Manipulating data files

Introduction

One of the most common tasks for scientists and engineers is working with data sets that have been generated by some external process or collector. If they are lucky, the data are stored in a file that has a standard format and can then be read into other programs such as Mathematica with ease using that program's importing functionality. Oftentimes, however, data are stored in files with nonstandard formats and reading that file into a program such as Mathematica requires some manual processing of that file to extract the required parts.

In this section we will walk through the steps of reading, manipulating, and visualizing a dataset that consists of solar radiation data collected by the Renewable Resource Data Center, an organization that is managed by the US Department of Energy (interested readers should visit rredc.nrel.gov).

Structure of graphics

All Mathematica graphics are constructed from objects called graphics primitives. These primitive elements (Point, Line, Polygon, Circle, etc.) are used by built-in functions such as Plot to create graphics. Although it is quite straightforward to create images using Mathematica's built-in functions, you will frequently find yourself having to create a graphic image for which no Mathematica function exists. This is analogous to the situation in programming where you often have to write a specialized procedure to solve a particular problem. We use the basic building blocks and put them together according to the rules governing the structure of the language and the nature of the problem at hand. In this section we will look at the building blocks of graphics programming and at how we put them together to make graphics.

Primitives, directives, and options

Graphics created with functions such as Plot and ListPlot are constructed of lines connecting points, with options governing the display.

Introduction

Up until this point, we have been primarily concerned with learning about programming constructs and styles so that we can write programs to manipulate data or solve problems from science, engineering, or mathematics. We have taken for granted that the space in which we do our experimenting, prototyping, and documenting has been the Mathematica notebook, an interface that has some similarities to a word processor document.

It is not uncommon now to add interactive elements to your documents to make them more useful for yourself or the intended reader of your documents. With programs, documentation, and papers all being created and used in electronic format, Mathematica provides a seamless and well-integrated interface to these elements.

Another tool that is useful, especially for educators, are buttons that allow you to hide your program code behind a familiar and easy-to-use interface element – the button. The user clicks on a button and an action happens that is determined by the underlying code.

Expressions

Introduction

Although it may appear different at first, everything that you will work with in Mathematica has a similar underlying structure. This means things like a simple computation, a data object, a graphic, the cells in your Mathematica notebook, even your notebook itself, all have a similar structure – they are all expressions, and an understanding of expressions is essential to mastering Mathematica.

Internal forms of expressions

When doing a simple arithmetic operation such as 3 + 4 ⋆ 5, you are usually not concerned with exactly how a system such as Mathematica actually performs the additions or multiplications. Yet you will find it extremely useful to be able to see the internal representation of such expressions as this will allow you to manipulate them in a consistent and powerful manner.

Internally, Mathematica groups the objects that it operates on into different types: integers are distinct from real numbers; lists are distinct from numbers.