Block pivoting implementation of a symmetric Toeplitz solver

Toeplitz matrices are characterized by a special structure that can be exploited in order to obtain fast linear system solvers. These solvers are difficult to parallelize due to their low computational cost and their closely coupled data operations. We propose to transform the Toeplitz system matrix into a Cauchy-like matrix since the latter can be divided into two independent matrices of half the size of the system matrix and each one of these smaller arising matrices can be factorized efficiently in multicore computers. We use OpenMP and store data in memory by blocks in consecutive positions yielding a simple and efficient algorithm. In addition, by exploiting the fact that diagonal pivoting does not destroy the special structure of Cauchy-like matrices, we introduce a local diagonal pivoting technique which improves the accuracy of the solution and the stability of the algorithm.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion (Project TIN2008-06570-C04-02 and TEC2009-13741), Vicerrectorado de Investigacion de la Universidad Politecnica de Valencia through PAID-05-10 (ref. 2705), and Generalitat Valenciana through project PROMETEO/2009/2013.Alonso-Jordá, P.; Dolz Zaragozá, MF.; Vidal Maciá, AM. (2014). Block pivoting implementation of a symmetric Toeplitz solver. Journal of Parallel and Distributed Computing. 74(5):2392-2399. https://doi.org/10.1016/j.jpdc.2014.02.003S2392239974

Bibliografía

Israel, Jerold H./Kamisar, Yale/Lafave, Wayne R./King, Nancy J., Proceso penal y Constitución de los Estados Unidos de Norteamérica, Casos destacados del Tribunal Supremo y Texto Introductorio, Gómez Colomer, Juan-Luis, et al. (Trad.) Valencia, Tirant Lo Blanch, 2012

Problematica del drenaje de aguas pluviales en zonas urbanas y del estudio hidraulico de las redes de colectores

Se analiza la problemática del drenaje de aguas pluviales en zonas urbanas, en particular en áreas de rápido y reciente desarrollo urbano como es el caso del litoral mediterráneo español. Se estudia la repercusión que tiene sobre el drenaje un proceso urbanizador no respetuoso con la hidrología de las cuencas naturales preexistentes. Asimismo se analiza de una forma conceptual la problemática que presenta la modelación numérica de los diferentes procesos involucrados en el drenaje urbano, especialmente el comportamiento hidráulico de las redes de colectores

Comparison of Clang Abstract Syntax Trees using string kernels

Abstract Syntax Trees (ASTs) are intermediate representations widely used by compiler frameworks. One of their strengths is that they can be used to determine the similarity among a collection of programs. In this paper we propose a novel comparison method that converts ASTs into weighted strings in order to get similarity matrices and quantify the level of correlation among codes. To evaluate the approach, we leveraged the corresponding strings derived from the Clang ASTs of a set of 100 source code examples written in C. Our kernel and two other string kernels from the literature were used to obtain similarity matrices among those examples. Next, we used Hierarchical Clustering to visualize the results. Our solution was able to identify different clusters conformed by examples that shared similar semantics. We demonstrated that the proposed strategy can be promisingly applied to similarity problems involving trees or strings

A similarity study of I/O traces via string kernels

Understanding I/O for data-intense applications is the foundation for the optimization of these applications. The classification of the applications according to the expressed I/O access pattern eases the analysis. An access pattern can be seen as fingerprint of an application. In this paper, we address the classification of traces. Firstly, we convert them first into a weighted string representation. Due to the fact that string objects can be easily compared using kernel methods, we explore their use for fingerprinting I/O patterns. To improve accuracy, we propose a novel string kernel function called kast2 spectrum kernel. The similarity matrices, obtained after applying the mentioned kernel over a set of examples from a real application, were analyzed using kernel principal component analysis and hierarchical clustering. The evaluation showed that two out of four I/O access pattern groups were completely identified, while the other two groups conformed a single cluster due to the intrinsic similarity of their members. The proposed strategy can be promisingly applied to other similarity problems involving tree-like structured data

A Pipeline for the QR Update in Digital Signal Processing

[EN] The input and output signals of a digital signal processing system can often be represented by a rectangular matrix as it is the case of the beamformer algorithm, a very useful particular algorithm that allows extraction of the original input signal once it is cleaned from noise and room reverberation. We use a version of this algorithm in which the system matrix must be factorized to solve a least squares problem. The matrix changes periodically according to the input signal sampled; therefore, the factorization needs to be recalculated as fast as possible. In this paper, we propose to use parallelism through a pipeline pattern. With our pipeline, some partial computations are advanced so that the final time required to update the factorization is highly reducedThis work was supported by the Spanish Ministry of Economy and Competitiveness under MINECO and FEDER projects TIN2014-53495-R and TEC2015-67387-C4-1-R.Dolz, MF.; Alventosa, FJ.; Alonso-Jordá, P.; Vidal Maciá, AM. (2019). A Pipeline for the QR Update in Digital Signal Processing. Computational and Mathematical Methods. 1:1-13. https://doi.org/10.1002/cmm4.1022S113

Convolutional neural nets for estimating the run time and energy consumption of the sparse matrix-vector product

Modeling the performance and energy consumption of the sparse matrix-vector product (SpMV) is essential to perform off-line analysis and, for example, choose a target computer architecture that delivers the best performance-energy consumption ratio. However, this task is especially complex given the memory-bounded nature and irregular memory accesses of the SpMV, mainly dictated by the input sparse matrix. In this paper, we propose a Machine Learning (ML)-driven approach that leverages Convolutional Neural Networks (CNNs) to provide accurate estimations of the performance and energy consumption of the SpMV kernel. The proposed CNN-based models use a blockwise approach to make the CNN architecture independent of the matrix size. These models are trained to estimate execution time as well as total, package, and DRAM energy consumption at different processor frequencies. The experimental results reveal that the overall relative error ranges between 0.5% and 14%, while at matrix level is not superior to 10%. To demonstrate the applicability and accuracy of the SpMV CNN-based models, this study is complemented with an ad-hoc time-energy model for the PageRank algorithm, a popular algorithm for web information retrieval used by search engines, which internally realizes the SpMV kernel