Towards an accurate performance modeling of parallel sparse factorization

Grigori, Laura; Li, Xiaoye S.

doi:10.1007/s00200-007-0036-y

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…In a subsequent paper, Li (2008) considers the performance of these methods when each node of the computer consists of a tightly coupled multicore processor. Grigori and Li (2007) present an accurate simulation-based performance model for SuperLU DIST, which includes the speed of the processors, memory systems, and the latency and bandwidth of the interconnect.…”

Section: Supernodal Lu Factorizationmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

174

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Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1 This informal yet practical definition captures the essence of the goal of direct methods for solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.

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Section: Supernodal Lu Factorizationmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

174

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“…Given these difficulties, many authors have explored instead empirical performance modeling approaches . These approaches consist in automatically discovering salient application characteristics using one or a combination of several techniques (e.g., instrumented application execution to obtain trace data , analysis of application trace data and of known benchmark trace data to infer application performance , analysis of application simulation driven by trace data , and simulation driven by static code analysis ). These automatically derived empirical models explicitly capture important characteristics of the implementation of the target application (e.g., memory accesses, branch behavior, and floating point unit usage).…”

Section: Related Workmentioning

confidence: 99%

Selecting linear algebra kernel composition using response time prediction

2014

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SUMMARYNumerical linear algebra libraries provide many kernels that can be composed to perform complex computations. For a given computation, there is typically a large number of functionally equivalent kernel compositions. Some of these compositions achieve better response times than others for particular data and when executed on a particular computer architecture. Previous research provides methods to enumerate (a subset of) these kernel compositions. In this work, we study the problem of determining the composition that yields the lowest response time. Our approach is based on a response time prediction for each candidate combination. While this prediction could in principle be obtained using analytical and/or empirical performance models, developing accurate such models is known to be challenging. Instead, we define a feature space that captures salient properties of kernel combinations and predict response time using supervised machine learning. We experiment with a standard set of machine learning algorithms and identify an effective algorithm for our kernel composition selection problem. Using this algorithm, our approach widely outperforms the strategy that would consist in always using the simplest kernel composition and is often close to the fastest kernel compositions among those evaluated. We quantify the potential benefit of our approach if it were to be implemented as part of an interactive computational tool. We find that although the potential benefit is substantial, a limiting factor is the kernel composition enumeration overhead.

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