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Use of Math Languages and Packages in Research?
CEHT asks: "As a research programmer at the university, I have encountered numerous times when I need to choose which language(s) or package(s) to use for different projects. Tradeoffs and performance issues have to be considered: results from one package may be more compatible with the data from other researchers, another package may find the solution faster and use less resources, and so forth. Maple,
Matlab, Magma, and Mathematica
are among the most well-known packages. Libraries such as IMSL is also popular. Of course, there are smaller (and mostly free) packages that tend to target specific types of problem, such as LiDIA, Singular, and LAPACK.
The question is, how useful are these [and other] math packages? Do researchers use only one or two packages for most of their projects? Or do people like to mix things a little by pulling the strength of different packages together to solve a math problem? If not, do researchers write C/C++ programs and use GMP or Matpack to solve math problems?"
Whenever I need to do anything like that, I use Octave.
But masters, remember that I am an ass: though it be not written down, yet forget not that I am an ass.
Having traversed from a predominantly engineering realm (computer science) to a predominantly scientific realm (neurobiology), my observations have been that the tools are selected mostly on habit or previous knowledge rather than fitness for use.
The most commonly-used analytical platform is probably Excel (or some similar tool like Statistica), but the more serious researchers, who are also the more mathematically-aware, nearly all use Matlab in my experience.
When efficiency is an issue, nearly everyone I've worked with turns either to IDL (a Matlab competitor that has more arcane syntax, but much higher processing speed) or writes a C/C++ program by taking algorithms from "Numerical Recipes in C".
Recently, I've also seen a rising use of Visual Basic, especially to do experimental control (although some Matlab hooks do exist for such), and, of course, LabView. Some diehards use LabView for data analysis as well, but their results are suspect just because the tool is so poorly fitted to the task.
And, of course, many data collection hardware manufacturers (CED, National Instruments, TDT, etc.) supply scripting languages to control their hardware and perform rudimentary and sometimes not-so-rudimentary calculations.
The best researchers select the most appropriate tool for the job, but, again in my experience, it seems the selection is normally based on previous experience and inertia. Those who know a particular tool well (eg, Excel, Matlab, SPSS, Mathematica) tend to keep using that tool, even if it is not well-suited. This means you get abberations like Matlab programs that control real-time experiments and LabView programs that do higher-order mathematics.
Why?
Because the largest fraction of a scientists' time should be spent on data collection, not experimental implementation, and the amount of time (for nearly all fields except those with astronomical amounts of data) spent executing code is dwarfed by the time developing it. Clearly this breaks down for certain applications, but most of the science currently being done (read: molecular biology, and no, not bioinformatics) is not algorithm-bound.
Since data analysis is such a huge, broad field, I expect to see radically different answers from other posters!
Put my fist through my alarm clock with its ding-dong death inside my ear. - The Blackjacks.
First a global kind of classification.....
octave/matlab... are mostly vector/array oriented languages and are useful for doing work in problems that are suited for such - you can experiment easily, then recode in C,fortran... if needed. apl and j are also in this group and should not be ignored - though they're used a bit less frequently.
Macsyma/mathematica/maple/maxima/derive are symbolic math languages and can solve interestingly sized problems and get symbolic answers (that is, things like sqrt(pi/2)) as well as numeric approximations. This can be a very useful tool to have - depending on what I'm doing I use such things a couple times a week (nice to check results done by hand, or to handle all the crufty part of a solution). Most will emit fortran code which can also be useful.
vtk, opendx/khoros(?) are visualization tools - most of the other packages have some visualization tools packaged in them, but vtk and opendx both offer quite a bit more power.
Now the incredibly non specific recommendation
My suggestion is to pick one of each of these and learn it - do enough in it so you know the language/system well. Otherwise you'll be struggling with the language as well as with the problem - and finding bugs will be close to impossible.
If I put on my "computer science professor" hat (probably a wise thing if I'm to keep the top of my head from turning bright red with sunburn), I usually try to recommend that all CS students learn a smattering of these things as well. When you need one of these tools, knowing its there and how to use it can save large and wonderful quantities of time.
And now some more specific comments
On the whole my choices would be as follows - note the caveats - some of them are pretty cave-rnous (sic). I don't have piles of money to spend, so tend to prefer the open source programs just on that basis.
For array/matrix manipulation I much prefer APL or one of its derivatives (check out aplus on sourceforge). Languages in the APL family are also fun to program once you learn how. However the terseness of the syntax (and with APL itself the odd character set) tends to make these a bit forbidding, so a more popular choice would be octave (open source) or matlab. I've had good luck with octave - it seems to handle most matlab programs well enough. If you've got piles of money, go for matlab.
For symbolic math, maxima (sourceforge) is good. Its commercial cousin Macsyma has usually ranked as about the best symbolic math packages for accuracy and power and seems less expensive than the others. Actually writing programs in either of these requires learning quite a bit about the innards of the system though. My second choice for symbolic math would be Mathematica - its programming language is well integrated with the system as a whole and and for general goodness and niceness of the interface it can't be beat. (The other commercial products are building on the best parts of the Mathematica interface - I've not checked recently, but they're getting much better fast.) The visualization capabilities of Mathematica are also very good. Maple is probably the most popular, so using it will probably make it easier to find someone to help you, but on the whole I've just never found Maple as easy to program as Mathematica and I tend to want to program almost everything.
For visualization both vtk and opendx are very nice systems. vtk is more aimed at a programming interface, opendx has a labviewish kind of programming environment. I like both and have both at hand. Both these systems are big enough that you'll want to make sure you understand them before you tackle a project with them.
They don't scale well, but spreadsheets can be very convenient for small models. Careful though, its easy to have errors even in middlin sized models that can be very hard to find.
Odd Zen Endz
As has been noted there are other systems, some smaller, some more specifically focussed on a single domain. Those tend to be harder to match to a problem - unless the problem is right in the center of the domain in question.
There used to be a program AXIOM which had a lot of nice features, but it seems to have gone to that Big Bit Bucket in the sky - but its base language "Aldor" is now available at aldor.org. I have a copy, but haven't looked deeply at it.
Sourceforge is also hosting a new project "lush" - which is a lisp system that has some integration of some of these features. To the extent that I've used it I'm impressed and will probably spend some time working deeper with it in the hopes that it will prove another valuable tool.