Beautiful Code [192]
A function that is not embedded in an object, and which takes as parameters standard data types, is a lot more likely to be used in many different contexts than a method deeply embedded in a complex object hierarchy. For instance, the previously mentioned weedUnlessInHash function, although written for use by the column object in the Gene Sorter, was designed not to depend on being in a column. So, this useful little function may see application in other contexts now as well.
The Design of the Gene Sorte > Conclusion
13.6. Conclusion
This chapter has been about one of the prettier pieces of code I've written. The program serves a useful purpose for biomedical researchers. The cart system makes it relatively easy to construct an interactive program over the Web, even though it uses a CGI interface. Both the user's model and the programmer's model of the program revolve around the idea of a big table with one row per gene and a variable number of columns that can represent many different types of data.
Although the Gene Sorter is written in C, the column code is done in a straightforward, polymorphic, object-oriented design. Additional columns can be added by editing simple text files with no additional programming required, and these same files help make it easy for a single version of the program to work on different genomic databases associated with a variety of organisms.
The design minimizes disk seeks, which continue to be a bottleneck, lagging CPU and memory speeds by a large margin. The code is written to be readable and reusable. I hope you will find some of the principles it is built on useful in your own programs.
How Elegant Code Evolves with Hardware The Case of Gaussian Elimination > The Effects of Computer Architectures on Matrix Algorithms
14. How Elegant Code Evolves with Hardware The Case of Gaussian Elimination
Jack Dongarra and Piotr Luszczek
The increasing availability of advanced-architecture computers, at affordable costs, has had a significant effect on all spheres of scientific computation. In this chapter, we'll show the need for designers of computing algorithms to make expeditious and substantial adaptations to algorithms, in reaction to architecture changes, by closely examining one simple but important algorithm in mathematical software: Gaussian elimination for the solution of linear systems of equations.
At the application level, science has to be captured in mathematical models, which in turn are expressed algorithmically and ultimately encoded as software. At the software level, there is a continuous tension between performance and portability on the one hand, and understandability of the underlying code. We'll examine these issues and look at trade-offs that have been made over time. Linear algebra—in particular, the solution of linear systems of equations—lies at the heart of most calculations in scientific computing. This chapter focuses on some of the recent developments in linear algebra software designed to exploit advanced-architecture computers over the decades.
There are two broad classes of algorithms: those for dense matrices and those for sparse matrices. A matrix is called sparse if it contains a substantial number of zero elements. For sparse matrices, radical savings in space and execution time can be achieved through specialized storage and algorithms. To narrow our discussion and keep it simple, we will look only at the dense matrix problem (a dense matrix is defined as one with few zero elements).
Much of the work in developing linear algebra software for advanced-architecture computers is motivated by the need to solve large problems on the fastest computers available. In this chapter, we'll discuss the development of standards for linear algebra software, the building blocks for software libraries, and aspects of algorithm design as influenced by the opportunities for parallel implementation. We'll explain motivations