Automatic optimisation of parallel linear algebra routines in systems with variable load

In this paper, we analyse the design of polylibraries, where the programs call for routines from different libraries according to the characteristics of the problem and of the system used to solve it. An architecture for this type of library is proposed. Our aim is to develop a methodology which can be used in the design of parallel libraries. To evaluate the viability of the proposed method, the typical linear algebra libraries hierarchy has been considered. Experiments have been performed in different systems and with linear algebra routines from different levels of the hierarchy. The results confirm the design of polylibraries as a good technique for speeding up computations.

The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/watt ratio. High-level linear algebra operations are computationally intense, often requiring O(N3) operations and would seem a natural fit for the processing power of the GPU. Our work is on CULA, a GPU accelerated implementation of linear algebra routines. We present results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with applications like system solution and least squares. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally.

In this paper we propose a set of optimizations for the BLAS-3 routines of LASs library (Linear Algebra routines on OmpSs) and perform a detailed analysis of the impact of the proposed changes in terms of performance and execution time. OmpSs allows to use regions in the dependences of the tasks. This helps not only in the programming of the algorithmic optimizations, but also in the reduction of the execution time achieved by such optimizations. Different strategies are implemented in order to reduce the amount of tasks created (when there is enough parallelism) during the execution of BLAS-3 operations in the original LASs. Also a better IPC is obtained thanks to a better memory hierarchy exploitation. More specifically, we increase the performance, in particular on big matrices, about 12% for TRSM, and 17% for GEMM with respect to the original version of LASs, even using less cores in the case of GEMM/SYMM. Moreover, when LASs is compared to the OpenMP reference dense linear algebra library PLASMA, performance is increased up to 12.5% for GEMM/SYMM, while for TRSM/TRMM this value raises to 15%.

Analysis of Load Average and its Relationship to Program Run Time on Networks of Workstations

We introduce a new scheduling language, based on the formalism of Multi-Dimensional Homomorphisms (MDH). In contrast to existing scheduling languages, our MDH-based language is designed to systematically "de-compose" computations for the memory and core hierarchies of architectures, and "re-compose" the computed intermediate results back to the final result -- we say "(de/re)-composition" for short. We argue that our scheduling langauge is easy to use and yet expressive enough to express well-performing (de/re)-compositions of popular related approaches, e.g., the TVM compiler, for MDH-supported computations (such as linear algebra routines and stencil computations). Moreover, our language is designed as auto-tunable, i.e., any optimization decision can optionally be left to the auto-tuning engine of our system, and our system can automatically recommend schedules for the user, based on its auto-tuning capabilities. Also, by relying on the MDH approach, we can formally guarantee the correctness of optimizations expressed in our language, thereby further enhancing user experience. Our experiments on GPU and CPU confirm that we can express optimizations that cannot be expressed straightforwardly (or at all) in TVM's scheduling language, thereby achieving higher performance than TVM, and also vendor libraries provided by NVIDIA and Intel, for time-intensive computations used in real-world deep learning neural networks.

Markov random field (MRF) models are a popular tool for vision and image processing. Gaussian MRF models are particularly convenient to work with because they can be implemented using matrix and linear algebra routines. However, recent research has focused on on discrete-valued and non-convex MRF models because Gaussian models tend to over-smooth images and blur edges. In this paper, we show how to train a Gaussian conditional random field (GCRF) model that overcomes this weakness and can outperform the non-convex field of experts model on the task of denoising images. A key advantage of the GCRF model is that the parameters of the model can be optimized efficiently on relatively large images. The competitive performance of the GCRF model and the ease of optimizing its parameters make the GCRF model an attractive option for vision and image processing applications.

Auto-tuning is a popular approach to program optimization: it automatically finds good configurations of a program’s so-called tuning parameters whose values are crucial for achieving high performance for a particular parallel architecture and characteristics of input/output data. We present three new contributions of the Auto-Tuning Framework (ATF), which enable a key advantage in general-purpose auto-tuning : efficiently optimizing programs whose tuning parameters have interdependencies among them. We make the following contributions to the three main phases of general-purpose auto-tuning: (1) ATF generates the search space of interdependent tuning parameters with high performance by efficiently exploiting parameter constraints; (2) ATF stores such search spaces efficiently in memory, based on a novel chain-of-trees search space structure; (3) ATF explores these search spaces faster, by employing a multi-dimensional search strategy on its chain-of-trees search space representation. Our experiments demonstrate that, compared to the state-of-the-art, general-purpose auto-tuning frameworks, ATF substantially improves generating, storing, and exploring the search space of interdependent tuning parameters, thereby enabling an efficient overall auto-tuning process for important applications from popular domains, including stencil computations, linear algebra routines, quantum chemistry computations, and data mining algorithms.

The increase in performance of the last generations of graphics processors (GPUs) has made this class of hardware a coprocessing platform of remarkable success in certain types of operations. In this paper we evaluate the performance of linear algebra and image processing routines, both on classical and unified GPU architectures and traditional processors (CPUs). From this study, we gain insights on the properties that make an algorithm likely to deliver high performance on a GPU.KeywordsGraphics processors (GPUs)general purpose computing on GPUlinear algebraimage processinghigh performance

The literature shows that variable amplitude loading can be much more severe than constant amplitude loading in a fatigue damage context. However, the underlying physical explanations for this are still unknown. Therefore, this paper investigates if the local energy release rate at each intralaminar crack tip in a tension/tension fatigue loaded multidirectional laminate can be used to determine the crack growth rate of these cracks subjected to variable amplitude loading. The local energy release rate is investigated through a developed finite element model in which any number of cracks can be included to account for their interaction. The position of the cracks is determined based on previous experimental work. The experimental results from the previous work are compared to the numerical results in this work. At similar crack density levels the energy release rates increase in the variable amplitude tests compared to constant amplitude tests, but not enough to significantly impact the crack growth rate. It is concluded that less than 5% of the increased crack density rate and crack growth rate caused by variable amplitude block loading is due to increases in local energy release rate. The primary reason is more likely found on a microstructural level.

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known that modular techniques such as the Chinese remainder algorithm or the p -adic lifting allow very good practical performance, especially when word size arithmetic is used. Therefore, finite field arithmetic becomes an important core for efficient exact linear algebra libraries. In this article, we study high performance implementations of basic linear algebra routines over word size prime fields: especially matrix multiplication; our goal being to provide an exact alternate to the numerical BLAS library. We show that this is made possible by a careful combination of numerical computations and asymptotically faster algorithms. Our kernel has several symbolic linear algebra applications enabled by diverse matrix multiplication reductions: symbolic triangularization, system solving, determinant, and matrix inverse implementations are thus studied.

International audience

This work presents a novel control technique that combines concepts of Sliding Surface with a Linear Algebra methodology for controller design. The result is a controller with an improved robustness, while the chattering effect attributed to great uncertainties is avoided. A First Order Plus Dead Time (FOPDT) model of the process is used to develop a controller based on Linear Algebra and the concept of sliding surface is used to improve its performance under uncertainties. An interesting feature of this new controller is its ability to follow variable references without overshoot, a highly desirable characteristic for most process systems, and avoids the chattering problem. Results of the control of a CSTR and a laboratory batch reactor using this novel technique are presented. Simulated and experimental results demonstrate the outstanding performance of this new control algorithm.

Hybrid (exotic) mesons, which are important predictions of quantum chromodynamics (QCD), are states of quarks and antiquarks bound by excited gluons. First principle lattice study of such states would help us understand the role of "dynamical" color in low energy QCD and provide valuable information for experimental search for these new particles. In this paper, we apply both improved gluon and quark actions to the hybrid mesons, which might be much more efficient than the previous works in reducing lattice spacing error and finite volume effect. Quenched simulations were done at β=2.6 and on a ξ=3 anisotropic 123×36 lattice using our PC cluster. We obtain 2013±26±71 MeV for the mass of the 1-+ hybrid meson [Formula: see text] in the light quark sector, and 4369±37±99 MeV in the charm quark sector; the mass splitting between the 1-+ hybrid meson [Formula: see text] in the charm quark sector and the spin averaged S-wave charmonium mass is estimated to be 1302±37±99 MeV. As a byproduct, we obtain 1438±32±57 MeV for the mass of a P-wave 1++[Formula: see text] or [Formula: see text] meson and 1499±28±65 MeV for the mass of a P-wave 1++[Formula: see text] meson, which are comparable to their experimental value 1426 MeV for the f1(1420) meson. The first error is statistical, and the second one is systematical. The mixing of the hybrid meson with a four quark state is also discussed.

This paper introduces new linear algebra routines for LU, Cholesky and QR factorizations and for the solution of dense symmetric eigenproblems aimed at shared memory, cache-based, systems. Results obtained on a range of platforms have shown that the new routines are much more efficient and scalable than the corresponding LAPACK routines.KeywordsShared MemoryShared Memory SystemTridiagonal FormCompiler DirectiveSymmetric Tridiagonal MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The use of viscoelastic sheets in the hull of vessels built from GFRP has been raised in previous works as an option to protect the vessel from the destructive damage of slamming. The present work proposes its use in boats previously built by adhering to the outside of the hulls of the ships. Its installation process is shown, and this new type of installation is compared. Through impact tests with GFRP panels, it is shown that the viscoelastic material maintains its property of absorbing slamming energy and protecting the interior of the laminate. Fatigue tests on the order of 5 × 104 cycles are carried out to evaluate the impact force, the accelerations that deform the laminate and the virtual energy work imposed on the panel. This option shows that designers have a new option to protect the hull of already built boats.