Parallel Sparse Matrix Vector Multiplication Using CSB

Parallel sparse Matrix-Vector and Matrix-Transpose-Vector multiplication using compressed sparse blocks Presentazione a cura di: Marco Cherubini, Andrea De Pirro, David Santucci, Andrea Tersigni, Luca Tracuzzi A. Buluc, J. T. Fineman, M. Frigo, J. R. Gilbert, C. E. Leiserson Calcolo Parallelo e Distribuito Anno Accademico 2009/2010 21 maggio 2010

Sommario ,[object Object],[object Object],[object Object],[object Object],[object Object]

Formati convenzionali: CSR ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Ax parallelo con CSR ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Formati convenzionali: CSC ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Il nuovo formato CSB ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Prod. Matrice-Vettore con CSB ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Prod. Matrice-Vettore con CSB Divisione in chunk -1

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Prod. Matrice-Vettore con CSB Split ricorsivo dei chunk y[ β..2β-1]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Prod. Matrice-Vettore con CSB Decomposizione Z-Morton in 4 quadranti

Analisi di complessità ,[object Object],[object Object],[object Object],[object Object]

Lemma 1 ,[object Object],[object Object]

Lemma 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Lemma 4 (continua) ,[object Object],[object Object],[object Object],[object Object]

Lemma 4 (continua) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Lemma 5 (continua) ,[object Object],[object Object],[object Object]

Lemma 5 (continua) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Teorema 6 ,[object Object],[object Object],[object Object],[object Object]

Teorema 6 (continua) ,[object Object],[object Object],[object Object],[object Object]

Corollario 7 e 8 ,[object Object],[object Object],[object Object],[object Object]

Lemma 9 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Corollario 10 ,[object Object],[object Object]

Sperimentazione ,[object Object],[object Object],[object Object],[object Object],[object Object]

Scelta del valore di β ,[object Object],[object Object]

Performance media di Ax e A T x ,[object Object],[object Object],[object Object],[object Object]

Risultati sperimentali (dim media) ,[object Object]

Risultati sperimentali (dim grande) ,[object Object]

CSR vs CSB ,[object Object],[object Object]

Parallel Sparse Matrix Vector Multiplication Using CSB

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