Compressed Multirow Storage Format for Sparse Matrices on Graphics Processing Units

Koza, Zbigniew; Matyka, Maciej; Szkoda, Sebastian; Mirosław, Łukasz

doi:10.1137/120900216

Cited by 24 publications

(10 citation statements)

References 20 publications

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“…Reference source not found.. This transition matrix is a compressed row format (CSR) [43,44] based on index of row ⟶ column delimited by commas generating the dictionary of the model which defines the transitions between nodes in the state-space and mapping of states. Through , we can know nothing more than the neighbours (child nodes) of the current node (states reachable through a single reaction), then we consider these neighbours (child nodes) as our only goal states and there can be many in numbers.…”

Section: Letmentioning

confidence: 99%

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Kosarwal¹,

Kulasiri²,

Samarasinghe³

2020

Preprint

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Background: Numerical solutions of the chemical master equation (CME) are important to understand the stochasticity of biochemical systems. However, solving CMEs is a formidable task due to the nonlinear nature of the reactions and size of the networks that result in different realisations and, most importantly, the exponential growth of the size of the state-space with respect to the number of different species in the system. When the size of the biochemical system is very large in terms of the number of variables, the solution to the CME becomes intractable. Therefore, we introduce the intelligent state projection (𝐼𝑆𝑃) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment to describe the dynamic behaviour of the system. 𝐼𝑆𝑃 is based on a state-space search and the data structure standards of artificial intelligence (𝐴𝐼) to explore and update the states of a biochemical system. To support the expansion in 𝐼𝑆𝑃, we also develop a Bayesian likelihood node projection (𝐵𝐿𝑁𝑃) function to predict the likelihood of the states. Results: To show the acceptability and effectiveness of our method, we apply the 𝐼𝑆𝑃 to several biological models previously discussed in the literature. According to the results of our computational experiments, we show that 𝐼𝑆𝑃 is effective in terms of speed and accuracy of the expansion, accuracy of the solution, and provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions: The 𝐼𝑆𝑃 is the de-novo method to address the accuracy as well as the performance problems for the solution of the CME. It systematically expands the projection space based on predefined inputs, which are useful in providing accuracy in the approximation and an exact analytical solution at the time of interest. The 𝐼𝑆𝑃 was more effective in terms of predicting the behaviour of the state-space of the system and in performance management, which is a vital step towards modelling large biochemical systems.

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Section: Letmentioning

confidence: 99%

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Kosarwal¹,

Kulasiri²,

Samarasinghe³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…However, the storage format considers only single precision. A similar idea of processing a sparse matrix in chunks larger than individual rows has been also exploited in the Compressed Multi-Row Storage (CMRS) format presented in [55]. CMRS extends the CSR format by dividing the matrix rows into strips; a warp is then assigned to a strip for processing.…”

Section: New Formats Based On Csrmentioning

confidence: 99%

Sparse Matrix-Vector Multiplication on GPGPUs

Filippone

Cardellini

Barbieri

et al. 2017

ACM Trans. Math. Softw.

103

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The multiplication of a sparse matrix by a dense vector (SpMV) is a centerpiece of scientific computing applications: it is the essential kernel for the solution of sparse linear systems and sparse eigenvalue problems by iterative methods. The efficient implementation of the sparse matrixvector multiplication is therefore crucial and has been the subject of an immense amount of research, with interest renewed with every major new trend in high performance computing architectures. The introduction of General Purpose Graphics Processing Units (GPGPUs) is no exception, and many articles have been devoted to this problem.With this paper we provide a review of the techniques for implementing the SpMV kernel on GPGPUs that have appeared in the literature of the last few years. We discuss the issues and tradeoffs that have been encountered by the various researchers, and a list of solutions, organized in categories according to common features. We also provide a performance comparison across different GPGPU models and on a set of test matrices coming from various application domains.

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“…The first step towards the implementation of this technique was the ability to use collaborative threads to process a single row (as opposed to the row-based parallelization just described). Advanced sparse matrix formats such as ELL-T [20], SIC [21], CMRS [22] or RgCSR [23] use slightly different approaches to map a row to one or more threads in a warp. Unfortunately, this thread mapping is not flexible (i.e.…”

Section: Related Workmentioning

confidence: 99%

Optimization techniques for sparse matrix–vector multiplication on GPUs

Maggioni

Berger-Wolf

2016

Journal of Parallel and Distributed Computing

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Sparse linear algebra is fundamental to numerous areas of applied mathematics, science and engineering. In this paper, we propose an efficient data structure named AdELL+ for optimizing the SpMV kernel on GPUs, focusing on performance bottlenecks of sparse computation. The foundation of our work is an ELL-based adaptive format which copes with matrix irregularity using balanced warps composed using a parametrized warp-balancing heuristic. We also address the intrinsic bandwidth-limited nature of SpMV with warp granularity, blocking, delta compression and nonzero unrolling, targeting both memory footprint and memory hierarchy efficiency. Finally, we introduce a novel online auto-tuning approach that uses a quality metric to predict efficient block factors and that hides preprocessing overhead with useful SpMV computation. Our experimental results show that AdELL+ achieves comparable or better performance over other state-of-the-art SpMV sparse formats proposed in academia (BCCOO) and industry (CSR+ and CSR-Adaptive). Moreover, our auto-tuning approach makes AdELL+ viable for real-world applications.

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Compressed Multirow Storage Format for Sparse Matrices on Graphics Processing Units

Cited by 24 publications

References 20 publications

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Sparse Matrix-Vector Multiplication on GPGPUs

Optimization techniques for sparse matrix–vector multiplication on GPUs

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