A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Comment: Revision accepted for publication by the Journal of Agricultural, Biological, and Environmental Statistic

Towards Ad-Hoc GPU Acceleration Of Parallel Eigensystem Computations

This paper explores the early implementation of high- performance routines for the solution of multiple large Hermitian eigenvector and eigenvalue systems on a Graphics Processing Unit (GPU). We report a perfor- mance increase of up to two orders of magnitude over the original EISPACK routines with a NVIDIA Tesla C2050 GPU, potentially allowing an order of magnitude in- crease in the complexity or resolution of a neutron scat- tering modeling application

Parallel Simulation of Biomacromolecules using the DFTB method

Cilem teto prace je akcelerace DFTB metody pouzivane k simulaci biomakromolekul. Casove nejnarocnejsi casti simulace jsou identifikovany a akcelerovany s pouzitim internich moznosti puvodniho reseni, paralelizace pomoci OpenMP a moznosti pouzit knihovnu MAGMA, ktera vyuziva hybridnich CPU/GPU algoritmu ke zrychleni operaci linearni algebry. Jednotlive metody akcelerace jsou popsany a otestovany na systemech vod ruznych velikosti. Vysledky testu, prokazujici zrychleni oproti jinym knihovnam implementujicim operace linearni algebry, minimalni dopad paralelizace kodu a problemy s pouzitim interni akcelerace, jsou prezentovany v zaveru prace.The purpose of this work is to accelerate DFTB method used for biomacromolecule simulation by paralellization. The most time consuming parts of simulation are identified and parallelized using internal options and CPU and GPU acceleration of used linear algebra routines and the code itself. Possibility to use MAGMA - hybrid GPU/CPU linear algebra library and OpenMP parallelization of the code were implemented. All of those methods are described and tested on water systems of different size. Test results of MAGMA acceleration, parallelization and problems with internal optimizations are presented at the end of the work

TMB: Automatic Differentiation and Laplace Approximation

TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (~10^6) and parameters (~10^3). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems. The package and examples are available at http://tmb-project.org

Automatic Tuning to Performance Modelling of Matrix Polynomials on Multicore and Multi-GPU Systems

[EN] Automatic tuning methodologies have been used in the design of routines in recent years. The goal of these methodologies is to develop routines which automatically adapt to the conditions of the underlying computational system so that efficient executions are obtained independently of the end- user experience. This paper aims to explore programming routines that can automatically be adapted to the computational system conditions thanks to these automatic tuning methodologies. In particular, we have worked on the evaluation of matrix polynomials on multicore and multi-GPU systems as a target application. This application is very useful for the computation of matrix functions like the sine or cosine but, at the same time, the application is very time consuming since the basic computational kernel, which is the matrix multiplication, is carried out many times. The use of all available resources within a node in an easy and efficient way is crucial for the end user.This work has been partially supported by Generalitat Valenciana under Grant PROM-ETEOII/2014/003, and by the Spanish MINECO, as well as European Commission FEDER funds, under Grant TEC2015-67387-C4-1-R and TIN2015-66972-C5-3-R, and network CAPAP-H. Also, we have work in cooperation with the EU-COST Programme Action IC1305, "Network for Sustainable Ultrascale Computing (NESUS)".Boratto, M.; Alonso-Jordá, P.; Gimenez, D.; Lastovetsky, A. (2017). Automatic Tuning to Performance Modelling of Matrix Polynomials on Multicore and Multi-GPU Systems. The Journal of Supercomputing. 73(1):227-239. https://doi.org/10.1007/s11227-016-1694-yS227239731Alberti PV, Alonso P, Vidal AM, Cuenca J, Giménez D (2004) Designing polylibraries to speed up linear algebra computations. IJHPCN 1(1/2/3):75–84Alonso P, Boratto M, Pinilla J, Ibañez J, Martinez J (2014) On the evaluation of matrix polynomials using several GPGPUs. Tech Rep Riunet/E10251/39615Anderson E, Bai Z, Bischof C, Demmel J, Dongarra J, Croz JD, Greenbaum A, Hammarling S, McKenney A, Ostrouchov S, Sorensen D (2013) LAPACK users guide, 2nd edn. SIAM, PhiladelphiaBlackford LS, Demmel J, Dongarra J, Duff I, Hammarling S, Henry G, Heroux M, Kaufman L, Lumsdaine A, Petitet A, Pozo R, Remington K, Whaley RC (2001) An updated set of basic linear algebra subprograms (blas). ACM Trans Math Softw 28:135–151Caron E, Uter F (2002) Parallel extension of a dynamic performance forecasting tool. Sci Ann Cuza Univ 11:80–93Chandra R (2001) Parallel programming in OpenMP. Morgan Kaufmann, BurlingtonDemmel J, Marques O, Parlett BN, Vömel C (2008) Performance and accuracy of LAPACK’s symmetric tridiagonal eigensolvers. SIAM J.Sci Comput 30(3):1508–1526Frigo M, Johnson S (1998) FFTW: an adaptive software architecture for the FFT. In: Proceedings of IEEE International Conference on Acoustics Speech and Signal Processing vol. 3, pp 1381–1384García L, Cuenca J, Giménez D (2007) Including improvement of the execution time in a software architecture of libraries with self-optimisation. In: ICSOFT 2007, Proceedings of the Second International Conference on Software and Data Technologies, Volume SE, Barcelona, Spain, pp 156–161, 22–25 JulyGarcía LP, Cuenca J, Giménez D (2014) On optimization techniques for the matrix multiplication on hybrid cpu+gpu platforms. Ann Multicore GPU Program 1(1):10–18Hasanov K, Quintin JN, Lastovetsky A (2014) Hierarchical approach to optimization of parallel matrix multiplication on large-scale platforms. J Supercomput 71(11):24–34Katagiri T, Kise K, Honda H (2005) RAO-SS: a prototype of run-time auto-tuning facility for sparse direct solvers. Tech Rep 22(1):1–10Katagiri T, Kise K, Honda H, Yuba T (2004) Effect of auto-tuning with user’s knowledge for numerical software. Proceedings of the 1st conference on computing frontiers, Ischia, Italy. ACM, New York, NY, USA, pp 12–25Nath R, Tomov S, Dongarra J (2010) An improved magma gemm for fermi graphics processing units. Int J High Perform Comput Appl 24(4):511–515Paterson MS, Stockmeyer LJ (1973) On the number of nonscalar multiplications necessary to evaluate polynomials. SIAM J Comput 2(1):60–66PLASMA (2015) Parallel linear algebra software for multicore architectures. Available in: http://www.netlib.org/plasma/ . Accessed 1 June 2015Tanaka T, Katagiri T, Yuba T (2007) D-spline based incremental parameter estimation in automatic performance tuning. In: International Conference on Applied Parallel Computing: State of the Art in Scientific Computing, PARA’06. Springer-Verlag, Berlin, Heidelberg, pp 986–995Vuduc R, Demmel J, Bilmes J (2004) Statistical models for empirical search-based performance tuning. Int J High Perform Comput Appl 18:65–94Whaley RC, Petitet A, Dongarra JJ (2001) Automated empirical optimizations of software and the ATLAS project. Parallel Comput 27:21–3

Architecture-Aware Configuration and Scheduling of Matrix Multiplication on Asymmetric Multicore Processors

Asymmetric multicore processors (AMPs) have recently emerged as an appealing technology for severely energy-constrained environments, especially in mobile appliances where heterogeneity in applications is mainstream. In addition, given the growing interest for low-power high performance computing, this type of architectures is also being investigated as a means to improve the throughput-per-Watt of complex scientific applications. In this paper, we design and embed several architecture-aware optimizations into a multi-threaded general matrix multiplication (gemm), a key operation of the BLAS, in order to obtain a high performance implementation for ARM big.LITTLE AMPs. Our solution is based on the reference implementation of gemm in the BLIS library, and integrates a cache-aware configuration as well as asymmetric--static and dynamic scheduling strategies that carefully tune and distribute the operation's micro-kernels among the big and LITTLE cores of the target processor. The experimental results on a Samsung Exynos 5422, a system-on-chip with ARM Cortex-A15 and Cortex-A7 clusters that implements the big.LITTLE model, expose that our cache-aware versions of gemm with asymmetric scheduling attain important gains in performance with respect to its architecture-oblivious counterparts while exploiting all the resources of the AMP to deliver considerable energy efficiency