Vicente Blanco Pérez

Modeling and Improving Locality for Irregular Problems: Sparse Matrix-Vector Product on Cache Memories as a Cache Study

In this paper we introduce a model for representing and improving the locality of sparse matrices for irregular problems. We focus our attention on the behavior of iterative methods for the solution of sparse linear systems with irregular patterns. In particular the product of a sparse matrix by a dense vector (SpM×V) is closely examined, as this is one of the basic kernels in such codes. As a representative level of the memory hierarchy, we consider the cache memory. In our model, locality is measured taking into account pairs of rows or columns of sparse matrices. In order to evaluate this locality four functions based on two parameters called entry matches and cache line matches are introduced. Using an analogy of this problem to the Traveling Salesman Problem we have applied two algorithms in order to solve it; one based on the construction of minimum spanning trees and the other on the nearest-neighbor heuristic. These techniques were tested over a set of sparse matrices. The results were assesed through the measurement of cache misse on a standard cache memory.

Principal Component Analysis on Vector Computers

Principal component analysis is a classical multivariate technique used as a basic tool in the field of image processing. Due to the iterative character and the high computational cost of these algorithms over conventional computers, they are good candidates for pipelined processing. In this work we analyse these algorithms from the viewpoint of vectorization and present an efficient implementation on the Fujitsu VP-2400/10. We systematically applied different code transformations to the algorithm making use of the vectorial capabilities of the system. In particular we have tested a number of vectorization techniques that optimize the reuse of the vector registers, exploit all levels of the memory hierarchy, and utilize the pipelined units in parallel (concurrency between them). We have considered images of 32×32 pixels and have divided the algorithm into three different stages. The speedups obtained for the native vectorizing compiler were 1.3, 1.3 and 7.9 for the different stages. These speedups were multiplied by factors of 5, 50 and 55 respectively, after applying our code transformations. The best improvement was achieved in the third stage of the algorithm, which is the most time consumming.

Performance Modeling of MPI Applications Using Model Selection Techniques

A new method for obtaining models of the performance of parallel applications based on statistical analysis is presented in this paper. This method is based on the Akaike’s information criterion (AIC) that provides an objective mechanism to rank different models by means of an experimental data fit. The input of the modeling process is a set of variables and parameters that can a priori influence the performance of the application. This set can be provided by the user. Using this information, the method automatically generates a set of candidate models. These models are fit to the experimental data and the AIC score of each model is calculated. The model with the best AIC score is selected as the best model. Also, using the AIC scores of all candidate models, useful statistical information is provided to help the user to evaluate the quality of the selected model, as well as indications of how to interactively improve this modeling process. As a first case of study, statistical models obtained for different implementations of the broadcast collective communication in Open MPI are shown. These models are very accurate, exceeding its adjustment to theoretical approaches based on the LogGP model. Finally, the NAS Parallel Benchmark is also characterized using this new method with good results in terms of accuracy.