraries: GSL[1], BLAS[2,3], OpenMP[4], GAMESS[5,6] and GAUSSIAN[7].Nature of problem: Momentum space properties for a multi-electron system.Solution method: Analytic Fourier transformation of Gaussian basis in position space to get momentum space basis followed by EMD evaluation on spherical or Cartesian grids. A numerical integration procedure is implemented for evaluating moments of EMD and Shannon information entropy on a polar grid.[1] Galassi et al, GNU Scientific Library Reference Manual (3rd Ed.), ISBN 0954612078.[2] L. S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, R. C. Whaley, An Updated Set of Basic Linear Algebra Subprograms (BLAS), ACM Trans. Math. Soft., 28-2 (2002), pp. 135–151.[3] J. Dongarra, Basic Linear Algebra Subprograms Technical Forum Standard, International Journal of High Performance Applications and Supercomputing, 16(1) (2002), pp. 1–111, and International Journal of High Performance Applications and Supercomputing, 16(2) (2002), pp. 115–199.[4] OpenMP Architecture Review Board, ”OpenMP Application Program Interface, Version 4.5”, November 2015.[5] ”General Atomic and Molecular Electronic Structure System” M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. MontgomeryJ. Comput. Chem. 14 1347–1363, 1993.[6] “Advances in electronic structure theory: GAMESS a decade later M.S. Gordon, M.W. Schmidt pp. 1167–1189, in Theory and Applications of Computational Chemistry: the first forty years C.E. Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (editors), Elsevier, Amsterdam, 2005.[7] Gaussian 09, Revision C.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2016.

SpMC: Modelling Spatial Random Fields with Continuous Lag Markov Chains

Currently, a part of the R statistical software is developed in order to deal with spatial models. More specifically, some available packages allow the user to analyse categorical spatial random patterns. However, only the spMC package considers a viewpoint based on transition probabilities between locations. Through the use of this package it is possible to analyse the spatial variability of data, make inference, predict and simulate the categorical classes in unobserved sites. An example is presented by analysing the well-known Swiss Jura data set. Introduction Originally, the spMC package (Sartore, 2013) was developed with the purpose of analysing categorical data observed in 3-D locations. It deals with stochastic models based on Markov chains, which may be used for the analysis of spatial random patterns in continuous multidimensional spaces (Carle and Fogg, 1997). Its results are easily interpretable and it is a good alternative to the T-PROGS software developed by Carle (1999), which is oriented towards modelling groundwater systems. The models considered in the spMC package are used to analyse any categorical random variable Z(s) at the d-dimensional position s 2 R d which satisfies the Markov property. Other R packages are also helpful for analysing categorical spatial data. For example, the gstat package (Pebesma, 2004) allows for analyses using traditional methods such as the parameter estimation of spatial models based on variograms and kriging techniques for predictions. All these methods and their variants are also available in other packages, e.g. geoRglm (Christensen and Ribeiro Jr, 2002) and RandomFields (Schlather, 2013). When Z(s) is assumed to be linked to a continuous hidden random process, these packages are useful for studying the covariance structure of the data. The spMC package extends the functionality of the T-PROGS software to R users. New useful functions are included for faster modelling of transition probability matrices, and efficient algorithms are implemented for improving predictions and simulations of categorical random fields. The main tasks and their functions are clearly summarised in Table 1. Three different fitting methods were implemented in the package. The first is based on the estimates of the main features that characterise the process, the second focuses on the minimisation of the discrepancies between the empirical and theoretical transition probabilities, and the third follows the maximum entropy approach. Once the model parameters are properly estimated, transition probabilities are calculated through the matrix- valued exponential function (see Higham, 2008, Algorithm 10.20 in Chapter 10). These transition probabilities are then combined to predict the category in an unsampled position. Three algorithms are used to simulate spatial random fields; those based on the kriging techniques (Carle and Fogg, 1996), those using fixed and random path methods (Li, 2007a; Li and Zhang, 2007), or those using multinomial categorical simulation proposed by Allard et al. (2011). In order to reduce computation time through OpenMP API (version 3.0; OpenMP Architecture Review Board, 2008), the setCores() function allows the user to change the number of CPU cores, so that one can mix shared memory parallel techniques with those based on the Message Passing Interface (The MPI Forum, 1993) as described in Smith (2000). Here, it will be shown how to perform a geostatistical analysis of the Jura data set (Goovaerts, 1997) using the spMC package (version 0.3.1). The data set consists of 359 sampled spatial coordinates and their respective observed realisations of two categorical variables (related to the rock-type and the land use) and some continuous variables (corresponding to the topsoil content).

Complete Formal Specification of the OpenMP Memory Model

OpenMP [OpenMP Architecture Review Board. OpenMP application program interface, version 2.5] is an important API for shared memory programming, combining shared memory's potential for performance with a simple programming interface. Unfortunately, OpenMP lacks a critical tool for demonstrating whether programs are correct: a formal memory model. Instead, the current official definition of the OpenMP memory model (the Open-MP 2.5 specification [OpenMP Architecture Review Board. OpenMP application program interface, version 2.5]) is in terms of informal prose. As a result, it is impossible to verify OpenMP applications formally since the prose does not provide a formal consistency model that precisely describes how reads and writes on different threads interact. We expand on our previous work that focused on the formal verification of OpenMP programs through a formal memory model [Greg Bronevetsky and Bronis de Supinski. Formal specification of the memory model. In International Workshop on OpenMP (IWOMP), (2006)]. As in that work, our formalization, which is derived from the existing prose model [OpenMP Architecture Review Board. OpenMP application program interface, version 2.5], provides a two-step process to verify whether an observed OpenMP execution is conformant. This paper extends the model to cover the entire specification. In addition to this formalization, our contributions include a discussion of ambiguities in the current prose-based memory model description. Although our formal model may not capture the current informal memory model perfectly, in part due to these ambiguities, our model reflects our understanding of the informal model's intent. We conclude with several examples that may indicate areas of the OpenMP memory model that need further refinement, however it is specified. Our goal is to motivate the OpenMP community to adopt those refinements eventually, ideally through a formal model, in later OpenMP specifications.

Special Issue on OpenMP—Guest Editors’ Introduction

OpenMP is an Application Programming Interface (API) widely accepted as a standard for high-level shared-memory parallel programming. OpenMP is a portable, scalable programming model that provides a simple and flexible interface for developing shared-memory parallel applications in Fortran, C, and C++. Since its introduction in 1997, OpenMP has gained support from the majority of high-performance compiler and hardware vendors. There is also active research in OpenMP compilers, runtime systems, tools, and environments. Under the direction of the OpenMP Architecture Review Board (ARB), the OpenMP standard continues to evolve. The community of OpenMP researchers and developers in academia and industry is organized under cOMPunity, a forum for the dissemination and exchange of information about and experiences with OpenMP. IWOMP is the consolidation of three OpenMP workshops: the European Workshop on OpenMP (EWOMP), the Workshop on OpenMP Applications and Tools (WOMPAT), and the Workshop on OpenMP Experiences and Implementation (WOMPEI) that took place on several occasions starting in 1999. Two consecutive issues of the International Journal of Parallel Programming are devoted to extend the best papers that were presented at the second International Workshop on OpenMP (IWOMP), celebrated in Reims (France), 12–15 June 2006.