9,469 research outputs found
A fast sparse block circulant matrix vector product
In the context of computed tomography (CT), iterative image reconstruction techniques are gaining attention because high-quality images are becoming computationally feasible. They involve the solution of large systems of equations, whose cost is dominated by the sparse matrix vector product (SpMV). Our work considers the case of the sparse matrices being block circulant, which arises when taking advantage of the rotational symmetry in the tomographic system. Besides the straightforward storage saving, we exploit the circulant structure to rewrite the poor-performance SpMVs into a high-performance product between sparse and dense matrices. This paper describes the implementations developed for multi-core CPUs and GPUs, and presents experimental results with typical CT matrices. The presented approach is up to ten times faster than without exploiting the circulant structure.Romero Alcalde, E.; Tomás Domínguez, AE.; Soriano Asensi, A.; Blanquer Espert, I. (2014). A fast sparse block circulant matrix vector product. En Euro-Par 2014 Parallel Processing. Springer. 548-559. doi:10.1007/978-3-319-09873-9_46S548559Bian, J., Siewerdsen, J.H., Han, X., Sidky, E.Y., Prince, J.L., Pelizzari, C.A., Pal, X.: Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam ct. Physics in Medicine and Biology 55, 6575–6599 (2010)Dalton, S., Bell, N.: CUSP: A C++ templated sparse matrix library version 0.4.0 (2014), http://cusplibrary.github.com/Feldkamp, L., Davis, L., Kress, J.: Practical cone-beam algorithm. Journal of the Optical Society of America 1, 612–619 (1984)Ganine, V., Legrand, M., Michalska, H., Pierre, C.: A sparse preconditioned iterative method for vibration analysis of geometrically mistuned bladed disks. Computers & Structures 87(5-6), 342–354 (2009)Hara, A.K., Paden, R.G., Silva, A.C., Kujak, J.L., Lawder, H.J., Pavlicek, W.: Iterative reconstruction technique for reducing body radiation dose at CT: Feasibility study. American Journal of Roentgenology 193, 764–771 (2009)Heroux, M.A., Bartlett, R.A., Howle, V.E., Hoekstra, R.J., Hu, J.J., Kolda, T.G., Lehoucq, R.B., Long, K.R., Pawlowski, R.P., Phipps, E.T., Salinger, A.G., Thornquist, H.K., Tuminaro, R.S., Willenbring, J.M., Williams, A., Stanley, K.S.: An overview of the Trilinos project. ACM Trans. Math. Softw. 31(3), 397–423 (2005)Im, E.J., Yelick, K., Vuduc, R.: Sparsity: Optimization framework for sparse matrix kernels. International Journal of High Performance Computing Applications 18(1), 135–158 (2004)Jones, E., Oliphant, T., Peterson, P., et al.: SciPy: Open source scientific tools for Python (2001), http://www.scipy.org/Kaveh, A., Rahami, H.: Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures. Acta Mechanica 217(1-2), 51–62 (2011)Kourtis, K., Goumas, G., Koziris, N.: Optimizing sparse matrix-vector multiplication using index and value compression. In: Proceedings of the 5th Conference on Computing Frontiers, CF 2008, pp. 87–96. ACM, New York (2008)Krotkiewski, M., Dabrowski, M.: Parallel symmetric sparse matrix–vector product on scalar multi-core CPUs. Parallel Computing 36(4), 181–198 (2010)Lee, B., Vuduc, R., Demmel, J., Yelick, K.: Performance models for evaluation and automatic tuning of symmetric sparse matrix-vector multiply. In: International Conference on Parallel Processing, ICPP 2004, vol. 1, pp. 169–176 (2004)Leroux, J.D., Selivanov, V., Fontaine, R., Lecomte, R.: Accelerated iterative image reconstruction methods based on block-circulant system matrix derived from a cylindrical image representation. In: Nuclear Science Symposium Conference Record, NSS 2007, vol. 4, pp. 2764–2771. IEEE (2007)NVIDIA: CUSPARSE library (2014), https://developer.nvidia.com/cusparsePan, X., Sidky, E.Y., Vannier, M.: Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? Inverse Problems 25, 123009 (2008)Rodríguez-Alvarez, M.J., Soriano, A., Iborra, A., Sánchez, F., González, A.J., Conde, P., Hernández, L., Moliner, L., Orero, A., Vidal, L.F., Benlloch, J.M.: Expectation maximization (EM) algorithms using polar symmetries for computed tomography CT image reconstruction. Computers in Biology and Medicine 43(8), 1053–1061 (2013)Sheep, L., Vardi, Y.: Maximum likelihood reconstruction for emmision tomography. IEEE Transactions on Medical Imaging 1, 113–122 (1982)Sidky, E.Y., Pan, X.: Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Physics in Medicine and Biology 53, 4777–4807 (2008)Soriano, A., Rodríguez-Alvarez, M.J., Iborra, A., Sánchez, F., Carles, M., Conde, P., González, A.J., Hernández, L., Moliner, L., Orero, A., Vidal, L.F., Benlloch, J.M.: EM tomographic image reconstruction using polar voxels. Journal of Instrumentation 8, C01004 (2013)Thibaudeau, C., Leroux, J.D., Pratte, J.F., Fontaine, R., Lecomte, R.: Cylindrical and spherical ray-tracing for ct iterative reconstruction. In: 2011 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), pp. 4378–4381 (2011)Vuduc, R., Demmel, J.W., Yelick, K.A.: OSKI: A library of automatically tuned sparse matrix kernels. Journal of Physics: Conference Series 16(1), 521 (2005)Vuduc, R.W., Moon, H.-J.: Fast sparse matrix-vector multiplication by exploiting variable block structure. In: Yang, L.T., Rana, O.F., Di Martino, B., Dongarra, J. (eds.) HPCC 2005. LNCS, vol. 3726, pp. 807–816. Springer, Heidelberg (2005)Williams, S., Oliker, L., Vuduc, R., Shalf, J., Yelick, K., Demmel, J.: Optimization of sparse matrix-vector multiplication on emerging multicore platforms. Parallel Computing 35(3), 178–194 (2009
A Library for Pattern-based Sparse Matrix Vector Multiply
Pattern-based Representation (PBR) is a novel approach to improving the performance of Sparse Matrix-Vector Multiply (SMVM) numerical kernels. Motivated by our observation that many matrices can be divided into blocks that share a small number of distinct patterns, we generate custom multiplication kernels for frequently recurring block patterns.
The resulting reduction in index overhead significantly reduces memory bandwidth requirements and improves performance. Unlike existing methods, PBR requires neither detection of dense blocks nor zero filling, making it particularly advantageous for matrices that lack dense nonzero concentrations. SMVM kernels for PBR can benefit from explicit prefetching and vectorization, and are amenable to parallelization. The analysis and format conversion to PBR is implemented as a library, making it suitable for applications that generate matrices dynamically at runtime. We present sequential and parallel performance results for PBR on two current multicore architectures, which show that PBR outperforms available alternatives for the matrices to which it is applicable,
and that the analysis and conversion overhead is amortized in realistic application scenarios
Optimising Sparse Matrix Vector multiplication for large scale FEM problems on FPGA
Sparse Matrix Vector multiplication (SpMV) is an important kernel in many scientific applications. In this work we propose an architecture and an automated customisation method to detect and optimise the architecture for block diagonal sparse matrices. We evaluate the proposed approach in the context of the spectral/hp Finite Element Method, using the local matrix assembly approach. This problem leads to a large sparse system of linear equations with block diagonal matrix which is typically solved using an iterative method such as the Preconditioned Conjugate Gradient. The efficiency of the proposed architecture combined with the effectiveness of the proposed customisation method reduces BRAM resource utilisation by as much as 10 times, while achieving identical throughput with existing state of the art designs and requiring minimal development effort from the end user. In the context of the Finite Element Method, our approach enables the solution of larger problems than previously possible, enabling the applicability of FPGAs to more interesting HPC problems
GraphBLAST: A High-Performance Linear Algebra-based Graph Framework on the GPU
High-performance implementations of graph algorithms are challenging to
implement on new parallel hardware such as GPUs because of three challenges:
(1) the difficulty of coming up with graph building blocks, (2) load imbalance
on parallel hardware, and (3) graph problems having low arithmetic intensity.
To address some of these challenges, GraphBLAS is an innovative, on-going
effort by the graph analytics community to propose building blocks based on
sparse linear algebra, which will allow graph algorithms to be expressed in a
performant, succinct, composable and portable manner. In this paper, we examine
the performance challenges of a linear-algebra-based approach to building graph
frameworks and describe new design principles for overcoming these bottlenecks.
Among the new design principles is exploiting input sparsity, which allows
users to write graph algorithms without specifying push and pull direction.
Exploiting output sparsity allows users to tell the backend which values of the
output in a single vectorized computation they do not want computed.
Load-balancing is an important feature for balancing work amongst parallel
workers. We describe the important load-balancing features for handling graphs
with different characteristics. The design principles described in this paper
have been implemented in "GraphBLAST", the first high-performance linear
algebra-based graph framework on NVIDIA GPUs that is open-source. The results
show that on a single GPU, GraphBLAST has on average at least an order of
magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL,
comparable performance to the fastest GPU hardwired primitives and
shared-memory graph frameworks Ligra and Gunrock, and better performance than
any other GPU graph framework, while offering a simpler and more concise
programming model.Comment: 50 pages, 14 figures, 14 table
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes
This work presents a new code-based key encapsulation mechanism (KEM) called
LEDAkem. It is built on the Niederreiter cryptosystem and relies on
quasi-cyclic low-density parity-check codes as secret codes, providing high
decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known
statistical attacks, and takes advantage of a new decoding algorithm that
provides faster decoding than the classical bit-flipping decoder commonly
adopted in this kind of systems. The main attacks against LEDAkem are
investigated, taking into account quantum speedups. Some instances of LEDAkem
are designed to achieve different security levels against classical and quantum
computers. Some performance figures obtained through an efficient C99
implementation of LEDAkem are provided.Comment: 21 pages, 3 table
Parallel structurally-symmetric sparse matrix-vector products on multi-core processors
We consider the problem of developing an efficient multi-threaded
implementation of the matrix-vector multiplication algorithm for sparse
matrices with structural symmetry. Matrices are stored using the compressed
sparse row-column format (CSRC), designed for profiting from the symmetric
non-zero pattern observed in global finite element matrices. Unlike classical
compressed storage formats, performing the sparse matrix-vector product using
the CSRC requires thread-safe access to the destination vector. To avoid race
conditions, we have implemented two partitioning strategies. In the first one,
each thread allocates an array for storing its contributions, which are later
combined in an accumulation step. We analyze how to perform this accumulation
in four different ways. The second strategy employs a coloring algorithm for
grouping rows that can be concurrently processed by threads. Our results
indicate that, although incurring an increase in the working set size, the
former approach leads to the best performance improvements for most matrices.Comment: 17 pages, 17 figures, reviewed related work section, fixed typo
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