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Derivation of optimal input parameters for minimizing execution time of matrix-based computations on a GPU

PARALLEL COMPUTING 2014年第10期40卷 628-645页

作者： White, Andrew Lee, Soo-Young Auburn Univ Dept Elect & Comp Engn Auburn AL 36849 USA

As GPUs are continually being utilized as coprocessors, the demand for optimally utilizing them for various computations continues to grow. The goal of this work is to derive input parameters which yield the minimum execution time for matrix-based computations executing on a GPU. Input parameters are defined as the dimensions of the grid and blocks assigned for execution on the GPU. Since input parameters inadequately represent the executional behavior of the GPU, execution metrics are formulated as functions of the input parameters to represent the behavior. The execution metrics are architecture independent and are utilized to derive optimal input parameters, which are input parameters that yield the minimum execution time. Optimal input parameters are derived for the following matrix-based computations: matrix-vector multiplication (Mv), matrix-matrix multiplication (MM), and convolution. The derivation allows for selection of optimal input parameters without executing code. Results, for all matrix-based computations and sizes tested, show that utilizing the derived optimal input parameters often yields the minimum execution time, and, at worst, execution time within 13.6% of the minimum. (C) 2014 Elsevier B.V. All rights reserved.

关键词： GPU Execution time matrix-based computations Input parameters

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System reliability and sensitivity under statistical dependence by matrix-based system reliability method

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STRUCTURAL SAFETY 2009年第2期31卷 148-156页

作者： Song, Junho Kang, Won-Hee Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA

A matrix-based system reliability (MSR) method has been recently proposed to compute the probabilities of general system events efficiently by simple matrix operations. The proposed matrix-based framework describes both a system event and the likelihood of its component events by vectors that are obtained by efficient matrix-based procedures. The probability of the system event is computed by the inner product of the two vectors. Therefore, the method is uniformly applicable to any type of system events including series, parallel, cut-set and link-set systems. In the case when one has incomplete information on component probabilities and/or on the statistical dependence between components, the matrix-based framework enables us to obtain the narrowest bounds on the system probability by linear programming. Various importance measures and conditional probabilities are also efficiently estimated by the proposed method. This paper presents the MSR method and further develops it in terms of statistical dependence and parameter sensitivity of system reliability. First, a method is developed to use the MSR method for systems with statistically dependent components. The correlation coefficients between the basic random variables or the component safety margins are represented by a Dunnett-Sobel class correlation matrix to identify the source of the statistical dependence and to make use of the matrix-based procedure developed for independent components. Second, a new matrix-based procedure is proposed to calculate the sensitivities of system reliability with respect to parameters. This paper demonstrates the MSR method and these further developments by two numerical examples of structural systems. First, the system fragility of a bridge structure is computed based on the analytical fragility models of the bridge components and the correlation coefficients between the seismic demands at different components. In the second example, the MSR method is used to estimate the proba

关键词： Complex system Importance measure matrix-based computations Progressive failure Sensitivity System reliability

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