Anthony D. Padula
Abstract
The Rice Vector Library is a collection of C++ classes expressing core concepts (vector, function,…) of calculus in Hilbert space with minimal implementation dependence, and providing standardized interfaces behind which to hide application-dependent implementation details (data containers, function objects). A variety of coordinate-free algorithms from linear algebra and optimization, including Krylov subspace methods and various relatives of Newton's method for nonlinear equations and constrained and unconstrained optimization, may be expressed purely in terms of this system of classes. The resulting code may be used without alteration in a wide range of control, design, and parameter estimation applications, in serial and parallel computing environments.
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Index Terms
- A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms
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Reviews
Markus Wolf
Designing a good library for an application domain is always a difficult task. The library has to be consistent, complete, and easy to use. The very best libraries present to the user an interface that is as easy to use as writing a text in the idiom of the application domain. The Rice Vector Library described in this paper is one such library. The paper gives a nice presentation of all the considerations and design decisions taken to get to an easy-to-use, consistent, complete, and well-performing library in the mathematical application domain of calculus in Hilbert spaces. The first section of the paper is an overview of design principles in object orientation that are beneficial for the design of easy-to-use libraries. Furthermore, it gives some pointers and references to other numeric libraries with an overlapping focus and a motivating example. The next section presents the core design principle of separating the domain classes of space and vector from the underlying data management, representing the mathematical practice of considering a vector space as an abstract object that satisfies certain axioms. The section also explains the inner workings of these classes and the principle of their implementation with C++. Furthermore, the motivating example is coded with the tools provided by the library. The code for the example does indeed look nearly the same as its mathematical formulation in the first section-the only changes are the replacement of Greek letters with their names and some mathematical notations with programming notations. The third section explains how numerical algorithms can be expressed with the templates of the library and the use of design patterns in a coordinate-free way-that is, staying true to the abstract concept of a vector space and independent of the common geometrical vector spaces. This section is followed by a short section that gives some hints for the implementation of Cartesian products and functional composition, followed by some examples of algorithms coded with the help of the library, instructions for downloading the library, and a short conclusion. The appendix contains an explanation of a further template package and how to combine the library with a parallel linear algebra package. Although the paper describes a library for a rather specialized mathematical application domain, the use of object-oriented principles and design patterns to arrive at a framework that makes writing code as close to a domain-specific language (DSL) as possible is very interesting. Furthermore, it can be understood with a limited mathematical background. Online Computing Reviews Service
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