Tips and Tricks

The list is one of the basic building tools for organizing data in JSL. The power of lists is that they can contain any kind of items (numbers, characters, other lists, ...), and they can grow and shrink as needed. However, if you just need a fixed list of numbers, you can get much better performance from a one-dimensional matrix.

Consider these two samples that make arrays of odd numbers.

// make a list of odd numbers

n = 1000;

y = {};

for (i = 1, i <= n, i++,

	y[i] = 2 * i - 1;

);

y[n];

// make a matrix of odd numbers

n = 1000;

y = J(1, n);	// creates a 1 x n matrix with all values set to 1

for (i = 1, i <= n, i++,

	y[i] = 2 * i - 1;

);

For a few hundred items, there's not much difference. But as n goes beyond 1000 (or if the above code is in a loop), you start to notice the difference in speed. For lists, there is a certain amount of overhead for growing dynamically and general flexibility.

Notice the J function can be used to create a new matrix of a given size. J_m,n is the name for the Unit Matrix in linear algebra.

Also notice that a one-dimensional matrix can be indexed with just one subscript. That is, we can use y[i] instead of y[1][i]. That makes it easier to treat matrices as lists, and in the loop above, which is the same in both cases.

Question until next time: How can the code be made even faster?

Vector plots show arrows on a two-dimensional plot and allow one to see four dimensions of data: x position, y position, arrow angle, and arrow length. Equivalently, the four dimensions can be x start position, y start position, x end position, and y end position. The latter form is most convenient for JMP. Though JMP doesn't have a menu command to create vector plots, arrows can be added to almost any plot without much trouble.

While lots of four-variable data sets can be adapted for vector display, I'll demonstrate with one of the most natural applications: wind data. This data set records wind speed and direction for various weather stations in the Chicago area. I used formulas to convert the speed and direction into end positions for the arrows and then added the following graphics script to a bivariate scatterplot using Customize from the graph's right-click menu.

Pen Size( 2 );

For Each Row( Arrow( {lon1, lat1}, {lon2, lat2} ) );

Here's a screen capture showing a little bit of the data table, graph, and customize dialog:

The next steps were to delete the rows with no wind and to turn off the points in the graph.

To provide context, I added the map of weather stations provided by the weather service. Placing a image in a graph is a bit tricky (and could be the subject of another post). There are two options: Draw the picture in another custom graphics script, or drag and drop an existing image into the graph. I chose the latter since I had an image file. First, I sized the graph to be the same size as the image, and then I dragged the image file into the center of the graph. After a few tries, the alignment was pretty good. (BTW, we're working on making this better in JMP 9.)

The plot shows relative wind readings taken at 6 p.m. on May 31, 2009. With the help of the background image, we can see how wind patterns vary in relation to Lake Michigan.

UPDATE 10/6/09: The data file, with scripts, is now available in the JMP File Exchange. Look for the file called "ChicagoWind.jmp" in the Data Visualization section.

Source of data and image: the National Severe Storms Laboratory Historical Weather Data Archives, Norman, Oklahoma.