Extreme Graphics with Extrema

To plot two-dimensional data, you can use:

GRAPH x y

where x and y are two vectors of equal length. The default is to draw the data joined by a solid line. If you want your data as a series of disconnected points, you can set the point type to a negative number, for example:

SET PLOTSYMBOL -1

Then you can go ahead and graph your data.

Parametric plots also are possible. Let's say you have an independent variable called t that runs from 0 to 2*Pi. You then can plot t*sin(t) and t*cos(t) with:

t = [0:2*pi:0.1]
x = t * sin(t)
y = t * cos(t)
graph x y

This will give you the plot shown in Figure 4.

Figure 4. Graphing a Parametric Plot

In scientific experiments, you usually have some value for error in your measurements. You can include this in your graphs as an extra parameter to the graph command, assuming these error values are stored in an extra variable. So, you could use:

graph x y yerr

to get a nice plot. Many options are available for the graph command (Figure 5).

Figure 5. The graph command has many available options.

More complicated data can be graphed in three dimensions. There are several types of 3-D graphs, including contour plots and surface plots. The simplest data structure would be a matrix, where the indices represent the x and y values, and the actual numbers in the matrix are the z values. If this doesn't work, you can represent the separate x, y and z values with three different vectors, all of the same length. The most basic contour graph can be made with the command:

CONTOUR m

where m is the matrix of values to be graphed. In this case, Extrema will make a selection of nice contour lines that create a reasonable graph.

You can draw a density plot of the same data with the density command, where the values in your matrix are assigned a color from a color map, and that is what gets graphed. Unless you say differently, Extrema will try to select a color map that fits your data the best. A surface plot tries to draw a surface in the proper perspective to show what surface is defined by the z values in your data.

Let's finish by looking at one of the more important analysis steps, fitting an equation to your data. The point of much of science is to develop equations that describe the data being observed, in the hope that you then will be able to predict what you would see under different conditions. Also, you may learn some important underlying physics by looking at the structure of the equation that fits your data. Let's look at a simple fitting of a straight line. Let's assume that the data is stored in two vectors called x and y. You'll also need two other variables to store the slope and intercept. Let's call them b and a. Then you can fit your data with the command:

SCALAR\FIT a b
FIT y=a+b*x

Then, if you want to graph your straight line fit and your data, you can do something like:

SET PLOTSYMBOL -1
SET PLOTSYMBOLCOLOR RED
GRAPH x y
SET PLOTSYMBOL 0
SET CURVECOLOR BLUE
GRAPH x a+b*x

Now that you have seen the basics of what Extrema can do, hopefully you will be inspired to explore it further. It should be able to meet most of your data-analysis needs, and you can have fun using the same tool that is being used by leading particle physicists.