Using graphics processors to accelerate the computation of the matrix inverse

We study the use of massively parallel architectures for computing a matrix inverse. Two different algorithms are reviewed, the traditional approach based on Gaussian elimination and the Gauss-Jordan elimination alternative, and several high performance implementations are presented and evaluated. The target architecture is a current general-purpose multi-core processor (CPU) connected to a graphics processor (GPU). Numerical experiments show the efficiency attained by the proposed implementations and how the computation of large-scale inverses, which only a few years ago would have required a distributed-memory cluster, take only a few minutes on a hybrid architecture formed by a multi-core CPU and a GPU

Unleashing GPU acceleration for symmetric band linear algebra kernels and model reduction

Linear algebra operations arise in a myriad of scientific and engineering applications and, therefore, their optimization is targeted by a significant number of high performance computing (HPC) research efforts. In particular, the matrix multiplication and the solution of linear systems are two key problems with efficient implementations (or kernels) for a variety of high per- formance parallel architectures. For these specific prob- lems, leveraging the structure of the associated matrices often leads to remarkable time and memory savings, as is the case, e.g., for symmetric band problems. In this work, we exploit the ample hardware concurrency of many-core graphics processors (GPUs) to accelerate the solution of symmetric positive definite band linear systems, introducing highly tuned versions of the corre- sponding LAPACK routines. The experimental results with the new GPU kernels reveal important reductions of the execution time when compared with tuned imple- mentations of the same operations provided in Intel’s MKL. In addition, we evaluate the performance of the GPU kernels when applied to the solution of model or- der reduction problems and the associated matrix equa- tions.Ernesto Dufrechou and Pablo Ezzatti acknowledge the support from Programa de Desarrollo de las Ciencias Básicas, and Agencia Nacional de Investigación e Innovacioón, Uruguay. Enrique S. Quintana-Ortí was sup- ported by project TIN2011-23283 of the Ministry of Science and Competitiveness (MINECO) and EU FEDER, and project P1-1B2013-20 of the Fundació Caixa Castelló-Bancaixa and UJI

Hyperspectral Unmixing on Multicore DSPs: Trading Off Performance for Energy

Wider coverage of observation missions will increase onboard power restrictions while, at the same time, pose higher demands from the perspective of processing time, thus asking for the exploration of novel high-performance and low-power processing architectures. In this paper, we analyze the acceleration of spectral unmixing, a key technique to process hyperspectral images, on multicore architectures. To meet onboard processing restrictions, we employ a low-power Digital Signal Processor (DSP), comparing processing time and energy consumption with those of a representative set of commodity architectures. We demonstrate that DSPs offer a fair balance between ease of programming, performance, and energy consumption, resulting in a highly appealing platform to meet the restrictions of current missions if onboard processing is required

Computación de alto desempeño para la reducción de modelos

El interés creciente por contar con modelos matemáticos que permitan realizar simulaciones, evaluar posibles diseños, estudiar impactos, etc. en distintos campos de ingeniería, pero a su vez la necesidad de que estos modelos sean tratables en un tiempo aceptable, dan origen al campo de trabajo de la reducción de modelos. Estas técnicas buscan, dado un modelo matemático, encontrar otro cuya dimensión sea considerablemente menor pero que presente un comportamiento similar al del modelo original. De esta forma, es posible utilizar el modelo reducido en posteriores simulaciones o estudios, disminuyendo así las necesidades de cómputo y tiempo de ejecución. Este trabajo presenta una pequeña introducción a la temática de reducción de modelos, con particular interés en los métodos basados en realizaciones balanceadas. Además, se estudia las técnicas de HPC y su aplicación para la aceleración de los métodos de reducción de modelos

The Impact of the Multi-core Revolution on Signal Processing

This paper analyzes the influence of new multi- core and many-core architectures on Signal Processing. The article covers both the architectural design and the programming models of current general-purpose multi-core processors and graphics processors (GPU), with the goal of identifying their possibilities and impact on signal processing applications

Application of Multi-core and GPU Architectures on Signal Processing: Case Studies

In this article part of the techniques and developments we are carrying out within the INCO2 group are reported. Results follow the interdisciplinary approach with which we tackle signal processing applications. Chosen case studies show different stages of development: We present algorithms already completed which are being used in practical applications as well as new ideas that may represent a starting point, and which are expected to deliver good results in a short and medium term

Polyphenol intake and mortality risk: a re-analysis of the PREDIMED trial

Background: Polyphenols may lower the risk of cardiovascular disease (CVD) and other chronic diseases due to their antioxidant and anti-inflammatory properties, as well as their beneficial effects on blood pressure, lipids and insulin resistance. However, no previous epidemiological studies have evaluated the relationship between the intake of total polyphenols intake and polyphenol subclasses with overall mortality. Our aim was to evaluate whether polyphenol intake is associated with all-cause mortality in subjects at high cardiovascular risk. Methods: We used data from the PREDIMED study, a 7,447-participant, parallel-group, randomized, multicenter, controlled five-year feeding trial aimed at assessing the effects of the Mediterranean Diet in primary prevention of cardiovascular disease. Polyphenol intake was calculated by matching food consumption data from repeated food frequency questionnaires (FFQ) with the Phenol-Explorer database on the polyphenol content of each reported food. Hazard ratios (HR) and 95% confidence intervals (CI) between polyphenol intake and mortality were estimated using time-dependent Cox proportional hazard models. Results: Over an average of 4.8 years of follow-up, we observed 327 deaths. After multivariate adjustment, we found a 37% relative reduction in all-cause mortality comparing the highest versus the lowest quintiles of total polyphenol intake (hazard ratio (HR) = 0.63; 95% CI 0.41 to 0.97; P for trend = 0.12). Among the polyphenol subclasses, stilbenes and lignans were significantly associated with reduced all-cause mortality (HR =0.48; 95% CI 0.25 to 0.91; P for trend = 0.04 and HR = 0.60; 95% CI 0.37 to 0.97; P for trend = 0.03, respectively), with no significant associations apparent in the rest (flavonoids or phenolic acids). Conclusions: Among high-risk subjects, those who reported a high polyphenol intake, especially of stilbenes and lignans, showed a reduced risk of overall mortality compared to those with lower intakes. These results may be useful to determine optimal polyphenol intake or specific food sources of polyphenols that may reduce the risk of all-cause mortality. Clinical trial registration ISRCTN35739639

Polyphenol intake and mortality risk: a re-analysis of the PREDIMED trial

Background: Polyphenols may lower the risk of cardiovascular disease (CVD) and other chronic diseases due to their antioxidant and anti-inflammatory properties, as well as their beneficial effects on blood pressure, lipids and insulin resistance. However, no previous epidemiological studies have evaluated the relationship between the intake of total polyphenols intake and polyphenol subclasses with overall mortality. Our aim was to evaluate whether polyphenol intake is associated with all-cause mortality in subjects at high cardiovascular risk. Methods: We used data from the PREDIMED study, a 7,447-participant, parallel-group, randomized, multicenter, controlled five-year feeding trial aimed at assessing the effects of the Mediterranean Diet in primary prevention of cardiovascular disease. Polyphenol intake was calculated by matching food consumption data from repeated food frequency questionnaires (FFQ) with the Phenol-Explorer database on the polyphenol content of each reported food. Hazard ratios (HR) and 95% confidence intervals (CI) between polyphenol intake and mortality were estimated using time-dependent Cox proportional hazard models. Results: Over an average of 4.8 years of follow-up, we observed 327 deaths. After multivariate adjustment, we found a 37% relative reduction in all-cause mortality comparing the highest versus the lowest quintiles of total polyphenol intake (hazard ratio (HR) = 0.63; 95% CI 0.41 to 0.97; P for trend = 0.12). Among the polyphenol subclasses, stilbenes and lignans were significantly associated with reduced all-cause mortality (HR =0.48; 95% CI 0.25 to 0.91; P for trend = 0.04 and HR = 0.60; 95% CI 0.37 to 0.97; P for trend = 0.03, respectively), with no significant associations apparent in the rest (flavonoids or phenolic acids). Conclusions: Among high-risk subjects, those who reported a high polyphenol intake, especially of stilbenes and lignans, showed a reduced risk of overall mortality compared to those with lower intakes. These results may be useful to determine optimal polyphenol intake or specific food sources of polyphenols that may reduce the risk of all-cause mortality

Dietary α‐Linolenic Acid, Marine ω‐3 Fatty Acids, and Mortality in a Population With High Fish Consumption: Findings From the PREvención con DIeta MEDiterránea (PREDIMED) Study

Background: Epidemiological evidence suggests a cardioprotective role of α‐linolenic acid (ALA), a plant‐derived ω‐3 fatty acid. It is unclear whether ALA is beneficial in a background of high marine ω‐3 fatty acids (long‐chain n‐3 polyunsaturated fatty acids) intake. In persons at high cardiovascular risk from Spain, a country in which fish consumption is customarily high, we investigated whether meeting the International Society for the Study of Fatty Acids and Lipids recommendation for dietary ALA (0.7% of total energy) at baseline was related to all‐cause and cardiovascular disease mortality. We also examined the effect of meeting the society's recommendation for long‐chain n‐3 polyunsaturated fatty acids (≥500 mg/day). Methods and Results: We longitudinally evaluated 7202 participants in the PREvención con DIeta MEDiterránea (PREDIMED) trial. Multivariable‐adjusted Cox regression models were fitted to estimate hazard ratios. ALA intake correlated to walnut consumption (r=0.94). During a 5.9‐y follow‐up, 431 deaths occurred (104 cardiovascular disease, 55 coronary heart disease, 32 sudden cardiac death, 25 stroke). The hazard ratios for meeting ALA recommendation (n=1615, 22.4%) were 0.72 (95% CI 0.56–0.92) for all‐cause mortality and 0.95 (95% CI 0.58–1.57) for fatal cardiovascular disease. The hazard ratios for meeting the recommendation for long‐chain n‐3 polyunsaturated fatty acids (n=5452, 75.7%) were 0.84 (95% CI 0.67–1.05) for all‐cause mortality, 0.61 (95% CI 0.39–0.96) for fatal cardiovascular disease, 0.54 (95% CI 0.29–0.99) for fatal coronary heart disease, and 0.49 (95% CI 0.22–1.01) for sudden cardiac death. The highest reduction in all‐cause mortality occurred in participants meeting both recommendations (hazard ratio 0.63 [95% CI 0.45–0.87]). Conclusions: In participants without prior cardiovascular disease and high fish consumption, dietary ALA, supplied mainly by walnuts and olive oil, relates inversely to all‐cause mortality, whereas protection from cardiac mortality is limited to fish‐derived long‐chain n‐3 polyunsaturated fatty acids. Clinical Trial Registration URL: http://www.Controlled-trials.com/. Unique identifier: ISRCTN35739639

Resolución de sistemas de ecuaciones lineales banda sobre procesadores actuales y arquitecturas multihebra. Aplicaciones en control.

Los sistemas de ecuaciones lineales o problemas de mínimos cuadrados aparecen en un amplio abanico de aplicaciones científico-técnicas. En ocasiones la matriz ligada al problema presenta una estructura banda o bien es una matriz dispersa que puede ser convertida en una matriz banda; en estos casos explotar la estructura banda de la matriz puede reducir considerablemente el coste computacional y de almacenamiento de resolución del problema. El objetivo principal de la presente tesis es el diseño, desarrollo y evaluación de una biblioteca de rutinas para la resolución de sistemas de ecuaciones lineales y problemas de mínimos cuadrados con estructura banda sobre arquitecturas de altas prestaciones. Tras evaluar la eficiencia y funcionalidad de las bibliotecas LAPACK y BLAS para operar con matrices banda, se han propuesto nuevas implementaciones más eficientes para las operaciones contempladas en estas bibliotecas, así como nuevas rutinas que implementan operaciones que amplian su funcionalidad, como por ejemplo una rutina para el cálculo de la factorización QR de una matriz banda. Los nuevos códigos se han aplicado a problemas de resolución de modelos, demostrando su eficiencia y escalabilidad