MRRR-based Eigensolvers for Multi-core Processors and Supercomputers

The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to tridiagonal form. For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR or MR3 in short) - introduced in the late 1990s - is among the fastest methods. To compute k eigenpairs of a real n-by-n tridiagonal T, MRRR only requires O(kn) arithmetic operations; in contrast, all the other practical methods require O(k^2 n) or O(n^3) operations in the worst case. This thesis centers around the performance and accuracy of MRRR.Comment: PhD thesi

Adaptive heterogeneous parallelism for semi-empirical lattice dynamics in computational materials science.

With the variability in performance of the multitude of parallel environments available today, the conceptual overhead created by the need to anticipate runtime information to make design-time decisions has become overwhelming. Performance-critical applications and libraries carry implicit assumptions based on incidental metrics that are not portable to emerging computational platforms or even alternative contemporary architectures. Furthermore, the significance of runtime concerns such as makespan, energy efficiency and fault tolerance depends on the situational context. This thesis presents a case study in the application of both Mattsons prescriptive pattern-oriented approach and the more principled structured parallelism formalism to the computational simulation of inelastic neutron scattering spectra on hybrid CPU/GPU platforms. The original ad hoc implementation as well as new patternbased and structured implementations are evaluated for relative performance and scalability. Two new structural abstractions are introduced to facilitate adaptation by lazy optimisation and runtime feedback. A deferred-choice abstraction represents a unified space of alternative structural program variants, allowing static adaptation through model-specific exhaustive calibration with regards to the extrafunctional concerns of runtime, average instantaneous power and total energy usage. Instrumented queues serve as mechanism for structural composition and provide a representation of extrafunctional state that allows realisation of a market-based decentralised coordination heuristic for competitive resource allocation and the Lyapunov drift algorithm for cooperative scheduling

The CECAM Electronic Structure Library and the modular software development paradigm

First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, from the compiler up, with the exception of linear-algebra and message-passing libraries. This model has been quite successful for decades. The rapid progress in methodology, however, has resulted in an ever increasing complexity of those programs, which implies a growing amount of replication in coding and in the recurrent re-engineering needed to adapt to evolving hardware architecture. The Electronic Structure Library (\esl) was initiated by CECAM (European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure programs and redesign them as free, open-source libraries. They include ``heavy-duty'' ones with a high degree of parallelisation, and potential for adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by scientists when implementing new ideas. It is a community effort, undertaken by developers of various successful codes, now facing the challenges arising in the new model. This modular paradigm will improve overall coding efficiency and enable specialists (computer scientists or computational scientists) to use their skills more effectively. It will lead to a more sustainable and dynamic evolution of software as well as lower barriers to entry for new developers

Techniques in Active and Generic Software Libraries

Reusing code from software libraries can reduce the time and effort to construct software systems and also enable the development of larger systems. However, the benefits that come from the use of software libraries may not be realized due to limitations in the way that traditional software libraries are constructed. Libraries come equipped with application programming interfaces (API) that help enforce the correct use of the abstractions in those libraries. Writing new components and adapting existing ones to conform to library APIs may require substantial amounts of "glue" code that potentially affects software's efficiency, robustness, and ease-of-maintenance. If, as a result, the idea of reusing functionality from a software library is rejected, no benefits of reuse will be realized. This dissertation explores and develops techniques that support the construction of software libraries with abstraction layers that do not impede efficiency. In many situations, glue code can be expected to have very low (or zero) performance overhead. In particular, we describe advances in the design and development of active libraries - software libraries that take an active role in the compilation of the user's code. Common to the presented techniques is that they may "break" a library API (in a controlled manner) to adapt the functionality of the library for a particular use case. The concrete contributions of this dissertation are: a library API that supports iterator selection in the Standard Template Library, allowing generic algorithms to find the most suitable traversal through a container, allowing (in one case) a 30-fold improvement in performance; the development of techniques, idioms, and best practices for concepts and concept maps in C++, allowing the construction of algorithms for one domain entirely in terms of formalisms from a second domain; the construction of generic algorithms for algorithmic differentiation, implemented as an active library in Spad, language of the Open Axiom computer algebra system, allowing algorithmic differentiation to be applied to the appropriate mathematical object and not just concrete data-types; and the description of a static analysis framework to describe the generic programming notion of local specialization within Spad, allowing more sophisticated (value-based) control over algorithm selection and specialization in categories and domains. We will find that active libraries simultaneously increase the expressivity of the underlying language and the performance of software using those libraries

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Granularity in Large-Scale Parallel Functional Programming

This thesis demonstrates how to reduce the runtime of large non-strict functional programs using parallel evaluation. The parallelisation of several programs shows the importance of granularity, i.e. the computation costs of program expressions. The aspect of granularity is studied both on a practical level, by presenting and measuring runtime granularity improvement mechanisms, and at a more formal level, by devising a static granularity analysis. By parallelising several large functional programs this thesis demonstrates for the first time the advantages of combining lazy and parallel evaluation on a large scale: laziness aids modularity, while parallelism reduces runtime. One of the parallel programs is the Lolita system which, with more than 47,000 lines of code, is the largest existing parallel non-strict functional program. A new mechanism for parallel programming, evaluation strategies, to which this thesis contributes, is shown to be useful in this parallelisation. Evaluation strategies simplify parallel programming by separating algorithmic code from code specifying dynamic behaviour. For large programs the abstraction provided by functions is maintained by using a data-oriented style of parallelism, which defines parallelism over intermediate data structures rather than inside the functions. A highly parameterised simulator, GRANSIM, has been constructed collaboratively and is discussed in detail in this thesis. GRANSIM is a tool for architecture-independent parallelisation and a testbed for implementing runtime-system features of the parallel graph reduction model. By providing an idealised as well as an accurate model of the underlying parallel machine, GRANSIM has proven to be an essential part of an integrated parallel software engineering environment. Several parallel runtime- system features, such as granularity improvement mechanisms, have been tested via GRANSIM. It is publicly available and in active use at several universities worldwide. In order to provide granularity information this thesis presents an inference-based static granularity analysis. This analysis combines two existing analyses, one for cost and one for size information. It determines an upper bound for the computation costs of evaluating an expression in a simple strict higher-order language. By exposing recurrences during cost reconstruction and using a library of recurrences and their closed forms, it is possible to infer the costs for some recursive functions. The possible performance improvements are assessed by measuring the parallel performance of a hand-analysed and annotated program

A comparison of statistical machine learning methods in heartbeat detection and classification

In health care, patients with heart problems require quick responsiveness in a clinical setting or in the operating theatre. Towards that end, automated classification of heartbeats is vital as some heartbeat irregularities are time consuming to detect. Therefore, analysis of electro-cardiogram (ECG) signals is an active area of research. The methods proposed in the literature depend on the structure of a heartbeat cycle. In this paper, we use interval and amplitude based features together with a few samples from the ECG signal as a feature vector. We studied a variety of classification algorithms focused especially on a type of arrhythmia known as the ventricular ectopic fibrillation (VEB). We compare the performance of the classifiers against algorithms proposed in the literature and make recommendations regarding features, sampling rate, and choice of the classifier to apply in a real-time clinical setting. The extensive study is based on the MIT-BIH arrhythmia database. Our main contribution is the evaluation of existing classifiers over a range sampling rates, recommendation of a detection methodology to employ in a practical setting, and extend the notion of a mixture of experts to a larger class of algorithms