HPCwire: Mathematica Takes on Parallelism

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April 09, 2009

Mathematica Takes on Parallelism

by John West, for HPCwire

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Like just about everyone else, I head into the SC conference season hungry for cool new hardware news. Throw in a quantum computing demonstration, or string together a couple thousand Atom processors into a computing prototype, and I head for the keyboard like a suburban American dad heads for the turkey on Thanksgiving day.

There are other kinds of announcements that happen during SC about new services, business models, software, machine installations, and so on. So many announcements, in fact, that it's not possible to do more than perfunctory service to most of them. This article is about one of the important developments I didn't cover during the November rush: the announcement of Mathematica 7.

On the day the exhibit floor opened at SC08, Wolfram Research announced the latest version of its flagship product, Mathematica 7. The tool has long been a part of the "thinking workflow" for engineers, scientists, and a host of other technical professionals. Mathematica allows uers to manipulate mathematical statements, and visualize the results, using mathematical notation directly rather than a special grammar or intermediate form. What is important about the Mathematica 7 announcement is that it marked the introduction of features that turn Mathematica into a gateway through which users can take advantage of the power of high performance and large-scale computing without changing their workflow and in many cases without being aware that they are working in parallel.

Mathematica is a symbolic manipulation environment that allows users to manipulate mathematical and logical expressions directly in the mathematical notation you'd expect to find in a textbook or use with pen and paper. Alongside this capability for symbolic manipulation lie sophicated numerical methods that allow the system to reduce expressions to numeric answers when appropriate. Reports from users of several of the most popular systems indicate that Mathematica, always strong with respect to symbolic manipulation, has closed the numerical gap it once had with respect to other packages.

I came from a MATLAB-centric environment, and so I was interested in knowing how the tools are different from one another. In contrast with Mathematica's focus on expression in symbolic language, MATLAB offers users a language that is similar to C and HPF, a distinction that reflects the fundamental difference in the kind of thinking the two tools are designed to support. There is a widely-held generality that if your interest is in numerical methods and matrix manipulation, MATLAB is the right choice. On the other hand, if you are more generally interested in mathematics, or need to express theoretical problems directly in the language of mathematics, Mathematica is the right choice. Both packages are quite sophisticated, and I find that this generalization isn't always helpful.

One user I spoke with described the choice between MATLAB and Mathematica as one that comes down to how your brain is wired: if you naturally start with equations on paper and then work your way out to data and programs, then Mathematica is likely to be a good fit for you. But if you like to start with data first and then try to find a model that fits what you observe, MATLAB is the way to go.

Either way, these environments and others like them offer users the ability to use a computer to answer questions or solve problems without having to reduce the problem to an expression in C or FORTRAN. And many of the available mathematics environments, MATLAB and Mathematica among them, offer rich support for parallel processing and a wide variety of third party tools.

But why does this matter?

Researchers using computer applications to facilitate their research can expect to face two discontinuities as the computational requirements of their applications grow and they require more computer resources. The first discontinuity occurs when an application moves from operating with a single thread of execution to multiple simultaneous threads. Today this transition can happen while the user stays in the familiar operating environment of his desktop, but he may also transition to a small shared resource. This shared resource could look a lot like his familiar desktop environment, or it might be a totally new environment that disrupts his existing workflow and toolsets. The application usually has to be rearchitected to take advantage of the performance potential offered by adding more execution threads, and this can require substantial new skills or even the addition of new team members to parallelize the application.

The next transition is to resources that permit simultaneous execution of a very large number of tasks: supercomputers. This often involves rearchitecting the application again to take advantage of orders of magnitude more parallelism. Unfortunately, the transition also nearly always involves a complete disruption of previous workflows, new tools, and new ways for the user to interact with the resource during development. Literally everything may be new, from the command line interface (no Gnome or Windows GUI on most supercomputers) to working with a batch queuing system. This is a problem for users who must adapt to an unfamiliar and often unfriendly environment at the same time that they are dealing with the fundamental issues of the science, and computer science, in their application that frequently arise at supercomputing scale.

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