## Sunday, January 23, 2011

### Excellent good-looking plots

When doing research one usually doesn't care about the aesthetics of plots or the visualized results, as long as they are clear enough to be interpreted. However, when making presentations or in publications, nice plots have an interesting impact and, even though they do not change how good results are, they still make things look more professional.

I have been usin Matlab for a while now. It is one of those softwares that you usually hate, especially if you come from a better-structured programming background. Leaving execution speed out of the equation, Matlab sucks in many ways but there a few pros that build up its popularity, such as extremely easy and straightforward debugging and the available toolboxes and functions on Matlab Central. However, it is very easy to find blogs like Abandon Matlab, where some posts really make the point about leaving Matlab forever and finding a better and more appropriate alternative.

Anyways, enough of Matlab hate. The point is that I was looking for nice plots and I remembered about that amazing piece of software called Mathematica. I will not discuss the differences between Mathematica and Matlab, but just say that they were made for different purposes. However, take a look at the following plots generated with Matlab and Mathematica respectively, from the same data (click to see the real image since blogger is automatically introducing some JPEG artifacts):

Matlab Mathematica
stem(x,y); hold on;
xlabel('x','Interpreter','LaTex');
ylabel('f(x)','Interpreter','LaTex');
data = Import["test.mat", "LabeledData"];
ListPlot[
Transpose[Flatten[{"x" /. data, "y" /. data}, 1]],
Filling -> Axis,
AxesLabel -> {x, f[x]}
]

The difference is easy to grasp by just looking at the plots: Mathematica does a great job, while Matlab looks just ok. Something I usually do to make Matlab plots is to apply a grid with grid on, but the plot still looks not as professional as with Mathematica. Obviously there is space for cheating here; maybe if you look at how much Mathematica code is needed you may say that I haven't been fair enough. However, most of the code in the Mathematica snippet is needed because the data is read from a Matlab MAT file.

In my opinion, the most amazing and simple detail that Mathematica uses and Matlab does not is antialiasing. It is a very subtle detail but it makes plots look softer and, somehow, more human and easier for our eyes to watch. There have been some attempts such as this script. However, that script is an smart user attempt to generate a plot with antialiasing but the antialiasing is simulated by resizing the plot, which still doesn't look as good as Mathematica's output (images not shown here but you can try it on your own).

Beyond that, there are some problems when exporting plots from Matlab. First, exporting to PDF generates a PDF file that contains a whole page such as A4 and the plot in the middle with huge white spaces around. This is very annoying when working with pdflatex and the PDF generated by Matlab must be cropped. Moreover, even if exporting to PNG, the final image file does not look exactly as what is seen on the computer screen. This can lead to an endless 'fight' with Matlab's exporting options, sometimes without success. All of this doesn't seem to happen to Mathematica, at least considering what I have tried so far. PDF files look great and have the exact size of the plot and can be inserted straight away into latex documents.

I don't want to go into much detail in this post since it could take a long time to discuss plot customization options in Matlab and Mathematica. My experience shows that Matlab works well to show the data properly and it is still interpretable, but it lacks the quality of softwares such as Mathematica or Matplotlib (this last one is another very nice plotting tool, free of charge). For more examples on the plotting power of Mathematica see here, and for Matplotlib here.