Multi-Platform LU-Decomposition Solution in OpenCL

Ehsan Nasiri, Rafat Rashid, Saurabh Verma
The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto
University of Toronto, 2012


   title={Multi-Platform LU-Decomposition Solution in OpenCL},

   author={Nasiri, E. and Rashid, R. and Verma, S.},



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The purpose of our project was to write a fast OpenCL LU-Decomposition (LUD) solution for the Intel/AMD CPU/GPU and Altera’s FPGA and record the amount of recoding required to optimize the algorithm for these platforms. LUD is the mathematical operation which factors a given matrix into the multiplication of a lower triangular and an upper triangular matrix. The complexity of many problems in different fields like biology, circuit design and discrete graphics boils down to this operation. Unfortunately the algorithm has a high computing complexity of O(n^3). Even with today’s high-end computing devices, a LUD operation could take hours to days to finish for large matrices. Therefore a cross platform LUD solution will be useful, both for ongoing research in this field and in the industry. We successfully met our objective of beating the runtime of the Blocked C++ algorithm run on CPU with our OpenCL CPU/GPU algorithms. We also developed the Test Framework that was used to evaluate and improve our algorithms further. We used the GNU Scientific library (GSL) to ensure our algorithms were producing the correct results. We were not able to optimize the OpenCL algorithm for FPGA due to problems with the DE4 board. We were informed by Altera that the board suffers from a large voltage drop when most of the device resources were utilized.
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