Graphs, Matrices, and the GraphBLAS: Seven Good Reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop on the Applications of Matrix Computational Methods in the Analysis of Modern Dat

A general framework for efficient FPGA implementation of matrix product

Original article can be found at: http://www.medjcn.com/ Copyright Softmotor LimitedHigh performance systems are required by the developers for fast processing of computationally intensive applications. Reconfigurable hardware devices in the form of Filed-Programmable Gate Arrays (FPGAs) have been proposed as viable system building blocks in the construction of high performance systems at an economical price. Given the importance and the use of matrix algorithms in scientific computing applications, they seem ideal candidates to harness and exploit the advantages offered by FPGAs. In this paper, a system for matrix algorithm cores generation is described. The system provides a catalog of efficient user-customizable cores, designed for FPGA implementation, ranging in three different matrix algorithm categories: (i) matrix operations, (ii) matrix transforms and (iii) matrix decomposition. The generated core can be either a general purpose or a specific application core. The methodology used in the design and implementation of two specific image processing application cores is presented. The first core is a fully pipelined matrix multiplier for colour space conversion based on distributed arithmetic principles while the second one is a parallel floating-point matrix multiplier designed for 3D affine transformations.Peer reviewe

GPU Accelerated Approach to Numerical Linear Algebra and Matrix Analysis with CFD Applications

A GPU accelerated approach to numerical linear algebra and matrix analysis with CFD applications is presented. The works objectives are to (1) develop stable and efficient algorithms utilizing multiple NVIDIA GPUs with CUDA to accelerate common matrix computations, (2) optimize these algorithms through CPU/GPU memory allocation, GPU kernel development, CPU/GPU communication, data transfer and bandwidth control to (3) develop parallel CFD applications for Navier Stokes and Lattice Boltzmann analysis methods. Special consideration will be given to performing the linear algebra algorithms under certain matrix types (banded, dense, diagonal, sparse, symmetric and triangular). Benchmarks are performed for all analyses with baseline CPU times being determined to find speed-up factors and measure computational capability of the GPU accelerated algorithms. The GPU implemented algorithms used in this work along with the optimization techniques performed are measured against preexisting work and test matrices available in the NIST Matrix Market. CFD analysis looked to strengthen the assessment of this work by providing a direct engineering application to analysis that would benefit from matrix optimization techniques and accelerated algorithms. Overall, this work desired to develop optimization for selected linear algebra and matrix computations performed with modern GPU architectures and CUDA developer which were applied directly to mathematical and engineering applications through CFD analysis