Array Computing and Curve Plotting

Abstract

Lists are introduced in Chapter 2 to store “tabular data” in a convenient way. An array is an object that is very similar to a list, but less flexible and computationally much more efficient. When using the computer to perform mathematical calculations, we often end up with a huge amount of numbers and associated arithmetic operations. Storing numbers in lists may in such contexts lead to slow programs, while arrays can make the programs run much faster. This may not be very important for the mathematical problems in this book, since most of the programs usually finish execution within a few seconds. Nevertheless, in more advanced applications of mathematics, especially the applications met in industry and science, computer programs may run for weeks and months. Any clever idea that reduces the execution time to days or hours is therefore paramount.

This chapter gives a brief introduction to arrays – how they are created and what they can be used for. Array computing usually ends up with a lot of numbers. It may be very hard to understand what these numbers mean by just looking at them. Since the human is a visual animal, a good way to understand numbers is to visualize them. In this chapter we concentrate on visualizing curves that reflect functions of one variable, e.g., curves of the form y = f(x). A synonym for curve is graph, and the image of curves on the screen is often called a plot. We will use arrays to store the information about points along the curve. It is fair to say that array computing demands visualization and visualization demands arrays.

All program examples in this chapter can be found as files in the folder src/plot.