GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

3-D GPU Based Real Time Diffuse Optical Tomographic System

3-Dimensional Diffuse Optical Tomographic (3-D DOT) image reconstruction algorithm is computationally complex and requires excessive matrix computations and thus hampers reconstruction in real time. In this paper, we present near real time 3D DOT image reconstruction that is based on Broyden approach for updating Jacobian matrix. The Broyden method simplifies the algorithm by avoiding re-computation of the Jacobian matrix in each iteration. We have developed CPU and heterogeneous CPU/GPU code for 3D DOT image reconstruction in C and MatLab programming platform. We have used Compute Unified Device Architecture (CUDA) programming framework and CUDA linear algebra library (CULA) to utilize the massively parallel computational power of GPUs (NVIDIA Tesla K20c). The computation time achieved for C program based implementation for a CPU/GPU system for 3 planes measurement and FEM mesh size of 19172 tetrahedral elements is 806 milliseconds for an iteration.

Paralelização do algoritmo FDK para reconstrução 3D de imagens tomográficas usando unidades gráficas de processamento e CUDA-C

A obtenção de imagens usando tomografia computadorizada revolucionou o diagnóstico de doenças na medicina e é usada amplamente em diferentes áreas da pesquisa científica. Como parte do processo de obtenção das imagens tomográficas tridimensionais um conjunto de radiografias são processadas por um algoritmo computacional, o mais usado atualmente é o algoritmo de Feldkamp, David e Kress (FDK). Os usos do processamento paralelo para acelerar os cálculos em algoritmos computacionais usando as diferentes tecnologias disponíveis no mercado têm mostrado sua utilidade para diminuir os tempos de processamento. No presente trabalho é apresentada a paralelização do algoritmo de reconstrução de imagens tridimensionais FDK usando unidades gráficas de processamento (GPU) e a linguagem CUDA-C. São apresentadas as GPUs como uma opção viável para executar computação paralela e abordados os conceitos introdutórios associados à tomografia computadorizada, GPUs, CUDA-C e processamento paralelo. A versão paralela do algoritmo FDK executada na GPU é comparada com uma versão serial do mesmo, mostrando maior velocidade de processamento. Os testes de desempenho foram feitos em duas GPUs de diferentes capacidades: a placa NVIDIA GeForce 9400GT (16 núcleos) e a placa NVIDIA Quadro 2000 (192 núcleos).

BarraCUDA - a fast short read sequence aligner using graphics processing units.

BACKGROUND: With the maturation of next-generation DNA sequencing (NGS) technologies, the throughput of DNA sequencing reads has soared to over 600 gigabases from a single instrument run. General purpose computing on graphics processing units (GPGPU), extracts the computing power from hundreds of parallel stream processors within graphics processing cores and provides a cost-effective and energy efficient alternative to traditional high-performance computing (HPC) clusters. In this article, we describe the implementation of BarraCUDA, a GPGPU sequence alignment software that is based on BWA, to accelerate the alignment of sequencing reads generated by these instruments to a reference DNA sequence. FINDINGS: Using the NVIDIA Compute Unified Device Architecture (CUDA) software development environment, we ported the most computational-intensive alignment component of BWA to GPU to take advantage of the massive parallelism. As a result, BarraCUDA offers a magnitude of performance boost in alignment throughput when compared to a CPU core while delivering the same level of alignment fidelity. The software is also capable of supporting multiple CUDA devices in parallel to further accelerate the alignment throughput. CONCLUSIONS: BarraCUDA is designed to take advantage of the parallelism of GPU to accelerate the alignment of millions of sequencing reads generated by NGS instruments. By doing this, we could, at least in part streamline the current bioinformatics pipeline such that the wider scientific community could benefit from the sequencing technology.BarraCUDA is currently available from http://seqbarracuda.sf.net.

GPU-accelerated optimization of fuel treatments for mitigating wildfire hazard

Fuel treatment is considered a suitable way to mitigate the hazard related to potential wildfires on a landscape. However, designing an optimal spatial layout of treatment units represents a difficult optimization problem. In fact, budget constraints, the probabilistic nature of fire spread and interactions among the different area units composing the whole treatment, give rise to challenging search spaces on typical landscapes. In this paper we formulate such optimization problem with the objective of minimizing the extension of land characterized by high fire hazard. Then, we propose a computational approach that leads to a spatially-optimized treatment layout exploiting Tabu Search and General-Purpose computing on Graphics Processing Units (GPGPU). Using an application example, we also show that the proposed methodology can provide high-quality design solutions in low computing time. © 2013 The Authors. Published by Elsevier B.V.

Real-time GPU color-based segmentation of football players

In this paper, we propose a multi-camera application capable of processing high resolution images and extracting features based on colors patterns over graphic processing units (GPU). The goal is to work in real time under the uncontrolled environment of a sport event like a football match. Since football players are composed for diverse and complex color patterns, a Gaussian Mixture Models (GMM) is applied as segmentation paradigm, in order to analyze sport live images and video. Optimization techniques have also been applied over the C++ implementation using profiling tools focused on high performance. Time consuming tasks were implemented over NVIDIA's CUDA platform, and later restructured and enhanced, speeding up the whole process significantly. Our resulting code is around 4-11 times faster on a low cost GPU than a highly optimized C++ version on a central processing unit (CPU) over the same data. Real time has been obtained processing until 64 frames per second. An important conclusion derived from our study is the scalability of the application to the number of cores on the GPU. © 2011 Springer-Verlag.

cudaMap: a GPU accelerated program for gene expression connectivity mapping

Background: Modern cancer research often involves large datasets and the use of sophisticated statistical techniques. Together these add a heavy computational load to the analysis, which is often coupled with issues surrounding data accessibility. Connectivity mapping is an advanced bioinformatic and computational technique dedicated to therapeutics discovery and drug re-purposing around differential gene expression analysis. On a normal desktop PC, it is common for the connectivity mapping task with a single gene signature to take >2h to complete using sscMap, a popular Java application that runs on standard CPUs (Central Processing Units). Here, we describe new software, cudaMap, which has been implemented using CUDA C/C++ to harness the computational power of NVIDIA GPUs (Graphics Processing Units) to greatly reduce processing times for connectivity mapping.

Results: cudaMap can identify candidate therapeutics from the same signature in just over thirty seconds when using an NVIDIA Tesla C2050 GPU. Results from the analysis of multiple gene signatures, which would previously have taken several days, can now be obtained in as little as 10 minutes, greatly facilitating candidate therapeutics discovery with high throughput. We are able to demonstrate dramatic speed differentials between GPU assisted performance and CPU executions as the computational load increases for high accuracy evaluation of statistical significance.

Conclusion: Emerging 'omics' technologies are constantly increasing the volume of data and information to be processed in all areas of biomedical research. Embracing the multicore functionality of GPUs represents a major avenue of local accelerated computing. cudaMap will make a strong contribution in the discovery of candidate therapeutics by enabling speedy execution of heavy duty connectivity mapping tasks, which are increasingly required in modern cancer research. cudaMap is open source and can be freely downloaded from http://purl.oclc.org/NET/cudaMap.

Shortening design time through multiplatform simulations with a portable OpenCL golden-model: the LDPC decoder case

Hardware designers and engineers typically need to explore a multi-parametric design space in order to find the best configuration for their designs using simulations that can take weeks to months to complete. For example, designers of special purpose chips need to explore parameters such as the optimal bitwidth and data representation. This is the case for the development of complex algorithms such as Low-Density Parity-Check (LDPC) decoders used in modern communication systems. Currently, high-performance computing offers a wide set of acceleration options, that range from multicore CPUs to graphics processing units (GPUs) and FPGAs. Depending on the simulation requirements, the ideal architecture to use can vary. In this paper we propose a new design flow based on OpenCL, a unified multiplatform programming model, which accelerates LDPC decoding simulations, thereby significantly reducing architectural exploration and design time. OpenCL-based parallel kernels are used without modifications or code tuning on multicore CPUs, GPUs and FPGAs. We use SOpenCL (Silicon to OpenCL), a tool that automatically converts OpenCL kernels to RTL for mapping the simulations into FPGAs. To the best of our knowledge, this is the first time that a single, unmodified OpenCL code is used to target those three different platforms. We show that, depending on the design parameters to be explored in the simulation, on the dimension and phase of the design, the GPU or the FPGA may suit different purposes more conveniently, providing different acceleration factors. For example, although simulations can typically execute more than 3x faster on FPGAs than on GPUs, the overhead of circuit synthesis often outweighs the benefits of FPGA-accelerated execution.

Calcul en n-dimensions sur GPU

Le code source de la libraire développée accompagne ce dépôt dans l'état où il était à ce moment. Il est possible de trouver une version plus à jour sur github (http://github.com/abergeron).

A multi-GPU algorithm for large-scale neuronal networks

Large-scale simulations of parts of the brain using detailed neuronal models to improve our understanding of brain functions are becoming a reality with the usage of supercomputers and large clusters. However, the high acquisition and maintenance cost of these computers, including the physical space, air conditioning, and electrical power, limits the number of simulations of this kind that scientists can perform. Modern commodity graphical cards, based on the CUDA platform, contain graphical processing units (GPUs) composed of hundreds of processors that can simultaneously execute thousands of threads and thus constitute a low-cost solution for many high-performance computing applications. In this work, we present a CUDA algorithm that enables the execution, on multiple GPUs, of simulations of large-scale networks composed of biologically realistic Hodgkin-Huxley neurons. The algorithm represents each neuron as a CUDA thread, which solves the set of coupled differential equations that model each neuron. Communication among neurons located in different GPUs is coordinated by the CPU. We obtained speedups of 40 for the simulation of 200k neurons that received random external input and speedups of 9 for a network with 200k neurons and 20M neuronal connections, in a single computer with two graphic boards with two GPUs each, when compared with a modern quad-core CPU. Copyright (C) 2010 John Wiley & Sons, Ltd.

Técnicas de paralelização em GPGPU aplicadas em algoritmo para remoção de ruído multiplicativo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Implementação do algoritmo de treinamento do classificador Floresta de Caminhos Ótimos em GPU

Pós-graduação em Ciência da Computação - IBILCE

Implementação do algoritmo de treinamento do classificador floresta de caminhos ótimos em GPU

Técnicas de reconhecimento de padrões tem como principal objetivo classificar um conjunto de amostras, sendo o processo de aprendizado a fase de maior consumo de tempo. O problema pode piorar em ferramentas de classificação interativas, o que pode ser inaceitável para grandes bases de dados. Um exemplo de classificador é o baseado em Floresta de Caminhos Ótimos [8] - OPF. Dado que muitos trabalhos tem sido orientados à implementação de algoritmos de reconhecimento de padrões em ambiente General Purpose Graphics Processing Unit - GPGPU, o presente estudo objetivou a implementação da etapa de treinamento do classificador Floresta de Caminhos Ótimos em CUDA, visando aumentar a sua eficiência. A otimização do classificador em CUDA demonstrou uma fase de treinamento mais rápida que a versão original.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.