Duff Aygıtı Tabanlı Seyrek Matris-Vektör Çarpımı

Year 2020, Volume: 22 Issue: 65, 315 - 324, 15.05.2020

Barış Aktemur

https://doi.org/10.21205/deufmd.2020226501

Abstract

Seyrek matris-vektör çarpımı (SpMV) pek çok mühendislik probleminde ve bilimsel hesaplamada sıklıkla kullanılan bir işlemdir. SpMV’nin hızlandırılması geniş bir yelpazedeki uygulamaları olumlu etkiler. Bu makalede Duff aygıtı olarak bilinen döngü açılımının SpMV’nin başarımına etkisini irdeliyoruz. Önerdiğimiz Duff aygıtı tabanlı SpMV gerçeklemesi, en geçerli seyrek matris saklama formatı olan CSR formatının düşük maliyetli bir ön işlemesi sonrası kullanılabilmektedir. Gerçek problemlerde kullanılan matrislerden oluşan veri kümesi ile deneysel bir değerlendirme yaptık ve önemli derecede hızlanma kaydedilebileceğini gözlemledik.

Keywords

Seyrek matris-vektör çarpımı, yüksek başarımlı hesaplama, Duff aygıtı

Sparse Matrix-Vector Multiplication Based on Duff’s Device

Abstract

Sparse
matrix-vector multiplication (SpMV) is used frequently in several engineering
problems and scientific computation. Optimizing SpMV positively impacts a wide
range of applications. In this paper, we investigate the effect of a
loop-unrolling method known as Duff’s device on the performance of SpMV. The
Duff’s device-based SpMV implementation that we propose can be used after a
low-cost preprocessing of the CSR representation – the most common sparse
matrix storage format – of a matrix. We have evaluated the approach on a
dataset consisting of matrices from real-world problems, and observed that
substantial speedup can be achieved.

Keywords

Sparse matrix-vector multiplication, high performance computing, Duff’s device

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