Operator Overloading Research Articles

PyMDO

We present pyMDO, an object-oriented framework that facilitates the usage and development of algorithms for multidisciplinary optimization (MDO). The resulting implementation of the MDO methods is efficient and portable. The main advantage of the proposed framework is that it is flexible, with a strong emphasis on object-oriented classes and operator overloading, and it is therefore useful for the rapid development and evaluation of new MDO methods. The top layer interface is programmed in Python and it allows for the layers below the interface to be programmed in C, C++, Fortran, and other languages. We describe an implementation of pyMDO and demonstrate that we can take advantage of object-oriented programming to obtain intuitive, easy-to-read, and easy-to-develop codes that are at the same time efficient. This allows developers to focus on the new algorithms they are developing and testing, rather than on implementation details. Examples demonstrate the user interface and the corresponding results show that the various MDO methods yield the correct solutions.

Optimal Control of Fluid Forces Using Second Order Automatic Differentiation

In resent years, the progress of computer and numerical computation technique allows not only complex numerical simulations but also resolution of the inverse analysis including optimal control problem. It is important to pursue high quality of the gradient computation in the inverse problem. Sometimes, it is called as the sensitivity analysis. In case of the inverse analysis, the minimization technique of a function is often used. Only first order variation of function is usually applied. But in order to minimize the functional exactly, it is also necessary to introduce the second order variation of the function. However, pursing variation is diffcult to formulate and to program. There is a method of computation to pursue the variation of functional automatically, i.e., Automatic Differentiation (AD). The AD is implemented with C++ programs using operator overloading technique. It computes the partial derivatives according to the differentiation rule of a composite function whenever basic operation is performed. Using AD, the first order variation can be obtained. Ordinary AD is called First Order Automatic Differentiation (FOAD). In addition, AD can be extended to the Second Order Automatic Differentiation (SOAD) to obtain second order variation. In this study, both FOAD and SOAD are applied to the optimal control problem of fluid forces. The control problem uses the minimization technique of the function. The purpose of this study is to present the application of SOAD in control problem. The Sakawa-Shindo Method using FOAD and the Steepest descent method using SOAD are compared as the minimization technique. The automatic differentiation is proposed as a new approach to the sensitivity analysis of the optimal control problem.

Fast higher-order derivative tensors with Rapsodia

A number of practical problems in physics can be solved by using accurate higher-order derivatives. Such derivatives can be obtained with automatic differentiation. However, one has to be concerned with the complexity of computing higher-order derivative tensors even for a modest order and number of independents. Initial experiments using univariate Taylor polynomials with interpolation and operator overloading with unrolled loops showed better runtimes than using other automatic differentiation tools. Motivated by these results, we developed the Rapsodia code generator that produces Fortran and C++libraries for the most common intrinsics. Here we explain the algorithmic approach, implementation, and present test results on a select set of applications. Further details on the Rapsodia tool, and an example for user extensions are given in the Appendix.

McCormick-Based Relaxations of Algorithms

Theory and implementation for the global optimization of a wide class of algorithms is presented via convex/affine relaxations. The basis for the proposed relaxations is the systematic construction of subgradients for the convex relaxations of factorable functions by McCormick [Math. Prog., 10 (1976), pp. 147–175]. Similar to the convex relaxation, the subgradient propagation relies on the recursive application of a few rules, namely, the calculation of subgradients for addition, multiplication, and composition operations. Subgradients at interior points can be calculated for any factorable function for which a McCormick relaxation exists, provided that subgradients are known for the relaxations of the univariate intrinsic functions. For boundary points, additional assumptions are necessary. An automated implementation based on operator overloading is presented, and the calculation of bounds based on affine relaxation is demonstrated for illustrative examples. Two numerical examples for the global optimization of algorithms are presented. In both examples a parameter estimation problem with embedded differential equations is considered. The solution of the differential equations is approximated by algorithms with a fixed number of iterations.

Efficient fair algorithms for message communication

A computer network serves distributed applications by communicating messages between their remote ends. Many such applications desire minimal delay for their messages. Beside this efficiency objective, allocation of the network capacity is also subject to the fairness constraint of not shutting off communication for any individual message. Processor Sharing (PS) is a de facto standard of fairness but provides significantly higher average delay than Shortest Remaining Processing Time (SRPT), which is an optimally efficient but unfair algorithm. In this paper, we explore efficient fair algorithms for message communication where fairness means that no message is delivered later than under PS. First, we introduce a slack system to characterize fair algorithms completely and develop efficient fair algorithms called Pessimistic Fair Sojourn Protocol (PFSP), Optimistic Fair Sojourn Protocol (OFSP), and Shortest Fair Sojourn (SFS). Then, we prove that a fair online algorithm does not assure minimal average delay attainable with fairness. Our analysis also reveals lower bounds on worst-case inefficiency of fair algorithms. We conduct extensive simulations for various distributions of message sizes and arrival times. During either temporary overload or steady-state operation, SFS and other newly proposed fair algorithms support SRPT-like efficiency and consistently provide much smaller average delay than PS.

Fast SIMDized Kalman filter based track fit

Modern high energy physics experiments have to process terabytes of input data produced in particle collisions. The core of many data reconstruction algorithms in high energy physics is the Kalman filter. Therefore, the speed of Kalman filter based algorithms is of crucial importance in on-line data processing. This is especially true for the combinatorial track finding stage where the Kalman filter based track fit is used very intensively. Therefore, developing fast reconstruction algorithms, which use maximum available power of processors, is important, in particular for the initial selection of events which carry signals of interesting physics. One of such powerful feature supported by almost all up-to-date PC processors is a SIMD instruction set, which allows packing several data items in one register and to operate on all of them, thus achieving more operations per clock cycle. The novel Cell processor extends the parallelization further by combining a general-purpose PowerPC processor core with eight streamlined coprocessing elements which greatly accelerate vector processing applications. In the investigation described here, after a significant memory optimization and a comprehensive numerical analysis, the Kalman filter based track fitting algorithm of the CBM experiment has been vectorized using inline operator overloading. Thus the algorithm continues to be flexible with respect to any CPU family used for data reconstruction. Because of all these changes the SIMDized Kalman filter based track fitting algorithm takes 1 μs per track that is 10000 times faster than the initial version. Porting the algorithm to a Cell Blade computer gives another factor of 10 of the speedup. Finally, we compare performance of the tracking algorithm running on three different CPU architectures: Intel Xeon, AMD Opteron and Cell Broadband Engine.

Parallel Languages and Compilers: Perspective From the Titanium Experience

We describe the rationale behind the design of key features of Titanium—an explicitly parallel dialect of Java for high-performance scientific programming—and our experiences in building applications with the language. Specifically, we address Titanium's partitioned global address space model, single program multiple data parallelism support, multi-dimensional arrays and array-index calculus, memory management, immutable classes (class-like types that are value types rather than reference types), operator overloading, and generic programming. We provide an overview of the Titanium compiler implementation, covering various parallel analyses and optimizations, Titanium runtime technology and the GASNet network communication layer. We summarize results and lessons learned from implementing the NAS parallel benchmarks, elliptic and hyperbolic solvers using adaptive mesh refinement, and several applications of the immersed boundary method.

'pMATLAB Parallel MATLAB Library'

MATLAB® has emerged as one of the languages most commonly used by scientists and engineers for technical computing, with approximately one million users worldwide. The primary benefits of MATLAB are reduced code development time via high levels of abstractions (e.g. first class multi-dimensional arrays and thousands of built in functions), interpretive, interactive programming, and powerful mathematical graphics. The compute intensive nature of technical computing means that many MATLAB users have codes that can significantly benefit from the increased performance offered by parallel computing. pMatlab provides this capability by implementing parallel global array semantics using standard operator overloading techniques. The core data structure in pMatlab is a distributed numerical array whose distribution onto multiple processors is specified with a “map” construct. Communication operations between distributed arrays are abstracted away from the user and pMatlab transparently supports redistribution between any block-cyclic-overlapped distributions up to four dimensions. pMatlab is built on top of the MatlabMPI communication library and runs on any combination of heterogeneous systems that support MATLAB, which includes Windows, Linux, MacOS X, and SunOS. This paper describes the overall design and architecture of the pMatlab implementation. Performance is validated by implementing the HPC Challenge benchmark suite and comparing pMatlab performance with the equivalent C+MPI codes. These results indicate that pMatlab can often achieve comparable performance to C+MPI, usually at one tenth the code size. Finally, we present implementation data collected from a sample of real pMatlab applications drawn from the approximately one hundred users at MIT Lincoln Laboratory. These data indicate that users are typically able to go from a serial code to an efficient pMatlab code in about 3 hours while changing less than 1% of their code.

The Design to Downsize a Conduction-Cooled LTS Pulse Coil for UPS-SMES as Protection From Momentary Voltage Drops

The stability margin of a conduction-cooled LTS pulse coil with stored energy of 1 MJ, which is used for UPS-SMES as protection from momentary voltage drops, is estimated from thermal analyses using the two-dimensional finite elementary method. How much the 1 MJ coil is able to be downsized is discussed. The winding conductor of this coil is a NbTi/Cu Rutherford cable, which is extruded with aluminum. Dyneema FRP and Litz wires are used as the spacers of this coil. In the design of this 1 MJ coil, the effects of spacers were neglected. In order to estimate the stability margin, thermal analyses was carried out by taking into account the thermal effects of spacers, for the coil during overload operation. And it was checked whether the maximum temperature The results showed that the 1 MJ coil has a large stability margin of 8 times the rated ac loss. In addition, new coils with a stability margin of about two times were designed. Possibilities for reducing the size and the cost of a 1 MJ LTS pulse coil are also shown.

The Hamel Representation: A Diagonalized Poincaré Form

The Poincaré equations, also known as Lagrange’s equations in quasicoordinates, are revisited with special attention focused on a diagonal form. The diagonal form stems from a special choice of generalized speeds that were first introduced by Hamel (Hamel, G., 1967, Theorctische Mechanik, Springer-Verlag, Berlin, Secs. 235 and 236) nearly a century ago. The form has been largely ignored because the generalized speeds create so-called Hamel coefficients that appear in the governing equations and are based on the partial derivative of a mass-matrix factorization. Consequently, closed-form expressions for the Hamel coefficients can be difficult to obtain. In this paper, a newly developed operator overloading technique is used within a simulation code to automatically generate the Hamel coefficients through an exact partial differentiation together with a numerical evaluation. This allows the diagonal form of Poincaré’s equations to be numerically integrated for system simulation. The diagonal form and the techniques used to generate the Hamel coefficients are applicable to general systems, including systems with closed kinematic chains. Because of Hamel’s original influence, these special Poincaré equations are called the Hamel representations and their usefulness in dynamic simulation and control is investigated.

Recruitment of Compensatory Pathways to Sustain Oxidative Flux With Reduced Carnitine Palmitoyltransferase I Activity Characterizes Inefficiency in Energy Metabolism in Hypertrophied Hearts

Transport rates of long-chain free fatty acids into mitochondria via carnitine palmitoyltransferase I relative to overall oxidative rates in hypertrophied hearts remain poorly understood. Furthermore, the extent of glucose oxidation, despite increased glycolysis in hypertrophy, remains controversial. The present study explores potential compensatory mechanisms to sustain tricarboxylic acid cycle flux that resolve the apparent discrepancy of reduced fatty acid oxidation without increased glucose oxidation through pyruvate dehydrogenase complex in the energy-poor, hypertrophied heart. We studied flux through the oxidative metabolism of intact adult rat hearts subjected to 10 weeks of pressure overload (hypertrophied; n=9) or sham operation (sham; n=8) using dynamic 13C-nuclear magnetic resonance. Isolated hearts were perfused with [2,4,6,8,10,12,14,16-(13)C8] palmitate (0.4 mmol/L) plus glucose (5 mmol/L) in a 14.1-T nuclear magnetic resonance magnet. At similar tricarboxylic acid cycle rates, flux through carnitine palmitoyltransferase I was 23% lower in hypertrophied (P<0.04) compared with sham hearts and corresponded to a shift toward increased expression of the L-carnitine palmitoyltransferase I isoform. Glucose oxidation via pyruvate dehydrogenase complex did not compensate for reduced palmitate oxidation rates. However, hypertrophied rats displayed an 83% increase in anaplerotic flux into the tricarboxylic acid cycle (P<0.03) that was supported by glycolytic pyruvate, coincident with increased mRNA transcript levels for malic enzyme. In cardiac hypertrophy, fatty acid oxidation rates are reduced, whereas compensatory increases in anaplerosis maintain tricarboxylic acid cycle flux and account for a greater portion of glucose oxidation than previously recognized. The shift away from acetyl coenzyme A production toward carbon influx via anaplerosis bypasses energy, yielding reactions contributing to a less energy-efficient heart.

Off-design analysis of SOFC hybrid system

This paper sets out the results of mathematical modeling and numerical simulations of the off-design (part-load) operation of the solid oxide fuel cell hybrid system (SOFC-HS). The governing equations of SOFC-HS modeling are given. An adequate simulator of the SOFC stack was made and described. The performance of the SOFC-HS with part- and over-load operation is shown, and adequate maps are given and described. The ranges of possible system operation conditions are determined.

An object-oriented framework for the development of scalable parallel multilevel preconditioners

We present the design of a high-performance object-oriented framework that enables the rapid development and usage of efficient, scalable, and portable implementations of multilevel preconditioners for distributed sparse real matrices, in both serial and (massively) parallel environments. The main feature of the proposed framework is the use of several programming paradigms for the different implementation layers, with a strong emphasis on object-oriented classes and operator overloading for the top layer, and optimized FORTRAN and C code for the layers underneath. We describe an implementation of the proposed framework that is based on the ML library, the algebraic multilevel preconditioning package of Trilinos, which supports state-of-the-art parallel smoothed aggregation methods, and can be used to define general algebraic and geometric multilevel and multigrid preconditioners and solvers. The article demonstrates that we can take advantage of object-oriented programming and operator overloading to obtain intuitive, easy-to-read, and easy-to-develop codes that are at the same time efficient and scalable. Several numerical experiments obtained on serial and parallel computers show that the overhead required by the object-oriented layer is very modest, therefore allowing developers to focus on the new algorithms they are developing and testing, rather than on implementation details.

An efficient overloaded implementation of forward mode automatic differentiation in MATLAB

The Mad package described here facilitates the evaluation of first derivatives of multidimensional functions that are defined by computer codes written in MATLAB. The underlying algorithm is the well-known forward mode of automatic differentiation implemented via operator overloading on variables of the class fmad. The main distinguishing feature of this MATLAB implementation is the separation of the linear combination of derivative vectors into a separate derivative vector class derivvec. This allows for the straightforward performance optimization of the overall package. Additionally, by internally using a matrix (two-dimensional) representation of arbitrary dimension directional derivatives, we may utilize MATLAB's sparse matrix class to propagate sparse directional derivatives for MATLAB code which uses arbitrary dimension arrays. On several examples, the package is shown to be more efficient than Verma's ADMAT package [Verma 1998a].

TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95

We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula. TaylUR makes heavy use of operator overloading and other Fortran 95 features such as elemental functions. Program summary Program title: TaylUR Catalogue identifier:ADXR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Programming language:Fortran 95 Computer:Any computer with a conforming Fortran 95 compiler Operating system:Any system with a conforming Fortran 95 compiler No. of lines in distributed program, including test data, etc.:6286 No. of bytes in distributed program, including test data, etc:14 994 Distribution format:tar.gz Nature of problem:Problems that require potentially high orders of derivatives with respect to some variables, such as e.g. expansions of Feynman diagrams in particle masses in perturbative Quantum Field Theory, and which cannot be treated using existing Fortran modules for automatic differentiation [C.W. Straka, ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables, Comput. Phys. Comm. 168 (2005) 123–139, arXiv:cs.MS/0503014; S. Stamatiadis, R. Prosmiti, S.C. Farantos, auto_deriv: Tool for automatic differentiation of a FORTRAN code, Comput. Phys. Comm. 127 (2000) 343–355]. Solution method:Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula. Restrictions:Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders. Unusual features:No mixed higher-order derivatives are computed. The complex conjugation operation assumes all independent variables to be real. Running time:The running time of TaylUR operations depends linearly on the number of variables. Its dependence on the Taylor expansion order varies from linear (for linear operations) through quadratic (for multiplication) to exponential (for elementary function calls).

Formal Constraints on Memory Management for Composite Overloaded Operations

The memory management rules for abstract data type calculus presented by Rouson, Morris &amp; Xu [15] are recast as formal statements in the Object Constraint Language (OCL) and applied to the design of a thermal energy equation solver. One set of constraints eliminates memory leaks observed in composite overloaded expressions with three current Fortran 95/2003 compilers. A second set of constraints ensures economical memory recycling. The constraints are preconditions, postconditions and invariants on overloaded operators and the objects they receive and return. It is demonstrated that systematic run‐time assertion checking inspired by the formal constraints facilitated the pinpointing of an exceptionally hard‐to‐reproduce compiler bug. It is further demonstrated that the interplay between OCL′s modeling capabilities and Fortran′s programming capabilities led to a conceptual breakthrough that greatly improved the readability of our code by facilitating operator overloading. The advantages and disadvantages of our memory management rules are discussed in light of other published solutions [11,19]. Finally, it is demonstrated that the run‐time assertion checking has a negligible impact on performance.

More dynamic imperative languages

We pursue entirely dynamic constructs for imperative object-oriented programming languages by shifting responsibilities from compile-time handling to runtime management. This accounts to the full range of language elements, going beyond statically defined: types, classes, inheritance, and function / operator overloading. The accommodation of the dynamic features in a language named Delta is discussed whose design emphasizes a minimal set of special-purpose language constructs. We demonstrate the way polymorphic higher-order functions, and polymorphic software patterns are directly programmable in a dynamic language context.

Validation of Predictive Workload Component of the Multimodal Information Design Support (Mids) System

Operators in military C4ISR environments are required to rapidly assess and respond to critical events accurately while monitoring ongoing operations. In order to assist in designing complex display systems to support C4ISR operators, it is critical to understand when and why information displayed exceeds human capacity. Common metrics for evaluating operator overload are subjective report, which rely on self-reporting techniques (e.g., NASA/TLX, SART). A new design tool, the Multimodal Information Design Support (MIDS) system, predicts times of operator overload and offers multimodal design guidelines to streamline cognitive processing, thus alleviating times of operator workload and optimizing situation awareness. This paper empirically validates MIDS” predictive power in determining situations which may cause operator overload by comparing MIDS output to subjective reports of workload and SA during C4ISR operations. Future studies will validate MIDS” design capabilities through redesign and evaluation of performance, workload and SA on the optimized C4ISR task environment.

Chronic left atrial volume and pressure overload in the goat: A new model of sustained atrial fibrillation

Purpose: The relationship between left atrium (LA) dilatation and atrial fibrillation (AF) has been extensively proved. The aim of this study was to develop an animal model of sustained AF, induced by controlled chronic left atrial overload. Methods: In 12 goats, a left thoracotomy was performed to implant a 8ram vascular graft (gore-tex ®) between the thoracic aorta and the LA. Intra operative atrial overload was monitored by volume and invasive pressure measurements. The LA was chronically instrumented with ukrasonic crystals and bipolar sensing/pacing electrodes. LA dilatation and electrophysiology were regularly evaluated in the conscious goats and compared with a control group with a non-functional shunt. Sustained AF (1 week) was the ultimate purpose. Anew invasive LA pressure was measured ahead of sacrifice. Results: Operatively there was manifest LA overload with calculated volume augmentation of 59.34-42.2% (from 42.3 to 67.4 mm 3, p<0.05) and mean pressure elevation from 9.24-6.9 mmHg to 18.04-8.5 mmHg (p<0.05). One animal was lost during follow up. At sacrifice (324-9.7 days), shunt patency was confirmed in 9 animals. In those, mean LA pressure was 204-7.8 mmHg (ns) and LA dilatation 104.0 mm 3 (p<0.05). AF duration increased significantly from 4.74-4.9 sec (day 0) to 1134-82.3 hours (p<0.05) after 16.14-6.9 days of open shunt. SIX animals presented sustained AF. In the control group, AF duration changed not

A multigrid preconditioner and automatic differentiation for non-equilibrium radiation diffusion problems

We study the efficient solution of non-equilibrium radiation diffusion problems. An implicit time discretization leads to the solution of systems of non-linear equations which couple radiation energy and material temperature. We consider the implicit Euler method, the mid-point scheme, the two-step backward differentiation formula, and a two-stage implicit Runge–Kutta method for time discretization. We employ a Newton–Krylov method in the solution of arising non-linear problems. We describe the computation of the Jacobian matrix for Newton’s method using automatic differentiation based on the operator overloading in Fortran 90. For GMRES iterations, we propose a simple multigrid preconditioner applied directly to the coupled linearized problems. We demonstrate the efficiency and scalability of the proposed solution procedure by solving one-dimensional and two-dimensional model problems.